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.     

Forming a large disc galaxy from a z < 1 major merger

Using high-resolution SPH simulations in a fully cosmological Λ cold dark matter context, we study the formation of a bright disc-dominated galaxy that originates from a 'wet' major merger at   z = 0.8  . The progenitors of the disc galaxy are themselves disc galaxies that formed from early major mergers between galaxies with blue colours. A substantial thin stellar disc grows rapidly following the last major merger and the present-day properties of the final remnant are typical of early-type spiral galaxies, with an i -band bulge-to-disc ratio ∼0.65, a disc scalelength of 7.2 kpc,   g − r = 0.5 mag  , an H  i linewidth ( W ₂₀/2) of 238 km s⁻¹ and total magnitude   i =−22.4  . The key ingredients for the formation of a dominant stellar disc component after a major merger are (i) substantial and rapid accretion of gas through cold flows followed at late times by cooling of gas from the hot phase, (ii) supernova feedback that is able to partially suppress star formation during mergers and (iii) relative fading of the spheroidal component. The gas fraction of the progenitors' discs does not exceed 25 per cent at   z < 3  , emphasizing that the continuous supply of gas from the local environment plays a major role in the regrowth of discs and in keeping the galaxies blue. The results of this simulation alleviate the problem posed for the existence of disc galaxies by the high likelihood of interactions and mergers for galaxy-sized haloes at relatively low z .     

The formation and survival of discs in a ΛCDM universe

We study the formation of galaxies in a Λ cold dark matter (ΛCDM) universe using high-resolution hydrodynamical simulations with a multiphase treatment of gas, cooling and feedback, focusing on the formation of discs. Our simulations follow eight isolated haloes similar in mass to the Milky Way and extracted from a large cosmological simulation without restriction on spin parameter or merger history. This allows us to investigate how the final properties of the simulated galaxies correlate with the formation histories of their haloes. We find that, at   z = 0  , none of our galaxies contains a disc with more than 20 per cent of its total stellar mass. Four of the eight galaxies nevertheless have well-formed disc components, three have dominant spheroids and very small discs, and one is a spheroidal galaxy with no disc at all. The   z = 0  spheroids are made of old stars, while discs are younger and formed from the inside-out. Neither the existence of a disc at   z = 0  nor the final disc-to-total mass ratio seems to depend on the spin parameter of the halo. Discs are formed in haloes with spin parameters as low as 0.01 and as high as 0.05; galaxies with little or no disc component span the same range in spin parameter. Except for one of the simulated galaxies, all have significant discs at   z ≳ 2  , regardless of their   z = 0  morphologies. Major mergers and instabilities which arise when accreting cold gas is misaligned with the stellar disc trigger a transfer of mass from the discs to the spheroids. In some cases, discs are destroyed, while in others, they survive or reform. This suggests that the survival probability of discs depends on the particular formation history of each galaxy. A realistic ΛCDM model will clearly require weaker star formation at high redshift and later disc assembly than occurs in our models.     

The origin of the density distribution of disc galaxies: a new problem for the standard model of disc formation

We present new models for the formation of disc galaxies that improve upon previous models by following the detailed accretion and cooling of the baryonic mass, and by using realistic distributions of specific angular momentum. Under the assumption of detailed angular momentum conservation, the discs that form have density distributions that are more centrally concentrated than an exponential. We examine the influence of star formation, bulge formation, and feedback on the outcome of the surface brightness distributions of the stars. Low angular momentum haloes yield disc galaxies with a significant bulge component and with a stellar disc that is close to exponential, in good agreement with observations. High angular momentum haloes, on the other hand, produce stellar discs that are much more concentrated than an exponential, in clear conflict with observations. At large radii, the models reveal distinct truncation radii in both the stars and the cold gas. The stellar truncation radii result from our implementation of star formation threshold densities, and are in excellent agreement with observations. The truncation radii in the density distribution of the cold gas reflect the maximum specific angular momentum of the gas that has cooled. We find that these truncation radii occur at H  i surface densities of roughly 1 M_⊙ pc⁻², in conflict with observations. We examine various modifications to our models, including feedback, viscosity, and dark matter haloes with constant-density cores, but show that the models consistently fail to produce bulge less discs with exponential surface brightness profiles. This signals a new problem for the standard model of disc formation: if the baryonic component of the protogalaxies out of which disc galaxies form has the same angular momentum distribution as the dark matter, discs are too compact.     

