• Astrophysics
• Cosmology
• Accretion disks
• Black holes
• first stars
• early Universe

The appearance of the first black holes is, along with the birth of the first stars, one of the most important events occurred within the first billion years of our Universe. The formation and evolution of these two classes of astrophysical objects are profoundly interwoven and they had a crucial role in the cosmic evolution, because of their ability to inject photons, mass, energy and momentum into the surrounding interstellar or intergalactic medium, altering the subsequent galaxy formation history.

Many questions in the cosmological picture remain still open, in particular the observational evidence of the existence of black holes as massive as 10^9 solar masses, named super-massive black holes (SMBH), when the Universe was few hundred million years old. This fact is in tension with the standard theory of black holes growth, because a stellar-mass seed would require a much longer time to accumulate such a big amount of mass. In the last decade, among all black holes formation channels, growing interest has been given to the Direct Collapse Black Hole (DCBH) scenario, that allows the formation of massive seeds of 10^5-10^6 solar masses if the proper environmental conditions are satisfied. The embryo of this object is supposed to grow via an accretion disk and, to this regard, the standard picture of a smooth accretion mode has been questioned by recent simulations, which suggest that accretion disks may undergo fragmentation due to gravitational instability, possibly limiting the growth of the seed. Moreover, observational evidence of black holes in this mass range are still missing and upcoming observational facilities such as JWST, ATHENA, WFIRST and SKA represent a great occasion to constrain the numerous theoretical models about black holes formation that have been proposed in the last years.

A precise modeling of the phenomenon would require the develop of a full 3D radiation-hydrodynamic code able to follow the evolution of the gas in an atomic-cooling halo, starting from cosmological conditions, in order to study the evolution of the accretion disk around a black hole embryo, predicting its observational features. The aim of this thesis is to constitute the first step in this direction, that is the development, starting from the beginning, of a numerical code in 2D-geometry without radiation transfer. After accurate tests of the code, attention is given to the study of the gravitational instability of a disk in the context of the DCBH formation.

The thesis is structured as follow. In the first two chapters the physical background is provided, starting from the cosmological context to primordial star formation, with focus on the role of the accretion disks. The problem of SMBH formation is posed and the possible channels of primordial black holes formation are reviewed, in particular the Direct Collapse Black Hole scenario, discussing the assumptions at the basis of this mechanism and their feasibility. A detailed description of the developed 2D-hydrodynamics code follows. Then, the physical model adopted in order to study our problem is illustrated, underlining the assumptions behind it. Finally, our results are presented and critically discussed. We analyze the accretion history onto the central object dividing it intro three distinct phases. Of each stage, we illustrate the main physical properties of the cloud, focusing on the evolution of the disk during the last stage, where gravitational instability occurs, causing recurring episodes of fragmentation. In particular, we show that, from the temporal window examined, the formation of a DCBH is likely to happen despite an irregular accretion mode. We compare our results with existing literature. Finally we discuss the validity of the assumptions made in designing the physical model and we outline the possible future works necessary to improve our results and to confront them with observations.