© ESO 2018

1. Introduction

In this paper we discuss a filament projected 1.9 kpc from the nucleus of M87, for which we have obtained a new far-ultraviolet (FUV) spectrum with HST-COS. Using this spectrum, we measure with 10–15 km s⁻¹ relative precision the broadening and bulk velocities of C II λ1335, N V λ1238, and Lyα, which originate from plasma associated with the filament. We also update kinematic measurements of C IV λ1549 and He II λ1640 from archival low-resolution spectra of the same sightline. These FUV lines provide us with unique information about the properties of the transition zone between hot gas and cold core of the filament, as these lines are bright in collisional excitation at a broad range of intermediate temperatures. We cannot prove that the boundary layer with which we associate these lines is powered only via electron thermal conductivity, but nevertheless this is a rare case when we see in detail and are able to measure random motions and outflow velocities, as well as line intensities and emission measures in many emission lines corresponding to different temperatures of collisionally excited plasma. Until now we had a similar situation only in the cases of the solar chromosphere and corona during solar flares, and in the upper atmospheres of some nearby stars.

We also report the detection of [Fe XXI] λ1354 in this sight-line, and show that it exhibits bulk motion in the opposite direction from the other FUV lines. The permitted FUV lines exhibit velocities from random motions σ_r ≈ 130 km s⁻¹ and bulk velocities v_r ≈ 140 km s⁻¹, consistent with previous measurements in other wavebands, and Lyα appears slightly broader due to resonant scattering. [Fe XXI] probably exhibits a lower velocity dispersion than these other lines, although it has significantly larger uncertainties due to a lower SN. We propose a model wherein the [Fe XXI] originates from the approaching face of the radio bubble which is expanding through out line of sight, while the filamentary emission originates from the receding edge of this radio lobe.

These observations also represent a first chance to combine C II λ1335 observations and far-infrared (FIR) [C II] λ158 μm observations for the same filament. The latter come from Herschel-PACS data downloaded from the archive which have been previously discussed by Werner et al. (2013). As we will show, we gain insight into the structure of both the cold (T < 10⁴ K) and warm (10⁴ K ≲ T ≲ 10⁵ K) phases of the filament through the simultaneous study of permitted and forbidden lines for the same ion, with different excitation temperatures and critical densities. We will show that the FIR and FUV C II lines exhibit similar radial velocities and velocity dispersions. The general agreement in kinematics for sightline (between the permitted FUV lines in this paper, archival observations of Hα, and the forbidden [C II] line) is remarkable. These lines have characteristic temperatures spanning more than three orders of magnitude and the observed σ_r slightly exceeds the sound speed for the warm gas but is highly supersonic for the cold gas. The observed random motions in this sightline must be driven by external forcing – probably the expansion of the radio lobe into the M87 ISM – and not internal turbulent motions in the multiphase gas itself.

We will also conclude that the cold phase contains orders of magnitude more mass than the FUV-emitting boundary layer. We propose a geometry for the filaments where this cold phase is located in numerous clumps with a low volume filling factor, and each clump is surrounded by a very thin FUV-emitting boundary layer. The random motions of these clumps produce the observed velocity dispersion in the permitted FUV lines. Our measurements also demonstrate the effectiveness of the UV lines (especially Lyα and He II λ304, and to a lesser degree [C II] λ158 μm), as coolants for the interstellar medium of M87. He II λ304 can also contribute to the photoionization of H and other elements. A by-product of our observations is the detection of absorption from interstellar gas in our Galaxy, observed in C II λ1335 and Lyα.

The phenomenon of filaments in the centers of galaxy clusters remains somewhat mysterious. Initially discovered through their bright Hα emission (Arp 1967), they are generally thought to be connected with cooling instabilities originating in the intracluster medium (ICM), as the cooling times at typical ICM temperatures near the center of the cluster (several keV) and densities (0.01–0.1 cm⁻³) are significantly shorter than the timescales for galaxy evolution. Empirically, this connection has support as well, in the observed correlation between the presence of a cool core in the ICM (corresponding to a low central entropy and a short cooling time) and the existence of Hα filaments (Cavagnolo et al. 2008).

At the same time, we know that the brightest central galaxies of galaxy clusters contain supermassive black holes (SMBHs). The energy released during accretion onto these SMBHs is powerful enough to prevent the formation of cooling flows (e.g., Tucker & David 1997; Churazov et al. 2001, 2002). Nevertheless, networks of filaments persist in such systems.

M87, the central galaxy of the Virgo Cluster, has an especially well-studied SMBH (Sargent et al. 1978; Young et al. 1978; Macchetto et al. 1997; Gebhardt & Thomas 2009; Walsh et al. 2013) due to its mass and proximity. The SMBH is relatively dormant while still approximately balancing cooling from the Virgo ICM (Churazov et al. 2001; Forman et al. 2005), but M87 also has an enormous system of low-temperature filaments extending from the nucleus several kpc to the east. In contrast to many other galaxy cluster filament systems, the filaments in M87 are not forming stars (Salomé & Combes 2008; Sparks et al. 2012), and represent a prototypical example of this class of “AGN-dominated” or “shock-dominated” filaments.

The bulk of the previous work on these filaments has been connected with attempts to image the filament region in the optical and X-ray and to find evidence for spectral lines corresponding to temperatures in the unstable range between 10⁴ K and 10⁷ K. (Arp 1967; Ford & Butcher 1979; Sparks et al. 1993, 2009, 2012; Ford et al. 1994; Harms et al. 1994; Macchetto et al. 1997; Simionescu et al. 2008; Werner et al. 2013). In this paper, we use data we obtained from HST-COS, which trace this temperature range directly but also permit us to measure velocity structure. These velocity measurements are an essential ingredient for theory and for numerical simulations, as they in principle can prove whether the cooling material is falling onto the SMBH or is uplifted in an outflow.

The [Fe XXI] line merits some additional discussion. As we showed in Anderson & Sunyaev (2016), there are several forbidden lines in the FUV from various species of highly ionized Iron, but in emission [Fe XXI] is the brightest, and in collisional excitation equilibrium (CIE) its emissivity peaks at log T = 7.05 K. This line is well-studied in solar flare spectra, and its ionization potential is 1.7 keV so photoionization is not expected to be important outside of AGN environments. While T ~ 10⁷ K plasma generally radiates primarily in X-rays, the ability to study its emission in the FUV allows us to measure kinematics of the hot plasma, which is generally impossible without microcalorimeters or mm wavelength observations of the kinematic Sunyaev-Zel’dovich effect from bulk motions and turbulence inside clusters of galaxies (Inogamov & Sunyaev 2003).

In Anderson & Sunyaev (2016) we used archival HST-COS data to provide tentative evidence for [Fe XXI] emission in several sightlines toward galaxy clusters with known reservoirs of 10⁷ K plasma, including the nucleus of M87 and the filament region studied here. Danforth et al. (2016) were able to confirm our suggestion of [Fe XXI] in the M87 nucleus, and here we will confirm its presence in the filaments. In this paper we present a detection of [Fe XXI] in the ISM of M87 at 4–5σ significance, which represents the second direct measurement to date of motions in the hot ICM of nearby galaxy clusters, after the measurement in Perseus with Hitomi (Hitomi Collaboration et al. 2016). The turbulent velocity we measure for [Fe XXI] in the core of Virgo is also similar to the turbulent velocity measured by Hitomi in the core of Perseus. [Fe XXI] is a useful complement to the exciting science possible with microcalorimeters, since it probes a slightly cooler phase (T ≈ 1 keV) of the ICM using independent instrumentation. Additionally, until the launch of another mission with a microcalorimeter, these FUV lines are the only currently accessible direct probe of turbulence in the hot ICM.

One question which has remained open is the excitation mechanism of the line emission from these filaments. In the nucleus of M87, there is a rotating cloud with r ~ 35 pc which is thought to be photoionized by emission from the central source (Sabra et al. 2003, Anderson & Sunyaev, in prep.), but the filamentary system studied here is projected 1.9 kpc from the nucleus, and it is not obvious that photoionization from the nucleus can ionize filaments at this distance. A similar issue of insufficient ionizing radiation is seen in the cores of many other LINER-type systems as well (Binette et al. 1993; Ho 2008; Eracleous et al. 2010), but the proximity of M87 offers a unique chance to find a resolution.

One possibility is strong variability in the nuclear emission, so that photoionization is still the primary excitation mechanism in the filaments. In this case, an AGN outburst several millennia ago would have provided the necessary photons to ionize the filaments at large radii. This is consistent with many observations that show high variability with a short duty cycle in AGN (Shankar et al. 2009), including in M87 (Harris et al. 1997; Perlman et al. 2011). In filaments which are actively forming stars, radiation from the young stars can also power the photoionization (e.g., O’Dea et al. 2004; McDonald et al. 2012), although as we mentioned above, young stars are not observed in M87.

The other possibility is a transition from photoionization in the nucleus to collisional excitation at larger radii. Collisional excitation is commonly proposed as a mechanism for heating filaments, either via thermal conduction (Boehringer & Fabian 1989; Nipoti & Binney 2004; Inogamov & Sunyaev 2010) or via collisions with suprathermal electrons from the hot ICM (Fabian et al. 2011). Sparks et al. (2012) argue for thermal conduction in the filaments of M87 as well. As we will show, there are likely shocks present in the filament as well, due to collisions of cold cloudlets moving with supersonic random velocities relative to one another in the core of the filament, which are another plausible mechanism for collisional excitation.

We use our spectroscopic results to distinguish between these cases, and they point to a mixture of collisional excitation and recombination in Lyα and Hα. However, with the exceptions of Hα and He II λ1640 (which is the Balmer-α transition in He⁺), a simple collisional model is able to reproduce the intensities and line ratios of the other FUV lines in this filament.

The structure of this paper is as follows. In Sect. 2 we describe and present our COS G130M observations of this system, and in Sect. 3 we discuss the FUV continuum and present fits to permitted emission lines such as C II, N V, and Lyα. In Sect. 4 we present the forbidden FUV emission line [Fe XXI], and in Sect. 5 we summarize the FUV line luminosities of this filament region and discuss their contribution to the total cooling budget of the ICM. In Sect. 6 we analyze these lines, discussing the excitation mechanisms for this line emission, the differential emission measure for the sightline, and the volume filling factor of the FUV-emitting plasma. In Sect. 7 we discuss [Fe XXI] and we propose a possible physical model to explain the different bulk velocity observed in [Fe XXI] compared to the other FUV lines. Finally, in Sect. 8 we discuss the cold phase of the filaments as traced by [C II] λ158 μm, and estimate the mass, dimensions, and filling factor of the filamentary gas in this phase. Throughout this paper we use a velocity relative to M87 of 1283 km s⁻¹ (Makarov et al. 2014) and a distance d = 16.7 Mpc (Blakeslee et al. 2009) for M87. Errorbars are quoted at the 1σ level unless otherwise stated.

2. HST-COS observations

This paper focuses on one particular Hα-emitting filament located in M87. As mentioned above, the filament is part of a network of filaments projected about 1.9 kpc from the nucleus of the galaxy, and has been observed in Hα+[N II] narrowband imaging, FUV imaging (Sparks et al. 2009) and FUV spectroscopy (Sparks et al. 2012) with HST. Additionally, spectrophometry with Herschel-PACS (Poglitsch et al. 2010) has mapped out the filament in [C II] 158 μm emission as well (Werner et al. 2013). Deep X-ray studies of the region have also been performed (Young et al. 2002; Werner et al. 2013), showing that the ICM around these filaments is multiphase, and that the X-ray emission can be described with a model containing at least two or three separate components.

Figure 1 shows the region of interest. Our sightline indicated with the red circle targets one of the filaments in the northern section of the system. The filament is clearly visible in Hα+[N II] emission, and also lies in an area which shows evidence of having a multiphase ICM, including a strong 1 keV component and even a tentative 0.5 keV component (Werner et al. 2013). The especially large emission measure of 1 keV plasma around this filament motivated our selection of this sight-line. We proposed to observe this sightline with HST-COS in order to detect [Fe XXI]λ1354.1 emission and to measure with medium-resolution spectroscopy the other FUV lines expected from the intermediate-temperature gas associated with the filament.

Fig. 1. Hα+[N II] image of the multiphase filamentary structures east of the nucleus of M87, constructed from archival HST-WFPC2 images as described in Sect. 6.2. The red circle in the center of the image indicates the location of our COS aperture, which targets the northern of two large filaments projected east of the nucleus. This filament is clearly separated from the other filament to the south, as there is no Hα bridge connecting the two filaments, and as we will show they have different velocities and likely originate on opposite sides of an expanding radio lobe. The dashed red box indicates the approximate size of the Herschel-PACS region from which we measure a [C II] 158 μm spectrum (see, e.g., Sect. 2.1). Comparison of this image to Fig. 2 of Werner et al. (2013) shows that the hot ICM in this sightline is multiphase and rich in 1 keV plasma, although the majority of the hot gas is in the slightly hotter 2 keV phase.

We successfully obtained 14 orbits with HST-COS in cycle 24 (proposal id 14623) to observe this filament using the G130M grating. Our observation was split across five different visits, each using a central wavelength of 1318 Å. We combined the x1dsum files from these five visits directly in counts space and then binned the results. We use 0.70 Å bins in Fig. 2 for display purposes, but for analysis and subsequent figures we use 0.21 Å bins, which corresponds to approximately three resels. For Lyα, which is much brighter than the rest of the spectrum, we use 0.07 Å bins. We estimate errors using Poisson statistics on the gross counts within each bin. For plotting purposes we show 1σ errors estimated using the Gehrels (1986) approximation, in similar manner to Tumlinson et al. (2013) and to the Hubble Spectroscopic Legacy Archive (Peeples et al. 2017), but for model fitting we compute the likelihoods of our models using Poisson statistics without the Gehrels approximation.

Fig. 2. Our COS G130M spectrum of the M87 filament, divided into segments B (top) and A (bottom) for visual clarity. We have binned the spectrum in this plot into 0.70 Å bins, and display 1σ errors on each bin as described in the text (Sect. 2). Prominent emission lines are identified and discussed in Sects. 3 and 4, and airglow lines are indicated with the shaded red regions and identified with red text.

Since the continuum emission may be spatially extended (see Sects. 2.2 and 3.1) we also checked the effect of the pipeline background subtraction by constructing alternate spectra reduced using the BOXCAR algorithm, but the results were unchanged within the uncertainties, and no qualitative differences were seen. We use the pipeline products downloaded from the HST archive for our scientific analysis here, which use the TWOZONE algorithm.

The resulting spectrum is shown in Fig. 2. A faint continuum with a few bright emission lines can be seen, and the N I λ1200, H I λ1216, and O I λ1302,1305 airglow lines are also clearly visible. In the next section, we discuss this spectrum in more detail.

This spectrum also suffers from reddening caused by Galactic dust. In this paper we display and perform modeling on reddened spectra, but in Sects. 5 and 6 we also cite de-reddened integrated fluxes. We compute the reddening correction using the Cardelli et al. (1989) extinction curves with R_V = 3.05 and E(B−V) ≈ 0.02, with the latter value based on a number of estimates for the extinction toward M87 but excluding the nucleus (e.g., Dopita et al. 1997; Danforth et al. 2016). While some of the filaments in M87 are dusty, there is little evidence of dust in M87 around the location of this filament, with an upper limit to the intrinsic absorption of A_V < 0.02 (Sparks et al. 1993).

2.1. Discussion of aperture sizes

The COS aperture has a circular footprint on the sky with a radius of 1.25″, and this corresponds to a physical radius of 101 pc at the distance of M87. Our sightline is projected 1.9 kpc from the nucleus of M87, and the filament which passes through our sightline has a projected length of a little over 1 kpc (of which just 200 pc falls within our field of view). Thus, the luminosities we measure in our spectrum only correspond to a portion of the total line luminosity of the filament, but in general we cite the measured aperture fluxes and luminosities in this paper.

There is also an issue of the absolute flux calibration for COS, which is highly accurate for point sources but can be more uncertain for extended emission. As we will discuss in the next subsection, the FUV emission is indeed somewhat extended along the cross-dispersion axis, which can affect the flux calibration. We checked in Sect. 2 that changing the pipeline background subtraction algorithm does not affect the measured fluxes within the uncertainties, so this does not appear to be a major issue for our analysis, probably because the source is fairly faint already, so the vignetted wings of the extended emission in the cross-dispersion direction are not very significant.

Additionally, we will also refer to archival Herschel-PACS data in this work. We use the level 2 rebinned data products, which have 9.4″ × 9.4″ spaxels. These cover an area 18 times larger than the COS aperture (see Fig. 1), so care must be taken in comparing our measurements from Herschel-PACS with those from HST-COS. In some cases we will also quote the measurements of Werner et al. (2013) for comparison, who also analyzed the Herschel observations but reprojected the data into 6″ × 6″ regions for their analysis.

Another issue with the Herschel data is that the [C II]λ158 μm emission which we detect with Herschel-PACS is not likely to be spatially uniform, since we associate it with the filaments, as we discuss in detail in Sect. 8. This complicates the conversion of the measured flux within the 9.4″ × 9.4″ or 6″ × 6″ box into the estimated flux within the COS aperture, so that the conversion is probably not accurate to better than a factor of a few. For the one instance in this work we attempt such a conversion (Sect. 8), our conclusions are therefore uncertain by a similar amount. We note this caveat here and emphasize it in that section, but our results are robust against uncertainties at that level, so it it does not qualitatively affect our conclusions.

2.2. Discussion of extended emission and interpretation of velocity dispersion

We will also be measuring the broadening of emission lines in this paper, and in general we will be interpreting this broadening as the result of physical motions (i.e., velocity dispersion) within the FUV-emitting gas. There are other effects which can cause these emission lines to appear broadened, however, and we briefly address them here.

One effect is thermal broadening. Using a typical expression for the line of sight thermal velocity dispersion ${\sigma }_{\mathrm{r}}=\sqrt{2 kT/M}$, for the temperatures at which these species are at the peak of their emissivity, we expect thermal broadening for Lyα, C II, C IV, and N V of 17 km s⁻¹, 8 km s⁻¹, 12 km s⁻¹, and 12 km s⁻¹ respectively. These are all negligible compared to the σ_r ≳ 120 km s⁻¹ which we will measure for these lines. [Fe XXI] is emitted at a much higher temperature, but Fe ions are also significantly heavier, so that the thermal broadening expected for [Fe XXI] is 58 km s⁻¹. In this case the thermal velocity is not negligible, and we discuss the physical interpretation of this line’s broadening more in Sect. 7.3.

