Ultra-violet photo-ionisation in far-infrared selected sources

TL;DR

This study investigates the relationship between ultra-violet photo-ionisation and far-infrared emission in Herschel-SPIRE sources, exploring whether AGN activity or massive stars dominate dust heating at high ionising photon rates.

Contribution

It provides observational evidence on the incidence of FIR emission at high ionising photon rates, challenging the idea of a critical ionisation threshold for FIR detection.

Findings

FIR emission detected at ionising photon rates much higher than HI ionisation threshold.

No clear critical ionising photon rate for FIR detection observed.

High ionising rates may be due to AGN or massive stars, not just HI ionisation.

Abstract

It has been reported that there is a deficit of stellar heated dust, as evident from the lack of far-infrared (FIR) emission, in sources within the Herschel-SPIRE sample with X-ray luminosities exceeding a ``critical value'' of L~10^37 W. Such a scenario would be consistent with the suppression of star formation by the AGN, required by current theoretical models. Since absorption of the 21-cm transition of neutral hydrogen (HI), which traces the star-forming reservoir, also exhibits a critical value in the ultra-violet band (above ionising photon rates of Q ~ 3 x 10^56 s^-1), we test the SPIRE sample for the incidence of the detection of 250 micron emission with Q. The highest value at which FIR emission is detected above the SPIRE confusion limit is Q = 8.9 x 10^57 s^-1, which is ~30 times that for the HI, with no critical value apparent. Since complete ionisation of the neutral atomic gas is expected at Q > 3 x 10^56 s-1., this may suggest that much of the FIR must arise from heating of the dust by the AGN. However, integrating the ionising photon rate of each star over the initial mass function, we cannot rule out that the high observed ionising photon rates are due to a population of hot, massive stars.

Tables

Table 1. Table 1: The estimated properties of stars of various temperatures. L ⋆ subscript 𝐿 ⋆ L_{\star} is the stellar luminosity estimated from the main sequence, followed by the radius required to equate this to the bolometric intensity obtained from the Planck function. The stellar mass is estimated from the mass–luminosity relation, L ⋆ / L ⊙ = ( M ⋆ / M ⊙ ) 3.5 subscript 𝐿 ⋆ subscript 𝐿 direct-product superscript subscript 𝑀 ⋆ subscript 𝑀 direct-product 3.5 L_{\star}/L_{\odot}=(M_{\star}/M_{\odot})^{3.5} , and the main sequence lifetime, t MS subscript 𝑡 MS t_{\rm MS} , from t MS ∝ 1 / M 2.5 proportional-to subscript 𝑡 MS 1 superscript 𝑀 2.5 t_{\rm MS}\propto 1/M^{2.5} . N stars subscript 𝑁 stars N_{\rm stars} is the number of stars of this mass according to the Salpeter initial mass function, normalised to a total stellar mass of 3 × 10 12 3 superscript 10 12 3\times 10^{12}  M ⊙ , followed by the star formation required to maintain this (see main text).

$T_{\star }$ [K]	20 000	35 000	50 000
$L_{\mathrm{total}}$ [L⊙]	4200	$2\times {10}^5$	$2\times {10}^6$
Radius [R⊙]	5.4	11	17
Mass [M⊙]	11	31	60
$t_{\mathrm{MS}}$ [yr]	$3\times {10}^7$	$2\times {10}^6$	$4\times {10}^5$
$Q_{\star }$ [s-1]	$2.7\times {10}^{46}$	$1.9\times {10}^{48}$	$3.4\times {10}^{49}$
$N_{\mathrm{stars}}$	$7.9\times {10}^8$	$7.0\times {10}^7$	$1.5\times {10}^7$
SFR [M⊙ yr-1]	$300$	$1100$	$2500$

Table 2. Table 2: The total ionising photon rates, Q total subscript 𝑄 total Q_{\rm total} , for various stellar mass distributions. M max subscript 𝑀 max M_{\rm max} is the maximum stellar mass permitted by limiting the total star formation rate to SFR = total 1 × 10 4 {}_{\rm total}=1\times 10^{4}  M ⊙  yr -1  (no AGN contribution to the FIR emission) and N stars subscript 𝑁 stars N_{\rm stars} is the number of stars of this mass.

