Further Observational Evidence for a Critical Ionising Luminosity in Active Galaxies

TL;DR

This study investigates the absence of HI 21-cm absorption in high-redshift active galaxies, supporting the idea of a critical ionising photon rate that ionizes all neutral gas, with implications for galaxy evolution.

Contribution

It provides observational evidence for a critical ionising luminosity threshold in active galaxies at z > 2.6, reinforcing the link between UV luminosity and neutral gas ionisation.

Findings

Zero detections in 16 out of 25 sources surveyed.

Expected about four detections based on lower-redshift data.

Significant support (~7 sigma) for a critical ionising photon rate of logQ=56.

Abstract

We report the results of a survey for HI 21-cm absorption at redshifts of z > 2.6 in a new sample of radio sources with the Green Bank and Giant Metrewave Radio Telescopes. From a total of 25 targets, we report zero detections in the 16 for which optical depth limits could be obtained. Based upon the detection rate for z > 0.1 associated absorption, we would expect approximately four detections. Of the 11 which have previously not been searched, there is sufficient source-frame optical/ultra-violet photometry to determine the ionising photon rate for four. Adding these to the literature, the hypothesis that there is a critical rate of logQ = 56 ionising photons per second is now significant at ~7 sigma. This reaffirms our assertion that searching z > 3 active galaxies for which optical redshifts are available selects sources in which the ultra-violet luminosity is sufficient to ionise all of the neutral gas in the host galaxy.

Tables

Table 1. Table 1: The observational results by IAU name (B1950 designation, see Table 2 for the full names as resolved by the NASA/IPAC Extragalactic Database). z 𝑧 z is the optical redshift of the source, Δ ​ S Δ 𝑆 \Delta S the rms noise reached per 20 km s − 1 superscript s 1 {\rm s}^{-1}  channel, S meas subscript 𝑆 meas S_{\rm meas} is the measured flux density, τ 3 ​ σ subscript 𝜏 3 𝜎 \tau_{3\sigma} the derived optical depth limit, where τ 3 ​ σ = − ln ⁡ ( 1 − 3 ​ Δ ​ S / S meas ) subscript 𝜏 3 𝜎 1 3 Δ 𝑆 subscript 𝑆 meas \tau_{3\sigma}=-\ln(1-3\Delta S/S_{\rm meas}) is quoted for these non-detections. These give the quoted column densities, where T s subscript 𝑇 s T_{\rm s} is the spin temperature and f 𝑓 f the covering factor; a blank field indicates that the observations were dominated by RFI or the presence of an RFI/instrumental spike close to the expected absorption redshift. The final two columns give the frequency and redshift range over which the limit applies (neglecting the spikes).