The other effect results from the filament being extended on the sky. The COS aperture is circular instead of having a narrow slit, and so extended emission along the dispersion axis can artificially broaden emission lines. Fortunately, the relatively good spectral resolution of G130M makes this much less of an issue than G140L (see Anderson & Sunyaev 2016), but it is not necessarily insignificant. We first consider the worst case of uniform aperture-filling emission, and measure the profile of the Lyα airglow line in our spectra. We find σ ≈ 76 km s⁻¹ for this line, and we can use this as an upper limit on the effect of artificial spectral broadening due to extended emission in this work.

We now estimate the degree to which the emission is extended along the dispersion axis in our observations. The five G130M observations of this filament targeted identical sky coordinates and have position angles of −7°, −10°, −10°, −10°, and −25°, so the filament subtends roughly the same portion of the COS field of view in each observation. These position angles place the filament roughly along the cross-dispersion axis, so we can expect the emission from the filament to be much more extended along the cross-dispersion axis than along the dispersion axis.

We show in Appendix A that the FUV emission from the filament is indeed somewhat extended along the cross-dispersion axis, but this does not therefore imply that there is a significant effect from extended emission from the filament along the dispersion axis. We claim in Sect. 8.1 that the diameter of the filament is about 0.24″, for which if the emission is uniformly distributed across the filament would correspond to an artificial velocity dispersion of about σ = 7 km s⁻¹. This would be added in quadrature to the physical broadening from the filament itself to obtain the measured velocity dispersions σ_r ≳ 120 km s⁻¹. Thus we expect that the effect of extended emission is negligible here.

The one exception is [Fe XXI], which we argue is not physically associated with the filament. In this case, it would be possible for the [Fe XXI] emission to fill the aperture. However, since the measured velocity dispersion for this line is rather uncertain $({\sigma }_{\mathrm{r}}={69}_{-27}^{+79} \mathrm{km} {\mathrm{s}}^{-1})$, it is difficult to constrain the degree of artificial broadening for this line. If the line is aperture-filling, and we add this artificial broadening in quadrature to the the thermal broadening of 58 km s⁻¹ estimated above, the total broadening would be 95 km s⁻¹, which can explain all of the observed broadening in the line, with no need for turbulence at all. We discuss this more in Sect. 7.3.

3. Observational results for FUV continuum and permitted lines

3.1. FUV continuum

Now we turn to the reduced FUV spectrum and discuss the observational results. The first result is that there is a faint FUV continuum visible across the G130M bandpass, which is about 50 times fainter than the FUV continuum in the nucleus of M87. We attribute this continuum to the so-called “FUV excess” in M87. The FUV excess in some early-type galaxies was first detected by the Orbiting Astronomical Observatory (Code 1969) and was measured in M87 by the International Ultraviolet Explorer (Bertola et al. 1980). The observed COS G130M continuum is similar in shape to the IUE spectrum. The origin of the FUV excess is somewhat unclear, but FUV excesses are common in elliptical galaxies and seem to be tied to some late stage of stellar evolution (see reviews by O’Connell 1999 and Brown 1999 and more recent work by Yi et al. 2011 and Boissier et al. 2018). Fitting a low-order polynomial to the observed FUV continuum, we estimate the observed FUV continuum luminosity (from 1160 Å to 1450 Å) in this aperture to be 2.4 × 10³⁸ erg s⁻¹. The dereddened value is 2.9 × 10³⁸ erg s⁻¹. This is consistent with the observed FUV continuum surface brightness measured by Ohl et al. (1998) in an overlapping waveband. We also remind the reader that there is no evidence for star formation in the M87 filaments (Salomé & Combes 2008; Sparks et al. 2012).

3.2. C II

C II λ1335 is a triplet for singly-ionized Carbon from the ²D to ²P⁰ states, with one of the lines transitioning to the ground state. The lines are at 1334.53 Å, 1335.66 Å, and 1335.71 Å in roughly a 1:0.2:2 ratio in emission in the laboratory (Moore 1970). In absorption, the latter two lines are frequently not detected, since they are transitions from excited states while the former line is resonant.

For our line fitting we employ Gaussian models with three free parameters: integrated flux F₀, velocity dispersion along the line of sight σ_r, and mean radial velocity v_r. For C II we specify three Gaussians, one for each component of the triplet. We give each component the same σ_r and v_r and freeze the fluxes to a 1:0.2:2 ratio, yielding a total of three free parameters for the fit. We generate a 3-dimensional grid of values for these model parameters, and compute the likelihood at each location in the grid for the data given the corresponding model. From the grid of likelihoods, we then compute medians and central 68% credible intervals for each parameter, marginalizing over the others. We verify in Appendix B that it is safe to neglect the COS line spread function in our modeling, which is roughly a Gaussian with σ ≈ 8 km s⁻¹ in the core and features non-Gaussian wings.

After fitting the C II emission from M87, we explore Galactic C II absorption, which is slightly displaced from the emission due to the redshift of M87. The 1334.5 Å line is resonant and produces very clear absorption (probably saturated) but the non- resonant lines are not robustly detected. We perform a double Gaussian fit to the absorption profile, using a single Gaussian for the saturated resonant line (the SN is not good enough to perform a more detailed fit) and allowing for the presence of a second absorption feature at the location of the strong 1335.7 Å non-resonant line. We fix the relative velocities of these two absorption features to the value from atomic physics (264 km s⁻¹) relative to the 1334.5 Å line, but allow them to have free normalizations and velocity dispersions (since the resonant line is saturated). There are therefore five free parameters in the absorption model. We perform a fit with these five parameters to the Galactic C II absorption profile in the same manner as above.

The results can be seen in Fig. 3. The simple Gaussian fit to the M87 C II emission profile is a good fit (using the 1σ errors from Fig. 3 for a χ² goodness-of-fit test, we find χ² = 86.5 for 88 d.o.f.), and the 1:0.2:2 ratio for the three components of the C II triplet seems reasonable. The best-fit and 1σ uncertainties for the model parameters are: $F_0={0.96}_{-0.08}^{+0.09}\times {10}^{-16} \mathrm{erg} {\mathrm{s}}^{-1} {\mathrm{cm}}^{-2}$ (sum of all three components), ${\sigma }_{\mathrm{r}}={128}_{-17}^{+23} \mathrm{km} {\mathrm{s}}^{-1}$, and v_r = 138 ± 18 km s⁻¹.

Fig. 3. Portion of the spectrum around the C II λ1335 triplet, with velocities relative to the 1334.5 Å resonant line in the rest frame of M87. The three components of the triplet are indicated with dotted red lines, and a linear estimate of the local background is indicated with the black dotted line. The overall model is shown with the red solid line, which includes redshifted C II emission as well as two Gaussians for Galactic C II absorption. Saturated absorption near the LSR (indicated with the vertical dotted line) is visible, as well as a tentative sign of absorption from the non-resonant 1335.7 Å line.

For comparison, Werner et al. (2013) also observed this same field in [C II] λ158 μm with Herschel-PACS, and for this region they found a velocity dispersion σ_r ≈ 130 km s⁻¹ and v_r ≈ 140 km s⁻¹ (no uncertainties given) within their 6″ × 6″ region. We analyzed the Herschel-PACS data ourselves using HIPE v. 15.0.1, and for the 9.4″ × 9.4″ spaxel containing our COS sightline the line is visible above the detector noise but not the uncertainties are fairly large. We find v_r = 108 ± 24 km s⁻¹ and σ_r = 107 ± 20 km s⁻¹. This is reasonably consistent with both the Werner et al. (2013) results and with our FUV data, although it is clear that the FUV data have a higher SN and better precision.

This match confirms the FUV C II and the FIR [C II] originate from the same system, and the Herschel-PACS imaging shows that this material is also approximately co-spatial with and has the same bulk velocity as the Hα filaments measured by Sparks et al. (1993), implying the C II is associated with the Hα-emitting filaments, although the Herschel-PACS resolution is too poor to localize [C II] to the exact location of the Hα emission within the COS aperture.

Given the good results from our fitting above and the agreement in velocity dispersions between the FIR and FUV measurements, we expect that C II is not heavily affected by scattering or absorption in the resonant line, so that the velocity dispersion we measure can be fully attributed to motions in the filament. In order to check this we fit an additional model which unties the width of the resonant line from the widths of the other two lines, in order to see if additional broadening in the resonant line is preferred by the data. A slightly broader line is indeed preferred, but the improvement is only Δχ² = 1.3 for 1 d.o.f., which is not significant. We conclude that there is no evidence for resonant scattering affecting our measurements of C II, and the measured velocity dispersions can best be attributed to intrinsic motions.

We also compare our FUV line flux to the FIR flux in [C II] λ158 μm. Werner et al. (2013) measure a line flux of 1.5 × 10⁻¹⁵ erg s⁻¹ cm⁻² over the 6″ × 6″ region which covers our sightline, and we measure a line flux of 2.4 ± 0.6 × 10⁻¹⁵ erg s⁻¹ cm⁻² in the larger 9.4″ × 9.4″ spaxel. This scaling of flux with length of the box (instead of area) supports a picture where the [C II] λ158 μm emission is associated with a long filament, and in this case the expected flux within the r = 1.25″ COS aperture would be 6 × 10⁻¹⁶ erg s⁻¹ cm⁻², or about a factor of five brighter than the FUV line flux. This corresponds to several thousand times as many 158 μm photons as compared to 1335 Å photons. We will discuss the implications of this result in much more detail in Sect. 8.

For the absorption lines, we measure a velocity dispersion of ${\sigma }_{\mathrm{r}}={41}_{-20}^{+35} \mathrm{km} {\mathrm{s}}^{-1}$ and a mean velocity of $v_{\mathrm{r}}=-{60}_{-13}^{+18} \mathrm{km} {\mathrm{s}}^{-1}$ relative to the LSR for the 1334.5 Å resonant line, although the line is saturated so the velocity dispersion is not physical. This corresponds to a lower limit on the Galactic C⁺ column density N_C+ > 2 × 10¹⁴ cm⁻², if the line were on the linear portion of the curve of growth. We weakly detect absorption at the expected location of the 1335.7 Å non-resonant line, but the significance is not very high (Δχ² = 1.5 for two parameters) and the line parameters are not well-constrained by the data, so our model for this line is strongly affected by the implicitly uniform priors assumed for each of the line parameters.

3.3. N V

N V is the ²P-²S transition in Lithium-like Nitrogen, analogous to C IV λ1549, and it produces a widely spaced doublet with a 2:1 flux ratio for lines at 1238.82 Å and 1242.81 Å respectively. We again employ a Gaussian model for N V emission, with two components corresponding to the two lines in the doublet. Again we fix the relative separation between the lines and fix their velocity dispersions, and require the lines to have the fixed 2:1 flux ratio so that there are three free parameters in total. The spectrum and our fit are shown in Fig. 4.

Fig. 4. Portion of the spectrum around the N V λ1239,1243 doublet, with velocities relative to the 1239 Å resonant line in the rest frame of M87. A linear estimate of the local background is indicated with the black dotted line, and the overall model is shown with the red solid line. We have also identified and labeled a faint C III λ1247.4 emission line in this spectrum.

Our Gaussian model does not yield quite as good a fit for NV as it does for C II, but it still gives an adequate fit (χ², d.o.f. = 60.9,52). The best-fit and 1σ uncertainties for the model parameters are: $F_0={1.71}_{-0.10}^{+0.12}\times {10}^{-16} \mathrm{erg} {\mathrm{s}}^{-1} {\mathrm{cm}}^{-2}$ (sum of both components), ${\sigma }_{\mathrm{r}}={189}_{-11}^{+12} \mathrm{km} {\mathrm{s}}^{-1}$, and $v_{\mathrm{r}}={148}_{-16}^{+14} \mathrm{km } {\mathrm{s}}^{-1}$. The mean velocity approximately matches the velocity of C II, but the velocity dispersion is higher for N V and the N V profiles do not look precisely Gaussian to the eye, unlike the C II triplet.

No Galactic N V absorption is visible, and we can put an upper limit on the Galactic N⁴⁺ column. Restricting fits to Gaussians with a velocity within 100 km s⁻¹ of the LSR and velocity dispersions σ_r < 200 km s⁻¹, we find a 2σ upper limit of $N_{{\mathrm{N}}^{4+}}<2\times {10}^{14}$ for Galactic absorption. There are a few other features in this spectrum as well. The weak emission line at +2070 km s⁻¹ is probably C III λ1247.4 in M87. A Gaussian fit to this line yields F₀ = 0.08 ± 0.05 × 10⁻¹⁶ erg s⁻¹ cm⁻², $v_{\mathrm{r}}={40}_{-70}^{+100} \mathrm{km} {\mathrm{s}}^{-1}$, and σ_r = 110 ± 60 km s⁻¹. We have not −70 been able to identify the strong absorption line at −500 km s⁻¹, although it appears to be weakly statistically significant.

3.4. Lyα

The most prominent line in the spectrum is Lyα, which we display in Fig. 5. This line requires a more complex model, since it is optically thick and since it is affected by Galactic neutral Hydrogen absorption. We neglect detailed modeling of the optical depth of the line in favor of a phenomenological fit using two Gaussians, one with positive integrated flux for the bulk of the line and one with negative integrated flux to produce the self-absorption profile at the top of the line. For the Galactic absorption, we include the damping wings of the Galactic Lyα profile in our model, multiplying both Gaussians by the Lorentzian wings of the Voigt profile. Following Danforth et al. (2016), who studied the profile of Lyα from the nucleus of M87, we adopt a column density of N_H = 1.4 × 10²⁰ cm⁻² for the Galactic absorption and place it at −1283 km s⁻¹, the velocity difference between the Milky Way and M87.

Fig. 5. Portion of the spectrum around Lyα. Geocoronal Lyα airglow contaminates the spectrum significantly at −1283 km s−1 relative to M87 (indicated with the dashed vertical line), and Galactic Lyα absorption also affects the spectrum considerably. We model the transmission through the Galactic disk with the blue dashed line, assuming a neutral Hydrogen column toward M87 of 1.4 × 1020 cm−2 (Danforth et al. 2016). We fit the Lyα from M87 with two Gaussians – one positive containing most of the line flux and a small negative one which models the self-absorption – and multiply both Gaussians by the Galactic transmission profile. The red solid line is the overall model and the red dotted line shows the model without Galactic absorption. The lower panel shows the residuals between the model and the data. There are several small-scale features in the Lyα which are not captured with our simple model. In order to estimate uncertainties in model parameters, we include the rms of these residuals as a systematic uncertainty term in the error budget, which changes the χ2 from 182.8 to 39.1, while keeping the best-fit model parameters essentially unchanged.

Our overall model therefore has six free parameters, corresponding to the integrated fluxes, velocity dispersions, and mean velocities of both the positive and negative Gaussians. Both Gaussians are multiplied by the the Lorentzian wings of the Voigt profile specified above, but the latter has no free parameters. The result is shown in Fig. 5.

The fit appears good by eye, although it is formally unacceptable (χ² = 182.8 for 93 d.o.f.) due to small-scale features which are more easily visible in the residuals panel of Fig. 5. Modeling these would require a much more extensive model for the filament, which is outside the scope of this paper. Instead, we compute the rms of these residuals (0.96 erg s⁻¹ cm⁻² Å⁻¹) and incorporate it into our error budget as a systematic error. This changes the χ² to 39.1 and increases the uncertainties on model parameters to more appropriate values, while keeping the best-fit values for these parameters essentially unchanged. Our final results for the two Gaussians are: $(F0,F1)=({111.4}_{-1.0}^{+1.5},-{12.1}_{-1.2}^{+0.8})\times {10}^{-16} \mathrm{erg} {\mathrm{s}}^{-1} {\mathrm{cm}}^{-2}$, $({\sigma }_{r0},{\sigma }_{r1})=(171\pm 2,{48}_{-4}^{+5}) \mathrm{km } {\mathrm{s}}^{-1}$, $(v_{r0},v_{r1})=(147\pm 2,{157}_{-4}^{+3}) \mathrm{km} {\mathrm{s}}^{-1}$. Galactic absorption removes about 18% of the flux, so that the unabsorbed line luminosity within the COS aperture is 3.3 × 10³⁸ erg s⁻¹ and the observed line luminosity is 2.7 × 10³⁸ erg s⁻¹. It is also interesting to note that Lyα has the same mean velocity as C II and N V. This implies that all three lines (plus Hα) are being emitted from the same system.

It is also notable that the profile is asymmetric after correcting for Galactic absorption; this is evidence that the Lyα photons within the optically thick filament are not being injected at the rest-frame frequency of Lyα, in the frame of the filament. In particular, the blueward shift implies a blueshift in the filament frame. The characteristic equation for the double-peaked profile of optically thick Lyα is derived by Harrington (1973), Neufeld (1990), and Dijkstra et al. (2006) for optically thick slab and cloud geometries. It has three free parameters: temperature T , optical depth at line center τ, and injection velocity v_i. For a temperature of 1.6 × 10⁴ K and a line center optical depth of 10⁴ (based on the column densities inferred in Sect. 6.4), we estimate that the asymmetry can be explained by an injection velocity of about 10 km s⁻¹. This is small compared to the velocity of random motions σ_r ≈ 130 km s⁻¹ estimated for the filament from C II, Hα, and N V, and we hypothesize that this injection velocity is due to an outflow of matter from the filament (see Sect. 8.7). This injection velocity is also comparable to the offset between v_r0 and v_r1 in our modeling of the line.

We also consider the uncertainty in our adopted value N_H, which as we mentioned is fixed at the value measured by Danforth et al. (2016) for the nucleus of M87. Their sightline is projected about 20″ from our sightline, which for a distance of d kpc corresponds to a physical separation of 0.1d pc. Thus, since the absorption stems from neutral Hydrogen in the Galactic ISM (d ≲ 10), our value of N_H could be different if the cold neutral medium varies on sub-pc scales, which is certainly possible (Heiles & Troland 2003). We therefore perform a seven-parameter fit, allowing N_H to vary, and estimate the allowable range for N_H. We find a 90% credible interval spanning 1.0 × 10²⁰ cm⁻² − 2.0 × 10²⁰ cm⁻².

