2.1.1. Optical depth and column density

The main observable in any absorption line survey is the ratio of the line ( $\Delta{S}$ ) to continuum flux density ( $S_{\text{c}}$ ), which is used to determine the optical depth $\tau$ as a function of velocity v as follows

(1) \begin{equation} \tau(v) = -\ln{\left(1 + \frac{\Delta{S}(v)}{c_{\text{f}}\,S_{\text{c}}(v)}\right)}.\end{equation}

The source covering factor, $c_{\text{f}}$ , accounts for the areal fraction of continuum flux density that is subtended by the absorber of average optical depth $\tau$ . For a transition ${\text{l}} \rightarrow {\text{u}}$ of species X, the column density of particles inferred from the velocity-integrated optical depth, $\int{\tau_{\text{lu}} (v)\,\textrm{d}{v}}$ , is then given by

(2) \begin{equation}N_{\text{X}} = \frac{8\pi}{c^{3}}\frac{\nu_{\text{lu}}^{3}}{g_{\text{u}}}\frac{f(T_{\text{lu}})}{A_{\text{ul}}}\int{\tau_{\text{lu}} (v)\,\textrm{d}{v}},\end{equation}

where

(3) \begin{equation}f(T_{\text{lu}}) = \frac{Q(T_{\text{lu}})\,e^{E_{u}/k_{\text{B}}T_{\text{lu}}}}{e^{h\nu_{\text{lu}}/k_{\text{B}}T_{\text{lu}}}-1},\end{equation}

and $\nu_{\text{lu}}$ is the rest frequency, $g_{\text{u}}$ is the statistical weight of u, $A_{\text{ul}}$ is the Einstein coefficient for spontaneous emission, $E_{u}$ is the upper energy level, and $Q(T_{\text{lu}})$ is the partition function assuming a single excitation temperature, $T_{\text{lu}}$ (e.g. Wiklind & Combes Reference Wiklind and Combes1995).

For the H i 21-cm line we ignore $n > 1$ states, so that $Q(T_{\text{lu}}) = g_{\text{l}}\exp({-}E_{\text{l}}/k_{\text{B}}T_{\text{lu}}) + g_{\text{u}}\exp({-}E_{\text{u}}/k_{\text{B}}T_{\text{lu}})$ , and $h\,\nu_{\text{lu}} \ll k_{\textrm B}\,T_{\text{lu}}$ , so that

(4) \begin{equation} f(T_{\text{lu}}) = \frac{g_{\text{l}}\,e^{h\nu_{\text{lu}}/k_{\text{B}}T_{\text{lu}}} + g_u}{e^{h\nu_{\text{lu}}/k_{\text{B}}T_{\text{lu}}}-1} \approx (g_{\text{l}} + g_{\text{u}})\frac{k_{\text{B}}T_{\text{lu}}}{h\nu_{\text{lu}}},\end{equation}

where $g_{\text{l}} = 1$ and $g_{\text{u}} = 3$ . Denoting the 21-cm excitation temperature as $T_{\text{lu}} = T_{\text{s}}$ (the spin temperature) and using the known Einstein coefficient $A_{\text{ul}} = 2.85 \times 10^{-15}\,\textrm{s}^{-1}$ , the H i column density (in atoms $\textrm{cm}^{-2}$ ) is then given by

(5) \begin{equation} N_{\text{HI}} \approx 1.823 \times 10^{18} T_{\text{s}} \int{\tau(v)\,\textrm{d}v},\end{equation}

where $T_{\text{s}}$ is in K and the velocity v is in $\textrm{km}\,\textrm{s}^{-1}$ . This is the key equation that relates the inferred 21-cm optical depth to the physical properties of the H i gas.

2.1.2. The spin temperature

The relationship given by Equation (5) shows that for a fixed column density of neutral gas the 21-cm optical depth is inversely proportional to the spin temperature. Depending on the gas density and intensity of illuminating sources, excitation of the hyperfine transition in H i, and hence $T_{\text{s}}$ , is determined by particle collisions, Lyman- $\alpha$ radiation, or 21-cm radiation (e.g. Wouthuysen Reference Wouthuysen1952; Purcell & Field Reference Purcell and Field1956; Field Reference Field1958, Reference Field1959; Bahcall & Ekers Reference Bahcall and Ekers1969; Liszt Reference Liszt2001).

In our own Galaxy, where multiple sight lines with simultaneous 21-cm emission and absorption enable detailed study of the physical conditions, the neutral ISM is found to comprise two stable thermal phases in pressure equilibrium; the cold (CNM) and warm (WNM) neutral medium (Wolfire et al. Reference Wolfire, McKee, Hollenbach and Tielens2003). There is also observational evidence for a significant fraction of an intermediate unstable phase (UNM) that is thought to be generated by dynamical processes such as turbulence and supernova shocks (e.g. Heiles & Troland Reference Heiles and Troland2003; Murray et al. Reference Murray, Stanimirović, Goss, Heiles, Dickey, Babler and Kim2018).

In the denser CNM gas ( $n \sim 100\,\textrm{cm}^{-3}$ ), particle collisions thermalise the 21-cm transition so that the spin temperature is approximately equal to the kinetic temperature ( $T_{\text{s}} \approx T_{\text{k}} \sim 100$ K). Although this is not the case in the more diffuse WNM gas ( $n \sim 0.1\,\textrm{cm}^{-3}$ ), excitation of the 21-cm transition is still coupled to the kinetic temperature of the gas through a combination of particle collisions and scattering of the ambient Lyman- $\alpha$ radiation field (the Wouthuysen-Field effect; Wouthuysen Reference Wouthuysen1952; Field Reference Field1958, Reference Field1959), so that $T_{\text{s}} \lesssim T_{\text{k}} \sim 10\,000$ K (Liszt Reference Liszt2001; Murray et al. Reference Murray, Stanimirović, Goss, Heiles, Dickey, Babler and Kim2018).

Hence, for typical ISM conditions, the spin temperature is an increasing function of the gas kinetic temperature so that any measurement of the absorption line is weighted in favour of colder H i gas on our line of sight. The relationship in Equation (5) can therefore either be thought of as the inferred column density of total H i gas, where $T_{\text{s}}$ is the $N_{\text{HI}}$ -weighted harmonic mean over all thermal components, or as the column density of cooler absorbing H i gas, in which case $T_{\text{s}}$ is the spin temperature of the absorbing component.

In the Milky Way ISM, the neutral phases exist in the mass ratio CNM:UNM:WNM = 28:20:52 (Murray et al. Reference Murray, Stanimirović, Goss, Heiles, Dickey, Babler and Kim2018), corresponding to a mass-weighted harmonic mean spin temperature of $T_{\text{s}} \approx 300$ K (see also Dickey et al. Reference Dickey, Strasser, Gaensler, Haverkorn, Kavars, McClure-Griffiths, Stil and Taylor2009). At greater distances, $T_{\text{s}}$ can be measured for random sight lines through galaxies where an existing measurement of the H i column density is available from 21-cm emission or Lyman- $\alpha$ absorption. The $T_{\text{s}}$ measured for Damped Lyman- $\alpha$ Absorbers (DLAs; $N_{\text{HI}} \geq 2 \times 10^{20}\,\textrm{cm}^{-2}$ ) varies significantly between ${\approx}100$ and $10\,000$ K, presumably due to variance in the physical conditions of the gas probed by each sight line (see Kanekar et al. Reference Kanekar2014a). However, despite this sight-line variance, the harmonic mean $T_{\text{s}}$ for all DLAs at $z < 1$ is consistent with that of the Milky Way ISM (Allison Reference Allison2021). We therefore adopt 300 K as our fiducial value of the spin temperature here.

Since the 21-cm absorption line is sensitive to the colder H i gas, it is complementary to the 21-cm emission and Lyman- $\alpha$ absorption lines that trace the total H i gas, and is an important probe of the evolution of star forming gas in galaxies over the history of the Universe.

