Integer Polynomial Optimization in Fixed Dimension

We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an integer polynomial over the lattice points of a convex polytope, we show an algorithm to compute lower and upper bounds for the optimal value. For polynomials that are non-negative over the polytope, these sequences of bounds lead to a fully polynomial-time approximation scheme for the optimization problem.Comment: In this revised version we include a stronger complexity bound on our algorithm. Our algorithm is in fact an FPTAS (fully polynomial-time approximation scheme) to maximize a non-negative integer polynomial over the lattice points of a polytop

A Spitzer view of protoplanetary disks in the gamma Velorum cluster

We present new Spitzer Space Telescope observations of stars in the young ~5 Myr gamma Velorum stellar cluster. Combining optical and 2MASS photometry, we have selected 579 stars as candidate members of the cluster. With the addition of the Spitzer mid-infrared data, we have identified 5 debris disks around A-type stars, and 5-6 debris disks around solar-type stars, indicating that the strong radiation field in the cluster does not completely suppress the production of planetesimals in the disks of cluster members. However, we find some evidence that the frequency of circumstellar primordial disks is lower, and the IR flux excesses are smaller than for disks around stellar populations with similar ages. This could be evidence for a relatively fast dissipation of circumstellar dust by the strong radiation field from the highest mass star(s) in the cluster. Another possibility is that gamma Velorum stellar cluster is slightly older than reported ages and the the low frequency of primordial disks reflects the fast disk dissipation observed at ~5 Myr.Comment: Accepted for publication in the Astrophysical Journal: 32 pages; 11 Figure

Quantifying Resonant Structure in NGC 6946 from Two-dimensional Kinematics

We study the two-dimensional kinematics of the H-alpha-emitting gas in the nearby barred Scd galaxy, NGC 6946, in order to determine the pattern speed of the primary m=2 perturbation mode. The pattern speed is a crucial parameter for constraining the internal dynamics, estimating the impact velocities of the gravitational perturbation at the resonance radii, and to set up an evolutionary scenario for NGC 6946. Our data allows us to derive the best fitting kinematic position angle and the geometry of the underlying gaseous disk, which we use to derive the pattern speed using the Tremaine-Weinberg method. We find a main pattern speed Omega_p=22 km/s/kpc, but our data clearly reveal the presence of an additional pattern speed Omega_p=47 km/s/kpc in a zone within 1.25 kpc of the nucleus. Using the epicyclic approximation, we deduce the location of the resonance radii and confirm that inside the outer Inner Lindblad Resonance radius of the main oval, a primary bar has formed rotating at more than twice the outer pattern speed. We further confirm that a nuclear bar has formed inside the Inner Lindblad Resonance radius of the primary bar, coinciding with the inner Inner Lindblad Resonance radius of the large-scale m=2 mode oval.Comment: Accepted for publication in ApJ Letter

Testing Mass Determinations of Supermassive Black Holes via Stellar Kinematics

We investigate the accuracy of mass determinations M_BH of supermassive black holes in galaxies using dynamical models of the stellar kinematics. We compare 10 of our M_BH measurements, using integral-field OASIS kinematics, to published values. For a sample of 25 galaxies we confront our new M_BH derived using two modeling methods on the same OASIS data.Comment: 4 pages, 4 figures, LaTeX. To appear in "Hunting for the Dark: The Hidden Side of Galaxy Formation", Malta, 19-23 Oct. 2009, eds. V.P. Debattista and C.C. Popescu, AIP Conf. Ser., in pres

Supermassive black holes from OASIS and SAURON integral-field kinematics

Supermassive black holes are a key element in our understanding of how galaxies form. Most of the progress in this very active field of research is based on just ~30 determinations of black hole mass, accumulated over the past decade. We illustrate how integral-field spectroscopy, and in particular our OASIS modeling effort, can help improve the current situation.Comment: 4 pages, 2 figures, LaTeX. To appear in the proceedings of IAU Symposium 245 "Formation and Evolution of Galaxy Bulges", M. Bureau, E. Athanassoula, and B. Barbuy, ed

