© The Authors 2023

1. Introduction

The nearby galaxy M 87 (≈16.8 Mpc distant) is host to the most studied astrophysical jet. A bright optical knot was found with the Hubble Space Telescope (HST) ∼870 mas from the nucleus (Biretta et al. 1999). It is the most superluminal feature ever witnessed in the jet that was typified by subluminal motion at that time. Thus, it experienced tremendous observational attention. In early 2005, it flared in the optical/UV and X-ray to end up becoming brighter than the nucleus (Harris et al. 2006). It was a likely candidate to be the source of a TeV flare in this epoch (Abramowski et al. 2012). HST-1 has been described in terms of a re-collimation shock (Stawarz et al. 2006), however, the current work offers an alternative explanation of its origins, namely, that of a dissipative region of the relativistic central spine of the jet.

The notion of a sheath and a highly relativistic spine has been used to understand high-energy phenomena in blazars (and M 87, in particular) that were difficult to reconcile with single-zone models (Ghisellini et al. 2005; Tavecchio & Ghisellini 2008). However, direct observations of the physical nature and dynamics of the spine has been elusive. On sub-mas scales, cross-sections of the jet in the highest sensitivity images (as of 2022) with 43 GHz and 86 GHz Very Long Baseline Interferometry (VLBI), in 2013 and 2014, respectively, detected a predominantly double-ridged (edge brightened) morphology (Hada 2017; Walker et al. 2018; Punsly 2022). Analyses of the large (ridge) peak to central trough intensity ratios in cross-sectional slices require a source that is a bright thick-walled tubular jet. This jet would then envelop a nearly invisible core or spine at 0.35 mas < z < 0.65 mas, where z is the axial displacement from the nucleus (Punsly 2022). New high-resolution, 86 GHz VLBI with the Global Millimetre VLBI Array, the phased Atacama Large Millimetre/submillimetre Array and the Greenland Telescope in 2018 detected a very narrow central feature that points back towards the vicinity of the ring of emission surrounding the black hole (Lu et al. 2023). Curiously, the detected feature is bright enough that it should have been detected in the 2013 and 2014 cross-sections (even with lower resolution), but it was not apparent (Punsly & Chen 2021; Punsly 2022). Thus, it seems to a be variable feature that is not modeled in the numerical simulation library of the Event Horizon Telescope Collaboration (EHTC hereafter, Porth et al. 2019). An order of magnitude farther out, there is observational evidence of faint disjoint narrow features along the axis, but these do not connect to the region close to the source (Asada et al. 2016; Hada 2017). The dynamics of the spine within an arc-second of the source is unknown. This has motivated efforts to find direct observational evidence of strong spine dissipation that might reveal its energetics and composition.

Previously published VLBI images that clearly resolve the jet from HST-1 in the axial direction have not been sensitive enough to detect jet emission that extends continuously to HST-1. There is a detection gap, from z ∼ 400 mas to HST-1, z ∼ 870 mas, even with low frequency Very Long Baseline Array (VLBA) observations, 1.7 GHz and 327 MHz (Cheung et al. 2007), Rampadarath et al. (2009). In Sect. 2 of this paper, we use new sensitive high dynamic range images from archival Very Large Array (VLA) data at 22 GHz to resolve HST-1 from the jet in the axial direction and trace the jet direction continuously in the gap. There is a mild bend of the jet northward, so that HST-1 lies along the jet centerline or “spine”. We argue in Sect. 3 that the flare in HST-1 that began in 2005 might be a “spinal disruption event”. This flare is ideal for the purposes of determining energetics. We note that there is a wealth of observations over many epochs and frequency (Harris et al. 2006, 2009; Perlman et al. 2011)¹. In Sect. 4, previous equipartition models of the flare in 2005 from Harris et al. (2006) are interpreted in the context of the spine. In Sect. 5, estimates of the energy fluxes of the spine and the surrounding tubular jet from sub-mas scales are combined to make up a unified picture of the jet over the last 200 yr. The jet power in recent epochs is crucial to the EHTC data analysis. The data are difficult to interpret and have become conflated with a library of numerical simulations which, in turn, are down-selected using the constraint of a viable jet power. A better knowledge of the jet power is more important than ever as the conflation process is becoming more aggressive. It is now proposed that image reconstruction should be biased by “viable” numerical models (Medeiros et al. 2023). The range of viable jet powers considered by the EHTC is a factor of few hundred and the result here is at the very low end of the range.