2.2.1. Intervening 21-cm absorbers

Until recently, surveys for intervening 21-cm absorbers have been largely constrained by narrow bandwidths and/or fields of view to targeted observations of the following:

• Known ‘quasar-galaxy pairs’, where the line of sight to a distant radio quasar passes close to a galaxy in the nearby Universe (e.g. Gupta et al. Reference Gupta, Srianand, Bowen, York and Wadadekar2010; Borthakur et al. Reference Borthakur, Tripp, Yun, Bowen, Meiring, York and Momjian2011; Reeves et al. Reference Reeves, Sadler, Allison, Koribalski, Curran and Pracy2015; Reeves et al. Reference Reeves2016; Borthakur Reference Borthakur2016; Dutta et al. Reference Dutta, Srianand, Gupta, Momjian, Noterdaeme, Petitjean and Rahmani2017a),

• Sight lines with known optical/UV DLAs (see Kanekar et al. Reference Kanekar2014a and references therein),

• Known (optical) Mg ii $\lambda\lambda$ 2796, 2803 Å absorbers, used as a proxy for DLAs at $z<1.7$ (e.g. Lane Reference Lane2000; Lane & Briggs Reference Lane and Briggs2001; Kanekar et al. Reference Kanekar, Prochaska, Ellison and Chengalur2009; Gupta et al. Reference Gupta, Srianand, Petitjean, Noterdaeme and Saikia2009; Gupta et al. Reference Gupta, Srianand, Petitjean, Bergeron, Noterdaeme and Muzahid2012; Dutta et al. Reference Dutta, Raghunathan, Gupta and Joshi2020), and

• Fe ii $\lambda$ 2600 Å absorbers (e.g. Dutta et al. Reference Dutta, Srianand, Gupta, Joshi, Petitjean, Noterdaeme, Ge and Krogager2017b).

Detection rates among quasar-galaxy pairs in the nearby Universe are typically 5–15 % and are inversely related to the impact parameter, suggesting that the coldest H i gas detected in 21-cm absorption is largely confined to the inner discs of galaxies (e.g. Borthakur Reference Borthakur2016; Curran et al. Reference Curran, Reeves, Allison and Sadler2016b; Dutta et al. Reference Dutta, Srianand, Gupta, Momjian, Noterdaeme, Petitjean and Rahmani2017a; Curran Reference Curran2020).

The detection rates for 21-cm absorbers in redshifted DLAs are typically higher ( ${\sim}50$ %; Kanekar et al. Reference Kanekar2014a) and consistent with sight lines that are known to intercept high-column-density neutral gas. 21-cm line observations of DLAs provide some evidence for an increase in the mean spin temperature at high redshifts, and an anti-correlation with metallicity, that would be expected for an evolution of the neutral gas that follows the star formation history of the Universe (Kanekar et al. Reference Kanekar2014a; Allison Reference Allison2021, see also Curran Reference Curran2019).

2.2.2. Associated 21-cm absorbers

The majority of searches for associated 21-cm absorbers have been limited to radio sources with known optical spectroscopic redshifts. It is possible that this may select against detection of H i at high redshifts ( $z \gtrsim 1$ ), since optically identified active galactic nuclei (AGN) that are UV luminous in their rest-frame could ionise or excite the neutral gas (Curran et al. Reference Curran, Whiting, Wiklind, Webb, Murphy and Purcell2008; Curran & Whiting Reference Curran and Whiting2010, Reference Curran and Whiting2012). This hypothesis is supported by observational evidence that the absorption signal strength is inversely related to the UV luminosity, and that very few 21-cm absorbers are detected in AGN for $L_{\text{UV}} \gtrsim 10^{23}\,\textrm{W}\,\textrm{Hz}^{-1}$ (e.g. Curran et al. Reference Curran, Whiting, Sadler and Bignell2013; Aditya & Kanekar Reference Aditya and Kanekar2018b; Curran et al. Reference Curran, Hunstead, Johnston, Whiting, Sadler, Allison and Athreya2019; Grasha et al. Reference Grasha, Darling, Bolatto, Leroy and Stocke2019; Chowdhury et al. Reference Chowdhury, Kanekar and Chengalur2020b; Mhaskey et al. Reference Mhaskey, Paul, Gupta and Mukherjee2020, see also Aditya et al. Reference Aditya, Jorgenson, Joshi, Singh, An and Chandola2021).

Likewise, since 21-cm photons directly excite the hyperfine transition, a similar selection bias may also exist for radio luminosity (e.g. Curran et al. Reference Curran, Whiting, Wiklind, Webb, Murphy and Purcell2008; Aditya et al. Reference Aditya, Kanekar and Kurapati2016; Aditya & Kanekar Reference Aditya and Kanekar2018b). However, as yet there is no evidence that this affects the detection rate of associated 21-cm absorbers (e.g. Curran et al. Reference Curran, Hunstead, Johnston, Whiting, Sadler, Allison and Athreya2019; Grasha et al. Reference Grasha, Darling, Bolatto, Leroy and Stocke2019).

The factors that determine the detection of H i absorption in active galaxies are complex and require careful consideration of the properties of the radio sources and their hosts. Reasonably high detection rates ( ${\sim}30$ %) are achieved towards compact steep spectrum (CSS) and GHz-peaked spectrum (GPS) radio sources, of which those that are associated with radio galaxies, rather than quasars (i.e. type-1 AGN), are most prolific (e.g. Véron-Cetty et al. Reference Véron-Cetty, Woltjer, Staveley-Smith and Ekers2000; Vermeulen et al. Reference Vermeulen2003; Gupta et al. Reference Gupta, Salter, Saikia, Ghosh and Jeyakumar2006; Chandola et al. Reference Chandola, Sirothia and Saikia2011; Geréb et al. Reference Geréb, Maccagni, Morganti and Oosterloo2015; Aditya & Kanekar Reference Aditya and Kanekar2018a). These are either young ( $t_{\text{age}} \lesssim 10$ kyr) or confined older radio sources (An & Baan Reference An and Baan2012), with linear extents typically smaller than their host galaxies ( $d \lesssim 10$ kpc) and so preferentially located behind high column densities of neutral gas, possibly in a circumnuclear disc or torus (Pihlström et al. Reference Pihlström, Conway and Vermeulen2003; Orienti et al. Reference Orienti, Morganti and Dallacasa2006; Curran et al. Reference Curran, Whiting, Sadler and Bignell2013).

Similarly, searches for 21-cm absorption in highly dust-reddened quasars, interacting, and merging galaxies have been very successful in detecting associated absorbers ( $\sim$ 80 %; e.g. Carilli et al. Reference Carilli, Menten, Reid, Rupen and Yun1998; Yan et al. Reference Yan, Stocke, Darling, Momjian, Sharma and Kanekar2016; Maccagni et al. Reference Maccagni, Morganti, Oosterloo, Geréb and Maddox2017; Dutta et al. Reference Dutta, Srianand and Gupta2018, Reference Dutta, Srianand and Gupta2019), again consistent with a model whereby accreted circumnuclear gas has not yet been cleared away by the active nucleus. In contrast, larger radio sources have a significantly lower detection rate ( ${\sim}15$ %; e.g. Morganti et al. Reference Morganti, Oosterloo, Tadhunter, van Moorsel, Killeen and Wills2001; Gupta et al. Reference Gupta, Salter, Saikia, Ghosh and Jeyakumar2006; Chandola et al. Reference Chandola, Gupta and Saikia2013; Maccagni et al. Reference Maccagni, Morganti, Oosterloo, Geréb and Maddox2017), where a large fraction of the flux density is located beyond the extent of H i gas in the host galaxy. In all cases, these previous surveys were targeted towards sources that were selected based on their core flux density, leading to a selection bias that favours detection of associated absorption. Hence although future wide-field 21-cm absorption line surveys are expected to yield far more associated absorbers at cosmological distances than previously achieved, the detection rates are likely to be significantly lower (e.g. Allison et al. Reference Allison, Sadler and Meekin2014, Reference Allison2020).

2.2.3. Wide-field & spectroscopically blind surveys

As already discussed, previous work has focused mainly on targeted searches for extragalactic 21-cm absorption lines and as yet there have been few large-area, spectroscopically blind surveys. Notably, in early work Darling et al. (Reference Darling, Giovanelli, Haynes, Bolatto and Bower2004) detected a 21-cm absorber from a large spectroscopically blind survey of radio sources using the Green Bank Telescope (GBT). Later, Darling et al. (Reference Darling, Macdonald, Haynes and Giovanelli2011) carried out the first wide-field 21-cm absorption in the nearby Universe, using early data from the Arecibo Legacy Fast Arecibo L-band Feed Array (ALFALFA) survey (Giovanelli et al. Reference Giovanelli2005), searching for H i absorption against more than 7000 radio sources at $z < 0.058$ over a $517\,\textrm{deg}^2$ area of sky. Although they only detected a single associated absorber (in the merging system UGC 6081), their results within this volume were consistent with that expected given the known H i column density frequency distribution function and for spin temperatures greater than 100 K. More recently, Grasha et al. (Reference Grasha, Darling, Leroy and Bolatto2020) used the GBT to carry out a spectroscopically blind survey of 252 radio sources covering redshifts between $z = 0$ and $2.74$ , obtaining ten detections of known absorbers. Again, their results were consistent with expectations based on the known distribution of H i column densities in the local and high-z Universe, and spin temperatures in the typical ISM range.

