The peculiar motions of early-type galaxies in two distant regions - V. The Mg-sigma relation, age and metallicity

We have examined the Mg-sigma relation for early-type galaxies in the EFAR sample and its dependence on cluster properties. A comprehensive maximum likelihood treatment of the sample selection and measurement errors gives fits to the global Mg-sigma relation of Mg b^'=0.131 log sigma -0.131 and Mg_2=0.257 log sigma -0.305. The slope of these relations is 25 per cent steeper than that obtained by most other authors owing to the reduced bias of our fitting method. The intrinsic scatter in the global Mg- sigma relation is estimated to be 0.016 mag in Mg b^' and 0.023 mag in Mg_2. The Mg- sigma relation for cD galaxies has a higher zero-point than for E and S0 galaxies, implying that cDs are older and/or more metal-rich than other early-type galaxies with the same velocity dispersion. We investigate the variation in the zero-point of the Mg- sigma relation between clusters. We find that it is consistent with the number of galaxies observed per cluster and the intrinsic scatter between galaxies in the global Mg-sigma relation. We find no significant correlation between the Mg-sigma zero-point and the cluster velocity dispersion, X-ray luminosity or X-ray temperature over a wide range in cluster mass. These results provide constraints for models of the formation of elliptical galaxies. However, the Mg-sigma relation on its own does not place strong limits on systematic errors in Fundamental Plane (FP) distance estimates resulting from stellar population differences between clusters. We compare the intrinsic scatter in the Mg-sigma and Fundamental Plane relations with stellar population models in order to constrain the dispersion in ages, metallicities and M/L ratios for early-type galaxies at fixed velocity dispersion. We find that variations in age or metallicity alone cannot explain the measured intrinsic scatter in both Mg- sigma and the FP. We derive the joint constraints on the dispersion in age and metallicity implied by the scatter in the Mg-sigma and FP relations for a simple Gaussian model. We find upper limits on the dispersions in age and metallicity at fixed velocity dispersion of 32 per cent in delta t/t and 38 per cent in delta Z/Z if the variations in age and metallicity are uncorrelated; only strongly anticorrelated variations lead to significantly higher upper limits. The joint distribution of residuals from the Mg- sigma and FP relations is only marginally consistent with a model having no correlation between age and metallicity, and is better matched by a model in which age and metallicity variations are moderately anticorrelated (delta t/t ~ 40 per cent, delta Z/Z ~ 50 per cent and rho ~ -0.5), with younger galaxies being more metal-rich

The peculiar motions of early-type galaxies in two distant regions - II. The spectroscopic data

We present the spectroscopic data for the galaxies studied in the EFAR project, which is designed to measure the properties and peculiar motions of early-type galaxies in two distant regions. We have obtained 1319 spectra of 714 early-type galaxies over 33 observing runs on 10 different telescopes. We describe the observations and data reductions used to measure redshifts, velocity dispersions and the Mgb and Mg_2 Lick linestrength indices. Detailed simulations and intercomparison of the large number of repeat observations lead to reliable error estimates for all quantities. The measurements from different observing runs are calibrated to a common zero-point or scale before being combined, yielding a total of 706 redshifts, 676 velocity dispersions, 676 Mgb linestrengths and 582 Mg_2 linestrengths. The median estimated errors in the combined measurements are Delta cz=20 km s^-1, Delta sigma sigma =9.1 per cent, Delta Mgb Mgb=7.2 per cent and Delta Mg_2=0.015 mag. Comparison of our measurements with published data sets shows no systematic errors in the redshifts or velocity dispersions, and only small zero-point corrections to bring our linestrengths on to the standard Lick system. We have assigned galaxies to physical clusters by examining the line-of-sight velocity distributions based on EFAR and ZCAT redshifts, together with the projected distributions on the sky. We derive mean redshifts and velocity dispersions for these clusters, which will be used in estimating distances and peculiar velocities and to test for trends in the galaxy population with cluster mass. The spectroscopic parameters presented here for 706 galaxies combine high-quality data, uniform reduction and measurement procedures, and detailed error analysis. They form the largest single set of velocity dispersions and linestrengths for early-type galaxies published to date

The Peculiar Motions of Early-Type Galaxies in Two Distant Regions -- VII. Peculiar Velocities and Bulk Motions