Source	$z$	Tel.	$\Delta S$ [mJy]	$S_{\mathrm{meas}}$ [Jy]	${\tau }_{3\sigma }$	$N_{\text{H}\text{ i}}$ [${\text{cm}}^{-2}$]	$\nu$-range [MHz]	$z$-range
0032+276	2.9642	GBT	57	1.250		—	354.23 – 359.83	2.9474 – 3.0099
…	…	GMRT	38	0.676			356.50 – 360.33	2.9420 –2.9843
0239+108a	2.6800	GBT	48	1.032		—	380.48 – 391.06	2.6322 – 2.7332
0319+121b	2.6620	GBT	61	1.510		—	382.51 – 393.83	2.6067 – 2.7134
0511+009	2.6794	GBT	64	5.208			380.71 – 390.73	2.6352 – 2.7309
0521–262	3.109	GMRT	–	—	—	—-	rfi dominant
0609+607	2.7020	GBT	54	1.364			378.74 – 389.48	2.6469 – 2.7503
0620+389c	3.4690	GBT	44	2.926			312.11 – 323.60	3.3894 – 3.5509
…	…	GMRT	11	0.226			315.92 – 319.75	3.4422 – 3.4961
0749+426d	3.5892	GMRT	19	0.771			307.60 – 311.43	3.5609 – 3.6177
0800+618e	3.0330	GMRT	–	–	—	—-	rfi dominant
0830+115	2.9786	GBT	35	3.906			351.37 – 359.90	2.9467 – 3.0425
0834–201	2.7520	GBT	78	4.223			375.10 – 384.38	2.6953 – 2.7868
0902+490f	2.6887	GBT	60	0.916			379.26 – 390.94	2.6334 – 2.7452
0913+003	3.074	GMRT	–	—	—	—-	rfi dominant
1004+141g	2.7070	GBT	110	0.614		—	378.66 – 386.95	2.6708 – 2.7511
1013+208	3.1186	GBT	42	1.094		—	340.34 – 350.54	3.0521 – 3.1735
1327+504	2.6540	GBT	69	0.682			383.69 – 394.47	2.6008 – 2.7020
1354–174	3.1470	GBT	41	3.912			337.49 – 347.84	3.0836 – 3.2088
1402+044	3.2153	GBT	53	1.429			331.44 – 342.91	3.1422 – 3.2856
…	…	GMRT	17	0.351			335.04 – 338.88	3.1915 – 3.2395
1427+543	3.0134	GBT	47	2.606		—	348.32 – 359.74	2.9484 – 3.0779
…	…	GMRT	68	0.429			352.00 – 355.83	2.9918 – 3.0352
1446–111	2.6326	GBT	75	0.038	—	—-	385.43 – 396.71	2.5805 – 2.6852
1556–245	2.8130	GBT	65	1.754			369.89 – 378.24	2.7553 – 2.8401
1614+051	3.2150	GMRT	11	0.024	—	—	335.07 – 338.90	3.1912 – 3.2391
1745+624	3.8890	GBT	67	0.045	—	—	285.20 – 296.26	3.7945 – 3.9805
2318–087	3.1639	GMRT	74	0.505			339.21 – 343.04	3.1406 – 3.1874
2351–154	2.6680	GBT	81	0.794		—	381.41 – 393.10	2.6133 – 2.7241

Table 2. Table 2: The ionising photon rates [photons s -1 ] of the targets for which a limit to the absorption strength could be obtained.

NED name	IAU	$z$	${\log }_{10}{Q}_{\text{H}\text{ i}}$
B2 0032+27	0032+276	2.9642	—
PKS 0239+108	0239+108	2.680	—
PKS 0319+12	0319+121	2.662	—
PMN J0513+0100	0511+009	2.6770	—
PKS 0521–262†	0521–262	3.109	—
BZQ J0614+6046	0609+607	2.702	—
B2 0620+38	0620+389	3.469	—
B3 0749+426	0749+426	3.5892	$57.71\pm 0.78$
WISE J080518.15+614424.0†	0800+618	3.033	—
[HB89] 0830+115	0830+115	2.9786	—
[HB89] 0834–201	0834–201	2.752	$57.52\pm 0.12$
SDSS J090527.46+485049.9†	0902+490	2.6887	$57.99\pm 0.20$
SDSS J091551.69+000713.2†	0913+003	3.074	—
[HB89] 1004+141	1004+141	2.707	—
PKS 1014+208	1013+208	3.1186	—
SDSS J132905.80+500926.5	1327+504	2.654	—
PKS 1354–17	1354–174	3.147	—
[HB89] 1402+044	1402+044	3.2153	$57.04\pm 0.47$
SDSS J142921.87+540611.1	1427+543	3.0134	$56.69\pm 0.51$
PKS B1446-111†	1446–111	2.6326	—
[HB89] 1556–245	1556–245	2.813	$57.77\pm 0.78$
[HB89] 1614+051†	1614+051	3.2150	—
4C +62.29†	1745+624	3.889	$58.51\pm 0.07$
PKS 2318–087	2318–087	3.1639	—
[HB89] 2351–154	2351–154	2.668	$56.94\pm 0.90$

