Large 21 cm signals from AGN-dominated reionization

TL;DR

This paper predicts that AGN-dominated reionization significantly amplifies 21 cm brightness temperature fluctuations, making them detectable by current and future experiments, and offers a new perspective on the role of AGN in reionization.

Contribution

It introduces high-dynamic-range simulations of AGN-driven reionization, linking observed galaxy relations to 21 cm signals and assessing their observability.

Findings

AGN reionization increases 21 cm variance up to tenfold.

Enhanced large-scale 21 cm power due to AGN clustering.

AGN reionization detectable by LOFAR, HERA, SKA1.

Abstract

We present here predictions for the spatial distribution of 21 cm brightness temperature fluctuations from high-dynamic-range simulations for AGN-dominated reionization histories that have been tested against available Lyman-alpha and CMB data. We model AGN by extrapolating the observed M-sigma relation to high redshifts and assign them ionizing emissivities consistent with recent UV luminosity function measurements. We assess the observability of the predicted spatial 21 cm fluctuations by ongoing and upcoming experiments in the late stages of reionization in the limit in which the hydrogen 21 cm spin temperature is significantly larger than the CMB temperature. Our AGN-dominated reionization histories increase the variance of the 21 cm emission by a factor of up to ten compared to similar reionization histories dominated by faint galaxies, to values close to 100 mK^2 at scales accessible to experiments (k < 1 h/cMpc). This is lower than the sensitivity claimed to have been already reached by ongoing experiments by only a factor of about two or less. When reionization is dominated by AGN, the 21 cm power spectrum is enhanced on all scales due to the enhanced bias of the clustering of the more massive haloes and the peak in the large scale 21 cm power is strongly enhanced and moved to larger scales due to bigger characteristic bubble sizes. AGN dominated reionization should be easily detectable by LOFAR (and later HERA and SKA1) at their design sensitivity, assuming successful foreground subtraction and instrument calibration. Conversely, these could become the first non-trivial reionization scenarios to be ruled out by 21 cm experiments, thereby constraining the contribution of AGN to reionization.

Figures

Equations

$${\zeta }_{\mathrm{eff}}f(\mathbf{x},R)\ge 1$$

$$f\propto {\rho }_m(R{)}^{-1}{\int }_{M_{\min }}^{\infty }dM{\frac{dN}{dM}|}_R{N}_{\gamma }(M),$$

$$\frac{d{Q}_V}{dt}=\frac{{\dot{n}}_{\mathrm{ion}}}{n_{\mathrm{H}}}-\frac{Q_V}{t_{\mathrm{rec}}}$$

$${\dot{n}}_{\mathrm{ion}}=\frac{{\Gamma }_{\mathrm{HI}}{Q}_V}{(1+z{)}^2{\sigma }_{\mathrm{H}}{\lambda }_{\mathrm{mfp}}}\left(\frac{{\alpha }_b+3}{{\alpha }_s}\right),$$

$$\begin{gathered} v_c=23.4\mathrm{km}{\mathrm{s}}^{-1}{\left(\frac{M}{10^8{h}^{-1}{M}_{\odot }}\right)}^{1/3} \\ \times {\left[\frac{{\Omega }_m}{{\Omega }_m^z}\frac{{\Delta }_c}{18{\pi }^2}\right]}^{1/6}{\left(\frac{1+z}{10}\right)}^{1/2}, \end{gathered}$$

$${\Omega }_m^z=\frac{{\Omega }_m(1+z{)}^3}{{\Omega }_m(1+z{)}^3+{\Omega }_{\Lambda }+{\Omega }_k(1+z{)}^2},$$

$${\Delta }_c=18{\pi }^2+82d-39d^2,$$

$$v_c\approx 314{\left[\frac{\sigma }{208\mathrm{km}{\mathrm{s}}^{-1}}\right]}^{0.84}\mathrm{km}{\mathrm{s}}^{-1}.$$

$$\frac{\sigma }{208\mathrm{km}{\mathrm{s}}^{-1}}\approx {\left[\frac{M_{\mathrm{bh}}}{1.56\times 10^8{\mathrm{M}}_{\odot }}\right]}^{1/4.02},$$

$$\frac{M_{\mathrm{bh}}}{10^8{\mathrm{M}}_{\odot }}=0.12{\left(\frac{M_{\mathrm{halo}}}{10^{12}{\mathrm{M}}_{\odot }}\right)}^{1.6}{\left[\frac{{\Omega }_m}{{\Omega }_m^z}\frac{{\Delta }_c}{18{\pi }^2}\right]}^{0.8}(1+z{)}^{2.4}.$$

$$r\equiv \frac{{\int }_{M_q}^{M_{\max }}dM{N}_{\gamma }^{\mathrm{agn}}(M)dN/dM}{{\int }_{M_{\min }}^{M_q}dM{N}_{\gamma }^{\mathrm{gal}}(M)dN/dM},$$

$$T_b(\mathbf{x})={\overline{T}}_b{x}_{\mathrm{HI}}(\mathbf{x})\Delta (\mathbf{x}),$$

$${\Delta }_{21}^2(k)=\frac{k^3}{2{\pi }^2}\cdot \frac{⟨{\widetilde{T_b}}^2(k)⟩}{V_{\mathrm{box}}},$$

$${\Delta }_{21}^2(k)=b_{\delta }{\Delta }_{\delta }^2(k)+b_x{\Delta }_{x_{\mathrm{HI}}}^2(k)+\text{cross-correlations}$$

