Formation of massive black holes in rapidly growing pre-galactic gas clouds

TL;DR

This study uses radiation hydrodynamics simulations to demonstrate that rapid growth in metal-free early Universe haloes can naturally lead to the formation of supermassive stars, which are potential seeds for supermassive black holes, emphasizing structure formation dynamics over LW flux.

Contribution

It shows that structure formation dynamics, especially rapid halo growth, are key to massive black hole seed formation, challenging the emphasis on critical Lyman-Werner flux levels.

Findings

Rapid halo growth induces conditions for supermassive star formation.

Massive black hole seeds could be more common in overdense early regions.

Formation of SMBH seeds is driven by structure dynamics, not just LW flux.

Abstract

The origin of supermassive black holes (SMBHs) that inhabit the centers of massive galaxies is largely unconstrained. Remnants from supermassive stars (SMSs) with masses around 10,000 solar masses provide the ideal seed candidates, known as direct collapse black holes. However, their very existence and formation environment in the early Universe are still under debate, with their supposed rarity further exacerbating the problem of modeling their ab-initio formation. SMS models have shown that rapid collapse, with an infall rate above a critical value, in metal-free haloes is a requirement for the formation of a proto-stellar core which will then form an SMS. Using a radiation hydrodynamics simulation of early galaxy formation, we show the natural emergence of metal-free haloes both massive enough, and with sufficiently high infall rates, to form an SMS. We find that haloes that are exposed to both a Lyman-Werner intensity of J_LW ~ 3 J_21 and that undergo at least one period of rapid growth early in their evolution are ideal cradles for SMS formation. This rapid growth induces substantial dynamical heating, amplifying the existing Lyman-Werner suppression originating from a group of young galaxies 20 kiloparsecs away. Our results strongly indicate that structure formation dynamics, rather than a critical Lyman-Werner (LW) flux, may be the main driver of massive black hole formation in the early Universe. We find that massive black hole seeds may be much more common in overdense regions of the early Universe than previously considered with a comoving number density up to 10^-3 Mpc^-3.

Tables

Table 1. Table 1: Properties of halo candidates hosting supermassive star formation

log10(Mhalo)	log10(mean Growth rate)	JLW/J21	Dgal	Tc	Gas infall rate
[M⊙]	[M⊙ per unit redshift]		[kpc]	[K]	[M⊙/yr]
7.84∗	7.78	2.71	12.7	2250	0.275
7.76†	7.53	3.23	11.8	4390	0.171
7.76	7.76	1.91	14.7	4220	0.286
7.75	7.65	0.583	35.5	1730	0.290
7.75	7.39	0.958	19.7	7570	0.0294
7.74	7.88	1.49	25.0	8670	0.0574
7.73	7.79	0.894	29.9	1760	0.396
7.70	7.22	2.62	18.3	6520	0.0292
7.67	7.90	0.16	124	1080	1.05
7.64	7.78	2.14	6.20	7890	0.0356

Equations

$${\Gamma }_{\mathrm{dyn}}=\alpha M_{\mathrm{halo}}^{-1/3}\frac{k_{\mathrm{B}}}{\gamma -1}\frac{d{M}_{\mathrm{halo}}}{dt},$$

$${\left(\frac{d{M}_{\mathrm{halo}}}{dt}\right)}_{\mathrm{crit}}=\frac{2\alpha }{3}\frac{\gamma -1}{k_{\mathrm{B}}}{M}_{\mathrm{halo}}^{-1/3}n\Lambda (T_{\mathrm{halo}})$$

$$\frac{M_{\min ,\mathrm{LW}}}{{\mathrm{M}}_{\odot }}=1.25\times 10^5+2.65\times 10^5{\left(\frac{J_{\mathrm{LW}}}{J_{21}}\right)}^{0.47},$$

$$c_{\mathrm{s}}=\sqrt{\frac{\gamma k_{\mathrm{B}}T}{\mu m_{\mathrm{H}}}},$$

$$Q\equiv \frac{c_{\mathrm{s}}\kappa }{\pi G\Sigma }.$$

$${\kappa }^2=\frac{2\Omega }{r}\frac{d(r^2\Omega )}{dr},$$

$$Q_{\mathrm{local}}\simeq \frac{{\Omega }^2}{\pi G\rho }$$

$$w_{\mathrm{g}}^2={\kappa }^2+k^2{v}_{\mathrm{rot}}^2-2\pi Gk\Sigma$$

$$|w_{\max }|=\frac{\kappa (1+Q_{\mathrm{eff}}^2{)}^{1/2}}{Q_{\mathrm{eff}}},$$

Full text

{affiliations}

Center for Relativistic Astrophysics, School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA; jwise@gatech.edu

Centre for Astrophysics and Relativity, School of Mathematical Sciences, Dublin City University, Dublin, Ireland

Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI 48824, USA

Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA

Center for Astrophysics and Space Sciences, University of California, San Diego, La Jolla, CA 92093, USA

San Diego Supercomputer Center, San Diego, La Jolla, CA 92093, USA

IBM, 2455 South Road, Poughkeepsie, NY 12601

Standard cold dark matter cosmologies predict large-scale structure forms hierarchically. Smaller objects forming at early times subsequently merge and grow into larger objects. The existence of SMBHs[15, 16] with masses around $10^{9}{~{}{\rm M_{\odot}}}$ (M⊙, solar mass) only 800 Myr after the Big Bang indicate that there must have been an early intense convergence of mass in rare locations.

