Critical Halo Mass Research Articles

Starbursts in low-mass haloes at Cosmic Dawn. I. The critical halo mass for star formation

ABSTRACT The first stars, galaxies, star clusters, and direct-collapse black holes are expected to have formed in low-mass (∼105–109 M⊙) haloes at Cosmic Dawn (z ∼ 10–30) under conditions of efficient gas cooling, leading to gas collapse towards the centre of the halo. The halo mass cooling threshold has been analysed by several authors using both analytical models and numerical simulations, with differing results. Since the halo number density is a sensitive function of the halo mass, an accurate model of the cooling threshold is needed for (semi-)analytical models of star formation at Cosmic Dawn. In this paper, the cooling threshold mass is calculated (semi-)analytically, considering the effects of H2-cooling and formation (in the gas phase and on dust grains), cooling by atomic metals, Lyman-α cooling, photodissociation of H2 by Lyman–Werner photons (including self-shielding by H2), photodetachment of H− by infrared photons, photoevaporation by ionization fronts, and the effect of baryon streaming velocities. We compare the calculations to several high-resolution cosmological simulations, showing excellent agreement. We find that in regions of typical baryon streaming velocities, star formation is possible in haloes of mass ≳ 1–2 × 106 M⊙ for z ≳ 20. By z ∼ 8, the expected Lyman–Werner background suppresses star formation in all minihaloes below the atomic cooling threshold (Tvir = 104 K). The halo mass cooling threshold increases by another factor of ∼4 following reionization, although this effect is slightly delayed (z ∼ 4–5) because of effective self-shielding.

Population III star formation in an X-ray background – I. Critical halo mass of formation and total mass in stars

ABSTRACT The first luminous objects forming in the universe produce radiation backgrounds in the far-ultraviolet and X-ray bands that affect the formation of Population III stars. Using a grid of cosmological hydrodynamics zoom-in simulations, we explore the impact of the Lyman–Warner (LW) and X-ray radiation backgrounds on the critical dark matter (DM) halo mass for Population III star formation and the total mass in stars per halo. We find that the LW radiation background lowers the H2 fraction and delays the formation of the Population III stars. On the other hand, X-ray irradiation anticipates the redshift of collapse and reduces the critical halo mass, unless the X-ray background is too strong and gas heating shuts down gas collapse into the haloes and prevents star formation. Therefore, an X-ray background can increase the number of DM haloes forming Population III stars by about a factor of 10, but the total mass in stars forming in each halo is reduced. This is because X-ray radiation increases the molecular fraction and lowers the minimum temperature of the collapsing gas (or equivalently the mass of the quasi-hydrostatic core) and therefore slows down the accretion of the gas on to the central protostar.

The influence of streaming velocities and Lyman–Werner radiation on the formation of the first stars

ABSTRACT The first stars in the Universe, the so-called Population III stars, form in small dark matter minihaloes with virial temperatures Tvir < 104 K. Cooling in these minihaloes is dominated by molecular hydrogen (H2), and so Population III star formation is only possible in those minihaloes that form enough H2 to cool on a short timescale. As H2 cooling is more effective in more massive minihaloes, there is therefore a critical halo mass scale Mmin above which Population III star formation first becomes possible. Two important processes can alter this minimum mass scale: streaming of baryons relative to the dark matter and the photodissociation of H2 by a high redshift Lyman–Werner (LW) background. In this paper, we present results from a set of high resolution cosmological simulations that examine the impact of these processes on Mmin and on Mave (the average minihalo mass for star formation), both individually and in combination. We show that streaming has a bigger impact on Mmin than the LW background, but also that both effects are additive. We also provide a fitting functions quantifying the dependence of Mave and Mmin on the streaming velocity and the strength of the LW background.