Equations

$$N_{\text{Hsci}}\approx 1.823\times 10^{18}\frac{T_{\mathrm{s}}}{f}\int \tau dv,$$

$$D_{\mathrm{L}}=D(z+1),\mathrm{where}D=\frac{c}{H_0}{\int }_0^z\frac{dz}{H_{\mathrm{z}}/H_0}$$

$$\frac{H_{\mathrm{z}}}{H_0}=\sqrt{{\Omega }_{\mathrm{m}}(z+1{)}^3+(1-{\Omega }_{\mathrm{m}}-{\Omega }_{\Lambda })(z+1{)}^2+{\Omega }_{\Lambda }},$$

$${\int }_{\nu }^{\infty }\frac{L_{\nu }}{h\nu }d\nu ,\mathrm{where}{\log }_{10}{L}_{\nu }=\alpha {\log }_{10}\nu +\mathcal{C}\Rightarrow L_{\nu }=10^{\mathcal{C}}{\nu }^{\alpha },$$

$$\frac{10^{\mathcal{C}}}{h}{\int }_{\nu }^{\infty }{\nu }^{\alpha -1}d\nu =\frac{10^{\mathcal{C}}}{\alpha h}{\left[{\nu }^{\alpha }\right]}_{\nu }^{\infty }=\frac{-10^{\mathcal{C}}}{\alpha h}{\nu }^{\alpha }\mathrm{where}\alpha <0,$$

Full text

††pagerange: Further Observational Evidence for a Critical Ionising Luminosity in Active Galaxies–References††pubyear: 2017

1 Introduction

While absorption of the 21-cm spin-flip transition of neutral hydrogen (H i) is readily detected in near-by galaxies, it is conspicuous by its absence from the redshifted Universe. H i 21-cm absorption traces the cool component of the gas, the reservoir for star formation, which can be detected in either quiescent galaxies intervening the line-of-sight to a more distant radio source or associated with the host galaxy of the radio source itself. While the detection of hydrogen at radio wavelengths is not susceptible to the dust extinction effects of optical/ultra-violet band searches (Carilli et al., 1998; Curran et al., 2006, 2017), after over three decades of searching (e.g. Davis & May 1978; de Waard et al. 1985) there are only 50 detections each of H i 21-cm at $z\stackrel{{\scriptstyle>}}{{{}_{\sim}}}0.1$ in either intervening or associated absorption (compiled in Curran et al. 2016b). This is despite H i being detected through Lyman-$\alpha$ absorption in 12 000 damped Lyman-$\alpha$ absorbers (DLAs) and sub-DLAs111A DLA is defined as having a neutral hydrogen column density exceeding $N_{\rm HI}=2\times 10^{20}$ atoms $\hbox{{\rm cm}}^{-2}$, with sub-DLAs having lower column densities, although exhibiting the same characteristic damping wings in the absorption profile. (Noterdaeme et al., 2012), mainly at $z\stackrel{{\scriptstyle>}}{{{}_{\sim}}}1.7$ where the Lyman-$\alpha$ transition is redshifted into the atmospheric observing window.222At lower redshifts, a high H i column density is inferred from the equivalent width of the Mg ii absorption and other metal ion transitions which can be detected by ground-based telescopes (e.g. Rao et al. 2006). By comparison, the detection of H i 21-cm absorption occurs overwhelmingly at redshifts of $z\stackrel{{\scriptstyle<}}{{{}_{\sim}}}1$, or less than half the look-back time to the origin of the Universe. While much of this can be attributed to the past availability of the suitable radio bands, detection rates at $z\stackrel{{\scriptstyle>}}{{{}_{\sim}}}1$ are demonstrably lower than at $z\stackrel{{\scriptstyle<}}{{{}_{\sim}}}1$ (Kanekar & Chengalur 2003; Curran et al. 2013c).