The new surveys will build on this earlier, single-dish work, making use of advances in radio telescope technology and radio-quiet observatories to detect 21-cm absorption across a range of redshifts towards thousands of radio sources. Notably the new interferometers, such as ASKAP and the South African Meer-Karoo Array Telescope (MeerKAT; Jonas & MeerKAT Team Reference Jonas2016), are particularly well suited to this task since they can provide sufficiently flat spectral baselines across the bandwidths required to cover these larger redshift intervals (e.g. Allison et al. Reference Allison2020; Gupta et al. Reference Gupta2021).

3.1.1. Overview

ASKAP is a radio interferometer that comprises 36 identical 12 m antennas, each equipped with a PAF that can be used to electronically form up to 36 beams that sample a $31\,\textrm{deg}^{2}$ field of view at 800 MHz (Hotan et al. Reference Hotan2021; see Figure 1). It is located at the Murchison Radio Astronomy Observatory (MRO), near the Boolardy Station in Murchison Shire, Western Australia ( $26^\circ 42^{\prime}11^{\prime\prime}\ \textrm{S}$ , $116^\circ 40^{\prime}14^{\prime\prime}\ \textrm{E}$ ). The telescope operates at frequencies between 700 and 1 800 MHz and can therefore be used to detect the H i 21-cm line at redshifts up to $z = 1$ , and the OH 18-cm lines up to $z = 1.37$ .

Figure 1. A 12-m ASKAP antenna, equipped with a Mark-II Phased Array Feed – Photo Credit: Robert Hollow, CSIRO.

When making full use of the available 288 MHz bandwidthFootnote ^a the correlator generates 18.5 kHz channels, corresponding to radial velocities of $3.1\,\textrm{km}\,\textrm{s}^{-1}$ at 1800 MHz and $7.9\,\textrm{km}\,\textrm{s}^{-1}$ at 700 MHz. This spectral resolution is well-matched to the expected line widths of intervening 21-cm absorbers, with at least three channels across the average FWHM of lines reported in the literature ( ${\approx}30\,\textrm{km}\,\textrm{s}^{-1}$ ; see Curran et al. Reference Curran, Duchesne, Divoli and Allison2016c).

The array consists of a ‘core’ of 30 antennas that give good surface brightness sensitivity, and six outer antennas that provide up to 6 km baselines for higher spatial resolution imaging. In the case of FLASH, the continuum imaging will make full use of the longest antenna baselines, with a spatial resolution of about 10 arcsec, to provide as much source morphology information as possible. The spectral-line cubes will be imaged with close-to-natural weighting ( ${\approx}20$ arcsec) to retain optimal sensitivity for absorption-line detection. We note that this resolution is not sufficient to unambiguously determine the spatial distribution of detected absorbers and/or background sources, the majority of which will be unresolved (e.g. Becker et al. Reference Becker, White and Helfand1995). Further spatial interpretation of the FLASH-detected absorbers and their background sources will require follow-up observations at ${\sim}10$ mas resolution using very long baseline interferometry (e.g. Braun Reference Braun2012).

3.1.2. ASKAP sensitivity

The sensitivity of a radio telescope is typically defined in terms of its system temperature ( $T_{\text{sys}}$ ), antenna efficiency ( $\eta$ ) and collecting area (A). For ASKAP, the ratio $T_{\text{sys}}/\eta$ varies from a maximum of about 120 K at 700 MHz to 65 K at 1300 MHz (Hotan et al. Reference Hotan2021), which for the single antenna area of $A = 113.1\,\textrm{m}^{2}$ correspond to system equivalent flux densities (SEFD, $S_{\text{sys}}$ ) between 2930 and 1590 Jy. The expected noise per spectral channel ( $\sigma_{\text{chan}}$ ) can then be calculated using the following radiometer equation for interferometric arrays,

(6) \begin{equation} \sigma_{\text{chan}} = \frac{S_{\text{sys}}}{\sqrt{n_{\text{pol}}\,n_{\text{ant}}(n_{\text{ant}}-1)\,\Delta{t}\,\Delta{\nu_{\text{chan}}}}},\end{equation}

where $n_{\text{pol}}$ is the number of polarisation channels, $n_{\text{ant}}$ is the number of antennas, $\Delta{t}$ is the integration time and $\Delta{\nu_{\text{chan}}}$ is the channel bandwidth. Within a 2 h observation with the 36-antenna dual-polarisation array the noise level is expected to be between 2.7 and $5.1\,\textrm{mJy}\,\textrm{beam}^{-1}$ per 18.5 kHz channel across the full range of available ASKAP frequenciesFootnote ^b.

3.2.1. Choice of survey frequency and sky coverage

The baseline survey parameters of FLASH are 2 h per pointing covering the entire southern sky below $\delta \approx +40\,\deg$ , at frequencies between 711.5 and 999.5 MHz. These were chosen to optimise the discovery potential and detection yield for 21-cm absorption, which is quantified in terms of the co-moving absorption path length ( $\Delta{X}$ ). This is the total co-moving interval over which intervening 21-cm absorbers may be detected, thus also providing a metric by which other 21-cm line surveys can be compared with FLASH.

To estimate $\Delta{X}$ we use the completeness-corrected procedure described in Appendix A. This takes into account the completeness to spectral lines of a specific width and peak signal-to-noise, based on the analysis of an ASKAP-12 survey by Allison et al. (Reference Allison2020). The data from that earlier survey contained a channelisation error that contributed a multiplicative non-Gaussian component to the noise level, thus elevating the threshold required to achieve a reliable detection. Although this channelisation error has now been corrected it is likely that any blind absorption-line survey such as FLASH will still include a background level of false-positive detections due to multiplicative non-Gaussian noise (resulting from either hardware and/or data processing errors). We therefore consider the earlier ASKAP-12 data to be representative of FLASH, but expect that the false-positive error rate may decrease over time as our identification techniques improve.

To simulate a realistic wide-field survey with ASKAP, we use an input catalogue of background sources using the National Radio Astronomy Observatory Very Large Array Sky Survey (NVSS; Condon et al. Reference Condon, Cotton, Greisen, Yin, Perley, Taylor and Broderick1998) catalogue, and apply a statistical distribution for the source redshifts based on the model of De Zotti et al. (Reference De Zotti, Massardi, Negrello and Wall2010) (see Appendix A for further details).

In Figure 2, we show the resulting $\Delta{X}$ as a function of observed frequency and integration time per pointing for different $N_{\text{HI}}$ sensitivities, assuming a fiducial spin temperature $T_{\text{s}} = 300$ K, source covering factor $c_{\text{f}} = 1$ and FWHM $\Delta{v} = 30\,\textrm{km}\,\textrm{s}^{-1}$ . The absorption path length increases with decreasing column density sensitivity, due to fainter radio sources being included in the survey. The shape of these curves is determined by a combination of the sensitivity (SEFD) of ASKAP as a function of frequency, the underlying redshift distribution of radio sources (with a median $z \approx 1$ ) and the increase in comoving interval with redshift for a fixed redshift interval. The absorption path length peaks at a frequency of about 800 MHz, where the sensitivity of ASKAP starts to reduce significantly at lower frequencies. It is clear from this plot that the frequency range chosen for FLASH maximises the total absorption path length for the survey. Likewise, for a fixed total survey time, the discovery potential of a wide-field absorption-line survey at the sensitivity of ASKAP is optimised by maximising the sky area.

Figure 2. The 21-cm absorption path length ( $\Delta{X}$ ) as a function of observed frequency ( $\nu$ ) across the ASKAP band. Solid lines denote the baseline FLASH survey parameters, which are a 2 h integration time per pointing, covering the entire sky south of $\delta \approx +40\deg$ . Dashed and dot-dashed lines correspond to higher integration times per pointing for the same total survey time. Coloured lines represent column density sensitivity limits of $N_{\text{HI}} = 2 \times 10^{20}$ (blue) and $N_{\text{HI}} = 2 \times 10^{21}\,\textrm{cm}^{-2}$ (red), assuming $T_{\text{s}} = 300$ K, $c_{\text{f}} = 1$ , $\Delta{v}_{\text{FWHM}} = 30\,\textrm{km}\,\textrm{s}^{-1}$ . The green shaded region shows the FLASH frequency band, and the grey hatched those frequencies most affected by RFI.