Large-scale galactic turbulence: can self-gravity drive the observed H i velocity dispersions?

Observations of turbulent velocity dispersions in the H  i component of galactic discs show a characteristic floor in galaxies with low star formation rates and within individual galaxies the dispersion profiles decline with radius. We carry out several high-resolution adaptive mesh simulations of gaseous discs embedded within dark matter haloes to explore the roles of cooling, star formation, feedback, shearing motions and baryon fraction in driving turbulent motions. In all simulations the disc slowly cools until gravitational and thermal instabilities give rise to a multiphase medium in which a large population of dense self-gravitating cold clouds are embedded within a warm gaseous phase that forms through shock heating. The diffuse gas is highly turbulent and is an outcome of large-scale driving of global non-axisymmetric modes as well as cloud–cloud tidal interactions and merging. At low star formation rates these processes alone can explain the observed H  i velocity dispersion profiles and the characteristic value of  ∼10 km s⁻¹  observed within a wide range of disc galaxies. Supernovae feedback creates a significant hot gaseous phase and is an important driver of turbulence in galaxies with a star formation rate per unit area  ≳10⁻³ M_⊙ yr⁻¹ kpc⁻²  .     

Pre-enriched, not primordial ellipticals

We follow the chemical evolution of a galaxy through star formation and its feedback into the interstellar medium (ISM), starting from primordial gas and allowing for gas to inflow into the region being modelled. We attempt to reproduce observed spectral line strengths for early-type galaxies in order to constrain their star formation histories (SFH). The efficiencies and times of star formation are varied, as are the amount and duration of inflow. We evaluate the chemical enrichment and the mass of stars made with time. Single stellar population (SSP) data are then used to predict line strengths for composite stellar populations. The results are compared with observed line strengths in 10 ellipticals, including some features which help to break the problem of age–metallicity degeneracy in old stellar populations. We find that the elliptical galaxies modelled require high metallicity SSPs (> 3 Z⊙) at later times. In addition, the strong lines observed cannot be produced by an initial starburst in primordial gas, even if a large amount of inflow is allowed for during the first few × 10⁸ yr. This is because some pre-enrichment is required for lines in the bulk of the stars to approach the observed line strengths in ellipticals. These strong lines are better modelled by a system with a delayed burst of star formation, following an early SFH which can be a burst or more steady star formation. Such a model is representative of star formation in normal ellipticals or spirals, respectively, followed by a starburst and gas inflow during a merger or strong interaction with a gas-rich galaxy. Alternatively, a single initial burst of normal stars with a Salpeter initial mass function could produce the observed strong lines if it followed some pre-enrichment process which did not form long-lived stars (e.g. population III stars).     

When is star formation episodic? A delay differential equation 'negative feedback' model

We introduce a differential equation for star formation in galaxies that incorporates negative feedback with a delay. When the feedback is instantaneous, solutions approach a self-limiting equilibrium state. When there is a delay, even though the feedback is negative, the solutions can exhibit cyclic and episodic solutions. We find that periodic or episodic star formation only occurs when two conditions are satisfied. First the delay time-scale must exceed a cloud consumption time-scale. Secondly, the feedback must be strong. This statement is quantitatively equivalent to requiring that the time-scale to approach equilibrium be greater than approximately twice the cloud consumption time-scale. The period of oscillations predicted is approximately four times the delay time-scale. The amplitude of the oscillations increases with both feedback strength and delay time.
We discuss applications of the delay differential equation (DDE) model to star formation in galaxies using the cloud density as a variable. The DDE model is most applicable to systems that recycle gas and only slowly remove gas from the system. We propose likely delay mechanisms based on the requirement that the delay time is related to the observationally estimated time between episodic events. The proposed delay time-scale accounting for episodic star formation in galaxy centres on periods similar to   P ∼ 10 Myr  , irregular galaxies with   P ∼ 100 Myr  , and the Milky Way disc with   P ∼ 2  Gyr, could be that for exciting turbulence following creation of massive stars, that for gas pushed into the halo to return and interact with the disc and that for spiral density wave evolution, respectively.     

