Avishai Dekel

Profiles of dark haloes. Evolution, scatter, and environment

We study dark-matter halo density profiles in a high-resolution N-body simulation of aCDM cosmology. Our statistical sample contains �5000 haloes in the range 10 11 10 14 h −1 M⊙ and the resolution allows a study of subhaloes inside host haloes. The profiles are parameterized by an NFW form with two parameters, an inner radius rs and a virial radius Rvir, and we define the halo concentration cvirRvir/rs. We find that, for a given halo mass, the redshift dependence of the median concentration is cvir / (1 + z) −1 . This corresponds to rs(z) � constant, and is contrary to earlier suspicions that cvir does not vary much with redshift. The implications are that high- redshift galaxies are predicted to be more extended and dimmer than expected before. Second, we find that the scatter in halo profiles is large, with a 1� �(logcvir) = 0.18 at a given mass, corresponding to a scatter in maximum rotation velocities of �Vmax/Vmax = 0.12. We discuss implications for modelling the Tully-Fisher relation, which has a smaller reported intrinsic scatter. Third, subhaloes and haloes in dense environments tend to be more concentrated than isolated haloes, and show a larger scatter. These results suggest that cvir is an essential parameter for the theory of galaxy modelling, and we briefly discuss implications for the universality of the Tully- Fisher relation, the formation of low surface brightness galaxies, and the origin of the Hubble sequence. We present an improved analytic treatment of halo formation that fits the measured relations between halo parameters and their redshift dependence, and can thus serve semi-analytic studies of galaxy formation.

Virial shocks in galactic haloes

We investigate the conditions for the existence of an expanding virial shock in the gas falling within a spherical dark matter halo. The shock relies on pressure support by the shock-heated gas behind it. When the radiative cooling is efficient compared with the infall rate, the post-shock gas becomes unstable; it collapses inwards and cannot support the shock. We find for a monatomic gas that the shock is stable when the post-shock pressure and density obey γ e f f ≡ (d In P/dt)/(d In p/dt) > 10/7. When expressed in terms of the pre-shock gas properties at radius r it reads as ρrΛ(T)/u 3 < 0.0126, where p is the gas density, u is the infall velocity and A(T) is the cooling function, with the post-shock temperature T u 2 . This result is confirmed by hydrodynamical simulations, using an accurate spheri-symmetric Lagrangian code. When the stability analysis is applied in cosmology, we find that a virial shock does not develop in most haloes that form before z ∼ 2, and it never forms in haloes less massive than a few 10 1 1 M O .. In such haloes, the infalling gas is not heated to the virial temperature until it hits the disc, thus avoiding the cooling-dominated quasi-static contraction phase. The direct collapse of the cold gas into the disc should have non-trivial effects on the star formation rate and on outflows. The soft X-ray produced by the shock-heated gas in the disc is expected to ionize the dense disc environment, and the subsequent recombination would result in a high flux of La emission. This may explain both the puzzling low flux of soft X-ray background and the La emitters observed at high redshift.

FORMATION OF MASSIVE GALAXIES AT HIGH REDSHIFT: COLD STREAMS, CLUMPY DISKS, AND COMPACT SPHEROIDS

We present a simple theoretical framework for massive galaxies at high redshift, where the main assembly and star formation occurred, and report on the first cosmological simulations that reveal clumpy disks consistent with our analysis. The evolution is governed by the interplay between smooth and clumpy cold streams, disk instability, and bulge formation. Intense, relatively smooth streams maintain an unstable dense gas-rich disk. Instability with high turbulence and giant clumps, each a few percent of the disk mass, is self-regulated by gravitational interactions within the disk. The clumps migrate into a bulge in 10 dynamical times, or 0.5 Gyr. The cosmological streams replenish the draining disk and prolong the clumpy phase to several Gigayears in a steady state, with comparable masses in disk, bulge, and dark matter within the disk radius. The clumps form stars in dense subclumps following the overall accretion rate, ~100 M ? yr?1, and each clump converts into stars in ~0.5 Gyr. While the clumps coalesce dissipatively to a compact bulge, the star-forming disk is extended because the incoming streams keep the outer disk dense and susceptible to instability and because of angular momentum transport. Passive spheroid-dominated galaxies form when the streams are more clumpy: the external clumps merge into a massive bulge and stir up disk turbulence that stabilize the disk and suppress in situ clump and star formation. We predict a bimodality in galaxy type by z ~ 3, involving giant-clump star-forming disks and spheroid-dominated galaxies of suppressed star formation. After z ~ 1, the disks tend to be stabilized by the dominant stellar disks and bulges. Most of the high-z massive disks are likely to end up as todays early-type galaxies.

