The metallicity distribution of G dwarfs in the solar neighbourhood and the chemical evolution of the Galaxy

Based on a new metallicity distribution for G dwarfs within 25 pc of the sun this paper discusses in detail four galactic chemical evolution models in an inhomogeneous interstellar medium. It is shown that both the so-called simple model and the collapse model deviate greatly from the observations, while the two models labelled PIE (Prompt Initial Enrichment) and PPY (Proportional Yield) not only give much better fit, but also alleviate the so-called G-dwarf problem. The indications are that the outer halo has little influence on the chemical evolution near the Sun.     

A revision of the solar neighbourhood metallicity distribution

We present a revised metallicity distribution of dwarfs in the solar neighbourhood. This distribution is centred on solar metallicity. We show that previous metallicity distributions, selected on the basis of spectral type, are biased against stars with solar metallicity or higher. A selection of G-dwarf stars is inherently biased against metal-rich stars and is not representative of the solar neighbourhood metallicity distribution. Using a sample selected on colour, we obtain a distribution where approximately half the stars in the solar neighbourhood have metallicities higher than [Fe/H]=0 . The percentage of mid-metal-poor stars ([Fe/H]<−0.5) is approximately 4 per cent, in agreement with present estimates of the thick disc.
In order to have a metallicity distribution comparable to chemical evolution model predictions, we convert the star fraction to mass fraction, and show that another bias against metal-rich stars affects dwarf metallicity distributions, due to the colour (or spectral type) limits of the samples. Reconsidering the corrections resulting from the increasing thickness of the stellar disc with age, we show that the simple closed-box model with no instantaneous recycling approximation gives a reasonable fit to the observed distribution. Comparisons with the age–metallicity relation and abundance ratios suggest that the simple closed-box model may be a viable model of the chemical evolution of the Galaxy at solar radius.     

Metal enrichment history of the proto-galactic interstellar medium

To investigate the metal enrichment history of the primordial interstellar medium (ISM), we have studied the long-term evolution of supernova remnants (SNRs) and how SNRs distribute the heavy metals into the ISM when they explode. With the assumed IMF for massive stars, we have computed the multiple supernova explosions and evolution in an inhomogeneous ISM. We compare the predicted metallicity distribution of metal deficient halo stars with the observed one. This revised version was published online in September 2006 with corrections to the Cover Date.     

F stars: Evidence for ‘two-dimensional’ age-metallicity relation and a new light on the enrichment history of the solar neighbourhood

From theuvby photometry and proper motions for about 5500 nearby F stars we have found the following: (i) F stars, taken in narrow ranges of metallicity, show at [Fe/H]<0 rather distinct cut-off in their distribution along the Main Sequence (MS) at the blue side, which is suggested to be an indication for the MS turn-off in stellar groups of fixed metallicity; (ii) the corresponding turn-off age from theoretical isochrones strongly correlates with the mean peculiar velocity of the turn-off stars; (iii) the sub-groups of stars of different colours have essentially the same mean peculiar velocity at low metallicity, but at high metallicity the velocities of the red subgroups are much larger than those of the blue ones. We argue that these properties of F stars lead to a two-dimensional age-metallicity relation with the following main features: (i) a very large spread of metal abundance for old stars, (ii) narrowing of the metallicity range toward younger ages, (iii) increase of mean metallicity toward younger ages. This AMR seems to require a major revision of current models of the chemical evolution of the Galaxy: it suggests that the spatial distribution of metal abundance in the interstellar medium was initially highly inhomogeneous, the inhomogeneities being smoothed out and the mean metallicity being increased as the time went on.We also find an evidence for the evolution of the gaseous matter, from which the open clusters are formed, to be somehow decoupled from the evolution of the overall ISM.     

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.     

The formation of a disk galaxy within a slowly growing dark halo

The formation of a disk galaxy within a slowly growing dark halo is simulated with a new chemo-dynamical model. The model describes the evolution of the stellar populations, the multi-phase ISM and all important interaction. I find, that the galaxy forms radially from inside-out and vertically from top-to-bottom. The derived stellar age distributions show that the inner halo is the oldest component, followed by the outer halo, the triaxial bulge, the halo-disk transition region and the disk. Despite the still idealized model, the final galaxy resembles present-day disk galaxies in many aspects. In particular, the stellar metallicity distribution in the halo of the model resembles the one of M31. The bulge in the model shows, at least two stellar subpopulations, an early collapse population and a population that formed later out of accreted disk mass. In the stellar metallicity distribution of the disk, I find a pronounced ‘G-dwarf problem’ which is the result of a pre-enrichment of the disk ISM with metal-rich gas from the bulge. This revised version was published online in September 2006 with corrections to the Cover Date.     

