Identifying Direct Collapse Black Hole Seeds through Their Small Host Galaxies

We track the evolution of ACHs in our simulation to demonstrate that before they grow significantly in mass (within ∼75 Myr of their birth), newly formed DCBHs remain in halos (or subhalos) with BH mass to stellar mass ratios well above what is expected in the Pop III seed scenario. Note that most ACHs are not thought to host DCBH formation, but as described below, our conclusions apply to ∼10⁵ M_⊙ BH seeds formed in almost any ACH. We identify the 7929 halos that cross the atomic cooling threshold (M_a = 3 × 10⁷ M_⊙) between z = 10 and the next simulation snapshot 15 Myr later (z = 9.8). We then follow the properties of these halos through time. For those that fall into a larger halo but remain a subhalo, we record both the subhalo and host halo properties.

Assuming Eddington-limited growth as expected for black holes with M_BH ≳ 10⁵ M_⊙ (Inayoshi et al. 2016), we estimate the mass of a growing DCBH as ${M}_{\mathrm{BH}}={M}_{{\rm{i}}}{e}^{t/{t}_{{\rm{E}}}}$, where t_E is the e-folding timescale set by the Eddington limit, M_i is the initial seed mass, and t is the duration of time since DCBH formation (assumed to coincide with the second snapshot in our simulation just after ACH formation). We then compute the BH mass to stellar mass of each ACH by assuming the stellar mass is given by ${M}_{* }={M}_{{\rm{h}}}\tfrac{{{\rm{\Omega }}}_{b}}{{{\rm{\Omega }}}_{m}}{f}_{* }$, where M_h is the total halo mass and f_* is the star formation efficiency. We use fiducial values of M_i = 10⁵ M_⊙, t_E = 30 Myr and f_* = 0.05 to estimate the BH mass to stellar mass ratio for a DCBH in each ACH as a function of cosmic time. We report this ratio as $\tfrac{{M}_{\mathrm{BH}}}{{M}_{* }}\left(\tfrac{0.05}{{f}_{* }}\right)$, due to its simple dependence on the star formation efficiency. Our assumption of t_E = 30 Myr corresponds to a radiative efficiency of  ≈ 0.06, which is predicted for a Schwarzschild BH. Our conclusions do not depend sensitively on this exact choice. We note that the environments of newly formed DCBHs may lead to outflows driven by radiative pressure that could reduce f_* below our fiducial value (Smith et al. 2017). This would serve to increase $\tfrac{{M}_{\mathrm{BH}}}{{M}_{* }}$, strengthening our overall conclusions.

In Figure 1, we plot the distribution of $\tfrac{{M}_{\mathrm{BH}}}{{M}_{* }}\left(\tfrac{0.05}{{f}_{* }}\right)$ at z = 8.8, 75 Myr after the formation of our ACHs. By this time the DCBHs are assumed to have grown to M_BH = 1.2 × 10⁶ M_⊙. We compare this to the BH mass to stellar mass ratio expected for "light" Pop III seeds. Although their initial mass function remains uncertain, the first Pop III stars are thought to have masses of ∼10–1000 M_⊙ (Hirano et al. 2015) and form at very high redshift in small ∼10^5–6 M_⊙ dark matter "minihalos."

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The growth of Pop III BH remnants has been tracked in simulations (Alvarez et al. 2009; Taylor & Kobayashi 2014; Habouzit et al. 2017; Smith et al. 2018) and semi-analytic calculations (Volonteri et al. 2003; Tanaka & Haiman 2009). To make our comparisons we focus on the cosmological hydrodynamical simulations of Habouzit et al. (2017). These simulations seed SMBHs on the fly in dense low-metallicity gas with ∼1000 M_⊙ BHs (in the same vein as Bellovary et al. 2011), which then grow with an accretion rate capped by the Eddington limit. Several different supernovae feedback prescriptions are utilized. For the weaker thermal feedback prescription, the largest ratio found for all of the galaxies with M_BH ≈ 10⁶ M_⊙ is M_BH/M_* ≈ 2.5 × 10⁻³, which we plot for comparison with our DCBHs. This is a conservative choice, as their stronger (more realistic) feedback prescriptions give lower values of this ratio. We also note that the semi-analytic simulations of Volonteri et al. (2003; see their Figure 11) find $\tfrac{{M}_{\mathrm{BH}}}{{M}_{* }}\left(\tfrac{0.05}{{f}_{* }}\right)\approx {10}^{-5}$ at M_BH ≈ 10⁶ M_⊙ for two representative cases, which is significantly lower than our conservative limit in Figure 1 (see also Smith et al. 2018, who found even less Pop III seed growth). Additionally, inefficient accretion due to radiative feedback from the growing BH itself (Milosavljević et al. 2009) would lower M_BH/M_* in the Pop III case.

In the left panel of Figure 1, $\tfrac{{M}_{\mathrm{BH}}}{{M}_{* }}\left(\tfrac{0.05}{{f}_{* }}\right)$ is plotted for the largest halo hosting the DCBHs (i.e., if it is in a subhalo, we use the larger host halo mass to compute M_*). While the vast majority of ACHs have several orders of magnitude higher M_BH/M_* than the Pop III limit, we do find a small fraction of halos relatively close to this value. This is because some ACHs quickly fall into a much larger nearby halo. Fortunately, almost all of these ACHs remain subhalos separated from their larger host halos. This can be seen in the right panel of Figure 1, where we show $\tfrac{{M}_{\mathrm{BH}}}{{M}_{* }}\left(\tfrac{0.05}{{f}_{* }}\right)$ computing the stellar mass from the subhalo mass if the DCBH is in a substructure within the larger halo. We note that when an ACH falls into massive neighbor (M_h > 10¹⁰ M_⊙), its total mass never exceeds the atomic cooling threshold by more than a factor of two. Except for one ACH that has completely merged and mixed with its larger neighbor (the point with the lowest ratio in the right panel of Figure 1), the BH mass to stellar mass ratio for our DCBHs is more than an order of magnitude higher than our conservative upper limit in the Pop III scenario.

