Total Cluster Mass Research Articles

CLASH-VLT: A highly precise strong lensing model of the galaxy cluster RXC J2248.7−4431 (Abell S1063) and prospects for cosmography

We perform a comprehensive study of the total mass distribution of the galaxy cluster RXCJ2248 ($z=0.348$) with a set of high-precision strong lensing models, which take advantage of extensive spectroscopic information on many multiply lensed systems. In the effort to understand and quantify inherent systematics in parametric strong lensing modelling, we explore a collection of 22 models where we use different samples of multiple image families, parametrizations of the mass distribution and cosmological parameters. As input information for the strong lensing models, we use the CLASH HST imaging data and spectroscopic follow-up observations, carried out with the VIMOS and MUSE spectrographs, to identify bona-fide multiple images. A total of 16 background sources, over the redshift range $1.0-6.1$, are multiply lensed into 47 images, 24 of which are spectroscopically confirmed and belong to 10 individual sources. The cluster total mass distribution and underlying cosmology in the models are optimized by matching the observed positions of the multiple images on the lens plane. We show that with a careful selection of a sample of spectroscopically confirmed multiple images, the best-fit model reproduces their observed positions with a rms of $0.3$ in a fixed flat $\Lambda$CDM cosmology, whereas the lack of spectroscopic information lead to biases in the values of the model parameters. Allowing cosmological parameters to vary together with the cluster parameters, we find (at $68\%$ confidence level) $\Omega_m=0.25^{+0.13}_{-0.16}$ and $w=-1.07^{+0.16}_{-0.42}$ for a flat $\Lambda$CDM model, and $\Omega_m=0.31^{+0.12}_{-0.13}$ and $\Omega_\Lambda=0.38^{+0.38}_{-0.27}$ for a universe with $w=-1$ and free curvature. Using toy models mimicking the overall configuration of RXCJ2248, we estimate the impact of the line of sight mass structure on the positional rms to be $0.3\pm 0.1$.(ABRIDGED)

Constancy of the cluster gas mass fraction in the R h = ct Universe

The ratio of baryonic to dark matter densities is assumed to have remained constant throughout the formation of structure. With this, simulations show that the fraction f gas ( z ) of baryonic mass to total mass in galaxy clusters should be nearly constant with redshift z . However, the measurement of these quantities depends on the angular distance to the source, which evolves with z according to the assumed background cosmology. An accurate determination of f gas ( z ) for a large sample of hot ( kT e >5 keV), dynamically relaxed clusters could therefore be used as a probe of the cosmological expansion up to z <2. The fraction f gas ( z ) would remain constant only when the correct cosmology is used to fit the data. In this paper, we compare the predicted gas mass fractions for both Λ cold dark matter ( Λ CDM) and the R h = ct Universe and test them against the three largest cluster samples (LaRoque et al. 2006 Astrophys. J. 652, 917–936 ( doi:10.1086/508139 ); Allen et al. 2008 Mon. Not. R. Astron. Soc. 383, 879–896 ( doi:10.1111/j.1365-2966.2007.12610.x ); Ettori et al. 2009 Astron. Astrophys. 501, 61–73 ( doi:10.1051/0004-6361/200810878 )). We show that R h = ct is consistent with a constant f gas in the redshift range z ≲ 2 , as was previously shown for the reference Λ CDM model (with parameter values H 0 =70 km s −1 Mpc −1 , Ω m =0.3 and w Λ =−1). Unlike Λ CDM, however, the R h = ct Universe has no free parameters to optimize in fitting the data. Model selection tools, such as the Akaike information criterion and the Bayes information criterion (BIC), therefore tend to favour R h = ct over Λ CDM. For example, the BIC favours R h = ct with a likelihood of approximately 95% versus approximately 5% for Λ CDM.

