Theory Group Concepción

Departamento de Astronomía, Universidad de Concepción, Chile

Formation of the first supermassive black holes


Supermassive black holes are common in galaxies, and have already been observed at very early cosmic times, including an active black hole with about one billion solar masses at redshift 6.4 (Fan et al. 2003) and an active black hole with about twice that mass at redshift 7.085 (Mortlock et al. 2011). The age of the Universe at that time was about 760 million years after the Big Bang (see e.g. Ned Wright's cosmology calculator), i.e. about 1/20 of the age of the Universe today.

To form such massive black holes at so early times requires extremely high accretion rates, on average more than 1 solar mass per year. The latter is extremely high in an astronomical context, and typically larger than the Eddington limit. As this limit is particularly restrictive at low black hole masses, it is often considered to be advantageous if the initial seed black holes are already more massive, so that it becomes more straightforward to maintain high accretion rates. There is no consensus yet on how this can be achieved, though different scenarios have been tested at this point and some trends are emerging.

Perhaps the ideal case to form very massive black holes is the so-called ''Direct Collapse Model'', assuming that a massive gas cloud collapses directly into one single object. This is an evidently difficult scenario, requiring highly efficient angular momentum transport to prevent fragmentation, as well as a high gas pressure to favor the formation of one single object. To achieve this, it is best if metals and dust are not present, to avoid their contributions to the cooling. In the case of a primordial gas, molecular hydrogen can cool the gas down to temperatures of about 300 K (see first stars page), leading to stellar masses of 100 solar. If molecular hydrogen is however efficiently destroyed by radiative backgrounds, the only remaining coolant is atomic hydrogen, leading to temperatures close to 10.000 K.

Fig. 1: The atomic and molecular hydrogen cooling function as a function of gas temperature (credit: NED).

Such an primordial atomic hydrogen gas provides the ideal conditions for forming very massive objects, though clearly it is a highly idealized case. We will explore in the following how massive objects form under these conditions, and then start relaxing them by considering weaker radiation backgrounds and the presence of dust grains.

Fragmentation in primordial atomic gas

To explore if the direct collapse scenario is feasible in a primordial atomic gas, we pursued a systematic fragmentation study based on 9 different simulations, each of them running with about 256 CPUs for approximately one month. The following snapshot shows the density structure in the central region after about 4 dynamical times:

Fig. 2: Fragmentation in a primordial atomic gas (Latif et al. 2013a).

The results show that fragmentation occurs in about 3 out of 9 simulations. While these clumps still had low masses, we pursued a set of additional simulations with a lower resolution, but following the time evolution over about 20.000 years. After that time, the masses of the central clumps are considerably enhanced, with a typical value of about 100.000 solar masses:

Fig. 3: Mass of the most massive object in different simulations after an accretion time of 20.000 years (Latif et al. 2013b). (The different colors correspond to simulations with and without turbulence subgrid models. LES: with; ILES: without.)

In addition to the high masses, we found a rather characteristic behavior of the accretion rate, which is first increasing as a result of the increasing central mass, and subsequently decreasing or flattening due to angular momentum conservation:

Fig. 4: Characteristic time evolution of the accretion rates (Latif et al. 2013b).

While the direct collapse scenario seems to work under such idealized conditions, the required UV flux to dissociate the molecular hydrogen and keep the gas atomic is very high. This is particularly true when adopting more realistic stellar radiation backgrounds, and when considering 3D effects like the virialization shock, which is often not done in more simplified models. The latter however enhances the ionization degree and stimulates the formation of molecular hydrogen, thus requiring an even stronger radiation background (see Latif et al. (2014a) for a detailed discussion. In realistic cases, the thermal evolution is thus more complex, as can be seen here (still with slightly optimistic assumptions on the shape of the radiative background):

Fig. 5: Thermal evolution in two different halos for different radiation backgrounds parametrized through J21 (Latif et al. 2014b).

As the molecular hydrogen cooling may substantially decrease the pressure in the central region and therefore enhance fragmentation, it was essential to explore how the mass of the most massive object depends on the strength of the radiative background. We find a clear trend of decreasing mass with decreasing strength of the background:

Fig. 6: Mass of the central object as a function of the strength of the UV radiation backgrounds parametrized through J21 (Latif et al. 2014b). Under realistic conditions, one can therefore expect that, while massive objects may still form, fragmentation should at least be enhanced and the masses more moderate. The problem becomes even more severe when considering even trace amounts of dust, which strongly contribute to the cooling at high densities, and thus considerably decrease the temperature:

Fig. 7: Thermal evolution in the presence of dust (Latif et al. 2016).

Such a decrease in the temperature has a significant impact on the density distribution, favoring the formation of filaments and inducing a transition towards the formation of less massive objects:

Fig. 8: Impact of dust on the density distribution (Latif et al. 2016). Overall, it therefore seems relatively likely that, under realistic conditions, fragmentation will occur, leading to the formation of a dense massive cluster rather than one single object. However, even in this case, a massive black hole may still form. For instance, such a cluster can become gravitationally unstable, leading to run-away collapse and the formation of one massive object from the core of the cluster. Or, if it is dense and long-lived enough, collisions in the cluster may be frequent enough to form massive objects through mergers, and in particular the presence of gas may favor such effects.

In the future, a dedicated focus is therefore to explore the conditions under which such clusters could still lead to the formation of central massive objects. We explore this using a combination of hydrodynamics-codes (particularly GRADSPH coupled with the astrochemistry package KROME as well as N-body codes like the AMUSE package or the Nbody6-code to address these questions both in the gas-dominated and the protostar-dominated regime.

This work is supported by the following grants:

© Theory Group Concepcion 2019