EDP Sciences logo
Subscriber Authentication Point
Search
Menu
Home All issues Volume 635 (March 2020) A&A, 635 (2020) A166 Full HTML
Free Access
Issue
A&A
Volume 635, March 2020
Article Number A166
Number of page(s) 7
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/201937112
Published online 27 March 2020

© ESO 2020

1. Introduction

Absorption of the 21-cm flux from distant radio sources through the discs of nearby galaxies provides information on the neutral hydrogen (H I) gas. In particular, a comparison of the absorption strength to the total H I column density yields the spin temperature of the gas, which is a measure of the population of the upper hyperfine level relative to the lower level. This can be increased via excitation by 21-cm absorption (Purcell & Field 1956), excitation above the ground state by Lyman-α absorption (Field 1959) and collisional excitation (Bahcall & Ekers 1969). The spin temperature gives the fraction of the cold neutral medium (CNM, where T ∼ 100 K and n ∼ 10 cm−3) to the warm neutral medium (WNM, where T ∼ 2000 K and n ∼ 0.4 cm−3, Sofue 2018). Both the total gas density (e.g. Toomre 1963) and fraction of cool neutral gas (Curran et al. 2016) exhibit a decrease in abundance with the galactocentric radius. The latter, based on the then 90 sight-lines searched for H I 21-cm absorption, has, however, since been refuted by subsequent studies (Borthakur 2016; Dutta et al. 2017). A flat 21-cm absorption strength in conjunction with a decreasing column density would result in temperature climb outwards across the disc. This runs contrary to what is seen in the Milky Way, where the mean spin temperature maintains ⟨Tspin ⟩ = 250 − 400 K over radii of 8–25 kpc (Dickey et al. 2009).

From the decrease in 21-cm absorption strength with the impact parameter, Curran et al. (2016) find the mean spin temperature to peak, with ⟨Tspin ⟩≈2900 K, at ρ ≈ 10 kpc. This, however, was based on a sample of just 27 sight-lines with measured column densities. Additionally, given that spin temperatures of ≈500 K and ≈200 K were found for the inner and outer disc, respectively, this was deemed to be consistent with the Galactic values. With these new data, the number of sight-lines is now 143, for which 39 have column density measurements. Here we add the new data to the previous, confirming that the 21-cm absorption strength is anti-correlated with impact parameter, in addition to using the column densities to determine the mean spin temperature of the gas across the disc.

2. Analysis

2.1. Absorption strength versus impact parameter

The addition of subsequent data (Borthakur 2016; Dutta et al. 2017; Allison et al. 2020) to that used in Curran et al. (2016)1, brings the number of sight-lines from 90 to 143. This comprises 22 detections of 21-cm absorption and 121 upper limits. In order to include these, we re-sample the limits to a common spectral resolution/profile width of 10 km s−1 (see Curran 2012) and then flag these as censored data points using the Astronomy SURVival Analysis (ASURV) package (Isobe et al. 1986).

Plotting the integrated optical depth versus the impact parameter (Fig. 1), a generalised non-parametric Kendall-tau test gives a probability of P(τ) = 2.87 × 10−4 of the observed ∫τdv–ρ anti-correlation arising by chance. Assuming Gaussian statistics, this is significant at S(τ) = 3.63σ, cf. 3.31σ previously (Curran et al. 2016). Neither Borthakur (2016) nor Dutta et al. (2017) find a strong correlation, although the former only test their sample of one 21-cm absorption detection and 15 non-detections (all at ρ <  20 kpc) and the latter limit their impact parameters to ρ <  30 kpc, resulting in S(τ) = 2.42σ.

thumbnail Fig. 1.

Velocity integrated optical depth versus the impact parameter for all of the published searches. The circles represent the previous data (Curran et al. 2016 and references therein) and the squares the data since (Borthakur 2016; Dutta et al. 2017; Allison et al. 2020). The downward arrows signify the 3σ upper limits and the dotted vertical line shows the median impact parameter. Bottom panel: binned values, including the limits via the Kaplan–Meier estimator, in equally sized bins. The horizontal error bars show the range of points in the bin and the vertical error bars the 1σ uncertainty in the mean value.

The ∫τdv–ρ dependence is confirmed via the detection rates above and below the median impact parameter of ρ = 16 kpc. At ρ ≤ 16 kpc there are 19 detections and 53 non-detections, giving 26.4 per-cent detection rate. At ρ >  16 kpc there are three detections and 68 non-detections. Based on a likelihood of p = 0.264, the binomial probability of obtaining three detections or fewer out of 71 sight-lines is 6.16 × 10−6, which is significant at 4.50σ.

