Weak homology of elliptical galaxies

We start by studying a small set of objects characterized by photometric profiles that have been pointed out to deviate significantly from the standard R^{1/4} law. For these objects we confirm that a generic R^{1/n} law, with n a free parameter, can provide superior fits (the best-fit value of n can be lower than 2.5 or higher than 10), better than those that can be obtained by a pure R^{1/4} law, by an R^{1/4}+exponential model, and by other dynamically justified self--consistent models. Therefore, strictly speaking, elliptical galaxies should not be considered homologous dynamical systems. Still, a case for "weak homology", useful for the interpretation of the Fundamental Plane of elliptical galaxies, could be made if the best-fit parameter n, as often reported, correlates with galaxy luminosity L, provided the underlying dynamical structure also follows a systematic trend with luminosity. We demonstrate that this statement may be true even in the presence of significant scatter in the correlation n(L). Preliminary indications provided by a set of "data points" associated with a sample of 14 galaxies suggest that neither the strict homology nor the constant stellar mass--to--light solution are a satisfactory explanation of the observed Fundamental Plane (abridged).Comment: 34 pages, 11 figures, accepted by Astronomy and Astrophysic

The Evolution of Early-Type Galaxies in Distant Clusters III.: M/L_V Ratios in the z=0.33 Cluster CL1358+62

Keck spectroscopy and Hubble Space Telescope WFPC2 imaging over a 1.5x1.5 Mpc field of CL1358+62 at z=0.33 are used to study the Fundamental Plane of galaxies based on a new, large sample of 53 galaxies. First, we have constructed the Fundamental Plane for the 30 E and S0 galaxies and find that it has the following shape: r_e = sigma**(1.31+-0.13) * _e**(-0.86+-0.10), similar to that found locally. The 1-sigma intrinsic scatter about this plane is 14% in M/L(V), comparable to that observed in Coma. We conclude that these E and S0 galaxies are structurally mature and homogeneous, like those observed in nearby clusters. The M/L(V) ratios of these early-type galaxies are offset from the Coma Fundamental Plane by delta log M/L(V) = -0.13+- 0.03 (q0=0.1), indicative of mild luminosity evolution. This evolution suggests a formation epoch for the stars of z > 1. We have also analyzed the M/L(V) ratios of galaxies of type S0/a and later. These early-type spirals follow a different plane from the E and S0 galaxies, with a scatter that is twice as large as the scatter for the E/S0s. The difference in the tilt between the plane of the spirals and the plane of the E/S0s is shown to be due to a systematic correlation of velocity dispersion with residual from the plane of the early-type galaxies. These residuals also correlate with the residuals from the Color-Magnitude relation. Thus for spirals in clusters, we see a systematic variation in the luminosity-weighted mean properties of the stellar populations with central velocity dispersion. If this is a relative age trend, then luminosity-weighted age is positively correlated with dispersion. [abridged version]Comment: 18 pages, 8 figures; revised version, accepted by ApJ on 13 August 199

Toward Equations of Galactic Structure

We find that all classes of galaxies, ranging from disks to spheroids and from dwarf spheroidals to brightest cluster galaxies, lie on a two dimensional surface within the space defined by the logarithms of the half-light radius, r_e, mean surface brightness within r_e, I_e, and internal velocity, V^2 = (1/2)v_c^2 + sigma^2, where v_c is the rotational velocity and sigma is the velocity dispersion. If these quantities are expressed in terms of kpc, L_solar/pc^2, and km/s, then log r_e - log V^2 + log I_e + log Upsilon_e + 0.8 = 0, where we provide a fitting function for Upsilon_e, the mass-to-light ratio within r_e in units of M_solar/L_solar, that depends only on V and I_e. The scatter about this surface for our heterogeneous sample of 1925 galaxies is small (< 0.1 dex) and could be as low as ~ 0.05 dex, or 10%. This small scatter has three possible implications for how gross galactic structure is affected by internal factors, such as stellar orbital structure, and by external factors, such as environment. These factors either 1) play no role beyond generating some of the observed scatter, 2) move galaxies along the surface, or 3) balance each other to maintain this surface as the locus of galactic structure equilibria. We cast the behavior of Upsilon_e in terms of the fraction of baryons converted to stars, eta, and the concentration of those stars within the dark matter halo, xi = R_{200}/r_e. We derive eta = 1.9 x 10^{-5} (L/L^*) Upsilon_* V^{-3} and xi = 1.4 V/r_e. Finally, we present and discuss the distributions of eta and xi for the full range of galaxies. For systems with internal velocities comparable to that of the Milky Way (149 < V < 163 km/s), eta = 0.14 +- 0.05, and xi is, on average, ~ 5 times greater for spheroids than for disks. (Abridged)Comment: submitted to Ap

Universal IMF vs dark halo response in early-type galaxies: breaking the degeneracy with the fundamental plane

