Dark Energy and the Hubble Age

I point out that an effective upper limit of approximately 20 Gyr (for a Hubble constant of 72 km/s/Mpc) or alternatively on the $H_0$-independent quantity $H_0t_0 < 1.47$, exists on the age of the Universe, essentially independent of the unknown equation of state of the dominant dark energy component in the Universe. Unless astrophysical constraints on the age of the Universe can convincingly reduce the upper limit to below this value no useful lower limit on the equation of state parameter $w$ for this component can be obtained. Direct dating by stars does not provide a useful constraint, but model-dependent cosmological limits from supernovae and the CMB observations may. For a constant value of $w$, a bound $H_0t_0 -1.5$Comment: 4 pages, submitted to Ap. J. Lett (analytic asymptotic upper bound now added

Structure in a Loitering Universe

We study the formation of structure for a universe that undergoes a recent loitering phase. We compare the nonlinear mass distribution to that in a standard, matter dominated cosmology. The statistical aspects of the clustered matter are found to be robust to changes in the expansion law, an exception being that the peculiar velocities are lower by a factor of $\sim 3$ in the loitering model. Further, in the loitering scenario, nonlinear growth of perturbation occurs more recently ($z\sim 3-5$) than in the matter dominated case. Differences in the high redshift appearances of the two models will result but observable consequences depend critically on the chosen form, onset and duration of the loitering phase.Comment: 8 pages, (uses revtex.sty), 5 figures not included, available on request, UM AC 92-

The Effects of Clumping and Substructure on ICM Mass Measurements

We examine an ensemble of 48 simulated clusters to determine the effects of small-scale density fluctuations and large-scale substructure on X-ray measurements of the intracluster medium (ICM) mass. We measure RMS density fluctuations in the ICM which can be characterized by a mean mass-weighted clumping factor C = /^2 between 1.3 and 1.4 within a density contrast of 500 times the critical density. These fluctuations arise from the cluster history of accretion shocks and major mergers, and their presence enhances the cluster's luminosity relative to the smooth case. We expect, therefore, that ICM mass measurements utilizing models which assume uniform density at a given radius carry a bias of order sqrt(C) = 1.16. We verify this result by performing ICM mass measurements on X-ray images of the simulations and finding the expected level of bias. The varied cluster morphologies in our ensemble also allow us to investigate the effects of departures from spherical symmetry on our measurements. We find that the presence of large-scale substructure does not further bias the resulting gas mass unless it is pronounced enough to produce a second peak in the image of at least 1% the maximum surface brightness. We analyze the subset of images with no secondary peaks and find a bias of 9% and a Gaussian random error of 4% in the derived mass.Comment: To appear in ApJ

Velocity bias in a LCDM model

We use N-body simulations to study the velocity bias of dark matter halos, the difference in the velocity fields of dark matter and halos, in a flat low- density LCDM model. The high force, 2kpc/h, and mass, 10^9Msun/h, resolution allows dark matter halos to survive in very dense environments of groups and clusters making it possible to use halos as galaxy tracers. We find that the velocity bias pvb measured as a ratio of pairwise velocities of the halos to that of the dark matter evolves with time and depends on scale. At high redshifts (z ~5) halos move generally faster than the dark matter almost on all scales: pvb(r)~1.2, r>0.5Mpc/h. At later moments the bias decreases and gets below unity on scales less than r=5Mpc/h: pvb(r)~(0.6-0.8) at z=0. We find that the evolution of the pairwise velocity bias follows and probably is defined by the spatial antibias of the dark matter halos at small scales. One-point velocity bias b_v, defined as the ratio of the rms velocities of halos and dark matter, provides a more direct measure of the difference in velocities because it is less sensitive to the spatial bias. We analyze b_v in clusters of galaxies and find that halos are ``hotter'' than the dark matter: b_v=(1.2-1.3) for r=(0.2-0.8)r_vir, where r_vir is the virial radius. At larger radii, b_v decreases and approaches unity at r=(1-2)r_vir. We argue that dynamical friction may be responsible for this small positive velocity bias b_v>1 found in the central parts of clusters. We do not find significant difference in the velocity anisotropy of halos and the dark matter. The dark matter the velocity anisotropy can be approximated as beta(x)=0.15 +2x/(x^2+4), where x is measured in units of the virial radius.Comment: 13 pages, Latex, AASTeXv5 and natbi

Mass Estimates of X-Ray Clusters

We use cosmological gas dynamic simulations to investigate the accuracy of galaxy cluster mass estimates based on X-ray observations. The experiments follow the formation of clusters in different cosmological models and include the effects of gravity, pressure gradients, and hydrodynamical shocks. A subset of our ensemble also allows for feedback of mass and energy from galactic winds into the intracluster medium. We find that mass estimates based on the hydrostatic, isothermal beta-model are remarkably accurate when evaluated at radii where the cluster mean density is between 500-2500 times the critical density. Applied to 174 artificial ROSAT images constructed from the simulations, the distribution of the estimated-to-true mass ratio is nearly unbiased and has a standard deviation of 14-29%. The scatter can be considerably reduced (to 8-15%) by using an alternative mass estimator that exploits the tightness of the mass-temperature relation found in the simulations. The improvement over beta-model estimates is due to the elimination of the variance contributed by the gas outer slope parameter. We discuss these findings and their implications for recent measurements of cluster baryon fractions.Comment: TeX, 24p; 11 Postscript figs. Submitted to the Astrophysical Journa