Finally, we also considered modeling Lyα as the sum of two positive Gaussians, as Danforth et al. (2016) did for Lyα from the M87 nucleus. The number of degrees of freedom is the same as our fiducial model in Fig. 5, but the χ² is worse – higher by 18.8 – and the fit is qualitatively unable to capture the two peaks adequately. We therefore do not consider such a model further in this work.

3.5. O V]

O V] λ1218.34 is an intercombination line and corresponds to a higher effective temperature in CIE (~2 × 10⁵ K) than Lyα. It is almost always blended with Lyα and usually neglected since it is much fainter. However, it can reach 10% of the flux of Lyα in both CIE (Doschek et al. 1976; Roussel-Dupre 1982) and photoionization (Kwan & Krolik 1981; Kwan 1984; Netzer 1987) conditions, so it should not be dismissed out of hand when high-resolution spectroscopy is available. We searched for this line in our Lyα spectrum, but we see no evidence for it in our spectrum.

In a fit with Lyα as above, plus O V] fixed at the same velocity as the positive Lyα component, with free normalization and free velocity dispersion (capped at 200 km s⁻¹), our 2σ upper limit on the integrated O V] flux is 2 × 10⁻¹⁶ erg s⁻¹ cm⁻².

3.6. Other lines

3.6.1. O IV, S IV, and Si IV

Around 1400 Å there is a complex of blended emission lines from O IV, S IV, and Si IV. The complex is clearly visible in Fig. 2, but the SN is not high enough to separate these features from one another. For completeness, we fit two broad Gaussians to this complex in order to estimate the total flux from the these three species (which is 1.9 ± 0.3 × 10⁻¹⁶ erg s⁻¹ cm⁻²), but we do not attempt to disentangle them into individual lines.

Si IV has resonant absorption lines at 1393.8 Å and 1402.8Å, and we detect this absorption from the Galaxy. The best-fit velocity is $v_{\mathrm{LSR}}=-7_{-14}^{+26} \mathrm{km} {\mathrm{s}}^{-1}$ the width of the line is σ_r = 4 ± 3 km s⁻¹ (marginally consistent with the expected thermal velocity of 7 km s⁻¹, and the absorbing column is at least $N_{{\mathrm{Si}}^{\mathrm{3+}}}>3\times {10}^{12} {\mathrm{cm}}^{-2}$. We again express the column as a 2σ lower limit, although the absorption does not appear to be saturated, the SN of the continuum is not good enough to exclude this possibility definitively.

3.6.2. C IV and He II

C IV λ1549 and He II λ1640 lie outside the range of G130M, but they are detected in the low-resolution COS G140L spectrum of the same sightline (Sparks et al. 2012). We measured fluxes for these lines in Anderson & Sunyaev (2016), using data from propsal ids 12271 and 13439, and show the new fits in Fig. 6 based on our new estimates of the error vectors. We use these new values in Table 1 in this paper as well. The G140L observations have the same coordinates as our G130M sightline to within the HST precision (~0.1″) and similar position angles as well.

Fig. 6. Portion of the archival low-resolution COS G140L spectrum around the C IV λ1549 doublet (upper panel) and He II λ1640 multiplet (lower panel), with velocities in the upper panel relative to the 1548 Å strong line in the rest frame of M87. A linear estimate of the local background is indicated with the black dotted line, and the overall model is shown with the red solid line. These lines have similar vr to the other FUV lines in this paper, but larger σr due to the extended nature of the emission (see Sect. 8.1).

4. Observations of [Fe XXI]

In this section we consider one additional emission line – the forbidden FUV line [Fe XXI] λ1354.1. This is different from all the other FUV lines discussed in the previous section in that its characteristic temperature in CIE is 1.1 × 10⁷ K, so it traces the hot (1 keV) intracluster medium instead of the intermediate-temperature gas in the filaments. We discussed this line in Anderson & Sunyaev (2016), where we showed tentative (≈ 2.2σ) evidence of it in this same sightline, based on low-resolution COS G140L archival spectra.

With the higher-resolution G130M data, we see stronger evidence for this line. Figure 7 shows the spectrum around [Fe XXI] λ1354.1, and the line is clearly visible. Unlike the other lines we have discussed, however, this line is slightly blueshifted. Our best-fit model has $F_0={1.8}_{-0.5}^{+0.7}\times {10}^{-17} \mathrm{erg} {\mathrm{s}}^{-1} {\mathrm{cm}}^{-2}$, ${\sigma }_{\mathrm{r}}={69}_{-27}^{+79} \mathrm{km} {\mathrm{s}}^{-1}$ and, $v_{\mathrm{r}}={92}_{-22}^{+34} \mathrm{km} {\mathrm{s}}^{-1}$. As we discussed in Anderson & Sunyaev (2016), geocoronal O I has multiplets at 1304 Å and 1356 Å; the latter doublet falls within 1000 km s⁻¹ of redshifted [Fe XXI] and with the low resolution and SN of the archival G140L data (which can have linewidths of more than 1000 km s⁻¹ for emission lines that fill the aperture) we pointed out the possibility of contamination by this doublet in the putative [Fe XXI] feature.

Fig. 7. Portion of the spectrum around the [Fe XXI] λ1354.1, with velocities relative to it in the rest frame of M87. A linear estimate of the local background is indicated with the black dotted line, and the overall model is shown with the red solid line. Our best-fit model for this line has $F_0={0.18}_{-0.05}^{+0.07}\times {10}^{-16} \mathrm{erg} {\mathrm{s}}^{-1} {\mathrm{cm}}^{-2},{\sigma }_{\mathrm{r}}={69}_{-27}^{+79} \mathrm{km} {\mathrm{s}}^{-1}$, and $v_{\mathrm{r}}=-{92}_{-22}^{+34} \mathrm{km} {\mathrm{s}}^{-1}$, and the 2σ upper limit on the velocity dispersion is σr < 229 km s−1. Unlike the other lines presented in this paper, [Fe XXI] traces T ~ 107 K plasma, and it appears to be slightly blueshifted while all the other FUV lines are redshifted. We discuss the implications of this blueshift, and potential geometries which can explain it, in Sect. 7.1.

In the new G130M observations, geocoronal O I λ1304 is several times weaker than in the G140L archival data, and no O I λ1356 airglow is detected (with the superior spectral resolution of G130M, it would have been easily identifiable and separable if present). We also checked using the timefilter routine that a G130M spectrum composed only of data taken during orbital night shows the same features as the full G130M spectrum, which further confirms that geocoronal O I λ1356 is not important in the G130M data. We therefore attribute the higher flux, width, and blueshift of [Fe XXI] in the archival G140L data to contamination from geocoronal O I λ1356 in those data, and we favor the new values presented here, which have better spectral resolution and no geocoronal contamination.

With our new data, the uncertainties are reduced enormously, and while the line is unfortunately at the faint end of the possible range of fluxes inferred from the G140L data, a blueshift persists in both observations. This demonstrates that the observed clump of T ~ 10⁷ K plasma is moving in a direction with a substantially different radial velocity as compared to the filament in our sightline, although the difference in velocity is only significant at about 2.5σ. The overall significance of the G130M detection is 4−5σ, depending on the binning and on the value of the pseudorandom seed used during the RANDCORR step in the COS calibration pipeline. It is also the most significant positive residual in the spectrum other than the lines which we fit in Sect. 3, and this can also be seen visually in Fig. 2. For comparison, the nearby positive residual at +800 km s⁻¹ is only significant at 2.7σ (or lower, depending again on the binning).

5. FUV line luminosities and cooling budget of M87

In Table 1, we summarize the emission line modeling for our COS spectrum. We also compute the luminosities for each of the FUV lines, using the dereddened fluxes and assuming a distance of 16.7 Mpc. For comparison, the Hα line luminosity within this aperture is 1.8–2.4 × 10³⁷ erg s⁻¹ (see Sect. 6.2) and the [C II] λ158 μm line luminosity within this aperture (assuming the emission is associated with the filament) is 2 × 10³⁷ erg s⁻¹ (see Sect. 3.2). The 0.5–7.0 keV X-ray luminosity within this aperture is 3 × 10³⁸ erg s⁻¹ (see Sect. 6.4).

The [C II] λ158 μm FIR line is therefore comparable in luminosity to the permitted FUV lines, and the strongest of the FUV lines – Lyα – is comparable in luminosity to the entire column of hot X-ray emitting ICM along the line of sight.

We also consider the luminosities in some of these lines integrated over the whole nucleus of M87. Sparks et al. (1993) measure an Hα+[N II] line luminosity of 3 × 10⁴⁰ erg s⁻¹ for the entire M87 filamentary nebula, and for the Hα:[N II] ratio discussed below (Sect. 6.2) this corresponds to an Hα luminosity of 9 × 10³⁹ erg s⁻¹. If the nebula has a spatially constant Lyα:Hα ratio, as is suggested by their similarity in this filament (Sect. 6.2) and in the central 100 pc of the nucleus (Anderson & Sunyaev, in prep.), then the Lyα luminosity over the entire filamentary nebula is 2 × 10⁴¹ erg s⁻¹. Finally, from the Herschel-PACS data, the [C II] λ 158 μm luminosity from the full 47″ × 47″ PACS field of view is 1.3 × 10³⁹ erg s⁻¹. It is difficult to know how much cold gas lies in the filaments closer to the nucleus of M87, but the total [C II] λ158 μm luminosity from M87 very likely exceeds 10⁴⁰ erg s⁻¹.

Based on the β-model fit of Churazov et al. (2008) and the profiles in Russell et al. (2015), we estimate a broad-band (0.5–8.0 kev) X-ray luminosity of ≈1 × 10⁴² erg s⁻¹ from the hot gas in the central 30″ of M87. Thus, we predict that the Lyα emission from the filamentary nebula covering the nucleus of M87 is just a factor of ≈5 less luminous than the volume-filling hot gas in the M87 interstellar medium.

Finally, we include for comparison the V-band luminosity of M87 in our sightline, taken from the surface brightness profile measured by Kormendy et al. (2009). This optical emission is produced by the stars in M87 and completely dwarfs the ultraviolet luminosity, which is not surprising near the center of such a massive elliptical galaxy.

In Table 2, we present measurements and/or upper limits for Galactic absorption obtained in the previous section. The lower limit on the C⁺ column comes from the saturation of the line, and the upper limits on the N³⁺ and O³⁺ columns come from our non-detections of these lines in absorption at the rest-frame velocity of the Galaxy. The errorbars on the neutral Hydrogen column are based on the FUV absorption measurements (Sect. 3.4).

One interesting result which we can see from this table is that the ratio of C⁺ to neutral Hydrogen in the Galactic ISM along this sightline is >1.4 × 10⁻⁶. At solar abundance (Grevesse & Sauval 1998), the C:H ratio is 3.3 × 10⁻⁴, so this implies that at least 0.4% of the Carbon in the neutral ISM is ionized.

6. Analysis of FUV results, part 1: emission from the filament

6.1. Are the FUV lines and the FUV continuum connected?

In this subsection, we show that the FUV lines are not produced by the stars which produce the FUV continuum, and that the FUV continuum is also not bright enough to produce the observed line emission either through photoexcitation or recombinations.

For the first issue, as we review in Anderson & Sunyaev (2016), the FUV excess continuum spectrum does not typically produce line emission, and indeed it would be very surprising to see FUV line emission from such an old stellar population. Moreover, in this paper we have showed that the typical line profiles of the FUV emission lines are narrow and slightly redshifted, whereas the stars in M87 near this filament have zero net velocity (Emsellem et al. 2011; Krajnović et al. 2011) and velocity dispersion σ_r ≈ 300 km s⁻¹ (Gebhardt & Thomas 2009). Thus the line emission is not associated with the stars in M87, but rather to the gaseous filament in our aperture.

For the second issue, we computed in Sect. 3.1 the dereddened FUV continuum luminosity in our sightline, integrated from 1160 Å to 1450 Å, which is 2.9 × 10³⁸ erg s⁻¹. The dereddened Lyα luminosity from this sightline is already 3.0 × 10³⁸ erg s⁻¹, and the FUV excess spectrum gradually decreases toward shorter wavelengths, so it is clear this continuum does not provide the photons necessary to power these lines from the filament.

6.2. Excitation mechanisms for Lyα and Hα

The ratio of Lyα to Hα is a useful diagnostic of the excitation conditions in a cloud of gas. For recombination radiation at T_e ~ 10⁴ K, as would be expected from a photoionized plasma, this ratio is about 8.2. For collisional excitation of Hydrogen, the ratio can be 10 or 20 times higher (see Tables 11.4 and 11.5 in Osterbrock & Ferland 2006).

We measured the Lyα luminosity (corrected for Galactic absorption) in Sect. 3.4. Here we also measure the Hα luminosity for this same sightline using archival data. We follow the procedure of Werner et al. (2013), downloading from the archive an HST-WFPC2 image of this region using the F658N filter (proposal id 5122), which covers the redshifted Hα+[N II] lines from M87 as well as some optical continuum. We subtract the latter by scaling an F814W image of the same region (proposal id 5941) to match the narrowband image in regions without filament emission. The resulting Hα+[N II] count rate within the 1.25″ radius of our COS aperture is 0.34–0.46 ct s⁻¹.

Next, we use the pysynphot package v.0.9.8.7 (STScI Development Team 2013) in order to convert this count rate into a flux. As in Werner et al. (2013) we specify a ratio of 0.81:1:1.45 for [N II]λ6548:Hα:[N II]λ6583 (based on measurements of the southern filament by Ford & Butcher 1979) and we give each line a velocity dispersion σ_r = 130 km s⁻¹ at the redshift of M87. This yields an Hα+[N II] flux of 2.2–2.9 × 10⁻¹⁵ erg s⁻¹ cm⁻² within our aperture, or an Hα flux of 5.1–6.8 × 10⁻¹⁶ erg s⁻¹ cm⁻².

This is approximately consistent with the result from Sparks et al. (2009) that the ratio of C IV to Hα+[N II] flux appears uniform across the filamentary nebula, with a value of 0.5. Using this ratio and the same Hα:[N II] ratio as above we can convert our C IV flux into an Hα flux, which yields 7.2 × 10⁻¹⁶ erg s⁻¹ cm⁻².

Correcting our Hα by a factor of 1.04 to account for extinction, the resulting Lyα:Hα ratio is therefore around 17–23. This is clearly an intermediate value between collisional excitation and recombination. This is in contrast to observations of A1795 and A2597 (O’Dea et al. 2004) where the Lyα:Hα ratio is lower by a factor of 2–3, pointing to recombination radiation in these cases. Unlike M87, however, the filaments in these clusters are thought to be star-forming, and the presence of young stars in the filaments provides an important additional source of ionizing radiation which is absent in M87.

If there is any dust in this filament, then it will affect Lyα much more than Hα, and so the intrinsic Lyα:Hα ratio will be pushed upwards, favoring collisional excitation more strongly.

There is also the possibility of photoionization by EUV lines with hν >13.6 eV, which can arise from the boundary layer itself, even in the absence of an external photoionizing field. We discuss this further in Sect. 6.3.2. We also note that the intermediate Lyα:Hα ratio rules out photoionization by the counter-jet as the dominant mechanism for FUV emission in the filament, since collisional excitation is clearly important as well.

6.3. Differential emission measure

Finally, while we showed that recombinations are somewhat important for Lyα and Hα, we can still gain insight by assuming in this section that CIE holds for each of the species we consider in this paper. With this assumption, we can estimate the emission measure of the plasma producing each line. We do this in Fig. 8, following a similar analysis as in Anderson & Sunyaev (2016). In this figure, we plot the emission measure, defined here as $$\mathrm{EM}\equiv {\displaystyle \int n_{\mathrm{e}}^2}\mathrm{d}V=\frac{L}{ϵ(T)\times Z}$$(1)

where L is the line luminosity for a given transition, ϵ = ϵ(T) is the volume emissivity of the line-emitting species in CIE, which includes the variation of ionization fraction as a function of temperature, and Z is the chemical abundance of the relevant element relative to Hydrogen. We assume solar abundances using the abundance tables of Grevesse & Sauval (1998), and we obtain ϵ(T) from the CHIANTI database v. 8.0.2 (Dere et al. 1997; Del Zanna et al. 2015). The resulting EM curves are shown in Fig. 8 for Lyα, C II, C IV, N V, He II, and [Fe XXI]. In general, it can be expected that the EM of a species is close to the minimum value along its curve in Fig. 8. It is natural that lines with a higher atomic number are radiated at higher temperatures (or equivalently, at lower densities due to pressure equilibrium), and occupy a higher part of the filament volume. We also remind the reader that under typical astrophysical conditions, plasma at T ~10⁵ K is highly thermally unstable (e.g., McKee & Ostriker 1977).

Fig. 8. Emission measure curves for Hα and each of the FUV lines we measure, assuming the line is produced under CIE and using Eq. (1). In general it can be expected that the EM of a species is close to the minimum value along its curve, and the 1σ uncertainties on line flux are propagated into this plot as the shaded regions around each curve (which are usually smaller than the width of the curve used in the plot). For comparison, we also plot with black points the emission measure of various phases of the hot ICM, as measured by Werner et al. (2013), and we note that the EM of T ~ 1 × 107 K plasma implied by our measurement of [Fe XXI] matches the X-ray measurement. Next, we specify a pressure of 4 × 106 cm−3 K (Churazov et al. 2008) which assumes no projection effects, so that distance r from the nucleus of M87 is equal to the observed impact parameter b. Our physical model is a cylindrical filament with a radius rc = 10 pc (see Sect. 8.1) filled with clumps that occupy a volume filling factor fc of the filament volume (see Eq. (2)). Assuming the FUV lines are emitted from the filament, we plot lines of constant fc. The FUV-emitting plasma must have a volume filling factor 10−5 ≲ fc ≲ 10−2, with the exception of He II which we discuss in Sect. 6.3.2. Finally, we overlay a normalized model of the EM for a solar flare (Dere & Cook 1979), which offers a rough match to the observed FUV lines, with the exception of He II and Hα, which have contributions from photoionization as we discuss in the text.