$M_{\mathrm{total}}$ [M⊙]	$4\times {10}^{11}$			$4\times {10}^{12}$			$4\times {10}^{13}$
IMF index	$\alpha =-2.35$	$\alpha =-2.60$	$\alpha =-2.85$	$\alpha =-2.35$	$\alpha =-2.60$	$\alpha =-2.85$	$\alpha =-2.35$	$\alpha =-2.60$	$\alpha =-2.85$
$M_{\max }$ [M⊙]	43	110	550	6	9	17	1	1	1
$N_{\mathrm{stars}}$	$5\times {10}^6$	$1\times {10}^5$	400	$5\times {10}^9$	$1\times {10}^9$	$7\times {10}^7$	$4\times {10}^{12}$	$3\times {10}^{12}$	$2\times {10}^{12}$
$Q_{\mathrm{total}}$ [s-1]	$9\times {10}^{56}$	$2\times {10}^{57}$	$4\times {10}^{62}$	$2\times {10}^{55}$	$8\times {10}^{55}$	$3\times {10}^{56}$	$1\times {10}^{47}$	$2\times {10}^{47}$	$4\times {10}^{47}$

Table 3. Table 3: As Table 2 , but limiting the total star formation rate to SFR = total 5 000 {}_{\rm total}=5\,000  M ⊙  yr -1  (50% AGN contribution to the FIR emission).

$M_{\mathrm{total}}$ [M⊙]	$4\times {10}^{11}$			$4\times {10}^{12}$			$4\times {10}^{13}$
IMF index	$\alpha =-2.35$	$\alpha =-2.60$	$\alpha =-2.85$	$\alpha =-2.35$	$\alpha =-2.60$	$\alpha =-2.85$	$\alpha =-2.35$	$\alpha =-2.60$	$\alpha =-2.85$
$M_{\max }$ [M⊙]	23	51	190	3	4	6	$0.7$	$0.6$	$0.6$
$N_{\mathrm{stars}}$	$2\times {10}^7$	$1\times {10}^6$	8000	$4\times {10}^{12}$	$7\times {10}^9$	$1\times {10}^9$	$1\times {10}^{13}$	$9\times {10}^{12}$	$8\times {10}^{12}$
$Q_{\mathrm{total}}$ [s-1]	$3\times {10}^{56}$	$4\times {10}^{56}$	$3\times {10}^{53}$	$1\times {10}^{54}$	$1\times {10}^{55}$	$3\times {10}^{56}$	$1\times {10}^{43}$	$2\times {10}^{43}$	$1\times {10}^{43}$

Table 4. Table 4: The 250  μ 𝜇 \mu m detection statistics above and below L X = 10 44 subscript 𝐿 X superscript 10 44 L_{\mathrm{X}}=10^{44} erg s -1 ( 10 37 superscript 10 37 10^{37}  W) for the L X = 10 37 − 10 39 subscript 𝐿 X superscript 10 37 superscript 10 39 L_{\mathrm{X}}=10^{37}-10^{39} W— z = 1 − 3 𝑧 1 3 z=1-3 sample, the L X > 10 35 subscript 𝐿 X superscript 10 35 L_{\mathrm{X}}>10^{35}  W ( > 10 42 absent superscript 10 42 >10^{42} erg s -1 ) sample and the whole sample ( Page et al. 2012 ), in addition to the effect on each by including source number 40. p 𝑝 p gives the probability of a detection based upon the detection rate at L X < 10 37 subscript 𝐿 X superscript 10 37 L_{\mathrm{X}}<10^{37} W, with the last two columns giving the binomial probability and significance of this observed number of 250  μ 𝜇 \mu m detections or fewer at L X > 10 37 subscript 𝐿 X superscript 10 37 L_{\mathrm{X}}>10^{37} W.

Sample	W			Source	$n_{\mathrm{total}}$	$L_X\ge {10}^{37}$ W		$P\left(\mathrm{bin}\right)$	$S\left(\mathrm{bin}\right)$
	Non-detections	Detections	$p$	No. 40		Non-detections	Detections
$L_X={10}^{36}-{10}^{38}$ W	34	10	0.227	Yes	66	21	1	0.0257	$2.23\sigma$
				No	65	21	0	$4.485\times {10}^{-3}$	$2.84\sigma$
$L_X>{10}^{35}$ W	122	23	0.159	Yes	176	30	1	0.0325	$2.14\sigma$
				No	175	30	0	$5.620\times {10}^{-3}$	$2.77\sigma$
Whole sample	149	24	0.139	Yes	205	30	1	0.0585	$1.89\sigma$
				No	204	30	0	0.0113	$2.53\sigma$