解决G矮星问题的银河系化学演化三成分模型

为解释著名的G矮星问题,提出银河系化学演化的三成分模型,即由银晕、厚盘和薄盘所构成的演化模型．相邻演化阶段间隔着一个快速坍缩过程．对不同星族成分的演化过程分别进行模拟,并在总体上得到一个太阳附近区域的G矮星丰度分布函数．检验了三种不同的模型：初始富化模型、比例生成模型和坍缩模型．利用最小二乘拟合得到最佳模型的参数．结果表明,太阳附近区域的化学演化受物质交换的影响较小,至少在银河系演化的晚期,可将太阳附近区域看作封闭系统．同时,单位质量中新合成的重元素比例对三种恒星成分可分别近似为常数,其差别则说明不同星族恒星的初始质量函数存在着显著差异．     

The Chemical Evolution of the Galactic Bulge

In this paper we review the chemical evolution models for the Galactic bulge: in particular, we discuss the predictions of models as compared with the available abundance data and infer the mechanism as well as the time scale for the formation of the Galactic bulge. We show that good chemical evolution models reproducing the observed metallicity distribution of stars in the bulge predict that the [α/Fe] >0 over most of the metallicity range. This is a very important constraint indicating that the bulge of our Galaxy formed at the same time and even faster than the inner Galactic halo. We also discuss predictions for the evolution of light elements such as D and ⁷Li and conclude that the D astration should be maximum due to the high star formation rate required for the bulge whereas the evolution of the abundance of Li should be similar to that observed in the solar neighbourhood, but with an higher Li abundance in the interstellar medium at the present time. This revised version was published online in July 2006 with corrections to the Cover Date.     

Distribution of metals in dwars stars in the solar neighbourhood

A preliminary method is proposed to handle the intrinsic chemical inhomogeneity in models of chemical evolution of the solar neighbourhood. If we assume a Gaussian spread in metallicity (z[Fe/H]) about a mean metallicity in the birth function of stars, the metallicity distribution of stars as a function of time is investigated, assuming that the mean metallicityz evolves linearly with time. Metallicity ([Fe/H]) histograms are plotted for A-, F-, G-, and K-dwarfs of the local disk population based on our compilation of data from several sources, and compared with the existing ones. We have applied the above method on these distributions to check whether distribution of the local A-, F-, and K-dwarfs could be fitted reasonably well with a single set of parameters derived from a fit to the metallicity distribution of the G-dwarfs.     

Solving the G-dwarf problem with a three-component model of the chemical evolution of the Galaxy

A three-component chemical evolution model of the Galaxy is presented, which we believe will cast a new light on the G-dwarf problem. The model is based on a scenario of the Galaxy consisting of three major evolutionary phases: halo, thick disk and thin disk, separated by two short interludes of rapid collapse. The evolution of different stellar populations are treated separately, the combination of which yields an overall metallicity distribution function for the solar neighbourhood. We tested three different models using the same set of basic equations: the “prompt initial enrichment” (PIE) model, the “proportional yield” (PPY) model and the “collapse” (CLP) model. Best-fit parameters are derived. The results show that the different populations have remarkably different IMFs, while mass exchange has only minimally affected the chemical evolution in the solar vicinity, so that the solar vicinity can be regarded as a closed system, at least in the late stage of the Galactic evolution.     

太阳附近G矮星金属含量分布和化学演化

利用新的太阳附近２５ｐｃ内的Ｇ矮星金属含量分布函数,本文在假定星际介质丰度非均匀情况下,讨论了四种化学演化模型的合理性．结果表明,简单模型和坍缩模型与实际情况相差较大,而ＰＩＥ模型和ＰＰＹ模型不仅对金属含量分布函数拟合较好,而且传统的Ｇ矮星问题也可以得到解释．这表明太阳附近可能受银晕影响较小．     

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).     