We present peculiar velocities for 85 clusters of galaxies in two large volumes at distances between 6000 and 15 000 km s−1 in the directions of Hercules-Corona Borealis and Perseus-Pisces-Cetus (the EFAR sample). These velocities are based on Fundamental Plane (FP) distance estimates for early-type galaxies in each cluster. We fit the FP using a maximum likelihood algorithm which accounts for both selection effects and measurement errors, and yields FP parameters with smaller bias and variance than other fitting procedures. We obtain a best-fitting FP with coefficients consistent with the best existing determinations. We measure the bulk motions of the sample volumes using the 50 clusters with the best-determined peculiar velocities. We find that the bulk motions in both regions are small, and consistent with zero at about the 5 per cent level. The EFAR results are in agreement with the small bulk motions found by Dale et al. on similar scales, but are inconsistent with pure dipole motions having the large amplitudes found by Lauer & Postman and Hudson et al. The alignment of the EFAR sample with the Lauer & Postman dipole produces a strong rejection of a large-amplitude bulk motion in that direction, but the rejection of the Hudson et al. result is less certain because their dipole lies at a large angle to the main axis of the EFAR sample. We employ a window function covariance analysis to make a detailed comparison of the EFAR peculiar velocities with the predictions of standard cosmological models. We find that the bulk motion of our sample is consistent with most cosmological models that approximately reproduce the shape and normalization of the observed galaxy power spectrum. We conclude that existing measurements of large-scale bulk motions provide no significant evidence against standard models for the formation of structure

The peculiar motions of early-type galaxies in two distant regions - VII. Peculiar velocities and bulk motions

We present peculiar velocities for 84 clusters of galaxies in two large volumes at distances between 6000 and 15000 km/s in the directions of Hercules-Corona Borealis and Perseus-Pisces-Cetus. These velocities are based on Fundamental Plane (FP) distance estimates for early-type galaxies in each cluster. We fit the FP using a maximum likelihood algorithm which accounts for both selection effects and measurement errors, and yields FP parameters with smaller bias and variance than other fitting procedures. We find a best-fit FP with coefficients consistent with the best existing determinations. We measure the bulk motions of the sample volumes using the 50 clusters with the best-determined peculiar velocities. We find the bulk motions in both regions are small, and consistent with zero at about the 5% level. The EFAR results are in agreement with the small bulk motions found by Dale et al. (1999) on similar scales, but are inconsistent with pure dipole motions having the large amplitudes found by Lauer & Postman (1994) and Hudson et al. (1999). The alignment of the EFAR sample with the Lauer & Postman dipole produces a strong rejection of a large-amplitude bulk motion in that direction, but the rejection of the Hudson et al. result is less certain because their dipole lies at a large angle to the main axis of the EFAR sample. We find the bulk motion of our sample is consistent with most cosmological models that approximately reproduce the shape and normalisation of the observed galaxy power spectrum. We conclude that existing measurements of large-scale bulk motions provide no significant evidence against standard models for the formation of structure.Comment: to appear in MNRAS, 27 pages, EFAR paper

The peculiar motions of early-type galaxies in two distant regions. IV. The photometric fitting procedure

The EFAR project is a study of 736 candidate early-type galaxies in 84 clusters lying in two regions toward Hercules-Corona Borealis and Perseus-Cetus at distances cz ~ 6000--15,000 km s-1. In this paper we describe a new method of galaxy photometry adopted to derive the photometric parameters of the EFAR galaxies. The algorithm fits the circularized surface brightness profiles as the sum of two seeing-convolved components, an R1/4 and an exponential law. This approach allows us to fit the large variety of luminosity profiles displayed by the EFAR galaxies homogeneously and to derive (for at least a subset of these) bulge and disk parameters. Multiple exposures of the same objects are optimally combined and an optional sky-fitting procedure has been developed to correct for sky-subtraction errors. Extensive Monte Carlo simulations are analyzed to test the performance of the algorithm and estimate the size of random and systematic errors. Random errors are small, provided that the global signal-to-noise ratio of the fitted profiles is larger than ~300. Systematic errors can result from (1) errors in the sky subtraction, (2) the limited radial extent of the fitted profiles, (3) the lack of resolution due to seeing convolution and pixel sampling, (4) the use of circularized profiles for very flattened objects seen edge-on, and (5) a poor match of the fitting functions to the object profiles. Large systematic errors are generated by the widely used simple R1/4 law to fit luminosity profiles when a disk component, as small as 20% of the total light, is present. The size of the systematic errors cannot be determined from the shape of the chi 2 function near its minimum because extrapolation is involved. Rather, we must estimate them by a set of quality parameters, calibrated against our simulations, which take into account the amount of extrapolation involved to derive the total magnitudes, the size of the sky correction, the average surface brightness of the galaxy relative to the sky, the radial extent of the profile, its signal-to-noise ratio, the seeing value, and the reduced chi 2 of the fit. We formulate a combined quality parameter Q, which indicates the expected precision of the fits. Errors in total magnitudes MTOT less than 0.05 mag and in half-luminosity radii Re less than 10% are expected if Q = 1, and less than 0.15 mag and 25% if Q = 2; 89% of the EFAR galaxies have fits with Q = 1 or Q = 2. The errors on the combined fundamental plane quantity FP = log Re-0.3, where is the average effective surface brightness, are smaller than 0.03 even if Q = 3. Thus, systematic errors on MTOT and Re only have a marginal effect on the distance estimates that involve FP. We show that the sequence of R1/n profiles, recently used to fit the luminosity profiles of elliptical galaxies, is equivalent (for n <= 8) to a subsample of R1/4 and exponential profiles, with appropriate scale lengths and disk-to-bulge ratios. This suggests that the variety of luminosity profiles shown by early-type galaxies may be due to the presence of a disk component

