The sigma - L correlation in Nearby Early-Type Galaxies

Early-type galaxy velocity dispersions and luminosities are correlated. The correlation estimated in local samples (< 100 Mpc) differs from that measured more recently in the SDSS. This is true even when systematics in the SDSS photometric and spectroscopic parameters have been accounted-for. We show that this is also true for the ENEAR sample if galaxy luminosities are estimated using distances which have been corrected for peculiar motions. We then show that, because the estimate of the `true' distance is derived from a correlation with velocity dispersion, in this case the D_n-sigma relation, using it in the sigma-L relation leads to an artificially tight relation with a biased slope. Making no correction for peculiar velocities results in a sigma-L relation which is very similar to that of the SDSS, although with larger scatter. We also measure the sigma-L correlation in a mock ENEAR catalog, in which the underlying galaxy sample has the same sigma-L correlation as seen in the SDSS. The mock catalog produces the same D_n-sigma relation as the data, the same biased slope when D_n-sigma distances are used to estimate luminosities, and good agreement with the input sigma-L relation when redshift is used as the distance indicator. This provides further evidence that the true sigma-L relation of ENEAR galaxies is indeed very similar to that of SDSS early-types. Our results suggest that local sigma-L relations which are based on Fundamental Plane distances should also be re-evaluated. Our findings also have important implications for black hole demographics; the best direct estimates of the masses of supermassive black holes come from local galaxies, so estimates of the black hole mass function are more safely made by working with the Mbh-sigma correlation than with Mbh-L.Comment: 9 pages, 9 figures. Accepted by AJ. A new appendix describes systematics effects we found in the SDSS velocity dispersion measurements (sigmas < 150 km/s are biased towards larger values; this bias was not present in the Bernardi et al. 2003 sample) and luminosity measurement

Redshift-distance Survey of Early-type Galaxies: The D_n-sigma Relation

In this paper R-band photometric and velocity dispersion measurements for a sample of 452 elliptical and S0 galaxies in 28 clusters are used to construct a template D_n-sigma relation. This template relation is constructed by combining the data from the 28 clusters, under the assumption that galaxies in different clusters have similar properties. The photometric and spectroscopic data used consist of new as well as published measurements, converted to a common system, as presented in a accompanying paper. The resulting direct relation, corrected for incompleteness bias, is log{D_n} =1.203 log{sigma} + 1.406; the zero-point has been defined by requiring distant clusters to be at rest relative to the CMB. This zero-point is consistent with the value obtained by using the distance to Virgo as determined by the Cepheid period-luminosity relation. This new D_n-sigma relation leads to a peculiar velocity of -72 (\pm 189) km/s for the Coma cluster. The scatter in the distance relation corresponds to a distance error of about 20%, comparable to the values obtained for the Fundamental Plane relation. Correlations between the scatter and residuals of the D_n-sigma relation with other parameters that characterize the cluster and/or the galaxy stellar population are also analyzed. The direct and inverse relations presented here have been used in recent studies of the peculiar velocity field mapped by the ENEAR all-sky sample.Comment: 46 pages, 20 figures, and 7 tables. To appear in AJ, vol. 123, no. 5, May 200

Redshift-Distance Survey of Early-type Galaxies. I. Sample Selection, Properties and Completeness

This is the first in a series of papers describing the recently completed all-sky redshift-distance survey of nearby early-type galaxies (ENEAR) carried out for peculiar velocity analysis. The sample is divided into two parts and consists of 1607 elliptical and lenticular galaxies with cz < 7000 km/s and with blue magnitudes brighter than m_B=14.5 (ENEARm), and of galaxies in clusters (ENEARc). Galaxy distances based on the Dn-sigma and Fundamental Plane (FP) relations are now available for 1359 and 1107 ENEARm galaxies, respectively, with roughly 80% based on new data gathered by our group. The Dn-sigma and FP template distance relations are derived by combining 569 and 431 galaxies in 28 clusters, respectively, of which about 60% are based on our new measurements. The ENEARm redshift-distance survey extends the earlier work of the 7S and the recent Tully-Fisher surveys sampling a comparable volume. In subsequent papers of this series we intend to use the ENEAR sample by itself or in combination with the SFI Tully-Fisher survey to analyze the properties of the local peculiar velocity field and to test how sensitive the results are to different sampling and to the distance indicators. We also anticipate that the homogeneous database assembled will be used for a variety of other applications and serve as a benchmark for similar studies at high-redshift.Comment: 43 pages, 15 figures, submitted to the Astronomical Journa

