Stellar population models of Lick indices with variable element abundance ratios

We provide the whole set of Lick indices from CN1 to TiO2 of Simple Stellar Population models with, for the first time, variable element abundance ratios, [alpha/Fe]=0.0, 0.3, 0.5, [alpha/Ca]=-0.1, 0.0, 0.2, 0.5, and [alpha/N]=-0.5, 0.0. The models cover ages between 1 and 15 Gyr, metallicities between 1/200 and 3.5 solar. Our models are free from the intrinsic alpha/Fe bias that was imposed by the Milky Way template stars up to now, hence they reflect well-defined alpha/Fe ratios at all metallicities. The models are calibrated with Milky Way globular clusters for which metallicities and alpha/Fe ratios are known from independent spectroscopy of individual stars. The metallicities that we derive from the Lick indices Mgb and Fe5270 are in excellent agreement with the metallicity scale by Zinn & West (1984), and we show that the latter provides total metallicity rather than iron abundance. We can reproduce the relatively strong CN-absorption features CN1 and CN2 of galactic globular clusters with models in which nitrogen is enhanced by a factor three. An enhancement of carbon, instead, would lead to serious inconsistencies with the indices Mg1 and C24668. The calcium sensitive index Ca4227 of globular clusters is well matched by our models with [Ca/Fe]= 0.3, including the metal-rich Bulge clusters NGC 6528 and NGC 6553. From our alpha/Fe enhanced models we infer that the index [MgFe] defined by Gonzalez (1993) is quite independent of alpha/Fe, but still slightly decreases with increasing alpha/Fe. We define a slight modification of this index that is completely independent of alpha/Fe and serves best as a tracer of total metallicity. Searching for blue indices that give similar information as Mgb and Fe, we find that CN1 and Fe4383 may be best suited to estimate alpha/Fe ratios of objects at redshifts z~1. (Abridged)Comment: 17 pages, 7 figures, plus 8 pages model tables. Accepted by MNRAS. Models are also available in at ftp://ftp.mpe.mpg.de/people/dthomas/SSP

Constraints on galaxy formation from alpha-enhancement in luminous elliptical galaxies

We explore the formation of alpha-enhanced and metal-rich stellar populations in the nuclei of luminous ellipticals under the assumption of two extreme galaxy formation scenarios based on hierarchical clustering, namely a fast clumpy collapse and the merger of two spirals. We investigate the parameter space of star formation time-scale, IMF slope, and stellar yields. In particular, the latter add a huge uncertainty in constraining time-scales and IMF slopes. We find that -- for Thielemann, Nomoto & Hashimoto nucleosynthesis -- in a fast clumpy collapse scenario an [alpha/Fe] overabundance of approx. 0.2 dex in the high metallicity stars can be achieved with a Salpeter IMF and star formation time-scales of the order 10^9 yr. The scenario of two merging spirals which are similar to our Galaxy, instead, fails to reproduce alpha-enhanced abundance ratios in the metal-rich stars, unless the IMF is flattened during the burst ignited by the merger. This result is independent of the burst time-scale. We suggest that abundance gradients give hints to distinguish between the two extreme formation scenarios considered in this paper.Comment: Accepted for publication in MNRAS, LaTex 2.09 with mn.sty, 13 pages, 5 figure

Generating Survival Times to Simulate Cox Proportional Hazards Models

This paper discusses techniques to generate survival times for simulation studies regarding Cox proportional hazards models. In linear regression models, the response variable is directly connected with the considered covariates, the regression coefficients and the simulated random errors. Thus, the response variable can be generated from the regression function, once the regression coefficients and the error distribution are specified. However, in the Cox model, which is formulated via the hazard function, the effect of the covariates have to be translated from the hazards to the survival times, because the usual software packages for estimation of Cox models require the individual survival time data. A general formula describing the relation between the hazard and the corresponding survival time of the Cox model is derived. It is shown how the exponential, the Weibull and the Gompertz distribution can be used to generate appropriate survival times for simulation studies. Additionally, the general relation between hazard and survival time can be used to develop own distributions for special situations and to handle flexibly parameterized proportional hazards models. The use of other distributions than the exponential distribution only is indispensable to investigate the characteristics of the Cox proportional hazards model, especially in non-standard situations, where the partial likelihood depends on the baseline hazard

Configuration mixing within the energy density functional formalism: pathologies and cures

Configuration mixing calculations performed in terms of the Skyrme/Gogny Energy Density Functional (EDF) rely on extending the Single-Reference energy functional into non-diagonal EDF kernels. The standard way to do so, based on an analogy with the pure Hamiltonian case and the use of the generalized Wick theorem, is responsible for the recently observed divergences and steps in Multi-Reference calculations. We summarize here the minimal solution to this problem recently proposed [Lacroix et al, arXiv:0809.2041] and applied with success to particle number restoration[Bender et al, arXiv:0809.2045]. Such a regularization method provides suitable corrections of pathologies for EDF depending on integer powers of the density. The specific case of fractional powers of the density[Duguet et al, arXiv:0809.2049] is also discussed.Comment: 5 pages, Proceedings of the French-Japanese Symposium, September 2008. To be published in Int. J. of Mod. Phys.

