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

The Universality of the Fundamental Plane of E and S0 Galaxies. Spectroscopic data

We present here central velocity dispersion measurements for 325 early-type galaxies in eight clusters and groups of galaxies, including new observations for 212 galaxies. The clusters and groups are the A262, A1367, Coma (A1656), A2634, Cancer and Pegasus clusters, and the NGC 383 and NGC 507 groups. The new measurements were derived from medium dispersion spectra, that cover 600 A centered on the Mg Ib triplet at lambda ~ 5175. Velocity dispersions were measured using the Tonry & Davis cross-correlation method, with a typical accuracy of 6%. A detailed comparison with other data sources is made.Comment: 12 pages, 5 tables, 3 figures, to appear in AJ. Note that tables 2 and 3 are in separate files, as they should be printed in landscape forma

Near-Infrared Imaging of Early-Type Galaxies III. The Near-Infrared Fundamental Plane

Near-infrared imaging data on 251 early-type galaxies in clusters and groups are used to construct the near-infrared Fundamental Plane (FP) r_eff ~ sigma_0^1.53 _eff^-0.79. The slope of the FP therefore departs from the virial expectation of r_eff ~ sigma_0^2 _eff^-1 at all optical and near-infrared wavelengths, which could be a result of the variation of M/L along the elliptical galaxy sequence, or a systematic breakdown of homology among the family of elliptical galaxies. The slope of the near-infrared FP excludes metallicity variations as the sole cause of the slope of the FP. Age effects, dynamical deviations from a homology, or any combination of these (with or without metallicity), however, are not excluded. The scatter of both the near-infrared and optical FP are nearly identical and substantially larger than the observational uncertainties, demonstrating small but significant intrinsic cosmological scatter for the FP at all wavelengths. The lack of a correlation of the residuals of the near-infrared FP and the residuals from the Mg_2-sigma relation indicates that the thickness of these relations cannot be ascribed only to age or metallicity effects. Due to this metallicity independence, the small scatter of the near-infrared FP excludes a model in which age and metallicity effects ``conspire'' to keep the optical FP thin. All of these results suggest that the possible physical origins of the FP relations are complicated due to combined effects of variations of stellar populations and structural parameters among elliptical galaxies.Comment: to appear in The Astronomical Journal; 35 pages, including 13 Postscript figures and 1 table; uses AAS LaTeX style file

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

Near-Infrared Imaging of Early-Type Galaxies IV. The Physical Origins of the Fundamental Plane Scaling Relations

The physical origins of the Fundamental Plane (FP) scaling relations are investigated for early-type galaxies observed at optical and near-infrared wavelengths. The slope for the FP is shown to increase systematically with wavelength from the U-band through the K-band. A distance-independent construction of the observables is described which provides an accurate measurement of the change in the FP slope between any pair of bandpasses. The variation of the FP slope with wavelength is strong evidence of systematic variations in stellar content along the elliptical galaxy sequence. The intercept of the diagnostic relationship between log(D_K/D_V) and log(sigma_0) shows no significant dependence on environment within the uncertainties of the Galactic extinction corrections, demonstrating the universality of the stellar populations contributions at the level of Delta(V-K)=0.03 mag to the zero-point of the global scaling relations. Several other constraints on the properties of early-type galaxies --- the slope of the Mg_2-sigma_0 relation, the effects of stellar populations gradients, and deviations of early-type galaxies from a dynamically homologous family --- are included to construct an empirical, self-consistent model which provides a complete picture of the underlying physical properties which are varying along the early-type galaxy sequence. This empirical approach demonstrates that there are significant systematic variations in both age and metallicity along the elliptical galaxy sequence, and that a small, but systematic, breaking of dynamical homology (or a similar, wavelength independent effect) is required. Predictions for the evolution of the slope of the FP with redshift are described. [abriged]Comment: to appear in The Astronomical Journal; 40 pages, including 10 Postscript figures and 3 tables; uses AAS LaTeX style file

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

Harmonic analysis of iterated function systems with overlap

In this paper we extend previous work on IFSs without overlap. Our method involves systems of operators generalizing the more familiar Cuntz relations from operator algebra theory, and from subband filter operators in signal processing.Comment: 37 page

Flows on scales of 150 Mpc?

We investigate the reality of large-scale streaming on scales of up to 150 Mpc using the peculiar motions of galaxies in three directions. New R-band CCD photometry and spectroscopy for elliptical galaxies is used. The Fundamental Plane distance indicator is calibrated using the Coma cluster and an inhomogeneous Malmquist bias correction is applied. A linear bulk-flow model is fitted to the peculiar velocities in the sample regions and the results do not reflect the bulk flow observed by Lauer and Postman (LP). Accounting for the difference in geometry between the galaxy distribution in the three regions and the LP clustersconfirms the disagreement; assuming a low-density CDM power spectrum, we find that the observed bulk flow of the galaxies in our sample excludes the LP bulk flow at the 99.8% confidence level.Comment: 16 pages, 1 figur

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