Full text

††pubyear: 2016††pagerange: Large 21 cm signals from AGN-dominated reionization–A

1 Introduction

Hydrogen reionization is generally thought to occur at redshifts $z\sim 6$–$15$ by Lyman continuum photons that are widely believed to be produced by young stars in low-mass galaxies (Mitra et al., 2015). However, the idea that active galactic nuclei (AGN) could have been the dominant source of ionizing radiation during the epoch of reionization has recently gained traction again (Giallongo et al., 2015; Madau & Haardt, 2015; Chardin et al., 2015; Khaire et al., 2016; Chardin et al., 2017; Mitra et al., 2016; D’Aloisio et al., 2016).

The resurgence of AGN as credible source of ionising photons at high redshift is due to a number of recent developments. First, the claimed discovery of 19 low-luminosity ($M_{1450}>-22.6$) AGN between redshifts $z=4.1$ and $6.3$ by Giallongo et al. (2015) using a novel X-ray/NIR selection criterion may suggest that the faint end of the quasar UV luminosity function is steeper at these redshifts than previously thought (Hopkins et al., 2007; Haardt & Madau, 2012). Using far-UV spectral slopes from composite spectra of low-redshift quasars, and assuming a Lyman continuum escape fraction of 100%, Giallongo et al. (2015) argued that AGN brighter than $M_{1450}=-18$ can potentially produce all of the metagalactic hydrogen photoionization rate inferred from the Ly$\alpha$ forest at $4<z<6$. Second, Becker et al. (2015) reported a large scatter in the Ly$\alpha$ opacity between different sightlines close to redshift $z=6$. Chardin et al. (2015) showed that these opacity fluctuations extend to substantially larger scales ($\gtrsim 50\,h^{-1}$cMpc) than expected in reionization histories dominated by low-luminosity galaxies (see also Davies & Furlanetto 2016). Chardin et al. (2017) further demonstrated that opacity fluctuations on such large scales arise naturally if there is a significant contribution ($\gtrsim 50\%$) of AGN to the ionising emissivity at the redshift of the observed opacity fluctuations ($z\sim 5.5$–$6$) as would be expected for a QSO luminosity that is consistent with the measurements of Giallongo et al. (2015). Third, measurements of the Lyman continuum escape fraction from high-redshift galaxies are still elusive. Although high-redshift galaxies as faint as rest-frame UV magnitude $M_{\mathrm{UV}}=-12.5$ ($L\sim 10^{-3}L^{*}$) at $z=6$ (Livermore et al., 2017) and redshifts as high as $z=11.1$ (Oesch et al., 2016) have now been reported, the escape of Lyman continuum photons has been detected in only a small number of comparatively bright ($L>0.5L^{*}$) low-redshift ($z<4$) galaxies. In these galaxies, the escape fraction is typically found to be 2–20% (Vanzella et al., 2010; Boutsia et al., 2011; Siana et al., 2015; Mostardi et al., 2015; Grazian et al., 2016; Japelj et al., 2017; Micheva et al., 2017b) but reionization would require escape fraction of about 20% in galaxies down to $M_{\mathrm{UV}}=-13$ (Finkelstein, 2016; Robertson et al., 2015; Khaire et al., 2016). Finally, incidence of high-redshift AGN is also consistent with the shallow bright-end slopes of the high-redshift ($z\sim 7$) UV luminosity function of galaxies relative to a Schechter-function representation (Bowler et al., 2012, 2014; Bradley et al., 2014; Bowler et al., 2015) and the hard spectra of these bright galaxies (Stark et al., 2015a, b, 2017).

It is thus pertinent to ask what a significant contribution of AGN to the ionising emissivity during reionization implies for the search for the 21 cm signal from the epoch of reionization. In this paper, we therefore present predictions for the 21 cm power spectrum from redshifts $z=7$–$10$ in models of reionization in which the hydrogen-ionizing emissivity is dominated by AGN and compare them to galaxy-dominated models. We use the excursion set method to derive the large-scale ionization field in high-dynamic-range cosmological simulations, using the calibration scheme developed by Choudhury et al. (2015) to incorporate 21 cm signal from self-shielded high density regions (Kulkarni et al., 2016). AGN are modelled by placing black holes in haloes by assuming the $z=0$ Mbh–$\sigma$ relation between the black hole mass and the bulge stellar velocity dispersion (Kulkarni & Loeb, 2012; Ferrarese, 2002). We describe our simulations and the AGN model in Section 2. Section 3 presents our predictions for the 21 cm signal and its observability in ongoing and future experiments. We discuss the case for and against reionization by AGN in Section 4, and end by summarising our results in Section 5. Our $\Lambda$CDM cosmological model has $\Omega_{\mathrm{b}}=0.0482$, $\Omega_{\mathrm{m}}=0.308$, $\Omega_{\Lambda}=0.692$, $h=0.678$, $n=0.961$, $\sigma_{8}=0.829$, and $Y_{\mathrm{He}}=0.24$ (Planck Collaboration, 2014).

