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. 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

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

Thermodynamic characteristics of the classical n-vector magnetic model in three dimensions

The method of calculating the free energy and thermodynamic characteristics of the classical n-vector three-dimensional (3D) magnetic model at the microscopic level without any adjustable parameters is proposed. Mathematical description is perfomed using the collective variables (CV) method in the framework of the $\rho^4$ model approximation. The exponentially decreasing function of the distance between the particles situated at the N sites of a simple cubic lattice is used as the interaction potential. Explicit and rigorous analytical expressions for entropy,internal energy, specific heat near the phase transition point as functions of the temperature are obtained. The dependence of the amplitudes of the thermodynamic characteristics of the system for $T>T_c$ and $T<T_c$ on the microscopic parameters of the interaction potential are studied for the cases $n=1,2,3$ and $n\to\infty$. The obtained results provide the basis for accurate analysis of the critical behaviour in three dimensions including the nonuniversal characteristics of the system.Comment: 25 pages, 5 figure

Universal features of the order-parameter fluctuations : reversible and irreversible aggregation

We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behaviour can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the finite-size scaling analysis. The relation between order parameter, criticality and scaling law of fluctuations has been established and the connexion between the scaling function and the critical exponents has been found. We give examples in out-of-equilibrium aggregation models such as the Smoluchowski kinetic equations, or of at-equilibrium Ising and percolation models.Comment: 19 pages, 10 figure

Formal modeling and analysis of cognitive agent behavior

From an external perspective, cognitive agent behavior can be described by specifying (temporal) correlations of a certain complexity between stimuli (input states) and (re)actions (output states) of the agent. From an internal perspective the agent’s dynamics can be characterized by direct (causal) temporal relations between internal and mental states of the agent. The latter type of specifications can be represented in a relatively simple, executable format, which enables different types of analysis of the agent’s behavior. In particular, simulations of the agent’s behavior under different (environmental) circumstances can be explored. Furthermore, by applying verification techniques, automated analysis of the consequences of the agent’s behavior can be carried out. To enable such types of analysis when only given an external behavioral specification, this has to be transformed first into some type of executable format. An automated procedure for such a transformation is proposed in this paper. The application of the transformation procedure is demonstrated for a number of cases, showing examples of the types of analysis as mentioned for different forms of behavior

Stability of a cubic fixed point in three dimensions. Critical exponents for generic N

The detailed analysis of the global structure of the renormalization-group (RG) flow diagram for a model with isotropic and cubic interactions is carried out in the framework of the massive field theory directly in three dimensions (3D) within an assumption of isotropic exchange. Perturbative expansions for RG functions are calculated for arbitrary $N$ up to the four-loop order and resummed by means of the generalized Pad$\acute{\rm e}$-Borel-Leroy technique. Coordinates and stability matrix eigenvalues for the cubic fixed point are found under the optimal value of the transformation parameter. Critical dimensionality of the model is proved to be equal to $N_c=2.89 \pm 0.02$ that agrees well with the estimate obtained on the basis of the five-loop \ve-expansion [H. Kleinert and V. Schulte-Frohlinde, Phys. Lett. B342, 284 (1995)] resummed by the above method. As a consequence, the cubic fixed point should be stable in 3D for $N\ge3$, and the critical exponents controlling phase transitions in three-dimensional magnets should belong to the cubic universality class. The critical behavior of the random Ising model being the nontrivial particular case of the cubic model when N=0 is also investigated. For all physical quantities of interest the most accurate numerical estimates with their error bounds are obtained. The results achieved in the work are discussed along with the predictions given by other theoretical approaches and experimental data.Comment: 33 pages, LaTeX, 7 PostScript figures. Final version corrected and added with an Appendix on the six-loop stud

Critical structure factors of bilinear fields in O(N)-vector models

We compute the two-point correlation functions of general quadratic operators in the high-temperature phase of the three-dimensional O(N) vector model by using field-theoretical methods. In particular, we study the small- and large-momentum behavior of the corresponding scaling functions, and give general interpolation formulae based on a dispersive approach. Moreover, we determine the crossover exponent $\phi_T$ associated with the traceless tensorial quadratic field, by computing and analyzing its six-loop perturbative expansion in fixed dimension. We find: $\phi_T=1.184(12)$, $\phi_T=1.271(21)$, and $\phi_T=1.40(4)$ for $N=2,3,5$ respectively.Comment: 27 page