For the intervening absorbers it has been argued that this is due to an evolution in the spin temperature, $T_{\rm s}$, of the gas, where the fraction of the cold neutral medium (CNM, where $T\sim 150$ K and $n\sim 10$ $\hbox{{\rm cm}}^{-3}$) decreases with redshift (Kanekar & Chengalur, 2003; Kanekar et al., 2014). However, given that the comparison of the 21-cm absorption strength with the total neutral hydrogen column density, from the Lyman-$\alpha$ transition, can at best yield the spin temperature/covering factor degeneracy ($T_{\rm s}/f$), Curran et al. (2005) argued that an apparent evolution in $T_{\rm s}$ could be caused by the assumption that $f=1$ for the high redshift absorbers. Furthermore, by accounting for the effects of an expanding Universe, a standard $\Lambda$ cosmology means that at redshifts of $z\stackrel{{\scriptstyle>}}{{{}_{\sim}}}1$ the absorber is always at a similar angular diameter distance as the background continuum source, i.e. $DA_{\rm abs}\approx DA_{\rm QSO}$. In contrast, at $z\stackrel{{\scriptstyle<}}{{{}_{\sim}}}1$ $DA_{\rm abs}<DA_{\rm QSO}$ is possible (when $z_{\rm abs}<z_{\rm QSO}$), suggesting that the mix of “spin temperatures” at $z\stackrel{{\scriptstyle<}}{{{}_{\sim}}}1$ and exclusively high values at $z\stackrel{{\scriptstyle>}}{{{}_{\sim}}}1$ (Kanekar & Chengalur, 2003), is in fact the effect of geometry on the covering factor (Curran & Webb, 2006; Curran, 2012). By deconstructing the covering factor, via the angular diameter distances and high resolution imaging of the background sources, there is now compelling evidence that the fraction of the CNM in intervening absorbers may trace the star formation history of the Universe (Curran, 2017).

For the associated absorbers, since, by definition, $z_{\rm abs}\approx z_{\rm QSO}$, the same geometric effects cannot account for the difference in the detection rates between the low and high redshift sources. From a survey of H i 21-cm absorption at $z\stackrel{{\scriptstyle>}}{{{}_{\sim}}}3$, Curran et al. (2008) suggested that their exclusively non-detections were due to the high redshifts selecting sources with high rest-frame ultra-violet luminosities ($L_{\rm UV}\stackrel{{\scriptstyle>}}{{{}_{\sim}}}10^{23}$ W Hz*-1*). Since an examination of the literature showed that H i 21-cm had never been detected at these luminosities, irrespective of redshift, they suggested that the non-detection of cool neutral gas was due to the high redshift selection yielding only sources where the UV luminosity was sufficient to excite the gas to below the detection limit. This observational result has since been confirmed several times for various heterogeneous samples (Curran et al. 2011a, 2013b, 2013c, 2016a, 2017; Allison et al. 2012; Geréb et al. 2015; Aditya et al. 2016; Grasha et al. 2017)333Grasha et al. (2017), which is still in submission, reports 0 new detections of H i 21-cm absorption out of 89 new searches over $0.02<z<3.8$ (see Grasha & Darling 2011)., showing this to be an ubiquitous effect.

In order to investigate why there is an apparent critical UV luminosity and why this is $L_{\rm UV}\sim 10^{23}$ W Hz*-1*, Curran & Whiting (2012) applied the equation of photoionsation equilibrium (Osterbrock, 1989) to a gas disk with an exponential density distribution (Begeman et al., 1991) and found that an ionising photon rate of $Q_{\text{H{\sc\,i}}}\equiv\int^{\infty}_{\nu}({L_{\nu}}/{h\nu})\,d{\nu}\approx 3\times 10^{56}$ s*-1* (a monochromatic $\lambda=912$ Å luminosity of $L_{\rm UV}\sim 10^{23}$ W Hz*-1*) will ionise a gas disk with the same scale-length as the Milky Way (Kalberla et al., 2007). This suggests that the observed critical luminosity is sufficient to ionise all of the neutral gas in a large spiral galaxy, thus explaining why H i 21-cm has never been detected where $L_{\rm UV}\stackrel{{\scriptstyle>}}{{{}_{\sim}}}10^{23}$ W Hz*-1*. Since the vast majority of $z\stackrel{{\scriptstyle>}}{{{}_{\sim}}}1$ radio sources for which redshifts are available are believed to have luminosities above the critical value (see figure 4 of Morganti et al. 2015), this would mean that even the Square Kilometre Array (SKA) will be unable to detect H i 21-cm absorption in these objects.