For comparison, we also plot in Fig. 8 the emission measure of various phases of the hot ICM, as measured by Werner et al. (2013), scaled to our distance and to solar abundance. They identify three components in the ICM along this sightline, at 0.5 keV, 1 keV, and 2 keV, and give emission measures for each. It is reassuring that the EM of 1 keV (10⁷ K) plasma implied by our COS observation of [Fe XXI] matches the Werner et al. (2013) X-ray measurement.

Next, as in Anderson & Sunyaev (2016), we estimate the corresponding electron density of the line-emitting plasma under the additional assumption of pressure equilibrium, specifying a pressure of P = 1.91P_e = 4 × 10⁶ cm⁻³ K (Churazov et al. 2008). This is the pressure measured for the Virgo ICM at a deprojected radius of 1.9 kpc, so we refer to this case as the “r = b” case and note that the true pressures and densities are likely to be lower (see Sect. 7.1). The implied densities at 10⁴ K agree to within a factor of two with the densities measured by Werner et al. (2013) for the nearby S filament based on observations of the [S II] λ6716,6731 doublet.

6.3.1. Solar flare DEM

We compare these emission measures to observations of the differential emission measure (DEM) for an M2 X-ray class solar flare on 1973 August 9 (Dere & Cook 1979), which are included in the CHIANTI package (flare_ext.dem). At the highest temperatures (log T ≥ 7.2 K) the values have been extended by the CHIANTI team, so we denote this portion of the DEM with a dotted line. solar flares are the most prominent source of [Fe XXI] emission from the Sun and provide a unique environment with multiphase gas ranging from below 10⁴ K to above 10⁷ K, which is primarily collisionally excited. Under the hypothesis that our filament is also a collisional multiphase plasma, we adopt a solar flare DEM as a crude approximation for what we might expect in this sightline. We multiply the DEM (DEM = dE M/dT) by temperature and plot the result in Fig. 8. We have multiplied the solar flare DEM by an arbitrary normalization factor to shift it in the vertical direction so that its magnitude matches the emission measures appropriate for the M87 filament instead of a solar flare.

6.3.2. Anomalous He II

The solar flare DEM is a reasonable match for every observed FUV line except He II and the optical Hα line which we discussed in Sect. 6.2. We pointed out in Anderson & Sunyaev (2016) that there is no obvious collisional solution for reproducing the observed He II:C IV ratio in this filament spectrum. Moreover, He II presents the same difficulty in the solar spectrum. Jordan (1975) first showed this for He II λ304 and for He I λ584, which were observed to be 6 and 15 times brighter than the expectations from collisional ionization equilibrium (CIE) models. He II λ304 is the Lyα transition for He⁺, and if Helium recombinations occur, the He⁺ Balmer-α transition (which is He II λ1640) will be boosted significantly over the value from collisional excitation. This has been explored by many authors in the solar context (e.g., Kohl 1977; Raymond et al. 1979; Laming & Feldman 1992, 1993; Golding et al. 2017) and there seems to be a consensus that a combination of collisional excitation, recombinations from photoionization, and repeated resonant scattering of He II EUV lines is required to explain their unexpectedly high intensity.

We postulate that similar conditions should be present in this filament, which explains the mixture of recombinations and collisional excitation determined in Sect. 6.2 from the Hα flux. Hα and He II λ1640 are probably the lines most affected by these effects, so that recombinations would be less important for the other FUV lines.

If this is correct, then He II λ304 from this filament should be extremely bright, and its line profile also exhibit similar resonant broadening as seen in Lyα. To get a sense of the expected luminosity of He II λ304, we make predictions in CHIANTI using the solar flare DEM described above. For the pressure specified above, CHIANTI predicts a He II 304 Å flux which is nearly 90% of the Lyα flux. We use this value in Table 1. However, if this is underpredicted by a factor of 6, as in the solar case, the true He II 304 Å luminosity could be as high as 2 × 10³⁹ erg s⁻¹ just along this sightline. This will have implications for the ionization fraction of the Virgo ICM (which should already be very highly ionized due to its temperature). A large luminosity of He II 304 Å photons will further reduce the neutral fraction at T ~1 × 10⁷ K below the CIE value of 7 × 10⁻⁹ (Dere et al. 1997; Del Zanna et al. 2015) since these photons are more effective at ionizing H atoms compared to X-ray photons.

6.4. Filling factor of FUV-emitting plasma in the filaments

In Figs. 8 and 13 we have drawn curves of constant filament volume filling factor f_c. We define this filling factor as $$f_{\mathrm{c}}\equiv \frac{V_{\mathrm{eff}}}{V_{\mathrm{cy1}}}=\frac{\mathrm{EM}/n_{\mathrm{e}}^2}{\pi r_{\mathrm{c}}^{2}l}=\mathrm{EM}\times \frac{{(1.91 k{T}_{\mathrm{e}}/P)}^2}{\pi r_{\mathrm{c}}^{2}l}.$$(2)

It corresponds to the fraction of the volume in the cylindrical filament which is producing the line emission, and does not depend directly on the fraction of the aperture which is filled by the filament. V_eff is the effective volume of plasma which produces a given emission line and is obtained from the emission measure as $V_{\mathrm{eff}}=\mathrm{EM}/n_{\mathrm{e}}^2$. V_cy1 is the volume of the cylindrical filament, which we take to be $\pi r_{\mathrm{c}}^{2}l$ with r_c = 10 pc (see Sect. 8.1) and l = 202 pc is the diameter of our COS aperture. If the filament is inclined relative to the aperture at an angle θ then this will be an underestimate by a factor of sin(θ), and therefore the filling factor will be overestimated by a factor of sin(θ).

In Fig. 8, Lyα, C II, C IV, and N V all have filling factors 0.01 > f_c > 10⁻⁵. Since He II is so much weaker than C IV in CIE, He II photons produced following photoionizations (see Sect. 6.3.2) likely comprise a higher fraction of the total for this line than the other permitted lines, so that our purely collisional assumptions imply an anomalously high f_c of 0.2. Hα is also inconsistent with Lyα, which proves that photoionization is also important for this line; see Sect. 6.2. Lyα is also a resonant line, so for this line we should interpret f_c in connection with the scattering volume, which may larger than the effective volume we use for other lines at similar temperatures. In Fig. 13, which places the filament at a greater distance from the nucleus with a correspondingly lower pressure, the inferred filling factors for these lines are about nine times higher (0.1 > f_c > 10⁻⁴). As we will discuss in Sect. 6.5, these two cases roughly bracket the plausible values for f_c.

In either case, it is clear that the filling factor of the FUV-emitting plasma is very low; even within the filament, the FUV-emitting material only comprises a small fraction of the total volume. We hypothesize this plasma occurs in very thin conductive boundary layers between the hotter T ~ 10⁷ K plasma and a cooler phase which we discuss in Sect. 8. Since the permitted FUV lines are such powerful coolants, maintaining constant energy flow through the boundary layer requires the intermediate-temperature plasma to occupy a very small volume (e.g., Basko & Sunyaev 1973 for the case of illumination by X-rays of the companion in a close X-ray binary system, also see McKee & Cowie 1977), so this very low f_c may indeed be physical. It is well-known that a similar rapid change of electron temperature occurs in the solar chromosphere between T_e ~2 × 10³ K and T_e ~2 × 10⁶ K (e.g., Mariska 1992 and references therein). Moreover, as N V has the highest ionization potential among these permitted lines, it likely arises from the outer layers of the boundary, which may be the most turbulent and unstable, explaining the extra broadening observed in this line.

[Fe XXI], on the other hand, has an implied filling factor f_c > 1. This is evidence that this line, and the T ~10⁷ K plasma which produces it, are not physically associated with the filament, so that the above analysis does not apply for this line. Instead, as we describe in the next section, this plasma is more likely to be approximately volume-filling and associated with a cool phase of the M87 ISM (or alternatively the cool core of the Virgo ICM). Thus, we can use the observed velocity dispersion of this line to measure the turbulence in the Virgo ICM, which we do in the next section. The 0.5 keV and 2 keV components identified by Werner et al. (2013) and shown in Fig. 8 also have f_c > 1, and can be interpreted in a similar way, though unfortunately we do not have any FUV lines in our observation which can be used to measure their kinematics.

Figure 9 shows a sketch of the implied geometry. Since our model is somewhat more complicated than a uniform-density cylinder, it is worth emphasizing the robustness of the major features of our model. The major assumptions are collisional excitation of the FUV lines, pressure equilibrium with the hot ICM, and an approximately cylindrical geometry for the filament which is based on Hα imaging and other sources (Sect. 8.1). For collisional excitation, we showed in Sect. 6.2 that collisional excitation is important even for recombination lines like Hα, and it can be expected to be more important for the other FUV lines (also see Sect. 6.3.2). For pressure equilibrium, underpressurizing the filament by a significant degree would destroy the filament within a few crossing times. The Werner et al. (2013) optical density diagnostics also imply that these filaments are approximately in pressure equilibrium, and Heckman et al. (1989) have showed similar results for other filamentary systems as well.

Fig. 9. Schematic of filament geometry. The large circle shows the HST-COS aperture, which is a circle with a radius of 1.25″ (101 pc) at the distance of M87. The ambient ICM temperature is T ≈ 2 keV, but there is also a significant T ≈ 1 keV component within our field of view, which we argue is projected in front of the filament and is associated with the other side of the eastern radio lobe. In our model, the filament is a cylindrical structure with a radius rc ~ 10 pc, containing cold (T ~ 103 K) clumps with a low volume filling fraction fc. The clumps are surrounded by thin “skins” or “shells” which are multiphase and contain the intermediate-temperature plasma that produces the bright FUV emission lines studied in this paper.

Thus we conclude that the FUV emission from the permitted lines is genuinely localized within sub-pc scales, as implied by Figs. 8 and 13. With these small emitting regions in mind, it is worth pointing out that the FUV lines still represent significantly more cooling than the X-ray emission. Werner et al. (2013) measure an average surface brightness in the 0.7–0.9 keV band of 1.2 × 10⁻¹⁶ erg s⁻¹ cm⁻² arcsec⁻² from these filaments, corresponding to a flux of 5.9 × 10⁻¹⁶ erg s⁻¹ cm⁻² from a field of view matching the COS aperture. If we assume the emission is dominated by the 2 keV component we can use an APEC model (Smith et al. 2001) with solar abundance and assume a Galactic Hydrogen column of 1.9 × 10²⁰ cm⁻² (Kalberla et al. 2005) to convert to the 0.5–7.0 keV band. This yields an unabsorbed X-ray flux of 7.8 × 10⁻¹⁵ erg s⁻¹ cm⁻², which corresponds to about 2/3 of the luminosity in the Lyα line alone. Thus, while the effective path length of the 2 keV emission is close to 10 kpc, the sub-pc FUV-emitting regions are still more important for cooling, which attests to the strength and importance of these permitted FUV transitions in the much smaller field of view of COS.

6.5. Inferred physical conditions of FUV-emitting plasma in the filaments

The small scales also imply short timescales in the filament and the boundary layer. The exact values for these timescales depend on the ambient pressure of the hot ICM (assuming the filament is in pressure equilibrium with the hot gas), and as we will show in Sect. 7.1 this pressure is somewhat uncertain due to the uncertain three-dimensional position of the filament. We know that the filament lies at least r = 1.9 kpc from the nucleus of M87, as this is the observed impact parameter, and we adopt a fiducial distance r = 7.3 kpc as explained in Sect. 7.1. Equation (3) in that section gives a parameterization of the pressure as a function of radius, which is valid up to about r = 10 kpc. Using this equation, here we compute a number of derived parameters for the intermediate-temperature gas in the filament.

First, the electron density at a given temperature is just n_e = P/1.91T_e. Using C IV as an example, at its peak emissivity we expect T_e = 1.1 × 10⁵ K, so for our fiducial distance we have an electron density of 4 cm⁻³ for the C IV-emitting plasma. The adiabatic sound speed is given by $c=\sqrt{\gamma P/\rho }$, so for the the C IV-emitting plasma, the adiabatic sound speed is 51 km s⁻¹ (this parameter is pressure-independent). The characteristic path length is derived in Anderson & Sunyaev (2016), and for the C IV-emitting plasma at our fiducial distance, it is 0.006 pc. Combining this with the adiabatic sound speed we infer a dynamical time of 114 yr.

The cooling time can be estimated using the density and the cooling functions tabulated by Sutherland & Dopita (1993). For the C IV-emitting plasma at the fiducial distance, the cooling time is 185 yr, assuming solar metallicity. Finally, the mass in this T ~10⁵ K phase within our COS field of view, as traced by the C IV emission line, is 30M_⊙.

Using Eq. (3), it is possible to infer these parameters for any other choice of pressure and temperature as well. For a different choice of pressure P as compared to our fiducial choice P₀, most of these quantities are decreased by a factor of (P/P₀)², except the cooling time which is just decreased by a factor of P/P₀.

7. Analysis of FUV results, part 2: [Fe XXI] and the T ~ 10⁷ K plasma

7.1. Blueshifted [Fe XXI]

In this subsection we address the measured blueshift for [Fe XXI] relative to M87 and relative to the redshifted filaments. To visualize this more clearly, in Fig. 10 we plot the Gaussian models we have fit to each FUV line in Sects. 3 and 4. These Gaussians do not necessarily look like the line profiles in Figs. 3–7 since most of these lines are multiplets, and here we are only plotting the underlying Gaussian model used for each component of the multiplet. It is clear that C II, N V, and Lyα are approximately consistent with one another, while [Fe XXI] has a clearly different bulk velocity and velocity dispersion. The COS G130M relative wavelength calibration is accurate to 15 km s⁻¹, and the C II velocity measured from the same segment agrees with similar precision with our independent Herschel measurements (Sect. 3.2), so an instrumental error is unlikely to explain this difference. The flat-top on the model uncertainty region for [C II] in the N filament arises due to the large uncertainty in its bulk velocity. The wavelength of [Fe XXI] is also well-known; we use a rest-frame wavelength of 1354.1 for the line, and this value seems accurate to about 1 km s⁻¹ based on solar measurements (Young et al. 2015).

Fig. 10. Model Gaussian profiles used in fitting each component for emission lines or multiplets toward the N and S filaments in M87, with velocity vr relative to M87. Lines fit in this paper are shown with solid lines (red for redshifted lines and blue for blueshifted lines), and data for Hα come from Ford & Butcher (1979). The shaded region denotes 1σ uncertainty in the model profile. All of the lines in the N filament have approximately the same profiles, except for [Fe XXI], which approximately matches the line profiles observed for the nearby S filament. We hypothesize that the two filaments trace opposite sides of the radio lobe, and in our sightline the approaching side of the filament has not cooled much below 107 K while the receding side has cooled down to 103 K or below. We note that [Fe XXI] is only observed in the N filament, but we show it in both columns to allow for easier comparison with the other lines.

The only other system where bulk velocities have been measured for both filaments and the ICM is the Perseus cluster (Hitomi Collaboration et al. 2016), and in that case the X-ray calorimeter measurements of a velocity gradient with radius in the ICM are consistent with the observed velocity gradient of an Hα- and CO-emitting filament in the same region (Hitomi Collaboration et al. 2016; Salomé et al. 2011).

In both Virgo and Perseus, the filaments are observed near the interface between the ICM and radio lobes from the SMBH (Hines et al. 1989; McNamara et al. 1996). However, the geometries and orientation angles of these two filament systems are quite different from one another, and unlike M87, the filaments in Perseus host massive reservoirs of CO molecular gas and active star formation (Salomé et al. 2006).

In M87, our target filament is located near the edge of a radio bubble inflated by the counter-jet (Hines et al. 1989; Sparks et al. 1992), and if the counter-jet has a similar orientation angle as the jet, then it is misaligned from pointing directly away from Earth by just 10°–25° (Biretta et al. 1999; Acciari et al. 2009; Wang & Zhou 2009). The stellar velocity dispersion at the projected radius of the filament is 300 km s⁻¹ and the profile is fairly flat with radius (Gebhardt & Thomas 2009), so it is unlikely the filament is in a stable circular orbit around M87.

We hypothesize, following Hines et al. (1989), that the filament is associated with the radio lobe and is outflowing, which explains the observed redshift. Figure 1 shows another image of the region, along with our annotations. We use the Hα+[N II] image from Fig. 1, with a mask applied to remove the noise in regions away from the filaments, as well as the F814W continuum image plotted using a logarithmic scale in order to show the extent of the stellar component. We also overplot 1.69 Ghz radio contours downloaded from the VLA image archive (project BC079), showing the extent of the inner radio lobes and emphasizing the well-known result that the Hα filaments avoid the radio lobes and are often found at the edges of the lobes (e.g., Hines et al. 1989; Sparks et al. 1993; Young et al. 2002).

Fig. 11. Multiband image of the center of M87, constructed from archival HST-WFPC2 (red and green) and VLA (blue) data as described in Sect. 7.1. Note that the superposition of red and green can appear yellow in the central nebula if this figure is printed. The presence of the filaments at the outer projected edge of the E radio lobe is obvious, and based on Hα and [C II]λ158 μm measurements, plus our own FUV measurements, the northern filament is receding relative to M87 at vr ≈ 140 km s−1, while Hα and [CII]λ158 μm show that the southern filament is moving toward the Earth relative to the motion of M87 by about 100 km s−1. We hypothesize that these filaments represent the two faces of the expanding radio bubble. A natural explanation for the blueshift of [Fe XXI] in our sightline (indicated by the white circle) is that the filamentary emission arises from the receding edge of the lobe while the [Fe XXI] emission arises from the approaching edge of the lobe, which is at a different temperature T ~ 107 K.

7.2. What is the true distance between the northern filament and the M87 nucleus?

The impact parameter b between the N filament and the nucleus of M87 is 1.9 kpc, so this sets a lower limit on the true distance r between the filament and the nucleus. This is the case we consider in Fig. 8, which we will call the “r = b” case.

For the geometry we discussed in Sect. 7.1, where we instead place the filament along the propagation axis of the counter-jet, we can estimate the true distance between the filament and M87. Figure 12 shows a schematic of this proposed model, which we will call the fiducial case. The northern and southern filaments are located on the edges of the expanding radio bubble, but due to its expansion the southern filament is blueshifted relative to Earth while the northern filament is redshifted. In the simplest case where the northern filament is located at the intersection of the counter-jet and the radio bubble (i.e., θ_fil = θ_jet), we can estimate its distance r from the nucleus to be 1.9 kpc / sin 15° ≈ 7.3 kpc.