2 Models of AGN-dominated reionization

Our 21 cm predictions are based on cosmological hydrodynamical simulations that are part of the Sherwood simulation suite (nottingham.ac.uk/astronomy/sherwood; Bolton et al. 2017). Sources of ionizing radiation are placed in haloes identified in the simulation, and an ionization field is obtained using the well-known excursion set approach. This ionization field is then calibrated to a given reionization history, while accounting for residual neutral gas in high-density areas within ionized regions. The reionization histories used for calibration are chosen carefully such that they are consistent with Ly$\alpha$ and CMB data as described in Choudhury et al. (2015). In this manner, our models self-consistently predict, at high resolution, the large-scale distribution of neutral hydrogen for reionization histories consistent with constraints during the late stages of reionization.

Kulkarni et al. (2016) provide more details of our implementation of the excursion set method of deriving the large-scale ionization field and its subsequent calibration to Ly$\alpha$ and CMB data. We recapitulate an outline of the method here to mention important parameter values and set up notation. We obtain the gas density field from the underlying cosmological simulation by projecting the relevant particles onto a grid using the cloud-in-cell (CIC) scheme. From the gas density field, we derive the ionization field corresponding to a distribution of sources with specific ionizing emissivities. Denoting the total number of ionizing photons produced by a halo of mass $M$ as $N_{\gamma}(M)$, a grid cell at position $\mathbf{x}$ is ionized if the condition

[TABLE]

is satisfied in a spherical region centred on the cell for some radius $R$ (Furlanetto et al., 2004; Choudhury et al., 2009; Mesinger et al., 2011). Here,

[TABLE]

where $\rho_{m}(R)$ is the average matter density and $dN/dM|_{R}$ is the halo mass function in the sphere of radius $R$ and $M_{\mathrm{min}}$ is the minimum mass of halos that emit Lyman continuum photons. The quantity $f$ is proportional to the collapsed fraction $f_{\mathrm{coll}}$ into haloes of mass $M>M_{\mathrm{min}}$ if $N_{\gamma}(M)\propto M$. The parameter $\zeta_{\mathrm{eff}}$ here is the effective ionizing efficiency, which corresponds to the number of photons in the IGM per hydrogen atom in stars, compensated for the number of hydrogen recombinations in the IGM. It is the only parameter that determines the large scale ionization field in this approach. Cells that do not satisfy the criterion in Equation (1) are neutral. We denote the ionized volume fraction in a cell $i$ as $Q_{i}$. The total volume-weighted ionized fraction is then $Q_{V}\equiv\sum_{i}Q_{i}/n_{\mathrm{cell}}$, where $n_{\mathrm{cell}}$ is the total number of grid cells.

We calibrate the large-scale ionization field obtained by the above procedure to a chosen reionization history, incorporating inhomogeneities within ionized regions, using the method developed by Choudhury et al. (2015). We begin by fixing a reionization model, which is specified by the redshift evolution of the volume-weighted ionization fraction $Q_{V}$. Our simulated ionization field is calibrated to the given reionization model in two steps. In the first step, the effective ionization parameter $\zeta_{\mathrm{eff}}$ is tuned to get the volume-weighted ionization fraction predicted by the reionization history at the corresponding redshift. In the second step, we obtain the photoionization rate distribution within the ionized regions by solving the globally averaged radiative transfer equation

[TABLE]

for the photoionization rate $\Gamma_{\mathrm{HI}}$. Here, $\dot{n}_{\mathrm{ion}}$ is the average comoving photon emissivity, $n_{\mathrm{H}}$ is the average hydrogen density, and $t_{\mathrm{rec}}$ is the recombination time-scale. We implement self-shielding in ionized regions using the fitting function obtained by Rahmati et al. (2013) from radiative transfer simulations.111This self-shielding is insensitive to the presence of hard ionizing photons, such as those from AGN, due to diminished ionization cross-section (Rahmati et al., 2013). This creates cells with excess neutral hydrogen fraction, thereby reducing the mean free path of Lyman continuum photons. The mean free path $\lambda_{\mathrm{mfp}}$ enters Equation (3) via $\dot{n}_{\mathrm{ion}}$, which is related to the photoionization rate by (Kuhlen & Faucher-Giguère, 2012; Becker & Bolton, 2013)

[TABLE]

where $\sigma_{\mathrm{H}}$ is the hydrogen photoionization cross-section, $\alpha_{s}$ is the spectral index of the ionizing sources at $\lambda<912$ Å and $\alpha_{b}$ is the spectral index of the ionizing “background” within ionized regions.

The Sherwood simulation suite has been run using the energy- and entropy-conserving TreePM smoothed particle hydrodynamical (SPH) code p-gadget-3, which is an updated version of the gadget-2 code (Springel et al., 2001; Springel, 2005). Our base simulation was performed in a periodic cube of length 160 $h^{-1}$cMpc on a side. The number of gas and dark matter particles were both initially $2048^{3}$. This corresponds to a dark matter particle mass of $M_{\mathrm{dm}}=3.44\times 10^{7}$ $h^{-1}$M⊙ and gas particle mass of $M_{\mathrm{gas}}=6.38\times 10^{6}$ $h^{-1}$M⊙. In the redshift range relevant to this paper, we use snapshots of the particle positions at $z=10,8,$ and $7$. Haloes are identified using the friends-of-friends algorithm. At $z=7$, the minimum halo mass in our simulation is $2.3\times 10^{8}$ $h^{-1}$M⊙; the maximum halo mass is $3.1\times 10^{12}$ $h^{-1}$M⊙.