Given this critical luminosity above which all of the gas in the host is ionised, in order to detect the cool, star-forming gas within high redshift radio sources, we need to dispense with the reliance upon an optical redshift, thus avoiding the selection of the most UV luminous objects. Through their wide instantaneous bandwidths, the SKA pathfinders are ideally suited to spanning a large range of redshift space in a single tuning (e.g. Allison et al. 2015; Maccagni et al. 2017).444Since the nature of the absorber is usually determined from an optical spectrum, other techniques for distinguishing intervening from associated absorption must be explored, with machine learning showing some promise (Curran et al., 2016b). However, these are generally limited to frequencies of $\stackrel{{\scriptstyle>}}{{{}_{\sim}}}700$ MHz, i.e. H i 21-cm at redshifts of $z\stackrel{{\scriptstyle<}}{{{}_{\sim}}}1$, therefore requiring the SKA to find the missing cold neutral gas at high redshift. In the meantime, we can continue to search for H i 21-cm absorption, via various search strategies, with currently available instruments (e.g. Curran et al. 2016a). From newly obtained redshifts for a sample of strong flat spectrum radio sources (see Sect. 2.1), we can perform a large survey for associated 21-cm absorption in active galaxies over redshift ranges spanning most of the Universe’s history. Here we present the results of our high redshift ($z\stackrel{{\scriptstyle>}}{{{}_{\sim}}}2.6$) survey with the Green Bank Telescope (GBT) and the Giant Metrewave Radio Telescope (GMRT).

2 Observations and analysis

2.1 The sample

The Second Realization of the International Celestial Reference Frame by Very Long Baseline Interferometry (ICRF2, Ma et al. 2009), constitutes a sample of strong flat spectrum radio sources, of which 1682 now have known redshifts (Titov & Malkin 2009; Titov et al. 2013 and references therein), yielding a tuning frequency in the search for 21-cm absorption. Being VLBI sources, all have significant compact flux, thus maximising the chance of a high covering factor and thus optical depth (Curran et al., 2013a). The original aim of the survey was to form part of a large observing campaign to search and quantify the incidence of associated H i 21-cm absorption over all redshifts, although observing time was only granted for the high redshift ($z\stackrel{{\scriptstyle>}}{{{}_{\sim}}}2.6$) proposals. As mentioned above (Sect. 1), we believe that such a high redshift selection will yield only sources above the critical UV luminosity, where the detection of H i 21-cm is unlikely. However, having a preconceived suspicion of the outcome should not preclude it from being tested.

2.2 Observations and data reduction

2.2.1 GBT observations

In the ICRF2, 1456 of the sources have declinations accessible to the GBT, in addition to being at a redshift which places the 21-cm transition into a GBT band. For this, the high redshift survey, we used the PF1 290–395 MHz receiver (H i 21-cm over $z=2.6-3.9$). We formed our target list by prioritising sources with flux densities estimated to be in excess of 1 Jy at the redshifted 21-cm frequency. Excluding the two which already had published searches at the time, left 24 targets. The observations were performed over 24–26 February 2014 with each source observed for a total of 1.3 hours in two orthogonal linear polarisations (XX & YY). The Prime Focus 1 (PF1) receiver was used, backed by the GBT spectrometer, with a bandwidth of 12.5 MHz, in order to minimise RFI while maintaining a velocity coverage of $\Delta v\approx\pm 5500$ km ${\rm s}^{-1}$. A channel width of 11 kHz gave a spectral resolution of $\approx 10$ km ${\rm s}^{-1}$. The data were analysed, flagged for RFI and averaged using the gbtidl software.

