Nonisotropic 3-level Quantum Systems: Complete Solutions for Minimum Time and Minimum Energy

We apply techniques of subriemannian geometry on Lie groups and of optimal synthesis on 2-D manifolds to the population transfer problem in a three-level quantum system driven by two laser pulses, of arbitrary shape and frequency. In the rotating wave approximation, we consider a nonisotropic model i.e. a model in which the two coupling constants of the lasers are different. The aim is to induce transitions from the first to the third level, minimizing 1) the time of the transition (with bounded laser amplitudes), 2) the energy of lasers (with fixed final time). After reducing the problem to real variables, for the purpose 1) we develop a theory of time optimal syntheses for distributional problem on 2-D-manifolds, while for the purpose 2) we use techniques of subriemannian geometry on 3-D Lie groups. The complete optimal syntheses are computed.Comment: 29 pages, 6 figure

Extragalactic Globular Clusters in the Near Infrared: IV. Quantifying the Age Structure using Monte-Carlo Simulations

In previous papers of the series we used a combination of optical and near-infrared colours to derive constraints on the relative age structure in globular cluster systems. Here, we present the details, strength and limitations of our method based on Monte-Carlo simulations of colour-colour diagrams and cumulative age distributions. The simulations are based on general informations about the globular cluster systems (e.g. colour-ranges, the number ratios between sub-populations) and the different single stellar population models (SSP's) which are used to derive relative ages. For both the modeled systems and the observed globular cluster systems we derive the cumulative age distribution and introduce two parameters to define it, the so-called 50 % age and the result of the reduced $\chi$$^2$test of the comparison between models and observations. The method was tested successfully on several systems and allowed to reveal significant intermediate age populations in two of them.Comment: 14 pages, 20 figures, accepted for publication in A&

Stellar Content from high resolution galactic spectra via Maximum A Posteriori

This paper describes STECMAP (STEllar Content via Maximum A Posteriori), a flexible, non-parametric inversion method for the interpretation of the integrated light spectra of galaxies, based on synthetic spectra of single stellar populations (SSPs). We focus on the recovery of a galaxy's star formation history and stellar age-metallicity relation. We use the high resolution SSPs produced by PEGASE-HR to quantify the informational content of the wavelength range 4000 - 6800 Angstroms. A detailed investigation of the properties of the corresponding simplified linear problem is performed using singular value decomposition. It turns out to be a powerful tool for explaining and predicting the behaviour of the inversion. We provide means of quantifying the fundamental limitations of the problem considering the intrinsic properties of the SSPs in the spectral range of interest, as well as the noise in these models and in the data. We performed a systematic simulation campaign and found that, when the time elapsed between two bursts of star formation is larger than 0.8 dex, the properties of each episode can be constrained with a precision of 0.04 dex in age and 0.02 dex in metallicity from high quality data (R=10 000, signal-to-noise ratio SNR=100 per pixel), not taking model errors into account. The described methods and error estimates will be useful in the design and in the analysis of extragalactic spectroscopic surveys.Comment: 31 pages, 23 figures, accepted for publication in MNRA

Near Infrared spectroscopy of post-starburst galaxies: a limited impact of TP-AGB stars on galaxy SEDs

We present VLT-ISAAC NIR spectro-photometric observations of 16 post-starburst (PSB) galaxies aimed at constraining the debated influence of TP-AGB stars on the SED of galaxies with stellar ages of 0.5-2 Gyr, critical for high-redshift studies. PSB galaxies have negligible on-going star formation and a SED dominated by the stars formed in a recent (<2 Gyr) burst. By spectroscopically selecting PSB galaxies with mean luminosity-weighted ages between 0.5 and 1.5 Gyr and a broad range of metallicities, we explore the parameter space around the peak of the relative energy output of TP-AGB stars. Crucially, we target galaxies at z~0.2, so that two main spectral features of TP-AGB stars (C-molecule band-head drops at 1.41 and 1.77mum), which are heavily absorbed by our atmosphere for targets at z~0, move inside the H and K atmospheric windows and can be constrained for the first time to high accuracy. Our findings provide key constraints to stellar population synthesis models: i) The NIR regions around 1.41 and 1.77mum (rest-frame) are featureless for all galaxies in our sample over the whole range of relevant ages and metallicities at variance with the Maraston (2005) TP-AGB heavy models, which exhibit marked drops there; ii) No flux boosting is observed in the NIR. The optical-NIR SEDs of most of our PSB galaxies can be consistently reproduced with Bruzual & Charlot (2003) models, using either simple stellar populations of corresponding light-weighted ages and metallicities, or a more realistic burst plus an old population containing <~60% of the total stellar mass. In contrast, all combinations of this kind based on the Maraston (2005) models are unable to simultaneously reproduce the smoothness of the NIR spectra and the relatively blue optical-NIR colours in the observations. The data collected in this study appear to disfavour TP-AGB heavy models with respect to TP-AGB light ones.Comment: MNRAS accepted. 21 pages, 11 figures. New version improves mainly on clarity of figures and discussion of burst fraction/SF

