Astrophysical observations of high redshift quasars indicate that ∼ 10^9 M black holes exist when the Universe is just 800 Myr old after the Big Bang. The origin of these supermassive black holes (SMBHs) is still a mystery. In particular, it is extremely puzzling how they could become so massive in such a short time. A popular idea is that there exist heavy seed black holes in the early Universe and they grow massive by accreting baryons.
Assuming Eddington accretion, we can relate the black hole mass (MBH) and its seed mass (Mseed) as:
where, ∆t is the elapse time and τ = 450/fEdd(€ / (1-€) Myr is the e-folding time. € is the radiative efficiency and commonly assumed to be 0.1, and fEdd is the Eddington ratio (the ratio which relates the AGN bolometric luminosity with the Eddington luminosity), characterizing the accretion efficiency.
Considering J1007+2115, the most massive known quasar with the mass of 1.5 × 10^9 M at redshift, z > 7.5 and taking eddington ratio, fEdd ~ 1, researchers estimated Mseed ∼ 10⁴ M if it forms at z ∼ 30, i.e., ∆t = 597 Myr to its observed z = 7.51. Such a seed is too massive to be produced from collapsed Population III stars, but it could form through the direct collapse of pristine baryonic gas. The latter scenario predicts Mseed ∼ 10^5–10^6 M. However, observations showed there is another population of high redshifts SMBHs with fEdd much less than 1. For example, J1205-0000 is observed at redshift 6.7 with mass of black hole 2.2 × 10^9 M and eddington ratio of 0.16. The Eddington accretion then implies it grows from a seed with a mass of 2×10^8 M at z ∼ 30, too heavy to be produced via the direct collapse of gas.
In this recent study, Feng, Yu and Zhong proposed a scenario where a self-interacting dark matter (SIDM) halo experiences gravothermal instability and its central region collapses into a seed black hole (of high redshifts). Dark matter self-interactions can transport heat in the halo over cosmological timescales. As a gravothermal system, the halo has negative heat capacity and it is genuinely unstable. The central halo would become hot eventually and collapse to a singular state at late stages of the evolution. Thus SIDM has a natural mechanism in triggering gravitational stabilities, a necessary condition to form a black hole. Previous (but recent) studies also showed that SIDM is favored for explaining diverse dark matter distributions over a wide range of galactic systems.
“It is intriguing to explore an SIDM scenario that may explain the origin of the high-redshift SMBHs and observations of galaxies at z ∼ 0”, said Wei-Xiang Feng.
Feng, Yu & Xhong adopted a typical baryon mass profile for high-redshift protogalaxies as shown in graph above, (with the baryons, the halo does not form a large density core and it quickly evolves into the collapse phase. Its density keeps increasing and eventually becomes super-exponential in the end) and showed the collapse time can be shortened by a factor of 100, compared to the SIDM-only case. Even for the self-scattering cross section per unit mass σ/m ∼ 1 cm²/g, broadly consistent with the value used to explain galactic observations, the central halo could collapse sufficiently fast to form a seed for redshift, z ≥ 7. Depending on the halo mass, this scenario could explain both populations of high-redshift SMBHs with fEdd ∼ 1 and 0.1. It also has a built-in mechanism to dissipate angular momentum remanent of the central halo, i.e., viscosity induced by the self-interactions. The host halo must be on high tails of density fluctuations, implying that high-redshifts SMBHs are expected to be rare in this scenario, and the predicted host mass broadly agrees with the dynamical mass inferred from observations. They further showed when the 3D velocity dispersion of SIDM particles in the collapsed central region reaches 0.57c, the general relativistic (GR) instability can be triggered.
Their results indicated that self-interacting dark matter can provide a unified explanation for diverse dark matter distributions in galaxies today and the origin of SMBHs at redshifts z ∼ 6–7.
References: Wei-Xiang Feng, Hai-Bo Yu, Yi-Ming Zhong, “Seeding Supermassive Black Holes with Self-Interacting Dark Matter”, ArXiv, pp. 1-5, 2020. Link: https://arxiv.org/abs/2010.15132
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