Supersonic Gas Streams Enhance the Formation of Massive Black Holes in the Early Universe

Sep 28, 2017
30 pages
Published in:
  • Science 357 (2017) 1375
e-Print:

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Abstract: (arXiv)
The origin of super-massive black holes in the early universe remains poorly understood.Gravitational collapse of a massive primordial gas cloud is a promising initial process,but theoretical studies have difficulty growing the black hole fast enough.We report numerical simulations of early black hole formation starting from realistic cosmological conditions.Supersonic gas motions left over from the Big Bang prevent early gas cloud formation until rapid gas condensation is triggered in a proto-galactic halo. A protostar is formed in the dense, turbulent gas cloud, and it grows by sporadic mass accretion until it acquires 34,000 solar masses.The massive star ends its life with a catastrophic collapse to leave a black hole -- a promising seed for the formation of a monstrous black hole.
Note:
  • Published in Science, combined with updated SOM, additional images and movies are available at http://www-utap.phys.s.u-tokyo.ac.jp/naoki.yoshida/Blackhole/0929e.html
  • Materials and Methods
    • Cosmological Simulations
      • We perform a set of three-dimensional cosmological simulations to study the primordial star formation by incorporating the effect of baryonic streaming motions. The streaming motions can be included in a straightforward manner because the distribution of the streaming velocity is coherent over a length scale of a few comoving megaparsecs (cMpc), which is larger than regions that contain atomic-hydrogen cooling halos of interest to super-massive black hole
        • (SMBH) formation (7). Because the cosmological streaming velocity (SV) is not correlated with the local overdensity (30), the initial streaming direction can be set arbitrarily. We introduce the initial relative velocity between baryonic and cold dark matter components vbc as a constant uniform velocity along one axis into the cosmological initial conditions generated at redshift zini = 499. The root-mean-square value of vbc is σbc,rec = 30 km s-1 at the epoch of cosmological recombination zrec = 1089 (31). We set 3σbc(zini) as the initial value in our cosmological simulations, i.e. vbc(zini) = 90 km s-1
          • (1 + zini)/(1 + zrec) ∼ 41 km s-1
            • We run four simulations starting from different initial conditions: three cases (Run-A, B, and C) with the same SV but with different density fluctuations, and one reference case (RunRef) without SV. The initial amplitudes of the density fluctuation are σ8 = 2.0 for Run-A and
              • σ8 = 1.2 for Run-B and Run-C which are higher than the observational constraint σ8 ∼ 0.8 (31)
                • For the main case Run-B, we selected a target dark matter halo whose central velocity dispersion is ∼ 160 km s-1 at z = 7, being consistent with the estimated value of the host galaxies of observed SMBH (10). Run-A is expected to represent a rare, high-density peak. The reference run is initiated from the fiducial cosmological initial conditions with σ8 = 0.8. We adopt the standard Matter cosmology with the Planck cosmological parameters (31): matter density Ωm = 0.3086, baryon density Ωb = 0.04825, dark energy density ΩΛ = 0.6914 in units of the critical density, the Hubble constant of h = 0.6777, and the primordial spectral index ns = 0.96
                  • Λ-Cold Dark
                  • We generate the initial conditions in a (10 h-1 cMpc)3 cosmological volume using MUSIC (32). The cosmological simulations are performed by using the parallel N-body / Smoothed
                    • Particle Hydrodynamics (SPH) code GADGET (33) suitably modified for primordial star formation (34). We use a hierarchical zoom-in technique to generate the initial conditions for the target halos with higher mass and spatial resolutions. The particle masses of the dark matter and baryonic components in the zoom-in regions are 16.4 and 3.0 M, respectively. During the cloud collapse, we pose a strict refinement criterion that the local Jeans length is always resolved by 15 times the local SPH smoothing length. We achieve this by progressively increasing the spatial resolution using the particle-splitting technique (35). In all runs, we stop the cosmological SPH simulation when the hydrogen number density nH at the cloud center reaches
                      • [1012]
                        cm-3
                        • At this point, we define that a protostar is formed at the maximum density site
                          • Although a protostar is actually to be formed when the central density exceeds 1020 cm-3
                            • [17]
                              the time difference between the two epochs is very small. In all runs, we find a single protostar at the end point of our SPH simulations
                              • To characterize the main star-forming gas clouds, we define two relevant length and mass scales, the virial and Jeans scales. The virial length scale is defined as the radial distance from the center within which the mean density (including dark matter) is 200 times the cosmic mean value. The Jeans scale is defined as the radius where the ratio of the enclosed mass to the local effective Jeans mass, MJeans = (π/6)(v3 eff/G3/2
                                • ρ1/2
                                  • takes its maximum (Fig. S2). To evaluate the effective Jeans mass, we consider the additional dynamical support generated by the streaming velocity, veff = c2 s + vbc(z)2 where vbc(z) = 3σbc,rec(1 + z)/(1 + zrec). The actual values for the main gas clouds are summarized in Table S1
                                    • From the mass of the host dark matter halo evaluated at the time when a dense gas cloud is formed within it, we can estimate the number density of the early black holes (BHs) as follows. Since the cosmological streaming velocity and the local over-density are not correlated at the length scales of our interest here (30), the number density of the intermediate-mass BHs formed as in the present study can be estimated by multiplying the number density of the host dark matter halos and the probability distribution of the streaming velocity. Using the halo mass function of (36) with our standard cosmological parameters (31), we obtain the abundance of dark matter halos with mass > 107
                                      • M to be ∼ 5000 per cubic cGpc (comoving gigaparsecs) at z = 30, and ∼ 8.9 × 105 per cubic cGpc at z = 25. The probability of such halos being located in regions with more than 3σ streaming motions is ∼ 5.9 × 10-6 and that for more than
                                        • 2.7σ is ∼ 6.9 × 10-5
                                          • (37, 38). Multiplying these numbers yields the BH number density of
                                            • ∼ 0.03-61 cGpc-3
                                              • Gravito-Radiation-Hydrodynamic Simulations
                                                • The accretion process of the new-born protostar is followed by using the three-dimensional hydrodynamic code PLUTO (39) augmented by self-gravity (40) and radiation transfer (41)
                                                  • This gravito-radiation-hydrodynamics framework was further coupled to the protostellar evolution code STELLAR (42) suitably modified to study primordial star formation (23). We use the gas opacity for a gas with primordial composition