We use the relations between aperture stellar velocity dispersion (\sigma_ap), stellar mass (M_sps), and galaxy size (R_e) for a sample of \sim 150,000 early-type galaxies from SDSS/DR7 to place constraints on the stellar initial mass function (IMF) and dark halo response to galaxy formation. We build LCDM based mass models that reproduce, by construction, the relations between galaxy size, light concentration and stellar mass, and use the spherical Jeans equations to predict \sigma_ap. Given our model assumptions (including those in the stellar population synthesis models), we find that reproducing the median \sigma_ap vs M_sps relation is not possible with {\it both} a universal IMF and a universal dark halo response. Significant departures from a universal IMF and/or dark halo response are required, but there is a degeneracy between these two solutions. We show that this degeneracy can be broken using the strength of the correlation between residuals of the velocity-mass (\Delta log \sigma_ap) and size-mass (\Delta log R_e) relations. The slope of this correlation, d_vr \equiv \Delta log \sigma_ap/\Delta log R_e, varies systematically with galaxy mass from d_vr \simeq -0.45 at M_sps \sim 10^{10}M_sun, to d_vr \simeq -0.15 at M_sps \sim 10^{11.6} M_sun. The virial fundamental plane (FP) has d_vr=-1/2, and thus we find the tilt of the observed FP is mass dependent. Reproducing this tilt requires {\it both} a non-universal IMF and a non-universal halo response. Our best model has mass-follows-light at low masses (Msps < 10^{11.2}M_sun) and unmodified NFW haloes at M_sps \sim 10^{11.5} M_sun. The stellar masses imply a mass dependent IMF which is "lighter" than Salpeter at low masses and "heavier" than Salpeter at high masses.Comment: 19 pages, 16 figures, accepted to MNRAS. More extensive discussion, 4 new figures, conclusions unchange

Exploiting Homology Information in Nontemplate Based Prediction of Protein Structures

In this paper we describe a novel strategy for exploring the conformational space of proteins and show that this leads to better models for proteins the structure of which is not amenable to template based methods. Our strategy is based on the assumption that the energy global minimum of homologous proteins must correspond to similar conformations, while the precise profiles of their energy landscape, and consequently the positions of the local minima, are likely to be different. In line with this hypothesis, we apply a replica exchange Monte Carlo simulation protocol that, rather than using different parameters for each parallel simulation, uses the sequences of homologous proteins. We show that our results are competitive with respect to alternative methods, including those producing the best model for each of the analyzed targets in the CASP10 (10th Critical Assessment of techniques for protein Structure Prediction) experiment free modeling category

Sliced Wasserstein Kernel for Persistence Diagrams

Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they are routinely used to describe topological properties of complicated shapes. PDs enjoy strong stability properties and have proven their utility in various learning contexts. They do not, however, live in a space naturally endowed with a Hilbert structure and are usually compared with specific distances, such as the bottleneck distance. To incorporate PDs in a learning pipeline, several kernels have been proposed for PDs with a strong emphasis on the stability of the RKHS distance w.r.t. perturbations of the PDs. In this article, we use the Sliced Wasserstein approximation SW of the Wasserstein distance to define a new kernel for PDs, which is not only provably stable but also provably discriminative (depending on the number of points in the PDs) w.r.t. the Wasserstein distance $d_1$ between PDs. We also demonstrate its practicality, by developing an approximation technique to reduce kernel computation time, and show that our proposal compares favorably to existing kernels for PDs on several benchmarks.Comment: Minor modification

Semi-empirical catalog of early-type galaxy-halo systems: dark matter density profiles, halo contraction and dark matter annihilation strength

With SDSS galaxy data and halo data from up-to-date N-body simulations we construct a semi-empirical catalog (SEC) of early-type systems by making a self-consistent bivariate statistical match of stellar mass (M_star) and velocity dispersion (sigma) with halo virial mass (M_vir). We then assign stellar mass profile and velocity dispersion profile parameters to each system in the SEC using their observed correlations with M_star and sigma. Simultaneously, we solve for dark matter density profile of each halo using the spherical Jeans equation. The resulting dark matter density profiles deviate in general from the dissipationless profile of NFW or Einasto and their mean inner density slope and concentration vary systematically with M_vir. Statistical tests of the distribution of profiles at fixed M_vir rule out the null hypothesis that it follows the distribution predicted by N-body simulations for M_vir ~< 10^{13.5-14.5} M_solar. These dark matter profiles imply that dark matter density is, on average, enhanced significantly in the inner region of halos with M_vir ~< 10^{13.5-14.5} M_solar supporting halo contraction. The main characteristics of halo contraction are: (1) the mean dark matter density within the effective radius has increased by a factor varying systematically up to ~ 3-4 at M_vir = 10^{12} M_solar, and (2) the inner density slope has a mean of ~ 1.3 with rho(r) ~ r^{-alpha} and a halo-to-halo rms scatter of rms(alpha) ~ 0.4-0.5 for 10^{12} M_solar ~< M_vir ~< 10^{13-14} M_solar steeper than the NFW profile (alpha=1). Based on our results we predict that halos of nearby elliptical and lenticular galaxies can, in principle, be promising targets for gamma-ray emission from dark matter annihilation.Comment: 43 pages, 20 figures, JCAP, revised and accepted versio