The Peculiar Motions of Early‐Type Galaxies in Two Distant Regions. IV. The Photometric Fitting Procedure

The EFAR project is a study of 736 candidate early-type galaxies in 84 clusters lying in two regions toward Hercules-Corona Borealis and Perseus-Cetus at distances cz ≈ 6000-15,000 km s-1. In this paper we describe a new method of galaxy photometry adopted to derive the photometric parameters of the EFAR galaxies. The algorithm fits the circularized surface brightness profiles as the sum of two seeing-convolved components, an R1/4 and an exponential law. This approach allows us to fit the large variety of luminosity profiles displayed by the EFAR galaxies homogeneously and to derive (for at least a subset of these) bulge and disk parameters. Multiple exposures of the same objects are optimally combined and an optional sky-fitting procedure has been developed to correct for sky-subtraction errors. Extensive Monte Carlo simulations are analyzed to test the performance of the algorithm and estimate the size of random and systematic errors. Random errors are small, provided that the global signal-to-noise ratio of the fitted profiles is larger than ≈ 300. Systematic errors can result from (1) errors in the sky subtraction, (2) the limited radial extent of the fitted profiles, (3) the lack of resolution due to seeing convolution and pixel sampling, (4) the use of circularized profiles for very flattened objects seen edge-on, and (5) a poor match of the fitting functions to the object profiles. Large systematic errors are generated by the widely used simple R1/4 law to fit luminosity profiles when a disk component, as small as 20% of the total light, is present. The size of the systematic errors cannot be determined from the shape of the χ2 function near its minimum because extrapolation is involved. Rather, we must estimate them by a set of quality parameters, calibrated against our simulations, which take into account the amount of extrapolation involved to derive the total magnitudes, the size of the sky correction, the average surface brightness of the galaxy relative to the sky, the radial extent of the profile, its signal-to-noise ratio, the seeing value, and the reduced χ2 of the fit. We formulate a combined quality parameter Q, which indicates the expected precision of the fits. Errors in total magnitudes MTOT less than 0.05 mag and in half-luminosity radii Re less than 10% are expected if Q = 1, and less than 0.15 mag and 25% if Q = 2; 89% of the EFAR galaxies have fits with Q = 1 or Q = 2. The errors on the combined fundamental plane quantity FP = log Re-0.3SBe, where SBe is the average effective surface brightness, are smaller than 0.03 even if Q = 3. Thus, systematic errors on MTOT and Re only have a marginal effect on the distance estimates that involve FP. We show that the sequence of R1/n profiles, recently used to fit the luminosity profiles of elliptical galaxies, is equivalent (for n ≤ 8) to a subsample of R1/4 and exponential profiles, with appropriate scale lengths and disk-to-bulge ratios. This suggests that the variety of luminosity profiles shown by early-type galaxies may be due to the presence of a disk component

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

Spatially-resolved electronic and vibronic properties of single diamondoid molecules

Diamondoids are a unique form of carbon nanostructure best described as hydrogen-terminated diamond molecules. Their diamond-cage structures and tetrahedral sp3 hybrid bonding create new possibilities for tuning electronic band gaps, optical properties, thermal transport, and mechanical strength at the nanoscale. The recently-discovered higher diamondoids (each containing more than three diamond cells) have thus generated much excitement in regards to their potential versatility as nanoscale devices. Despite this excitement, however, very little is known about the properties of isolated diamondoids on metal surfaces, a very relevant system for molecular electronics. Here we report the first molecular scale study of individual tetramantane diamondoids on Au(111) using scanning tunneling microscopy and spectroscopy. We find that both the diamondoid electronic structure and electron-vibrational coupling exhibit unique spatial distributions characterized by pronounced line nodes across the molecular surfaces. Ab-initio pseudopotential density functional calculations reveal that the observed dominant electronic and vibronic properties of diamondoids are determined by surface hydrogen terminations, a feature having important implications for designing diamondoid-based molecular devices.Comment: 16 pages, 4 figures. to appear in Nature Material