Simulating galactic outflows with kinetic supernova feedback

Feedback from star formation is thought to play a key role in the formation and evolution of galaxies, but its implementation in cosmological simulations is currently hampered by a lack of numerical resolution. We present and test a subgrid recipe to model feedback from massive stars in cosmological smoothed particle hydrodynamics simulations. The energy is distributed in kinetic form among the gas particles surrounding recently formed stars. The impact of the feedback is studied using a suite of high-resolution simulations of isolated disc galaxies embedded in dark haloes with total mass 10¹⁰ and  10¹²  h ⁻¹ M_⊙  . We focus, in particular, on the effect of pressure forces on wind particles within the disc, which we turn off temporarily in some of our runs to mimic a recipe that has been widely used in the literature. We find that this popular recipe gives dramatically different results because (ram) pressure forces on expanding superbubbles determine both the structure of the disc and the development of large-scale outflows. Pressure forces exerted by expanding superbubbles puff up the disc, giving the dwarf galaxy an irregular morphology and creating a galactic fountain in the massive galaxy. Hydrodynamic drag within the disc results in a strong increase in the effective mass loading of the wind for the dwarf galaxy, but quenches much of the outflow in the case of the high-mass galaxy.     

Numerical simulations of the formation and chemical evolution of galaxies

We present the results of a set of three-dimensional SPH-Treecode simulations which model the formation and early evolution of disc galaxies, including the generation and return of heavy elements to the interstellar medium by star formation. Starting from simple initial conditions which are given by a uniform density sphere of gas which is embedded in a dark matter halo and in solid-body rotation, we are able to form realistic disc galaxies, and find that an exponential gas disc is quickly formed. Star formation within this exponential disc naturally leads to the formation of abundance gradients which are in broad agreement with those observed, although they are slightly shallower than some observations.
We investigate the systematic effects of variation of mass, rotation and star formation parameters on the abundance gradients. We find that the abundance gradients are most sensitive to changes in the star formation parameters or rotation. Including a critical-density cut-off in the star formation law causes abundance gradients to be steepened.
Analysis of gas flows within the models shows radial flows which are a function of angle of azimuth around the galaxies, with alternating inward and outward flows. This motion is linked to the presence of a bar, whose strength is related to the amount of star formation in the models, and there is a gentle drift of mass inwards. The shallow abundance gradients may be linked to these radial flows.     

Milky Way type galaxies in a ΛCDM cosmology

We analyse a sample of 52 000 Milky Way (MW) type galaxies drawn from the publicly available galaxy catalogue of the Millennium Simulation with the aim of studying statistically the differences and similarities of their properties in comparison to our Galaxy. Model galaxies are chosen to lie in haloes with maximum circular velocities in the range 200–250 km s⁻¹ and to have bulge-to-disc ratios similar to that of the MW. We find that model MW galaxies formed 'quietly' through the accretion of cold gas and small satellite systems. Only ≈12 per cent of our model galaxies experienced a major merger during their lifetime. Most of the stars formed ' in situ ', with only about 15 per cent of the final mass gathered through accretion. Supernovae (SNe) and active galactic nuclei (AGN) feedback play an important role in the evolution of these systems. At high redshifts, when the potential wells of the MW progenitors are shallower, winds driven by SNe explosions blow out a large fraction of the gas and metals. As the systems grow in mass, SNe feedback effects decrease and AGN feedback takes over, playing a more important role in the regulation of the star formation activity at lower redshifts. Although model MW galaxies have been selected to lie in a narrow range of maximum circular velocities, they nevertheless exhibit a significant dispersion in the final stellar masses and metallicities. Our analysis suggests that this dispersion results from the different accretion histories of the parent dark matter haloes. Statistically, we also find evidences to support the MW as a typical Sb/Sc galaxy in the same mass range, providing a suitable benchmark to constrain numerical models of galaxy formation.     