Equations

$$Q=\frac{10^{\cal C}}{h}\int^{\infty}_{\nu_{0}}\nu^{\alpha-1}\,d{\nu}=\frac{10^{\cal C}}{\alpha h}\Bigg{[}\nu^{\alpha}\Bigg{]}^{\infty}_{\nu_{0}}=\frac{-10^{\cal C}}{\alpha h}\nu_{0}^{\alpha},$$

$$S_{\nu }\propto \frac{{\nu }^{3+\beta }}{e^{h\nu /k{T}_{\mathrm{dust}}}-1},$$

$$I_{\mathrm{FIR}}={\int }_{3.0\times 10^{11}\text{Hz}}^{7.5\times 10^{12}\text{Hz}}\frac{2\pi h{\nu }^{3+\beta }}{c^2}\frac{1}{e^{h\nu /k{T}_{\mathrm{dust}}}-1}d\nu ,$$

$$\begin{array}{r}{Q}_{\star }h=L_{\mathrm{UV}}=4\pi R_{\star }^2{\int }_{{\nu }_0}^{\infty }{I}_{\nu }d\nu ,\\ \text{ where }{I}_{\nu }=\frac{2\pi h{\nu }^3}{c^2}\frac{1}{e^{h\nu /k{T}_{\star }}-1},\end{array}$$

Full text

1 Introduction

Feedback between active galactic nuclei (AGN) and their host galaxies is complex, with the central engine ionising the very material which feeds it (e.g. Di Matteo et al. 2005; Fabian 2012). The ionisation can arise from powerful outflows into the surrounding neutral medium (jet/radio-mode, e.g. Cano-Díaz et al. 2012; Farrah et al. 2012), as well as by ultra-violet (Silk & Rees 1998) and X-ray (Fabian 1999) radiation emanating from the accretion disk surrounding the super-massive black hole (radiative/quasar-mode, Hardcastle et al. 2007; Heckman & Best 2014). Both mechanisms will suppress star formation through ionisation and heating of the neutral gas, this suppression being required by current theoretical models to reproduce the observed properties of active galaxies (e.g. Croton et al. 2006). Observational evidence of this has recently been claimed, where powerful AGN, as evident through their X-ray luminosity, lack $\lambda=250$ $\mu$m far-infrared (FIR) emission over the redshift range $1<z<3$. In the rest-frame this corresponds to wavelengths of $63-125\leavevmode\nobreak\ \mu$m, which trace the dust heated by stars (e.g. Dale & Helou 2002), and so the absence of FIR emission is interpreted as the suppression of star formation in the X-ray luminous sources (Page et al., 2012).

Powerful AGN are also extremely bright in the UV, which is redshifted into the optical band at $z\stackrel{{\scriptstyle>}}{{{}_{\sim}}}3$, allowing quasi-stellar objects (QSOs) to be visible to ground-based telescopes over much of the observable Universe. Observational evidence for high UV luminosities rendering the star-forming material undetectable in the hosts of radio-loud QSOs (quasars) was suggested by the exclusive non-detection of the 21-cm transition of neutral hydrogen (H i) above a “critical” UV luminosity of $L_{\rm UV}\sim 10^{23}$ W Hz*-1*(Curran et al., 2008). H i 21-cm absorption traces the cool, star-forming, component of the gas and a subsequent model of a quasar placed within an exponential gas disk found that this luminosity, which corresponds to $Q\sim 3\times 10^{56}$ ionising ($\lambda\leq 912$ Å) photons s*-1*, is just sufficient to ionise all of the neutral gas in the Milky Way (Curran & Whiting, 2012). Given that this is a large spiral galaxy, complete ionisation of the neutral gas would explain why H i has never yet been detected in sources with these UV luminosities (Curran et al., 2008, 2011, 2013a, 2013b, 2016, 2017a, 2017b, 2019; Allison et al., 2012; Grasha & Darling, 2011; Geréb et al., 2015; Aditya et al., 2016, 2017; Aditya & Kanekar, 2018; Curran & Duchesne, 2018; Grasha et al., 2019). Since H i 21-cm absorption traces the reservoir for star formation, we may also expect the 250 $\mu$m emission to be absent in the sources above the critical UV ionising photon rate, a possibility we investigate here.

2 Analysis

2.1 Source matching

The Herschel Multi-tiered Extragalactic Survey (HerMES, Oliver et al. 2012), utilised by Page et al. (2012), covers a $\sim 340$ deg2 field, operating at wavelengths of $\lambda=250$, 350 and 500 $\mu$m (Spectral and Photometric Imaging Receiver, SPIRE) and 100 and 160 $\mu$m (Photodetector Array Camera and Spectrometer, PACS). We constructed a subset of extragalactic sources within the SPIRE dataset using the StarFinder source-finder software (Diolaiti et al., 2000), with cross-identification being performed between the single-band catalogues (Roseboom et al., 2010), resulting in a merged catalogue of 340 968 sources. We then searched the NASA/IPAC Extragalactic Database (NED) for sources within 6 arcsec of the SPIRE positions (as per Page et al., see Appendix A), which were cross-matched according to the minimum separation between sources, while ensuring no duplicate matches. After filtering out SPIRE sources without a counterpart nor a redshift, there were 62 073 sources remaining. Of these, 14 457 have spectroscopic redshifts (Fig. 1).