THE SINS SURVEY OF z ∼ 2 GALAXY KINEMATICS: PROPERTIES OF THE GIANT STAR-FORMING CLUMPS ∗

We have studied the properties of giant star-forming clumps in five z ~ 2 star-forming disks with deep SINFONI AO spectroscopy at the ESO VLT. The clumps reside in disk regions where the Toomre Q-parameter is below unity, consistent with their being bound and having formed from gravitational instability. Broad H?/[N II] line wings demonstrate that the clumps are launching sites of powerful outflows. The inferred outflow rates are comparable to or exceed the star formation rates, in one case by a factor of eight. Typical clumps may lose a fraction of their original gas by feedback in a few hundred million years, allowing them to migrate into the center. The most active clumps may lose much of their mass and disrupt in the disk. The clumps leave a modest imprint on the gas kinematics. Velocity gradients across the clumps are 10-40 km s?1 kpc?1, similar to the galactic rotation gradients. Given beam smearing and clump sizes, these gradients may be consistent with significant rotational support in typical clumps. Extreme clumps may not be rotationally supported; either they are not virialized or they are predominantly pressure supported. The velocity dispersion is spatially rather constant and increases only weakly with star formation surface density. The large velocity dispersions may be driven by the release of gravitational energy, either at the outer disk/accreting streams interface, and/or by the clump migration within the disk. Spatial variations in the inferred gas phase oxygen abundance are broadly consistent with inside-out growing disks, and/or with inward migration of the clumps.

Modelling the galaxy bimodality: shutdown above a critical halo mass

We reproduce the blue and red sequences in the observed joint distribution of colour and magnitude for galaxies at low and high redshifts using hybrid N-body/semi-analytic simulations of galaxy formation. The match of model and data is achieved by mimicking the effects of cold flows versus shock heating coupled to feedback from active galactic nuclei (AGNs), as predicted by Dekel and Birnboim. After a critical epoch z ∼ 3, only haloes below a critical shock-heating mass M shock ∼ 10 12 Menjoy gas supply by cold flows and form stars, while cooling and star formation are shut down abruptly above this mass. The shock-heated gas is kept hot because being dilute it is vulnerable to feedback from energetic sources such as AGNs in their self-regulated mode. The shutdown explains in detail the bright-end truncation of the blue sequence at ∼L ∗, the appearance of luminous red-and-dead galaxies on the red sequence starting already at z ∼ 2, the colour bimodality, its strong dependence on environment density and its correlations with morphology and other galaxy properties. Before z ∼ 2-3, even haloes above the shock-heating mass form stars by cold streams penetrating through the hot gas. This explains the bright star forming galaxies at z ∼ 3-4, the early appearance of massive galaxies on the red sequence, the high cosmological star formation rate at high redshifts and the subsequent low rate at low redshifts.

The effect of galaxy mass ratio on merger-driven starbursts

We employ numerical simulations of galaxy mergers to explore the effect of galaxy mass ratio on merger-driven starbursts. Our numerical simulations include radiative cooling of gas, star formation, and stellar feedback to follow the interaction and merger of four disc galaxies. The galaxy models span a factor of 23 in total mass and are designed to be representative of typical galaxies in the local universe. We find that the merger-driven star formation is a strong function of merger mass ratio, with very little, if any, induced star formation for large mass ratio mergers. We define a burst efficiency that is useful to characterize the merger-driven star formation and test that it is insensitive to uncertainties in the feedback parametrization. In accord with previous work we find that the burst efficiency depends on the structure of the primary galaxy. In particular, the presence of a massive stellar bulge stabilizes the disc and suppresses merger-driven star formation for large mass ratio mergers. Direct, coplanar merging orbits produce the largest tidal disturbance and yield the most intense burst of star formation. Contrary to naive expectations, a more compact distribution of gas or an increased gas fraction both decrease the burst efficiency. Owing to the efficient feedback model and the newer version of smoothed particle hydrodynamics employed here, the burst efficiencies of the mergers presented here are smaller than in previous studies.