To model ionizing emission by AGN, we assume that in high-mass haloes that host luminous AGN, the total number of photons $N_{\gamma}$ is proportional to the black hole mass $M_{\rm bh}$. In order to estimate the mass of black holes in these haloes, we follow the approach of Kulkarni & Loeb (2012) and employ the $M_{\rm bh}$–$\sigma$ relation (cf. Mao & Kim, 2016). The virial velocity (defined as the circular velocity at virial radius) for a halo of mass $M$ at redshift $z$ is given by

[TABLE]

where

[TABLE]

and $\Delta_{c}$ is the overdensity of the halo relative to the critical density, given by

[TABLE]

where $d=\Omega_{m}^{z}-1$ (Barkana & Loeb, 2001). Further, we equate the halo virial velocity with the circular velocity $v_{c}$ of its constituent spheroid and obtain the velocity dispersion of the spheroid using the relation (Ferrarese, 2002)

[TABLE]

Equation (8) combined with the measured $M_{\rm bh}$–$\sigma$ relation at redshift $z=0$ (Tremaine et al., 2002)

[TABLE]

gives

[TABLE]

We assume that haloes with mass below a threshold mass $M_{q}$ have $N_{\gamma}(M)=N_{\gamma}^{\mathrm{gal}}(M)\propto M_{\mathrm{halo}}$. Ionizing photons from these low-mass haloes are sourced by star formation.222While AGN have harder spectra than star-forming galaxies, the effect of harder photons on the structure of the hydrogen ionization fronts is small (Thomas & Zaroubi, 2008; Ghara et al., 2015; Kakiichi et al., 2016). The excursion set method therefore remains applicable. On the other hand, high-mass haloes with mass greater than the threshold $M_{q}$ have $N_{\gamma}(M)=N_{\gamma}^{\mathrm{agn}}(M)\propto M_{\mathrm{bh}}$ where $M_{\mathrm{bh}}$ is given by Equation (10). These high-mass haloes produce ionizing photons due to AGN. The ratio

[TABLE]

quantifies the relative photon contribution of AGN and galaxies. Our AGN models are thus described by two parameters $r$ and $M_{q}$. (Appendix A gives further details on our AGN ionizing emissivity model.)

In our fiducial AGN-dominated model, we fix the value of the threshold mass $M_{q}$ to that corresponding to a circular velocity of $v_{c}=175$ km$/$s. (We will discuss the effect on our results of changing this threshold to $v_{c}=150$ km$/$s and $v_{c}=200$ km$/$s below.) At lower circular velocities, cold gas mass available to grow supermassive black holes can decrease rapidly due to an increasing effect of supernova feedback (e.g., Kauffmann & Haehnelt, 2000; Haehnelt & Kauffmann, 2002; Brook et al., 2012). This is reflected in a drop in the black hole mass function for black hole masses smaller than $M_{\mathrm{bh}}\sim 10^{7}~{}\mathrm{M}_{\odot}$, particularly for $z>1$ (Merloni & Heinz, 2008; Kelly & Merloni, 2012). With $M_{q}$ fixed, a desired total AGN emissivity is achieved in the model by setting the value of the parameter $r$. We calibrate the AGN emissivity evolution to values close to the fit by Madau & Haardt (2015) to the integrated 1 Ry emissivity from AGN down to UV luminosities of $0.01L_{*}$. This emissivity evolution is shown by the red curve in the right panel of Figure 1. In this panel, red filled circles denote ionizing emissivity from AGN in our model; red open circles refer to the total ionizing emissivity, which also includes contribution from star-forming galaxies. The ionizing emissivity of AGN in our model closely matches that from the model of Madau & Haardt (2015). We also have some contribution to $\dot{n}_{\mathrm{ion}}$ from star-forming galaxies in our model, particularly at $z=10$, as seen from the red open circles in Figure 1. For comparison, the grey points in Figure 1 show the photon emissivity in the galaxy-dominated “Late/Default” model of Kulkarni et al. (2016).

Having chosen a source model, we now need to choose a suitable reionization history to calibrate our simulation. As discussed above in relation to Equation (3), this calibration will provide us with the photoionization rate and ionized hydrogen fraction throughout our simulation box. The AGN-dominated ionizing emissivity evolution considered by Madau & Haardt (2015) gives rise to a reionization history that is very close to the “Very Late” reionization history as described by Kulkarni et al. (2016). For ease of comparison we thus choose this reionization history to calibrate our simulation. The red curve in the left panel of Figure 1 shows the evolution of the volume-weighted ionized fraction $Q_{V}$ in this Very Late model. For comparison, the grey curve in this panel shows the evolution of $Q_{V}$ in the “Late/Default” model of Kulkarni et al. (2016). In the Very Late model, ionized regions overlap and the universe is completely reionized at $z=6$, similar to the Late/Default model, but $Q_{V}$ evolves more rapidly at $z>6$ (Kulkarni et al., 2016). This model agrees reasonably well with the background photoionization rate determined from the Ly$\alpha$ forest at $z<6$ (Faucher-Giguère et al., 2009; Becker & Bolton, 2013) and from quasar proximity zones at $z\sim 6$ (Wyithe & Bolton, 2011; Calverley et al., 2011), albeit with notable differences (Puchwein et al., 2015; Chardin et al., 2015). The value of the electron scattering optical depth to the last scattering surface in this model is $\tau=0.055$, in good agreement with the most recent Planck measurement ($\tau=0.058\pm 0.012$; Planck Collaboration 2016), as seen in the middle panel of Figure 1.