A Detailed Study of the Mass Distribution of the Galaxy Cluster RXC J2248.7-4431

In this work we use strong gravitational lensing techniques to constrain the total mass distribution of the galaxy cluster RXC J2248.7-4432 (RXC J2248, zlens = 0.348), also known as Abell S1063, observed within the Cluster Lensing And Supernova survey with Hubble (CLASH). Thanks to its strong lensing efficiency and exceptional data quality from the VIsible Multi-Object Spectrograph (VIMOS) and Multi Unit Spectroscopic Explorer (MUSE) on the Very Large Telescope, we can build a parametric model for the total mass distribution. Using the positions of the multiple images generated by 7 multiply-lensed background sources with measured spectroscopic redshifs, we find that the best-fit parametrisation for the cluster total mass distribution is composed of an elliptical pseudo-isothermal mass distribution with a significant core for the overall cluster halo, and of truncated pseudo-isothermal mass profiles for the cluster galaxies. This model is capable to predict the positions of the multiple images with an unprecedented precision of ≈ 0”.3. We also show that varying freely the cosmological parameters of the ΛCDM model, our strong lensing model can constrain the underlying geometry of the universe via the angular diameter distances between the lens and the sources and the observer and the sources.

The binary fraction and mass segregation in Alpha Persei open cluster

Abstract We have obtained membership probabilities of stars within a field of ${\sim }3\deg$ from the centre of the open cluster Alpha Persei using proper motions and photometry from the PPMXL and Wide-field Infrared Survey Explorer catalogues. We have identified 810 possible stellar members of Alpha Persei. We derived the global and radial present-day mass function (MF) of the cluster and found that they are well matched by two-stage power-law relations with different slopes at different radii. The global MF of Alpha Persei shows a turnover at m = 0.62 M⊙ with low- and high-mass slopes of αlow = 0.50 ± 0.09 (0.1 < m/ M⊙ < 0.62) and αhigh = 2.32 ± 0.14 (0.62 ≤ m/ M⊙ < 4.68), respectively. The high-mass slope of the cluster increases from 2.01 inside 1$_{.}^{\circ}$10 to 2.63 outside 2$_{.}^{\circ}$2, whereas the mean stellar mass decreases from 0.95 to 0.57 M⊙ in the same regions, signifying clear evidence of mass segregation in the cluster. From an examination of the high-quality colour–magnitude data of the cluster and performing a series of Monte Carlo simulations, we obtained a binary fraction of fbin = 34 ± 12 per cent for stars with 0.70 < m/ M⊙ < 4.68. This is significantly larger than the observed binary fraction, indicating that this open cluster contains a large population of unresolved binaries. Finally, we corrected the MF slopes for the effect of unresolved binaries and found low- and high-mass slopes of αlow = 0.89 ± 0.11 and αhigh = 2.37 ± 0.09 and a total cluster mass of 352 M⊙ for Alpha Persei.

Cluster gas fraction as a test of gravity

We propose a new cosmological test of gravity, by using the observed mass fraction of X-ray-emitting gas in massive galaxy clusters. The cluster gas fraction, believed to be a fair sample of the average baryon fraction in the Universe, is a well-understood observable, which has previously mainly been used to constrain background cosmology. In some modified gravity models, such as f(R) gravity, gas temperature in a massive cluster is determined by the effective mass (the mass that would have produced the same gravitational effect assuming standard gravity as the cluster actually does in f(R) gravity) of that cluster, which can be larger than its true mass. On the other hand, X-ray luminosity is determined by the true gas density, which in both modified gravity and Λ-cold-dark-matter models depends mainly on Ωb/Ωm and hence the true total cluster mass. As a result, the standard practice of combining gas temperatures and X-ray surface brightnesses of clusters to infer their gas fractions can, in modified gravity models, lead to a larger – in f(R) gravity this can be 1/3 larger – value of Ωb/Ωm than that inferred from other observations such as the cosmic microwave background. Our quick calculation shows that the Hu–Sawicki n = 1 f(R) model with |$|\bar{f}_{R0}|=5\times 10^{-5}$| is in tension with the gas fraction data of the 42 clusters analysed by Allen et al. We also discuss the implications for other modified gravity models.

Rhapsody-G simulations: galaxy clusters as baryonic closed boxes and the covariance between hot gas and galaxies

Within a sufficiently large cosmic volume, conservation of baryons implies a simple `closed box' view in which the sum of the baryonic components must equal a constant fraction of the total enclosed mass. We present evidence from Rhapsody-G hydrodynamic simulations of massive galaxy clusters that the closed-box expectation may hold to a surprising degree within the interior, non-linear regions of haloes. At a fixed halo mass, we find a significant anti-correlation between hot gas mass fraction and galaxy mass fraction (cold gas + stars), with a rank correlation coefficient of -0.69 within $R_{500c}$. Because of this anti-correlation, the total baryon mass serves as a low-scatter proxy for total cluster mass. The fractional scatter of total baryon fraction scales approximately as $0.02 (\Delta_c/100)^{0.6}$, while the scatter of either gas mass or stellar mass is larger in magnitude and declines more slowly with increasing radius. We discuss potential observational tests using cluster samples selected by optical and hot gas properties; the simulations suggest that joint selection on stellar and hot gas has potential to achieve 5% scatter in total halo mass.

