Revisiting the Cooling Flow Problem in Galaxies, Groups, and Clusters of Galaxies

We present a study of 107 galaxies, groups, and clusters spanning ~3 orders of magnitude in mass, ~5 orders of magnitude in central galaxy star formation rate (SFR), ~4 orders of magnitude in the classical cooling rate (dM/dt) of the intracluster medium (ICM), and ~5 orders of magnitude in the central black hole accretion rate. For each system in this sample, we measure dM/dt using archival Chandra X-ray data and acquire the SFR and systematic uncertainty in the SFR by combining over 330 estimates from dozens of literature sources. With these data, we estimate the efficiency with which the ICM cools and forms stars, finding e_cool = SFR/(dM/dt) = 1.4 +/- 0.4% for systems with dM/dt > 30 Msun/yr. For these systems, we measure a slope in the SFR-dM/dt relation greater than unity, suggesting that the systems with the strongest cool cores are also cooling more efficiently. We propose that this may be related to, on average, higher black hole accretion rates in the strongest cool cores, which could influence the total amount (saturating near the Eddington rate) and dominant mode (mechanical vs radiative) of feedback. For systems with dM/dt < 30 Msun/yr, we find that the SFR and dM/dt are uncorrelated, and show that this is consistent with star formation being fueled at a low (but dominant) level by recycled ISM gas in these systems. We find an intrinsic log-normal scatter in SFR at fixed dM/dt of 0.52 +/- 0.06 dex, suggesting that cooling is tightly self-regulated over very long timescales, but can vary dramatically on short timescales. There is weak evidence that this scatter may be related to the feedback mechanism, with the scatter being minimized (~0.4 dex) in systems for which the mechanical feedback power is within a factor of two of the cooling luminosity.Comment: 16 pages, 10 figures, 6 tables. Submitted to ApJ. Comments welcome

The mass-L_x relation for moderate luminosity X-ray clusters

We present measurements of the masses of a sample of 25 moderate X-ray luminosity clusters of galaxies from the 160 square degree ROSAT survey. The masses were obtained from a weak lensing analysis of deep F814W images obtained using the Advanced Camera for Surveys (ACS). We present an accurate empirical correction for the effect of charge transfer (in)efficiency on the shapes of faint galaxies. A significant lensing signal is detected around most of the clusters. The lensing mass correlates tightly with the cluster richness. We measured the intrinsic scatter in the scaling relation between M_2500 and L_X and find the best fit power law slope and normalisation to be alpha=0.68+-0.07 and M_X=(1.2+-0.12)10^14M_sun (for L_X=2x10^44 erg/s). These results agree well with a number of recent studies, but the normalisation is lower compared to the study of Rykoff et al. (2008b). One explanation for this difference may be the fact that (sub)structures projected along the line-of-sight boost both the galaxy counts and the lensing mass. Such superpositions lead to an increased mass at a given L_X when clusters are binned by richness.Comment: accepted for publication in the Astrophysical Journal; 15 pages, 11 figure

Homogeneous cooling of rough, dissipative particles: Theory and simulations

We investigate freely cooling systems of rough spheres in two and three dimensions. Simulations using an event driven algorithm are compared with results of an approximate kinetic theory, based on the assumption of a generalized homogeneous cooling state. For short times $t$, translational and rotational energy are found to change linearly with $t$. For large times both energies decay like $t^{-2}$ with a ratio independent of time, but not corresponding to equipartition. Good agreement is found between theory and simulations, as long as no clustering instability is observed. System parameters, i.e. density, particle size, and particle mass can be absorbed in a rescaled time, so that the decay of translational and rotational energy is solely determined by normal restitution and surface roughness.Comment: 10 pages, 10 eps-figure

Microscopic origin of granular ratcheting

Numerical simulations of assemblies of grains under cyclic loading exhibit ``granular ratcheting'': a small net deformation occurs with each cycle, leading to a linear accumulation of deformation with cycle number. We show that this is due to a curious property of the most frequently used models of the particle-particle interaction: namely, that the potential energy stored in contacts is path-dependent. There exist closed paths that change the stored energy, even if the particles remain in contact and do not slide. An alternative method for calculating the tangential force removes granular ratcheting.Comment: 13 pages, 18 figure

