History of Star Formation and Chemical Enrichment in the Milky Way Disk

Based on a physical treatment of the star formation law similar to that given by Efstathiou, we have improved our two-component chemical evolution model for the Milky Way disk. Two gas infall rates are compared, one exponential, one Gaussian. It is shown that the star formation law adopted in this paper depends more strongly on the gas surface density than that in Chang et al. It has large effects on the history of star formation and gas evolution of the whole disk. In the solar neighborhood, the history of chemical evolution and star formation is not sensitive to whether the infall rate is Gaussian or exponential. For the same infall time scale, both forms predict the same behavior for the current properties of the Galactic disk. The model predictions do depend on whether or not the infall time scale varies with the radius, but current available observations cannot decide which case is the more realistic. Our results also show that it would be inadequate to describe the gradient evolution along the Gala     

星系中原子和分子气体的半解析模型

星际气体是星系中重子物质的重要组成部分,其中的分子气体（主要是分子氢H₂）以及原子气体（主要是中性氢HI）对于星系中发生的各个物理过程至关重要。本文在前人的星系形成和演化的半解析模型基础上,加入了描述星系盘中分子气体和原子气体成分的物理模型,来研究分子气体和原子气体对于星系形成和演化所起的作用。我们主要使用了马普天体物理所Munich Group的L-Galaxies半解析星系形成模型,并借鉴了星系化学演化模型的方法,把半解析模型中的每一个星系盘分成了多个同心圆圈,然后在每个圈中分别追踪气体下落、分子气体和原子气体转化、恒星形成、金属增丰、超新星爆发加热冷气体等发生在星系盘上的物理过程,并且每个同心圈都是独立演化的。在我们的模型中,一个基本假设是每个时间步内气体都是以指数形式下落到星系盘上,并且直接叠加在已有的气体径向面密度轮廓之上,其中指数盘的标长r_d正比于星系所在暗物质晕的维里半径r_vir与旋转参量λ的乘积。我们的模型使用了两种描述分子气体形成的模型:一种是基于Krumholz等人解析模型的结果,其中分子气体的比例与局域气体面密度以及局域气体金属丰度相关;另一种是分子气体比例与星际压强相关的模型,根据Obreschkow等人的近似,分子气体的比例与气体面密度以及恒星质量面密度相关。由于恒星形成过程发生在星际巨分子云之中,并且根据Leroy等人的观测结果,恒星形成率面密度近似正比于分子气体的面密度,因此我们在模型中使用了与分子气体面密度相关的恒星形成规律。     

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 G-dwarf problem in the solar neighbourhood: a Lagrangian picture

Recent data on the empirical metallicity distribution of G dwarfs in the disk solar neighbourhood are fitted in two different ways. We use an extended Poisson distribution in the limit where the probability of star formation is small, and a Gauss distribution in the limit where a large number of physical variables is required to determine stellar metal abundance. Both are found to reproduce the data at the same (acceptable) extent, with a slight preference for the former. The emprirical, differential metallicity distribution of G dwarfs in the disk solar neighbourhood is compared with its theoretical counterpart, in the picture of a closed, comoving model of chemical evolution. The limits of the currently used infall models are discussed and a scenario of galactic formation and evolution is presented. The Galactic history is thought as made of two main phases: contraction (which produces the extended component) and equilibrium (which gives the disk). In this view, the stars observed within the solar cylinder did not necessarily arise from the primordial gas which later collapsed into the disk solar neighbourhood. It is found that the G-dwarf problem is strongly alleviated, with the possible exception of the low-metallicity and high-metallicity tail of the distribution. The best choice of parameters implies: (i) a metal yield in the contraction phase which is larger by a factor of about 5 with respect to the equilibrium phase; (ii) a model halo mass fraction of about 0.3; (iii) a model disk mass fraction of about 0.6. It provides additional support to the idea of a generalized Schmidt star formation law, which is different in different phases of evolution. The model, cumulative, G-dwarf metallicity distribution in the disk solar neighbourhood is found to predict too may low-metallicity stars with respect to its empirical counterpart, related to a Poissonian or Gaussian fit. The main resons for the occurrence of a G-dwarf problem are discussed. Finally, a stochastic process of star formation, related to a Poisson distribution, is briefly outlined.     