The normal chemistry of multiple stellar populations in the dense globular cluster NGC 6093 (M 80)

We present the abundance analysis of 82 red giant branch stars in the dense, metal-poor globular cluster NGC 6093 (M 80), the largest sample of stars analysed in this way for this cluster. From high-resolution UVES spectra of 14 stars and intermediate resolution GIRAFFE spectra for the other stars we derived abundances of O, Na, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Ba, La, Ce, Pr, Nd, Sm, Eu. On our UVES metallicity scale the mean metal abundance of M 80 is [Fe/H] = −1.791 ± 0.006 ± 0.076 (±statistical ±systematic error) with σ = 0.023 (14 stars). M 80 shows star-to-star variations in proton-capture elements, and the extension of the Na-O anti-correlation perfectly fit the relations with (i) total cluster mass; (ii) horizontal branch morphology; and (iii) cluster concentration previously found by our group. The chemistry of multiple stellar populations in M 80 does not look extreme. The cluster is also a representative of halo globular clusters concerning the pattern of α-capture and Fe-group elements. However we found that a significant contribution from the s-process is required to account for the distribution of neutron-capture elements. A minority of stars in M 80 seem to exhibit slightly enhanced abundances of s-process species, compatible with those observed in M 22 and NGC 1851, although further confirmation from larger samples is required.

Primordial star clusters at extreme magnification

Gravitationally lensed galaxies with magnification ~10-100 are routinely detected at high redshifts, but magnifications significantly higher than this are hampered by a combination of low probability and large source sizes. Magnifications of ~1000 may nonetheless be relevant in the case of intrinsically small, high-redshift objects with very high number densities. Here, we explore the prospects of detecting compact (< 10 pc), high-redshift (z > 7) Population III star clusters at such extreme magnifications in large-area surveys with planned telescopes like Euclid, WFIRST and WISH. We find that the planned WISH 100 sq. deg ultradeep survey may be able to detect a small number of such objects, provided that the total stellar mass of these star clusters is > 10000 solar masses. If candidates for such lensed Population III star clusters are found, follow-up spectroscopy of the surrounding nebula with the James Webb Space Telescope or groundbased Extremely Large Telescopes should be able to confirm the Population III nature of these objects. Multiband photometry of these objects with the James Webb Space Telescope also has the potential to confirm that the stellar initial mass function in these Population III star clusters is top-heavy, as supported by current simulations.

Deep near-infrared adaptive-optics observations of a young embedded cluster at the edge of the RCW 41 H II region

We investigate the star formation activity in a young star forming cluster embedded at the edge of the RCW 41 HII region. As a complementary goal, we aim at demonstrating the gain provided by Wide-Field Adaptive Optics instruments to study young clusters. We used deep, JHKs images from the newly commissioned Gemini-GeMS/GSAOI instrument, complemented with Spitzer IRAC observations, in order to study the photometric properties of the young stellar cluster. GeMS is an AO instrument, delivering almost diffraction limited images over a field of 2' across. The exquisite angular resolution allows us to reach a limiting magnitude of J = 22 for 98% completeness. The combination of the IRAC photometry with our JHKs catalog is used to build color-color diagrams, and select Young Stellar Objects (YSOs) candidates. We detect the presence of 80 Young Stellar Object (YSO) candidates. Those YSOs are used to infer the cluster age, which is found to be in the range 1 to 5 Myr. We find that 1/3 of the YSOs are in a range between 3 to 5 Myr, while 2/3 of the YSO are < 3 Myr. When looking at the spatial distribution of these two populations, we evidence a potential age gradient across the field, suggesting sequential star formation. We construct the IMF, and show that we can sample the mass distribution well into the brown dwarf regime (down to 0.01 Msun). The logarithmic mass function rises to peak at 0.3 Msun, before turning over and declining into the brown dwarf regime. The total cluster mass derived is estimated to be 78 +/- 18 Msun, while the ratio of brown dwarfs to star derived is 18 p/- 5 %. When comparing with other young clusters, we find that the IMF shape of the young cluster embedded within RCW 41 is consistent with those of Trapezium, IC 348 or Chamaeleon I, except for the IMF peak, which happens to be at higher mass. This characteristic is also seen in clusters like NGC 6611 or even Taurus.