A method of open cluster membership determination

A new method for the determination of open cluster membership based on a cumulative effect is proposed. In the field of a plate the relative x and y coordinate positions of each star with respect to all the other stars are added. The procedure is carried out for two epochs t_1 and t_2 separately, then one sum is subtracted from another. For a field star the differences in its relative coordinate positions of two epochs will be accumulated. For a cluster star, on the contrary, the changes in relative positions of cluster members at t_1 and t_2 will be very small. On the histogram of sums the cluster stars will gather to the left of the diagram, while the field stars will form a tail to the right. The procedure allows us to efficiently discriminate one group from another. The greater the distance between t_1 and t_2 and the more cluster stars present, the greater is the effect. The accumulation method does not require reference stars, determination of centroids and modelling the distribution of field stars, necessary in traditional methods. By the proposed method 240 open clusters have been processed, including stars up to m<13. The membership probabilities have been calculated and compared to those obtained by the most commonly used Vasilevskis-Sanders method. The similarity of the results acquired the two different approaches is satisfactory for the majority of clusters.Comment: 10 pages, 5 figure

A 15-Kiloparsec X-Ray Disk in the Elliptical Galaxy NGC 1700

We present Chandra observations of the young elliptical galaxy NGC 1700. The X-ray isophotes are highly flattened between semimajor axes of 30 and 80 arcseconds, reaching a maximum ellipticity of approximately 0.65 at 60 arcsec (15 kpc). The surface brightness profile in the spectrally soft, flattened region is shallower than that of the starlight, indicating that the emission comes from hot gas rather than stellar sources. The flattening is so extreme that the gas cannot be in hydrostatic equilibrium in any plausible potential. A likely alternative is that the gas has significant rotational support. A simple model, representing isothermal gas distributed about a particular angular momentum, can reproduce the X-ray morphology while staying consistent with stellar kinematics. The specific angular momentum of the gas matches that of the stars in the most isophotally distorted outer part of the galaxy, and its cooling time matches the time since the last major merger. We infer that the gas was acquired in that merger, which involved a pre-existing elliptical galaxy with a hot ISM. The hot gas carried the angular momentum of the encounter, and has since gradually settled into a rotationally flattened, cooling disk.Comment: 11 pages, 2 figures, AASTeX 5.0. Accepted for publication in The Astrophysical Journa

A Richness Study of 14 Distant X-ray Clusters From the 160 Square Degree Survey

We have measured the surface density of galaxies toward 14 X-ray-selected cluster candidates at redshifts greater than z=0.46, and we show that they are associated with rich galaxy concentrations. We find that the clusters range between Abell richness classes 0-2, and have a most probable richness class of one. We compare the richness distribution of our distant clusters to those for three samples of nearby clusters with similar X-ray luminosities. We find that the nearby and distant samples have similar richness distributions, which shows that clusters have apparently not evolved substantially in richness since redshift z =0.5. We compare the distribution of distant X-ray clusters in the L_x--richness plane to the distribution of optically-selected clusters from the Palomar Distant Cluster Survey. The optically-selected clusters appear overly rich for their X-ray luminosities when compared to X-ray-selected clusters. Apparently, X-ray and optical surveys do not necessarily sample identical mass concentrations at large redshifts. This may indicate the existence of a population of optically rich clusters with anomalously low X-ray emission. More likely, however, it reflects the tendency for optical surveys to select unvirialized mass concentrations, as might be expected when peering along large-scale filaments.Comment: The abstract has been abridged. Accepted for publication in the Astrophysical Journa

Two Clusters with Radio-quiet Cooling Cores

Radio lobes inflated by active galactic nuclei at the centers of clusters are a promising candidate for halting condensation in clusters with short central cooling times because they are common in such clusters. In order to test the AGN-heating hypothesis, we obtained Chandra observations of two clusters with short central cooling times yet no evidence for AGN activity: Abell 1650 and Abell 2244. The cores of these clusters indeed appear systematically different from cores with more prominent radio emission. They do not have significant central temperature gradients, and their central entropy levels are markedly higher than in clusters with stronger radio emission, corresponding to central cooling times ~ 1 Gigayear. Also, there is no evidence for fossil X-ray cavities produced by an earlier episode of AGN heating. We suggest that either (1) the central gas has not yet cooled to the point at which feedback is necessary to prevent it from condensing, possibly because it is conductively stabilized, or (2) the gas experienced a major heating event $\gtrsim 1$ Gyr in the past and has not required feedback since then. The fact that these clusters with no evident feedback have higher central entropy and therefore longer central cooling times than clusters with obvious AGN feedback strongly suggests that AGNs supply the feedback necessary to suppress condensation in clusters with short central cooling times.Comment: ApJ Letter, in pres