A grid of chemical evolution models as a tool to interpret spiral and irregular galaxies data

We present a generalization of the multiphase chemical evolution model (CEM) applied to a wide set of theoretical galaxies with different masses and evolutionary rates. This generalized set of models has been computed using the so-called universal rotation curve from Persic, Salucci & Steel to calculate the radial mass distribution of 44 theoretical protogalaxies. This distribution is a fundamental input which, besides its own effect on the galaxy evolution, defines the characteristic collapse time-scale or gas infall rate on to the disc. We have adopted 10 sets of values, between 0 and 1, for the molecular cloud and star formation efficiencies, as corresponding to their probability nature, for each one of the radial distributions of total mass. Thus, we have constructed a biparametric grid of models, depending on those efficiency sets and on the rotation velocity, whose results are valid in principle for any spiral or irregular galaxy. The model results provide the time-evolution of different regions of the disc and the halo along galactocentric distance, measured by the gas (atomic and molecular) and stellar masses, the star formation rate (SFR) and chemical abundances of 14 elements, for a total of 440 models. This grid may be used to estimate the evolution of a given galaxy for which only present time information, such as radial distributions of elemental abundances, gas densities and/or star formation, which are the usual observational constraints of chemical evolution models (CEMs), is available.     

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.     

星系形成与演化半解析理论研究的新进展

发展了的星系形成和演化的半解析理论,可以很好地再现不同红移时宇宙恒星形成率密度（ＳＦＲ）和中性气体共动密度的最新观测结果。对该理论各个不确定性因素对结果的影响作了说尽的讨论,并指出在中等红移星系间的相互作用可能是主宰恒星形成的决定性因素,根据宇宙学模型对观测和半解析理论的影响,对宇宙学参数作出限制。     

Star formation and chemical evolution of damped Lyman α systems

In this paper, we investigate the star formation and chemical evolution of damped Lyman α systems (DLAs) based on the disc galaxy formation model developed by Mo, Mao & White. We propose that the DLAs are the central galaxies of less-massive dark haloes present at redshifts z ∼3, and they should inhabit haloes of moderately low circular velocity. The empirical Schmidt law of star formation rates, and closed box model of chemical evolution that an approximation known as instantaneous recycling is assumed, are adopted. In our models, when the predicted distribution of metallicity for DLAs is calculated, two cases are considered. One is that, using the closed-box model, empirical Schmidt law and star formation time, the distribution of metallicity can be directly calculated. The other is that, when the simple gravitational instability of a thin isothermal gas disc as first discussed by Toomre is considered, the star formation occurs only in the region where the surface density of gas satisfies the critical value, not everywhere of a gas disc. In this case, we first obtain the region where the star formation can occur by assuming that the disc has a flat rotation curve and rotational velocity is equal to the circular velocity of the surrounding dark matter halo, and then calculate the metallicity distribution as in case one. We assume that star formation in each DLA lasts for a period of 1 Gyr from redshifts z =3. There is only one output parameter in our models, i.e. the stellar yield, which relates to the time of star formation history and is obtained by normalizing the predicted distribution of metallicity to the mean value of 1/13 Z_⊙ as presented by Pettini et al.. The predicted metallicity distribution is consistent with the current (rather limited) observational data. A random distribution of galactic discs is taken into account.     