2.2 Photometry fitting

2.2.1 Ultra-violet

In order to obtain the UV luminosities, we queried NED, the Wide-Field Infrared Survey Explorer (WISE, Wright et al. 2010), the Two Micron All Sky Survey (2MASS, Skrutskie et al. 2006) and the Galaxy Evolution Explorer (GALEX data release GR6/7)111http://galex.stsci.edu/GR6/#mission databases. Each flux density measurement, $S_{\nu}$, 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.

The ionising photon rate is defined as $Q\equiv\int^{\infty}_{\nu_{0}}(L_{\nu}/h\nu)d{\nu}$ (Osterbrock, 1989), where $\nu_{0}=3.29\times 10^{15}$ Hz for the ionisation of neutral hydrogen. For the fitting, we require at least three $\nu\stackrel{{\scriptstyle>}}{{{}_{\sim}}}10^{15}$ Hz photometry points to which we fit a power-law, giving $\log_{10}L_{\nu}=\alpha\log_{10}\nu+{\cal C}\Rightarrow L_{\nu}=10^{\cal C}\nu^{\alpha}$, where $\alpha$ is the spectral index and ${\cal C}$ the intercept. This gives the ionising photon rate as

[TABLE]

where $\alpha<0$.

2.2.2 Far-infrared

Since we were also interested in the effect of the UV continuum on the dust temperature, we added the photometric data of the three SPIRE bands to that above, where we only included the data detected at $S_{\nu}>3\sigma_{\rm conf}$, where $\sigma_{\rm conf}=6$ mJy is the SPIRE confusion limit (Nguyen et al., 2010; Smith et al., 2012). For $T_{\rm dust}\stackrel{{\scriptstyle<}}{{{}_{\sim}}}h\nu/k$ (Younger et al., 2009), where $h$ is the Planck constant and $k$ the Boltzmann constant, we fitted a modified blackbody (Fig. 2) spectrum of the form

[TABLE]

where $\beta$ is the spectral emissivity index (e.g. Casey 2012).

For this, we used a non-linear least-squares fitting of both $\beta$ and $T_{\rm dust}$ simultaneously, giving the distribution shown in Fig. 3.

This yields a mean dust temperature of $\left<T_{\rm dust}\right>=31$ K and a mean spectral emissivity index of $\left<\beta\right>=0.99$. This is considerably lower than the canonical $\beta=1.5$ (Blain et al. 2003; Younger et al. 2009 and references therein), although this was used as the initial estimate. Forcing $\beta=1.5$ could not satisfactorily fit the data, although we do note that $\beta\approx 1.0$ may not be unexpected (Hildebrand, 1983).

3 Effects of the ultra-violet continuum

3.1 Critical ionising photon rate

As stated in the introduction, our main motivation was to test whether the critical ionising photon rate found for H i 21-cm absorption also applied to FIR emission, where an apparent critical X-ray luminosity may suggest the suppression of star formation. The highest ionising photon rate at which 21-cm absorption has been detected is $Q=2.5\times 10^{56}$ s*-1*, above which there are 87 non-detections, which is significant at $5.66\sigma$ (Curran et al. 2019). Since 21-cm absorption traces the cool, neutral gas that fuels the star formation, we may therefore expect a similar critical rate if the FIR emission is dominated primarily by stellar activity.

Of the sample, there is sufficient UV photometry for 3315 sources, of which 1347 are considered 250 $\mu$m detections (where $S_{250\mu{\rm m}}>18$ mJy, Sect. 2.2.2), giving a detection rate of 40.6%.

As seen from Fig. 4, unlike for 21-cm absorption, the detections and non-detections share the same range of ionising photon rates, with 250 $\mu$m emission being detected up to $Q=8.9\times 10^{57}$ s*-1*. This is considerably higher than that observed for H i 21-cm absorption and the model prediction that all of the neutral gas in a large galaxy is ionised at $Q\stackrel{{\scriptstyle>}}{{{}_{\sim}}}3\times 10^{56}$ s*-1* (Curran & Whiting, 2012). Thus, unlike the X-ray emission (Page et al. 2012, but see Appendix A), we see no distinction between the distribution of FIR detections and non-detections at high ionising photon rates.