REVISED MASS-TO-LIGHT RATIOS FOR NEARBY GALAXY GROUPS AND CLUSTERS

We present a detailed investigation of the cluster stellar mass-to-light (M*/L) ratio and cumulative stellar masses, derived on a galaxy-by-galaxy basis, for 12 massive (M500 ~ 10^14 - 10^15 Msun), nearby clusters with available optical imaging data from the Sloan Digital Sky Survey Data Release 10 and X-ray data from the Chandra X-ray Observatory. Our method involves a statistical cluster membership using both photometric and spectroscopic redshifts when available to maximize completeness whilst minimizing contamination effects. We show that different methods of estimating the stellar mass-to-light ratio from observed photometry result in systematic discrepancies in the total stellar masses and average mass-to-light ratios of cluster galaxies. Nonetheless, all conversion methodologies point to a lack of correlation between M*/Li and total cluster mass, even though low-mass groups contain relatively more blue galaxies. We also find no statistically significant correlation between M*/Li and the fraction of blue galaxies. For the mass range covered by our sample, the assumption of a Chabrier IMF yields an integrated M*/Li = 1.7 +/- 0.2 Msun/Lsun, a lower value than used in most similar studies, though consistent with the study of low-mass galaxy groups by Leauthaud et al. (2012). A light (diet) Salpeter IMF would imply a ~60% increase in M*/Li.

The state of globular clusters at birth – II. Primordial binaries

(abridged) In this paper, we constrain the properties of primordial binary populations in Galactic globular clusters using the MOCCA Monte Carlo code for cluster evolution. Our results are compared to the observations of Milone et al. (2012) using the photometric binary populations as proxies for the true underlying distributions, in order to test the hypothesis that the data are consistent with an universal initial binary fraction near unity and the binary orbital parameter distributions of Kroupa (1995). With the exception of a few possible outliers, we find that the data are to first-order consistent with the universality hypothesis. Specifically, the present-day binary fractions inside the half-mass radius r$_{\rm h}$ can be reproduced assuming either high initial binary fractions near unity with a dominant soft binary component as in the Kroupa distribution combined with high initial densities (10$^4$-10$^6$ M$_{\odot}$ pc$^{-3}$), or low initial binary fractions ($\sim$ 5-10%) with a dominant hard binary component combined with moderate initial densities near their present-day values (10$^2$-10$^3$ M$_{\odot}$ pc$^{-3}$). This apparent degeneracy can be broken using the binary fractions outside r$_{\rm h}$- only high initial binary fractions with a significant soft component combined with high initial densities can contribute to reproducing the observed anti-correlation between the binary fractions outside r$_{\rm h}$ and the total cluster mass. We further illustrate using the simulated present-day binary orbital parameter distributions and the technique introduced in Leigh et al. (2012) that the relative fractions of hard and soft binaries can be used to further constrain the initial cluster density and mass-density relation. Our results favour an initial mass-density relation of the form r$_{\rm h} \propto$ M$_{\rm clus}^{\alpha}$ with $\alpha <$ 1/3.

CLASH-VLT: The stellar mass function and stellar mass density profile of thez= 0.44 cluster of galaxies MACS J1206.2-0847