Exploring the evolution of spiral galaxies

We have constructed a family of simple models for spiral galaxy evolution to allow us to investigate observational trends in star formation history with galaxy parameters. The models are used to generate broad-band colours from which ages and metallicities are derived in the same way as the data. We generate a grid of model galaxies and select only those that lie in regions of parameter space covered by the sample. The data are consistent with the proposition that the star formation history of a region within a galaxy depends primarily on the local surface density of the gas but that one or two additional ingredients are required to explain the observational data fully. The observed age gradients appear steeper than those produced by the density dependent star formation law, indicating that the star formation law or infall history must vary with galactocentric radius. Furthermore, the metallicity–magnitude and age–magnitude correlations are not reproduced by a local density dependence alone. These correlations require one or both of the following: (i) a combination of mass dependent infall and metal enriched outflow, or (ii) a mass dependent galaxy formation epoch. Distinguishing these possibilities on the basis of current data is extremely difficult.     

银盘的径向金融丰度梯度

详细综棕了银盘（包括HII区，早B型星，行星状星云和疏散星团）径向元素丰度梯度的观测结果，分析了丰度梯度的空间和时间变化的情况，指出根据目前的观测结果，还很难确定在银盘的演化历史中径向元素丰度梯度是逐渐变平缓还是逐渐变陡，比较了目前各种化学演化模型对径向丰度梯度演化的预测结果，初步探讨了丰度梯度可能的产生机制及影响其演化的各种重要物理过程。     

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.     

An Analytic Model of Galactic Winds and Mass Outflows

Galactic winds and mass outflows are observed both in nearby starburst galaxies and in high-redshift star-forming galaxies. We develop a simple analytic model to understand the observed superwind phenomenon with a discussion of the model uncertainties. Our model is built upon the model of McKee & Ostriker for the interstellar medium. It allows one to predict how properties of a superwind, such as wind velocity and mass outflow rate, are related to properties of its starforming host galaxy, such as size, gas density and star formation rate. The model predicts a threshold of star formation rate density for the generation of observable galactic winds. Galaxies with more concentrated star formation activities produce superwinds with higher velocities. The predicted mass outflow rates are comparable to (or slightly larger than) the corresponding star formation rates. We apply our model to both local starburst galaxies and high-redshift Lyman break galaxies, and find its predictions to be in good agreement with current observations. Our model is simple and so can be easily incorporated into numerical simulations and semi-analytical models of galaxy formation.     

Origin and structure of the Galactic disc(s)

We examine the chemical and dynamical structure in the solar neighbourhood of a model Galaxy that is the endpoint of a simulation of the chemical evolution of the Milky Way in the presence of radial mixing of stars and gas. Although the simulation's star formation rate declines monotonically from its unique peak and no merger or tidal event ever takes place, the model replicates all known properties of a thick disc, as well as matching special features of the local stellar population such as a metal-poor extension of the thin disc that has high rotational velocity. We divide the disc by chemistry and relate this dissection to observationally more convenient kinematic selection criteria. We conclude that the observed chemistry of the Galactic disc does not provide convincing evidence for a violent origin of the thick disc, as has been widely claimed.     

A simple model for the relationship between star formation and surface density

We investigate the relationship between the star formation rate per unit area and the surface density of the interstellar medium (ISM; the local Kennicutt–Schmitt law) using a simplified model of the ISM and a simple estimate of the star formation rate based on the mass of gas in bound clumps, the local dynamical time-scales of the clumps and an efficiency parameter of around  ε≈ 5  per cent. Despite the simplicity of the approach, we are able to reproduce the observed linear relation between star formation rate and surface density of dense (molecular) gas. We use a simple model for the dependence of H₂ fraction on total surface density to argue why neither total surface density nor the H  i surface density is a good local indicator of star formation rate. We also investigate the dependence of the star formation rate on the depth of the spiral potential. Our model indicates that the mean star formation rate does not depend significantly on the strength of the spiral potential, but that a stronger spiral potential, for a given mean surface density, does result in more of the star formation occurring close to the spiral arms. This agrees with the observation that grand design galaxies do not appear to show a larger degree of star formation compared to their flocculent counterparts.     