3.2 Dust heating

Interstellar dust has an absorption cross-section which peaks at ultra-violet wavelengths, thus making the re-emitted far-infrared radiation a sensitive tracer of dust heating. From the modified blackbody fits to the FIR photometry, we can also investigate heating of the dust by the ultra-violet emission. Of the 250 $\mu$m detections, there are 404 sources to which we could fit a modified blackbody and which have sufficient UV photometry (e.g. Fig. 2). These exhibit a strong correlation between the dust temperature and the ionising photon rate (Fig. 5),

with a generalised non-parametric Kendall-tau test giving a probability of $P(\tau)=5.28\times 10^{-12}$ for the $T_{\rm dust}-Q$ correlation arising by chance, which is significant at $S(\tau)=6.90\sigma$ assuming Gaussian statistics. However, due to the flux limitation introduced by the SPIRE confusion limit, there will be a bias towards the most FIR luminous, and thus most UV luminous, sources with increasing redshift. Given that for a (modified) blackbody, the temperature and intensity are not independent (Sect. 2.2.2), this will also lead to an apparent increase in the dust temperature.

In order to correct for this, we obtain the integrated intensity over 40–1000 $\mu$m (Yang et al. 2007, cf. Fig.2) from

[TABLE]

from which a specific intensity ($I_{250\,\mu{\rm m}}$) is compared to the corresponding specific luminosity ($L_{250\,\mu{\rm m}}$, e.g. Fig. 2) in order to provide the scaling to $L_{\rm FIR}$ (Fig. 6).

From this, we see that many of the luminosities are in excess of $L_{\rm FIR}\stackrel{{\scriptstyle>}}{{{}_{\sim}}}10^{12}$ L⊙, qualifying the sources as Ultra-Luminous Infrared Galaxies (ULIRGs). Normalising the ionising photon rate by the FIR luminosity (Fig. 7),

the correlation disappears. This and Fig. 6 therefore indicate that the increase in dust temperature with redshift222For example, $T_{\rm dust}=19-25$ K in near-by galaxies (Galametz et al., 2012), $T_{\rm dust}=31-36$ K in intermediate redshift starburst galaxies and AGN (Kovács et al. 2010; Magdis et al. 2013) and $T_{\rm dust}\approx 40$ K in intermediate and high redshift ULIRGs (Yang et al. 2007 and Younger et al. 2009, respectively)., is due to the flux limitation introducing a bias towards the most FIR (and UV) luminous sources.

3.3 Stellar versus AGN activity

The FIR emission is believed to be dominated by stellar heating (Rieke & Lebofsky 1979 and references therein), whereas the mid-infrared (MIR, $\lambda=24$ $\mu$m) emission can arise in photon dominated/Hii regions (e.g. Galliano et al. 2018), as well as from AGN heated dust in the circumnuclear torus (Hatziminaoglou et al., 2010).333Invoked by unified schemes of AGN (e.g. Antonucci 1993; Urry & Padovani 1995). However, the absence of the same critical ionising photon rate, which completely ionises the neutral atomic gas, and thus suppresses the star formation, at $Q\stackrel{{\scriptstyle>}}{{{}_{\sim}}}3\times 10^{56}$ s*-1* (Curran & Whiting, 2012), may suggest that much of the FIR emission also arises from dust heated by the AGN (e.g. de Grijp et al. 1985; Curran et al. 2001; Nardini et al. 2010).

For a blackbody with $T=5770$ K and a radius of $R_{\odot}=696\times 10^{8}$ m, the ionising photon rate of the Sun is $Q_{\odot}=7.9\times 10^{35}$ s*-1*. Thus, UV luminosities corresponding to $Q\stackrel{{\scriptstyle>}}{{{}_{\sim}}}10^{57}$ s*-1* (Fig. 4) would require $\stackrel{{\scriptstyle>}}{{{}_{\sim}}}10^{21}$ solar mass stars, and so, while an older (lower mass) population of stars could contribute significantly to the FIR luminosity (Calzetti et al., 2010; Groves et al., 2012; Li et al., 2013), these cannot account for the UV luminosity. In order to explore the stellar masses required, the ionising photon rate of a star is obtained from the integrated intensity, $I_{\nu}$, via

[TABLE]

$\nu_{0}=3.29\times 10^{15}$ Hz corresponds to $\lambda=912$ Å, where the hydrogen is ionised, and $T_{\star}$ is the surface temperature of the star. To obtain the luminosity we require a value for the surface area of the star ($4\pi R_{\star}^{2}$), which we estimate from the comparison of the bolometric intensity, $I=\int^{\infty}_{0}I_{\nu}d{\nu}$, with the bolometric luminosity obtained from the main sequence using $\log_{10}L_{\star}=6.50\log_{10}T_{\star}-24.37$. Examples of the derived properties are given in Table 1.