Baryonic conversion tree: the global assembly of stars and dark matter in galaxies from the Sloan Digital Sky Survey

Using the spectroscopic sample of the Sloan Digital Sky Survey Data Release 1 (SDSS DR1), we measure how gas was transformed into stars as a function of time and stellar mass: the baryonic conversion tree (BCT). There is a clear correlation between early star formation activity and present-day stellar mass: the more massive galaxies have formed approximately 80 per cent of their stars at   z > 1  , while for the less massive ones the value is only approximately 20 per cent. By comparing the BCT with the dark matter merger tree, we find indications that star formation efficiency at   z > 1  had to be approximately a factor of two higher than today (∼10 per cent) in galaxies with present-day stellar mass larger than  2 × 10¹¹ M_⊙  , if this early star formation occurred in the main progenitor. Therefore, the λ cold dark matter (LCDM) paradigm can accommodate a large number of red objects. On the other hand, in galaxies with present-day stellar mass less than  10¹¹ M_⊙  , efficient star formation seems to have been triggered at   z ∼ 0.2  . We show that there is a characteristic mass  ( M _*∼ 10¹⁰ M_⊙)  for feedback efficiency (or lack of star formation). For galaxies with masses lower than this, feedback (or star formation suppression) is very efficient while for higher masses it is not. The BCT, determined here for the first time, should be an important observable with which to confront theoretical models of galaxy formation.     

The formation of galaxy discs

Galaxy disc formation must incorporate the multiphase nature of the interstellar medium. The resulting two-phase structure is generated and maintained by gravitational instability and supernova energy input, which yield a source of turbulent viscosity that is able to compete effectively in the protodisc phase with early angular momentum loss of the baryonic component via dynamical friction in the dark halo. Provided that star formation occurs on the viscous drag time-scale, this mechanism provides a means of accounting for disc sizes and radial profiles. The star formation feedback is self-regulated by turbulent gas pressure limited percolation of the supernova remnant heated hot phase, but can run away in gas-rich protodiscs to generate compact starbursts. A simple analytic model is derived for a Schmidt-like global star formation law in terms of the cold gas volume density.     

The first galaxies: assembly, cooling and the onset of turbulence

We investigate the properties of the first galaxies at   z ≳ 10  with highly resolved numerical simulations, starting from cosmological initial conditions and taking into account all relevant primordial chemistry and cooling. A first galaxy is characterized by the onset of atomic hydrogen cooling, once the virial temperature exceeds  ≃10⁴ K  , and its ability to retain photoheated gas. We follow the complex accretion and star formation history of a  ≃5 × 10⁷ M_⊙  system by means of a detailed merger tree and derive an upper limit on the number of Population III (Pop III) stars formed prior to its assembly. We investigate the thermal and chemical evolution of infalling gas and find that partial ionization at temperatures  ≳10⁴ K  catalyses the formation of  H₂  and hydrogen deuteride, allowing the gas to cool to the temperature of the cosmic microwave background. Depending on the strength of radiative and chemical feedback, primordial star formation might be dominated by intermediate-mass Pop III stars formed during the assembly of the first galaxies. Accretion on to the nascent galaxy begins with hot accretion, where gas is accreted directly from the intergalactic medium and shock heated to the virial temperature, but is quickly accompanied by a phase of cold accretion, where the gas cools in filaments before flowing into the parent halo with high velocities. The latter drives supersonic turbulence at the centre of the galaxy and could lead to very efficient chemical mixing. The onset of turbulence in the first galaxies thus likely marks the transition to Pop II star formation.     

Chemical evolution with radial mixing

Models of the chemical evolution of our Galaxy are extended to include radial migration of stars and flow of gas through the disc. The models track the production of both iron and α-elements. A model is chosen that provides an excellent fit to the metallicity distribution of stars in the Geneva–Copenhagen survey (GCS) of the solar neighbourhood and a good fit to the local Hess diagram. The model provides a good fit to the distribution of GCS stars in the age–metallicity plane, although this plane was not used in the fitting process. Although this model's star formation rate is monotonically declining, its disc naturally splits into an α-enhanced thick disc and a normal thin disc. In particular, the model's distribution of stars in the ([O/Fe], [Fe/H]) plane resembles that of Galactic stars in displaying a ridge line for each disc. The thin-disc's ridge line is entirely due to stellar migration, and there is the characteristic variation of stellar angular momentum along it that has been noted by Haywood in survey data. Radial mixing of stellar populations with high  σ _z   from inner regions of the disc to the solar neighbourhood provides a natural explanation of why measurements yield a steeper increase of  σ _z   with age than predicted by theory. The metallicity gradient in the interstellar medium is predicted to be steeper than in earlier models, but appears to be in good agreement with data for both our Galaxy and external galaxies. The models are inconsistent with a cut-off in the star formation rate at low gas surface densities. The absolute magnitude of the disc is given as a function of time in several photometric bands, and radial colour profiles are plotted for representative times.     

