What triggers black-hole growth? Insights from star formation rates

We present a new semi-analytic model for the common growth of black holes (BHs) and galaxies within a hierarchical Universe. The model is tuned to match the mass function of BHs at z=0 and the luminosity functions of active galactic nuclei (AGNs) at z<4. We use a new observational constraint, which relates the luminosity of AGNs to the star-formation rate (SFR) of their host galaxies. We show that this new constraint is important in various aspects: a) it indicates that BH accretion events are episodic; b) it favours a scenario in which BH accretion is triggered by merger events of all mass ratios; c) it constrains the duration of both merger-induced star-bursts and BH accretion events. The model reproduces the observations once we assume that only 4 per cent of the merger events trigger BH accretion; BHs accretion is not related to secular evolution; and only a few per cent of the mass made in bursts goes into the BH. We find that AGNs with low or intermediate luminosity are mostly being triggered by minor merger events, in broad agreement with observations. Our model matches various observed properties of galaxies, such as the stellar mass function at z<4 and the clustering of galaxies at redshift zero. This allows us to use galaxies as a reliable backbone for BH growth, with reasonable estimates for the frequency of merger events. Other modes of BH accretion, such as disk-instability events, were not considered here, and should be further examined in the future.Comment: accepted to MNRAS, minor changes from version

Magnetically Regulated Gas Accretion in High-Redshift Galactic Disks

Disk galaxies are in hydrostatic equilibrium along their vertical axis. The pressure allowing for this configuration consists of thermal, turbulent, magnetic and cosmic ray components. For the Milky Way(MW) the thermal pressure contributes ~10% of the total pressure near the plane, with this fraction dropping towards higher altitudes. Out of the rest, magnetic fields contribute ~1/3 of the pressure to distances of ~3kpc above the disk plane. In this letter we attempt to extrapolate these local values to high redshift, rapidly accreting, rapidly star forming disk galaxies and study the effect of the extra pressure sources on the accretion of gas onto the galaxies. In particular, magnetic field tension may convert a smooth cold-flow accretion to clumpy, irregular star formation regions and rates. The infalling gas accumulates on the edge of the magnetic fields, supported by magnetic tension. When the mass of the infalling gas exceeds some threshold mass, its gravitational force cannot be balanced by magnetic tension anymore, and it falls toward the disk's plane, rapidly making stars. Simplified estimations of this threshold mass are consistent with clumpy star formation observed in SINS, UDF, GOODS and GEMS surveys. We discuss the shortcomings of pure hydrodynamic codes in simulating the accretion of cold flows into galaxies, and emphasize the need for magneto-hydrodynamic simulationsComment: 12 pages, 3 figures, accepted to ApJ

Constructing Merger Trees that Mimic N-Body Simulations

We present a simple and efficient empirical algorithm for constructing dark-matter halo merger trees that reproduce the distribution of trees in the Millennium cosmological $N$-body simulation. The generated trees are significantly better than EPS trees. The algorithm is Markovian, and it therefore fails to reproduce the non-Markov features of trees across short time steps, except for an accurate fit to the evolution of the average main progenitor. However, it properly recovers the full main progenitor distribution and the joint distributions of all the progenitors over long-enough time steps, $\Delta \omega \simeq \Delta z>0.5$, where $\omega \simeq 1.69/D(t)$ is the self-similar time variable and $D(t)$ refers to the linear growth of density fluctuations. We find that the main progenitor distribution is log-normal in the variable $\sigma^2(M)$, the variance of linear density fluctuations in a sphere encompassing mass $M$. The secondary progenitors are successfully drawn one by one from the remaining mass using a similar distribution function. These empirical findings may be clues to the underlying physics of merger-tree statistics. As a byproduct, we provide useful, accurate analytic time-invariant approximations for the main progenitor accretion history and for halo merger rates.Comment: 13 pages, 9 figures. Accepted for MNRAS. Minor changes from version

The Coarse Geometry of Merger Trees in \Lambda CDM

We introduce the contour process to describe the geometrical properties of merger trees. The contour process produces a one-dimensional object, the contour walk, which is a translation of the merger tree. We portray the contour walk through its length and action. The length is proportional to to the number of progenitors in the tree, and the action can be interpreted as a proxy of the mean length of a branch in a merger tree. We obtain the contour walk for merger trees extracted from the public database of the Millennium Run and also for merger trees constructed with a public Monte-Carlo code which implements a Markovian algorithm. The trees correspond to halos of final masses between 10^{11} h^{-1} M_sol and 10^{14} h^{-1} M_sol. We study how the length and action of the walks evolve with the mass of the final halo. In all the cases, except for the action measured from Markovian trees, we find a transitional scale around 3 \times 10^{12} h^{-1} M_sol. As a general trend the length and action measured from the Markovian trees show a large scatter in comparison with the case of the Millennium Run trees.Comment: 7 pages, 5 figures, submitted to MNRA

Conditional Mass Functions and Merger Rates of Dark Matter Halos in the Ellipsoidal Collapse Model