We performed a suite of cosmological radiation hydrodynamics simulations (named Renaissance; see Methods) to elucidate the formation of the first generations of stars and galaxies in the Universe[11, 12] with the code Enzo[17]. It includes models for the formation of massive metal-free (Population III; Pop III) stars and subsequent metal-enriched stars not unlike ones found in the Galaxy. We follow the impact of their ionizing radiation[18] and supernova explosions on their environments as galaxies first assemble, both of which play an important role in regulating early galaxy formation.

Motivated by possible early SMS formation, we analyze the region from the Renaissance Simulation suite that is centered on the densest cosmological volume of 133.6 comoving Mpc3 and contains 822 galaxies at its ending redshift of $z=15$ (270 Myr after the Big Bang). We identify candidate SMS host haloes by searching the simulation for metal-free atomic cooling haloes without prior star formation at $z=15$. We place no constraints on the level of LW flux impacting the haloes. There are 670 atomic cooling haloes, ten of which are metal-free and have not hosted prior star formation (see Extended Data Table 1). The remaining atomic cooling haloes have formed stars prompted by either H2 or metal line cooling and are not conducive for SMS (and subsequent direct collapse black hole) formation. Out of these ten haloes, we concentrate on two “target” haloes—the most massive halo (MMH) and, separately, the most irradiated halo (LWH)—in this study. We resample their mass distributions at $z=20$ at a mass resolution higher by a factor of 169 and resimulate them to study their gravitational collapse in more detail.

Both haloes assemble in a region 10–25 kpc away from a group of young galaxies that have photo-ionized, photo-heated, and chemically enriched their adjacent environments (Fig. 1). At $z=18$, the young galaxies near the MMH (Fig. 1a through 1d) have created an amorphous H ii region with a maximum extent of 20 kpc. As the star formation rates grow in these young (massive) galaxies, the LW intensities increase from $J_{\rm LW}\simeq 1~{}J_{21}$ at $z=18$ within 5 physical kpc of the galaxies to $30~{}J_{21}$ at $z=15$. The only other source of LW radiation comes from four nearby haloes hosting Pop III stars, 3–5 kpc from the LWH. Both target haloes are impacted by a LW intensity $J_{\rm LW}\simeq 3~{}J_{21}$ at $z=15$ (Fig. 1d, 1h). This total flux impinging on the target haloes is 6–600 times lower than previous critical estimates for SMS formation[19, 20, 21].

The metal-enriched regions around these galaxy congregations only reach a distance of 5 kpc, far from the target haloes. These heavy elements originate from both their Pop III progenitors and ongoing star formation in the galaxies. Over the next 60 Myr, the ionizing radiation from the young growing galaxies near both target haloes extends the H ii regions to nearly 40 kpc in radius, evident in Fig. 1. This leaves the vast majority of the intergalactic medium and associated collapsed haloes chemically pristine but nonetheless bathed in LW radiation, helping to prevent Pop III star formation.

During the halo assembly process (Fig. 2a), the LW intensity increases from $0.3~{}J_{21}$ to $3~{}J_{21}$ at $z=15$ (Fig. 2b), corresponding to a minimum halo mass $M_{\rm crit}\simeq 3\times 10^{6}~{}{~{}{\rm M_{\odot}}}$ that can support H2 cooling[22] and primordial star formation. However, the MMH (LWH) gravitationally collapse only after they reach the atomic cooling limit at $z=16.4(15.3)$, having masses of $2.6(5.8)\times 10^{7}~{}{~{}{\rm M_{\odot}}}$, an order of magnitude above $M_{\rm crit}$. Upon closer inspection, we find that both target haloes experience a period of intense growth in mass (Fig 2a). The MMH grows by a factor of 30 over 30 Myr ($z=21-19$) as it virializes. The LWH experiences two rapid growth events. It first increases from $2\times 10^{5}{~{}{\rm M_{\odot}}}$ to $3\times 10^{6}~{}{~{}{\rm M_{\odot}}}$ between $z=19-18$ (15 Myr), at which point its mass fluctuates just above $M_{\rm crit}$. At redshift $z=15.8$, it then dramatically grows by a factor of nine within a span of 10 Myr. Most of the accreted matter originates from the parent filament, a major merger, and several minor halo mergers. The currently standard cold dark matter paradigm has this unique prediction of intense matter convergence below the atomic cooling limit and is not present in cosmologies that suppress power below this scale. Nevertheless it is rare, only occurring in \sim$$3\times 10^{-4} of haloes (see Methods) with similar masses and existing in an overdense large-scale environment.

