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

The LCO/Palomar 10,000 km/sec Cluster Survey. I. Properties of the Tully-Fisher Relation

The first results from a Tully-Fisher (TF) survey of cluster galaxies are presented. The galaxies are drawn from fifteen Abell clusters that lie in the redshift range 9000-12,000 km/sec and are distributed uniformly around the celestial sky. The data set consists of R-band CCD photometry and long- slit H-alpha spectroscopy. The rotation curves (RCs) are characterized by a turnover radius (r_t) and an asymptotic velocity v_a, while the surface brightness profiles are characterized in terms of an effective exponential surface brightness I_e and a scale length r_e. The TF scatter is minimized when the rotation velocity is measured at 2.0 +/- 0.2 r_e; a significantly larger scatter results when the rotation velocity is measured at > 3 or < 1.5 scale lengths. This effect demonstrates that RCs do not have a universal form, as has been suggested by Persic, Salucci, and Stel. In contrast to previous studies, a modest but statistically significant surface-brightness dependence of the TF relation is found, log v = const + 0.28*log L + 0.14*log I_e. This indicates a stronger parallel between the TF relation and the FP relations of elliptical galaxies than has previously been recognized. Future papers in this series will consider the implications of this cluster sample for deviations from Hubble flow on 100-200 Mpc scales.Comment: 35 pages, 8 figures, uses aaspp4.sty. Submitted to ApJ. Also available at http://astro.stanford.edu/jeff

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

Exploring Cluster Ellipticals as Cosmological Standard Rods

We explore the possibility to calibrate massive cluster ellipticals as cosmological standard rods using the Fundamental Plane relation combined with a correction for luminosity evolution. Though cluster ellipticals certainly formed in a complex way, their passive evolution out to redshifts of about 1 indicates that basically all major merging and accretion events took place at higher redshifts. Therefore, a calibration of their luminosity evolution can be attempted. We propose to use the Mg$-\sigma$ relation for that purpose because it is independent of distance and cosmology. We discuss a variety of possible caveats, ranging from dynamical evolution to uncertainties in stellar population models and evolution corrections to the presence of age spread. Sources of major random and systematic errors are analysed as well. We apply the described procedure to nine elliptical galaxies in two clusters at $z=0.375$ and derive constraints on the cosmological model. For the best fitting $\Lambda$-free cosmological model we obtain: $q_o \approx 0.1$, with 90% confidence limits being $0 < q_o < 0.7$ (the lower limit being due to the presence of matter in the Universe). If the inflationary scenario applies (i.e. the Universe has flat geometry), then, for the best fitting model, matter and $\Lambda$ contribute about equally to the critical cosmic density (i.e. $\Omega_m \approx \Omega_\Lambda \approx 0.5$). With 90% confidence $\Omega_\Lambda$ should be smaller than 0.9.Comment: 21 pages, including 5 eps-figures, Latex, uses aasms4.sty, accepted by ApJ main journa

The Fundamental Plane at z=1.27: First Calibration of the Mass Scale of Red Galaxies at Redshifts z>1

We present results on the Fundamental Plane (FP) of early-type galaxies in the cluster RDCS J0848+4453 at z=1.27. Internal velocity dispersions of three K-selected early-type galaxies are determined from deep Keck spectra. Structural parameters are determined from HST NICMOS images. The galaxies show substantial offsets from the FP of the nearby Coma cluster, as expected from passive evolution of their stellar populations. The offsets from the FP can be expressed as offsets in M/L ratio. The M/L ratios of the two most massive galaxies are consistent with an extrapolation of results obtained at z=0.02-0.83. The evolution of early-type galaxies with masses >10^11 M_sun is well described by ln M/L(B) = (-1.06 +- 0.09) z, corresponding to passive evolution of -1.50 +- 0.13 mag at z=1.3. Ignoring selection effects, the best fitting stellar formation redshift is z*=2.6, corresponding to a luminosity weighted age at the epoch of observation of ~2 Gyr. The M/L ratios of these two galaxies are also in excellent agreement with predictions from models that include progenitor bias. The third galaxy is a factor ~10 less massive than the other two, shows strong Balmer absorption lines in its spectrum, and is offset from the Coma Fundamental Plane by 2.9 mag in rest-frame B. Despite their large range in M/L ratios, all three galaxies fall in the ``Extremely Red Object'' (ERO) class with I-H>3 and R-K>5, and our results show that it is hazardous to use simple models for converting luminosity to mass for these objects. Measurements of M/L ratios at high redshift can be considered first steps to empirically disentangle luminosity and mass evolution at the high mass end of the galaxy population, lifting an important degeneracy in the interpretation of evolution of the luminosity function. [SHORTENED]Comment: Accepted for publication in the Astrophysical Journa

RXJ0142.0+2131: I. The galaxy content of an X-ray-luminous galaxy cluster at z=0.28