2. Imaging the adjacent jet upstream of HST-1

The 1.7 GHz VLBA observations are not sensitive enough to detect emission in the gap 400 mas < z < 870 mas (Cheung et al. 2007). Thus, they cannot determine the local jet direction just upstream of HST-1. The best observations for imaging this region are 22 GHz VLA, due to the sensitivity that can be achieved. The synthesized beam is about two to three times the jet width based on extrapolating the outer edges of the 1.7 GHz VLBA jet from Fig. 1 of Cheung et al. (2007). Some 22 GHz images were previously published (Chen et al. 2011). Yongjun Chen graciously recreated the image FITS files for two of these observations with improved signal-to-noise ratio (S/N) for the purposes of this article. An inspection of the residual images associated with the 2011 paper showed a significant emission structure pattern that was morphologically similar to the original structure. This means there was still some emission left in the residual image. This suggests that more “cleaning” was required to create a new residual image that looks like the noise distribution over the whole field, thereby improving the S/N. An earlier version of the 12/31/2004 image appeared in Chen et al. (2011). In spite of the modest resolution, intensity cross-sections orthogonal to the jet determine the centroid of the local jet emission to ≈1/10 of the synthesized beam width for a S/N > 5 (Cotton et al. 1998). The centroids of the cross-sections define the jet direction. This is achieved by linear fitting these centroids over the range, z ∼ 400 mas to z ≳ 700 mas, using least squares with uncertainty in both variables (Reed 1989). Since the beam is considerably wider than the jet, the peak intensity will represent the centroid position. The uncertainty of the peak position is 1/10 the synthesized beam, unless the maximum is achieved at more than one point. The cross-section can be tangent to the contour over a finite range of points which can be noticed with large magnification of the image. In this circumstance, the uncertainty is the distance between the maxima added in quadrature with 1/10 of the synthesized beam. Finding the position angle (PA) of the parallel cross-cuts is an iterative process. The intensity peaks are found and a “line of centroids” fitted. The cross-cut PA is varied until the fitted line of centroids is perpendicular to the cross-cuts. Figure 1 shows two epochs in order to see if the jet direction found is independent of observation. The contours were chosen to be approximately evenly spaced in the z coordinate (approximately 1/4 to 1/3 of a beam width in spacing). Each fit has the same number of points. The process is not completely uniform or perfect. There is always one spacing per fit that is approximately twice as large as the others when using the log scale option for the contour spacing. The points that are chosen for the fit lay on the extremum of the z coordinate of the contour and correspond to the location where the cross-cut is tangent to the contour. Since, the fit and the radio image are created with two different softwares, this choice of points facilitates a very accurate overlay (alignment) of the fit on the radio image. Therefore, obtaining an accurate fitted jet axis with its uncertainty on the radio image itself. The range of fits (the red lines) is indicated by the standard error of the regression (Reed 1989). 2003 has a smaller spread in the standard error of the fit because HST-1 was fainter and it did not skew the centroid of the flux density beyond 700 mas (i.e., there is an additional, closer, reliable centroid in the linear fit). The standard error from the best fit line is maximal at the endpoints of the fitted region, reaching ∼ ± 3 mas. Based on a short extrapolation of the fit, the primary result is that the position of HST-1 aligns with the jet axis that is immediately upstream to within < 6 mas in 2003. Figure 1 traces the jet trajectory with three linear pieces. The inner jet, z < 400 mas, is indicated by a black dashed line with the traditional PA = −67° (Hada et al. 2016). The outer dashed black line is an “eyeball” fit to the faint trajectory beyond HST-1. It is significant that the jet which appears to be very straight for 870 mas makes an abrupt bend at HST-1, as illustrated in Fig. 1. This occurs before the flare and persists during the flare. This would need to be an integral part of any physical description of HST-1.

Fig. 1. 22 GHz images have the sensitivity to reveal the jet direction in the gap (in 1.7 GHz and 327 MHz VLBA images) between z ≈ 400 mas and HST-1. The red lines in the gap are the range of the standard error in the linear fit to the peak intensity (identified with the jet center-line). HST-1 lies on a short extrapolation of the jet center-line to within ±6 mas. The image from December 31, 2004 is at the beginning of the flare. The Gaussian beam FWHM in blue provides a scale for the image.