In order to obtain the total ionising luminosity, we integrate both the initial mass function (IMF or $\xi$) and $Q_{\star}$ over the whole mass range, which we normalise to the approximate stellar mass of the Milky Way (Fig. 8).

The total stellar mass is given by $M_{\rm total}=\int_{M_{1}}^{M_{2}}M\xi dM$ and is dominated by the low mass stars, whereas the total ionising photon rate is dominated by the massive stars (cf. Table 1). If we truncate the IMF at $M_{\star}=25$ M⊙ ($T_{\star}\approx 30\,000$ K, $t_{\rm MS}\approx 3\times 10^{6}$ yr) for the maximum possible mass, we obtain $Q_{\rm total}=3\times 10^{56}$ s*-1*, whereas setting this to $M_{\star}=100$ M⊙ ($T_{\star}\approx 65\,000$ K, $t_{\rm MS}\approx 1\times 10^{5}$ yr), gives $Q_{\rm total}=7\times 10^{57}$ s*-1*.

Thus, the total ionising photon rate from the stellar population within the source is very much dependent upon the upper end of the stellar mass distribution. Assuming no significant AGN contribution, the highest FIR luminosities of the sample indicate star formation rates of $\sim 10^{4}$ M⊙ yr*-1* (e.g. Kennicutt 1998), which we can use to constrain the upper mass end. In this instance, integrating over all star formation rates444The specific star formation rate at a given mass is estimated from SFR $=N_{\rm stars}M/t_{\rm MS}$. For example, from Table 1, we expect $8\times 10^{8}$ stars of $\approx 10$ M⊙, which have a lifetime of $t_{\rm MS}\approx 3\times 10^{7}$ yr. This therefore requires SFR$\,\approx 8\times 10^{8}\times 10/3\times 10^{7}\approx 300$ M⊙ yr*-1*  to maintain the observed luminosity., a total of SFR${}_{\rm total}\,=1\times 10^{4}$ M⊙ yr*-1* is reached for a maximum stellar mass of $M_{\star}\approx 40$ M⊙, which gives $Q_{\rm total}=9\times 10^{56}$ s*-1*. However, even at relatively large look-back times, e.g. $\sim 10$ Gyr ($z\sim 2$), this implies a total stellar mass of $\sim 10^{13}$ M⊙, for a constant star formation rate over these first $\sim 3$ Gyr. In addition to the total stellar mass, a steeper IMF would affect the stellar contribution to $Q_{\rm total}$, for instance, $\alpha=-2.65$ for $1<{\rm M}_{\odot}\ <10$ stars (Bastian et al., 2010), $\alpha=-5$ for $25<{\rm M}_{\odot}\ <120$ stars in the Magellanic Clouds (Massey, 2002) or $\alpha=-2.45\text{ to }-2.85$ in external galaxies (Úbeda et al., 2007; Bruzzese et al., 2015; Weisz et al., 2015). We therefore show the total ionising photon for a range of total masses and IMF indices in Table 2.

Since the total stellar mass is dominated by the more numerous, least massive, cooler stars, ionising photon rates above the critical 21-cm value favour $M_{\rm total}\stackrel{{\scriptstyle<}}{{{}_{\sim}}}4\times 10^{11}$ M⊙, although it should be borne in mind that SFR${}_{\rm total}=1\times 10^{4}$ M⊙ yr*-1* is most likely an upper limit, due to an AGN contribution to the FIR luminosity (Morić et al., 2010; Nardini et al., 2010). For example, for a 50% contribution, the critical ionising photon rate is reached by just two of the canonical Galactic models ($M_{\rm total}=4\times 10^{11}$ M⊙, Table 3).

This still begs the question of how the continual star formation is fuelled, although the stellar contribution to $Q_{\rm total}$ will decrease further with an increasing AGN contribution. Furthermore, we have not accounted for shielding by dust nor how much this attenuates the observed UV flux. Also, while the critical $Q_{\rm total}=3\times 10^{56}$ s*-1* is sufficient to ionise all of the neutral atomic gas in the Milky Way (where $n\stackrel{{\scriptstyle<}}{{{}_{\sim}}}10$ $\hbox{{\rm cm}}^{-3}$, Kalberla & Kerp 2009), since $Q\propto n^{2}$ (Osterbrock, 1989), denser gas (e.g. in molecular clouds where $n\stackrel{{\scriptstyle>}}{{{}_{\sim}}}10^{3}$ $\hbox{{\rm cm}}^{-3}$) requires much higher ionising photon rates (Roos et al., 2015). Simulations of a stellar population distributed within a galactic disk would be required in order to determine whether a distribution of UV luminous point sources would result in a Strömgren sphere of “infinite” radius, as is the case for a single centrally located $Q\stackrel{{\scriptstyle>}}{{{}_{\sim}}}10^{56}$ s*-1* ionising source (Curran & Whiting, 2012).