2.2. Spin temperature versus impact parameter

Several of the sight-lines have been detected in 21-cm emission from which the column density can be obtained from the brightness temperature of the line emission, Tb [K]. In the optically thin regime (τ ≲ 0.3) the column density, NH I [cm−2] is given by

N H I = 1.823 × 10 18 ∫ T b d v , $$ \begin{aligned} N_{{\text{H}}{\small {\text{I}}}} = 1.823\times 10^{18} \int \! T_{\rm b}\,\mathrm{d}{ v}, \end{aligned} $$(1)

and in absorption the column density is related to the spin temperature, Tspin [K], via

N H I = 1.823 × 10 18 T spin f ∫ τ d v , $$ \begin{aligned} N_{{\text{H}}{\small {\text{I}}}} =1.823\times 10^{18}\,\frac{T_{\rm spin}}{f}\int \!\tau \,\mathrm{d}{ v}, \end{aligned} $$(2)

where f is the covering factor; the fraction of the background flux intercepted by the absorbing gas. Thus, the comparison of the velocity integrated optical depth with the column density yields the spin temperature degenerate with the covering factor, Tspin/f. For unresolved galaxies detected in 21-cm absorption at non-zero redshifts, the covering factor is dependent upon the relative absorber and emitter cross-sections as well as the redshift of the background source (Curran 2012). Given, that here the absorption is occuring through a nearby resolved disc, it is fair to assume that all of the background flux is intercepted, giving f ≈ 1.

2.2.1. Measured column densities

For 39 of the sight-lines 21-cm emission has been detected, giving the H I column density. Where this is not given (e.g. Borthakur 2016), we obtain the brightness temperature from the H I mass, MH I, via the integrated flux density of the emission (e.g. Rohlfs & Wilson 2000)

M H I = 236 D L 2 S int , where S int = 2 k Ω b λ 2 ∫ T b d v , $$ \begin{aligned} M_{{\text{H}}{\small {\text{I}}}} = 236 D_{\rm L}^2S_{\rm int}, \text{ where} S_{\rm int} = \frac{2k\Omega _{\rm b}}{\lambda ^2}\int \! T_{\rm b}\,\mathrm{d}{ v}, \end{aligned} $$(3)

DL is the luminosity distance [Mpc], Sint the integrated flux of the line [mJy km s−1], k the Boltzmann constant, Ωb the beam solid angle of the telescope at the wavelength λ [m] and ∫​Tb dv the velocity integrated brightness temperature [K km s−1].

In Fig. 2 we show the distribution of column density with impact parameter for the sight-lines with detected 21-cm emission. From this, we see that the column density is fairly consistent out to ρ ≈ 25 kpc, with a possible elevation at ≈15 kpc. In Fig. 3, we show the resulting spin temperatures, which exhibits a similar Tspin/f bump as previously (Curran et al. 2016), the binning of the data giving ⟨ T spin / f ⟩ = 1370 − 700 + 1440 $ \langle T_{\mathrm{spin}}/f\rangle =1370^{+1440}_{-700} $ K at ρ ≈ 5 kpc, ⟨ T spin / f ⟩ = 2310 − 670 + 940 $ \langle T_{\mathrm{spin}}/f\rangle =2310^{+940}_{-670} $ K at ρ ≈ 14 kpc and ⟨ T spin / f ⟩ = 1100 − 220 + 470 $ \langle T_{\mathrm{spin}}/f\rangle =1100^{+470}_{-220} $ K at ρ ≈ 25 kpc. These temperatures are considerably higher than in the Milky Way (Sect. 1).

thumbnail Fig. 2.

Column density versus the impact parameter for the sight-lines detected in 21-cm emission.

thumbnail Fig. 3.

Spin temperature/covering factor obtained from the column density (Fig. 2), versus the impact parameter. The upward arrows signify lower limits.

Determining the spin temperature through the comparison of Eqs. (1) and (2) relies upon the same sight-line being probed, which may not be the case here: in absorption we observe a “pencil-beam” through the gas, whereas for emission we observe over the whole telescope beam, which results in dilution if the beam size exceeds that of the emitting gas (rbeam >  rgas). The linear extent of the beam is given by rbeam = θbeamDA, where θbeam is the angular beam size [radians] and DA the angular diameter distance (e.g. Peacock 1999) to the galaxy [kpc], obtained from the redshift (Fig. 4). Showing NH I versus rbeam in Fig. 5, we see a clear dependence between the measured column density and the beam width.

thumbnail Fig. 4.

Redshift distribution of the target galaxies. The galaxies span the redshift range 0 ≲ z ≤ 0.4367, with 21-cm emission being detected to z = 0.0462 (filled histogram).

thumbnail Fig. 5.

Column density measured across the telescope beam versus the linear extent of the beam for the sight-lines detected in 21-cm emission. The telescopes used are the Very Large Array (VLA, Carilli & van Gorkom 1992; Borthakur et al. 2011, 2014), the Australia Telescope Compact Array (ATCA, Reeves et al. 2015, 2016), the Giant Metre-Wave Radio Telescope (GMRT, Dutta et al. 2016), the Arecibo telescope (Corbelli & Schneider 1990) and the Green Bank Telescope (GBT, Haschick & Burke 1975; Borthakur et al. 2011; Borthakur 2016).