3. Considering the plausibility of associating HST-1 with the jet spine

Figure 2 is a 1.7 GHz image from 2005.82 of HST-1 with a Gaussian fit (both the image FITS file and Gaussian fit were generously provided by C. C. Cheung). The fit and the image are for the dominant, component c that seems to be responsible for the flare in 2005. The fit does not pertain to the weaker components. It is the same image FITS file used to create the insert in the right hand corner of Fig. 1 of Cheung et al. (2007). All the components were briefly described as unresolved (Cheung et al. 2007). No Gaussian fits were published, but an elliptical fit to component c was made in support of the analysis of Cheung et al. (2007). It is not a fit to the entire HST-1 complex. Adding a weak point source at the eastern edge (component d) might make a small change. The components a and b are too faint to appear given the lowest contour level that is chosen in the image of Fig. 2 of this paper. At this early stage of flare evolution, the Gaussian fit is a very elongated feature that is formally unresolved, transversely. We note that it is the best fit assuming just one component that makes up the preponderance of flux emitted by the flare. The main conclusion of this fit is that it is necessarily highly elongated and it is also rather closely aligned with the local jet PA found in Fig. 1, namely, ΔPA = 12.5°.

Fig. 2. 1.7 GHz VLBA image from 2005.82 of HST-1. The Gaussian fit to the component ejected during the 2005 flare, component c, is very elongated along a direction that is close to the local upstream jet direction in Fig. 1. The single Gaussian fit is an ellipse, 9.2 mas × 1.3 mas (unresolved) at PA = −51°. Components a and b are off to the right and are too faint to be revealed by this contour map. The Gaussian beam FWHM in blue provides a scale for the image.

The putative spine is a powerful, highly relativistic central component of the jet. It is generally believed to be a Poynting jet with an ordered magnetic field that is predominantly toroidal (Ghisellini et al. 2005; Gabuzda et al. 2018). At high frequency (optical and UV), the Faraday rotation that is prominent at radio frequencies is minimal since the rotation angle scales inversely with the frequency squared (Chen et al. 2011). Consequently, the observed polarization direction should represent the intrinsic polarization of the emitted radiation at its source. Thus, we would expect very large optical and UV polarization aligned with the jet direction when the spine radiates (Gabuzda 2018).

By comparison, HST-1 is a historically bright superluminal knot in the M 87 from P-band to X-rays, as observed 2005. It is located within 6 mas of the jet center-line. The initial configuration of the luminous ejection in 2005 is very elongated and almost parallel to the local upstream jet axis. It has been noted that the ejections in the complex as well as the direction of the parsec scale jet change direction over time (Giroletti et al. 2012; Ro et al. 2023). However, the initial elongation of the flaring knot, HST-1, is closely aligned with the jet direction. It has a high (25%−40%) optical and UV polarization that is a aligned within a few degrees of the local jet axis (Perlman et al. 2011). This is either a group of strong coincidences or the 2005 flare of HST-1 arises from the dissipation of the spine. The primary tenet of this paper is based on the notion that there are too many coincidences to ignore.

4. Energy flux estimates of HST-1 in 2005

In this section, the previous equipartition model of HST-1 in Harris et al. (2006) is revisited in the context of the energetics of the spine. One of the big unknowns in that work was the apparent velocity of the ejected material that formed the predominant contribution to the luminosity of HST-1 in 2005. It was subsequently shown with 1.7 GHz VLBA that a powerful knot of emission emerged in 2005.04 (the component c shown in Fig. 2) and traveled downstream at β_app = v_app/c = 1.14 ± 0.14 (Cheung et al. 2007). So, β_app constrains the range of viable models in Harris et al. (2006).

From Rees (1966) and Ginzburg & Syrovatskii (1969), we have:

$$\begin{array}{c}\hfill {\beta }_{\mathrm{app}}\equiv \frac{v_{\mathrm{app}}}{c}=\frac{\beta sin\theta }{1-\beta cos\theta },\end{array}$$(1)

where θ is the LOS (chosen to be 18° here) and β is the velocity of HST-1 viewed in the cosmological rest frame of M 87 with θ = 90° (M 87 frame hereafter). Table 1 is arranged as follows. Everything in bold face is new and the other is data from Harris et al. (2006). Equation (1) indicates a narrow range of Doppler factors, δ, in Col. 1 that are associated with β_app = v_app/c = 1.14 ± 0.14 (in boldface), where:

$$\begin{array}{c}\hfill \delta =1/[\mathrm{\Gamma }(1-\beta cos\theta )].\end{array}$$(2)