Importantly, we find that ACHs that become satellites of large neighbors remain separated from their larger host halos by distances that can be resolved with future observations. In Figure 2, we plot the distances between the centers of DCBH-hosting subhalos and their larger host halos for the 20 ACHs that end up in host halos with M_h > 10¹⁰ M_⊙ (corresponding to $\tfrac{{M}_{\mathrm{BH}}}{{M}_{* }}\left(\tfrac{0.05}{{f}_{* }}\right)\lt 0.015$). Aside from one ACH that has completely merged, these satellite halos are at separations ≳1 kpc. A physical distance of 1 kpc corresponds to 022 at z = 8.8. Thus, almost all of these halos are sufficiently separated to be spatially resolved in X-ray observations with Lynx, which is planned to have 05 angular resolution and 02 positional accuracy for faint sources (A. Vikhlinin 2018, private communication), and by infrared observations with JWST (∼01 resolution). Thus, from Figures 1 and 2, we can see that except for the one ACH which completely merges and mixes with a massive neighbor, DCBHs seeds have $\tfrac{{M}_{\mathrm{BH}}}{{M}_{* }}\left(\tfrac{0.05}{{f}_{* }}\right)\gtrsim 0.1$, even after they have grown an order of magnitude in mass. Thus we propose that identifying DCBHs with X-ray observations and comparing with infrared observations to put limits on the stellar mass can likely distinguish DCBHs from Pop III seeds. In the DCBH case, we expect JWST to detect a very small stellar host (or none at all), or else detect a galaxy that is offset by ∼1'' from the black hole X-ray source. In the Pop III case, we expect JWST to detect a much brighter host in the near-infrared with M_BH/M_* < 2.5 × 10⁻³.

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As discussed above, we find one ACH (out of ∼8000) that completely merges and mixes with a very massive (M_h > 10¹⁰ M_⊙) neighbor within 75 Myr after DCBH formation. A DCBH in such a halo would be more challenging to distinguish from a BH grown from a Pop III seed due to its lower BH mass to stellar mass ratio. Because the number density of ∼10⁹ M_⊙ SMBHs at z ≳ 6 is very low (∼1 Gpc⁻³), it is important to check that it is not halos like this 1 in ∼8000 ACH that are biased toward DCBH formation. It is generally thought that DCBHs form preferentially in ACHs exposed to strong Lyman–Werner (LW) radiation, so one might worry that it is the halos with the highest LW exposure that end up merging completely with massive neighbors, making them hard to distinguish from Pop III seeds. Here we explain that the complete merger is mainly due to the orbital properties of the ACH and its larger neighbor, and that DCBH formation should not be biased to occur in a halo like this, compared to other ACHs that merge with their massive neighbor but remain in satellites that can be spatially resolved.

In Figure 3, we plot properties of the 20 ACHs (at the time of DCBH formation) that eventually merge with massive neighbors (M_h > 10¹⁰ M_⊙). In the right panel, we plot the LW intensity seen by each ACH at the time of DCBH formation as a function of the distance from the host halo 75 Myr later (i.e., the LW intensity at z = 9.8 and the distance at z = 8.8). The LW intensity is computed by adding the contribution from all of the halos in the simulation box above the atomic cooling threshold (halos seeing the strongest LW flux have a negligible contribution from the background outside of the box, as most of the flux comes from nearby neighbors). Each halo's LW luminosity is computed by assuming that 4000 LW photons are produced per baryon incorporated into stars and that the star formation rate is given by SFR = M_*/(0.1t_H), where ${M}_{* }={M}_{{\rm{h}}}\tfrac{{{\rm{\Omega }}}_{b}}{{{\rm{\Omega }}}_{m}}{f}_{* }$ and 0.1t_H is the dynamical time of the halo at that redshift. From the left panel of Figure 3, we see that, among the ACHs that merge with large halos, there is no clear correlation between their initial observed LW intensity and the distance they end up as satellites from the larger halo after merger. Thus, even if DCBHs form preferentially near massive neighbors, the vast majority, ∼90% (18 out of 20 halos in our simulation), are likely to remain in satellite halos at distances from their host that can be spatially resolved with Lynx.

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So what causes one halo to completely merge and mix into a massive neighbor, but not the others? We find that the distance between the satellites and their host halos at z = 8.8 correlates with how bound their orbits are at DCBH formation (z = 9.8). This is illustrated in the right panel of Figure 3, where we show $\tfrac{1}{2}{v}^{2}-{{GM}}_{{\rm{b}}}/r$ at the time of DCBH formation versus the separation 75 Myr later. Here v is the velocity of the ACH relative to the massive neighbor, M_b is the mass of the large neighbor, and r is their separation at z = 9.8. More tightly bound halos (lower values of this quantity) systematically end up at smaller separations from their massive neighbors. The halo that completely merges (i.e., d = 0) is one of the more tightly bound halos, but not the most tightly bound. Its complete merger is likely determined by the detailed characteristics of its orbit. There is no obvious reason DCBH formation should preferentially occur in ACHs that are tightly bound and on orbits that will mix with larger neighbors. Thus, we conclude that within 75 Myr, the vast majority of DCBHs will either be in a halo or subhalo sufficiently small such that the high BH mass to stellar mass ratio will make the heavy seed distinguishable from Pop III models.