Abundance Ratios in Extreme Metal-Poor Stars

In extremely metal-poor stars ([Fe/H]≤ − 2.5) the neutron capture elementsare characterized by a 300-fold dispersion in M/Fe ratios which decreases with increasing metallicity, the median M/Fe ratio increases with increasing [Fe/H], but the averageM/Fe number ratio is approximately constant. These observations are consistent witha highly dispersed intrinsic yield of neutron-capture elements in supernova (SN) events,and a progression to increasing metallicity by stochastic chemical evolution.The abundance trends indicate that the synthesis of elements heavier thanbarium was dominated by the r-process. The Sr/Ba ratio shows a dispersionwhich suggests a stochastic source of Sr in excess of the r-process value;possibly due to the alpha-rich freeze out.The iron-peak elements Cr, Mn, and Co show non-solar abundance ratios forextreme metal-poor stars, and no measurableintrinsic dispersion relative to iron. We discuss chemical evolution models which explain these observations. This revised version was published online in July 2006 with corrections to the Cover Date.     

Stellar Yields and Chemical Evolution — I. Abundance Ratios and Delayed Mixing in the Solar Neighbourhood

We analyse two recent computations of Type II supernova nucleosynthesis by Woosley & Weaver (hereafter WW95) and Thielemann, Nomoto & Hashimoto (hereafter TNH96), focusing on the ability to reproduce the observed [Mg/Fe] ratios in various galaxy types. We show that the yields of oxygen and total metallicity are in good agreement. However, TNH96 models produce more magnesium in the intermediate and less iron in the upper mass range of Type II supernovae than WW95 models. To investigate the significance of these discrepancies for chemical evolution, we calculate simple stellar population yields for both sets of models and different initial mass function slopes. We conclude that the Mg yields of WW95 do not suffice to explain the [Mg/Fe] overabundance either in giant elliptical galaxies and bulges or in metal-poor stars in the solar neighbourhood and the Galactic halo. Calculating the chemical evolution in the solar neighbourhood according to the standard infall model, we find that, using WW95 and TNH96 nucleosynthesis, the solar magnesium abundance is underestimated by 29 and 7 per cent, respectively.   We include the relaxation of the instantaneous mixing approximation in chemical evolution models by splitting the gas component into two different phases. In additional simulations of the chemical evolution in the solar neighbourhood, we discuss various time-scales for the mixing of the stellar ejecta with the interstellar medium. We find that a delay of the order of 10⁸ yr leads to a better fit of the observational data in the [Mg/Fe]–[Fe/H] diagram without destroying the agreement with solar element abundances and the age–metallicity relation.     

On rejuvenation in massive binary systems

We introduce a set of stellar models for massive stars whose evolution has been affected by mass transfer in a binary system, at a range of metallicities. As noted by other authors, the effect of such mass transfer is frequently more than just rejuvenation. We find that, whilst stars with convective cores which have accreted only H-rich matter rejuvenate as expected, those stars which have accreted He-rich matter (e.g. at the end stages of conservative mass transfer) evolve in a way that is qualitatively similar to rejuvenated stars of much higher metallicity. Thus, the effects of non-conservative evolution depend strongly on whether He-rich matter is amongst the portion accreted or ejected. This may lead to a significant divergence in binary evolution paths with only a small difference in initial assumptions. We compare our models to observed systems and find approximate formulae for the effect of mass accretion on the effective age and metallicity of the resulting star.     

On the Galactic disc age–metallicity relation

A comparison is made between the age–metallicity relations obtained from four different types of studies: F and G stars in the solar neighbourhood, analysis of open clusters, galactic structure studies with the stellar population synthesis technique and chemical evolution models. Metallicities of open clusters are corrected for the effects of the radial gradient, which we find to be −0.09 dex kpc⁻¹ and most likely constant in time. We do not correct for the vertical gradient, because its existence and value are not firmly established.
Stars and clusters trace a similar age–metallicity relation, showing an excess of rather metal-rich objects in the age range 5–9 Gyr. Galactic structure studies tend to give a more metal-poor relation than chemical evolution models. Neither relation explains the presence of old, relatively metal-rich stars and clusters. This might be caused by uncertainties in the ages of the local stars, or pre-enrichment of the disc with material from the bulge, possibly as a result of a merger event in the early phases of the formation of our Galaxy.     