How galaxies lose their angular momentum

The processes are investigated by which gas loses its angular momentum during the protogalactic collapse phase, leading to disc galaxies that are too compact with respect to the observations. High-resolution N -body/SPH simulations in a cosmological context are presented including cold gas and dark matter (DM). A halo with quiet merging activity since redshift   z ∼ 3.8  and with a high-spin parameter is analysed that should be an ideal candidate for the formation of an extended galactic disc. We show that the gas and the DM have similar specific angular momenta until a merger event occurs at   z ∼ 2  with a mass ratio of 5:1. All the gas involved in the merger loses a substantial fraction of its specific angular momentum due to tidal torques and dynamical friction processes falls quickly into the centre. In contrast, gas infall through small subclumps or accretion does not lead to catastrophic angular momentum loss. In fact, a new extended disc begins to form from gas that was not involved in the 5:1 merger event and that falls in subsequently. We argue that the angular momentum problem of disc galaxy formation is a merger problem: in cold dark matter cosmology substantial mergers with mass ratios of 1:1 to 6:1 are expected to occur in almost all galaxies. We suggest that energetic feedback processes could in principle solve this problem, however only if the heating occurs at the time or shortly before the last substantial merger event. Good candidates for such a coordinated feedback would be a merger-triggered starburst or central black hole heating. If a large fraction of the low angular momentum gas would be ejected, late-type galaxies could form with a dominant extended disc component, resulting from late infall, a small bulge-to-disc ratio and a low baryon fraction, in agreement with observations.     

Merging time-scales of stellar subclumps in young star-forming regions

Recent observations and hydrodynamical simulations of star formation inside a giant molecular cloud have revealed that, within a star-forming region, stars do not form evenly distributed throughout this region, but rather in small subclumps. It is generally believed that these subclumps merge and form a young star cluster. The time-scale of this merging process is crucial for the evolution and the possible survival of the final star cluster. The key issue is whether this merging process happens faster than the time needed to remove the residual gas of the cloud. A merging time-scale shorter than the gas-removal time would enhance the survival chances of the resulting star cluster. In this paper, we show by means of numerical simulations that the time-scale of the merging is indeed very fast. Depending on the details of the initial subclump distribution, the merging may occur before the gas is expelled from the newly formed cluster via either supernovae or the winds from massive stars. Our simulations further show that the resulting merger objects have a higher effective star formation efficiency than the overall star-forming region and confirm the results that mass-segregated subclumps form mass-segregated merger objects.     

The star formation rate in disc galaxies: thresholds and dependence on gas amount

We reassess the applicability of the Toomre criterion in galactic discs and we study the local star formation law in 16 disc galaxies for which abundance gradients are published. The data we use consist of stellar light profiles, atomic and molecular gas (deduced from CO with a metallicity-dependent conversion factor), star formation rates (from Hα emissivities), metallicities, dispersion velocities and rotation curves. We show that the Toomre criterion applies successfully to the case of the Milky Way disc, but it has limited success with the data of our sample; depending on whether or not the stellar component is included in the stability analysis, we find average values for the threshold ratio of the gas surface density to the critical surface density in the range 0.5–0.7. We also test various star formation laws proposed in the literature, i.e. either the simple Schmidt law or modifications of it, that take into account dynamical factors. We find only small differences among them as far as the overall fit to our data is concerned; in particular, we find that all three star formation laws (with parameters derived from the fits to our data) match observations in the Milky Way disc particularly well. In all cases we find that the exponent n of our best-fitting star formation rate has slightly higher values than in other recent works and we suggest several reasons that may cause that discrepancy.