The mass assembly of high-redshift black holes

ABSTRACT We use the Delphi semi-analytic model to study the mass assembly and properties of high-redshift (z > 4) black holes over a wide mass range, $10^3 \lt M_{\rm bh}/{\rm \rm M_\odot }\lt 10^{10}$. Our black hole growth implementation includes a critical halo mass ($M_{\mathrm{ h}}^{\mathrm{ crit}}$) below which the black hole is starved and above which it is allowed to grow either at the Eddington limit or proportionally to the gas content of the galaxy. As a consequence, after an initial growth phase dominated by black hole mergers down to z ∼ 7 (9), supermassive black holes in z = 4 halo masses of $M_\mathrm{ h}|_{z=4} \sim 10^{11.75} \, (10^{13.4}) \, {\rm \rm M_\odot }$ mainly grow by gas accretion from the interstellar medium. In particular, we find that (i) while most of the accretion occurs in the major branch for $M_\mathrm{ h}|_{z=4} \sim 10^{11\!-\!12} \, {\rm \rm M_\odot }$ haloes, accretion in secondary branches plays a significant role in assembling the black hole mass in higher mass haloes ($M_\mathrm{ h}|_{z=4} \gtrsim 10^{12} \, {\rm \rm M_\odot }$); (ii) while the Eddington ratio increases with decreasing redshift for low-mass ($M_{\mathrm{ bh}} \lt 10^5 \, {\rm \rm M_\odot }$) black holes, it shows the opposite trend for larger masses. In addition, since the accretion rate depends on the gas mass present in the host halo, the duty cycle of the Eddington-limited accretion phase – which can last up to ≈650 Myr – is crucially linked to the joint assembly history of the black hole and its host halo.

The physical drivers of the atomic hydrogen–halo mass relation

ABSTRACT We use the state-of-the-art semi-analytic galaxy formation model, shark, to investigate the physical processes involved in dictating the shape, scatter, and evolution of the Hi–halo mass (HIHM) relation at 0 ≤ z ≤ 2. We compare shark with Hi clustering and spectral stacking of the HIHM relation derived from observations finding excellent agreement with the former and a deficiency of Hi in shark at Mvir ≈ 1012–13 M⊙ in the latter. In shark, we find that the Hi mass increases with the halo mass up to a critical mass of ≈1011.8 M⊙; between ≈1011 and 1013 M⊙, the scatter in the relation increases by 0.7 dex and the Hi mass decreases with the halo mass on average (till $M_{\rm vir}\sim 10^{12.5}\, \rm M_{\odot }$, after which it starts increasing); at $M_{\rm vir}\gtrsim 10^{13}\, \rm M_{\odot }$, the Hi content continues to increase with increasing halo mass, as a result of the increasing Hi contribution from satellite galaxies. We find that the critical halo mass of ≈1012 M⊙ is set by feedback from active galactic nuclei (AGNs) which affects both the shape and scatter of the HIHM relation, with other physical processes playing a less significant role. We also determine the main secondary parameters responsible for the scatter of the HIHM relation, namely the halo spin parameter at ${M}_{\rm vir}\, \lt $ 1011.8 M⊙, and the fractional contribution from substructure to the total halo mass ($M_{\rm h}^{\rm sat}/M_{\rm vir}$) for ${M}_{\rm vir}\, \gt $ 1013 M⊙. The scatter at 1011.8 M⊙$\lt \, {M}_{\rm vir}\, \lt $ 1013 M⊙ is best described by the black hole-to-stellar mass ratio of the central galaxy, reflecting the relevance of AGN feedback. We present a numerical model to populate dark matter-only simulations with Hi at 0 ≤ z ≤ 2 based solely on halo parameters that are measurable in such simulations.