Gravitational Lensing Limits on the Average Redshift of Submillimeter Sources

The submillimeter universe has now been explored with the Submillimeter Common User Bolometer Array (SCUBA) camera on the James Clerk Maxwell Telescope, and a claim has been made to the presence of a new population of optically unidentified starforming galaxies at high redshifts (z \gtrsim 3). Such a population dramatically alters current views on the star formation history of the universe as well as galaxy formation and evolution. Recently, new radio identifications of the Hubble Deep Field submm sources have led to the suggestion that some of these sources are at low redshifts, however, submm source redshift distribution is still not well determined. Here, we present an upper limit to the average redshift by comparing the expected number of gravitationally lensed submm sources due to foreground cluster potentials to current observed statistics of such lensed sources. The upper limit depends on the cosmological parameters, and at the 68% confidence level, < 3.1, 4.8, 5.2, or 8.0 for (Omega,Lambda) values of (0.3,0.7), (0.5,0.5), (0.3,0.0) or (1.0,0.0) respectively. These upper limits are consistent with redshift distribution for 850 micron sources implied by starformation history models based on measured background radiation at far-infrared and submm wavelengths.Comment: Accepted for publication in ApJ Letters (4 pages, including 1 table

Gravitational Lensing as a Probe of Quintessence

A large number of cosmological studies now suggest that roughly two-thirds of the critical energy density of the Universe exists in a component with negative pressure. If the equation of state of such an energy component varies with time, it should in principle be possible to identify such a variation using cosmological probes over a wide range in redshift. Proper detection of any time variation, however, requires cosmological probes beyond the currently studied range in redshift of $\sim$ 0.1 to 1. We extend our analysis to gravitational lensing statistics at high redshift and suggest that a reliable sample of lensed sources, out to a redshift of $\sim$ 5, can be used to constrain the variation of the equation of state, provided that both the redshift distribution of lensed sources and the selection function involved with the lensed source discovery process are known. An exciting opportunity to catalog an adequate sample of lensed sources (quasars) to probe quintessence is now available with the ongoing Sloan Digital Sky Survey. Writing $w(z)\approx w_0 + z (dw/dz)_0$, we study the expected accuracy to which the equation of state today $w_0$ and its rate of change $(dw/dz)_0$ can simultaneously be constrained. Such a determination can rule out some missing-energy candidates, such as classes of quintessence models or a cosmological constant.Comment: Accepted for publication in ApJ Letters (4 pages, including 4 figures

Hydrodynamic simulations of correlation and scatter in galaxy cluster maps

The two dimensional structure of hot gas in galaxy clusters contains information about the hydrodynamical state of the cluster, which can be used to understand the origin of scatter in the thermodynamical properties of the gas, and to improve the use of clusters to probe cosmology. Using a set of hydrodynamical simulations, we provide a comparison between various maps currently employed in the X-ray analysis of merging clusters and those cluster maps anticipated from forthcoming observations of the thermal Sunyaev-Zel'dovich effect. We show the following: 1) an X-ray pseudo-pressure, defined as square root of the soft band X-ray image times the temperature map is a good proxy for the SZ map; 2) we find that clumpiness is the main reason for deviation between X-ray pseudo-pressure and SZ maps; 3) the level of clumpiness can be well characterized by X-ray pseudo-entropy maps. 4) We describe the frequency of deviation in various maps of clusters as a function of the amplitude of the deviation. This enables both a comparison to observations and a comparison to effects of introduction of complex physical processes into simulation.Comment: 7 pages, A&A in pres

Quantitative Estimates of Environmental Effects on the Star Formation Rate of Disk Galaxies in Clusters of Galaxies

A simple model is constructed to evaluate the change of star formation rate of a disk galaxy due to environmental effects in clusters of galaxies. Three effects, (1) tidal force from the potential well of the cluster, (2) increase of external pressure when the galaxy plows into the intracluster medium, (3) high-speed encounters between galaxies, are investigated. General analysis indicates that the star formation rate increases significantly when the pressure of molecular clouds rises above $\sim 3\times 10^5 cm^{-3} K$ in $\sim 10^8$ yr. The tidal force from the potential well of the cluster increases pressures of molecular clouds in a disk galaxy infalling towards the cluster center. Before the galaxy reaches the cluster center, the star formation rate reaches a maximum. The peak is three to four times larger than the initial value. If this is the main mechanism of the Butcher-Oemler effect, blue galaxies are expected to be located within $\sim 300$ kpc from the center of the cluster. However this prediction is inconsistent with the recent observations. The increase of external pressure when the galaxy plows into the intracluster medium does not change star formation rate of a disk galaxy significantly. The velocity perturbation induced by a single high-speed encounter between galaxies is too small to affect star formation rate of a disk galaxy, while successive high-speed encounters (galaxy harassment) trigger star formation activity because of the accumulation of gas in the galaxy center. Therefore, the galaxy harassment remains as the candidate for a mechanism of the Butcher-Oemler effect.Comment: 12 pages, 13 figures. To be published in Ap