2.2.2. Galactic column density

In order to bypass the effect of beam dilution on the column density, we can apply well constrained profiles in similar galaxies to our sample. One option is to use the Milky Way, where the total (north and south, Kalberla & Dedes 2008) disc distribution is shown in Fig. 6. We overlay the mean integrated optical depths of the 21-cm absorption for a constant spin temperature of Tspin/f ≈ 4000 K, which traces the column density out to r ≈ 20 kpc, beyond which the spin temperature decreases due to the edge of the stellar disc being reached. These spin temperatures are much higher than observed in the Milky Way (Dickey et al. 2009) and, unlike the Galactic values, appear to be further elevated at r ≈ 10 kpc.

thumbnail Fig. 6.

Radial column density distribution of the Milky Way (total disc, Kalberla & Dedes 2008) overlain with the exponential fit to the r ≥ 12.5 kpc data (Kalberla & Kerp 2009) and a log-polynomial to all of the data. The error bars show the column density of the 21-cm absorption for Tspin/f = 4000 K (right axis).

Using both the exponential fit (for 12.5 ≤ r ≤ 35 kpc, Kalberla & Kerp 2009) and the log-polynomial fit (for r ≤ 40 kpc), which provides a better trace of the inner disc, we show the spin temperature profile in Fig. 7. Where the radii overlap, these give similar results and, again, a peak in the spin temperature of Tspin/f ≈ 15 000 K at r ≈ 10 − 15 kpc, with the inner and outer stellar disc having temperatures Tspin/f ≈ 3000 − 5000 K (see Table 1).

thumbnail Fig. 7.

Spin temperature/covering factor values obtained from the polynomial (thin bars) and exponential (thick bars) fits to the Galactic column density distribution (Fig. 6).

Table 1.

Values of ⟨Tspin/f ⟩ [K] at various impact parameters for the various column density profiles (Sects. 2.2.2–2.2.4).

Dispensing with the assumed column density profile, we can compare the mean 21-cm absorption strengths (Fig. 1) directly with those of the Milky Way. Dickey et al. (2009) give these in terms of ∫τd./L, where the path length L = NH I/nH I and nH I is the volume density of the gas. From the column density (Fig. 6) and mid-pane volume density profiles (Kalberla & Dedes 2008) of the Milky Way, we obtain the path length distribution shown in Fig. 8, which exhibits the flaring of the scale-height of the H I disc (Kalberla et al. 2007). Showing the resulting integrated optical depths in Fig. 9, we see that the mean sample strengths are significantly weaker than the Galactic values, especially in the inner disc. For a given column density profile this will result in higher spin temperatures for the sample, thus indicating that a very different profile is required to yield temperatures similar to that in the Milky Way.

thumbnail Fig. 8.

Top: volume density profile of the Milky Way (total disc, Kalberla & Dedes 2008), overlain with the exponential and a log-polynomial fit. Bottom: resulting path length profile.

thumbnail Fig. 9.

Binned mean velocity integrated optical depth of the sample (thin bars) in comparison to the Milky Way: the data from each of the Canadian Galactic Plane Survey (CGPS, Taylor et al. 2003), the Southern Galactic Plane Survey (SGPS, McClure-Griffiths et al. 2005) and the VLA Galactic Plane Survey (VGPS, Stil et al. 2006) are shown as points, with the thick bars showing the binned values.

2.2.3. Mean sample column density

Another option for the column density profile is to use those of the sample itself, which we show in Fig. 10, where available2. The profiles are very diverse and so we model the column density distribution via a weighted log-polynomial and a weighted exponential fit to the mean values. These show reasonable agreement out to r ≈ 20 kpc, beyond which the polynomial appears to provide the best mean trace. In Fig. 11, we show the spin temperature profile generated by both fits. Again, these are higher than in the Milky Way, but lower than that obtained using the Galactic column density distribution. There is, however, a similar peak in the spin temperature, T spin / f = 7000 − 2500 + 4000 $ T_{\mathrm{spin}}/f =7000^{+4000}_{-2500} $ K at r ≈ 12 kpc, with Tspin/f ≈ 2000 − 3000 K in the remainder of the stellar disc.

thumbnail Fig. 10.

H I column density profiles from the high resolution observations of Reeves et al. (2015, 2016). The error bars show the mean values and the ±1σ uncertainties. The thick unbroken curve shows the (1/σ) weighted log-polynomial fit and the broken line the weighted exponential fit to the mean values.

thumbnail Fig. 11.

As per Fig. 7 but for the mean sample column density distribution (Fig. 10).

We acknowledge that this is based upon the mean column density distribution, where the individual cases differ drastically. Ideally, we would determine the spin temperature from the 21-cm absorption strength scaled by the relevant column density for each individual sight-line. Doing this for the high resolution observations (Fig. 12), we see, however, that due, partly at least, to the high impact parameters probed, this yields almost exclusive limits, most of which are relatively weak. Thus, we have little choice but to use the averaged 21-cm absorption strengths (Fig. 1), normalised by a mean column density distribution in order to yield a (mean) spin temperature profile.

thumbnail Fig. 12.

Spin temperature/covering factor values at various impact parameters for the 21-cm observations and column density profiles of Reeves et al. (2015, 2016). The symbols are per Fig. 3, where the limits with Tspin/f <  TCMB have been capped at Tspin/f ≥ 2.7 K.