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

The current paper investigates how the empirical, G-dwarf metallicity distribution constrains simple, comoving models of chemical evolution. In doing this, the application of the models to a data sample, performed in a previous paper, is refined and extended. The key idea is that (i) different star formation rates with different mass spectra take place in different phases of evolution, i.e. contraction and equilibrium, and (ii) disk formation begins at a time t = T_d and ends at t = T_c, which marks the transition from contraction to equilibrium. In this view, the lowest-metallicity point of the empirical, differential distribution, consistent with a linear fit, is related to the beginning of disk formation, and an apparent discontinuity point to the transition from contraction to equilibrium. In addition, different linear fits hold on the left (early distribution) and on the right (late distribution) of the discontinuity point. Models consistent with the empirical, G-dwarf metallicity distribution are related to linear fits on the early and late side. Homologous solutions during the equilibrium phase are analysed in detail with respect to changes in T_c and T_a, the age of the Galaxy. Then we are left with a single free parameter which is relevant to the chemical evolution, i.e. the mass spectrum exponent during the equilibrium phase. The allowed values for the other parameters, thought as a function of the above mentioned one, are plotted for each case. A Salpeter mass spectrum exponent, p = −2.35, is ruled out by the theoretical, lower stellar mass limit, contrary to a Scalo mass spectrum exponent, p = −2.90, in contrast with previous literature. The reasons for this discrepancy are discussed. Our results are marginally consistent with a same initial mass function during the contraction and equilibrium phase, but in this case the disk mass fraction is of the is same order, or less, than the halo mass fraction. It is also investigated how the empirical age-metallicity relation constrains the duration of the contraction phase, for a reasonable upper limit of T_a. Keeping in mind that the empirical, G-dwarf metallicity distribution has not been corrected for the large cosmic scatter shown by the empirical, age-metallicity relation, we find a duration of disk formation, T_c — T_d = 1.07–1.5 Gyr, by a factor 3–5 less than it is found by use of simple infall models. The reasons of this difference are explained. The idea of a massive, white dwarf halo, which seems to be indicated by microlensing experiments, is ruled out by the empirical, G-dwarf metallicity distribution, in the light of the current model and provided the solar neighbourhood is a typical region of the Galaxy. More refined models involving e.g., the relax of instantaneous recycling would change our results, but the trend is expected to be only slightly altered.     

The effects of spatially distributed ionisation sources on the temperature structure of H <Emphasis Type="SmallCaps">ii</Emphasis> regions

Spatially resolved studies of star-forming regions show that the assumption of spherical geometry is not realistic in most cases, with a major complication posed by the gas being ionised by multiple non-centrally located stars or star clusters. Geometrical effects including the spatial configuration of ionising sources affect the temperature and ionisation structure of these regions. We try to isolate the effects of multiple non-centrally located stars, via the construction of 3D photoionisation models using the 3D Monte Carlo photoionisation code mocassin with very simple gas density distributions, but various spatial configurations for the ionisation sources.Emission-line spectra from H?ii regions are often used to study the metallicity of star-forming regions, as well as for providing a constraint on temperatures and luminosities of the ionising sources. Empirical metallicity diagnostics must often be calibrated with the aid of photoionisation models. However, most studies so far have been carried out by assuming spherical or plane-parallel geometries, with major limitations on the allowed gas and dust density distributions and with the spatial distribution of multiple, non-centrally located ionising sources not being accounted for. We compare integrated emission-line spectra from our models and quantify any systematic errors caused by the simplifying assumption of a single, central location for all ionising sources. We find that the dependence of the metallicity indicators on the ionisation parameter causes a clear bias, due to the fact that models with a fully distributed configuration of stars always display lower ionisation parameters than their fully concentrated counterparts. The errors found imply that the geometrical distribution of ionisation sources may partly account for the large scatter in metallicities derived using model-calibrated empirical methods.     

Radial mixing and the transition between the thick and thin Galactic discs

The analysis of the kinematics of solar neighbourhood stars shows that the low- and high-metallicity tails of the thin disc are populated by objects which orbital properties suggest an origin in the outer and inner Galactic disc, respectively. Signatures of radial migration are identified in various recent samples, and are shown to be responsible for the high-metallicity dispersion in the age–metallicity distribution. Most importantly, it is shown that the population of low-metallicity wanderers of the thin disc (−0.7 < [Fe/H] < −0.3 dex) is also responsible for the apparent hiatus in metallicity with the thick disc (which terminal metallicity is about −0.2 dex). It implies that the thin disc at the solar circle has started to form stars at about this same metallicity. This is also consistent with the fact that 'transition' objects, which have α-element abundance intermediate between that of the thick and thin discs, are found in the range [−0.4, −0.2] dex. Once the metal-poor thin disc stars are recognized for what they are – wanderers from the outer thin disc – the parenthood between the two discs can be identified on stars genuinely formed at the solar circle through an evolutionary sequence in [α/Fe] and [Fe/H]. Another consequence is that stars that can be considered as truly resulting of the chemical evolution at the solar circle have a metallicity restricted to about [−0.2, +0.2] dex, confirming an old idea that most chemical evolution in the Milky Way have preceded the thin disc formation.