Fig. 12. Schematic of our “fiducial” model for the locations of the northern and southern filaments to the east of the M87 nucleus. The two filaments are indicated with red letters, and we place them on the edge of the radio bubble (see Fig. 11). We also place a red oval near the southern filament which contains the 1 keV plasma detected in our sightline. Due to the expansion of the radio bubble, the northern filament appears red-shifted relative to Earth while the southern filament appears blueshifted. While the impact parameter b between the northern filament and the M87 nucleus (indicated with the black dot) is just 1.9 kpc, in our fiducial model the true distance r between the filament and the nucleus is much higher: r = b/sin θfil. In our fiducial model we take θfil = θjet = 15°, so that r ≈ 7.3 kpc. The pressure in the filament depends on the radius r, as we discuss in Sect. 7.3 and in Eq. (3).

We discuss the implications of these two cases on the pressure, filling factor, and velocity of the filament next. First, we parameterize the pressure as a function of radius using Fig. 5 of Churazov et al. (2008). We obtain a reasonable fit for 1 kpc ≤ r ≤ 10 kpc using the third-order polynomial $$P(r)\approx -4667r^3+(1.495\times {10}^5)r^2-(1.573\times {10}^6)r+6.159\times {10}^6$$(3)

for r in kpc and P in erg cm⁻³. Thus, the the deprojected pressure in the hot phase decreases by roughly a factor of 4.5 between r = 1.9 kpc and r = 7.3 kpc. In Fig. 13 we therefore recompute the densities and volume filling factors f_c from Fig. 8, now assuming a pressure of 8 × 10⁵ erg cm⁻³. This corresponds to the geometry considered in this section, with the impact parameter at b = 1.9 kpc but the true distance from the nucleus at r = 7.3 kpc. This geometry is plausible for the FUV lines corresponding to the filament.

Fig. 13. Emission measure curves for Hα and each of the FUV lines we measure, assuming the line is produced under CIE and the plasma has solar abundances. In this plot, however, we assume a pressure several times lower than the pressure used for that Fig. 8. The motivation for this change is the geometry discussed in Sect. 7.1, where the filament is behind the E radio lobe and the counter-jet, so its true distance from the nucleus of M87 is r = 7.3 kpc while the impact parameter is still b = 1.9 kpc. We argue geometry likely applies to all the lines in this plot except for [Fe XXI], so we refer to this as the fiducial case for most of the subsequent discussion. Compared to the r = b case, the corresponding densities are therefore reduced by a factor of 4.5, and the corresponding filament volume filling factors fc are increased by a factor of 20 (see Sects. 6.5 and 7.2). Thus the FUV-emitting plasma must have a volume filling factor 10−3 ≲ fc ≲ 10−1.

However, as we showed in Anderson & Sunyaev (2016), the effective path length goes as P⁻², so decreasing the pressure by a factor of 4.5 increases the effective path length by a factor of 20. For the [Fe XXI]-emitting plasma, the effective path length increases from about 0.5 kpc (Fig. 8) to 10 kpc (Fig. 13). We think the former value is much more likely, given the impact parameter of 1.9 kpc and the preference of 1 keV plasma to lie in and around the filaments. This leads us to the idea that the T ~10⁷ K plasma lies closer to the nucleus, while the filament is projected behind this plasma and lies at a larger radius from the nucleus of M87.

The 0.5 keV component of the hot phase has an effective path length about 20 times smaller than the 1 keV component. It is still larger than the estimated size of the filament (see Sect. 8.1), but in the r = b case the difference is only a factor of two or so. It is therefore possible to interpret the 0.5 keV component as a high-temperature extension of the filaments, and the spatial association of the 0.5 keV components with the filaments in Werner et al. (2013) supports this hypothesis. The 1 keV component, however, has a much higher emission measure and extends spatially far beyond the filaments, so it is possible to imagine 1 keV plasma existing on both sides of the radio bubble, with the approaching face dominating the signal, as we propose in our fiducial model.

In Sect. 6.5, we present a number of derived quantities (density, effective path length, cooling time, etc.) for intermediate-temperature plasma as traced by the FUV permitted lines, as a function of r.

In terms of the velocity of the filament, the radial component v_r ≈ 140 km s⁻¹, so our fiducial geometry would imply a total speed relative to M87 of 140 km s⁻¹/cos15° ≈ 145 km s⁻¹. In the unrealistic case of constant speed (deceleration is more likely) the travel time for the outflow is 49 Myr.

On the other hand, since the filament is located at the edge of the radio lobe which may be expanding buoyantly, this expansion may introduce a strong tangential component to the velocity of the filament, so that its total speed would be significantly higher. This agrees with the predictions of Churazov et al. (2001), who estimate a buoyant velocity of about half the local ambient sound speed in simulations of M87. Since c_s ≈ 730 (510) km s⁻¹ for an ambient temperature of 2 (1) keV assuming μ = 0.6 and γ = 5/3, their expected buoyant velocity is several times larger than the observed v_r of our filament. For comparison, based on X-ray and radio data Forman et al. (2017) estimate that this radio lobe and a shock front at larger radii were both produced in an outburst about 12 Myr ago, which is reasonably consistent with our estimate if the deceleration is not too strong or if the true velocity is somewhat higher.

We can further support this idea by noticing the connection between the bulk velocity of the nearby southern filament (see Figs. 1 and 10) and the observed [Fe XXI] blueshift. Our COS spectrum does not cover this filament, but we measure the velocity for [C II] λ158 μm from the archival Herschel-PACS data, finding v_r = −108 ± 5 km s⁻¹ and σ_r = 130 ± 6 km s⁻¹. Kinematics for Hα are also measured for both filaments by Ford & Butcher (1979) and Sparks et al. (1993), and we adopt the former values for this figure (v_r = 119 km s⁻¹ and v_r = −87 km s⁻¹). Ford & Butcher (1979) measure σ_r = 71 km s⁻¹ for the S filament as well but do not report σ_r for the N filament, so we use the same value for both filaments.

It is notable that both lines in the S filament have very similar values of v_r and σ_r as the values we measure for [Fe XXI]. One wonders if the southern filament might represent the approaching side of the radio lobe as it expands tangentially to the east, while the northern filament might represent the receding side of the lobe. If this is true, the blueshifted [Fe XXI] might also be physically associated with the approaching side of the lobe, which in our sightline might not have cooled as far as the receding side, so instead of forming a T ~ 10³ K filament it forms a reservoir of 10⁷ K plasma to emit [Fe XXI]. This is one potential explanation for the different velocities for these different phases, and it is worth re-emphasizing the complicated and distributed geometry of the 1 keV plasma in this field (see Fig. 2 of Werner et al. 2013).

A different possibility relates to magnetic fields. If the filament is produced from a cooling instability in the ICM, as the density increases the magnetic field strength could correspondingly increase, from a few μG potentially to a few mG. Magnetized multiphase plasma can certainly exhibit multi-directional flows associated with different phases; an example of exactly this behavior is seen in solar flares (e.g., Innes et al. 2001; Young et al. 2013). While the conditions in the M87 filament are obviously very different than in a solar flare, the role of magnetic fields in galaxy cluster filaments is already appreciated and is the subject of ongoing study (e.g., Brüggen & Kaiser 2001; Ferland et al. 2009; Sharma et al. 2010).

Finally, we note that the S filament is likely projected along the radial direction as well. Optical [S II] measurements of the S filament by Werner et al. (2013) show that it has an electron density of approximately 30 cm⁻³, which at T ≈ 1.6 × 10⁴ K corresponds to a total pressure of 9 × 10⁵ erg cm⁻³. The impact parameter for the S filament relative to the M87 nucleus is around 3–4 kpc, but the pressure from Eq. (3) is still at least twice this high at a distance of 4 kpc. A distance of 6.8 kpc for the S filament can reproduce the observed pressure, which is fairly similar to our fiducial estimate for the N filament as well.

7.3. ICM turbulence measured by [Fe XXI]

In Fig. 14 we present the probability distribution function for the velocity dispersion in [Fe XXI], marginalized over the integrated flux and the radial velocity, based on our analysis in Sect. 4. As described previously, our procedure is to adopt the median of the pdf as the central value for the parameter and then adopt the 68% credible interval as the 1σ uncertainties. This procedure yields ${\sigma }_{\mathrm{r}}={69}_{-27}^{+79} \mathrm{km} {\mathrm{s}}^{-1}$, which is indicated in the plot as well. However, the pdf is skewed and non-Gaussian, such that the maximum likelihood velocity dispersion is 47 km s⁻¹, which barely lies within our 68% credible interval.

Fig. 14. Probability distribution function for σr, the velocity distribution along the line of sight for [Fe XXI], marginalized over vr and F0. The three dashed lines indicate the median value and the central 68% credible interval, $({\sigma }_{\mathrm{r}}={69}_{-27}^{+79} \mathrm{km} {\mathrm{s}}^{-1})$ which just barely includes the maximum likelihood value of 47 km s−1. Subtracting the thermal velocity we obtain an estimate of the turbulent velocity along the line of sight for the 1 keV phase of the ICM: $v_{\mathrm{LOS}}={60}_{-35}^{+84} \mathrm{km} {\mathrm{s}}^{-1}$. The 95% upper limit on vLOS is 227 km s−1 after subtracting the thermal velocity, or 214 km s−1 if we assume the emission is also aperture-filling and artificially broadened by this effect as well.

As discussed in Sect. 2.2, the thermal velocity of Iron ions at the temperature corresponding to the peak emissivity of [Fe XXI] (log T = 7.05) is 58 km s⁻¹. We subtract the radial component of this velocity in quadrature from the total velocity dispersion in order to estimate the turbulent velocity along the line $v_{\mathrm{LOS}}=\sqrt{{\sigma }_{\mathrm{r}}^2-{(58 \mathrm{km} {\mathrm{s}}^{-\mathrm{1}})}^2/3}\approx {60}_{-35}^{+84} \mathrm{km} {\mathrm{s}}^{-1}$. The maximum likelihood value is v_LOS = 33 km s⁻¹, but the central 68% credible interval extends to v_LOS = 144 km s⁻¹ and the 95% upper limit on the turbulence is 227 km s⁻¹. The tail toward large values of σ_r is due to our uniform prior on σ_r; deeper observations with a higher SN would allow us to constrain σ_r more precisely. As discussed in Sect. 2.2 and in Appendix A, there may also be artificial broadening from the [Fe XXI] emission being extended, which if the emission is uniformly aperture-filling can be as large as 76 km s⁻¹. We do not include this term explicitly in the above analysis since we do not have any direct observational constraints on the extent of [Fe XXI] along the dispersion axis, but we note that it can fully explain the remaining velocity dispersion, so that the resulting turbulent velocities can be interpreted as upper limits. Including both thermal broadening and 76 km s⁻¹ for fully extended emission, the 95% upper limit on the turbulence becomes v_LOS < 214 km s⁻¹.

Next we estimate the dynamical implications of this turbulence. We write the total pressure due to turbulence as $P_{\mathrm{turb}}=\rho v_{\mathrm{LOS}}^2=\mu m_{p}n{v}_{\mathrm{LOS}}^2$, where n is the total (ion + electron) density, and we take μ = 0.6. The thermal pressure is P_th = nkT . Combining these equations yields (see also Werner et al. 2009): $$\frac{P_{\mathrm{turb}}}{P_{\mathrm{th}}}=\gamma {\left(\frac{v_{\mathrm{LOS}}}{c_{\mathrm{s}}}\right)}^2.$$(4)

Assuming log T = 7.05 and γ = 5/3, the adiabatic sound speed is 507 km s⁻¹. The resulting turbulent pressure we infer is $2_{-1}^{+11}\%$ of the thermal pressure. As pointed out by Inogamov & Sunyaev (2003), the large mass of Fe ions keeps their thermal velocity low, which is what allows us to measure turbulent velocities even at these moderate values.

The long tail to the right is due to our uniform prior on σ_r; deeper observations with a higher SN are needed in order to allow us to constrain the posterior more tightly.

7.4. Upper limit on Lyα absorption from M87 – constraints on photoionization in the hot halo

Since we interpret the filament as lying behind the T ~ 10⁷ K gas, we also checked for evidence of absorption in the filament spectrum from this hot gas in M87. We first explored adding a component to our Lyα modeling to account for the small neutral Hydrogen column in the hot M87 ISM, for which the 2 keV component has the largest column density. We fix this absorption component to have a velocity relative to M87 of v₀ = −100 km s⁻¹ and we fix its velocity dispersion to σ₀ = 730 km s⁻¹, which is roughly the expected thermal broadening for H atoms at 2 keV, although the final result is not extremely sensitive to either of these choices. We find a 2σ upper limit N_H < 1 × 10¹³ cm⁻². For purely collisional excitation, the neutral fraction expected in T ≈ 2 × 10⁷ K plasma is about 1 × 10⁻⁸ (Dere et al. 1997; Del Zanna et al. 2015), so the electron column in the hot phase should be N_e < 1 × 10²¹ cm⁻².

By applying Eq. (1) from Anderson & Sunyaev (2016) to the emission measure of 2 keV plasma measured by Werner et al. (2013), we find an effective electron column of 3 × 10²¹ cm⁻² for the 2 keV plasma within our aperture, assuming a constant pressure of 4 × 10⁶ erg cm⁻³ as in Fig. 8. This a factor of three higher than our 2σ upper limit. The inferred effective electron column scales inversely with the pressure, so this discrepancy can be mitigated somewhat by assuming a lower average pressure for the column of 2 keV plasma. However, this analysis shows there is probably some need for photoionizations to reduce the neutral H fraction in the M87 ISM below its CIE value (see Sect. 6.2).

8. The cold phase of the filament as traced by [C II] λ158 μm

In this section we discuss the three-dimensional structure of the filament system in more detail. Recall from Sect. 6.4 that we associate the bulk of the FUV emission from very thin (Δr ≪ 1 pc) “skins” which form a conductive interface between the ambient T ~ 10⁷ K medium and cooler clumps which comprise the core of the filament. Now we turn to the emission directly associated with the cores. In Sect. 3.2 we presented observations of the highly efficient transitions C II λ1335 and [C II] λ158 μm which demonstrated that energy losses in both these lines are comparable, within the coarse spatial resolution offered by Herschel-PACS. This means the filament region radiates several thousand times more infrared photons than FUV photons. We attempt to understand that result here.

Figure 15 shows the expected ratio of these two lines in CIE and in the low-density limit. We have used the effective collision strengths tabulated in Liang et al. (2012) in order to estimate this ratio. For additional context, we plot in the inset the emissivities of these two lines in the low-density limit, as derived from CHIANTI. The FUV multiplet peaks in emissivity at around T = 4 × 10⁴ K, dropping dramatically toward higher or lower temperatures, and at the peak of its emissivity the ratio of the FUV flux to the FIR line flux is about 150. The observed ratio (see Sect. 3.2) is about 0.2, with uncertainty of a factor of a few due to the difference in aperture sizes (see Sect. 2.1). Thus the overall discrepancy between the CIE expectation and the observation is around a factor of 750 – much larger than can be explained by the different aperture sizes or the uncertainty in COS flux calibration.

Fig. 15. The main plot shows the expected flux ratio between the C II λ1335 triplet and the [C II] λ158 μm forbidden line as a function of temperature, in the low-density limit (n ≲ 10–100 cm−3). The inset shows the emissivities of the FUV triplet and the FIR line as a function of temperature, again in the low-density limit. The FUV emissivity is strongly peaked around T ~ 4 × 104 K (indicated with the dotted black line in both plots), and at this temperature the expected flux ratio is about 150. The observed ratio, denoted with the red shaded region, is about 0.2, so the discrepancy between the CIE expectation and the observation is a factor of 750. We therefore invoke a two-phase model: the C II λ1335 emission can be associated with a T ~ 4 × 104 K phase of the thin “skin” surrounding the filament core, while the [C II] λ158 μm emission can be associated with clumps at T ~ 103 K which comprise the core of the filament, which we discuss in Sect. 8.

This discrepancy can be understood in the case of strongly dust-obscured star-forming galaxies, where matter is transparent for IR radiation but fully opaque for the FUV. However, as we have shown there is no evidence for this degree of absorption by dust within the filament. Importantly, the ratios of the three C II FUV lines are consistent with their expected values in the optically thin case, without any resonant scattering effects.

Another possibility we consider is that the C II λ1335 and [C II] λ158 μm trace different locations along the filament. The Herschel-PACS image from Werner et al. (2013) uses 6″ × 6″ extraction regions, from which we estimated the [C II] λ158 μm flux in Sect. 3.2 by multiplying the flux per spaxel by the ratio of the length of the COS aperture to the length of the spaxel, which assumes the [C II] λ158 μm emission is associated with the filament. If we instead multiply the flux within the spaxel by the ratio of areas (which would be appropriate if the emission were spatially uniform), the [C II] λ158 μm flux inferred within our aperture would be lower by about 35%. This does not help significantly, and we do not consider uniform, aperture-filling [C II] λ158 μm further here. However, this analysis does introduce the question of how to explain the [C II] λ158 μm flux in this field at all, which we address in the rest of this section.

8.1. Size of filament

We begin by summarizing observational constraints on the size of the filament. From visual inspection of the F658N images and the images in Sparks et al. (2009), the filaments appear to be marginally resolved with a half-width of 0.4″ or so, but this number is rather uncertain. We adopt a fiducial radius r_c for the filament r_c ~ 10 pc. This corresponds to a radius of 0.12″, which is about the right size to be broadened by the WFPC2 psf into the observed filament. This radius is uncertain by about a factor of two, so that r_c could plausibly be anywhere from about 5 pc to about 20 pc.

We have further evidence for r_c around this order of magnitude from the values of σ_r measured for C IV and He II in the low-resolution G140L archival data (Sect. 3.6.2). We find σ_r = 465 ± 50 km s⁻¹ and ${\sigma }_{\mathrm{r}}={375}_{-50}^{+65} \mathrm{km} {\mathrm{s}}^{-1}$ respectively for these lines, which is much larger than the σ_r ≈ 130 km s⁻¹ we infer for the other lines from the filament. In Anderson & Sunyaev (2016), we attribute this large velocity dispersion to the extended nature of the emission; for the lower-resolution G140L spectrograph, aperture-filling emission can have a measured velocity dispersion as high as 2000 km s⁻¹. If the emission fills 10%-20% of the aperture, then the spatial broadening would be about the right order of magnitude to produce the observed σ_r for the G140L lines.