GalICS 2.1: a new semianalytic model for cold accretion, cooling, feedback, and their roles in galaxy formation

ABSTRACT Dekel & Birnboim proposed that the mass-scale that separates late-type and early-type galaxies is linked to the critical halo mass $M_{\rm vir}^{\rm crit}$ for the propagation of a stable shock and showed that they could reproduce the observed bimodality scale for plausible values of the metallicity of the accreted gas Zaccr and the shock radius rs. Here, we take their analysis one step further and present a new semianalytic model that computes rs from first principles. This advancement allows us to compute $M_{\rm vir}^{\rm crit}$ individually for each halo. Separating cold-mode and hot-mode accretion has little effect on the final galaxy masses if feedback does not preferentially couple to the hot gas. We also present an improved model for stellar feedback where ${\sim }70{{\ \rm per\ cent}}$ of the wind mass is in a cold galactic fountain with a shorter reaccretion time-scale at high masses. The latter is the key mechanism that allows us to reproduce the low-mass end of the mass function of galaxies over the entire redshift range 0 < z < 2.5. Cooling must be mitigated to avoid overpredicting the number density of galaxies with stellar mass $M_{\rm stars}\gt 10^{11}\, {\rm M}_\odot$ but is important to form intermediate-mass galaxies. At $M_{\rm vir}\gt 3\times 10^{11}\, {\rm M}_\odot$, cold accretion is more important at high z, where gas is accreted from smaller solid angles, but this is not true at lower masses because high-z filaments have lower metallicities. Our predictions are consistent with the observed metallicity evolution of the intergalactic medium at 0 < z < 5.

On the Prevalence of Supermassive Black Holes over Cosmic Time

Abstract We investigate the abundance of supermassive black hole (SMBH) seeds in primordial galaxy halos. We explore the assumption that dark matter halos outgrowing a critical halo mass M c have some probability p of having spawned an SMBH seed. Current observations of local, intermediate-mass galaxies constrain these parameters: for M c = 1011 M ⊙, all halos must be seeded, but when adopting smaller M c masses the seeding can be much less efficient. The constraints simultaneously put lower limits on the number density of black holes in the local and high-redshift universe. Reproducing z ∼ 6 quasar space densities depends on their typical halo mass, which can be constrained by counting nearby Lyman Break Galaxies and Lyman-alpha emitters. For both observables, our simulations demonstrate that single-field predictions are too diverse to make definitive statements, in agreement with mixed claims in the literature. If quasars are not limited to the most massive host halos, they may represent a tiny fraction (≈10−5) of the SMBH population. Finally, we produce a wide range of predictions for gravitational events from SMBH mergers. We define a new diagnostic diagram for the Laser Interferometer Space Antenna to measure both SMBH space density and the typical delay between halo merger and black hole merger. While previous works have explored specific scenarios, our results hold independent of the seed mechanism, seed mass, obscuration, fueling methods and duty cycle.

Dark matter annihilation feedback in cosmological simulations – II. The influence on gas and halo structure

We present new cosmological hydrodynamic simulations that incorporate Dark Matter Annihilation Feedback (DMAF), whereby energy released from the annihilation of dark matter particles through decay channels such as photon or positron-electron pairs provide additional heating sources for local baryonic material. For annihilation rates comparable to WIMP-like particles, we find that the key influence of DMAF is to inhibit gas accretion onto halos. Such diminished gas accretion early in the lifetimes of halos results in reduced gas fractions in smaller halos, and the delayed halo formation times of larger structures, suggesting that DMAF could impact the stellar age distribution in galaxies, and morphology of dwarfs. For a dark matter particle mass of $m_\chi\sim10$~MeV, there is a `critical halo mass' of $\sim10^{13}$ M$_{\odot}$ at $z=0$, below which there are large differences when compared to $\Lambda$CDM, such as a reduction in the abundance of halo structures as large as 25 percent, reduced gas content by 50 percent and central gas densities reduced down to 10 percent within halos of mass $\sim10^{12}$ M$_{\odot}$ but with increasing effects in smaller halos. Higher dark matter particle mass models have a smaller `critical halo mass'. For a $m_\chi\sim100$~MeV model, we find differences start appearing below halo masses of $\sim10^{12}$ M$_\odot$ and a $m_\chi\gtrsim 1$~GeV model, this mass scale lies below the resolution of our simulations, though we still observe changes in the morphology of dwarf galaxies.

