Direct Collapse to Supermassive Black Hole Seeds with Radiative Transfer: Isolated Halos

Direct collapse within dark matter (DM) halos is a promising path to form supermassive black hole (SMBH) seeds at high redshifts. The outer part of this collapse remains optically thin, and has been studied intensively using numerical simulations. However, the innermost region of the collapse is expected to become optically thick and requires us to follow the radiation field in order to understand its subsequent evolution. So far, the adiabatic approximation has been used exclusively for this purpose. We apply radiative transfer in the flux-limited diffusion (FLD) approximation to solve the evolution of coupled gas and radiation, for isolated halos. For direct collapse within isolated DM halos, we find that (1) the photosphere forms at ~10^{-6} pc and rapidly expands outward. (2) A central core forms, with a mass of ~1 Mo, supported by thermal gas pressure gradients and rotation. (3) Growing thermal gas and radiation pressure gradients dissolve it. (4) This process is associated with a strong anisotropic outflow, and another core forms nearby and grows rapidly. (5) Typical radiation luminosity emerging from the photosphere encompassing these cores is ~5 x 10^{37}-5 x 10^{38} erg/s, of order the Eddington luminosity. (6) Two variability timescales are associated with this process: a long one, which is related to the accretion flow within the central ~10^{-4}-10^{-3} pc, and ~0.1 yr, which is related to radiation diffusion. (7) Adiabatic models have been run for comparison and their evolution differs profoundly from that of the FLD models, by forming a central geometrically-thick disk. Overall, an adiabatic equation of state is not a good approximation to the advanced stage of direct collapse, mainly because the radiation in the FLD is capable of escaping due to anisotropy in the optical depth and associated gradients.Comment: 19 pages, 17 figures, MNRAS, in press; correcting typo

Direct Collapse to Supermassive Black Hole Seeds with Radiation Transfer: Cosmological Halos

We have modeled direct collapse of a primordial gas within dark matter halos in the presence of radiative transfer, in high-resolution zoom-in simulations in a cosmological framework, down to the formation of the photosphere and the central object. Radiative transfer has been implemented in the flux-limited diffusion (FLD) approximation. Adiabatic models were run for comparison. We find that (a) the FLD flow forms an irregular central structure and does not exhibit fragmentation, contrary to adiabatic flow which forms a thick disk, driving a pair of spiral shocks, subject to Kelvin-Helmholtz shear instability forming fragments; (b) the growing central core in the FLD flow quickly reaches ~10 Mo and a highly variable luminosity of 10^{38}-10^{39} erg/s, comparable to the Eddington luminosity. It experiences massive recurrent outflows driven by radiation force and thermal pressure gradients, which mix with the accretion flow and transfer the angular momentum outwards; and (c) the interplay between these processes and a massive accretion, results in photosphere at ~10 AU. We conclude that in the FLD model (1) the central object exhibits dynamically insignificant rotation and slower than adiabatic temperature rise with density; (2) does not experience fragmentation leading to star formation, thus promoting the fast track formation of a supermassive black hole (SMBH) seed; (3) inclusion of radiation force leads to outflows, resulting in the mass accumulation within the central 10^{-3} pc, which is ~100 times larger than characteristic scale of star formation. The inclusion of radiative transfer reveals complex early stages of formation and growth of the central structure in the direct collapse scenario of SMBH seed formation.Comment: 19 pages, 16 figures, MNRAS, accepted for publicatio

Formation of Supermassive Black Holes in the Early Universe: High-Resolution Numerical Simulations of Radiation Transfer Inside Collapsing Gas

Observations of high-redshift quasars reveal that super massive black holes (SMBHs) with masses exceeding 109 M⊙ formed as early as redshift z ~ 7 [1,3,6]. This means that SMBHs have already formed ~700 million years after the Big Bang. How did such SMBHs could grow so quickly? In this work, we use a modified and improved version of the blockstructured adaptive mesh refinement (AMR) code ENZO [2] to provide high spatial and temporal resolution for modeling the formation of SMBHs via direct collapse within dark matter (DM) halos at high redshifts. The radiation hydrodynamics equations are solved in the flux-limited diffusion (FLD) approximation in the full cosmological background [5]. The chemical species are assumed to be in local thermodynamic equilibrium (LTE). We follow the evolution of the collapsing gas from a kilo-parsec scale down to 0.001 AU --- 11 decades in radius