Context. The study of the galaxy stellar mass function (SMF) in relation to the galaxy environment and the stellar mass density profile, rho(r), is a powerful tool to constrain models of galaxy evolution. Aims. We determine the SMF of the z=0.44 cluster of galaxies MACS J1206.2-0847 separately for passive and star-forming (SF) galaxies, in different regions of the cluster, from the center out to approximately 2 virial radii. We also determine rho(r) to compare it to the number density and total mass density profiles. Methods. We use the dataset from the CLASH-VLT survey. Stellar masses are obtained by SED fitting on 5-band photometric data obtained at the Subaru telescope. We identify 1363 cluster members down to a stellar mass of 10^9.5 Msolar. Results. The whole cluster SMF is well fitted by a double Schechter function. The SMFs of cluster SF and passive galaxies are statistically different. The SMF of the SF cluster galaxies does not depend on the environment. The SMF of the passive population has a significantly smaller slope (in absolute value) in the innermost (<0.50 Mpc), highest density cluster region, than in more external, lower density regions. The number ratio of giant/subgiant galaxies is maximum in this innermost region and minimum in the adjacent region, but then gently increases again toward the cluster outskirts. This is also reflected in a decreasing radial trend of the average stellar mass per cluster galaxy. On the other hand, the stellar mass fraction, i.e., the ratio of stellar to total cluster mass, does not show any significant radial trend. Conclusions. Our results appear consistent with a scenario in which SF galaxies evolve into passive galaxies due to density-dependent environmental processes, and eventually get destroyed very near the cluster center to become part of a diffuse intracluster medium.

LoCuSS: hydrostatic mass measurements of the high-LX cluster sample – cross-calibration of Chandra and XMM–Newton

We present a consistent analysis of Chandra and XMM-Newton observations of an approximately mass-selected sample of 50 galaxy clusters at $0.15<z<0.3$ -- the "LoCuSS High-$L_X$ Sample". We apply the same analysis methods to data from both satellites, including newly developed analytic background models that predict the spatial variation of the Chandra and XMM-Newton backgrounds to $<2\%$ and $<5\%$ precision respectively. To verify the cross-calibration of Chandra and XMM-Newton-based cluster mass measurements, we derive the mass profiles of the 21 clusters that have been observed with both satellites, extracting surface brightness and temperature profiles from identical regions of the respective datasets. We obtain consistent results for the gas and total hydrostatic cluster masses: the average ratio of Chandra- to XMM-Newton-based measurements of $M_{\rm gas}$ and $M_X$ at $r_{500}$ are $0.99\pm0.02$ and $1.02\pm0.05$, respectively with an intrinsic scatter of $\sim3\%$ for gas masses and $\sim8\%$ for hydrostatic masses. Comparison of our hydrostatic mass measurements at $r_{500}$ with the latest LoCuSS weak-lensing results indicate that the data are consistent with non-thermal pressure support at this radius of $\sim7\%$. We also investigate the scaling relation between our hydrostatic cluster masses and published integrated Compton parameter $Y_{sph}$ measurements from the Sunyaev-Zel'dovich Array. We measure a scatter in mass at fixed $Y_{sph}$ of $\sim16\%$ at $\Delta=500$, which is consistent with theoretical predictions of $\sim10-15\%$ scatter.

DARK MATTER HALOS IN GALAXIES AND GLOBULAR CLUSTER POPULATIONS

We combine a new, comprehensive database for globular cluster populations in all types of galaxies with a new calibration of galaxy halo masses based entirely on weak lensing. Correlating these two sets of data, we find that the mass ratio $\eta \equiv M_{GCS}/M_{h}$ (total mass in globular clusters, divided by halo mass) is essentially constant at $\langle \eta \rangle \sim 4 \times 10^{-5}$, strongly confirming earlier suggestions in the literature. Globular clusters are the only known stellar population that formed in essentially direct proportion to host galaxy halo mass. The intrinsic scatter in $\eta$ appears to be at most 0.2 dex; we argue that some of this scatter is due to differing degrees of tidal stripping of the globular cluster systems between central and satellite galaxies. We suggest that this correlation can be understood if most globular clusters form at very early stages in galaxy evolution, largely avoiding the feedback processes that inhibited the bulk of field-star formation in their host galaxies. The actual mean value of $\eta$ also suggests that about $1/4$ of the \emph{initial} gas mass present in protogalaxies collected into GMCs large enough to form massive, dense star clusters. Finally, our calibration of $\langle \eta \rangle$ indicates that the halo masses of the Milky Way and M31 are $(1.2\pm0.5)\times 10^{12} M_{\odot}$ and $(3.9\pm1.8)\times 10^{12} M_{\odot}$ respectively.