2.2.2 GMRT observations

In the ICRF2, 416 of the sources have declinations accessible to the GMRT, of which 54 have 21-cm shifted to within the 90-cm band (305–360 MHz, H i 21-cm over $z=2.9-3.7$). We prioritised sources with flux densities estimated to be in excess of 0.5 Jy at the redshifted 21-cm frequency. As per the GBT observations, the flux limit was chosen in order to attain high sensitivities, while still retaining a sizable number of targets. If the radio luminosity is correlated with the UV luminosity, it is conceivable that this selection may bias against the detection of cool, neutral gas. Although there is a correlation (Curran & Whiting, 2010), there is no critical rest-frame 1.4 GHz luminosity (Curran et al., 2008), with the relationship probably arising from both luminosities being correlated with the redshift.

Excluding the potential targets with published searches for 21-cm absorption at the time left 16 targets. The observations were taken with the full 30 antenna array over 9–13 November 2013 and 28–29 March 2014, with each source observed for a total of two hours in two orthogonal circular polarisations (LL & RR). For bandpass calibration 3C 48, 3C 147 and 3C 298 were used, with the phases being self calibrated apart from 1427+543, 1427+543, 0521–262 & 2318–087, which used a strong near-by unresolved source. For the backend we used the FX correlator over a bandwidth of 4 MHz, which over 512 channels gave a spectral resolution of $\approx 7$ km ${\rm s}^{-1}$. The data were calibrated and flagged using the miriad interferometry reduction package. After averaging the two polarisations, a spectrum was extracted from the cube. None of the sources was resolved by the synthesised beam, which ranged from $10.7\arcsec\times 9.4\arcsec$ to $30.2\arcsec\times 11.1\arcsec$.

3 Results

3.1 Observational results

Of the 29 spectra, three were completely dominated by RFI and a further three had close to zero flux. In Fig. 1 we show the remaining 23 spectra, from 19 different targets.

Of these, seven have RFI/instrumental spikes close to the expected frequency of the putative absorption, which may conceal any possible detection (Table 1).555All of the spikes arise in spectra taken with the GBT, since the single dish limits the options to mitigate the RFI. Another consequence is that the large beam at these frequencies (${\rm HPBW}\approx 40\arcmin$), means that the off-measurement is very likely to contain another radio source. This will affect the flux calibration, leading to the differences from the GMRT values for the same source (which has ${\rm HPBW}\stackrel{{\scriptstyle<}}{{{}_{\sim}}}0.5\arcmin$ and no off-measurement), although the optical depths are expected to be unaffected (Ries, 2012). This leaves 16 good spectra of 14 different targets, 11 of which have not been previously searched.

In the optically thin regime (where $\tau\stackrel{{\scriptstyle<}}{{{}_{\sim}}}0.3$), the total neutral hydrogen column density is related to the velocity integrated optical depth of the H i 21-cm absorption via

[TABLE]

where $T_{\rm s}$ is the spin temperature of the gas, which is a measure of the excitation from the lower hyperfine level (Purcell & Field, 1956; Field, 1959) and $\int\!\tau dv$ is the observed velocity integrated optical depth of the absorption. In order to compare our limits with previous surveys, all spectra are re-sampled to the same spectral resolution (20 km ${\rm s}^{-1}$, as in Fig. 1), which is used as the FWHM to obtain the integrated optical depth limit, thus giving the $N_{\text{H{\sc\,i}}}f/T_{\rm spin}$ limit per channel (see Curran 2012).

Of the 11 new sources searched, for which a limit could be obtained, there were no detections of H i 21-cm absorption.