Lastly, as Fig. 6 shows, many of the highest FIR luminous sources are classified as QSOs, and so known to host a powerful AGN. Although, forming only a small fraction (5%) of the sources for which the FIR luminosity can be derived (Fig. 9),

we see that the mean luminosity for the QSOs is an order of magnitude higher than for the galaxies (as is also the case for the UV, Fig. 5), lending support to the argument of an AGN contribution to the FIR emission in the most luminous sources. There does remain, however, a number of galaxies with these same luminosities.

4 Conclusions

For the past decade evidence has been building of a critical photo-ionisation rate in the ultra-violet band, above which all of the gas in the host galaxy is ionised. All of the observational evidence comes from searches of H i 21-cm absorption in redshifted radio sources, which has never been detected above rates of $Q=2.5\times 10^{56}$ s*-1* ($L_{\rm UV}\stackrel{{\scriptstyle>}}{{{}_{\sim}}}10^{23}$ W Hz*-1*, Curran et al. 2008, 2019). This observational result is supported by a model of a quasar placed within an exponential gas disk, for which $Q\stackrel{{\scriptstyle>}}{{{}_{\sim}}}3\times 10^{56}$ s*-1* is sufficient to ionise all of the neutral atomic gas in a large spiral (Curran & Whiting, 2012). However, current 21-cm absorption searches are insensitive to column densities of $N_{\rm HI}\ll 10^{20}$ atoms $\hbox{{\rm cm}}^{-2}$, and so the observations cannot rule out that the gas is merely heated or partially ionised to below the detection limit. Furthermore, the quasars with $L_{\rm UV}\stackrel{{\scriptstyle>}}{{{}_{\sim}}}10^{23}$ W Hz*-1*, tend to be type-1 objects, implying a direct view to the naked AGN, whereas at $L_{\rm UV}\stackrel{{\scriptstyle<}}{{{}_{\sim}}}10^{23}$ W Hz*-1*, both type-1 (unobscured) and type-2 (obscured AGN) objects exhibit a 50% detection rate for 21-cm absorption (Curran & Whiting, 2010). This would suggest that the non-detection of H i above the critical UV luminosity is primarily an orientation effect, although it would mean that the low luminosity type-1 AGN are somehow different from their high luminosity counterparts.

Thus, it is of great interest to confirm the possibility of a critical ionising luminosity in another band. Page et al. (2012) report a critical X-ray luminosity ($L_{\mathrm{X}}\sim 10^{37}$ W) above which 250 $\mu$m emission is not detected in $1<z<3$ SPIRE sources, leading to the conclusion that the star formation is suppressed in these objects. Since 21-cm absorption traces the reservoir for star formation, if the FIR emission is due mainly to stellar heated dust, we may also expect a critical UV luminosity above which the 250 $\mu$m emission is suppressed. By matching the SPIRE sources to their NED counterparts, we obtain 14 457 extragalactic objects with spectroscopic redshifts. Of these, there is sufficient UV photometry to determine the ionising photon rate for 3315, and of the FIR detections (i.e. detected above the SPIRE confusion limit of $3\sigma_{\rm conf}=18$ mJy) 2013 sources for which a modified blackbody could be fit, yielding the dust temperature. From these, we find:

• •

A mean dust temperature of $\left<T_{\rm dust}\right>=31.4\pm 0.2$ K and a mean spectral emissivity index of $\left<\beta\right>=0.991\pm 0.001$.

• •

No apparent critical ionising photon rate, with 250 $\mu$m emission being detected up to $Q=8.9\times 10^{57}$ s*-1*. If the 21-cm results and model are reliable, this suggests that the FIR emission does not exclusively trace the stellar heated dust, implying a significant contribution from an AGN.

• •

A strong correlation between the dust temperature and the ionising photon rate, which we suspect is driven mainly by the Malmquist bias. Normalising the ionising photon rate by the total FIR luminosity, causes the correlation to disappear. Since the number of luminous AGN is expected to increase with redshift, this may also suggest that the low temperature (FIR) emission can arise from AGN heating of the dust.