Massive open star clusters using the VVV survey

Context: Young massive clusters are key to map the Milky Way's structure, and near-IR large area sky surveys have contributed strongly to the discovery of new obscured massive stellar clusters. Aims: We present the third article in a series of papers focused on young and massive clusters discovered in the VVV survey. This article is dedicated to the physical characterization of VVV CL086, using part of its OB-stellar population. Methods: We physically characterized the cluster using $JHK_S$ near-infrared photometry from ESO public survey VVV images, using the VVV-SkZ pipeline, and near-infrared $K$-band spectroscopy, following the methodology presented in the first article of the series. Results: Individual distances for two observed stars indicate that the cluster is located at the far edge of the Galactic bar. These stars, which are probable cluster members from the statistically field-star decontaminated CMD, have spectral types between O9 and B0V. According to our analysis, this young cluster ($1.0$ Myr $<$ age $< 5.0$ Myr) is located at a distance of $11^{+5}_{-6}$ kpc, and we estimate a lower limit for the cluster total mass of $(2.8^{+1.6}_{-1.4})\cdot10^3 {M}_{\odot}$. It is likely that the cluster contains even earlier and more massive stars.

The effects of structure anisotropy on lensing observables in an exact general relativistic setting for precision cosmology

The study of relativistic, higher order, and nonlinear effects has become necessary in recent years in the pursuit of precision cosmology. We develop and apply here a framework to study gravitational lensing in exact models in general relativity that are not restricted to homogeneity and isotropy, and where full nonlinearity and relativistic effects are thus naturally included. We apply the framework to a specific, anisotropic galaxy cluster model which is based on a modified NFW halo density profile and described by the Szekeres metric. We examine the effects of increasing levels of anisotropy in the galaxy cluster on lensing observables like the convergence and shear for various lensing geometries, finding a strong nonlinear response in both the convergence and shear for rays passing through anisotropic regions of the cluster. Deviation from the expected values in a spherically symmetric structure are asymmetric with respect to path direction and thus will persist as a statistical effect when averaged over some ensemble of such clusters. The resulting relative difference in various geometries can be as large as approximately 2%, 8%, and 24% in the measure of convergence (1−κ) for levels of anisotropy of 5%, 10%, and 15%, respectively, as a fraction of total cluster mass. For the total magnitude of shear, the relative difference can grow near the center of the structure to be as large as 15%, 32%, and 44% for the same levels of anisotropy, averaged over the two extreme geometries. The convergence is impacted most strongly for rays which pass in directions along the axis of maximum dipole anisotropy in the structure, while the shear is most strongly impacted for rays which pass in directions orthogonal to this axis, as expected. The rich features found in the lensing signal due to anisotropic substructure are nearly entirely lost when one treats the cluster in the traditional FLRW lensing framework. These effects due to anisotropic structures are thus likely to impact lensing measurements and must be fully examined in an era of precision cosmology.

CLASH-VLT: CONSTRAINTS ON THE DARK MATTER EQUATION OF STATE FROM ACCURATE MEASUREMENTS OF GALAXY CLUSTER MASS PROFILES

A pressureless scenario for the Dark Matter (DM) fluid is a widely adopted hypothesis, despite the absence of a direct observational evidence. According to general relativity, the total mass-energy content of a system shapes the gravitational potential well, but different test particles perceive this potential in different ways depending on their properties. Cluster galaxy velocities, being $\ll$c, depend solely on the gravitational potential, whereas photon trajectories reflect the contributions from the gravitational potential plus a relativistic-pressure term that depends on the cluster mass. We exploit this phenomenon to constrain the Equation of State (EoS) parameter of the fluid, primarily DM, contained in galaxy clusters. We use the complementary information provided by the kinematic and lensing mass profiles of the galaxy cluster MACS 1206.2-0847 at $z=0.44$, as obtained in an extensive imaging and spectroscopic campaign within the CLASH survey. The unprecedented high quality of our data-set and the properties of this cluster are well suited to determine the EoS parameter of the cluster fluid. Since baryons contribute at most $15\%$ to the total mass in clusters and their pressure is negligible, the EoS parameter we derive describes the behavior of the DM fluid. We obtain the most stringent constraint on the DM EoS parameter to date, $w=(p_r+2\,p_t)/(3\,c^2\rho)=0.00\pm0.15\mathrm{(stat)}\pm0.08\mathrm{(syst)}$, averaged over the radial range $0.5\,\mathrm{Mpc}\leq$$r$$\leq$$r_{200}$, where $p_r$ and $p_t$ are the radial and tangential pressure, and $\rho$ is the density. We plan to further improve our constraint by applying the same procedure to all clusters from the ongoing CLASH-VLT program.