Although the limits are not as sensitive as many of the other searches, particularly those at low redshift (Fig. 2)666For example, at $z>2$ the most sensitive limit is $N_{\text{H{\sc\,i}}}=10^{17}\,(T_{\rm s}/f)$ $\hbox{{\rm cm}}^{-2}$ and at $z\leq 2$ there are seven searches below this limit., there are 42 detections and 116 previous non-detections over the range of sensitivities searched [$N_{\text{H{\sc\,i}}}=0.1-2.4\times 10^{19}\,(T_{\rm s}/f)$ $\hbox{{\rm cm}}^{-2}$]. This gives a detection rate of 27% over all redshifts within these sensitivity limits, which is close to the overall detection rate (30.5%, Sect. 3.2) and comparable to the 25% found by Gupta et al. (2006). Note that the highest detection rate, of 40%, was obtained by Vermeulen et al. (2003) in a survey of $z\stackrel{{\scriptstyle<}}{{{}_{\sim}}}1$ compact radio sources777Not only do compact sources tend to have lower ultra-violet luminosities (Curran & Whiting, 2010; Allison et al., 2012), but there is an anti-correlation between the optical depth of the 21-cm absorption and the extent of the radio source (Curran et al., 2013a)., where we may expect a maximum of $\approx 50$%, due to the alignment between the gaseous disk and continuum source along our sight-line (see Curran & Whiting 2010). From binomial statistics, we therefore expect $3.8\pm 1.6$ new detections for the 14 different targets with good spectra.

3.2 Ionising photon rates

Following our usual procedure (e.g. Curran et al. 2013b), for each target we obtained the photometry from NASA/IPAC Extragalactic Database (NED), the Wide-Field Infrared Survey Explorer (WISE, Wright et al. 2010), Two Micron All Sky Survey (2MASS, Skrutskie et al. 2006) and the Galaxy Evolution Explorer (GALEX data release GR6/7)888http://galex.stsci.edu/GR6/#mission databases. Each flux, $S_{\nu}$, was corrected for Galactic extinction (Schlegel et al., 1998), before being converted to a specific luminosity at the source-frame frequency, via $L_{\nu}=4\pi\,D_{\rm L}^{2}\,S_{\nu}/(z+1)$, where $D_{\rm L}$ is the luminosity distance to the source, given by

[TABLE]

is the line-of-sight co-moving distance (e.g. Peacock 1999), in which $c$ is the speed of light, $H_{0}$ the Hubble constant, $H_{\rm z}$ the Hubble parameter at redshift $z$ and

[TABLE]

where we use a standard $\Lambda$ cosmology, with $H_{0}=71$ km s*-1* Mpc*-1*, $\Omega_{\rm m}=0.27$ and $\Omega_{\Lambda}=0.73$. We then fit a power law to the UV rest-frame data, allowing the ionising photon rate, $Q_{\text{H{\sc\,i}}}\equiv\int^{\infty}_{\nu}({L_{\nu}}/{h\nu})\,d{\nu}$, to be derived from

[TABLE]

$\alpha$ is the spectral index and ${\cal C}$ the intercept, which gives

[TABLE]

for the ionising photon rate.

Although there was only sufficient photometry for four of the targets which also had good spectra (Fig. 3), we can add these to the previous searches (Fig. 4)999Compiled from de Waard et al. (1985); Mirabel (1989); van Gorkom et al. (1989); Uson et al. (1991); Carilli et al. (1992, 1998, 2007); Moore et al. (1999); Peck et al. (1999, 2000); Röttgering et al. (1999); Morganti et al. (2001); Ishwara-Chandra et al. (2003); Vermeulen et al. (2003); Curran et al. (2006, 2008, 2011a, 2011b, 2013b, 2013c, 2016a, 2017); Gupta et al. (2006); Orienti et al. (2006); Kanekar et al. (2009); Emonts et al. (2010); Salter et al. (2010); Chandola et al. (2011, 2013); Allison et al. (2012, 2015); Yan et al. (2012, 2016); Geréb et al. (2015); Srianand et al. (2015); Aditya et al. (2016, 2017); Grasha et al. (2017)..