Condition for dust evacuation from the first galaxies

Dust enables low-mass stars to form from low-metallicity gas by inducing fragmentation of clouds via the cooling by its thermal emission. Dust may, however, be evacuated from star-forming clouds due to radiation force from massive stars. We here study the condition for the dust evacuation by comparing the dust evacuation time with the time of cloud destruction due to either expansion of HII regions or supernovae. The cloud destruction time has weak dependence on the cloud radius, while the dust evacuation time becomes shorter for a cloud with the smaller radius. The dust evacuation thus occurs in compact star-forming clouds whose column density is $N_{\rm H} \simeq 10^{24} - 10^{26} ~{\rm cm^{-2}}$. The critical halo mass above which the dust evacuation occurs becomes lower for higher formation redshift, e.g., $\sim 10^{9}~M_{\odot}$ at redshift $z \sim 3$ and $\sim 10^{7}~M_{\odot}$ at $z \sim 9$. In addition, metallicity of the gas should be less than $\sim 10^{-2} ~ Z_{\odot}$. Otherwise the dust attenuation reduces the radiation force significantly. From the dust-evacuated gas, massive stars are likely to form even with metallicity above $\sim 10^{-5}~Z_{\odot}$, the critical value for low-mass star formation due to the dust cooling. This can explain the dearth of ultra-metal poor stars with the metallicity lower than $\sim 10^{-4}~Z_{\odot}$.

AGN feedback in dwarf galaxies?

Dwarf galaxy anomalies, such as their abundance and cusp-core problems, remain a prime challenge in our understanding of galaxy formation. The inclusion of baryonic physics could potentially solve these issues, but the efficiency of stellar feedback is still controversial. We analytically explore the possibility of feedback from Active Galactic Nuclei (AGN) in dwarf galaxies and compare AGN and supernova (SN) feedback. We assume the presence of an intermediate mass black hole within low mass galaxies and standard scaling relations between the relevant physical quantities. We model the propagation and properties of the outflow and explore the critical condition for global gas ejection. Performing the same calculation for SNe, we compare the ability of AGN and SNe to drive gas out of galaxies. We find that a critical halo mass exists below which AGN feedback can remove gas from the host halo and that the critical halo mass for AGN is greater than the equivalent for SNe in a significant part of the parameter space, suggesting that AGN could provide an alternative and more successful source of negative feedback than SNe, even in the most massive dwarf galaxies.

The formation of hot gaseous haloes around galaxies

We use a suite of hydrodynamical cosmological simulations from the Evolution and Assembly of GaLaxies and their Environments (EAGLE) project to investigate the formation of hot hydrostatic haloes and their dependence on feedback mechanisms. We find that the appearance of a strong bimodality in the probability density function (PDF) of the ratio of the radiative cooling and dynamical times for halo gas provides a clear signature of the formation of a hot corona. Haloes of total mass $10^{11.5}-10^{12}{\rm{M}}_{\odot}$ develop a hot corona independent of redshift, at least in the interval $z=0-4$ where the simulation has sufficiently good statistics. We analyse the build up of the hot gas mass in the halo, $M_{\rm{hot}}$, as a function of halo mass and redshift and find that while more energetic galactic winds powered by SNe increases $M_{\rm{hot}}$, AGN feedback reduces it by ejecting gas from the halo. We also study the thermal properties of gas accreting onto haloes and measure the fraction of shock-heated gas as a function of redshift and halo mass. We develop analytic and semianalytic approaches to estimate a `critical halo mass', $M_{\rm{crit}}$, for hot halo formation. We find that the mass for which the heating rate produced by accretion shocks equals the radiative cooling rate, reproduces the mass above which haloes develop a significant hot atmosphere. This yields a mass estimate of $M_{\rm{crit}} \approx 10^{11.7}{\rm{M}}_{\odot}$ at $z=0$, which agrees with the simulation results. The value of $M_{\rm{crit}}$ depends more strongly on the cooling rate than on any of the feedback parameters.