3 Results: 21 cm signal

The top panel of Figure 2 shows the evolution of the 21 cm brightness temperature from redshift $z=10$ to $6$ in our fiducial $v_{c}>175$ km/s AGN-dominated model. The 21 cm brightness temperature is approximated as

[TABLE]

where the mean temperature $\overline{T}_{b}\approx 22\mathrm{mK}[(1+z)/7]^{1/2}$ (Choudhury et al., 2009). The above relation neglects the impact of redshift space distortions due to peculiar velocities, and possible fluctuations in the spin temperature, i.e., it implicitly assumes that the spin temperature is much greater than the CMB temperature and that the Ly$\alpha$ coupling is sufficiently complete throughout the IGM. This is a good approximation in the redshift range considered here, when the global ionized fraction is greater than a few per cent (Pritchard & Loeb, 2012; Majumdar et al., 2014; Ghara et al., 2015). For comparison, the middle panel of Figure 2 shows the evolution of the 21 cm brightness in the galaxies-dominated Very Late model considered by Kulkarni et al. (2016). The reionization history of this model is identical to that of our AGN-dominated model, so the differences in the brightness distribution between the top and middle panels of Figure 2 arise solely due to differences in the source model. The AGN-dominated model has fewer, larger, and more clustered ionized regions than the galaxies-dominated model (cf. McQuinn et al. 2007). Figure 2 also shows the galaxies-dominated Late/Default model of Kulkarni et al. (2016) in the bottom panel. The source model as well as the reionization history are now different from our AGN-dominated model. This is reflected in a strikingly different morphology of 21-cm-bright regions.

We derive the power spectrum of the 21 cm fluctuations in our model as

[TABLE]

where $\widetilde{T_{b}}(k)$ is the Fourier transform of the brightness temperature defined in Equation (12), the average is over the simulation box, and $V_{\mathrm{box}}=(160~{}\mathrm{cMpc}/h)^{3}$ is the comoving box volume. Figure 3 shows our main results at redshifts $z=7$, $8$, and $10$ in its left, middle, and right panels, respectively. The red curve in all panels shows the 21 cm power spectrum in our fiducial AGN-dominated model, in which AGN are hosted by haloes with $v_{c}>175$ km/s. The power spectrum is characterised by a bump at large scales and an increase towards the smallest scales. At redshifts $z=7$–$10$ shown, the bump occurs at $k\sim 0.2$ cMpc${}^{-1}h$ and has an amplitude of approximately $\Delta_{21}^{2}\sim 40$–$70$ mK2. This is significantly higher than in the galaxies-dominated models. (Note that $k=0.2$ cMpc${}^{-1}h$ corresponds to a length scale of 30 $h^{-1}$cMpc, which is well-sampled in our simulation cube, which is 160 $h^{-1}$cMpc on each side.) We can compare the large-scale power in our AGN-dominated model with that in the galaxies-dominated Very Late model in Figure 3, in which the galaxies-dominated model is shown by the dashed grey curves. The large-scale power in the AGN-dominated model is larger than that in the galaxies-dominated model by factor of 2 at $z=7$ and a factor of 10 at $z=10$. As we will see below, this enhancement is due to the enhanced size and clustering of ionized regions, which is also visually apparent in Figure 2. The large-scale 21 cm power in our fiducial AGN-dominated model is also higher than the large-scale power in the Late/Default model of Kulkarni et al. (2016). Power spectra from the latter model are shown by the solid grey curves in Figure 3. The enhancement factor here is about 3 at $z=7$ and 2 at $z=10$. At redshifts $z=8$ and $10$, the Late/Default model has higher power than the galaxies-dominated Very Late model at large scales, because of the higher $Q_{V}$, which translates to larger bubble size, as is evident from Figure 2.

In Figure 3 we also show the effect of changing the circular velocity threshold for AGN-hosting haloes. The red curve in this figure shows the 21 cm power spectrum in our fiducial AGN-dominated model, when AGN are hosted by haloes with $v_{c}>175$ km/s. The blue and green curves show the power spectra when the circular velocity threshold is changed to 200 km/s and 150 km/s, respectively. The main effect of this change on the large-scale 21 cm power is to shift the position of the bump. As all three models are calibrated to the same Very Late reionization history, they have identical ionization fraction $Q_{V}$ at each redshift. Therefore, when the circular velocity threshold is reduced, the number of AGN-hosting haloes increases and consequently, in order to hold $Q_{V}$ fixed, the size of individual ionized regions decreases. This moves the bump in the 21 cm power spectrum to smaller scales (cf. Iliev et al. 2012).