3.2.2. Field placement and pointing centres

In Figure 3, we show the positions of the pointing centres chosen for the FLASH survey. These provide an optimal sampling of the sky with uniform sensitivity. The total number of FLASH pointings is 903, equating to a total integration time for the survey of about 1806 hr. Table 2 shows an indicative subset of the list of planned pointing centres for the 903 fieldsFootnote ^c FLASH uses the same pointing centres as the 888 MHz Rapid ASKAP Continuum Survey (RACS; McConnell et al. Reference McConnell2020), and the corresponding RACS field name is also shown for reference in Table 2.

Figure 3. The arrangement of the 903 planned ASKAP pointing centres for the FLASH survey, shown on the celestial sphere (adapted from Figure 3 of McConnell et al. Reference McConnell2020).

Table 2. Pointing centres for the fields to be used for the FLASH survey. The first ten fields are listed below, and the full list of 903 FLASH fields is available as an online table.

3.3.1. Intervening 21-cm absorbers

We estimate the number of detected intervening absorbers by integrating the H i column density frequency distribution function, $f(N_{\text{HI}})$ , measured from previous 21-cm emission and DLA surveys over the expected comoving absorption path and column density sensitivity. Further details of this procedure are described in Section A.4.

In Table 3 we show the results for the expected total redshift path ( $\Delta{z}$ ) and comoving absorption path length ( $\Delta{X}$ ) for different column density sensitivities, along with the corresponding number of intervening absorbers ( $\mathcal{N}_{\text{abs}}^{\text{int}}$ ) of that column density or less. In addition to our fiducial spin temperature of 300 K, we also give results for $T_{\text{s}} = 100$ and 1 000 K covering the expected range of possible mean spin temperatures. As previously mentioned, these are highly dependent on the source covering factor $c_{\text{f}}$ and line width, and so the values quoted are purely indicative. However, it is clear that FLASH is most sensitive to DLA systems that have column densities $N_{\text{HI}} \sim 2 \times 10^{21}\,\textrm{cm}^{-2}$ (‘super-DLAs’), and is expected to discover between several hundred and a few thousand new 21-cm absorbers. Therefore FLASH will provide a sample that is about an order of magnitude more than the current literature. In Figure 4, we show the number of detected absorbers as a function of observed frequency, highlighting that the number of absorbers for FLASH is optimised by using the lowest frequencies available with ASKAP.

Table 3. Estimates of the 21-cm line total redshift interval, comoving path length and number of detections for the full FLASH survey at redshifts $0.4 < z < 1$ .

^aIntervening absorbers, assuming a fixed $T_{\text{s}}$ , $c_{\text{f}} = 1$ and $\Delta{v}_{\text{FWHM}} = 30\,\textrm{km}\,\textrm{s}$ ^–1.

^bAssociated absorbers, assuming $\lambda_{\text{asc}} = 10$ %, $\tau = 0.05$ and $\Delta{v}_{\text{FWHM}} = 120\,\textrm{km}\,\textrm{s}$ ^–1.

Figure 4. The expected number of intervening (for $T_{\text{s}} = 300$ K, $c_{\text{f}} = 1$ , $\Delta{v}_{\text{FWHM}} = 30\,\textrm{km}\,\textrm{s}^{-1}$ ) and associated 21-cm absorbers (for $\lambda_{\text{asc}} = 10\%$ , $\tau = 0.05$ , $\Delta{v}_{\text{FWHM}} = 120\,\textrm{km}\,\textrm{s}^{-1}$ ) detected in FLASH as a function of frequency (see text for further details). The green region shows the FLASH frequency band and the grey hatched region those frequencies most affected by RFI.

We note that our estimate of $\Delta{z} = 6\,100$ for a sensitivity of $N_{\text{HI}} = 2 \times 10^{20}\,\textrm{cm}^{-2}$ at $T_{\text{s}} = 100$ K is significantly less than that estimated by Gupta et al. (Reference Gupta2016) for FLASH (see their Table 1 and Figure 1). This is the result of different assumptions about the completeness and line width used in each work. In determining a detection limit for FLASH, Gupta et al. assume a relatively narrow line width of $5\,\textrm{km}\,\textrm{s}^{-1}$ (equal to the resolution of most extragalactic 21-cm surveys), and that any feature greater than 5 times the signal-to-noise ratio will be reliably recovered with confidence. This results in a redshift path that is about 10 times that found here. Given that the distribution of known line widths is much wider than this and that we believe our estimate of the recovery of lines in data to be more accurate, our estimate is more likely to be a true representation of the final survey redshift path.

3.3.2. Associated 21-cm absorbers

We predict the number of detected associated 21-cm absorbers by integrating the source redshift distribution over the redshift path that is sensitive to absorption, and then multiplying by a fixed detection rate, $\lambda_{\text{asc}}$ (see Section A.5 for further details of the method). As discussed in Section 2.2, the factors that determine the associated absorber detection rate are complex and require careful consideration of the properties of the sampled radio sources and their host galaxies (see Morganti & Oosterloo Reference Morganti and Oosterloo2018 for a review). Here we adopt a fiducial rate of $\lambda_{\text{asc}} = 10$ % for associated H i absorption in the volume searched by FLASH. This is a factor of $2 - 3$ times lower than the typical detection rates obtained by previous targeted surveys, which typically selected samples of radio sources based on a core flux density limit (see e.g. Maccagni et al. Reference Maccagni, Morganti, Oosterloo, Geréb and Maddox2017). A lower detection rate is more realistic for wide-field flux-density-selected surveys. Indeed the actual detection rate could be even less than assumed here, and hence our predictions are purely indicative of the results that may be obtained from a large unbiased radio-selected survey.

We use a peak optical depth of $\tau_{\text{peak}} = 0.05$ and line width $\Delta{v}_{\text{FHWM}} = 120\,\textrm{km}\,\textrm{s}^{-1}$ for the associated absorbers (e.g. Curran et al. Reference Curran, Duchesne, Divoli and Allison2016c), corresponding to a column density of $N_{\text{HI}} \approx 3 \times 10^{21}\,\textrm{cm}^{-2}$ for $T_{\text{s}} = 300$ K. The sensitivity of each sight line to associated absorption is calculated assuming an unrealistic $c_{\text{f}} = 1$ , which is accounted for by adopting a detection rate that is significantly lower than that obtained for compact radio sources. In Figure 4, we show the number of associated absorbers as a function of frequency, which rises considerably with H i redshift and peaks at $z_{\text{HI}} = 0.8$ . This behaviour is largely governed by the source redshift distribution, except at the highest redshifts where the ASKAP sensitivity rapidly declines. This highlights that the choice of frequencies for FLASH is optimal for detecting both intervening and associated absorbers. We note that this assumes that the intrinsic detection rate is constant with redshift, which is unlikely to be the case since the cold gas content of radio galaxies will evolve with the host population (e.g. Heckman & Best Reference Heckman and Best2014). However, the detection of any such evolution is an important science case for the survey.

FLASH is expected to detect about 2000 associated absorbers, which is an order of magnitude greater than currently known. In their review of associated H i absorption, Morganti & Oosterloo (Reference Morganti and Oosterloo2018) predict a higher yield for FLASH of 5500 absorbers (see their Table 2), based on the detection limit given by Gupta et al. (Reference Gupta2016) and a detection rate of $\lambda_{\text{asc}} = 25\,\%$ from the results of Maccagni et al. (Reference Maccagni, Morganti, Oosterloo, Geréb and Maddox2017). Morganti et al. use the semi-empirical simulations of Wilman et al. (Reference Wilman2008) to create an input catalogue of radio sources, while we use the observed NVSS catalogue and apply a statistical redshift distribution. Remarkably, despite the different methods and assumptions employed, the disagreement between these two estimates is almost entirely accounted for by the adopted detection rate. Finally, by taking an absorption-weighted mean over sight lines, we find that the expected flux density of sources with detected associated absorption is approximately 530 mJy, which corresponds to a radio luminosity of $L \approx 3 \times 10^{27}\,\textrm{W}\,\textrm{Hz}^{-1}$ at $z = 0.8$ . Therefore, we expect that most associated absorbers detected in FLASH will be associated with the most powerful radio galaxies in the Universe.