The next three columns are the magnetic field, B, the plasmoid radius from time variability arguments, and the energy stored in the plasmoid from the models described, respectively, in Harris et al. (2003, 2006). In Col. 5, Q_fill = E_min/T is the energy flux required to fill the plasmoid in the variability time scale, T (Harris et al. 2006). T was estimated by Harris et al. (2006) from the 2005 X-ray light curve.. The next two columns are the velocity and Lorentz factor in the M 87 frame. The remaining columns are new. They are motivated by the fact that the spine is believed to be a Poynting jet, where B in Col. 2 is an ordered magnetic field. From the angular momentum conservation, B is almost purely toroidal, and B^ϕ ≈ ΓB in the M 87 frame (Punsly 2008). The poloidal Poynting power, S^z, in perfect MHD and approximate azimuthal symmetry is Punsly (2008):

$$\begin{array}{c}\hfill \begin{array}{cc}& S^z=\frac{c}{4\pi }{\displaystyle \int }-B^{\varphi }{E}^{\perp }\mathrm{d}{A}_{\perp },E^{\perp }\approx -\beta B^{\varphi },\hfill \\ \hfill & S^z=2c{\displaystyle \int }{\mathrm{\Gamma }}^2\beta U_B\mathrm{d}{A}_{\perp },\hfill \end{array}\end{array}$$(3)

where “⊥” is the orthogonal direction to z and ϕ (azimuthal angle) and the normal cross-sectional area element is dA_⊥. Also, U_B and U_p are the energy densities of the field and particles in the jet rest frame. E^⊥ and S^z are tabulated in Cols. 8 and 9, respectively. Column 10 is the particle energy flux in the M 87 frame, 𝒦. The total jet power in Col. 11 is:

$$\begin{array}{c}\hfill Q_{\mathrm{total}}=S^z+\mathcal{K},\mathcal{K}={\displaystyle \int }{U}_{\mathrm{p}}{\mathrm{\Gamma }}^2\beta c\mathrm{d}{A}_{\perp },U_{\mathrm{p}}=U_B,\end{array}$$(4)

where Q_total is larger than Q_fill in the range of δ relevant to HST-1 in 2005.

5. Discussion and conclusion

In Sect. 2, we show that HST-1 lies along the central axis of the jet. In Sect. 3, we argue that the superluminal motion, shape, location, and the large, axis-aligned, optical/UV polarization strongly support an identification with the relativistic spine of the jet. In Sect. 4, the equipartition models in Table 1 indicate an energy flux of Q_spine ≡ Q_total ≈ 2.5 × 10⁴¹ ergs s⁻¹. As mentioned in the introduction, the spinal disruption analysis provides an alternative to re-collimation shock models of HST-1. As such, it is not intended as a critique of the otherwise common interpretation that HST-1 might be a re-collimation shock.

A possible explanation of the sudden spine dissipation is given by the data shown in Fig. 1. The jet slowly drifts a few degrees for z < 870 mas and there is nothing that makes it dissipate violently as it propagates. At HST-1, the jet suddenly bends by ∼16°. The bend seems to have disrupted the propagation, causing the spine to dissipate, making it conspicuous for the first time along its flow. It is possible that an obstruction may have caused the jet deflection. This is supported by the HST detection of an ionized disk of gas $0\stackrel{″}{.}25$ from the nucleus (Ford et al. 1994). As there are density enhancements near the jet axis, an obstruction is certainly plausible.

In order to assess the estimated value of Q_spine, it is useful to provide the context of the surrounding tubular jet. In the region of 0.35 mas < z < 0.65 mas (in 2013 and 2014) it is a mildly relativistic, protonic tubular region that comprises ≈58% of the total jet volume (Punsly 2022). Each arm of the bilaterally symmetric tubular jet of radius, R, and wall thickness, W, transports Q_{tubular jet} ≈ [(W/0.25R)^0.46]5.3 × 10⁴¹ ergs s⁻¹ (Punsly & Chen 2021). The wall thickness of the jet in this region was estimated to be W ≈ 0.35R (Punsly 2022). This implies a tubular jet power of Q_{tubular jet} ≈ 6.1 × 10⁴¹ ergs s⁻¹.