8.2. Is the filament really cylindrical?

In this subsection, we briefly justify our assumption that the filament is, at least to first order, cylindrical in shape, extending more than a kpc in length but having a width of just a few tens of pc. This physical picture is supported by the Hα+[N II] imaging in Fig. 1, in which the filament appears cylindrical. We further justify it in Fig. 16, which shows the average HST-WFPC2 surface brightness profile in the F658N filter (which includes the Hα+[N II] feature) measured across the northern filament from NE to SW. We average the surface brightness profile in a box of length 1″ which extends along the filament, centered in the location of our COS aperture.

Fig. 16. Average HST-WFPC2 surface brightness profiles in the F851W filter (which measures the red stellar continuum) and the F658N filter (which includes the Hα+[N II] feature as well as some continuum) measured across the northern filament from NE to SW. We average the surface brightness profiles in a box of length 1″ which extends along the filament, centered in the location of our COS aperture. The filament is clearly visible above the red stellar continuum from M87. The relatively well-defined edges of the filament show that it has a roughly cylindrical geometry, as suggested by the imaging in Fig. 1, and it would require an unlikely geometrical coincidence for the filament to be a sheet or pancake seen in projection.

The filament is clearly visible above the red stellar continuum from M87 (the continuum is visible in the F658N filter as well as the line emission, and is also dominant in the F851W filter which we plot for comparison), and it seems to have a width of about half an arcsecond, as described in the previous subsection. The edges of the filament are also relatively well-defined, which suggests the filament truly is intrinsically thin. This argues against the possibility that the filament is actually a sheet or pancake “draped” over the interface between the radio lobe and the Virgo ICM, since the curvature of the radio lobe would tend to smooth out the edges of the sheet as seen in projection.

8.3. Production and excitation of C⁺ ions in filament

One obvious solution which could explain the [C II] λ158 μm flux is to assume the existence of a rather cold (T_e ≲ 8000 K) phase in the core of the filament where the FUV C II λ1335 emission cannot be excited by collisions due to the rather high energy of the transition (ΔE = 9.3 eV).

For such a cold phase, in CIE the fraction of C in the ionized C⁺ phase is near zero, but we see in our spectrum an FUV continuum from the stars in M87 which is capable of ionizing C atoms above the CIE expectation. We estimate this flux by integrating the extrapolated dereddened continuum which we fit in Sect. 3.1 from 912 Å (the Lyman limit) to 1101 Å (the ionization edge for C⁺), inferring a C-ionizing flux of 5 × 10⁻¹⁵ erg s⁻¹ within our COS aperture. To convert this value into an ionizing flux at the surface of the filament, we assume a uniform spatial distribution of stars within M87, so that the incident flux on the filament is higher than our observed flux by the ratio of 4π sterad to the angular size of the COS aperture on the sky (4.9 square arcsec). This gives a flux incident on the filaments F ~ 5 × 10⁻⁴ erg s⁻¹ cm⁻². If the counter-jet is illuminating the filament, the ionizing flux may be even higher, but as we will show next, the fraction of C in the C⁺ state is already nearly 100%, and the Lyα:Hα ratio (Sect. 6.2) also shows that photoionizations do not dominate the excitation of the filament.

We next assume C ionizations are the dominant source of free electrons in the cold filament core, which is consistent with expectations from chemical networks (e.g., Sternberg & Dalgarno 1995) for the C⁺-dominated portion of photodissociation regions. (If the FUV flux is so high that Hydrogen becomes significantly ionized, then the free electron density goes up by many orders of magnitude, but also the recombination rate rises accordingly, which is not observed). We can then find a steady-state solution for the C ionization balance in the cold core of the filament. The recombination rate is given by ${\alpha }_{\mathrm{c}}{n}_{\mathrm{e}}{n}_{C+}\approx {\alpha }_{\mathrm{c}}{n}_{C+}^2$, where α_c ≈ 1 × 10⁻¹² cm³ s⁻¹ is the recombination coefficient for C⁺ ions at a temperature of a few thousand K (Nahar & Pradhan 1997). The photoionization rate is (F/hν)σ_Cn_C where F is the flux from the previous paragraph, we take hν = 2 × 10⁻¹¹ erg, and estimate σ_c ≈ 2 × 10⁻¹⁷ cm⁻² (Nahar & Pradhan 1997). Finally, the total amount of Carbon is fixed; for a given temperature, we can estimate the total Hydrogen density from pressure equilibrium arguments, and then assuming solar abundance we know the total Carbon density. We will use T = 1000 K as a reference value.

We have a range of possible pressures for the filament, and here we consider two choices which approximately bracket the possible cases (see Sects. 6.5 and 7.2); in one case the distance from the nucleus is equal to the projected distance of 1.9 kpc (as in Fig. 8) and in the other the filament is located behind the observed radio lobe in the direction of the counter-jet, in which case the distance is 7.3 kpc and the pressure is several times lower (as in Fig. 13). We consider the latter case as the more probable geometry for the filament but we provide results under both cases for completeness. For the latter case (which we call the “fiducial case” in this section) we have n_H ≈ 500(1000 K/T) cm⁻³, and for the former case (which we call the “r = b” case in this section) we have n_H ≈ 2000 (1000 K/T) cm⁻³. Then at solar abundance the total Carbon density in these two respective cases is n_C + n_C+ ≈ 0.2 (1000 K/T) cm⁻³ or 0.7(1000 K/T) cm⁻³. Solving this system of equations, we find respective ionization fractions for the C in the filament of 99.96% or 99.86% at T = 1000 K. Even at a lower temperature of T = 100 K, the ionization fraction is still 99.7% or 98.6% for the fiducial or r = b cases respectively.

This yields an optical depth for C-ionizing photons at T = 1000 K of $$\tau \equiv \sigma n_C{r}_0\approx 0.003\left(\frac{r_0}{1\mathrm{ pc}}\right)$$(4a)

for the fiducial case, or $$\tau \approx 0.06\left(\frac{r_0}{1\mathrm{ pc}}\right)$$(4b)

for the r = b case. As long as the cold clumps are less than either r₀ ~ 360 pc (fiducial) or r₀ ~ 17 pc (r = b) in size, Carbon in the filament will nearly all be ionized to the C⁺ state. Additionally, absorption of soft X-ray photons leading to the production of secondary electrons and an electron-photon cascade could further increase the C⁺ fraction and allow the Carbon in larger clumps to remain ionized as well. We also have an upper limit on the size of clumps from the observed width of the filament (r_c ~ 10 pc).

Collisional excitation of these C⁺ ions will produce the observed [C II] λ158 μm emission. The most important relevant species for collisional excitations are free electrons, neutral H atoms, or molecular Hydrogen (see, e.g., Draine 2011). Since these clumps are small enough to be optically thin to C-ionizing photons, they are unlikely to be able to sustain much molecular Hydrogen. The solar abundance of Carbon relative to Hydrogen (and therefore also the ratio of electrons to neutral H atoms) is 3.3 × 10⁻⁴ (Grevesse & Sauval 1998), while the effective cross sections for collisions with free electrons are about 10³ times larger than the effective cross sections for collisions with atomic Hydrogen (Hayes & Nussbaumer 1984). Thus we expect that collisions with neutral H atoms should be the most important. Our picture is therefore a cylindrical filament of radius r_c composed of number of small, cold clumps with a relatively low volume filling factor f_c.

We also point out that saturation may be important since [C II] λ158 μm will be near the critical density. At temperatures near 10³ K, the critical density for collisions with H atoms goes approximately as $2300T_3^{-0.15} {\mathrm{cm}}^{-3}$ (Draine 2011), which is close to the expected Hydrogen density in pressure equilibrium (n_H ≈ 2000 cm⁻³ or n_H ≈ 700 cm⁻³ for the two respective pressures). The critical density for collisions with electrons is $17 T_3^{0.5} {\mathrm{cm}}^{-3}$ (Draine 2011), and as long as the cold core is mostly neutral (n_e/n_H ≲ 0.0085, which is guaranteed if the electrons are produced from ionizations of Carbon at the solar abundance) [C II] λ158 μm will also be sub-critical for electron collisions. We note that [C II] λ158 μm will become saturated at temperatures significantly lower than 10³ K, as the neutral H density will quickly rise above the critical density.

8.4. Mass and filling factor of clumps in filament

The total [C II] λ158 μm flux within the 9.4″ × 9.4″ region which covers the COS sightline is 2.4 ± 0.6 × 10⁻¹⁵ erg s⁻¹ cm⁻², corresponding to a [C II] λ158 μm luminosity of 8 × 10³⁷ erg s⁻¹. The filament passes diagonally through the spaxel, subtending a distance l ≈ 1 kpc. We use the [C II] λ158 μm cooling functions for collisions with atomic Hydrogen from Tielens & Hollenbach (1985), for an assumed temperature of T = 1000 K. For an optically thin cylinder we have $$L_{\mathrm{CII}}={\Lambda }_{\mathrm{CII}}{n}_{\mathrm{H}}{n}_{\mathrm{C+}}(\pi r_{\mathrm{c}}^{2}l f_{\mathrm{c}})$$(5)

As we found above that nearly all of the C atoms are ionized, we solve for f_c for each case. For the fiducial case we obtain $$f_{\mathrm{c}}=0.010{(r_{\mathrm{c}}/10\mathrm{ pc})}^{-2}$$(6a)

and for the r = b case we find $$f_{\mathrm{c}}=0.001{(r_{\mathrm{c}}/10\mathrm{ pc})}^{-2}$$(6b)

In Fig. 17 we extend this analysis to other temperatures and compare the emission measure of [C II] λ158 μm-emitting gas with the emission measure of the plasma which emits the C II λ1335 FUV triplet. We have again estimated the emissivity of the FIR line for C⁺ excited by collisions with neutral H based on Tielens & Hollenbach (1985), and then applied Eq. (1) to compute the corresponding emission measure. The emission measure curve for C II λ1335 is the same as in Figs. 8 and 13. We also plot curves of constant f_c for each line, assuming a filament radius r_c = 10, using Eq. (5).

Fig. 17. Estimated emission measures of gas emitting in the [C II] λ158 μm (FIR) line and in the C IIλ1335 (FUV) triplet in our sightline. The latter curve is identical to the curve for C II in Figs. 8 and 13, and the FIR curve is derived as described in Sect. 8.4, assuming nearly all the C in the filament is in the C+ state, and that collisions with atomic Hydrogen excite the [C II] λ158 μm transition. The red point shows our fiducial choice of temperature for the cold clumps, T = 1000 K, although we expect any value from 100 ≲ T ≲ 5000 K is possible. We have also drawn lines of constant filament volume filling factor fc, as in Fig. 8 and 13, using Eq. (5). We note that the FIR-emitting gas must have a higher fc than the FUV-emitting gas assuming the latter is at its peak emissivity at T ≈ 4 × 104 K. This result holds for both choices of pressure, indicated by the upper and lower panels. This supports our model of cold FIR-emitting clumps in the filament surrounded by thin conductive boundary layers which emit the FUV lines.

There is no clear best temperature for [C II] λ158 μm, and probably any value from 100 ≲ T ≲ 5000 K is possible. For both choices of pressure, any value of T in this range still results in the FIR line-emitting phase having a larger filling factor than the FUV line-emitting phase, supporting our general picture of cold clumps which emit [C II] λ158 μm, surrounded by thin conductive boundary layers which produce C II λ1335 and the other permitted FUV lines.

With estimates of the density, size, and volume filling fraction, we can compute the mass of the cold phase within our COS aperture. For the fiducial case, with T = 1000 K we have M_c ≈ 8000 M_⊙. The filling factor of clumps scales approximately linearly with temperature and their density scales inversely with temperature, so the inferred mass does not depend strongly on the assumed temperature. There are small variations (factor of ~3 over the 100 ≲ T ≲ 5000 K temperature range) due to the temperature dependence of the emissivity of C⁺ ions, however. For the b = r case, with T = 1000 K we have M_c ≈ 4000 M_⊙, and again this value can vary by about a factor of three across the temperature range. The final plausible range of masses is therefore 1000 M_⊙ ≲ M_c ≲ 2 × 10⁴ M_⊙.

If we assume equipartition between atomic and molecular gas phases and scale to the larger and brighter southern filament, this is still a bit smaller than the estimate for the molecular gas mass in the southern filament (0.4–2 × 10⁶ M_⊙) obtained by Werner et al. (2013) using somewhat different considerations. However, we still infer a fairly large amount of cold gas, compared with the ~10–100 M_⊙ of intermediate-temperature gas within our aperture, and we discuss some implications of this result in the next subsection.

The average neutral Hydrogen column density from the cold clumps can depend on the temperature, size of the clumps, and filling factor in detail, but if we assume a constant covering fraction within the cylinder we can make a simple estimate. For the fiducial case with T = 1000 K, r_c = 10 pc, and f_c = 0.01, we have N_H ~ 3 × 10²⁰ cm⁻², and again there are variations with temperature on the order of a factor of three. For the r = b case with T = 1000 K, r_c = 10 pc, and f_c = 0.001, we have N_H ~ 1 × 10²⁰ cm⁻² with the same factor-of-three variations. Thus the plausible range of column densities is 3 × 10¹⁹ cm⁻² ≲ N_H ≲ 9 × 10²⁰ cm⁻².

8.5. Consistency with other observations

First, we check our results against existing observational limits. The most stringent comes from Sparks et al. (1993), who measure visual extinction in the nucleus of M87 and place a limit A_V < 0.02 at the location of this filament. For dust with a Galactic dust-to-gas ratio of 1.9 × 10²¹ cm⁻² / A_V (Bohlin et al. 1978), this upper limit implies N_H ≲ 4 × 10¹⁹ cm⁻², which is within the range of values we estimated in the previous subsection. (We note that these are all measurements of intrinsic absorption within M87; the Galactic column is around 1.4 × 10²⁰ cm⁻² in this direction).

An alternative estimate of the extinction is possible for the nearby southern filament, where the Hα:Hβ ratio implies E(B−V) = 0.28 (Ford & Butcher 1979; Werner et al. 2013) and therefore the total N_H ≈ 2 × 10²¹ cm⁻². Neutral columns N_H > 10²¹ cm⁻² are also measured in filaments in the cores of other nearby massive galaxy clusters, such as Centaurus (Mittal et al. 2011) and Perseus (Mittal et al. 2012). Our estimate of N_H for the northern filament is below these larger columns inferred for other filaments, and closer to the smaller columns implied by the Sparks et al. (1993) upper limit.

Second, di Serego Alighieri et al. (2013) detect dust in the center of M87, with a total dust mass of 2 × 10⁵ M_⊙ within the central arcminute. For dust:gas mass ratios of 10³−10⁴, as are observed in the Perseus filaments (Mittal et al. 2012), this implies a mass of 10⁸−10⁹ M_⊙ in neutral gas in the center of M87. If the average filament has a column N_H ~ 3 × 10²⁰ cm⁻² and we use the result from Sparks et al. (1993) that the filaments subtend an area of 1250 arcsec², then the total cold gas mass implied is 3 × 10⁷ M_⊙ for the center of M87. There are large enough uncertainties in both of these estimates that an unusual dust:gas ratio in M87 is not necessarily implied, although it is possible.

Third, depending on the exact geometry, it is possible for the neutral Hydrogen in the filaments to absorb soft X-rays (τ ~ 0.1 for 1 keV photons, depending on gas-phase metallicity). However, the location of our filament (as well as the nearby southern filament) shows enhanced soft X-ray surface brightness relative to its surroundings (Young et al. 2002; Sparks et al. 2004; Forman et al. 2007; Million et al. 2010). This can actually be explained in the context of our model (Sect. 7.1), however, since we place the filament behind the T ~ 1 keV plasma along our line of sight; it therefore does not contribute to the absorption of the soft X-ray emission.

Finally, a key difference between the M87 filaments and the filaments in Perseus and Centaurus is the lack of star formation in M87. This is probably due to the lower mass of atomic gas in the M87 filaments as compared to these other systems.

While the exact dimensions and mass of the cold phase of the filament are therefore somewhat uncertain, the large ratio of [C II] λ158 μm to C II λ1335 demonstrates conclusively the existence of a cold phase with T ≲ several thousand K, and it is clear that this phase contains the majority of the material associated with the filaments. More work is needed in order to fully understand its mass, dimensions, and phase structure. In particular, ALMA observations would be especially useful, as ALMA has the sensitivity and angular resolution to detect molecular gas in these filaments, if it exists. Detection or non-detection of molecular gas at sub-arcsecond resolution would allow us to constrain the size, mass, and temperature of the clumps or strands which comprise the cold phase of the filament.

8.6. The velocity dispersion in the filament is explained by the random motion of clumps

Figure 18 shows two different ways to produce velocity dispersion which we consider in this paper. The left panel is a standard turbulent cascade in a single-phase plasma. This is how we understand the observed σ_r for [Fe XXI], which traces turbulence in the T ~ 10⁷ K volume-filling intracluster medium in front of the radio lobe in our sightline (see Sect. 6.4). The right panel is velocity dispersion arising from random motions of clumps confined within a cylindrical filament. In this case, the measured σ_r does not relate to pressure support within the clumps, but rather to their characteristic velocity as they move around in the filament. We also remind the reader that broadening can also come from thermal motions and from instrumental effects if the emission is extended, as we discuss in Sects. 2.2 and 7.3, but that these effects are not likely to be very important except possibly in the case of [Fe XXI].

Fig. 18. A diagram showing the two types of velocity dispersion we consider in this paper. The left panel is our explanation for the observed velocity dispersion in [Fe XXI] – a turbulent cascade in the hot, volume-filling intracluster medium (see Sect. 7.3). The right panel is our explanation for the observed velocity dispersion in the other lines we discuss in this paper. These other lines all have about the same value of σr ≈ 130 km s−1 even though they are emitted from gas at characteristic temperatures ranging from below 103 K up to several times 105 K, we interpret the velocity dispersion we measure for these lines as the result of random motions from clumps which are magnetically confined inside the filament. We also note that Lyα is broadened additionally by the large optical depth that Lyα photons experience as they escape from the boundary layers around these clumps.

