Simulations of Clusters of Galaxies

The degree of complexity and, to a somewhat lesser degree, realism in simulations has advanced rapidly in the past few years. The simplest approach - modeling a cluster as collisionless dark matter and collisonal, non--radiative gas is now fairly well established. One of the most fruitful results of this approach is the {\sl morphology--cosmology connection} for X-ray clusters. Simulations have provided the means to make concrete predictions for the X-ray morphologies of clusters in cosmologies with different $\Omega_o$, with the result that low $\Omega_o$ cosmologies fair rather poorly when compared to observations. Another result concerns the accuracy of \xray binding mass estimates. The standard, hydrostatic, isothermal model estimator is found to be accurate to typically better than $50\%$ at radii where the density contrast is between $10^2$ and $10^3$. More complicated approaches, which attempt to explicitly follow galaxy formation within the proto--cluster environment are slowly being realized. The key issue of {\sl dynamical biasing} of the galaxy population within a cluster is being probed, but conclusive answers are lacking. The dynamics of multi--phase gas, including conversion of cold, dense gas into stars and the feedback therefrom, is the largest obstacle hindering progress. An example demonstrating the state--of--the--art in this area is presented.Comment: to appear in Proceedings of the XIVth Moriond Astrophysics Meeting. 10 pages, uuencoded, compressed postscript file includes figures (~1 Mb after unpacked

Gas dynamic simulations of galaxy formation

Results are presented from a simulation modeling the formation of a group of galaxies in a 'standard' cold, dark matter universe with delta = 1, h sub 0 = 50 km/(s(Mpc)), baryon fraction omega sub b = 0.1 and spectrum normalization sigma sub 8 = 0.6 (bias parameter b = 1.7). Initial conditions are generated within a periodic box with comoving length 16 Mpc in a manner constrained to produce a small cluster of total mass approximately 10 exp 14 solar mass. Two sets of 643 particles are used to model the dark matter and baryon fluids. Each gas particle represents 1.08 x 10 exp -8 solar mass, implying an L* galaxy is resolved by approximately 1000 particles. The system is evolved self-consistently in three dimensions using the combined N-body/hydrodynamic scheme P3MSPH up to a final redshift z = 1. Evolving to the present is prohibited by the fact that the mean density in the simulated volume is above critical and the entire volume would be going nonlinear beyond this point, We are currently analyzing another run with somewhat poorer mass resolution which was evolved to the present

Clues to galaxy activity from rich cluster simulations

New simulations of rich cluster evolution are used to evaluate the first infall hypothesis of Gunn and Dressler - the idea that the enhanced fraction of active galaxies seen in high redshift clusters is due to a one-time burst of star formation triggered by the rapid rise in external pressure as a galaxy plows into the hot intracluster medium (ICM). Using three-dimensional simulations which contain both baryonic gas and collisionless dark material, local static pressure histories for test orbits of galaxies are generated and a simple trigger threshold based on dP/dt/P sub ISM is applied to define an active fraction of the population. The results lend qualitative and quantitative support to the first infall interpretation