2.2.4. Simulated column density

Both the column density profiles of the Milky Way and the mean sample yield spin temperatures much higher than Galactic values. This could be due to the relatively high column densities, with NH I ∼ 1021 cm−2 at r ≈ 0 in both cases. Lower column densities can be obtained from the mean profile generated by the IllustrisTNG simulations for the 567 z = 0 galaxies with log10M = 11.8 − 11.9 M⊙ (Nelson et al. 2019, Fig. 13). Comparing the 21-cm absorption strength with the column density distribution, we find, as for the Galactic distribution (Fig. 6), that the profile is well fit for a constant Tspin/f, asides from a peak at r ≈ 12 kpc and a drop in spin temperature beyond the stellar disc. However, the spin temperature required is much lower than the Tspin/f ≈ 4000 K from the Galactic NH I distribution, with the profile (Fig. 14) giving Tspin/f ≈ 1200 − 1500 K in the stellar disc, with the r ≈ 12 kpc peak persisting (with T spin / f = 3300 − 1200 + 1900 $ T_{\mathrm{spin}}/f =3300^{+1900}_{-1200} $ K, Fig. 14).

thumbnail Fig. 13.

Mean H I column density from an ensemble of z = 0 galaxies from the TNG (left axis), with the integrated column density of the 21-cm absorption overlain (for Tspin/f = 1500 K, right axis). The shaded region shows the 16th and 84th percentiles (1σ) of the population variation in the TNG.

thumbnail Fig. 14.

Spin temperature/covering factor values obtained from the mean TNG column density profile (Fig. 13).

3. Discussion

All of the above models (summarised in Table 1) lead to significantly higher spin temperatures than in the Milky Way, with each exhibiting a peak at r ≈ 12 kpc. Beyond this, the decrease in spin temperature is most likely due to the H I disc extending beyond the stellar disc (e.g. Curran et al. 2008; Walter et al. 2008). However, temperatures similar to that within the inner Milky Way are not reached until r ≈ 30 kpc. The high Tspin/f values could be accounted for by covering factors f ∼ 0.1, although we expect f ∼ 1 for the absorption of unresolved quasar emission through a resolved disc.

Regarding the peak, in spiral galaxies, including the Milky Way (Lockman 1976), the ionised gas (H II) regions are concentrated in the spiral arms, at radii of up to r ≈ 15 kpc (e.g. Hodge 1969; Hodge & Kennicutt 1983; James et al. 2009), believed to be caused by OB stars (Morgan et al. 1953)3. The ionising (λ ≤ 912 Å) photon rate from each star is given by Q ⋆ ≡ ∫ ν 0 ∞ ( L ν /hν) dν $ Q_{\star}\equiv\int^{\infty}_{\nu_0}({L_{\nu}}/{h\nu})\,d{\nu} $, where ν0 = 3.29 × 1015 Hz, Lν is the specific luminosity at frequency ν and h the Planck constant. For a radiative recombination rate coefficient of αB and proton and electron volume densities np and ne, respectively, the equilibrium between the photo-ionisation and recombination of protons and electrons is (Osterbrock 1989)

Q ⋆ = 4 π ∫ 0 r s n p n e α B r 2 d r ⇒ Q ⋆ = 4 3 π r s 3 n H I 2 α B , $$ \begin{aligned} Q_{\star } = 4\pi \int ^{r_{\rm s}}_{0}\,n_{\rm p}\,n_{\rm e}\,\alpha _{\rm B}\,r^2\, \mathrm{d}r \Rightarrow Q_{\star } =\frac{4}{3}\pi r_{\rm s}^3 n_{{\text{H}}{\small {\text{I}}}}^2 \alpha _{\rm B}, \end{aligned} $$(4)

for a neutral plasma, np = ne = nH I of constant density, defining the Strömgren sphere.

For a star of effective temperature T⋆, we obtain the ionsing photon rate from the integrated intensity of the Planck function, Iν,

Q ⋆ = 4 π R ⋆ 2 ∫ ν 0 ∞ I ν h ν d ν , where I ν = 2 π h ν 3 c 2 1 e h ν / k T ⋆ − 1 $$ \begin{aligned} Q_{\star }= 4\pi R_{\star }^2\int ^{\infty }_{\nu _0}\frac{I_{\nu }}{h\nu }\mathrm{d}{\nu }, \text{ where} I_{\nu }= \frac{2\pi h\nu ^3}{c^2} \frac{1}{e^{h\nu /kT_{\star }}-1} \end{aligned} $$(5)

and 4π R ⋆ 2 $ 4\pi R_{\star}^2 $ is the surface area of the star. We estimate this by comparing the bolometric intensity, I = ∫ 0 ∞ I ν d ν $ I= \int^{\infty}_{0}I_{\nu}d{\nu} $, with the bolometric luminosity obtained from the main sequence (log10LMS = 6.50log10T⋆ − 24.37), giving the values of Q⋆ listed in Table 2.

Table 2.

Estimated properties of stars of various effective temperatures, T⋆.