The Star Formation Epoch of the Most Massive Early-Type Galaxies

We present new Keck spectroscopy of early-type galaxies in three galaxy clusters at z~0.5. We focus on the fundamental plane (FP) relation, and combine the kinematics with structural parameters determined from HST images. The galaxies obey clear FP relations, which are offset from the FP of the nearby Coma cluster due to passive evolution of the stellar populations. The z~0.5 data are combined with published data for 11 additional clusters at 0.18<z<1.28, to determine the evolution of the mean M/L(B) ratio of cluster galaxies with masses M>10^11 M_sun, as implied by the FP. We find dlog(M/L(B))/dz = -0.555+-0.042, stronger evolution than was previously inferred from smaller samples. The observed evolution depends on the luminosity-weighted mean age of the stars in the galaxies, the initial mass function (IMF), selection effects due to progenitor bias, and other parameters. Assuming a normal IMF but allowing for various other sources of uncertainty we find z* = 2.01+-0.20 for the luminosity-weighted mean star formation epoch. The main uncertainty is the slope of the IMF in the range 1-2 Solar masses: we find z* = 4.0 for a top-heavy IMF with slope x=0. The M/L(B) ratios of the cluster galaxies are compared to those of recently published samples of field early-type galaxies at 0.32<z<1.14. Assuming that progenitor bias and the IMF do not depend on environment we find that the present-day age of stars in massive field galaxies is 4.1 +- 2.0 % (~0.4 Gyr) less than that of stars in massive cluster galaxies, consistent with most, but not all, previous studies of local and distant early-type galaxies. This relatively small age difference is surprising in the context of expectations from ``standard'' hierarchical galaxy formation models. [ABRIDGED]Comment: Accepted for publication in ApJ. Minor corrections to match published versio

Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives

We consider the problem of finding commuting self-adjoint extensions of the partial derivatives {(1/i)(\partial/\partial x_j):j=1,...,d} with domain C_c^\infty(\Omega) where the self-adjointness is defined relative to L^2(\Omega), and \Omega is a given open subset of R^d. The measure on \Omega is Lebesgue measure on R^d restricted to \Omega. The problem originates with I.E. Segal and B. Fuglede, and is difficult in general. In this paper, we provide a representation-theoretic answer in the special case when \Omega=I\times\Omega_2 and I is an open interval. We then apply the results to the case when \Omega is a d-cube, I^d, and we describe possible subsets \Lambda of R^d such that {e^(i2\pi\lambda \dot x) restricted to I^d:\lambda\in\Lambda} is an orthonormal basis in L^2(I^d).Comment: LaTeX2e amsart class, 18 pages, 2 figures; PACS numbers 02.20.Km, 02.30.Nw, 02.30.Tb, 02.60.-x, 03.65.-w, 03.65.Bz, 03.65.Db, 61.12.Bt, 61.44.B

The Sloan-Lens ACS Survey II: stellar populations and internal structure of early-type lens galaxies

We derive Fundamental Plane parameters of 15 early-type lens galaxies identified by the Sloan Lens ACS (SLACS) Survey. The size of the sample allows us to investigate for the first time the distribution of lens galaxies in the FP space. After correcting for evolution, we find that lens galaxies occupy a subset of the local FP. The edge-on projection (approximately M vs M/L) is indistinguishable from that of normal early-type galaxies. However -- within the fundamental plane -- the lens galaxies appear to concentrate at the edge of the region populated by normal early-type galaxies. We show that this is a result of our selection procedure (approximately velocity dispersion sigma>240km/s). We conclude that SLACS lenses are a fair sample of high velocity dispersion early-type galaxies. By comparing the central stellar velocity dispersion that of the best fit lens model, we find == =1.01+-0.02 with 0.065 rms scatter. We conclude that within the Einstein radii the SLACS lenses are very well approximated by isothermal ellipsoids, requiring a fine tuning of the stellar and dark matter distribution (bulge-halo ``conspiracy''). Interpreting the offset from the local FP in terms of evolution of the stellar mass-to-light ratio, we find for the SLACS lenses d log M/L_B/dz=-0.69+-0.08 (rms 0.11) consistent with the rate found for field early-type galaxies and with a scenario where most of the stars were formed at high redshift (>2) with secondary episodes of star formation providing less than ~10% of the stellar mass below z=1. We discuss star formation history and structural homogeneity in the context of formation mechanisms such as collisionless (``dry'') mergers. [Abridged]Comment: 2006, ApJ, 604, 622; 13 pages, 7 figures, 2 tables. Replaced Table 2, since the previous version was incorrectly sorted. Updated references. No changes in plots or content. More info available at SLACS website www.slacs.or

