Mass function of haloes: scale invariant models

Press-Schechter theory gives a simple, approximate functional form of the mass function of dark matter haloes. Sheth and Tormen (ST) refined this mass function to give an improved analytical fit to results of N-body simulations. These forms of the halo mass function are universal (independent of cosmology and power spectrum) when scaled in suitable variables. Using large suites of LCDM N-body simulations, studies in the last few years have shown that this universality is only approximate. We explore whether some of the deviations from universality can be attributed to the power spectrum by computing the mass function in N-body simulations of various scale-free models in an Einstein-de Sitter cosmology. This choice of cosmology does not introduce any scale into the problem. These models have the advantage of being self-similar, hence stringent checks can be imposed while running these simulations. This set of numerical experiments is designed to isolate any power spectrum dependent departures from universality of mass functions. We show explicitly that the best fit ST parameters have a clear dependence on power spectrum. Our results also indicate that an improved analytical theory with more parameters is required in order to provide better fits to the mass function.Comment: 8 pages, four figure

High redshift supermassive blackholes: accretion through cold flows

We use zoom-in techniques to re-simulate three high-redshift (z > 5.5) halos which host 10^9 solar mass blackholes from the ~ Gpc volume, MassiveBlack cosmological hydrodynamic simulation. We examine a number of factors potentially affecting supermassive blackhole growth at high redshift in cosmological simulations. These include numerical resolution, feedback prescriptions and formulation of smoothed particle hydrodynamics. We find that varying the size of the region over which feedback energy is deposited directly, either for fixed number of neighbours or fixed volume makes very little difference to the accretion history of blackholes. Changing mass resolution by factors of up to 64 also does not change the blackhole growth history significantly. We find that switching from the density-entropy formulation to the pressure-entropy formulation of smoothed particle hydrodynamics slightly increases the accretion rate onto blackholes. In general numerical details appear to have small effects on the main fueling mechanism for blackholes at these high redshifts. We examine the fashion by which this occurs, finding that the insensitivity to simulation technique seems to be a hallmark of the cold flow feeding picture of these high-z supermassive blackholes. We show that the gas that participates in critical accretion phases, in these massive objects at z > 6~7 is in all cases colder, denser, and forms more coherent streams than the average gas in the halo. This is also mostly the case when the blackhole accretion is feedback regulated (z < 6), however the distinction is less prominent. For our resimulated halos, cold flows appear to be a viable mechanism for forming the most massive blackholes in the early universe, occurring naturally in LambdaCDM models of structure formation. Not requiring fine tuning of numerical parameters, they seem to be physically inevitable in these objects.Comment: 15 pages, 12 figure

Halo mass function in scale invariant models

Sheth-Tormen mass function has been widely used to quantify the abundance of dark matter halos. It is a significant improvement over the Press-Schechter mass function as it uses ellipsoidal collapse in place of spherical collapse. Both of these mass functions can be written in a form that is universal, i.e., independent of cosmology and power spectrum when scaled in suitable variables. However, cosmological simulations have shown that this universality is approximate. In this paper, we investigate the power spectrum dependence of halo mass function through a suite of dark-matter-only N-body simulations of seven power-law models in an Einstein-de Sitter cosmology. This choice of cosmology and a power-law power spectrum ensures the self-similar evolution of dark matter distribution, allowing us to isolate the power spectrum dependence of mass function. We find that the mass function shows a clear non-universality. We present fits for the parameters of the Sheth-Tormen mass function for a range of power-law power-spectrum indices. We find a mild evolution in the overall shape of the mass function with the epoch. Finally, we extend our result to LCDM cosmology. We show that the Sheth-Tormen mass function with parameter values derived from a matched power-law EdS cosmology provides a better fit to the LCDM mass function than the standard Sheth-Tormen mass function. Our results indicate that an improved analytical theory is required to provide better fits to the mass function.Comment: 11 pages, 10 figures. This is a much expanded and upgraded version of 0908.2702. Submitted to MNRA

Galaxy Shapes and Intrinsic Alignments in The MassiveBlack-II Simulation

The intrinsic alignment of galaxy shapes with the large-scale density field is a contaminant to weak lensing measurements, as well as being an interesting signature of galaxy formation and evolution (albeit one that is difficult to predict theoretically). Here we investigate the shapes and relative orientations of the stars and dark matter of halos and subhalos (central and satellite) extracted from the MassiveBlack-II simulation, a state-of-the-art high resolution hydrodynamical cosmological simulation which includes stellar and AGN feedback in a volume of $(100{h^{-1}\mathrm{Mpc}})^3$. We consider redshift evolution from $z=1$ to $0.06$ and mass evolution within the range of subhalo masses, $10^{10} -6.0 \times 10^{14.0}{h^{-1}M_{\odot}}$. The shapes of the dark matter distributions are generally more round than the shapes defined by stellar matter. The projected root-mean-square (RMS) ellipticity per component for stellar matter is measured to be $e_\text{rms} = 0.28$ at $z=0.3$ for $M_{subhalo}> 10^{12.0}{h^{-1}M_{\odot}}$, which compares favourably with observational measurements. We find that the shapes of stellar and dark matter are more round for less massive subhalos and at lower redshifts. By directly measuring the relative orientation of the stellar matter and dark matter of subgroups, we find that, on average, the misalignment between the two components is larger for less massive subhalos. The mean misalignment angle varies from $\sim 30^{\circ}-10^{\circ}$ for $M \sim 10^{10} - 10^{14} {h^{-1}M_{\odot}}$ and shows a weak dependence on redshift. We also compare the misalignment angles in central and satellite subhalos at fixed subhalo mass, and find that centrals are more misaligned than satellites. We present fitting formulae for the shapes of dark and stellar matter in subhalos and also the probability distributions of misalignment angles.Comment: 18 pages, 18 figures, submitted to MNRA

Intrinsic alignments of galaxies in the MassiveBlack-II simulation: analysis of two-point statistics

The intrinsic alignment of galaxies with the large-scale density field is an important astrophysical contaminant in upcoming weak lensing surveys. We present detailed measurements of the galaxy intrinsic alignments and associated ellipticity-direction (ED) and projected shape ($w_{g+}$) correlation functions for galaxies in the cosmological hydrodynamic MassiveBlack-II (MB-II) simulation. We carefully assess the effects on galaxy shapes, misalignment of the stellar component with the dark matter shape and two-point statistics of iterative weighted (by mass and luminosity) definitions of the (reduced and unreduced) inertia tensor. We find that iterative procedures must be adopted for a reliable measurement of the reduced tensor but that luminosity versus mass weighting has only negligible effects. Both ED and $w_{g+}$ correlations increase in amplitude with subhalo mass (in the range of $10^{10} - 6.0\times 10^{14}h^{-1}M_{\odot}$), with a weak redshift dependence (from $z=1$ to $z=0.06$) at fixed mass. At $z \sim 0.3$, we predict a $w_{g+}$ that is in reasonable agreement with SDSS LRG measurements and that decreases in amplitude by a factor of $\sim 5$--18 for galaxies in the LSST survey. We also compared the intrinsic alignments of centrals and satellites, with clear detection of satellite radial alignments within their host halos. Finally, we show that $w_{g+}$ (using subhalos as tracers of density) and $w_{\delta+}$ (using dark matter density) predictions from the simulations agree with that of non-linear alignment models (NLA) at scales where the 2-halo term dominates in the correlations (and tabulate associated NLA fitting parameters). The 1-halo term induces a scale dependent bias at small scales which is not modeled in the NLA model.Comment: 25 pages, 27 figures, revised after referee comments, accepted for publication in MNRA