Applying these to Eq. (4) yields the Strömgren radius of each star. For the radiative recombination rate coefficient, αB, we assume that the electron temperature is equivalent to the spin temperature (Te = Tspin). Arising from different heating/cooling processes, this is may not be justified although, given that α ∝ T e $ \alpha\propto\sqrt{T_{\mathrm{e}}} $, the temperature dependence is not strong4. From Eq. (4) we see that the Strömgren radius is dominated by the volume density, which we obtain at a given Galactocentric radius by assuming the log-polynomial L − r profile of the sample (Fig. 15). These give the Strömgren radii shown in Fig. 16. Due to the decrease in gas density, for a homogeneous, dust-free medium, we see that the size of the sphere increases significantly with galactocentric radius.

thumbnail Fig. 15.

Estimated volume densities for the various column density profiles obtained from the Galactic log-polynomial path length fit (Fig. 8).

thumbnail Fig. 16.

Strömgren radius versus the Galactocentric radius for stars of different effective temperatures obtained from the log-polynomial volume density fit to the sample (Fig. 15). The thick grey dotted curve shows the half-path length, L/2 (where L = NH I/nH I), for the mean of the sample and the dashed line for the Milky Way (Fig. 8).

In disc galaxies the star formation rate is found to increase with galactocentric radius (Muñoz-Mateos et al. 2007; Azzollini et al. 2009). This could be the result of the denser environments closer to the galactic centre suppressing the star formation (Boissier et al. 2007; Welikala et al. 2008). The outward growth of galactic discs would mean that the large radii are dominated by the younger (and more short-lived) stellar populations (Trujillo & Pohlen 2005; Muñoz-Mateos et al. 2007), giving a larger fraction of the more luminous stars (Table 1). For the O-type stars (T⋆ ≳ 30 000 K), we see that the Strömgren radius for an individual star is comparable to the width of the H I disc at r ≳ 20 kpc. Given the approximations, the values are uncertain, although it is apparent that, due to the decreasing density of the surrounding medium, the Strömgren radii exhibit a steep increase, which is consistent with the gas being highly ionised at large impact parameters.

4. Conclusions

From the absorption of the 21-cm continuum from 90 sight-lines towards distant radio sources through the discs of nearby spiral galaxies, Curran et al. (2016) reported an anti-correlation between the abundance of cool, star-forming, gas and the galactocentric radius. Since the abundance of this gas normalised by the total H I column density gives a measure of the spin temperature, such an anti-correlation would be expected if the mean spin temperature where constant across the disc, as it is in the Milky Way (out to r ≈ 20 kpc, Dickey et al. 2009). The correlation has, however, been disputed by subsequent data (increasing the number of sight-lines to 143, Borthakur 2016; Dutta et al. 2017)5. Including the new data in our analysis, we find the ∫τdv–ρ anti-correlation to increase in significance to S(τ) = 3.63σ from 3.31σ (Curran et al. 2016), thus demonstrating that, like all of the neutral atomic gas, the cold component decreases in abundance with galactocentric radius.

Comparing the mean 21-cm absorption strengths with the measured column densities, we find a possible peak in the spin temperature of ⟨Tspin/f ⟩ ≈2300 K at ρ ≈ 14 kpc, compared to ⟨Tspin/f ⟩ ≲1400 K in the remainder of the stellar disc. We show, however, that the measured column densities obtained from the 21-cm emission are likely to suffer significant dilution due to the beam subtending beyond the disc. Applying better constrained column density profiles, we find:

  • For the Galactic distribution, a peak of ⟨Tspin/f ⟩ ≈15 000 K at ρ ≈ 12 kpc, with ⟨Tspin/f ⟩ ≳3000 K in the remainder of the disc.

  • For the mean profile of the sample galaxies, where sufficiently high resolution data are available, a peak of ⟨Tspin/f ⟩ ≈7000 K at ρ ≈ 12 kpc, with ⟨Tspin/f ⟩ ≳2000 K in the remainder of the disc.

  • For the mean of a simulated ensemble of spiral galaxies, a peak of ⟨Tspin ⟩ ≈3300 K at r ≈ 12 kpc, with ⟨Tspin/f ⟩ ≳1000 K in the remainder of the disc.

All of these spin temperatures are considerably higher than observed in the Milky Way (⟨Tspin ⟩ ≈ 250 − 400 K, Dickey et al. 2009), being closer to those observed in other low redshift galaxies detected through the absorption of background quasar light, namely damped Lyman-α absorption systems (DLAs), where Tspin ≳  1000 K at z ≈ 0. At the peak of the star formation history at z ∼ 2, however, the mean spin temperatures of the DLAs approach those in the Milky Way (Curran 2019).

We speculate that the elevated gas temperature at these radii may be coincident with the regions of highly ionised gas observed in some nearby spirals. At r ≳ 10 kpc, where nH I ≲ 0.1 cm−3, the radius of the H II region around each O-type star exceeds rs ∼ 100 pc, which is a significant fraction of the path length through the gaseous disc. Hence the presence of hot stars, in conjunction with the low gas densities, does indeed suggest that the gas is highly ionised at large Galactocentric radii.

2

From high resolution observations with the ATCA (Reeves et al. 2015, 2016).