On the mass and density of the stellar disk of M33

The disk surface density of the nearby spiral galaxy M33 is estimated assuming that it is marginally stable against gravitational perturbations. For this purpose we used the radial profile of line-of-sight velocity dispersion of the disk planetary nebulae obtained by Ciardullo et al. (2004). The surface density profile we obtained is characterized by the radial scalelength which is close to the photometrical one and is in a good agreement with the rotation curve of M33 and with the mass-to-light ratio which follows from the stellar population model. However at the galactocentric distance r > 7 kpc the dynamical overheating of the disk remains quite possible. The thickness of the stellar disk of M33 should increase outwards from the center. The dark halo to total mass ratio is estimated as a function of r. The effective oxygen yield obtained in the frame of instantaneous recycling approximation using the disk surface density and the observed gradient of O/H increases with radius. It may indicate that the role of accretion of metalpoor gas in the chemical evolution of interstellar medium decreases outwards.     

H i and CO observations of Arp 104: a spiral–elliptical interacting pair

We present data probing the spatial and kinematical distribution of both the atomic (H  i ) and molecular (CO) gas in NGC 5218, the late-type barred spiral galaxy in the spiral–elliptical interacting pair, Arp 104. We consider these data in conjunction with far-infrared and radio-continuum data, and N -body simulations, to study the galaxies interactions, and the star formation properties of NGC 5218. We use these data to assess the importance of the bar and tidal interaction on the evolution of NGC 5218, and the extent to which the tidal interaction may have been important in triggering the bar. The molecular gas distribution of NGC 5218 appears to have been strongly affected by the bar; the distribution is centrally condensed with a very large surface density in the central region. The N -body simulations indicate a time-scale since perigalacticon of  ∼3 × 10⁸ yr  , which is consistent with the interaction having triggered or enhanced the bar potential in NGC 5218, leading to inflow and the large central molecular gas density observed. Whilst NGC 5218 appears to be undergoing active star formation, its star formation efficiency is comparable to a 'normal' SBb galaxy. We propose that this system may be on the brink of a more active phase of star formation.     

Modelling star formation and feedback in simulations of interacting galaxies

We discuss a heuristic model to implement star formation and feedback in hydrodynamical simulations of galaxy formation and evolution. In this model, gas is allowed to cool radiatively and to form stars at a rate given by a simple Schmidt-type law. We assume that supernova feedback results in turbulent motions of gas below resolved scales, a process that can pressurize the diffuse gaseous medium effectively, even if it lacks substantial thermal support. Ignoring the complicated detailed physics of the feedback processes, we try to describe their net effect on the interstellar medium with a fiducial second reservoir of internal energy, which accounts for the kinetic energy content of the gas on unresolved scales. Applying the model to three-dimensional, fully self-consistent models of isolated disc galaxies, we show that the resulting feedback loop can be modelled with smoothed particle hydrodynamics such that converged results can be reached with moderate numerical resolution. With an appropriate choice of the free parameters, Kennicutt's phenomenological star formation law can be reproduced over many orders of magnitude in gas surface density. We also apply the model to mergers of equal-mass disc galaxies, typically resulting in strong nuclear starbursts. Confirming previous findings, the presence of a bulge can delay the onset of the starburst from the first encounter of the galaxies until their final coalescence. The final density profiles of the merger remnants are consistent with de Vaucouleurs profiles, except for the innermost region, where the newly created stars give rise to a luminous core with stellar densities that may be in excess of those observed in the cores of most elliptical galaxies. By comparing the isophotal shapes of collisionless and dissipative merger simulations we show that dissipation leads to isophotes that are more discy than those of corresponding collisionless simulations.     

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.     