Fast and Slow Rotators: The build-up of the Red Sequence

Using the unique dataset obtained within the course of the SAURON project, a radically new view of the structure, dynamics and stellar populations of early-type galaxies has emerged. We show that galaxies come in two broad flavours (slow and fast rotators), depending on whether or not they exhibit clear large-scale rotation, as indicated via a robust measure of the specific angular momentum of baryons. This property is also linked with other physical characteristics of early-type galaxies, such as: the presence of dynamically decoupled cores, orbital structure and anisotropy, stellar populations and dark matter content. I here report on the observed link between this baryonic angular momentum and a mass sequence, and how this uniquely relates to the building of the red sequence via dissipative/dissipationless mergers and secular evolution.Comment: 4 pages, 1 figure. To appear in the Proceedings of IAU Symposium 245 "Formation and Evolution of Galaxy Bulges", Eds M. Bureau, E. Athanassoula, and B. Barbu

IMF - metallicity: a tight local relation revealed by the CALIFA survey

Variations in the stellar initial mass function (IMF) have been invoked to explain the spectroscopic and dynamical properties of early-type galaxies. However, no observations have yet been able to disentangle the physical driver. We analyse here a sample of 24 early-type galaxies drawn from the CALIFA survey, deriving in a homogeneous way their stellar population and kinematic properties. We find that the local IMF is tightly related to the local metallicity, becoming more bottom-heavy towards metal-rich populations. Our result, combined with the galaxy mass-metallicity relation, naturally explains previous claims of a galaxy mass-IMF relation, derived from non-IFU spectra. If we assume that - within the star formation environment of early-type galaxies - metallicity is the main driver of IMF variations, a significant revision of the interpretation of galaxy evolution observables is necessary.Comment: Accepted for publication in ApJL. 6 pages, 4 figure

The stellar mass assembly of galaxies from z=0 to z=4. Analysis of a sample selected in the rest-frame near-infrared with Spitzer

Using a sample of ~28,000 sources selected at 3.6-4.5 microns with Spitzer observations of the HDF-N, the CDF-S, and the Lockman Hole (surveyed area: ~664 arcmin^2), we study the evolution of the stellar mass content of the Universe at 0<z<4. We calculate stellar masses and photometric redshifts, based on ~2,000 templates built with stellar and dust emission models fitting the UV-to-MIR SEDs of galaxies with spectroscopic redshifts. We estimate stellar mass functions for different redshift intervals. We find that 50% of the local stellar mass density was assembled at 0<z<1 (average SFR:0.048 M_sun/yr/Mpc^3), and at least another 40% at 1<z<4 (average SFR: 0.074 M_sun/yr/Mpc^3). Our results confirm and quantify the ``downsizing'' scenario of galaxy formation. The most massive galaxies (M>10^12.0 M_sun) assembled the bulk of their stellar content rapidly (in 1-2 Gyr) beyond z~3 in very intense star formation events (producing high specific SFRs). Galaxies with 10^11.5<M/M_sun<10^12.0 assembled half of their stellar mass before z~1.5, and more than 90% of their mass was already in place at z~0.6. Galaxies with M<10^11.5 M_sun evolved more slowly (presenting smaller specific SFRs), assembling half of their stellar mass below z~1. About 40% of the local stellar mass density of 10^9.0<M/M_sun<10^11.0 galaxies was assembled below z~0.4, most probably through accretion of small satellites producing little star formation. The cosmic stellar mass density at z>2.5 is dominated by optically faint (R>25) red galaxies (Distant Red Galaxies or BzK sources) which account for ~30% of the global population of galaxies, but contribute at least 60% to the cosmic stellar mass density. Bluer galaxies (e.g., Lyman Break Galaxies) are more numerous but less massive, contributing less than 50% to the global stellar mass density at high redshift.Comment: Published in ApJ. 38 pages, 10 figures, 5 tables, 2 appendices. Some changes to match the final published versio