4.1.1. Radio-loud AGN with associated 21-cm absorption

No optical pre-selection is used in the FLASH survey, and we can therefore detect H i gas even when no optical galaxy is visible. However, we expect most associated 21-cm absorbers to lie in the kinds of massive galaxies that host radio-loud AGN, that is close to the locus of the black points in Figure 5. QSOs with associated H i absorption may be even brighter than this, while some host galaxies of high-excitation radio sources (HERGs) could be one or two magnitudes fainter (e.g. Ching et al. Reference Ching2017, see the blue points in Figure 5). Thus most associated absorbers detected by FLASH should have an optical/IR counterpart visible in WISE mid-IR images, and coincident with the radio position (or the radio centroid for an extended source).

Figure 5. Optical and mid-IR properties of the hosts of radio AGN similar to those that will be observed in FLASH. In both plots, vertical dashed lines show the redshift range covered by the main FLASH survey ( $0.4 < z < 1$ ) and the vertical dotted line shows the point at which current large-area spectroscopic galaxy surveys start to become incomplete ( $z \sim 0.75$ ). Left: Observed SDSS r-band magnitude versus redshift for several galaxy classes. Red points show luminous red galaxies (LRGs, spectroscopic redshifts from the 2SLAQ Survey, Cannon et al. Reference Cannon2006), while black and blue points show low-excitation and high-excitation radio galaxies, respectively (LERGs/HERGs, spectroscopic redshifts from Ching et al. Reference Ching2017). The horizontal dotted lines show the photometric limit of the SDSS catalogue (r=22), and the expected single-visit depth for LSST (r = 24.3). Right: WISE W1 band (3.4 $\mu$ m) magnitude versus redshift for low-excitation radio galaxies (LERGs, black circles), high-excitation radio galaxies (HERGs, blue circles) and radio-loud QSOs (cyan triangles), all from the Ching et al. (Reference Ching2017) catalogue. The horizontal dotted line shows the completeness limit of the WISE catalogue (W1=17.2).

Figure 6 compares the radio luminosity of the radio AGN in which H i was detected by Maccagni et al. (Reference Maccagni, Morganti, Oosterloo, Geréb and Maddox2017) and Murthy et al. (Reference Murthy, Morganti, Oosterloo and Maccagni2021) at $z < 0.4$ with two associated absorption lines detected in ASKAP commissioning at $z \sim 0.5$ (Allison et al. Reference Allison2015; Glowacki et al. Reference Glowacki2019). These early ASKAP detections are associated with extremely bright radio sources with radio luminosities above $10^{27}\,\textrm{W}\,\textrm{Hz}^{-1}$ , but FLASH should also be able to detect H i absorption (and especially lines with high optical depth) in sources as faint as 40 mJy. Thus FLASH can probe some sources with radio luminosities between $10^{25}$ and $10^{26}\,\textrm{W}\,\textrm{Hz}^{-1}$ in addition to the population of powerful sources above $10^{26}\,\textrm{W}\,\textrm{Hz}^{-1}$ – which are relatively rare in the local Universe but far more common at $z > 0.4$ (Pracy et al. Reference Pracy2016).

Figure 6. Radio luminosities of some representative objects in which associated H i has been detected. Blue points show detections from the lower-frequency samples published by Maccagni et al. (Reference Maccagni, Morganti, Oosterloo, Geréb and Maddox2017) and Murthy et al. (Reference Murthy, Morganti, Oosterloo and Maccagni2021), while red points show two detections from ASKAP commissioning data (PKS 1740-517, Allison et al. (Reference Allison2015) and PKS 1829-718, Glowacki et al. (Reference Glowacki2019)). The thick line at a flux density of 40 mJy indicates an approximate detection limit for absorption systems in the FLASH survey.

4.1.2. Host galaxies of intervening 21-cm absorption

The host galaxies of intervening 21-cm absorbers could in principle be associated with galaxies of almost any magnitude. The optical luminosity function of galaxies is very broad (e.g. Blanton et al. Reference Blanton2001), with absolute magnitudes ranging from $\textrm{M}_r = -23$ for the most massive and luminous galaxies to $\textrm{M}_r = -16$ or even fainter for dwarf galaxies. The ‘knee’ of the galaxy luminosity function in the local Universe is at $\textrm{M}_r = -20.8$ , but the observed r-band magnitude at higher redshift will depend on both $\textrm{M}_r$ and the k-correction.

Since the radius of the H i disk in nearby galaxies is known to scale extremely well with H i mass, however (Wang et al. Reference Wang, Koribalski, Serra, van der Hulst, Roychowdhury, Kamphuis and Chengalur2016) we would expect a sample of H i-selected galaxies to trace the H i mass function reasonably well. Since H i mass roughly scales with galaxy luminosity (Maddox et al. Reference Maddox, Hess, Obreschkow, Jarvis and Blyth2015), we might expect most galaxies associated with intervening H i absorbers to be late-type galaxies with stellar mass above $\sim10^9\,\textrm{M}_\odot$ (e.g. Rodríguez-Puebla et al. Reference Rodírguez-Puebla, Calette, Avila-Reese, Rodriguez-Gomez and Huertas-Company2020). Such galaxies should be detectable in targeted follow-up optical imaging if they are not already visible in archival imaging surveys.

The impact parameter for intervening 21-cm absorbers is generally expected to be less than 20 kpc (e.g. Borthakur Reference Borthakur2016; Curran et al. Reference Curran, Reeves, Allison and Sadler2016b; Dutta et al. Reference Dutta, Srianand, Gupta, Momjian, Noterdaeme, Petitjean and Rahmani2017a; Curran Reference Curran2020) even though the H i disks of gas-ich galaxies may extend out as far as 60 kpc at lower H i column density ( $N_{\text{HI}} \sim 10^{18}\,\textrm{cm}^{-2}$ , Bland-Hawthorn et al. Reference Bland-Hawthorn, Maloney, Stephens, Zovaro and Popping2017). For impact parameters as high as 10–20 kpc, the intervening galaxy may be offset by several arcsec from the radio position. If the background radio source is an optically bright QSO and the impact parameter is low, this may also complicate the identification of the intervening galaxy. Despite these challenges, however, identifying the host galaxies of most FLASH detections should be tractable with a suitably designed follow-up programme.

4.1.3. Distinguishing associated and intervening absorbers

Table 5 summarises several ways of distinguishing associated and intervening H i absorbers, depending on the additional information is available.

Table 5. Methods for distinguishing associated and intervening H i absorption absorbers

The distinction is fairly straightforward when an optical identification and spectroscopic redshift are available for the radio source against which the absorption line is detected.

When the redshift of the radio source is unknown, intervening absorbers may still be identified if there is a significant astrometric offset between the radio source position and the nucleus of the intervening galaxy. For example, Allison et al. (Reference Allison2020) used data from the GAMA survey to identify an ASKAP H i line detection as an intervening absorber in the outer regions (impact parameter 17 kpc) of a massive early-type galaxy. In this case the radio-optical offset was 2.5 arcsec—significantly higher than the combined uncertainties in the optical and radio positions.

Finally, machine learning techniques (Curran et al. Reference Curran, Duchesne, Divoli and Allison2016c; Curran Reference Curran2021) have the potential to distinguish intervening and associated absorption lines based on radio spectral-line data alone. Current classifiers have a success rate of $\sim80$ % (Curran Reference Curran2021), and it is possible that the accuracy can be improved in future when a larger training set of absorbers becomes available.

4.2.1. Cold gas evolution from 21-cm absorbers

21-cm absorption-line surveys provide an important complementary measurement of the H i content of galaxies at these redshifts. If the background sources are selected based purely on their radio properties then they are free of any potential optical selection bias. This technique was recently demonstrated by Grasha et al. (Reference Grasha, Darling, Leroy and Bolatto2020), who carried out a survey for 21-cm absorption towards 252 compact radio sources with the GBT telescope, covering redshifts between $z = 0$ and 2.4. They successfully detected 10 absorbers and, assuming $T_{\text{s}}/c_{\text{f}}= 175$ K, were able to measure $\Omega_{\text{HI}}$ to a comparable precision with other methods at the same redshifts (see further discussion on the spin temperature below).

In Figure 7, we show the measurement of $\Omega_{\text{HI}}$ expected from FLASH, which is based on the expected number of intervening 21-cm absorbers shown in Table 3 (see Section A.6 for a description of the method). Given the number of intervening 21-cm absorbers expected to be detected, the standard deviation due to sample variance will only be only a few per cent over the redshift interval of the survey (as indicated by the width of the bar in Figure 7), which is a marked improvement on previous measurements at these redshifts. However, this measurement is strongly dependent on the assumed value of the spin temperature and covering factor for each absorber. Therefore, we also show how it varies with the typical range of spin of temperatures seen in DLAs, indicating how such a measurement can be used to infer the gas temperature (see below for further discussion).