The Possible z=0.83 Precursors of z=0 M* Early-type Cluster Galaxies

We examine the distribution of stellar masses of galaxies in MS 1054-03 and RX J0152.7-1357, two X-ray selected clusters of galaxies at z=0.83. Our stellar mass estimates, from spectral energy distribution fitting, reproduce the dynamical masses as measured from velocity dispersions and half-light radii with a scatter of 0.2 dex in the mass for early-type galaxies. When we restrict our sample of members to high stellar masses, > 1e11.1 Msun (M* in the Schechter mass function for cluster galaxies), we find that the fraction of early-type galaxies is 79 +/- 6% at z=0.83 and 87 +/- 6% at z=0.023 for the Coma cluster, consistent with no evolution. Previous work with luminosity-selected samples finds that the early-type fraction in rich clusters declines from =~80% at z=0 to =~60% at z=0.8. The observed evolution in the early-type fraction from luminosity-selected samples must predominately occur among sub-M* galaxies. As M* for field and group galaxies, especially late-types, is below M* for clusters galaxies, infall could explain most of the recent early-type fraction growth. Future surveys could determine the morphological distributions of lower mass systems which will confirm or refute this explanation.Comment: 5 pages in emulate ApJ format with three color figures. Accepted for publication in ApJ Letters, v642n2. Updated to correct grammatical and typographic errors found by the journa

On The Linearity of The Black Hole - Bulge Mass Relation in Active and in Nearby Galaxies

Analysis of PG quasar observations suggests a nonlinear relation between the black hole mass, M_BH, and the bulge mass, M_bulge, although a linear relation, as proposed for nearby galaxies, cannot be ruled out. New M_BH values for nearby galaxies from Gebhardt et al., and L_bulge measurements for Seyfert 1 galaxies from Virani et al., are used here to obtain a more accurate value for the slope of the M_BH-M_bulge relation. The combined sample of 40 active and non-active galaxies suggests a significantly nonlinear relation, M_BH\propto M_bulge^{1.53\pm 0.14}. Further support for a nonlinear relation is provided by the slope of the M_BH-stellar velocity dispersion relation found recently, and by the low M_BH found in late type spiral galaxies. The mean M_BH/M_bulge ratio is therefore not a universal constant, but rather drops from ~0.5% in bright (M_V ~ -22) ellipticals, to ~0.05% in low luminosity (M_V ~ -18) bulges. Hubble Space Telescope determinations of M_BH in late type spirals, and of the bulge magnitude in narrow line Seyfert 1 galaxies (both predicted to have low M_BH), can further test the validity of the nonlinear M_BH-M_bulge relation.Comment: Accepted for publication in ApJ, 9 pages inc. 2 figure

Mass-Selection and the Evolution of the Morphology-Density Relation from z=0.8 to z=0

We examined the morphology-density relations for galaxy samples selected by luminosity and by mass in each of five massive X-ray clusters from z=0.023 to 0.83 for 674 spectroscopically-confirmed members. Rest-frame optical colors and visual morphologies were obtained primarily from Hubble Space Telescope images. Morphology-density relations (MDR) are derived in each cluster from a complete, luminosity-selected sample of 452 galaxies with a magnitude limit M_V < M^{*}_{V} + 1. The change in the early-type fraction with redshift matches previous work for massive clusters of galaxies. We performed a similar analysis, deriving MDRs for complete, mass-selected samples of 441 galaxies with a mass-limit of 10^{10.6} M_{\sun}. Our mass limit includes faint objects, the equivalent of =~1 mag below L^{*} for the red cluster galaxies, and encompasses =~70% of the stellar mass in cluster galaxies. The MDRs in the mass-selected sample at densities of Sigma > 50 galaxies Mpc^{-2} are similar to those in the luminosity-selected sample but show larger early-type fractions. However, the trend with redshift in the fraction of elliptical and S0 galaxies with masses > 10^{10.6} M_{\sun} differs significantly between the mass- and luminosity-selected samples. The clear trend seen in the early-type fraction from z=0 to z=~ 0.8 is not found in mass-selected samples. The early-type galaxy fraction changes much less, and is consistent with being constant at 92% +/- 4% at \Sigma> 500 galaxies Mpc^{-2} and 83 +/- 3% at 50 < \Sigma < 500 galaxies Mpc^{-2}. This suggests that galaxies of mass lower than > 10^{10.6} M_{\sun} play a significant role in the evolution of the early-type fraction in luminosity-selected samples. (Abstract abridged)Comment: 18 pages in emulate ApJ format, with 10 color figures, Accepted to ApJ. Version updated to reflect published version, includes new references and a correction to table