A Universal, Local Star Formation Law in Galactic Clouds, Nearby Galaxies, High-Redshift Disks, and Starbursts

Star formation laws are rules that relate the rate of star formation in a particular region, either an entire galaxy or some portion of it, to the properties of the gas, or other galactic properties, in that region. While observations of Local Group galaxies show a very simple, local star formation law in which the star formation rate per unit area in each patch of a galaxy scales linearly with the molecular gas surface density in that patch, recent observations of both Milky Way molecular clouds and high-redshift galaxies apparently show a more complicated relationship in which regions of equal molecular gas surface density can form stars at quite different rates. These data have been interpreted as implying either that different star formation laws may apply in different circumstances, that the star formation law is sensitive to large-scale galaxy properties rather than local properties, or that there are high-density thresholds for star formation. Here we collate observations of the relationship between gas and star formation rate from resolved observations of Milky Way molecular clouds, from kpc-scale observations of Local Group galaxies, and from unresolved observations of both disk and starburst galaxies in the local universe and at high redshift. We show that all of these data are in fact consistent with a simple, local, volumetric star formation law. The apparent variations stem from the fact that the observed objects have a wide variety of three-dimensional size scales and degrees of internal clumping, so even at fixed gas column density the regions being observed can have wildly varying volume densities. We provide a simple theoretical framework to remove this projection effect, and we use it to show that all the data, from small solar neighborhood clouds with masses ~103 M ? to submillimeter galaxies with masses ~1011 M ?, fall on a single star formation law in which the star formation rate is simply ~1% of the molecular gas mass per local free-fall time. In contrast, proposed star formation laws in which the star formation timescale is set by the galactic rotation period are inconsistent with the data from the Milky Way and the Local Group, while those in which the star formation rate is linearly proportional to the gas mass above some density threshold fail both in the Local Group and for starburst galaxies.

Star formation in AEGIS field galaxies since z = 1.1: Staged galaxy formation and a model of mass-dependent gas exhaustion

We analyze star formation (SF) as a function of stellar mass (M☉) and redshift z in the All-Wavelength Extended Groth Strip International Survey, for star-forming field galaxies with M* ≳ 10^10 M☉ out to z = 1.1. The data indicate that the high specific SF rates (SFRs) of many less massive galaxies do not represent late, irregular or recurrent, starbursts in evolved galaxies. They rather seem to reflect the onset (initial burst) of the dominant SF episode of galaxies, after which SF gradually declines on gigayear timescales to z = 0 and forms the bulk of a galaxy’s M*. With decreasing mass, this onset of major SF shifts to decreasing z for an increasing fraction of galaxies (staged galaxy formation). This process may be an important component of the “downsizing” phenomenon. We find that the predominantly gradual decline of SFRs described by Noeske et al. can be reproduced by exponential SF histories (τ models), if less massive galaxies have systematically longer e-folding times τ, and a later onset of SF (zf). Our model can provide a first parameterization of SFR as a function of M* and z, and quantify mass dependences of τ and z, from direct observations of M* and SFRs up to z > 1. The observed evolution of SF in galaxies can plausibly reflect the dominance of gradual gas exhaustion. The data are also consistent with the history of cosmological accretion onto dark matter halos.

Stochastic nonlinear galaxy biasing

We propose a general formalism for galaxy biasing and apply it to methods for measuring cosmological parameters, such as regression of light versus mass, the analysis of redshift distortions, measures involving skewness, and the cosmic virial theorem. The common linear and deterministic relation g = bδ between the density fluctuation fields of galaxies g and mass δ is replaced by the conditional distribution P(g|δ) of these random fields, smoothed at a given scale at a given time. The nonlinearity is characterized by the conditional mean g|δ ≡ b(δ)δ, while the local scatter is represented by the conditional variance σ2b(δ) and higher moments. The scatter arises from hidden factors affecting galaxy formation and from shot noise unless it has been properly removed. For applications involving second-order local moments, the biasing is defined by three natural parameters: the slope of the regression of g on δ, a nonlinearity , and a scatter σb. The ratio of variances b2var and the correlation coefficient r mix these parameters. The nonlinearity and the scatter lead to underestimates of order 2/2 and σ2b/2 in the different estimators of β (~ Ω0.6/). The nonlinear effects are typically smaller. Local stochasticity affects the redshift-distortion analysis only by limiting the useful range of scales, especially for power spectra. In this range, for linear stochastic biasing, the analysis reduces to Kaisers formula for (not bvar), independent of the scatter. The distortion analysis is affected by nonlinear properties of biasing but in a weak way. Estimates of the nontrivial features of the biasing scheme are made based on simulations and toy models, and strategies for measuring them are discussed. They may partly explain the range of estimates for β.

Properties of dark matter haloes in clusters, filaments, sheets and voids

Using a series of high-resolution N-body simulations of the concordance cosmology we investigate how the formation histories, shapes and angular momenta of dark-matter haloes depend on environment. We first present a classification scheme that allows to distinguish between haloes in clusters, filaments, sheets and voids in the large-scale distribution of matter. This method (which goes beyond a simple measure of the local density) is based on a local-stability criterion for the orbits of test particles and closely relates to the Zel’dovich approximation. Applying this scheme to our simulations we then find that: i) Mass assembly histories and formation redshifts strongly depend on environment for haloes of mass M < M� (haloes of a given mass tend to be older in ′