We present a photometric and spectroscopic study of stellar populations in the X-ray-luminous cluster of galaxies RXJ0142.0+2131 at z=0.280. This paper analyses the results of high signal-to-noise spectroscopy, as well as g'-, r'-, and i'-band imaging, using the Gemini Multi-Object Spectrograph on Gemini North. Of 43 spectroscopic targets, we find 30 cluster members over a range in color. Central velocity dispersions and absorption-line strengths for lines in the range 3700A < lambda_rest < 5800A are derived for cluster members, and are compared with a low-redshift sample of cluster galaxies, and single stellar population (SSP) models. We use a combination of these indicators to estimate luminosity-weighted mean ages, metallicities ([M/H]), and alpha-element abundance ratios ([alpha/Fe]). RXJ0142.0+2131 is a relatively poor cluster and lacks galaxies with high central velocity dispersions. Although the red sequence and the Faber-Jackson relation are consistent with pure passive evolution of the early-type population with a formation redshift of z_form = 2, the strengths of the 4000A break and scaling relations between metal line indices and velocity dispersion reject this model with high significance. By inverting SSP models for the Hbeta_G, Mgb, and line indices, we calculate that, at a given velocity dispersion and metallicity, galaxies in RXJ0142.0+2131 have luminosity-weighted mean ages 0.14 +- 0.07 dex older than the low-redshift sample. We also find that [alpha/Fe] in stellar populations in RXJ0142.0+2131 is 0.14 +- 0.03 greater than at low redshift. All scaling relations are consistent with these estimated offsets. (abridged)Comment: AJ, accepted. 31 pages, 13 figures, uses emulateapj.cls. High-resolution figures available on request from first autho

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 Fundamental Plane in RX J0142.0+2131: a galaxy cluster merger at z=0.28

We present the Fundamental Plane (FP) in the z = 0.28 cluster of galaxies RX J0142.0+2131. There is no evidence for a difference in the slope of the FP when compared with the Coma cluster, although the internal scatter is larger. On average, stellar populations in RX J0142.0+2131 have rest-frame V-band mass-to-light ratios (M/L_V) 0.29+-0.03 dex lower than in Coma. This is significantly lower than expected for a passively-evolving cluster formed at z_f=2. Lenticular galaxies have lower average M/L_V and a distribution of M/L_V with larger scatter than ellipticals. Lower mass-to-light ratios are not due to recent star formation: our previous spectroscopic observations of RX J0142.0+2131 E/S0 galaxies showed no evidence for significant star-formation within the past ~4 Gyr. However, cluster members have enhanced alpha-element abundance ratios, which may act to decrease M/L_V. The increased scatter in the RX J0142.0+2131 FP reflects a large scatter in M/L_V implying that galaxies have undergone bursts of star formation over a range of epochs. The seven easternmost cluster galaxies, including the second brightest member, have M/L_V consistent with passive evolution and z_f = 2. We speculate that RX J0142.0+2131 is a cluster-cluster merger where the galaxies to the east are yet to fall into the main cluster body or have not experienced star formation as a result of the merger.Comment: 4 pages, 2 figures, accepted for publication in ApJ Letter

Photometric Properties of 47 Clusters of Galaxies: I. The Butcher-Oemler Effect

We present gri CCD photometry of 44 Abell clusters and 4 cluster candidates. Twenty one clusters in our sample have spectroscopic redshifts. Fitting a relation between mean g, r and i magnitudes, and redshift for this subsample, we have calculated photometric redshifts for the remainder with an estimated accuracy of 0.03. The resulting redshift range for the sample is 0.03<z<0.38. Color-magnitude diagrams are presented for the complete sample and used to study evolution of the galaxy population in the cluster environment. Our observations show a strong Butcher-Oemler effect (Butcher & Oemler 1978, 1984), with an increase in the fraction of blue galaxies (f_B) with redshift that seems more consistent with the steeper relation estimated by Rakos and Schombert (1995) than with the original one by Butcher & Oemler (1984). However, in the redshift range between ~ 0.08 and 0.2, where most of our clusters lie, there is a wide range of f_B values, consistent with no redshift evolution of the cluster galaxy population. A large range of f_B values is also seen between ~ 0.2 and 0.3, when Smail at al. (1998) x-ray clusters are added to our sample. The discrepancies between samples underscore the need for an unbiased sample to understand how much of the Butcher-Oemler effect is due to evolution, and how much to selection effects. We also tested the idea proposed by Garilli et al. (1996) that there is a population of unusually red galaxies which could be associated either with the field or clusters, but we find that these objects are all near the limiting magnitude of the images (20.5<r<22) and have colors that are consistent with those expected for stars or field galaxies at z ~ 0.7.Comment: 35 pages including 8 figures, submitted to A

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