Direct Collapse to Supermassive Black Hole Seeds with Radiative Transfer: Isolated Halos

Direct collapse within dark matter haloes is a promising path to form supermassive black hole seeds at high redshifts. The outer part of this collapse remains optically thin. However, the innermost region of the collapse is expected to become optically thick and requires to follow the radiation field in order to understand its evolution. So far, the adiabatic approximation has been used exclusively for this purpose. We apply radiative transfer in the flux-limited diffusion (FLD) approximation to solve the evolution of coupled gas and radiation for isolated haloes. We find that (1) the photosphere forms at 10−6 pc and rapidly expands outwards. (2) A central core forms, with a mass of 1 M⊙, supported by gas pressure gradients and rotation. (3) Growing gas and radiation pressure gradients dissolve it. (4) This process is associated with a strong anisotropic outflow; another core forms nearby and grows rapidly. (5) Typical radiation luminosity emerging from the photosphere is 5 × 1037–5 × 1038 erg s−1, of the order the Eddington luminosity. (6) Two variability time-scales are associated with this process: a long one, which is related to the accretion flow within the central 10−4–10−3 pc, and 0.1 yr, related to radiation diffusion. (7) Adiabatic models evolution differs profoundly from that of the FLD models, by forming a geometrically thick disc. Overall, an adiabatic equation of state is not a good approximation to the advanced stage of direct collapse, because the radiation is capable of escaping due to anisotropy in the optical depth and associated gradients

Direct Collapse to Supermassive Black Hole Seeds with Radiation Transfer: Cosmological Haloes

We have modelled direct collapse of a primordial gas within dark matter haloes in the presence of radiative transfer, in high-resolution zoom-in simulations in a cosmological framework, down to the formation of the photosphere and the central object. Radiative transfer has been implemented in the flux-limited diffusion (FLD) approximation. Adiabatic models were run for comparison. We find that (a) the FLD flow forms an irregular central structure and does not exhibit fragmentation, contrary to adiabatic flow which forms a thick disc, driving a pair of spiral shocks, subject to Kelvin–Helmholtz shear instability forming fragments; (b) the growing central core in the FLD flow quickly reaches ∼10M⊙ and a highly variable luminosity of 1038 − 1039 erg s−1⁠, comparable to the Eddington luminosity. It experiences massive recurrent outflows driven by radiation force and thermal pressure gradients, which mix with the accretion flow and transfer the angular momentum outwards; and (c) the interplay between these processes and a massive accretion, results in photosphere at ∼10 au. We conclude that in the FLD model (1) the central object exhibits dynamically insignificant rotation and slower than adiabatic temperature rise with density; (2) does not experience fragmentation leading to star formation, thus promoting the fast track formation of a supermassive black hole (SMBH) seed; (3) inclusion of radiation force leads to outflows, resulting in the mass accumulation within the central 10−3 pc, which is ∼100 times larger than characteristic scale of star formation. The inclusion of radiative transfer reveals complex early stages of formation and growth of the central structure in the direct collapse scenario of SMBH seed formation

Femtosecond laser-induced sub-wavelength plasma inside dielectrics: I. Field enhancement

The creation of high energy density ($\gtrsim10^6$ joules per cm$^3$) over-critical plasmas in a large volume has essential applications in the study of warm dense matter, being present in the hot cores of stars and planets. It was recently shown that femtosecond Bessel beams enable creating over-critical plasmas inside sapphire with sub-wavelength radius and several tens of micrometers in length. Here, the dependence of field structure and absorption mechanism on the plasma density transverse profile are investigated by performing self-consistent Particle-In-Cell (PIC) simulations. Two { limiting} cases are considered: one is a homogeneous step-like profile, that can sustain plasmon formation, the second is an inhomogeneous Gaussian profile, where resonance absorption occurs. Comparing experimental absorption measures to analytical predictions allows determining the plasma parameters used in PIC simulations. The PIC simulation results are in good agreement with experimental diagnostics of total absorption, near-field fluence distribution, and far-field radiation pattern. We show that in each case an ambipolar field forms at the plasma surface due to the expansion of the hot electrons and that electron sound waves propagate into the over-critical region.Comment: 13 pages, 10 figures, published in Physics of Plasma

Guidelines for Fortran Programming on Heterogeneous Architectures

General coding guidelines in Fortran are presented for the heterogeneousarchitectures. This includes the common compiler options, optimization, andvectorization by the developer and management of the memory