The moment of core collapse in star clusters with a mass function

Star clusters with multi-mass components dynamically evolve faster than those modeled with equal-mass components. Using a series of direct $N$-body simulations, we investigate the dynamical evolution of star clusters with mass functions, especially their core collapse time. Multi-mass clusters tend to behave like systems with a smaller number of particles, which we call the effective number of particles ($N_{eff}$) and for which $N_{eff} = M/m_{max}$ (here $M$ and $m_{max}$ are the total cluster mass and the mass of the most massive star in the cluster, respectively). We find that the time of core collapse is inversely proportional to the mass of the most massive star in the cluster and analytically confirm that this is because the core collapse of clusters with a mass function proceeds on the dynamical friction timescale of the most massive stars. As the mass of the most massive star increases, however, the core-collapse time, which is observed as a core bounce of the cluster core from the evolution of the core density or core radius, becomes ambiguous. We find that in that case the total binding energy of the hard binaries gives a good diagnosis for determining the moment of core collapses. Based on the results of our simulations, we argue that the core bounce becomes ambiguous when the mass of the most massive star exceeds 0.1\% of the total mass of the cluster.

THE ACS SURVEY OF GLOBULAR CLUSTERS. XIII. PHOTOMETRIC CALIBRATION IN COMPARISON WITH STETSON STANDARDS

In this study we compare the photometric data of 34 Milky Way globular clusters, observed within the ACS Treasury Program (PI: Ata Sarajedini) with the corresponding ground-based data, provided by the Photometric Standard Field Catalogs of Stetson (2000, 2005). We focus on the transformation between the HST/ACS F606W to V-band and F814W to I-band only. The goal is to assess the validity of the filter transformation equations by Sirianni et al.(2005) with respect to their dependence on metallicity, Horizontal Branch morphology, mass and integrated (V-I) colour of the various globular clusters. Such a dependence is expected due to the fact that the transformation equations are based on the observations of only one globular cluster, i.e., NGC 2419. Surprisingly, the correlation between offset and metallicity is found to be weak, with a low level significance. The correlation between offset and Horizontal Branch structure, as well as total cluster mass is still weaker. Based on the available data we do not find the photometric offset to be linked to multiple stellar populations, e.g., as found in NGC 0288, NGC 1851, and NGC 5139. The results of this study show that there are small systematic offsets between the transformed ACS- and observed ground based photometry, and that these are only weakly correlated, if at all, with various cluster parameters and their underlying stellar populations. As a result, investigators wishing to transform globular cluster photometry from the Sirianni et al.(2005) ground-based V, I system onto the Stetson (2000) system simply need to add 0.040 (+/-0.012) to the V-band magnitudes and 0.047 (+/-0.011) to the I-band magnitudes. This in turn means that the transformed ACS (V-I) colours match the ground-based values from Stetson (2000) to within ~0.01 mag.

The MUSIC of galaxy clusters – II. X-ray global properties and scaling relations

We present the X-ray properties and scaling relations of a large sample of clusters extracted from the Marenostrum MUltidark SImulations of galaxy Clusters (MUSIC) dataset. We focus on a sub-sample of 179 clusters at redshift z~0.11, with 3.2e14M_sun/h<M_vir<2e15Msun/h, complete in mass. We employed the X-ray photon simulator PHOX to obtain synthetic Chandra Observations and derive observable-like global properties of the intracluster medium (ICM), as X-ray temperature (T_X) and luminosity (L_X). T_X is found to slightly under-estimate the true mass-weighted temperature, although tracing fairly well the cluster total mass. We also study the effects of T_X on scaling relations with cluster intrinsic properties: total (M_500) and gas (M_g500) mass; integrated Compton parameter (Y_SZ) of the Sunyaev-Zel'dovich (SZ) thermal effect; Y_X=M_g500 T_X. We confirm that Y_X is a very good mass proxy, with a scatter on M_500-Y_X and Y_SZ-Y_X lower than 5%. The study of scaling relations among X-ray, intrinsic and SZ properties indicates that MUSIC clusters reasonably resemble the self-similar prediction, especially for correlations involving T_X. The observational approach also allows for a more direct comparison with real clusters, from which we find deviations mainly due to the physical description of the ICM, affecting T_X and, particularly, L_X.