The unknown source covering factor can be overcome by selecting only background sources with known compact morphologies that are smaller than the expected angular scale of the foreground absorber ( $\Delta{\theta} \lesssim 10$ mas at $z \sim 1$ ; Braun Reference Braun2012). If enough spatial information is known about the individual objects in the sample, then a proxy for $c_{\text{f}}$ can be determined by taking the ratio of the total to compact radio flux density at frequencies close to that expected for the redshifted 21-cm line (e.g. Kanekar et al. Reference Kanekar, Prochaska, Ellison and Chengalur2009). In the case of FLASH, the number of radio source targets is likely to be ${\sim}100\,000$ , rendering such a targeted high-resolution campaign difficult. Alternatively, one can assume a covering factor probability distribution for a given sample of background sources, which is then used as a prior for any future inference about the optical depth of the absorber (e.g. Allison et al. Reference Allison, Zwaan, Duchesne and Curran2016b; Allison Reference Allison2021).

Less is known about the spin temperature in individual absorbers. For a fixed column density and source covering factor, the equivalent width of the 21-cm absorption line is inversely related to the H i spin temperature (see Equation (5)). Hence detections of 21-cm absorption are weighted to line-of-sight gas that contains a greater fraction of the denser CNM (Wolfire et al. Reference Wolfire, McKee, Hollenbach and Tielens2003), where molecular cloud and star formation occur (Krumholz et al. Reference Krumholz, McKee and Tumlinson2009b). Crucially, this means that 21-cm absorption surveys provide an important probe of the colder neutral gas in galaxies.

Direct measurement of the spin temperature in 21-cm absorbers can be achieved if the H i column density is known by other means. The inferred spin temperature is then an $N_{\text{HI}}$ -weighted harmonic mean over the line-of-sight components of the neutral gas. In the nearby Universe this can be achieved by simultaneously detecting 21-cm emission and absorption in a foreground galaxy, with a few examples in the literature (e.g. Reeves et al. Reference Reeves2016; Borthakur Reference Borthakur2016; Gupta et al. Reference Gupta, Momjian, Srianand, Petitjean, Noterdaeme, Gyanchandani, Sharma and Kulkarni2018). However, future wide-field surveys (e.g. WALLABY; Koribalski et al. Reference Koribalski2020 and SHARP; van Cappellen et al. Reference van Cappellen2021, Morganti et al. in preparation) are expected to increase this sample by a few orders of magnitude.

At cosmological distances the spin temperature can instead be obtained by simultaneously detecting 21-cm and Lyman- $\alpha$ absorption, requiring a sample of radio-loud UV or optically selected quasars. Kanekar et al. (Reference Kanekar2014a) compiled the literature sample into a single study, finding that the spin temperatures of DLAs at $z > 2.4$ are higher than those at lower redshifts (at 4- $\sigma$ significance). Kanekar et al. also obtained an anti-correlation between the spin temperature and gas-phase metallicity of DLAs (at 3.5- $\sigma$ significance), suggesting that in the early Universe galaxies were depleted of the metals required to form CNM via fine structure cooling.

Such a direct study of the spin temperatures in FLASH-detected 21-cm absorbers would be very challenging since the radio source would need to be sufficiently bright at UV-wavelengths to detect Lyman- $\alpha$ absorption using the Hubble Space Telescope. However, we can instead use the statistical power of such a large sample by comparing the number of 21-cm absorbers detected in the survey with that expected from the $N_{\text{HI}}$ distribution function measured from 21-cm emission and DLA surveys. This can then be used to obtain a statistical measurement of the $N_{\text{HI}}$ -weighted harmonic mean spin temperature in galaxies at cosmological redshifts (Darling et al. Reference Darling, Macdonald, Haynes and Giovanelli2011; Allison et al. Reference Allison, Zwaan, Duchesne and Curran2016b; Grasha et al. Reference Grasha, Darling, Leroy and Bolatto2020; Allison Reference Allison2021), thereby enabling strong constraints to be placed on the evolution of the physical state of cold gas in galaxies over the past 8 billion yrs.

4.2.2. Statistical detection of HI emission from star-forming galaxies

The weak flux of H i emission from galaxies makes it difficult to detect at anything but low redshifts with current telescopes ( $z \lesssim 0.3$ ). To extend the measurements to higher redshift the signal from multiple galaxies has been stacked in radio observations using the known optical position and redshift of galaxies. This decreases the noise in the measurement by the square root of the number of coadded galaxies. Notably, H i stacking has been used by Lah et al. (Reference Lah2007), Lah et al. (Reference Lah2009), Rhee et al. (Reference Rhee, Zwaan, Briggs, Chengalur, Lah, Oosterloo and van der Hulst2013), Rhee et al. (Reference Rhee, Lah, Chengalur, Briggs and Colless2016), Rhee et al. (Reference Rhee, Lah, Briggs, Chengalur, Colless, Willner, Ashby and Le Fèvre2018), Bera et al. (Reference Bera, Kanekar, Chengalur and Bagla2019) and Chowdhury et al. (Reference Chowdhury, Kanekar, Chengalur, Sethi and Dwarakanath2020a). The most recent result is by Chowdhury et al. (Reference Chowdhury, Kanekar, Das, Dwarakanath and Sethi2021) where they measured the average H i emission signal from 2841 blue star-forming galaxies at $z = 1.18 - 1.39$ using 400 h using the Giant Metrewave Radio Telescope. FLASH only has observations of 2 h per field but it observes an extremely large area covering a large redshift range. This means that there are a large number of galaxies that can be used in the stacking analysis, compensating for the smaller integration time per field.

WiggleZ is an optical spectroscopic survey of star forming emission line galaxies carried out at the Anglo-Australian Telescope at Siding Spring, Australia between August 2006 and January 2011 (Drinkwater et al. Reference Drinkwater2010). It covers $1\,000\ \textrm{deg}^2$ with redshifts in the range $z < 1$ and median $z = 0.6$ . The FLASH survey covers the whole area on the sky and there are 152,057 redshifts that lie within the FLASH H i redshift range. An estimate of how well stacking WiggleZ galaxies in the FLASH data is shown in Figure 8. The estimated average H i mass is determined by assuming that the WiggleZ galaxies in each redshift bin are the largest H i mass galaxies in the volume probed, and then using the $z = 0$ H i mass function of Zwaan et al. (Reference Zwaan, Meyer, Staveley-Smith and Webster2005b) to allocate an H i mass. A correction for the completeness of the WiggleZ survey is included. This does not consider any evolution in the H i mass function which would increase the H i mass measured. The stacked observations will probe the high mass end of the H i mass function. Other H i surveys with their smaller area coverage will only have a few of these large galaxies. The uncertainties on the average H i mass are based on the parameters of FLASH and the number of galaxies stacked. The uncertainties at the low redshift end are reasonable but they rapidly become large at the high redshift end due to fewer redshifts, weaker H i 21-cm flux from the galaxies, and lower ASKAP sensitivity at the relevant frequencies. It should be noted that Li et al. (Reference Li, Staveley-Smith and Rhee2021) made a H i intensity mapping measurement at $0.73 < z < 0.78$ using WiggleZ galaxies with the Parkes telescope. The limited redshift range was due to RFI at this site. The redshift range probed by ASKAP that is reasonably constraining on the H i mass is a regime that has significant RFI at other telescope sites, thereby making the measurement relevant. There should be sufficient signal to noise at these lower redshifts to divide the sample into subsamples and measure their average H i mass. In particular, determining how the average H i mass varies with star formation rate at these redshifts will be of significant interest.

Figure 8. The estimated H i signal from coadding the WiggleZ in the FLASH data versus redshift. The bottom of the plot shows the number of WiggleZ galaxies coadded in each redshift bin. The top of the plot shows the estimated average H i for these galaxies along with the expected error in the measured signal based off the parameters of FLASH.

Another optical redshift survey that significantly overlaps with the FLASH area coverage is DESI (Dark Energy Spectroscopic Instrument) Survey (DESI Collaboration et al. Reference Collaboration2016). This survey is being carried out with the 4-metre Mayall Telescope at Kitt Peak National Observatory. The survey will cover $14\,000\,\deg^{2}$ spanning from the equator up to some fields north of $\delta = +40\,\deg$ . The overlap in sky area with FLASH is therefore large. Their ELG (Emission Line Galaxy) sample covers redshifts $z = 0.6$ to $1.6$ with 1220 objects per $\deg^2$ for a total of 17.1 million targets. This survey has started taking data and has a 5-yr lifetime overlapping well with the FLASH observation schedule. The stacked H i signal using DESI galaxies should be significantly better than that made with WiggleZ galaxies.