The role of minor mergers in the recent star formation history of early-type galaxies

We demonstrate that the large scatter in the ultra-violet (UV) colours of intermediate-mass early-type galaxies in the local Universe and the inferred low-level recent star formation in these objects can be reproduced by minor mergers in the standard LCDM cosmology. Numerical simulations of mergers with mass ratios less than or equal to 1:4, with reasonable assumptions for the ages, metallicities and dust properties of the merger progenitors, produce good agreement to the observed UV colours of the early-type population, if the infalling satellites are assumed to have (cold) gas fractions greater than 20%. Early-types that satisfy (NUV-r) < 3.8 are likely to have experienced mergers with mass ratios between 1:4 and 1:6 within the last ~1.5 Gyrs, while those that satisfy 3.8<(NUV-r)<5.5 are consistent with either recent mergers with mass ratios < 1:6 or mergers with higher mass ratios that occurred more than ~1.5 Gyrs in the past. We demonstrate that the early-type colour-magnitude relations and colour distributions in both the UV and optical spectral ranges are consistent with the expected frequency of minor merging activity in the standard LCDM cosmology at low redshift. We present a strong plausibility argument for minor mergers to be the principal mechanism behind the large UV scatter and associated low-level recent star formation observed in early-type galaxies in the nearby Universe.Comment: MNRAS in pres

The star formation histories of galaxies in the Sloan Digital Sky Survey

We present the results of a MOPED analysis of ~3 x 10^5 galaxy spectra from the Sloan Digital Sky Survey Data Release Three (SDSS DR3), with a number of improvements in data, modelling and analysis compared with our previous analysis of DR1. The improvements include: modelling the galaxies with theoretical models at a higher spectral resolution of 3\AA; better calibrated data; an extended list of excluded emission lines, and a wider range of dust models. We present new estimates of the cosmic star formation rate, the evolution of stellar mass density and the stellar mass function from the fossil record. In contrast to our earlier work the results show no conclusive peak in the star formation rate out to a redshift around 2 but continue to show conclusive evidence for `downsizing' in the SDSS fossil record. The star formation history is now in good agreement with more traditional instantaneous measures. The galaxy stellar mass function is determined over five decades of mass, and an updated estimate of the current stellar mass density is presented. We also investigate the systematic effects of changes in the stellar population modelling, the spectral resolution, dust modelling, sky lines, spectral resolution and the change of data set. We find that the main changes in the results are due to the improvements in the calibration of the SDSS data, changes in the initial mass function and the theoretical models used.Comment: replaced to match accepted version in MNRA

Differential stellar population models: how to reliably measure [Fe/H] and [alpha/Fe] in galaxies

We present differential stellar population models, which allow improved determinations of the ages, iron and alpha-element abundances of old stellar populations from spectral fitting. These new models are calibrated at solar abundances using the predictions from classical, semi-empirical stellar population models. We then use the predictive power of fully synthetic models to compute predictions for different [Fe/H] and [alpha/Fe]. We show that these new differential models provide remarkably accurate fits to the integrated optical spectra of the bulge globular clusters NGC6528 and NGC6553, and that the inferred [Fe/H] and [alpha/Fe] agree with values derived elsewhere from stellar photometry and spectroscopy. The analysis of a small sample of SDSS early-type galaxies further confirms that our alpha-enhanced models provide a better fit to the spectra of massive ellipticals than the solar-scaled ones. Our approach opens new opportunities for precision measurements of abundance ratios in galaxies.Comment: 5 pages, 5 figures, MNRAS in pres

The propagation of uncertainties in stellar population synthesis modeling I: The relevance of uncertain aspects of stellar evolution and the IMF to the derived physical properties of galaxies