3

Although it has been argued that the arms concentrate the gas without triggering star formation (Foyle et al. 2010). Furthermore, while Seigar & James (2002) find a correlation between spiral arm strength and star formation, Foyle et al. (2010) and Eden et al. (2013) find the inter-arm star formation rates to be similar to those in the arms. Compounding the issue further is the fact that the star formation rate is correlated with the molecular gas abundance, as traced through CO (Bigiel et al. 2008; Leroy et al. 2013), although the spiral arms to do not appear to host elevated CO levels (Elmegreen & Elmegreen 1987; Dickey et al. 2009; Koda et al. 2016).

5

With one additional sight-line from Allison et al. (2020).

Acknowledgments

I would like to thank the anonymous referee for their helpful feedback and Dylan Nelson for the IllustrisTNG data. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration and NASA’s Astrophysics Data System Bibliographic Service. This research has also made use of NASA’s Astrophysics Data System Bibliographic Service and ASURV Rev 1.2 (Lavalley et al. 1992), which implements the methods presented in Isobe et al. (1986).

References

  1. Allison, J. R., et al. 2020, MNRAS, submitted [Google Scholar]
  2. Azzollini, R., Beckman, J. E., & Trujillo, I. 2009, A&A, 501, 119 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  3. Bahcall, J. N., & Ekers, R. D. 1969, ApJ, 157, 1055 [NASA ADS] [CrossRef] [Google Scholar]
  4. Bigiel, F., Leroy, A., Walter, F., et al. 2008, AJ, 136, 2846 [NASA ADS] [CrossRef] [Google Scholar]
  5. Boisse, P., Dickey, J. M., Kazes, I., & Bergeron, J. 1988, A&A, 191, 193 [NASA ADS] [Google Scholar]
  6. Boissier, S., Gil de Paz, A., Boselli, A., et al. 2007, ApJS, 173, 524 [NASA ADS] [CrossRef] [Google Scholar]
  7. Borthakur, S. 2016, ApJ, 829, 128 [NASA ADS] [CrossRef] [Google Scholar]
  8. Borthakur, S., Tripp, T. M., Yun, M. S., et al. 2010, ApJ, 713, 131 [NASA ADS] [CrossRef] [Google Scholar]
  9. Borthakur, S., Tripp, T. M., Yun, M. S., et al. 2011, ApJ, 727, 52 [NASA ADS] [CrossRef] [Google Scholar]
  10. Borthakur, S., Momjian, E., Heckman, T. M., et al. 2014, ApJ, 795, 98 [NASA ADS] [CrossRef] [Google Scholar]
  11. Carilli, C. L., & van Gorkom, J. H. 1992, ApJ, 399, 373 [NASA ADS] [CrossRef] [Google Scholar]
  12. Corbelli, E., & Schneider, S. E. 1990, ApJ, 356, 14 [NASA ADS] [CrossRef] [Google Scholar]
  13. Curran, S. J. 2012, ApJ, 748, L18 [NASA ADS] [CrossRef] [Google Scholar]
  14. Curran, S. J. 2019, MNRAS, 484, 3911 [NASA ADS] [CrossRef] [Google Scholar]
  15. Curran, S. J., Koribalski, B. S., & Bains, I. 2008, MNRAS, 389, 63 [NASA ADS] [CrossRef] [Google Scholar]
  16. Curran, S. J., Reeves, S. N., Allison, J. R., & Sadler, E. M. 2016, MNRAS, 459, 4136 [NASA ADS] [CrossRef] [Google Scholar]
  17. Dickey, J. M., Strasser, S., Gaensler, B. M., et al. 2009, ApJ, 693, 1250 [NASA ADS] [CrossRef] [Google Scholar]
  18. Dutta, R., Gupta, N., Srianand, R., & O’Meara, J. M. 2016, MNRAS, 456, 4209 [NASA ADS] [CrossRef] [Google Scholar]
  19. Dutta, R., Srianand, R., Gupta, N., et al. 2017, MNRAS, 465, 588 [NASA ADS] [CrossRef] [Google Scholar]
  20. Eden, D. J., Moore, T. J. T., Morgan, L. K., Thompson, M. A., & Urquhart, J. S. 2013, MNRAS, 431, 1587 [NASA ADS] [CrossRef] [Google Scholar]
  21. Elmegreen, B. G., & Elmegreen, D. M. 1987, ApJ, 320, 182 [NASA ADS] [CrossRef] [Google Scholar]
  22. Field, G. B. 1959, ApJ, 129, 536 [NASA ADS] [CrossRef] [Google Scholar]
  23. Foyle, K., Rix, H.-W., Walter, F., & Leroy, A. K. 2010, ApJ, 725, 534 [NASA ADS] [CrossRef] [Google Scholar]
  24. Gupta, N., Srianand, R., Bowen, D. V., York, D. G., & Wadadekar, Y. 2010, MNRAS, 408, 849 [NASA ADS] [CrossRef] [Google Scholar]