The thin diagonal lines in each panel of Figure 3 show sensitivities set by thermal noise for five ongoing and upcoming 21 cm experiments: the Precision Array for Probing the Epoch of Reionization (PAPER; Parsons et al. 2014), Murchison Widefield Array (MWA; Bowman et al. 2013; Tingay et al. 2013), Low Frequency Array (LOFAR; van Haarlem et al. 2013; Pober et al. 2014), Hydrogen Epoch of Reionization Array (HERA; Pober et al. 2014), and the low frequency instrument from Phase 1 of the Square Kilometre Array (SKA1-LOW). We consider 1000 hr of observations and use experimental parameters identical to those considered by Kulkarni et al. (2016). Note that the sample variance from the limited number of $k$-modes measured in the survey volume also limits the sensitivity of the experiment. The sample variance scales as $\Delta^{2}(k)/\sqrt{N}$ and, due to the small amplitude of the power spectrum, is smaller ($<1$ mK2) than the thermal noise at all redshifts for all experiments considered here. Also note that we assume perfect foreground subtraction in this discussion. Foreground subtraction and calibration residuals will reduce the experimental sensitivity (Bernardi et al., 2009; Pober et al., 2013; Dillon et al., 2014). Due to the relatively smooth dependence of astrophysical foregrounds on frequency, this reduction in sensitivity particularly affects small $k$ values.

Due to limited baselines, current and upcoming 21 cm experiments are only sensitive to large scales. None of the experiments are sensitive to 21 cm power at $k\gtrsim 1$ cMpc${}^{-1}h$. SKA1-LOW and HERA have the highest sensitivities primarily due to large number of antenna elements. In the galaxies-dominated Late/Default model, at $z=10$ (129 MHz), the signal to noise ratio (SNR) is $\sim 100$ for these two experiments at $k\sim 0.1$ cMpc${}^{-1}h$. This is enhanced by a further factor of $\sim 2$ in the AGN-dominated model. At $z=7$ (178 MHz), the enhancement is by a factor of $\sim 3$. LOFAR is sensitive at scales corresponding to $k\lesssim 0.2$ cMpc${}^{-1}h$ at $z=10$ (129 MHz) and $k\lesssim 0.5$ cMpc${}^{-1}h$ at $z=7$ (178 MHz). At $k\sim 0.1$ cMpc${}^{-1}h$, the expected SNR for LOFAR is $\sim 10$ at $z=10$ and $\sim 50$ at $z=7$, for the galaxies-dominated Late/Default model. These SNRs are also enhanced by similar factors as for SKA1-LOW and HERA in AGN-dominated models. PAPER and MWA are the least sensitive of the five experiments, due to their relatively small number of antenna elements. Figure 3 shows that while galaxies-dominated models predict small SNRs for PAPER and MWA, the AGN-dominated models do predict SNRs of $\sim 2$ at $k\sim 0.1$ cMpc${}^{-1}h$ at redshifts $z=7$ (178 MHz) and $z=8$ (158 MHz). Also shown in Figure 3 are published measurements from the 64-element deployment of PAPER at $z=8.4$ (Ali et al., 2015). These are within a factor of $<2$ of the predicted power in our AGN-dominated model. Very clearly, the 21 cm signal will be significantly easier to detect if reionization is AGN-dominated. Conversely, these could become the first non-trivial models of reionization to be ruled out by 21 cm experiments, thereby constraining the contribution of AGN to reionization and thus complementing infrared surveys.

The enhancement in the large-scale 21 cm power in AGN-dominated reionization models can be better understood by decomposing the 21 cm power spectrum into contributions from the ionization field and the underlying matter density using Equation (12). This yields (Furlanetto et al., 2004; McQuinn et al., 2005; Furlanetto et al., 2006)

[TABLE]

where the first and second terms on the right-hand side are the power spectra of the matter density and the ionization field, respectively, and the last term denotes the cross-power spectrum between the ionization and matter density fields. The proportionality factors $b_{\delta}$ and $b_{x}$ are independent of $k$. This decomposition is shown in Figure 4 for our fiducial AGN-dominated model and the galaxies-dominated Very Late model at $z=8$. At small scales the 21 cm power spectrum is proportional to the matter power spectrum. At large scales, the cross-terms in Equation 14 are negative, with a magnitude of about 10% of the total power. The ionization field starts contributing power at large scales, creating a bump (Furlanetto et al., 2006). This can be understood by writing the power spectrum of the ionization field in terms of the size distribution of ionized regions in a halo model approach (Furlanetto et al., 2004; McQuinn et al., 2005). The scale at which the bump appears depends on the characteristic size of ionized regions and grows with decreasing redshift. When the ionization fraction is small even the large scale power is determined by the matter power spectrum. This is the case, for instance, in the galaxy-dominated Late/Default model at $z=10$ in Figure 3. However, as ionized regions grow, the bump moves to successively smaller $k$ values. This happens with decreasing redshifts, but in our case it also happens when when we put AGN in successively higher mass haloes, that is, when we increase the threshold circular velocity of AGN-hosting haloes, because all of our AGN-dominated models are calibrated to the same Very Late reionization history. When we increase the circular velocity cut-off, the number of AGN-hosting haloes is reduced and the size of ionized regions around each AGN-hosting halo increases in order to keep $Q_{V}$ fixed. This increases the spatial scale at which the power enhancement occurs. The amplitude of the peak in the power spectrum at large scales, however, does not increase arbitrarily with the circular velocity threshold. At some point, Poisson fluctuations dominate and the power approaches that corresponding to white noise. This is clearly seen in Figure 3 in all models: the peak in large-scale power is enhanced in the AGN-dominated models relative to the galaxies-dominated models with the same (Very Late) reionization history, but when $v_{c}$ is increased beyond 150 km/s, the peak simply moves to larger scales without increasing in amplitude. Thus, enhanced contribution from high mass haloes with constant total ionization fraction increases the large scale 21 cm power up to a limit and then moves the location of the peak to larger and larger scales. This large scale peak in the 21 cm power is perhaps the most important reionization signature for 21 cm experiments (Furlanetto et al., 2006).