New Clues on the Calcium Underabundance in Early-Type Galaxies

We use our new stellar population models, which include effects from variable element abundance ratios, to model the Ca4227 absorption line indices of early-type galaxies (Trager et al.), and to derive calcium element abundances. We find that calcium, although being an alpha-element, is depressed with respect to the other alpha-elements by up to a factor 2. This confirms quantitatively earlier speculations that early-type galaxies are calcium underabundant. We find a clear correlation between alpha/Ca ratio and central velocity dispersion, which implies that more massive galaxies are more calcium underabundant. Interestingly this correlation extends down to the dwarf spheroidal galaxies of the Local Group for which alpha/Ca ratios have been measured from high-resolution spectroscopy of individual stars (Shetrone et al.). The increase of the calcium underabundance with galaxy mass balances the higher total metallicities of more massive galaxies, so that calcium abundance in early-type galaxies is fairly constant and in particular does not increase with increasing galaxy mass. This result may be the key to understand why the CaII triplet absorption of early-type galaxies at 8600 A is constant to within 5 per cent over a large range of velocity dispersions (Saglia et al.; Cenarro et al.). The origin of the calcium underabundance in early-type galaxies remains yet to be understood. We argue that formation timescales are disfavoured to produce calcium underabundance, and that the option of metallicity dependent supernova yields may be the most promising track to follow.Comment: 5 pages, 2 figures. Accepted by MNRA

Spatially resolved spectroscopy of Coma cluster early-type galaxies IV. Completing the dataset

The long-slit spectra obtained along the minor axis, offset major axis and diagonal axis are presented for 12 E and S0 galaxies of the Coma cluster drawn from a magnitude-limited sample studied before. The rotation curves, velocity dispersion profiles and the H_3 and H_4 coefficients of the Hermite decomposition of the line of sight velocity distribution are derived. The radial profiles of the Hbeta, Mg, and Fe line strength indices are measured too. In addition, the surface photometry of the central regions of a subsample of 4 galaxies recently obtained with Hubble Space Telescope is presented. The data will be used to construct dynamical models of the galaxies and study their stellar populations.Comment: 40 pages, 7 figures, 6 tables. Accepted for publication in ApJ

Radially extended kinematics and stellar populations of the massive ellipticals NGC1600, NGC4125 and NGC7619. Constraints on the outer dark halo density profile

We present high quality long slit spectra along the major and minor axes out to 1.5-2 Re (14-22 kpc) of three bright elliptical galaxies (NGC1600, NGC4125, NGC7619) obtained at the Hobby-Eberly Telescope (HET). We derive stellar kinematic profiles and Lick/IDS indices (Hbeta, Mgb, Fe5015, Fe5270, Fe5335, Fe5406). Moreover, for NGC4125 we derive gas kinematics and emission line strengths. We model the absorption line strengths using Simple Stellar Populations models that take into account the variation of [\alpha/Fe] and derive ages, total metallicity and element abundances. Overall, we find that the three galaxies have old and [\alpha/Fe] overabundant stellar populations with no significant gradients. The metallicity is supersolar at the center with a strong negative radial gradient. For NGC4125, several pieces of evidence point to a recent dissipational merger event. We calculate the broad band color profiles with the help of SSP models. All of the colors show sharp peaks at the center of the galaxies, mainly caused by the metallicity gradients, and agree well with the measured colors. Using the Schwarzschild's axisymmetric orbit superposition technique, we model the stellar kinematics to constrain the dark halos of the galaxies. We use the tight correlation between the Mgb strength and local escape velocity to set limits on the extent of the halos by testing different halo sizes. Logarithmic halos - cut at 60 kpc -minimize the overall scatter of the Mgb-Vesc relation. Larger cutoff radii are found if the dark matter density profile is decreasing more steeply at large radii.Comment: Accepted for publication in Astronomy and Astrophysic

Dismissal protection and worker flows in small establishments

"Based on a large employer-employee matched data set, the paper investigates the effects of variable enforcement of German dismissal protection legislation on the employment dynamics in small establishments. Specifically, using a difference-in-differences approach, we study the effect of changes in the threshold scale exempting small establishments from dismissal protection provisions on worker flows. In contrast to the predictions of the theory, our results indicate that there are no statistically significant effects of the dismissal protection legislation on worker turnover." (Author's abstract, IAB-Doku) ((en))Kleinbetrieb, Kündigungsschutz, IAB-Linked-Employer-Employee-Datensatz, zwischenbetriebliche Mobilität