By calculating the ionising photon rate expected for each stellar mass, for a total star formation rate of SFR${}_{\rm total}=1\times 10^{4}$ M⊙ yr*-1*, the observed ionising photon rates ($Q\sim 10^{57}$ s*-1*) in the most luminous of the SPIRE sources can be reproduced by several initial mass functions, which give a sufficient population of massive stars. Exceeding the critical value above which all of the neutral atomic gas is believed to be ionised, this raises the question of what fuels the star formation. However, this is very much dictated by the choice of SFRtotal and if $<10^{4}$ M⊙ yr*-1*, due to a large AGN contribution to the FIR luminosity, lower values of $Q_{\rm total}$ are obtained. In order to address this, a valid IMF for such highly luminous sources is required to determine whether the stellar population can account for the observed ionising photon rates. If the case, in the model of Curran & Whiting (2012) the single large ionising source should be replaced with the putative stellar distribution embedded in the exponential gas disk, in order to determine whether such a population could completely ionise the gas.

Acknowledgements

We wish to thank the anonymous referee for their prompt and helpful comments. SWD acknowledges receipt of a Victoria Doctoral Scholarship and an Australian Government Research Training Program scholarship administered through Curtin University. This research has made use of Astropy, a community-developed core Python package for Astronomy (Astropy Collaboration, 2013), 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.

Appendix A UV photo-ionisation of the Chandra Deep Field North sources

The original aim of the project was to test the Page et al. (2012) sample for a similar absence of 250 $\mu$m emission above the critical UV luminosity where H i 21-cm absorption is not detected. As an initial step we reproduced the method of Page et al. (2012), cross-matching the Chandra Deep Field North (CDF-N, Alexander et al. 2003) with spectroscopic redshifts, obtained from Barger et al. (2008); Trouille et al. (2008), as well as the references listed in table S2 of Page et al.. For each source for which we could obtain a redshift, we calculated the k-corrected X-ray luminosity, $L_{\mathrm{X}}$, from the flux density, assuming $S_{\nu}\propto\nu^{-0.9}$. We then cross-matched these with the sources within 6 arc-sec of those searched by HerMES. These matches are unique, i.e., no sources within SPIRE are matched to multiple CDF-N AGN.

In Fig. 10, we show the resulting 2–8 keV X-ray luminosity versus redshift for the 250 $\mu$m searched sources.

This is identical to the distribution of Page et al. (2012), above the $L_{\mathrm{X}}<10^{42}$erg s*-1* ($<10^{35}$ W) cut, apart from an additional source at $z=1.3709$ (source number 40 in Trouille et al. 2008), which has $L_{\mathrm{X}}=1.6\times 10^{37}$ W and $S_{\rm FIR}=40.1$ mJy.555This source, SDSS J123553.13+621037.3, has a $0.64$ arc-sec offset from the optical offset and a $5.9$ arc-sec offset from the 250 $\mu$m source and so just falls within the 6 arc-sec search radius. Examining the statistics, below the $L_{\mathrm{X}}=10^{37}$ W cut-off, there are 10 FIR detections and 34 non-detections, giving a detection probability of $p=0.227$. Applying this to the $L_{\mathrm{X}}>10^{37}$ W sample, the binomial probability of obtaining zero 250 $\mu$m detections in 21 sources is $P({\rm bin})=4.485\times 10^{-3}$. This is significant at $S({\rm bin})=2.84\sigma$ and consistent with Page et al. finding a $>99\%$ ($>2.58\sigma$) significance from a single-tail Fisher’s exact test. This significance does, however, decrease when source number 40 is included or the whole sample tested (Table 4).

[FIGURE:]

Thus, the absence of 250 $\mu$m emission in luminous X-ray sources is not particularly significant, especially compared to $S({\rm bin})=5.66\sigma$ for the absence of 21-cm absorption in the UV luminous sources (Curran et al., 2019).

Following the SED fitting procedure described in Sect. 2.2, there is sufficient photometry to obtain the ionising photon rate for 103 of the CDF-N sources (Fig. 11).

The highest ionising photon rate at which 250 $\mu$m is detected is $Q=4.4\times 10^{55}$ s*-1*, which is consistent with the value above which H i 21-cm absorption remains undetected (Sect. 1). However, the $p=0.134$ detection rate below this gives a binomial probability of $P({\rm bin})=0.137$ for zero detections out of the 14 sources with $Q>4.4\times 10^{55}$ s*-1*, which is only significant at $S({\rm bin})=1.51\sigma$. Moreover, when tested over a larger sample no critical rate is apparent (Sect. 3.1). Furthermore, extending the Page et al. sample, using the Chandra Deep Field South (CDF-S, Xue et al. 2011) and COSMOS fields (Elvis et al., 2009), finds no evidence for suppressed star formation at high X-ray luminosities (Harrison et al., 2012).