Analytic models based on spherical and ellipsoidal gravitational collapse have been used to derive the mass functions of dark matter halos and their progenitors (the conditional mass function). The ellipsoidal model generally provides a better match to simulation results, but there has been no simple analytic expression in this model for the conditional mass function that is accurate for small time steps, a limit that is important for generating halo merger trees and computing halo merger rates. We remedy the situation by deriving accurate analytic formulae for the first-crossing distribution, the conditional mass function, and the halo merger rate in the ellipsoidal collapse model in the limit of small look-back times. We show that our formulae provide a closer match to the Millennium simulation results than those in the spherical collapse model and the ellipsoidal model of Sheth & Tormen (2002).Comment: 5 pages, 3 figures, accepted by MNRAS letter

An Analytic Model for the Evolution of the Stellar, Gas, and Metal Content of Galaxies

We present an analytic formalism that describes the evolution of the stellar, gas, and metal content of galaxies. It is based on the idea, inspired by hydrodynamic simulations, that galaxies live in a slowly-evolving equilibrium between inflow, outflow, and star formation. We argue that this formalism broadly captures the behavior of galaxy properties evolving in simulations. The resulting equilibrium equations for the star formation rate, gas fraction, and metallicity depend on three key free parameters that represent ejective feedback, preventive feedback, and re-accretion of ejected material. We schematically describe how these parameters are constrained by models and observations. Galaxies perturbed off the equilibrium relations owing to inflow stochasticity tend to be driven back towards equilibrium, such that deviations in star formation rate at a given mass are correlated with gas fraction and anti-correlated with metallicity. After an early gas accumulation epoch, quiescently star-forming galaxies are expected to be in equilibrium over most of cosmic time. The equilibrium model provides a simple intuitive framework for understanding the cosmic evolution of galaxy properties, and centrally features the cycle of baryons between galaxies and surrounding gas as the driver of galaxy growth.Comment: 11 pages, MNRAS, accepte

How do dwarf galaxies acquire their mass & when do they form their stars?

We apply a simple, one-equation, galaxy formation model on top of the halos and subhalos of a high-resolution dark matter cosmological simulation to study how dwarf galaxies acquire their mass and, for better mass resolution, on over 10^5 halo merger trees, to predict when they form their stars. With the first approach, we show that the large majority of galaxies within group- and cluster-mass halos have acquired the bulk of their stellar mass through gas accretion and not via galaxy mergers. We deduce that most dwarf ellipticals are not built up by galaxy mergers. With the second approach, we constrain the star formation histories of dwarfs by requiring that star formation must occur within halos of a minimum circular velocity set by the evolution of the temperature of the IGM, starting before the epoch of reionization. We qualitatively reproduce the downsizing trend of greater ages at greater masses and predict an upsizing trend of greater ages as one proceeds to masses lower than m_crit. We find that the fraction of galaxies with very young stellar populations (more than half the mass formed within the last 1.5 Gyr) is a function of present-day mass in stars and cold gas, which peaks at 0.5% at m_crit=10^6-8 M_Sun, corresponding to blue compact dwarfs such as I Zw 18. We predict that the baryonic mass function of galaxies should not show a maximum at masses above 10^5.5, M_Sun, and we speculate on the nature of the lowest mass galaxies.Comment: 6 pages, to appear in "A Universe of Dwarf Galaxies: Observations, Theories, Simulations", ed. M. Koleva, P. Prugniel & I. Vauglin, EAS Series (Paris: EDP

The specific star formation rate of high redshift galaxies: the case for two modes of star formation

We study the specific star formation rate (SSFR) and its evolution at z\gtsim 4, in models of galaxy formation, where the star formation is driven by cold accretion flows. We show that constant star formation and feedback efficiencies cannot reproduce the observed trend of SSFR with stellar mass and its observed lack of evolution at $z>4$. Model galaxies with \log(M_*) \ltsim 9.5 M$_{\odot}$ show systematically lower specific star formation rates by orders of magnitudes, while massive galaxies with M_* \gtsim 5 \times 10^{10} M$_{\odot}$ have up to an order of magnitude larger SSFRs, compared to recent observations by Stark et al.. To recover these observations we apply an empirical star formation efficiency in galaxies that scales with the host halo velocity dispersion as $\propto 1/\sigma^3$ during galaxy mergers. We find that this modification needs to be of stochastic nature to reproduce the observations, i.e. only applied during mergers and not during accretion driven star formation phases. Our choice of star formation efficiency during mergers allows us to capture both, the boost in star formation at low masses and the quenching at high masses, and at the same time produce a constant SSFR-stellar mass relation at z\gtsim 4 under the assumption that most of the observed galaxies are in a merger triggered star formation phase. Our results suggest that observed high-z low mass galaxies with high SSFRs are likely to be frequently interacting systems, which experienced bursts in their star formation rate and efficiency (mode 1), in contrast to low redshift z \ltsim 3 galaxies which are cold accretion-regulated star forming systems with lower star formation efficiencies (mode 2).Comment: 5 pages, accepted to MNRAS, replaced by version with including referees comment