This latter interpretation of velocity dispersion is our explanation for the observed velocity dispersion σ_r ≈ 130 km s⁻¹ which we measure for C II λ1335, N V, and Lyα, and which is also seen in [C II] λ158 μm and Hα from this region as well. A powerful piece of evidence for this interpretation is the fact that we measure approximately the same σ_r in the FUV lines which trace the boundary layer and in [C II] λ158 μm which traces the cold core of the filament. We therefore explain the observed velocity dispersion in these lines as the random motions of an ensemble of cold clouds in the filament. These random motions naturally produce a Gaussian line profile, somewhat analogously to the broad-line region of an AGN. The non-Gaussian profile observed for N V might be related to insufficient N V-emitting clumps causing the underlying clump velocity distribution to be undersampled for this line. Similar clumps are also seen in filaments in the nearby dwarf galaxy NGC 5253 (Consiglio et al. 2017), and we discussed the need for clumps with a low volume filling factor f_c in Sect. 8.1.

While the measured σ_r is close to the value measured by Hitomi Collaboration et al. (2016) for the ICM in Perseus, these motions are supersonic for the cooler gas in the filament. At T = 10³ K, the adiabatic sound speed is just 3 km s⁻¹, and so the Mach number of these motions is nearly 40. This makes it difficult to interpret σ_r for the cold phase as a turbulent cascade.

We have examined the 2D HST-COS spectrum in order to search for any clumpiness in the cross-dispersion direction, but the observed spectrum is indistinguishable from the line spread function in the cross-dispersion direction, which sets an upper limit of around 40 pc on the distance between bright clumps within the field of view. This upper limit is larger than the ~5 pc size of the clumps in filaments in NGC 5253, and also larger than the observed radius of the filament. It is likely that the filament is instead composed of many hundreds or thousands of clumps, would naturally produce a Gaussian velocity distribution while appearing smooth at HST-COS resolution.

We can get a lower limit on the characteristic clump size from simple mean free path arguments. The mean free path l for clumps in the filament can be related to the size of a clump r₀ by $l~(n{r}_{\mathrm{c}}^2)$, where n is the volume density of clumps (clumps per unit volume). From here we can derive $$l~\frac{r_0}{f_{\mathrm{c}}}.$$(7)

For f_c ~ 0.01 and l > r_c ~ 10 pc (since we want clumps not to collide frequently, in order for the system to survive), the clumps must have r₀ > 0.1 pc. For the fiducial case, our range of plausible values for f_c spans 10⁻³ ≲ f_c ≲ 0.1, which corresponds to a range of lower limits on r₀ between 0.01 pc and 1 pc.

There must also be some mechanism to confine the clumps within the filament, which can be either pressure confinement (from the hot ICM), magnetic confinement, or some combination of the two. For pressure confinement, the ram pressure force that a clump of radius r₀ experiences is approximately $\pi r_0^2{\rho }_{ICM}{\sigma }^2$, so the work done while crossing the filament is $\pi r_0^2{\rho }_{ICM}{\sigma }^2{r}_{\mathrm{c}}$, which can be equated to the kinetic energy of a clump $(2/3)\pi r_0^3{\rho }_c{\sigma }^2$. Thus we have $${\rho }_{ICM}/{\rho }_c\gtrsim r_0/r_{\mathrm{c}}$$(8)

as the condition for ram pressure to be able to confine a clump. This condition gives $$r_0\lesssim 0.0005(T/1000\mathrm{ K})\mathrm{ pc}.$$(9)

Thus ram pressure from the Virgo ICM is unlikely to be sufficient to confine the clumps within the filament, and assistance from magnetic fields is probably necessary.

8.7. Mass transfer rate?

We argued in Sect. 7.1 that the filament system has traveled from the nucleus for a few 10⁷ yr and in Sect. 6.4 that the FUV emission comes from plasma with cooling times less than 10³ yr. Such a situation can only arise if the filaments are a dynamical system, continually changing in mass and possibly in temperature. Thus we expect there to be times when the system is globally cooling (gaining mass from the ICM) and times when the filaments are globally heating (losing mass to the ICM).

Considering the latter possibility first, we also remind the reader of the slight asymmetry in the Lyα profile (Sect. 3.4) which is also a sign of a general outflow with a velocity v_r ~10 km s⁻¹. In order to estimate the properties of this putative outflow, we check whether heat conduction from the ICM into the filament is saturated (i.e., whether the mean free path of hot electrons is longer than the temperature scale height). This calculation requires an estimate of the clump size within the filament. We showed in Sect. 6.4 that this size is bounded by the range 0.001 pc < r₀ < 10 pc. For now we assume a clump size r₀ = 1 pc, which yields a saturation parameter σ₀ as defined by Cowie & McKee (1977) of σ₀ ≈ 4 × (1 pc/r₀) (taking T = 10⁷ K and n_e = 0.1 cm⁻³ in the ICM), so this clump size corresponds to moderately saturated conduction. Smaller clump sizes will yield more highly saturated conduction. The saturated heat flux (Eq. (7) of Cowie & McKee 1977) is about 0.004 erg s⁻¹ cm⁻² for the T ~ 10⁵ K intermediate-temperature shell in the fiducial case, and about a factor of three higher in the r = b case.

Taking Eqs. (21) and (22) from Cowie & McKee (1977), which apply in the unsaturated case, we can estimate the mass loss rate $\dot{m}$ and the evaporation rate τ for the filament, obtaining $\dot{m}\approx 0.0001(r_0/1 \mathrm{pc})M_{\odot } {\mathrm{yr}}^{-1}$ for both cases, τ ≈ 0.7(r₀/1 pc)²(1000 K/T)^2.5 Myr for the fiducial case, and τ ≈ 2.0(r₀/1 pc)²(1000 K/T)^2.5 Myr for the r = b case. Using Eqs. (63) and (64) instead, which apply in the case of highly saturated conduction, we find $\dot{m}\approx 7{(r_0/1 \mathrm{pc})}^2\times {10}^{-5} M_{\odot } {\mathrm{yr}}^{-1}$ and for both cases, τ ≈ 1(r₀/1 pc) Myr for the fiducial case, and τ ≈ 1(r₀/1 pc) Myr for the r = b case. These latter relations have an additional dependence on r₀ as well, through a factor of F(σ₀) which is of order unity; we compute this for r₀ = 1 in the above estimates. These sets of values are close to one another and bracket the moderately saturated case which we infer for r₀ = 1 pc.

The inferred evaporation time is much shorter than the travel time for the filaments which we estimated in Sect. 7.1. However, if there is a significant turbulent magnetic field around the clumps, this will strongly decrease the mean free path of electrons, which will correspondingly reduce the thermal conductivity. This will decrease the mass-loss rate and increase the lifetime of the filament system.

However, the correspondence in X-ray images between the soft X-ray flux and the Hα filaments (e.g., Young et al. 2002; Sparks et al. 2004; Forman et al. 2007; Million et al. 2010) also raises the possibility that the ICM may be cooling onto the filaments rather than evaporating them. The 0.7–0.9 keV band shows a significant flux excess over the other nearby bands, and in this band the flux from within our COS aperture is 5.9 × 10⁻¹⁶ erg s⁻¹ cm⁻² (see Sect. 6.4). If this flux were entirely due to a cooling flow, we can estimate the cooling rate using the cflow model in Xspec (v. 12.9.1). We set the metallicity to solar, the low-energy cutoff to 0.1 keV (the exact value is not important for this calculation), the high-energy cutoff to 3 keV. For the redshift of M87, we find that this flux corresponds to a cooling rate of 3 × 10⁻⁴ M_⊙ yr⁻¹. This is within a factor of three of the evaporation rate computed above, and while this cooling rate is likely an upper limit it still seems somewhat possible for cooling to balance heating in this filament. It therefore remains unclear whether the filament is actually growing or evaporating.

8.8. Collisions of clumps?

It is also worth considering the role of collisions between clumps in the filament. The crossing time for clumps within the filament is less than 10⁵ yr, and there will be shocks when clumps collide since the velocity of random motions σ_r ~ 130 km s⁻¹ is so much higher than the sound speed within the clumps (see Sect. 8.6). For a velocity dispersion σ_r ≈ 130 km s⁻¹, the thermalization temperature is of order T ~ 10⁶ K, with the exact value depending on the effective equation of state. In this temperature regime plasma is highly unstable (McKee & Ostriker 1977) and can be expected to cool, so these shocks will produce intermediate-temperature plasma which radiates in the permitted FUV lines we observe. The cooling time for the shock-heated plasma is also on the order of 10⁵ yr (Sutherland & Dopita 1993), comparable to the crossing time across the filament. It is possible to imagine a sort of equilibrium arising where the average rate of clump destruction through collisions is comparable to the production rate of clumps through cooling of shock-heated million-degree plasma.

This would provide an alternative source of intermediate-temperature T ~ 10⁵ K plasma, which could supplement the conductively-powered boundary layers around the cold clumps. This picture merits further investigation. For clumps of size r₀ ~1 pc, the mean free path is about 10² filament widths, so the typical time between collisions is about 10⁷ years, which is an order of magnitude larger than the evaporation time estimated in the previous section. For smaller values of r₀, both timescales vary linearly with r₀, so thermal conduction will continue to dominate. For larger values of r₀, the conduction becomes less saturated and $\tau \propto r_0^2$, so if clumps are sufficiently large then collisions may become more important than conduction. On the other hand, for sufficiently large clumps (i.e., r₀ = 3 pc, r_c = 10 pc, and f_c = 0.001), we expect less than one clump within the COS aperture, and this would not produce a Gaussian distribution of velocities as we observe for most lines, nor would it produce the area-filling Hα emission seen in Fig. 1. Thus our initial impression is that collisions of clumps are not the primary source of intermediate temperature plasma in this filament.

There may also be a radiative shock associated with the filament, since it occurs at the interface between an expanding radio lobe and the ICM. Recall also that the presence of filaments at such interfaces is a general phenomenon, and the filaments in M87 and other nearby clusters are usually observed to be perpendicular to these interface regions. Dopita & Sutherland (1996) considered this possibility in the general case and showed that photoionization in front of the shock can be important as well, and their model can reproduce the observed optical and FUV lines from the nucleus of M87 (Dopita et al. 1997). Inclusion of radiative shocks also complicates the picture we have developed. At this level of detail, hydrodynamical simulations are required, which is outside the scope of this paper. We remind the reader, however, that we have showed that most of the lines we observe can be adequately explained collisionally.

9. Conclusions

M87 is an ideal laboratory for studying the problem of coupling feedback from accreting SMBHs to the surrounding gas in the context of AGN feedback. In this paper we study an FUV spectrum which we obtained with the G130M grating on HST-COS, which covers an Hα- and C IV-emitting filament projected 1.9 kpc to the E of the nucleus of M87. This is a well-studied region full of multiphase gas at the edge of a radio lobe which is thought to be inflated by the SMBH in the nucleus.

We detect a faint FUV continuum we attribute to the so-called “FUV excess”, a fairly common phenomenon in early-type galaxies with old stellar populations which is thought to be connected to emission from evolved stars in these galaxies.

We also detect a number of lines in emission from this region, most of which we attribute to the multiphase plasma in the filament. In our HST-COS G130M spectrum, these lines include C II λ1335, Lyα, and N V λ1238, and we supplement them with archival COS G140L measurements of C IV λ1549 and He II λ1640 (Sparks et al. 2012; Anderson & Sunyaev 2016). The former three lines all show approximately the same radial velocity v_r ≈ 140 km s⁻¹. This radial velocity is also seen in Hα (Sparks et al. 1993) and [C II] λ158 μm measurements of the same filament. For C II λ1335 we measure a velocity dispersion ${\sigma }_{\mathrm{r}}={128}_{-17}^{+23} \mathrm{km} {\mathrm{s}}^{-1}$, which is also consistent with the σ_r = 107 ± 20 km s⁻¹ we measured in [C II] λ158 μm. Lyα appears broader (σ_r = 171 ± 2 km s⁻¹) which we attribute to the effects of resonant scattering due to the large optical depth for Lyα photons. N V also appears broader than C II $({\sigma }_{\mathrm{r}}={189}_{-11}^{+12} \mathrm{km} {\mathrm{s}}^{-1})$ but the lines are also noticeably non-Gaussian; we hypothesize N V is formed in a narrow boundary region between the cooler filament and the warmer ICM which may be especially unstable.

The overall agreement in kinematics for these lines is remarkable; the characteristic temperatures of these lines span four orders of magnitude, so that the observed σ_r is subsonic for the hotter gas and highly supersonic for the coolest gas in this sightline. We infer that the velocity dispersion is the product of random motions of clumps in the filament. The large velocity dispersion implies that cold clouds (and the warm gas surrounding the clouds) are moving with large relative velocities relative to one another, or possibly that the radial velocity of the gas in the filament fluctuates very strongly over scales of less than 100 pc. In the first case, collisions of clouds are inevitable, although their frequency depends on the cloud size. Under certain conditions, these collisions might be a very important reason for the heating of warm gas.

In addition to the overall bulk velocity v_r ≈ 140 km s⁻¹ and velocity dispersion σ_r ≈ 130 km s⁻¹ in the filament, we also find evidence of a v_r ≈ 10 km s⁻¹ outflow in the filament based on the asymmetry of the (Galactic-absorption-corrected) Lyα profile, which implies evaporation in the filament. However, the spatial coincidence between a soft X-ray excess in M87 and the Hα filaments could be evidence of cooling from the hot ICM onto the filaments. At the moment it is still unclear whether the filaments are in fact growing or evaporating.

We also detect, at 4−5σ depending on the binning, [Fe XXI] λ1354 from M87 in our sightline. This transition occurs in 10⁷ K plasma, and we therefore do not associate this line with the filament, but rather with gas which associated with the 1 keV phase of the ambient ICM. Our [Fe XXI] is slightly blueshifted $(v_{\mathrm{r}}=-{92}_{-22}^{+34} \mathrm{km} {\mathrm{s}}^{-1})$ which is different from the observed v_r for the filament emission. However, this is the same velocity as observed for the nearby southern filament. We propose that the southern filament traces the approaching side of the radio lobe, while the northern filament traces the receding side; our sightline naturally passes through both sides of the lobe and we speculate that the permitted FUV lines are coming from the latter while the [Fe XXI] is emitted by 1 keV plasma associated with the former. We also measure the velocity dispersion in [Fe XXI], which is only the second direct measurement to date of turbulence in the ICM of a galaxy cluster, and find a turbulent velocity along the line of sight $v_{\mathrm{LOS}}={60}_{-35}^{+84} \mathrm{km} {\mathrm{s}}^{-1}$. It will be very interesting to obtain HST-COS spectroscopy of the southern filament as well in order to check the kinematics of [Fe XXI]. If our picture is correct and the 1 keV plasma lies on the approaching side of the radio lobe, then our model makes a clear prediction that v_r and σ_r should be very similar for [FeXXI] in both sight-lines.

We also estimate the Lyα:Hα ratio along our sightline and find intermediate values (17–23), which points to a mixture of collisional excitation and recombination involved in producing these lines. Under the assumption of CIE we also estimate the emission measures of plasma emitting each of the FUV lines, and find generally good agreement between our observations (including [Fe XXI]) and the differential emission measure from a solar flare, which is a multiphase collisional plasma. This supports our conclusion that these lines are generally collisionally powered, but we note that He II is a significant outlier and probably requires a boost from recombinations, as does Hα.

These observations underscore the importance of studying the FUV lines from filaments in clusters. The bulk of the emission is radiated in the FUV (and the EUV, although there are currently no instruments available to observe extragalactic EUV radiation), and line ratios of FUV lines are very powerful for diagnosing physical conditions in the filamentary plasma. The total cooling rate in the FUV is likely over 10⁴¹ erg s⁻¹, even though the volume filing fraction of these filaments is negligible, underscoring their importance in the energy balance of the ICM in Virgo.

Additionally, [Fe XXI] is a uniquely powerful FUV line which can be exploited to measure the kinematics of the 1 keV component of the ICM. These observations are otherwise unobtainable at present, and they are very complementary to Hitomi and to the upcoming microcalorimeter studies of the hotter components of the ICM through kinematics of Fe Kα. Our observations along this sightline are currently photon-limited, and not systematics-limited, so deeper observations of 1 keV plasma using HST-COS promise to measure the kinematics of this plasma with higher precision in the future.

Finally, we also consider the cold (T ≲ a few thousand K) phase of the filament, which is probed by archival Herschel-PACS data showing strong [C II] λ158 μm emission from the filament region. The high [C II] λ158 μm: C II λ1335 ratio is very clear evidence that a cold phase must exist in the filament, and the inferred mass in this phase is in range 1 × 10³−2 × 10⁴ M_⊙ within our COS aperture. This is orders of magnitude larger than the tens of solar masses in intermediate temperature (T ~ 10⁴−10⁶ K) gas at the interface between the filament and the Virgo ICM, but still probably not massive enough to form stars. The filament is likely composed of a bundle of strands or clumps with a low volume filling factor. Observations of the cold phase with ALMA would be very helpful for understanding the mysterious cores of these filaments.

Acknowledgments

Based on observations made with the NASA-ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with program #14623. This work has been partially supported by the Russian Science Foundation through grant 14-22-00271. The authors would like to thank the referee for thoughtful and helpful comments, as well as Patricia Arévalo, Eugene Churazov, and Sara Heap for helpful discussions during the preparation of this paper, and Elaine Snyder at the HST-COS Helpdesk for assistance with understanding the COS calibrations.

References

Appendix A: Cross-dispersion profile of FUV emission

In this appendix we examine the cross-dispersion profiles of the FUV emission in our COS observations. To do this, we add together the individual flt files from each observation to produce a summed 2D spectrum, and then measure profiles in the cross-dispersion direction. Figure A.1 shows the results. In general the SN is rather low, so we can only perform this exercise for the brightest lines (Lyα and N V).