A model of supernova feedback in galaxy formation

A model of supernova feedback during disc galaxy formation is developed. The model incorporates infall of cooling gas from a halo, and outflow of hot gas from a multiphase interstellar medium (ISM). The star formation rate is determined by balancing the energy dissipated in collisions between cold gas clouds with that supplied by supernovae in a disc marginally unstable to axisymmetric instabilities. Hot gas is created by thermal evaporation of cold gas clouds in supernova remnants, and criteria are derived to estimate the characteristic temperature and density of the hot component and hence the net mass outflow rate. A number of refinements of the model are investigated, including a simple model of a galactic fountain, the response of the cold component to the pressure of the hot gas, pressure-induced star formation and chemical evolution. The main conclusion of this paper is that low rates of star formation can expel a large fraction of the gas from a dwarf galaxy. For example, a galaxy with circular speed 50 km s¹ can expel 6080 per cent of its gas over a time-scale of 1 Gyr, with a star formation rate that never exceeds 0.1 M yr¹. Effective feedback can therefore take place in a quiescent mode and does not require strong bursts of star formation. Even a large galaxy, such as the Milky Way, might have lost as much as 20 per cent of its mass in a supernova-driven wind. The models developed here suggest that dwarf galaxies at high redshifts will have low average star formation rates and may contain extended gaseous discs of largely unprocessed gas. Such extended gaseous discs might explain the numbers, metallicities and metallicity dispersions of damped Lyman systems.     

The G-dwarf problem in the Galactic spheroid

This paper has two parts: one about observational constraints, and the other about chemical evolution models. In the first part, the empirical differential metallicity distribution (EDMD) is deduced from two different samples involving (i) 268 K-giant bulge stars [Sadler, E.M., Rich, R.M., Terndrup, D.M., 1996. AJ 112, 171], and (ii) 149 globular clusters [Mackey, A.D., van den Bergh, S., 2005. MNRAS 360, 631], in addition to previous results (Caimmi, R., 2001b, AN 322, 241 (C01)) related to (iii) 372 solar neighbourhood halo subdwarfs [Ryan, S.G., Norris, J.E., 1991. AJ 101, 1865]. Under the assumption that each distribution is typical for the corresponding subsystem, the EDMD of the Galactic spheroid is determined by weighting the mass. The empirical age-metallicity relation (EAMR) involving absolute ages is deduced from recent results related to a homogeneous sample of globular clusters [De Angeli, F., Piotto, G., Cassisi, S., et al., 2005. AJ 130, 116]. In the second part, models of chemical evolution for the Galactic halo and bulge are computed, assuming the instantaneous recycling approximation. The EDMD data are fitted, to an acceptable extent, by simple models of chemical evolution implying both homogeneous and inhomogeneous star formation, provided that star formation is inhibited during halo formation and enhanced during bulge formation, with respect to the disk solar neighbourhood, taken to be representative of the whole disk. The initial mass function (IMF) is assumed to be a universal power law, which implies the same value of the true yield in different subsystems. The theoretical differential metallicity distribution (TDMD) is first determined for the halo and the bulge separately, and then for the Galactic spheroid by weighting the mass. The EAMR cannot be fitted into the Simple model that implies homogeneous star formation, but shows a non-monotonic trend characterized by large dispersion. On the other hand, simple models involving inhomogeneous star formation yield a theoretical age-metallicity relation (TAMR) which reproduces the data to an acceptable extent. For gas ouflow from the proto-halo, acceptable models give rise to different predictions in different alternatives. If the Galactic spheroid and disk underwent decoupled chemical evolution, i.e. no gas exchange between the related reservoirs, less than one third of the bulge mass outflowed from the proto-halo. If the Galactic spheroid and disk underwent coupled chemical evolution, i.e. some gas exchange between the related reservoirs, the existence of an unseen baryonic halo (or equivalent amount of gas lost by the Galaxy) with mass comparable to bulge mass, is necessarily needed. In this view, the outflowing proto-halo gas which remains bound to the Galaxy, produces both the bulge and the disk.