The impact of star formation feedback on the circumgalactic medium

We use idealized 3D hydrodynamic simulations to study the dynamics and thermal structure of the circumgalactic medium (CGM). Our simulations quantify the role of cooling, stellar feedback driven galactic winds and cosmological gas accretion in setting the properties of the CGM in dark matter haloes ranging from $10^{11}$ to $10^{12}$ M$_\odot$. Our simulations support a conceptual picture in which the properties of the CGM, and the key physics governing it, change markedly near a critical halo mass of M$_{\rm crit} \approx 10^{11.5}$ M$_\odot$. As in calculations without stellar feedback, above M$_{\rm crit}$ halo gas is supported by thermal pressure created in the virial shock. The thermal properties at small radii are regulated by feedback triggered when $t_{\rm cool}/t_{\rm ff}\lesssim10$ in the hot gas. Below M$_{\rm crit}$, however, there is no thermally supported halo and self-regulation at $t_{\rm cool}/t_{\rm ff}\sim10$ does not apply. Instead, the gas is out of hydrostatic equilibrium and largely supported against gravity by bulk flows (turbulence and coherent inflow/outflow) arising from the interaction between cosmological gas inflow and outflowing galactic winds. In these lower mass haloes, the phase structure depends sensitively on the outflows' energy per unit mass and mass-loading, which may allow measurements of the CGM thermal state to constrain the nature of galactic winds. Our simulations account for some of the properties of the multiphase halo gas inferred from quasar absorption line observations, including the presence of significant mass at a wide range of temperatures, and the characteristic OVI and CIV column densities and kinematics. However, we underpredict the neutral hydrogen content of the $z\sim0$ CGM.

The H i mass function as a probe of photoionization feedback on low-mass galaxy formation

We explore the galaxy formation physics governing the low mass end of the HI mass function in the local Universe. Specifically, we predict the effects on the HI mass function of varying i) the strength of photoionisation feedback and the redshift of the end of the epoch of reionization, ii) the cosmology, iii) the supernovae feedback prescription, and iv) the efficiency of star formation. We find that the shape of the low-mass end of the HI mass function is most affected by the critical halo mass below which galaxy formation is suppressed by photoionisation heating of the intergalactic medium. We model the redshift dependence of this critical dark matter halo mass by requiring a match to the low-mass end of the HI mass function. The best fitting critical dark matter halo mass decreases as redshift increases in this model, corresponding to a circular velocity of $\sim 50 \, {\rm km \,s}^{-1}$ at $z=0$, $\sim 30 \, {\rm km\, s}^{-1}$ at $z \sim 1$ and $\sim 12 \, {\rm km \, s}^{-1}$ at $z=6$. We find that an evolving critical halo mass is required to explain both the shape and abundance of galaxies in the HI mass function below $M_{\rm HI} \sim 10^{8} h^{-2} {\rm M_{\odot}}$. The model makes specific predictions for the clustering strength of HI-selected galaxies with HI masses > $10^{6} h^{-2} {\rm M_{\odot}}$ and $> 10^{7} h^{-2} {\rm M_{\odot}}$ and for the relation between the HI and stellar mass contents of galaxies which will be testable with upcoming surveys with the Square Kilometre Array and its pathfinders. We conclude that measurements of the HI mass function at $z \ge 0$ will lead to an improvement in our understanding of the net effect of photoionisation feedback on galaxy formation and evolution.

