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

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

Wavelets in mathematical physics: q-oscillators

We construct representations of a q-oscillator algebra by operators on Fock space on positive matrices. They emerge from a multiresolution scaling construction used in wavelet analysis. The representations of the Cuntz Algebra arising from this multiresolution analysis are contained as a special case in the Fock Space construction.Comment: (03/11/03):18 pages; LaTeX2e, "article" document class with "letterpaper" option An outline was added under the abstract (p.1), paragraphs added to Introduction (p.2), mat'l added to Proofs in Theorems 1 and 6 (pgs.5&17), material added to text for the conclusion (p.17), one add'l reference added [12]. (04/22/03):"number 1" replace with "term C" (p.9), single sentences reformed into a one paragraph (p.13), QED symbol moved up one paragraph and last paragraph labeled as "Concluding Remarks.

An extension of Wiener integration with the use of operator theory

With the use of tensor product of Hilbert space, and a diagonalization procedure from operator theory, we derive an approximation formula for a general class of stochastic integrals. Further we establish a generalized Fourier expansion for these stochastic integrals. In our extension, we circumvent some of the limitations of the more widely used stochastic integral due to Wiener and Ito, i.e., stochastic integration with respect to Brownian motion. Finally we discuss the connection between the two approaches, as well as a priori estimates and applications.Comment: 13 page

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

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