4 The case for and against reionization by AGN

While interest in early reionization by X-rays from faint AGN (Meiksin & White, 2004; Meiksin, 2005; Srbinovsky & Wyithe, 2007) was motivated by the large value of Thomson scattering optical depth measured from the first-year WMAP data ($\tau=0.166^{+0.076}_{-0.071}$; Spergel et al. 2003), there are now a number of arguments favouring a significant role of normal QSOs in reionization, as discussed in Section 1: the suggestion of a rather steep faint end of the QSO luminosity function at high redshift by Giallongo et al. (2015), large Ly$\alpha$ opacity fluctuations at very large scales in QSO absorption spectra (Becker et al., 2015; Chardin et al., 2015; Davies & Furlanetto, 2016), a lack of convincing detections of the escape of Lyman continuum photons from faint high-redshift galaxies (Grazian et al., 2016; Mostardi et al., 2015; Siana et al., 2015; Boutsia et al., 2011; Vanzella et al., 2010; Finkelstein, 2016; Robertson et al., 2015; Khaire et al., 2016), and finally, the emergence of a shallow bright end of the high-redshift ($z\gtrsim 7$) galaxy luminosity function (Bowler et al., 2012, 2014; Bradley et al., 2014; Bowler et al., 2015) with many bright galaxies showing possible AGN-like spectral signatures (Stark et al., 2015a, b, 2017). These observations all point towards a significant presence of luminous AGN at $z>6$, suggesting that AGN play a major role in reionization (Giallongo et al., 2015; Madau & Haardt, 2015; Chardin et al., 2015; Khaire et al., 2016; Chardin et al., 2017; Mitra et al., 2016; D’Aloisio et al., 2016).

On the other hand, however, it has also been argued that AGN-dominated reionization is in tension with several observations. D’Aloisio et al. (2016) considered the effect of AGN-dominated reionization on the Ly$\alpha$ opacity at $z>5$, He ii Ly$\alpha$ opacity at $z\sim 3.1$–$3.3$, and the thermal history of the IGM. In agreement with Chardin et al. (2015), these authors found that AGN did provide a plausible explanation for the large fluctuations in the Ly$\alpha$ opacity at $z>5$. However, they found that reionization of He ii occurs much earlier in these AGN-dominated models (see also Mitra et al. 2016). For instance, in the model of Madau & Haardt (2015), He ii reionization is complete at $z=4.5$, compared to $z=3$ in the standard scenario (Haardt & Madau, 2012). This early Helium reionization could result in higher IGM temperatures due to the associated photoheating. The temperature of the IGM at mean density is enhanced in AGN-dominated models by factors of $\sim 2$ relative to the standard models for $z=3.5$–$5$, in conflict with measurements. This inconsistency could be avoided by reducing the escape fraction of 4 Ry photons in AGN, but it is not clear if this can be achieved while requiring a 100% escape fraction of 1 Ry photons in order to explain the Ly$\alpha$ opacity fluctuations. Further evidence against AGN-dominated reionization models has emerged from metal-line absorbers at $z\sim 6$. In their cosmological radiation hydrodynamical simulations, Finlator et al. (2016) find that the hard spectral slopes of UV backgrounds in AGN-only reionization models produce too many C iv absorption systems relative to Si iv and C ii at $z\sim 6$. However, these simulations assume an $L_{\nu}\propto\nu^{-1.57}$ AGN SED at extreme UV (Vanden Berk et al., 2001; Telfer et al., 2002; Haardt & Madau, 2012). This slope is marginally harder than recent measurements ($L_{\nu}\propto\nu^{-1.7}$) from a stack of $z\sim 2.4$ quasars (Lusso et al., 2015). Finlator et al. (2016) also find that the N(Si iv)/N(C iv) column density ratio measurements prefer a somewhat harder and more intense $>4$ Ry background than the standard model of Haardt & Madau (2012). Using a large sample of X-ray-selected quasars in the redshift range $z=0$–$6$, Ricci et al. (2017) find that the faint end of the AGN UV luminosity function at $z\sim 6$ is likely to be much shallower that that reported by Giallongo et al. (2015). In their analysis, Ricci et al. (2017) use an AGN obscuration optical depth ($\log N_{\mathrm{H}}$) cut-off that reproduces low-redshift AGN UV luminosity functions and an X-ray-to-optical/UV luminosity ratio calibrated at redshifts $z=0.05$–$4$ (Lusso et al., 2010). These authors argue that the apparent contradiction with the results of Giallongo et al. (2015) could be explained by contamination from the AGN host galaxies. It has also been recently argued that the Lyman continuum escape fraction of AGN might not be 100% as is usually assumed (Micheva et al., 2017a). This may further reduce the contribution of AGN to reionization.