The green valley is a red herring: Galaxy Zoo reveals two evolutionary pathways towards quenching of star formation in early- and late-type galaxies★

We use SDSS+\textit{GALEX}+Galaxy Zoo data to study the quenching of star formation in low-redshift galaxies. We show that the green valley between the blue cloud of star-forming galaxies and the red sequence of quiescent galaxies in the colour-mass diagram is not a single transitional state through which most blue galaxies evolve into red galaxies. Rather, an analysis that takes morphology into account makes clear that only a small population of blue early-type galaxies move rapidly across the green valley after the morphologies are transformed from disk to spheroid and star formation is quenched rapidly. In contrast, the majority of blue star-forming galaxies have significant disks, and they retain their late-type morphologies as their star formation rates decline very slowly. We summarize a range of observations that lead to these conclusions, including UV-optical colours and halo masses, which both show a striking dependence on morphological type. We interpret these results in terms of the evolution of cosmic gas supply and gas reservoirs. We conclude that late-type galaxies are consistent with a scenario where the cosmic supply of gas is shut off, perhaps at a critical halo mass, followed by a slow exhaustion of the remaining gas over several Gyr, driven by secular and/or environmental processes. In contrast, early-type galaxies require a scenario where the gas supply and gas reservoir are destroyed virtually instantaneously, with rapid quenching accompanied by a morphological transformation from disk to spheroid. This gas reservoir destruction could be the consequence of a major merger, which in most cases transforms galaxies from disk to elliptical morphology, and mergers could play a role in inducing black hole accretion and possibly AGN feedback.

Studying the emergence of the red sequence through galaxy clustering: host halo masses at z > 2

We use the United Kingdom Infrared Telescope Deep Sky Survey (UKIDSS) Ultra Deep Survey (UDS), the deepest degree-scale near-infrared survey to date, to investigate the clustering of star-forming and passive galaxies to z ∼ 3.5. Our new measurements include the first determination of the clustering for passive galaxies at z > 2, which we achieve using a cross-correlation technique. We find that passive galaxies are the most strongly clustered, typically hosted by massive dark matter haloes with Mhalo > 5 × 1012 M⊙ irrespective of redshift or stellar mass. Our findings are consistent with models in which a critical halo mass determines the transition from star-forming to passive galaxies. Star-forming galaxies show no strong correlation between stellar mass and halo mass, but passive galaxies show evidence for an anticorrelation; low-mass passive galaxies appear, on average, to be located in the most massive haloes. These results can be understood if the termination of star formation is most efficient for galaxies of low stellar mass in very dense environments.

The emergence of the red sequence at z~2 seen through galaxy clustering in the UKIDSS UDS

AbstractWe use the UKIDSS Ultra-Deep Survey, the deepest degree-scale near-infrared survey to date, to investigate the clustering of star-forming and passive galaxies to z ~ 3.5. Our new measurements include the first determination of the clustering for passive galaxies at z > 2, which we achieve using a cross-correlation technique. We find that passive galaxies are the most strongly clustered, typically hosted by massive dark matter halos with Mhalo > 1013 M⊙ irrespective of redshift or stellar mass. Our findings are consistent with models in which a critical halo mass determines the transition from star-forming to passive galaxies.

The effects of X-ray and UV background radiation on the low-mass slope of the galaxy mass function

Even though the dark-matter power spectrum in the absence of biasing predicts a number density of halos n(M) ~ M^-2 (i.e. a Schechter alpha value of -2) at the low-mass end (M < 10^10 M_solar), hydrodynamic simulations have typically produced values for stellar systems in good agreement with the observed value alpha ~ -1. We explain this with a simple physical argument and show that an efficient external gas-heating mechanism (such as the UV background included in all hydro codes) will produce a critical halo mass below which halos cannot retain their gas and form stars. We test this conclusion with GADGET-2-based simulations using various UV backgrounds, and for the first time we also investigate the effect of an X-ray background. We show that at the present epoch alpha is depends primarily on the mean gas temperature at the star-formation epoch for low-mass systems (z <~ 3): with no background we find alpha ~ -1.5, with UV only alpha ~ -1.0, and with UV and X-rays alpha ~ -0.75. We find the critical final halo mass for star formation to be ~4x10^8 M_solar with a UV background and ~7x10^8 M_solar with UV and X-rays.