The total jet power (assuming bilateral symmetry) in the M 87 frame is Q(M 87)≡2[Q_spine + Q_{tubular jet}]. Combining the spine and tubular jet power estimates is made complicated by the different epochs of ejection from the central engine. The emission time of the spinal plasma at HST-1, ∼870 mas/(4.5 mas yr⁻¹)≈200 yr prior to the observation, has been estimated using a speed of ≈4.5 mas yr⁻¹ from Cheung et al. (2007). This is a crude estimate for demonstrative purposes only, as we know a relativistic velocity is expected in the spine and β_app = 1.14 ± 0.14 (4.5 mas yr⁻¹) is consistent with this. An ejection time of 1.5 yr before the observation of the tubular jet on sub-mas scales was estimated in Fig. 2 of Punsly (2021). New high-resolution VLBI images indicate that the tubular jet emerges from the central engine thick-walled, namely: it is not a Kelvin-Helmholtz instability generated boundary layer of the spine created farther downstream (Lu et al. 2023). If we assume that the fundamental physical process in the central engine that launches the two component jet is the same for 200 yr, then it reasonable to assume that it would preferentially channel most of its jet power into either the spine or tubular jet for 200 yr. If the spine (tubular jet) is more powerful, Q(M 87) emitted from the central engine was Q(M 87) < 4Q_spine ≈ 1.0 × 10⁴² ergs s⁻¹ (Q(M 87) < 4Q_{tubular jet} ≈ 2.4 × 10⁴² ergs s⁻¹) ∼200 (∼1.5) yr before the observation. The weakest conclusion that can be asserted is a value of Q(M 87) < 2.4 × 10⁴² ergs s⁻¹ at some instance at a time within the last ∼200 yr, provided that the equipartition assumption of the Harris et al. (2006) models is not grossly inaccurate (the tubular jet power estimate does not rely on this assumption). Alternatively, assuming a nearly constant central engine injection jet power for ∼200 yr indicates a total jet power of Q(M 87)≲2 × 10⁴² ergs s⁻¹ (i.e., typical of a Fanaroff-Riley 1 radio galaxy) in epochs of modern observation. This analysis indicates that the spine has not served as a powerful hidden reservoir for jet energy in the last 200 yr. Additionally, Q(M 87) found here is a factor of 30−300 less than estimates based on features ejected from the nucleus many hundreds to millions of years earlier (Owen et al. 2000; Forman et al. 2005; de Gasperin et al. 2012).

The bolometric luminosity, L_bol, of the inner jet is a consistency check. Before the EHT image, the inner jet emission was inseparable from disk emission in L_bol estimates (Prieto et al. 2016). Subtracting the EHT millimeter disk flux density in Event Horizon Telescope Collaboration (2019a) from lower resolution, quasi-simultaneous broadband data indicates L_bol(observed)≈5 − 6 × 10⁴¹ ergs s⁻¹ for z < 0.4 arcseconds, even during a flare state (Punsly, in prep.). From Eqs. (1) and (2), we know that L_bol in the M 87 frame will be Doppler de-boosted. However, the region producing the peak of the SED is unresolved and the relevant β (and de-boosting) is unknown. Regardless, Q ∼ 2 × 10⁴² ergs s⁻¹ is a sufficient energy budget to support L_bol.

The jet efficiency, η_jet, is defined by Q(M 87)≲2× 10⁴² erg s⁻¹ = η_jet Ṁc², where Ṁ is the accretion rate, η_jet≲ 0.035[(0.001 M_⊙ yr⁻¹)/Ṁ]. Here, Ṁ must be larger than the mass flow rate of the sub-mass tubular jet, ≈0.00014(W/0.35R)^0.46 M_⊙ yr⁻¹ (Punsly & Chen 2021). For example, EHTC has estimated Ṁ ≈ 2.7 × 10⁻³ M_⊙ yr⁻¹ in the single-zone approximation (Event Horizon Telescope Collaboration 2019b). Alternatively, if most of the accreted mass is ejected in the jet, then we have η_jet ≲ 0.25. Apparently, there is no requirement of black hole spin as a power source – unless all the accreted mass is ejected in the jet and in this case, it is likely needed. The requirement that the jet needs a black hole spin power source might be an artifact of comparing jet powers in the distant past with current nuclear luminosity.

Acknowledgments

Many thanks to Yongjun Chen for the VLA image FITS files and C.C. Cheung for the VLBA image FITS file and Gaussian fit. This manuscript benefitted from the improvements suggested by a supportive referee.

References

All Tables

All Figures

Fig. 1. 22 GHz images have the sensitivity to reveal the jet direction in the gap (in 1.7 GHz and 327 MHz VLBA images) between z ≈ 400 mas and HST-1. The red lines in the gap are the range of the standard error in the linear fit to the peak intensity (identified with the jet center-line). HST-1 lies on a short extrapolation of the jet center-line to within ±6 mas. The image from December 31, 2004 is at the beginning of the flare. The Gaussian beam FWHM in blue provides a scale for the image.

In the text

Fig. 2. 1.7 GHz VLBA image from 2005.82 of HST-1. The Gaussian fit to the component ejected during the 2005 flare, component c, is very elongated along a direction that is close to the local upstream jet direction in Fig. 1. The single Gaussian fit is an ellipse, 9.2 mas × 1.3 mas (unresolved) at PA = −51°. Components a and b are off to the right and are too faint to be revealed by this contour map. The Gaussian beam FWHM in blue provides a scale for the image.

In the text