It should be noted that stacking can also be carried out on the radio continuum of galaxies, providing a measure of the star formation rate without dust contamination. In this case, AGN contamination would need to be taken into account, but this should be a solvable problem.

4.3.1. Feedback and triggering

It is well-established that the properties of central supermassive black holes are tightly linked to the properties of their host galaxies (e.g. Kormendy & Richstone Reference Kormendy and Richstone1995; Magorrian et al. Reference Magorrian1998; Ferrarese & Merritt Reference Ferrarese and Merritt2000), with the connection generally attributed to AGN feedback processes (Di Matteo et al. Reference Di Matteo, Springel and Hernquist2005; Croton et al. Reference Croton2006; Weinberger et al. Reference Weinberger, Ehlert, Pfrommer, Pakmor and Springel2017). However, our understanding of the physical mechanisms responsible for AGN fuelling and feedback is still limited by the lack of observational evidence, particularly on scales close to the central AGN. In cases where the H i 21-cm absorption line is at the same redshift as the radio continuum source (i.e. associated 21-cm absorbers, see Section 2.2.2), this can provide insight into the interaction between the neutral gas and central radio AGN. H i absorption studies can provide a unique perspective as they directly trace the gas at the position of the AGN, are more sensitive to the cooler gas and have the potential to probe gas at higher spatial resolution.

The kinematics of the H i absorption line can separate whether the gas is infalling (Maccagni et al. Reference Maccagni, Morganti, Oosterloo and Mahony2014; Tremblay et al. Reference Tremblay2016), pointing towards a gas reservoir capable of fuelling the central nucleus, or outflowing (Morganti et al. Reference Morganti, Oosterloo and Tsvetanov1998; Geréb et al. Reference Geréb, Maccagni, Morganti and Oosterloo2015; Morganti et al. Reference Morganti, Fogasy, Paragi, Oosterloo and Orienti2013), providing observational evidence of AGN-driven feedback. Low-redshift H i absorption studies suggest that fast jet-driven outflows of H i gas (with velocities over $1\,000\,\textrm{km}\,\textrm{s}^{-1}$ ) dominate the feedback processes in powerful radio galaxies (Morganti et al. Reference Morganti, Tadhunter and Oosterloo2005; Mahony et al. Reference Mahony, Morganti, Emonts, Oosterloo and Tadhunter2013) with studies of the multi-phase gas properties showing that the bulk of the mass in outflow is often in the neutral or molecular form (Tadhunter et al. Reference Tadhunter, Morganti, Rose, Oonk and Oosterloo2014; Mahony et al. Reference Mahony, Oonk, Morganti, Tadhunter, Bessiere, Short, Emonts and Oosterloo2016; Morganti & Oosterloo Reference Morganti and Oosterloo2018). While this has been well studied in the nearby Universe, it is crucial to extend these studies to higher redshifts when feedback processes have the most impact (Hopkins & Beacom Reference Hopkins and Beacom2006). Recent studies searching for neutral gas outflows at $z\sim1$ have also shown evidence for fast outflows, although the sample size is still relatively small (Aditya & Kanekar Reference Aditya and Kanekar2018a; Aditya Reference Aditya2019). While FLASH will not be sensitive to the low optical depths typically observed in fast outflows for the majority of sources, it will provide a sample of powerful radio galaxies with large gas reservoirs which can be targeted with deeper observations using, for example, MeerKAT.

The large sample of associated absorbers detected by FLASH will also allow us to explore the neutral gas properties of source populations with different AGN fuelling mechanisms, in particular by exploring the difference in gas kinematics and detection rates in High-Excitation and Low-Excitation Radio Galaxies (HERGS/LERGS; see e.g. Chandola & Saikia Reference Chandola and Saikia2017; Chandola et al. Reference Chandola, Saikia and Li2020).

4.3.2. The evolution of high-powered radio galaxies

From the radio luminosity function for active galaxies at intermediate redshifts (Sadler et al. Reference Sadler2007), we estimate that the FLASH survey volume contains at least 10,000 radio galaxies with redshifts in the range $0.4<z<1$ and continuum flux densities above 50 mJy. These objects allow us to search for H i in the host galaxies of radio AGN at look-back times of 4–8 Gyr, when powerful radio galaxies were at least 3–5 times more abundant than they are today (Heckman & Best Reference Heckman and Best2014; Pracy et al. Reference Pracy2016). These high-powered (predominately FR-II) radio galaxies are believed to be associated with gas-rich galaxy mergers, and are expected to be much richer in cold gas than FR-Is (Heckman et al. Reference Heckman, Smith, Baum, van Breugel, Miley, Illingworth, Bothun and Balick1986; Carilli et al. Reference Carilli, Menten, Reid, Rupen and Yun1998), but large systematic studies of the cold gas in these powerful radio galaxies have not been possible with existing radio telescopes. As such, the FLASH survey can provide important new constraints on the redshift evolution of the H i content of radio galaxies.

4.3.3. The multi-phase gas in AGN

From associated absorbers we can determine properties of H i near the centres of active galaxies, likely physically close to the host galaxy AGN. The presence of an active supermassive black hole is known to have a variety of impacts on the evolutionary path of the host galaxy (Kauffmann et al. Reference Kauffmann2003; Di Matteo et al. Reference Di Matteo, Springel and Hernquist2005; Cattaneo et al. 2009; Fabian Reference Fabian2012; Kormendy & Ho Reference Kormendy and Ho2013), although there are still many unanswered questions about the nature of the relationship between the two and the balance between fuelling, feedback and quenching in obscured AGN (Morganti & Oosterloo Reference Morganti and Oosterloo2018; Hickox & Alexander Reference Hickox and Alexander2018; O’Dea & Saikia 2020). When we combine information on the neutral gas from FLASH with multiwavelength information on the total hydrogen content from X-ray absorption, the presence of dust from infrared emission, and the distribution of ionised gas from optical spectroscopy, we gain a comprehensive physical insight into the properties of the multi-phase gas in AGN as a whole. As part of FLASH, we will use our unprecedented sample of H i associated absorbers to bring together a new picture across the electromagnetic spectrum of this gas and how it relates back to the overall properties of each host galaxy and its evolution.

Early FLASH data has already revealed evidence in support of a physical relationship between the gas detected by H i absorption and soft X-ray absorption (Moss et al. Reference Moss2017; Glowacki et al. Reference Glowacki2017), and is supported by other studies (Vink et al. Reference Vink, Snellen, Mack and Schilizzi2006; Ostorero et al. Reference Ostorero2010, Reference Ostorero, Morganti, Diaferio, Siemiginowska, Stawarz, Moderski and Labiano2017, Reference Ursini, Bassani, Panessa, Bruni, Bazzano, Bird, Malizia and Ubertini2019). Alongside the new window on the radio sky provided by ASKAP, the eROSITA telescope was launched in July 2019 and will transform our view of the X-ray sky (Merloni et al. Reference Merloni2012). To facilitate further investigation into multiwavelength absorption tracers using these next-generation instruments, we have formed a collaboration between the FLASH team and the eROSITA-DE team (SEAFOG: Studies with eROSITA and ASKAP-FLASH of Obscured Galaxies) dedicated to bringing together all-sky information on gas absorption in AGN. SEAFOG will give us the first large-scale homogeneous dataset of H i absorption and X-ray absorption (also extremely well-matched in sensitivity and angular resolution), enabling us to perform an unbiased census of the population of H i and X-ray absorbers in order to definitively uncover the relationship between them.

FLASH also provides us with the possibility to study time variability in the multi-phase medium of active galaxies. Previous studies towards the nearby radio galaxy PKS 1718-649 have found variability in both radio continuum and X-ray absorption on the timescales of months (Tingay et al. Reference Tingay2015; Beuchert et al. Reference Beuchert2018, Moss et al. in prep). Modelling of the continuum variability indicates that the most likely mechanism here is free-free absorption (Macquart & Tingay Reference Macquart and Tingay2016), which suggests that we may be able to further trace this via variability in the H i absorption profile. This particular galaxy has very weak H i absorption (Veron-Cetty et al. Reference Veron-Cetty, Woltjer, Ekers and Staveley-Smith1995), meaning that it is difficult to correlate any possible H i absorption variability with the known radio continuum or X-ray variability.

