Effect of radiative transfer on damped Lyman-alpha and Lyman limit systems in cosmological SPH simulations

We study the effect of local stellar radiation and UVB on the physical properties of DLAs and LLSs at z=3 using cosmological SPH simulations. We post-process our simulations with the ART code for radiative transfer of local stellar radiation and UVB. We find that the DLA and LLS cross sections are significantly reduced by the UVB, whereas the local stellar radiation does not affect them very much except in the low-mass halos. This is because clumpy high-density clouds near young star clusters effectively absorb most of the ionizing photons from young stars. We also find that the UVB model with a simple density threshold for self-shielding effect can reproduce the observed column density distribution function of DLAs and LLSs very well, and we validate this model by direct radiative transfer calculations of stellar radiation and UVB with high angular resolution. We show that, with a self-shielding treatment, the DLAs have an extended distribution around star-forming regions typically on ~ 10-30 kpc scales, and LLSs are surrounding DLAs on ~ 30-60 kpc scales. Our simulations suggest that the median properties of DLA host haloes are: Mh = 2.4*10^10 Msun, SFR = 0.3 Msun/yr, M* = 2.4*10^8 Msun, and Z/Zsun = 0.1. About 30 per cent of DLAs are hosted by haloes having SFR = 1 - 20 Msun/yr, which is the typical SFR range for LBGs. More than half of DLAs are hosted by the LBGs that are fainter than the current observational limit. Our results suggest that fractional contribution to LLSs from lower mass haloes is greater than for DLAs. Therefore the median values of LLS host haloes are somewhat lower with Mh = 9.6*10^9 Msun, SFR = 0.06 Msun/yr, M* = 6.5*10^7 Msun and Z/Zsun = 0.08. About 80 per cent of total LLS cross section are hosted by haloes with SFR < 1 Msun/yr, hence most LLSs are associated with low-mass halos with faint LBGs below the current detection limit.Comment: 18 pages, 12 figures, accepted for publication in MNRA

Supermassive Black Hole Formation at High Redshifts via Direct Collapse: Physical Processes in the Early Stage

We use numerical simulations to explore whether direct collapse can lead to the formation of SMBH seeds at high-z. We follow the evolution of gas within DM halos of 2 x 10^8 Mo and 1 kpc. We adopt cosmological density profiles and j-distributions. Our goal is to understand how the collapsing flow overcomes the centrifugal barrier and whether it is subject to fragmentation. We find that the collapse leads either to a central runaway or to off-center fragmentation. A disk-like configuration is formed inside the centrifugal barrier. For more cuspy DM distribution, the gas collapses more and experiences a bar-like perturbation and a central runaway. We have followed this inflow down to ~10^{-4} pc. The flow remains isothermal and the specific angular momentum is efficiently transferred by gravitational torques in a cascade of nested bars. This cascade supports a self-similar, disk-like collapse. In the collapsing phase, virial supersonic turbulence develops and fragmentation is damped. For larger initial DM cores the timescales become longer. In models with more organized initial rotation, a torus forms and appears to be supported by turbulent motions. The evolution depends on the competition between two timescales, corresponding to the onset of the central runaway and off-center fragmentation. For less organized rotation, the torus is greatly weakened, the central accretion timescale is shortened, and off-center fragmentation is suppressed --- triggering the central runaway even in previously `stable' models. The resulting SMBH masses lie in the range 2 x 10^4 Mo - 2 x 10^6 Mo, much higher than for Population III remnants. We argue that the above upper limit appears to be more realistic mass. Corollaries of this model include a possible correlation between SMBH and DM halo masses, and similarity between the SMBH and halo mass functions, at time of formation.Comment: 20 pages, 15 figures, 3 tables. Accepted for publication in the Astrophysical Journa

Commutative Energetic Subsets of BCK-Algebras

The notions of a C-energetic subset and (anti) permeable C-value in BCK-algebras are introduced, and related properties are investigated. Conditions for an element t in [0, 1] to be an (anti) permeable C-value are provided. Also conditions for a subset to be a C-energetic subset are discussed. We decompose BCK-algebra by a partition which consists of a C-energetic subset and a commutative ideal

Supermassive Black Hole Seed Formation at High Redshifts: Long-Term Evolution of the Direct Collapse

We use cosmological adaptive mesh refinement (AMR) code Enzo zoom-in simulations to study the long term evolution of the collapsing gas within dark matter (DM) halos at high redshifts. This direct collapse process is a leading candidate for rapid formation of supermassive black hole (SMBH) seeds at high z. To circumvent the Courant condition at small radii, we have used the sink particle method, and focus on the evolution on scales ~0.01-10 pc. The collapse proceeds in two stages, with the secondary runaway happening within the central 10 pc, and with no detected fragmentation. The sink particles form when the collapsing gas requires additional refinement of the grid size at the highest refinement level. Their mass never exceeds ~10^3 Mo, with the sole exception of the central seed which grows dramatically to ~ 2 x 10^6 Mo in ~2 Myr, confirming the feasibility of this path to the SMBH. The time variability of angular momentum axis in the accreted gas results in the formation of two misaligned disks --- a small inner disk, and a more massive, outer disk which is inclined by ~45^o to the inner disk. The self-gravity of these disks is heavily diluted --- both disks lie within the Roche limit of the central seed. While the inner disk is geometrically thin and weakly asymmetric, the outer disk flares due to turbulent motions as a result of the massive inflow along a pair of penetrating filaments. The geometry of inflow via filaments determines the dominant and secondary Fourier modes in this disk --- these modes have a non-self-gravitational origin. We do not confirm that m=1 is a principal mode that drives the inflow in the presence of a central massive object. While the positions of the disks depend on the scale chosen to break the self-similar collapse, the overall configuration appears to be generic, and is expected to form when the central seed becomes sufficiently massive.Comment: 14 pages, 11 figures, MNRAS, in press, typos correcte