Fig. A.1. Cross-dispersion profiles for the two brightest lines in our FUV spectrum, along with the COS cross-dispersion line spread function and the cross-dispersion profile for Lyα airglow for comparison. These latter two profiles bracket the range of spatial extension in the cross-dispersion direction, with the lsf corresponding to zero extent and the airglow corresponding to uniformly aperture-filling emission. The filament approximately extends along the cross-dispersion axis in our observations. We infer standard deviations of 3.3 ± 0.1 pixels, 8.5 ± 0.2 pixels, 8.0 ± 0.2 pixels, and ${9.8}_{-1.8}^{+2.7}$ pixels for the four lines respectively, suggesting that Lyα and N V approximately extend along the entire cross-dispersion axis. This does not imply that they are similarly extended along the dispersion axis, however, and we expect that they are in fact not very extended in the dispersion direction.

For comparison, we also plot the COS line spread function in the cross-dispersion direction at 1221 Å, which roughly corresponds to the redshifted wavelength of Lyα from M87. We downloaded this profile from the COS website¹ for COS G130M at lifetime position 3 with the CENWAVE=1318 setting. To bracket the opposite case, where extended emission uniformly fills the aperture, we also measure the cross-dispersion profile for the Lyα airglow line in our observations. We fit Gaussians to each profile, estimating a standard deviation of 3.3 ± 0.1 pixels for the line spread function in the cross-dispersion direction and a standard deviation of 8.5 ± 0.2 pixels for Lyα airglow.

For Lyα, we can also fit a Gaussian to the profile, and obtain a standard deviation of 8.0 ± 0.2 pixels. For N V the SN is not very high but we obtain a standard deviation of ${9.8}_{-1.8}^{+2.7}$ pixels. This analysis is difficult due to vignetting and other effects, and the observed profiles are probably not simply linear combinations of the cross-dispersion line spread function and the uniform aperture-filling profile, but it seems that the emission comes close to spanning the entire cross-dispersion axis. Our expectation (see Sect. 2.2) is that the filament extends roughly along the cross-dispersion axis, so it is not surprising for the emission to fill the aperture along this axis.

Appendix B: Effects of COS line spread function

Since this paper employs a careful kinematic analysis of emission lines with COS, it is reasonable to check that the COS line spread function does not affect our results. We would not expect it to be a major issue, since the COS resel size is about 15 km s⁻¹, but the line spread function does have non-Gaussian wings which could theoretically be important to model for bright lines like Lyα. To test this, we downloaded the COS line spread function from the same website as in Appendix A, again selecting the line spread function centered at 1221 Å to correspond to redshifted Lyα from M87. We convolved our best-fit model for Lyα from M87 (see Fig. 5) with this line spread function, and plot the result in Fig. B.1.

Fig. B.1. Portion of the spectrum around Lyα, along with our best-fit model from Sect. 3.4 (blue) and this best-fit model convolved with the COS line spread function (red). The lower panel shows the residuals between both models and the data. The two models are nearly identical, and the convolution of the line spread function with the model increased the χ2 by only 0.8 when including a systematic error term as described in Sect. 3.4. We therefore conclude that the line spread function is not a significant source of error in our model fitting, and can safely be neglected in our analysis.

The two models are nearly identical. The model convolved with the lsf is formally a poorer fit, but the Δχ² is just 0.8, so the difference is not very significant. The systematic errors in fitting the complicated Lyα profile with our simple model clearly dominate over uncertainties caused by the line spread function. We therefore conclude that the line spread function is not a significant source of error in our model fitting.

All Tables

All Figures

Fig. 1. Hα+[N II] image of the multiphase filamentary structures east of the nucleus of M87, constructed from archival HST-WFPC2 images as described in Sect. 6.2. The red circle in the center of the image indicates the location of our COS aperture, which targets the northern of two large filaments projected east of the nucleus. This filament is clearly separated from the other filament to the south, as there is no Hα bridge connecting the two filaments, and as we will show they have different velocities and likely originate on opposite sides of an expanding radio lobe. The dashed red box indicates the approximate size of the Herschel-PACS region from which we measure a [C II] 158 μm spectrum (see, e.g., Sect. 2.1). Comparison of this image to Fig. 2 of Werner et al. (2013) shows that the hot ICM in this sightline is multiphase and rich in 1 keV plasma, although the majority of the hot gas is in the slightly hotter 2 keV phase.

In the text

Fig. 2. Our COS G130M spectrum of the M87 filament, divided into segments B (top) and A (bottom) for visual clarity. We have binned the spectrum in this plot into 0.70 Å bins, and display 1σ errors on each bin as described in the text (Sect. 2). Prominent emission lines are identified and discussed in Sects. 3 and 4, and airglow lines are indicated with the shaded red regions and identified with red text.

In the text

Fig. 3. Portion of the spectrum around the C II λ1335 triplet, with velocities relative to the 1334.5 Å resonant line in the rest frame of M87. The three components of the triplet are indicated with dotted red lines, and a linear estimate of the local background is indicated with the black dotted line. The overall model is shown with the red solid line, which includes redshifted C II emission as well as two Gaussians for Galactic C II absorption. Saturated absorption near the LSR (indicated with the vertical dotted line) is visible, as well as a tentative sign of absorption from the non-resonant 1335.7 Å line.

In the text

	Fig. 4. Portion of the spectrum around the N V λ1239,1243 doublet, with velocities relative to the 1239 Å resonant line in the rest frame of M87. A linear estimate of the local background is indicated with the black dotted line, and the overall model is shown with the red solid line. We have also identified and labeled a faint C III λ1247.4 emission line in this spectrum.
In the text

Fig. 5. Portion of the spectrum around Lyα. Geocoronal Lyα airglow contaminates the spectrum significantly at −1283 km s−1 relative to M87 (indicated with the dashed vertical line), and Galactic Lyα absorption also affects the spectrum considerably. We model the transmission through the Galactic disk with the blue dashed line, assuming a neutral Hydrogen column toward M87 of 1.4 × 1020 cm−2 (Danforth et al. 2016). We fit the Lyα from M87 with two Gaussians – one positive containing most of the line flux and a small negative one which models the self-absorption – and multiply both Gaussians by the Galactic transmission profile. The red solid line is the overall model and the red dotted line shows the model without Galactic absorption. The lower panel shows the residuals between the model and the data. There are several small-scale features in the Lyα which are not captured with our simple model. In order to estimate uncertainties in model parameters, we include the rms of these residuals as a systematic uncertainty term in the error budget, which changes the χ2 from 182.8 to 39.1, while keeping the best-fit model parameters essentially unchanged.

In the text

Fig. 6. Portion of the archival low-resolution COS G140L spectrum around the C IV λ1549 doublet (upper panel) and He II λ1640 multiplet (lower panel), with velocities in the upper panel relative to the 1548 Å strong line in the rest frame of M87. A linear estimate of the local background is indicated with the black dotted line, and the overall model is shown with the red solid line. These lines have similar vr to the other FUV lines in this paper, but larger σr due to the extended nature of the emission (see Sect. 8.1).

In the text

Fig. 7. Portion of the spectrum around the [Fe XXI] λ1354.1, with velocities relative to it in the rest frame of M87. A linear estimate of the local background is indicated with the black dotted line, and the overall model is shown with the red solid line. Our best-fit model for this line has $F_0={0.18}_{-0.05}^{+0.07}\times {10}^{-16} \mathrm{erg} {\mathrm{s}}^{-1} {\mathrm{cm}}^{-2},{\sigma }_{\mathrm{r}}={69}_{-27}^{+79} \mathrm{km} {\mathrm{s}}^{-1}$, and $v_{\mathrm{r}}=-{92}_{-22}^{+34} \mathrm{km} {\mathrm{s}}^{-1}$, and the 2σ upper limit on the velocity dispersion is σr < 229 km s−1. Unlike the other lines presented in this paper, [Fe XXI] traces T ~ 107 K plasma, and it appears to be slightly blueshifted while all the other FUV lines are redshifted. We discuss the implications of this blueshift, and potential geometries which can explain it, in Sect. 7.1.

In the text

Fig. 8. Emission measure curves for Hα and each of the FUV lines we measure, assuming the line is produced under CIE and using Eq. (1). In general it can be expected that the EM of a species is close to the minimum value along its curve, and the 1σ uncertainties on line flux are propagated into this plot as the shaded regions around each curve (which are usually smaller than the width of the curve used in the plot). For comparison, we also plot with black points the emission measure of various phases of the hot ICM, as measured by Werner et al. (2013), and we note that the EM of T ~ 1 × 107 K plasma implied by our measurement of [Fe XXI] matches the X-ray measurement. Next, we specify a pressure of 4 × 106 cm−3 K (Churazov et al. 2008) which assumes no projection effects, so that distance r from the nucleus of M87 is equal to the observed impact parameter b. Our physical model is a cylindrical filament with a radius rc = 10 pc (see Sect. 8.1) filled with clumps that occupy a volume filling factor fc of the filament volume (see Eq. (2)). Assuming the FUV lines are emitted from the filament, we plot lines of constant fc. The FUV-emitting plasma must have a volume filling factor 10−5 ≲ fc ≲ 10−2, with the exception of He II which we discuss in Sect. 6.3.2. Finally, we overlay a normalized model of the EM for a solar flare (Dere & Cook 1979), which offers a rough match to the observed FUV lines, with the exception of He II and Hα, which have contributions from photoionization as we discuss in the text.

In the text

Fig. 9. Schematic of filament geometry. The large circle shows the HST-COS aperture, which is a circle with a radius of 1.25″ (101 pc) at the distance of M87. The ambient ICM temperature is T ≈ 2 keV, but there is also a significant T ≈ 1 keV component within our field of view, which we argue is projected in front of the filament and is associated with the other side of the eastern radio lobe. In our model, the filament is a cylindrical structure with a radius rc ~ 10 pc, containing cold (T ~ 103 K) clumps with a low volume filling fraction fc. The clumps are surrounded by thin “skins” or “shells” which are multiphase and contain the intermediate-temperature plasma that produces the bright FUV emission lines studied in this paper.

In the text

Fig. 10. Model Gaussian profiles used in fitting each component for emission lines or multiplets toward the N and S filaments in M87, with velocity vr relative to M87. Lines fit in this paper are shown with solid lines (red for redshifted lines and blue for blueshifted lines), and data for Hα come from Ford & Butcher (1979). The shaded region denotes 1σ uncertainty in the model profile. All of the lines in the N filament have approximately the same profiles, except for [Fe XXI], which approximately matches the line profiles observed for the nearby S filament. We hypothesize that the two filaments trace opposite sides of the radio lobe, and in our sightline the approaching side of the filament has not cooled much below 107 K while the receding side has cooled down to 103 K or below. We note that [Fe XXI] is only observed in the N filament, but we show it in both columns to allow for easier comparison with the other lines.

In the text

Fig. 11. Multiband image of the center of M87, constructed from archival HST-WFPC2 (red and green) and VLA (blue) data as described in Sect. 7.1. Note that the superposition of red and green can appear yellow in the central nebula if this figure is printed. The presence of the filaments at the outer projected edge of the E radio lobe is obvious, and based on Hα and [C II]λ158 μm measurements, plus our own FUV measurements, the northern filament is receding relative to M87 at vr ≈ 140 km s−1, while Hα and [CII]λ158 μm show that the southern filament is moving toward the Earth relative to the motion of M87 by about 100 km s−1. We hypothesize that these filaments represent the two faces of the expanding radio bubble. A natural explanation for the blueshift of [Fe XXI] in our sightline (indicated by the white circle) is that the filamentary emission arises from the receding edge of the lobe while the [Fe XXI] emission arises from the approaching edge of the lobe, which is at a different temperature T ~ 107 K.

In the text

Fig. 12. Schematic of our “fiducial” model for the locations of the northern and southern filaments to the east of the M87 nucleus. The two filaments are indicated with red letters, and we place them on the edge of the radio bubble (see Fig. 11). We also place a red oval near the southern filament which contains the 1 keV plasma detected in our sightline. Due to the expansion of the radio bubble, the northern filament appears red-shifted relative to Earth while the southern filament appears blueshifted. While the impact parameter b between the northern filament and the M87 nucleus (indicated with the black dot) is just 1.9 kpc, in our fiducial model the true distance r between the filament and the nucleus is much higher: r = b/sin θfil. In our fiducial model we take θfil = θjet = 15°, so that r ≈ 7.3 kpc. The pressure in the filament depends on the radius r, as we discuss in Sect. 7.3 and in Eq. (3).

In the text

Fig. 13. Emission measure curves for Hα and each of the FUV lines we measure, assuming the line is produced under CIE and the plasma has solar abundances. In this plot, however, we assume a pressure several times lower than the pressure used for that Fig. 8. The motivation for this change is the geometry discussed in Sect. 7.1, where the filament is behind the E radio lobe and the counter-jet, so its true distance from the nucleus of M87 is r = 7.3 kpc while the impact parameter is still b = 1.9 kpc. We argue geometry likely applies to all the lines in this plot except for [Fe XXI], so we refer to this as the fiducial case for most of the subsequent discussion. Compared to the r = b case, the corresponding densities are therefore reduced by a factor of 4.5, and the corresponding filament volume filling factors fc are increased by a factor of 20 (see Sects. 6.5 and 7.2). Thus the FUV-emitting plasma must have a volume filling factor 10−3 ≲ fc ≲ 10−1.

In the text

Fig. 14. Probability distribution function for σr, the velocity distribution along the line of sight for [Fe XXI], marginalized over vr and F0. The three dashed lines indicate the median value and the central 68% credible interval, $({\sigma }_{\mathrm{r}}={69}_{-27}^{+79} \mathrm{km} {\mathrm{s}}^{-1})$ which just barely includes the maximum likelihood value of 47 km s−1. Subtracting the thermal velocity we obtain an estimate of the turbulent velocity along the line of sight for the 1 keV phase of the ICM: $v_{\mathrm{LOS}}={60}_{-35}^{+84} \mathrm{km} {\mathrm{s}}^{-1}$. The 95% upper limit on vLOS is 227 km s−1 after subtracting the thermal velocity, or 214 km s−1 if we assume the emission is also aperture-filling and artificially broadened by this effect as well.

In the text

Fig. 15. The main plot shows the expected flux ratio between the C II λ1335 triplet and the [C II] λ158 μm forbidden line as a function of temperature, in the low-density limit (n ≲ 10–100 cm−3). The inset shows the emissivities of the FUV triplet and the FIR line as a function of temperature, again in the low-density limit. The FUV emissivity is strongly peaked around T ~ 4 × 104 K (indicated with the dotted black line in both plots), and at this temperature the expected flux ratio is about 150. The observed ratio, denoted with the red shaded region, is about 0.2, so the discrepancy between the CIE expectation and the observation is a factor of 750. We therefore invoke a two-phase model: the C II λ1335 emission can be associated with a T ~ 4 × 104 K phase of the thin “skin” surrounding the filament core, while the [C II] λ158 μm emission can be associated with clumps at T ~ 103 K which comprise the core of the filament, which we discuss in Sect. 8.

In the text

Fig. 16. Average HST-WFPC2 surface brightness profiles in the F851W filter (which measures the red stellar continuum) and the F658N filter (which includes the Hα+[N II] feature as well as some continuum) measured across the northern filament from NE to SW. We average the surface brightness profiles in a box of length 1″ which extends along the filament, centered in the location of our COS aperture. The filament is clearly visible above the red stellar continuum from M87. The relatively well-defined edges of the filament show that it has a roughly cylindrical geometry, as suggested by the imaging in Fig. 1, and it would require an unlikely geometrical coincidence for the filament to be a sheet or pancake seen in projection.

In the text

Fig. 17. Estimated emission measures of gas emitting in the [C II] λ158 μm (FIR) line and in the C IIλ1335 (FUV) triplet in our sightline. The latter curve is identical to the curve for C II in Figs. 8 and 13, and the FIR curve is derived as described in Sect. 8.4, assuming nearly all the C in the filament is in the C+ state, and that collisions with atomic Hydrogen excite the [C II] λ158 μm transition. The red point shows our fiducial choice of temperature for the cold clumps, T = 1000 K, although we expect any value from 100 ≲ T ≲ 5000 K is possible. We have also drawn lines of constant filament volume filling factor fc, as in Fig. 8 and 13, using Eq. (5). We note that the FIR-emitting gas must have a higher fc than the FUV-emitting gas assuming the latter is at its peak emissivity at T ≈ 4 × 104 K. This result holds for both choices of pressure, indicated by the upper and lower panels. This supports our model of cold FIR-emitting clumps in the filament surrounded by thin conductive boundary layers which emit the FUV lines.

In the text

Fig. 18. A diagram showing the two types of velocity dispersion we consider in this paper. The left panel is our explanation for the observed velocity dispersion in [Fe XXI] – a turbulent cascade in the hot, volume-filling intracluster medium (see Sect. 7.3). The right panel is our explanation for the observed velocity dispersion in the other lines we discuss in this paper. These other lines all have about the same value of σr ≈ 130 km s−1 even though they are emitted from gas at characteristic temperatures ranging from below 103 K up to several times 105 K, we interpret the velocity dispersion we measure for these lines as the result of random motions from clumps which are magnetically confined inside the filament. We also note that Lyα is broadened additionally by the large optical depth that Lyα photons experience as they escape from the boundary layers around these clumps.

In the text

Fig. A.1. Cross-dispersion profiles for the two brightest lines in our FUV spectrum, along with the COS cross-dispersion line spread function and the cross-dispersion profile for Lyα airglow for comparison. These latter two profiles bracket the range of spatial extension in the cross-dispersion direction, with the lsf corresponding to zero extent and the airglow corresponding to uniformly aperture-filling emission. The filament approximately extends along the cross-dispersion axis in our observations. We infer standard deviations of 3.3 ± 0.1 pixels, 8.5 ± 0.2 pixels, 8.0 ± 0.2 pixels, and ${9.8}_{-1.8}^{+2.7}$ pixels for the four lines respectively, suggesting that Lyα and N V approximately extend along the entire cross-dispersion axis. This does not imply that they are similarly extended along the dispersion axis, however, and we expect that they are in fact not very extended in the dispersion direction.

In the text

Fig. B.1. Portion of the spectrum around Lyα, along with our best-fit model from Sect. 3.4 (blue) and this best-fit model convolved with the COS line spread function (red). The lower panel shows the residuals between both models and the data. The two models are nearly identical, and the convolution of the line spread function with the model increased the χ2 by only 0.8 when including a systematic error term as described in Sect. 3.4. We therefore conclude that the line spread function is not a significant source of error in our model fitting, and can safely be neglected in our analysis.

In the text