However, we expect with the much larger population of associated absorbers to be provided by FLASH, we will be able to find highly suitable targets to advance these studies. With eROSITA expected to revisit the sky eight times during its 5 yr operational period and the excellent GHz continuum follow-up capabilities of the Australia Telescope Compact Array, we see a unique opportunity to conduct contemporaneous observational follow-up of early FLASH H i absorption detections to search for correlated variability in radio continuum, hydrogen absorption and X-ray absorption simultaneously.

4.6.1. Intervening 21-cm absorbers

Coherent $\mu$ G magnetic fields in present day galaxies are thought to be the result of a large-scale dynamo, which orders and sustains fields via turbulence driven by supernova explosions or cosmic ray pressure and galactic differential rotation (Ferrière & Schmitt Reference Ferrière and Schmitt2000; Hanasz et al. Reference Hanasz, Wóltański and Kowalik2009). The seed field for the large-scale dynamo could be a weak pre-galactic field, or an already-amplified $\mu$ G field from a small-scale dynamo during the early phases of galaxy formation (e.g. Kronberg et al. Reference Kronberg, Lesch and Hopp1999; Furlanetto & Loeb Reference Furlanetto and Loeb2001; Arshakian et al. Reference Arshakian, Beck, Krause and Sokoloff2009; Rieder & Teyssier Reference Rieder and Teyssier2016). Testing these different theoretical models remains challenging due to the few galactic magnetic field measurements we have beyond the local Universe (e.g. Oren & Wolfe Reference Oren and Wolfe1995; Bernet et al. Reference Bernet, Miniati, Lilly, Kronberg and Dessauges-Zavadsky2008; Farnes et al. Reference Farnes, O’Sullivan, Corrigan and Gaensler2014; Kim et al. Reference Kim, Lilly, Miniati, Bernet, Beck, O’Sullivan and Gaensler2016; Mao et al. Reference Mao2017).

To overcome the intrinsic faintness of the polarised synchrotron emission from distant galaxies, we need to use absorption-type experiments—distant galaxies seen in projection against polarised background radio sources—to characterise their magnetic fields. Coherent magnetic fields in the intervening galaxy could produce a net Faraday rotation signal while turbulence in the intervening galaxy could depolarise the background radiation and induce Faraday complexities. Synergies between the FLASH and POSSUM surveys will offer an unique opportunity to study magnetic fields in intervening H i absorption galaxies in the redshift range $0.4 < z < 1.0$ . For FLASH detected 21-cm intervening absorbers with a polarised background continuum source, POSSUM will provide information on the Faraday rotation and depolarisation properties for the sight line. This will yield, for the first time, a statistically significant sample of few 10s to a few hundred 21-cm intervening absorbers with polarisation information. With a carefully selected sample of control sight lines towards background polarised sources without any intervening 21-cm absorption, we will statistically infer the typical Faraday rotation and depolarisation produced by the intervening galaxy population (Basu et al. Reference Basu, Mao, Fletcher, Kanekar, Shukurov, Schnitzeler, Vacca and Junklewitz2018). When possible, we will further convert these observables into magnetic field strength estimates using the FLASH H i column density constraints and an assumed ionisation fraction. As stated in Section 4.1, many host galaxies of FLASH 21-cm absorbers are expected to be identified/characterised, therefore, enabling one to directly link the derived magnetic field properties to physical properties of the absorber galaxies population. This has recently been demonstrated using FLASH commissioning data where H i absorption was detected towards the radio lobe of the powerful radio galaxy PKS 0409 $-$ 75, allowing the magnetic field of the absorbing galaxy at $z=0.67$ to be estimated (Mahony et al. Reference Mahony2022).

In addition, FLASH itself, with its full-Stokes data cube, could detect Zeeman splitting of the 21-cm absorption line and provide in-situ galactic magnetic field measurements for 21-cm intervening absorbers at intermediate redshifts $0.4 < z < 1.0$ . An upper limit of line-of-sight B field of 17 $\mu$ G was placed towards an 21-cm absorber at $z = 0.692$ (Wolfe et al. Reference Wolfe, Jorgenson, Robishaw, Heiles and Prochaska2011). Sufficiently long integration towards DLA systems could yield an interesting sample of in-situ magnetic field estimates out to $z \sim$ 1 galaxies and further constrain the time-scale of galactic magnetic field generation.

4.6.2. Associated 21-cm absorbers

The magnetic properties of H i 21-cm associated absorbers have never been previously studied. For associated absorbers, the Faraday rotation measurements come from within the AGN itself. With combined information from FLASH and polarised observations (like POSSUM), we can address the interplay between cold neutral and ionised gas in AGN and their magnetic fields in the immediate environment of the AGN. However, the magnetic fields within AGN are still not well understood (Agudo et al. Reference Agudo2015; Beck Reference Beck2009). Moreover, we do not understand the relationship between how Faraday rotation behaviour, and thus magnetic fields, play into AGN morphology (Anderson et al. Reference Anderson, Gaensler, Feain and Franzen2015; O’Sullivan et al. Reference O’Sullivan, Purcell, Anderson, Farnes, Sun and Gaensler2017).

Few polarisation studies have been done on 21-cm absorption sources. CSS sources are better studied, and many are detected with H i absorption (Section 2.2.2). Saikia & Gupta (Reference Saikia and Gupta2003) conducted a radio polarisation study using young resolved CSS sources from literature (without confirmed 21-cm absorption) and found asymmetric polarisation properties between the lobes of these sources. Teng et al. (Reference Teng, Veilleux and Baker2013) analysed the polarised spectra of 27 local ( $z < 0.12$ ) AGN with H i absorption. They found that H i absorption features were polarisation-dependent. Both studies suggest the polarisation behaviour of these sources could be explained by interactions between the radio jets and lobes and infalling or outflowing material.

In Section 4.3 we discuss how associated 21-cm absorbers can be used to study the interaction between neutral gas and the AGN. A large amount of cool gas content could cause increasing accretion rates, which could affect the magnetic fields. Higher accretion rates can cause stronger collimated jets (Allen et al. Reference Allen, Dunn, Fabian, Taylor and Reynolds2006) containing ordered or helical magnetic fields (Gabuzda Reference Gabuzda2018). In addition to gas triggering accretion, previous studies have shown that associated 21-cm absorbers have been associated with high-velocity outflows, possibly through large radio jets (Morganti et al. Reference Morganti, Sadler and Curran2015; Gupta et al. Reference Gupta2016). The mixing of large amounts of gas and magnetic fields can cause turbulent magnetic fields and depolarisation. O’Sullivan et al. (Reference O’Sullivan, Gaensler, Lara-López, van Velzen, Banfield and Farnes2015) showed that radiative-mode AGN also contained smaller fractional polarisation, indicating depolarisation attributed to the AGN’s gaseous environment.

There are 82 known associated 21-cm associated absorbers at $z > 0.1$ (Curran Reference Curran2021), most of which have been found through optical spectra (as discussed in Section 2.2.2) with no radio polarisation follow-up information to perform magnetism studies. However, with a sizeable polarised sample of associated H i absorbers from the combination of FLASH and POSSUM, statistical analysis can be done to determine these sources’ general magnetic properties and provide insight into the role of neutral gas and magnetic fields in the immediate AGN environment.

Specifically, FLASH and POSSUM can tell us whether associated 21-cm absorption sightlines contain enhanced Faraday rotation, increased depolarisation, and increased Faraday complexity compared to a control sample. Such properties can indicate stronger magnetic fields and mixing between magnetic fields and the surrounding gas, relating to outflows and environmental factors within associated absorbers. To confirm the role of such outflows in the magnetic fields of associated absorbers, the neutral gas velocity of the associated absorbers can be calculated from the FLASH catalogue and compared with the magnetic properties mentioned above. To complement this study, pre-existing multiwavelength data can provide information about the associated absorbers host galaxy’s mass, luminosity, and metallicity (inferring star formation history). Meanwhile, Faraday rotation growth with FLASH-derived redshifts would indicate the evolution of AGN gas and magnetic fields through cosmic time.

In addition to learning about magnetic fields and neutral gas in the immediate AGN environment, we can also learn about their ionisation states. As mentioned in Section 2, most associated absorbers have been detected for $z < 1$ , with a critical ionising luminosity as the proposed reason for this effect. Equation (7) shows that the RM is directly proportional to the number of free electrons $n_{\text{e}}$ along the line-of-sight. We can test whether Faraday rotation can also act as a proxy for the ionisation state of systems, allowing allow us to explore the idea of a critical ionising luminosity being responsible for the lack of 21-cm absorbers in the high redshift universe.