A definitive understanding of the AGN contribution to reionization will perhaps only emerge with deep large-area surveys to detect faint and intermediate brightness quasars at high redshifts, such as the Subaru High-z Exploration of Low-Luminosity Quasars (SHELLQs) project (Matsuoka et al., 2016) and the VISTA Extragalactic Infrared Legacy Survey (VEILS; Hönig et al. 2017), and later with the Wide Field Infrared Survey Telescope (WFIRST; Spergel et al. 2013) and Euclid (Laureijs et al., 2011).

5 Conclusions

We have presented predictions of the spatial distribution of the 21 cm brightness temperature fluctuations from AGN-dominated models of reionization using high-dynamic-range cosmological hydrodynamical simulations from the Sherwood simulation suite (Bolton et al., 2017) for reionization histories motivated by constraints from Ly$\alpha$ absorption and emission data as well as CMB data and based on a physically motivated AGN model.

Our main conclusion is that AGN-dominated reionization histories increase the large-scale 21 cm power by factors of up to ten. Conventional models typically predict values of 10–20 mK2 for the variance of the 21 cm brightness temperature at redshifts $z=7$–$10$ at scales accessible to ongoing and upcoming experiments ($k\lesssim 1$ cMpc${}^{-1}h$), but AGN-dominated models can increase this variance to values close to 100 mK2. This is because AGN reside in few highly clustered haloes, which increases the peak of the 21 cm power spectrum and moves the peak to larger scales. This bodes well for experiments that seek to detect this feature, and the predicted signal is lower than the sensitivity claimed to have been already reached by ongoing experiments by only a factor of about two or less.

Our models for the reionization history and Lyman continuum emissivity of AGN suggest that detection by LOFAR (and later HERA and SKA1) should be in easy reach of their design sensitivity, albeit assuming optimistic foreground subtraction and calibration residuals. Conversely, these models could become the first non-trivial hydrogen reionization scenarios to be ruled out by experiments, thereby complementing infrared searches for high-$z$ AGN, and constraining the contribution of AGN to reionization.

Acknowledgments

We thank the anonymous referee for a thoughtful referee report and acknowledge helpul discussions with Jonathan Chardin, Colin DeGraf, Kristian Finlator, Laura Keating and Dylan Nelson. Support by ERC Advanced Grant 320596 ‘The Emergence of Structure During the Epoch of Reionization’ is gratefully acknowledged. EP gratefully acknowledges support by the Kavli Foundation. We acknowledge PRACE for awarding us access to the Curie supercomputer, based in France at the Trés Grand Centre de Calcul (TGCC). This work used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grants ST/H008519/1 and ST/K00087X/1, STFC DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National E-Infrastructure. This research was supported by the Munich Institute for Astro- and Particle Physics (MIAPP) of the DFG cluster of excellence “Origin and Structure of the Universe”.

Appendix A AGN ionizing emissivity

In our simulations, AGN are implemented according to the procedure described in Section 2. In this work we assume that haloes with mass below a threshold mass $M_{q}$ have $N_{\gamma}(M)=N_{\gamma}^{\mathrm{gal}}(M)\propto M_{\mathrm{halo}}$. Ionizing photons from these low-mass haloes are sourced by star formation. On the other hand, high-mass haloes with mass greater than the threshold $M_{q}$ have $N_{\gamma}(M)=N_{\gamma}^{\mathrm{agn}}(M)\propto M_{\mathrm{bh}}$ where $M_{\mathrm{bh}}$ is given by Equation (10). These high-mass haloes produce ionizing photons due to AGN. The ratio $r$, defined in Equation (11), quantifies the relative photon contribution of AGN and galaxies. Our AGN models are thus described by two parameters $r$ and $M_{q}$. We fix the value of the threshold mass $M_{q}$ to that corresponding to a circular velocity of $v_{c}=175$ km$/$s in our fiducial model, but also consider the effect of varying this threshold to $v_{c}=150$ km$/$s and $v_{c}=200$ km$/$s in Figure 3. The left panel of Figure 5 shows the $N_{\gamma}$ assignment for AGN in our fiducial model ($v_{c}=175$ km$/$s) at redshifts $z=7$, 8, and 10. Below the threshold mass, $N_{\gamma}\propto M_{\mathrm{halo}}$ and above it $N_{\gamma}\propto M_{\mathrm{bh}}\propto M_{\mathrm{halo}}^{1.6}$, following Equation (10). The middle panel of Figure 5 shows $N_{\gamma}$ as a function of the halo circular velocity. We see that $N_{\gamma}$ sharply increases at $v_{c}=175$ km$/$s. This velocity corresponds to a different halo mass at each of the three redshifts considered here, as seen in the right panel of Figure 5. The magnitude of $N_{\gamma}$ increases with redshift to compensate for the decreasing number density of haloes above the velocity threshold. As described in Section 2, where we discuss our calibration procedure, the required total ionizing emissivity is dictated by our chosen reionization model.