  25. Gupta, N., Srianand, R., Noterdaeme, P., Petitjean, P., & Muzahid, S. 2013, A&A, 558, A84 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  26. Haschick, A. D., & Burke, B. F. 1975, ApJ, 200, L137 [NASA ADS] [CrossRef] [Google Scholar]
  27. Hodge, P. W. 1969, ApJ, 155, 417 [NASA ADS] [CrossRef] [Google Scholar]
  28. Hodge, P. W., & Kennicutt, Jr., R. C. 1983, ApJ, 267, 563 [NASA ADS] [CrossRef] [Google Scholar]
  29. Hwang, C.-Y., & Chiou, S.-H. 2004, ApJ, 600, 52 [NASA ADS] [CrossRef] [Google Scholar]
  30. Isobe, T., Feigelson, E., & Nelson, P. 1986, ApJ, 306, 490 [NASA ADS] [CrossRef] [Google Scholar]
  31. James, P. A., Bretherton, C. F., & Knapen, J. H. 2009, A&A, 501, 207 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  32. Kalberla, P. M. W., & Dedes, L. 2008, A&A, 487, 951 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  33. Kalberla, P. M. W., & Kerp, J. 2009, ARA&A, 47, 27 [NASA ADS] [CrossRef] [Google Scholar]
  34. Kalberla, P. M. W., Dedes, L., Kerp, J., & Haud, U. 2007, A&A, 469, 511 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  35. Kanekar, N., Athreya, R. M., & Chengalur, J. N. 2002, A&A, 382, 838 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  36. Koda, J., Scoville, N., & Heyer, M. 2016, ApJ, 823, 76 [NASA ADS] [CrossRef] [Google Scholar]
  37. Lavalley, M. P., Isobe, T., & Feigelson, E. D. 1992, Bull. Am. Astron. Soc., 24, 839 [NASA ADS] [Google Scholar]
  38. Leroy, A. K., Walter, F., Sandstrom, K., et al. 2013, AJ, 146, 19 [NASA ADS] [CrossRef] [Google Scholar]
  39. Lockman, F. J. 1976, ApJ, 209, 429 [NASA ADS] [CrossRef] [Google Scholar]
  40. McClure-Griffiths, N. M., Dickey, J. M., Gaensler, B. M., et al. 2005, ApJS, 158, 178 [NASA ADS] [CrossRef] [Google Scholar]
  41. Morgan, W. W., Whitford, A. E., & Code, A. D. 1953, ApJ, 118, 318 [Google Scholar]
  42. Muñoz-Mateos, J. C., Gil de Paz, A., Boissier, S., et al. 2007, ApJ, 658, 1006 [NASA ADS] [CrossRef] [Google Scholar]
  43. Nelson, D., Springel, V., Pillepich, A., et al. 2019, Comput. Astrophys. Cosmol., 6, 2 [Google Scholar]
  44. Osterbrock, D. E. 1989, Astrophysics of Gaseous Nebulae and Active Galactic Nuclei (Mill Valley, California: University Science Books) [CrossRef] [Google Scholar]
  45. Peacock, J. A. 1999, Cosmological Physics (Cambridge: Cambridge University Press) [Google Scholar]
  46. Purcell, E. M., & Field, G. B. 1956, ApJ, 124, 542 [NASA ADS] [CrossRef] [Google Scholar]
  47. Reeves, S. N., Sadler, E. M., Allison, J. R., et al. 2015, MNRAS, 450, 926 [NASA ADS] [CrossRef] [Google Scholar]
  48. Reeves, S. N., Sadler, E. M., Allison, J. R., et al. 2016, MNRAS, 457, 2613 [NASA ADS] [CrossRef] [Google Scholar]
  49. Rohlfs, K., & Wilson, T. L. 2000, Tools of Radio Astronomy (Berlin: Springer-Verlag) [Google Scholar]
  50. Seigar, M. S., & James, P. A. 2002, MNRAS, 337, 1113 [NASA ADS] [CrossRef] [Google Scholar]
  51. Sofue, Y. 2018, PASJ, 70, 50 [NASA ADS] [Google Scholar]
  52. Srianand, R., Gupta, N., Rahmani, H., et al. 2013, MNRAS, 428, 2198 [NASA ADS] [CrossRef] [Google Scholar]
  53. Stil, J. M., Taylor, A. R., Dickey, J. M., et al. 2006, AJ, 132, 1158 [NASA ADS] [CrossRef] [Google Scholar]
  54. Taylor, A. R., Gibson, S. J., Peracaula, M., et al. 2003, AJ, 125, 3145 [NASA ADS] [CrossRef] [Google Scholar]
  55. Toomre, A. 1963, ApJ, 138, 385 [NASA ADS] [CrossRef] [Google Scholar]
  56. Trujillo, I., & Pohlen, M. 2005, ApJ, 630, L17 [NASA ADS] [CrossRef] [Google Scholar]
  57. Walter, F., Brinks, E., de Blok, W. J. G., et al. 2008, AJ, 136, 2563 [NASA ADS] [CrossRef] [Google Scholar]
  58. Welikala, N., Connolly, A. J., Hopkins, A. M., Scranton, R., & Conti, A. 2008, ApJ, 677, 970 [NASA ADS] [CrossRef] [Google Scholar]
  59. Zwaan, M. A., Liske, J., Péroux, C., et al. 2015, MNRAS, 453, 1268 [NASA ADS] [CrossRef] [Google Scholar]

All Tables

Table 1.