The stellar masses, mean ages, metallicities, and star formation histories of galaxies are now commonly estimated via stellar population synthesis (SPS) techniques. SPS relies on stellar evolution calculations from the main sequence to stellar death, stellar spectral libraries, phenomenological dust models, and stellar initial mass functions (IMFs). The present work is the first in a series that explores the impact of uncertainties in key phases of stellar evolution and the IMF on the derived physical properties of galaxies and the expected luminosity evolution for a passively evolving set of stars. A Monte-Carlo Markov-Chain approach is taken to fit near-UV through near-IR photometry of a representative sample of low- and high-redshift galaxies with this new SPS model. Significant results include the following: 1) including uncertainties in stellar evolution, stellar masses at z~0 carry errors of ~0.3 dex at 95% CL with little dependence on luminosity or color, while at z~2, the masses of bright red galaxies are uncertain at the ~0.6 dex level; 2) either current stellar evolution models, current observational stellar libraries, or both, do not adequately characterize the metallicity-dependence of the thermally-pulsating asymptotic giant branch phase; 3) conservative estimates on the uncertainty of the slope of the IMF in the solar neighborhood imply that luminosity evolution per unit redshift is uncertain at the ~0.4 mag level in the K-band, which is a substantial source of uncertainty for interpreting the evolution of galaxy populations across time; 4) The more plausible assumption of a distribution of stellar metallicities, rather than a fixed value as is usually assumed, can have significant effects on the interpretation of colors blueward of the V-band. (ABRIDGED)Comment: 21 pages, 17 figures, ApJ in pres

Probing recent star formation with absorption-line strengths in hierarchical models and observations

Stellar population parameters derived from spectral line-strengths provide a powerful probe of galaxy properties and formation histories. We implement the machinery for extracting single-stellar-population-equivalent stellar population parameters from synthetic spectra generated by a hierarchical galaxy formation model. We find that the SSP-equivalent age is related to the light-weighted age in a complicated fashion that reflects the influence of recently-formed stars and is poorly correlated with the mass-weighted age. The tendency for SSP-equivalent ages to be biased young means that archaeological downsizing overstates the mass-weighted downsizing in age with mass. We find that the SSP-equivalent metallicity closely tracks the mass- and light-weighted metallicities, so that observed mass--metallicity relations for old galaxies closely reflect the underlying trends. We construct mock catalogues of early-type galaxies in a Coma cluster-sized halo and compare them directly to observations of early-type galaxies in the Coma cluster. The similarity of the SSP-equivalent ages in the observational samples and the mock catalogues gives us confidence that the star-formation quenching implemented in the hierarchical galaxy formation model produces roughly the correct amount of recent star formation. The SSP-equivalent metallicities are however too low and have the wrong slope as a function of velocity dispersion, and the SSP-equivalent ages of the model galaxies may have an incorrect slope as a function of velocity dispersion. (Abridged)Comment: Accepted for publication in Monthly Notices of the Royal Astronomical Society. 17 page

The stellar evolution of Luminous Red Galaxies, and its dependence on colour, redshift, luminosity and modelling

We present a series of colour evolution models for Luminous Red Galaxies (LRGs) in the 7th spectroscopic data release of the Sloan Digital Sky Survey (SDSS), computed using the full-spectrum fitting code VESPA on high signal-to-noise stacked spectra. The colour-evolution models are computed as a function of colour, luminosity and redshift, and we do not a-priori assume that LRGs constitute a uniform population of galaxies in terms of stellar evolution. By computing star-formation histories from the fossil record, the measured stellar evolution of the galaxies is decoupled from the survey's selection function, which also evolves with redshift. We present these evolutionary models computed using three different sets of Stellar Population Synthesis (SPS) codes. We show that the traditional fiducial model of purely passive stellar evolution of LRGs is broadly correct, but it is not sufficient to explain the full spectral signature. We also find that higher-order corrections to this model are dependent on the SPS used, particularly when calculating the amount of recent star formation. The amount of young stars can be non-negligible in some cases, and has important implications for the interpretation of the number density of LRGs within the selection box as a function of redshift. Dust extinction, however, is more robust to the SPS modelling: extinction increases with decreasing luminosity, increasing redshift, and increasing r-i colour. We are making the colour evolution tracks publicly available at http://www.icg.port.ac.uk/~tojeiror/lrg_evolution/.Comment: 29 pages, 34 figures, re-submitted to MNRAS after addressing the referee's repor