Gas within these growing haloes is dynamically heated as it strives for virial equilibrium, whose heating rate is linearly proportional to the halo mass growth rate[13]. Dynamical heating is only important when gas cooling is inefficient, particularly in rapidly growing low-mass haloes. In combination with the LW negative feedback, it can further suppress any attempt at collapse. Both target haloes sustain substantial dynamical heating during their rapid growth events, driven primarily through major mergers. We find that they are the dominant mechanism for preventing Pop III star formation in these haloes.

The simulations follow the evolution of the target haloes until a density of $10^{-15}~{}\mathrm{g\ cm}^{-3}$, at which point it is certain that a collapsed object will form (see Supplementary Videos). Both haloes form a gravitationally unstable core with a mass and radius of 30,000 (200,000) M⊙ and 3 (15) pc for the MMH (LWH), respectively. The MMH grows gradually after its rapid growth event, allowing the system to form a rotationally supported disk that is comparatively cold at 300 K to the surrounding 10,000 K gas. The medium within the cold disk is turbulent, which causes numerous weak shocks (Fig. 3d). The disk then fragments into three clumps (Fig. 3a, 3b), as thermal and rotational support cannot counteract their gravitational forces (see Methods), all of which proceed to collapse. The morphology of the LWH is completely different from the MMH because of a recent major merger. The collision causes a sheet-like overdensity (Fig. 3e) that cools to 300 K, becoming gravitationally unstable to fragmentation. A single clump fragments from the sheet (Fig. 3f) and undergoes a catastrophic collapse. All clumps in both target haloes have masses around 1000 M⊙.

The radial profiles of the gas density (Fig. 4a) generally follow a power-law with a slope of –2 that is expected for an isothermal collapse, which can be translated into a gas mass enclosed (Fig. 4b). Deviations from a power-law originate from the two other clumps in the MMH, seen as spikes around 1 pc, and the sheet-like structure in the LWH, seen as an inflection point around 1 pc. The gas inside the Jeans mass (marked with squares) becomes shielded from the extragalactic LW background, allowing for the H2 fraction to increase to $10^{-3}$, sufficient to cool the gas down to 300 K (Fig. 4c). Inside a radial mass coordinate of 1000 M⊙, adiabatic compression heats the gaseous core to 600–800 K.

The key indicator for SMS formation is rapid gas inflow onto the gravitationally unstable core, not the overall Jeans mass. It has been shown that accretion rates over \sim$$0.04{~{}{\rm M_{\odot}~{}yr^{-1}}} onto a nascent, central core will result in SMS formation[9, 23]. Their weak hydrogen ionizing luminosities cannot reverse these strong gas flows[24, 25]. The respective infall mass fluxes (Fig. 4d) at the Jeans mass are 0.17 and 2.1 M⊙ yr*-1* for the MMH and LWH at the final time, above the critical value for SMS formation. This ample supply of inflowing gas provides fuel for the clumps within the central unstable object. The infall rates onto the clumps (Extended Data Fig. 7a) are between 0.03 and 0.08 M⊙ yr*-1* at their boundaries but increase rapidly to $\sim$0.5 M⊙ yr*-1* at a radial mass coordinate of 10,000 M⊙, suggesting that cores continue to grow rapidly after the final snapshot of our simulation for 1 Myr, similar to the typical SMS lifetime (Extended Data Fig. 7b). We thus conclude that the two target haloes will host SMS formation, and subsequently, a direct collapse black hole (DCBH) with an initial seed mass at least 1,000 M⊙ and perhaps up to 10,000 M⊙ within 1 Myr.

Using the formation requirements previously discussed, we can estimate (see Methods) the DCBH formation rate per comoving volume to be $1.1_{-0.91}^{+1.7}\times 10^{-3}$ SMSs per comoving Mpc*-3* (68% confidence interval) that form through this new formation scenario in overdense regions of the Universe. Given that only 0.01–0.1% of the universe is in such an overdense region, the global number density of DCBH formation is predicted to be $10^{-7}-10^{-6}$ per comoving Mpc*-3*, 100–1000 times higher than other estimates[26].

SMSs and thus DCBHs forming in rapidly growing haloes, as proposed here, will be tens of kpc away from the large-scale overdensity. They will take hundreds of Myrs, a substantial fraction of the Universe’s age at $z>6$, to fall into the nearby group of galaxies. We predict that these DCBHs will evolve to form the population of faint quasars observed at $z\sim 6$ (ref. 27, 28). This population will be within the reach of the James Webb Space Telescope that will provide stringent constraints on their number densities, directly comparable to our results here.