Values of ⟨Tspin/f ⟩ [K] at various impact parameters for the various column density profiles (Sects. 2.2.2–2.2.4).

In the text
Table 2.

Estimated properties of stars of various effective temperatures, T⋆.

In the text

All Figures

thumbnail Fig. 1.

Velocity integrated optical depth versus the impact parameter for all of the published searches. The circles represent the previous data (Curran et al. 2016 and references therein) and the squares the data since (Borthakur 2016; Dutta et al. 2017; Allison et al. 2020). The downward arrows signify the 3σ upper limits and the dotted vertical line shows the median impact parameter. Bottom panel: binned values, including the limits via the Kaplan–Meier estimator, in equally sized bins. The horizontal error bars show the range of points in the bin and the vertical error bars the 1σ uncertainty in the mean value.
In the text
thumbnail Fig. 2.

Column density versus the impact parameter for the sight-lines detected in 21-cm emission.
In the text
thumbnail Fig. 3.

Spin temperature/covering factor obtained from the column density (Fig. 2), versus the impact parameter. The upward arrows signify lower limits.
In the text
thumbnail Fig. 4.

Redshift distribution of the target galaxies. The galaxies span the redshift range 0 ≲ z ≤ 0.4367, with 21-cm emission being detected to z = 0.0462 (filled histogram).
In the text
thumbnail Fig. 5.

Column density measured across the telescope beam versus the linear extent of the beam for the sight-lines detected in 21-cm emission. The telescopes used are the Very Large Array (VLA, Carilli & van Gorkom 1992; Borthakur et al. 2011, 2014), the Australia Telescope Compact Array (ATCA, Reeves et al. 2015, 2016), the Giant Metre-Wave Radio Telescope (GMRT, Dutta et al. 2016), the Arecibo telescope (Corbelli & Schneider 1990) and the Green Bank Telescope (GBT, Haschick & Burke 1975; Borthakur et al. 2011; Borthakur 2016).
In the text
thumbnail Fig. 6.

Radial column density distribution of the Milky Way (total disc, Kalberla & Dedes 2008) overlain with the exponential fit to the r ≥ 12.5 kpc data (Kalberla & Kerp 2009) and a log-polynomial to all of the data. The error bars show the column density of the 21-cm absorption for Tspin/f = 4000 K (right axis).
In the text
thumbnail Fig. 7.

Spin temperature/covering factor values obtained from the polynomial (thin bars) and exponential (thick bars) fits to the Galactic column density distribution (Fig. 6).
In the text
thumbnail Fig. 8.

Top: volume density profile of the Milky Way (total disc, Kalberla & Dedes 2008), overlain with the exponential and a log-polynomial fit. Bottom: resulting path length profile.
In the text
thumbnail Fig. 9.

Binned mean velocity integrated optical depth of the sample (thin bars) in comparison to the Milky Way: the data from each of the Canadian Galactic Plane Survey (CGPS, Taylor et al. 2003), the Southern Galactic Plane Survey (SGPS, McClure-Griffiths et al. 2005) and the VLA Galactic Plane Survey (VGPS, Stil et al. 2006) are shown as points, with the thick bars showing the binned values.
In the text
thumbnail Fig. 10.

H I column density profiles from the high resolution observations of Reeves et al. (2015, 2016). The error bars show the mean values and the ±1σ uncertainties. The thick unbroken curve shows the (1/σ) weighted log-polynomial fit and the broken line the weighted exponential fit to the mean values.
In the text
thumbnail Fig. 11.

As per Fig. 7 but for the mean sample column density distribution (Fig. 10).
In the text
thumbnail Fig. 12.

Spin temperature/covering factor values at various impact parameters for the 21-cm observations and column density profiles of Reeves et al. (2015, 2016). The symbols are per Fig. 3, where the limits with Tspin/f <  TCMB have been capped at Tspin/f ≥ 2.7 K.
In the text
thumbnail Fig. 13.

Mean H I column density from an ensemble of z = 0 galaxies from the TNG (left axis), with the integrated column density of the 21-cm absorption overlain (for Tspin/f = 1500 K, right axis). The shaded region shows the 16th and 84th percentiles (1σ) of the population variation in the TNG.
In the text
thumbnail Fig. 14.

Spin temperature/covering factor values obtained from the mean TNG column density profile (Fig. 13).
In the text
thumbnail Fig. 15.

Estimated volume densities for the various column density profiles obtained from the Galactic log-polynomial path length fit (Fig. 8).
In the text
thumbnail Fig. 16.

Strömgren radius versus the Galactocentric radius for stars of different effective temperatures obtained from the log-polynomial volume density fit to the sample (Fig. 15). The thick grey dotted curve shows the half-path length, L/2 (where L = NH I/nH I), for the mean of the sample and the dashed line for the Milky Way (Fig. 8).
In the text

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.