Of the 311 $z\geq 0.1$ sources for which limits can be obtained, 211 have sufficient photometry to determine the ionising photon rate. Of these, there are 43 detections and 98 non-detections with ionising photon rates up to the highest value where 21-cm absorption has been detected ($Q_{\text{H{\sc\,i}}}\leq 1.7\times 10^{56}$ s*-1*, Kanekar et al. 2009). Applying this 30.5% detection rate to the $Q_{\text{H{\sc\,i}}}>1.7\times 10^{56}$ s*-1* sources, gives a binomial probability of $8.72\times 10^{-12}$ of obtaining 0 detections and 70 non-detections, which is significant at $6.83\sigma$, assuming Gaussian statistics. This strengthens the case for a critical UV luminosity hindering the detection of H i 21-cm absorption at high redshift.

4 Summary

We have undertaken a survey for associated H i 21-cm absorption at redshifts of $z=2.6-3.9$ in 25 radio sources with the Green Bank and Giant Metrewave Radio Telescope, from which we obtain zero detections. Of the 14 for which limits could be obtained, 11 are new, with ten of these reaching optical depths of $\tau_{3\sigma}\leq 0.3$. All of the targets were selected from the sources in the Second Realization of the International Celestial Reference Frame by Very Long Baseline Interferometry, for which 1682 have measured redshifts spanning up to $z=6.2$. Our intent was to undertake a large survey over all of this redshift space in order to quantify the incidence of associated H i 21-cm absorption over the history of the Universe. However, observing time was only awarded for the highest redshift sample, where we do not expect absorption due to all of the neutral gas being ionised in the $z\stackrel{{\scriptstyle>}}{{{}_{\sim}}}1$ sources that have a reliable optical redshift (Curran & Whiting, 2012).

Nevertheless, the ICRF2 provides a large new sample of strong flat-spectrum radio sources within which to search for 21-cm absorption, and the expectation of a null result should not prevent us from testing it. Given the general $\approx 30$% detection rate at the sensitivities obtained, we expect $\approx 4$ new detections, although obtaining zero detections is within $\approx 2\sigma$ of this. In the context of all the previous searches, there still remains only two detections in this redshift range (Uson et al., 1991; Moore et al., 1999), both of which are below the ionising photon rate of $Q_{\text{H{\sc\,i}}}\sim 10^{56}$ s*-1* (a monochromatic $\lambda=912$ Å luminosity of $L_{\rm UV}\sim 10^{23}$ W Hz*-1*). The addition of the five new sources for which there is sufficient photometry101010The four new plus one searched in common with Aditya et al. (2016)., gives a binomial probability of $8.72\times 10^{-12}$ of the observed distribution occuring by chance. This is significant at $6.83\sigma$, which supports the hypothesis that $Q_{\text{H{\sc\,i}}}\sim 10^{56}$ s*-1* is sufficient to ionise all of the neutral gas in a large spiral galaxy (Curran & Whiting, 2012). This appears to be an ubiquitous effect, independent of source selection and applicable over all redshifts, with the selection of sources with $Q_{\text{H{\sc\,i}}}\stackrel{{\scriptstyle<}}{{{}_{\sim}}}10^{56}$ s*-1* being required to detect neutral hydrogen. This ionising photon rate corresponds to blue magnitudes of $B\stackrel{{\scriptstyle>}}{{{}_{\sim}}}22$ at $z\stackrel{{\scriptstyle>}}{{{}_{\sim}}}3$, for which there are currently no radio sources with a measured optical redshift known (Curran et al., 2013c; Morganti et al., 2015).

We therefore reiterate that the detection of neutral gas within the hosts of high redshift active galaxies requires us to dispense with the usual reliance upon an optical redshift to which to define the search frequency. The way forward is through wide-band observations of radio sources of unknown redshift with the Square Kilometre Array.

Acknowledgements

We wish to thank the anonymous referee for their helpful comments, as well as Katie Grasha and Jeremy Darling for a draft manuscript of their forthcoming paper. We also thank the staff of the GMRT who have made these observations possible. GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc 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. This research has also made use of NASA’s Astrophysics Data System Bibliographic Services.