The Lx-T Relation and Intracluster Gas Fractions of X-ray Clusters

We re-examine the X-ray luminosity-temperature relation using a nearly homogeneous data set of 24 clusters selected for statistically accurate temperature measurements and absence of strong cooling flows. The data exhibit a remarkably tight power-law relation between bolometric luminosity and temperature with a slope 2.88 \pm 0.15. With reasonable assumptions regarding cluster structure, we infer an upper limit on fractional variations in the intracluster gas fraction <(\delta\fgas/\fgas)^2)^1/2 \le 15%. Imaging data from the literature are employed to determine absolute values of fgas within spheres encompassing density contrast 500 and 200 with respect to the critical density. Comparing binding mass estimates based on the virial theorem (VT) and the hydrostatic, betamodel (BM), we find a temperature-dependent discrepancy in fgas between the two methods caused by sytematic variation of the outer slope parameter beta with temperature. There is evidence that cool clusters have a lower mean gas fraction that hot clusters, but it is not possible to assess the statistical significance of this effect in the present dataset. The temperature dependance of the ICM density structure, coupled with the increase of the gas fraction with T in the VT aproach, explains the steepening of the Lx-T relation. The small variation about the mean gas fraction within this majority sub-population of clusters presents an important constraint for theories of galaxy formation and supports arguments against an Einstein-deSitter universe based on the population mean gas fraction and primordial nucleosynthesis. The apparent trend of lower gas fractions and more extended atmospheres in low T systems are consistent with expectations of models incorporating the effects of galactic winds on the ICM. ABRIDGEDComment: 11 pages, 4 figures, uses mn.sty and epsf.sty, accepted for publication in MNRAS; minor modifications: discussion added on CF LX (Sec. 3.1);comparison with Allen & Fabian L-T results (Sec.3.1 & Sec.4.4); statistics precised (3.1), discussion clarified (Sec. 2.2,Sec. 4.4); slight mistake in the r-T and M-T relation calibration corrected and thus fgas in Fig.3, Fig 4, Tab 2 slightly change

Sensitivity of galaxy cluster dark energy constraints to halo modeling uncertainties

We perform a sensitivity study of dark energy constraints from galaxy cluster surveys to uncertainties in the halo mass function, bias and the mass-observable relation. For a set of idealized surveys, we evaluate cosmological constraints as priors on sixteen nuisance parameters in the halo modeling are varied. We find that surveys with a higher mass limit are more sensitive to mass-observable uncertainties while surveys with low mass limits that probe more of the mass function shape and evolution are more sensitive to mass function errors. We examine the correlations among nuisance and cosmological parameters. Mass function parameters are strongly positively (negatively) correlated with Omega_DE (w). For the mass-observable parameters, Omega_DE is most sensitive to the normalization and its redshift evolution while w is more sensitive to redshift evolution in the variance. While survey performance is limited mainly by mass-observable uncertainties, the current level of mass function error is responsible for up to a factor of two degradation in ideal cosmological constraints. For surveys that probe to low masses (10^13.5 h^-1 M_sun), even percent-level constraints on model nuisance parameters result in a degradation of ~ sqrt{2} (2) on Omega_DE (w) relative to perfect knowledge.Comment: 13 pages, 5 figures, accepted by PR

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

Galaxy Tracers and Velocity Bias

This paper examines several methods of tracing galaxies in N-body simulations and their effects on the derived galaxy statistics, especially measurements of velocity bias. Using two simulations with identical initial conditions, one following dark matter only and the other following dark matter and baryons, both collisionless and collisional methods of tracing galaxies are compared to one another and against a set of idealized criteria. None of the collisionless methods proves satisfactory, including an elaborate scheme developed here to circumvent previously known problems. The main problem is that galactic overdensities are both secularly and impulsively disrupted while orbiting in cluster potentials. With dissipation, the baryonic tracers have much higher density contrasts and much smaller cross sections, allowing them to remain distinct within the cluster potential. The question remains whether the incomplete physical model introduces systematic biases. Statistical measures determined from simulations can vary significantly based solely on the galaxy tracing method utilized. The two point correlation function differs most on sub-cluster scales with generally good agreement on larger scales. Pairwise velocity dispersions show less uniformity on all scales addressed here. All tracing methods show a velocity bias to varying degrees, but the predictions are not firm: either the tracing method is not robust or the statistical significance has not been demonstrated. Though theoretical arguments suggest that a mild velocity bias should exist, simulation results are not yet conclusive.Comment: ApJ, in press, 23 pages, plain TeX, 8 of 13 figures included, all PostScript figures (4.8 MB) available via anonymous ftp from ftp://astro.princeton.edu/summers/tracers . Also available as POPe-616 on http://astro.princeton.edu/~library/prep.htm