WHAT DOES CLUSTERING TELL US ABOUT THE BUILDUP OF THE RED SEQUENCE?

We analyze the clustering of red and blue galaxies from four samples spanning a redshift range of 0.4<z<2.0 to test the various scenarios by which galaxies evolve onto the red sequence. The data are taken from the UKIDSS Ultra Deep Survey, DEEP2, and COMBO-17. The use of clustering allows us to determine what fraction of the red sequence is made up of central galaxies and satellite galaxies. At all redshifts, including z=0, the data are consistent with ~60% of satellite galaxies being red or quenched, implying that ~1/3 of the red sequence is comprised of satellite galaxies. More than three-fourths of red satellite galaxies were moved to the red sequence after they were accreted onto a larger halo. The constant fraction of satellite galaxies that are red yields a quenching time for satellite galaxies that depends on redshift in the same way as halo dynamical times; t_Q ~ (1+z)^{-1.5}. In three of the four samples, the data favor a model in which red central galaxies are a random sample of all central galaxies; there is no preferred halo mass scale at which galaxies make the transition from star-forming to red and dead. The large errors on the fourth sample inhibit any conclusions. Theoretical models in which star formation is quenched above a critical halo mass are excluded by these data. A scenario in which mergers create red central galaxies imparts a weaker correlation between halo mass and central galaxy color, but even the merger scenario creates tension with red galaxy clustering at redshifts above 0.5. These results suggest that the mechanism by which central galaxies become red evolves from z=0.5 to z=0.

Downsizing by shutdown in red galaxies

We address the origin of the 'downsizing' of elliptical galaxies, according to which the stars in more massive galaxies formed earlier and over a shorter period than those in less massive galaxies. We show that this could be the natural result of a shutdown of star formation in dark matter haloes above a critical mass of ∼10 12 M ⊙ . This is demonstrated using a semi-analytic simulation of galaxy formation within the standard hierarchical scenario of structure formation. The assumed threshold mass is motivated by the prediction of stable shock heating above this mass and the finding that such a shutdown reproduces the observed distribution of galaxies in luminosity and colour. The shutdown at a critical halo mass introduces a characteristic stellar mass for the transition of galaxies into the 'red sequence' of the galaxy colour-magnitude diagram. Central galaxies of haloes that are more massive today have reached this mass earlier and can therefore grow further along the red sequence by dry mergers, ending up more massive and containing older stars. Small galaxies formed in haloes below the critical mass can shutdown late, when they fall into haloes above the critical mass and become satellites. While our semi-analytic simulation that incorporates an explicit shutdown reproduces downsizing as inferred from the stellar ages of ellipticals, we explain why it is much harder to detect downsizing using the mass functions of different galaxy types.

Tracking down a critical halo mass for killing galaxies through the growth of the red sequence

Abstract Red-sequence galaxies record the history of terminated star formation in the Universe and can thus provide important clues to the mechanisms responsible for this termination. We construct composite samples of published cluster and field galaxy photometry in order to study the build-up of galaxies on the red sequence, as parametrized by the dwarf-to-giant ratio (DGR). We find that the DGR in clusters is higher than that of the field at all redshifts, implying that the faint end of the red sequence was established first in clusters. We find that the DGR evolves with redshift for both samples, consistent with the ‘down-sizing’ picture of star formation. We examine the predictions of semi-analytic models for the DGR and find that neither the magnitude of its environmental dependence nor its evolution is correctly predicted in the models. Red-sequence DGRs are consistently too high in the models, the most likely explanation being that the strangulation mechanism used to remove hot gas from satellite galaxies is too efficient. Finally, we present a simple toy model including a threshold mass, below which galaxies are not strangled, and show that this can predict the observed evolution of the field DGR.