Mass Estimation of Merging Galaxy Clusters

We investigate the impact of mergers on the mass estimation of galaxy clusters using $N$-body + hydrodynamical simulation data. We estimate virial mass from these data and compare it with real mass. When the smaller subcluster's mass is larger than a quarter of that of the larger one, virial mass can be larger than twice of the real mass. The results strongly depend on the observational directions, because of anisotropic velocity distribution of the member galaxies. We also make the X-ray surface brightness and spectroscopic-like temperature maps from the simulation data. The mass profile is estimated from these data on the assumption of hydrostatic equilibrium. In general, mass estimation with X-ray data gives us better results than virial mass estimation. The dependence upon observational directions is weaker than in case of virial mass estimation. When the system is observed along the collision axis, the projected mass tends to be underestimated. This fact should be noted especially when the virial and/or X-ray mass are compared with gravitational lensing results.Comment: 21 pages, 13 figures, accepted for publication in PAS

Precision cluster mass determination from weak lensing

Weak gravitational lensing has been used extensively in the past decade to constrain the masses of galaxy clusters, and is the most promising observational technique for providing the mass calibration necessary for precision cosmology with clusters. There are several challenges in estimating cluster masses, particularly (a) the sensitivity to astrophysical effects and observational systematics that modify the signal relative to the theoretical expectations, and (b) biases that can arise due to assumptions in the mass estimation method, such as the assumed radial profile of the cluster. All of these challenges are more problematic in the inner regions of the cluster, suggesting that their influence would ideally be suppressed for the purpose of mass estimation. However, at any given radius the differential surface density measured by lensing is sensitive to all mass within that radius, and the corrupted signal from the inner parts is spread out to all scales. We develop a new statistic that is ideal for estimation of cluster masses because it completely eliminates mass contributions below a chosen scale (which we suggest should be about 20 per cent of the virial radius), and thus reduces sensitivity to systematic and astrophysical effects. We use simulated and analytical profiles to quantify systematic biases on the estimated masses for several standard methods of mass estimation, finding that these can lead to significant mass biases that range from ten to over fifty per cent. The mass uncertainties when using our new statistic are reduced by up to a factor of ten relative to the standard methods, while only moderately increasing the statistical errors. This new method of mass estimation will enable a higher level of precision in future science work with weak lensing mass estimates for galaxy clusters.Comment: 27 pages, 7 figures, submitted to MNRAS; v2 has expanded explanation for clarity, no change in results or conclusion

Cluster mass estimation through Fair Galaxies

We analyse a catalogue of simulated clusters within the theoretical framework of the Spherical Collapse Model (SCM), and demonstrate that the relation between the infall velocity of member galaxies and the cluster matter overdensity can be used to estimate the mass profile of clusters, even though we do not know the full dynamics of all the member galaxies. In fact, we are able to identify a limited subset of member galaxies, the 'fair galaxies', which are suitable for this purpose. The fair galaxies are identified within a particular region of the galaxy distribution in the redshift (line-of-sight velocity versus sky-plane distance from the cluster centre). This 'fair region' is unambiguously defined through statistical and geometrical assumptions based on the SCM. These results are used to develop a new technique for estimating the mass profiles of observed clusters and subsequently their masses. We tested our technique on a sample of simulated clusters; the mass profiles estimates are proved to be efficient from 1 up to 7 virialization radii, within a typical uncertainty factor of 1.5, for more than 90 per cent of the clusters considered. Moreover, as an example, we used our technique to estimate the mass profiles and the masses of some observed clusters of the Cluster Infall Regions in the Sloan Digital Sky Survey catalogue. The technique is shown to be reliable also when it is applied to sparse populated clusters. These characteristics make our technique suitable to be used in clusters of large observational catalogues.Comment: 11 pages, 11 figures, 5 tables - Slightly revised to match the version published on MNRAS; abstract update

Cluster mass estimation from lens magnification

The mass of a cluster of galaxies can be estimated from its lens magnification, which can be determined from the variation in number counts of background galaxies. In order to derive the mass one needs to make assumptions for the lens shear, which is unknown from the variation in number counts alone. Furthermore, one needs to go beyond the weak lensing (linear) approximation as most of the observational data is concentrated in the central parts of clusters, where the lensing is strong. By studying the lensing properties of a complete catalogue of galaxy cluster models, one can find reasonable approximations about the lens shear as a function of the lens convergence. We show that using these approximations one can fairly well reconstruct the surface mass distribution from the magnification alone.Comment: 4 pages including 1 figure, LaTex, using sprocl.sty (included), To appear in proceedings "Large Scale Structure: tracks and traces", Potsdam 1997, World Scientifi

Parameter estimation of coalescing supermassive black hole binaries with LISA

Laser Interferometer Space Antenna (LISA) will routinely observe coalescences of supermassive black hole (BH) binaries up to very high redshifts. LISA can measure mass parameters of such coalescences to a relative accuracy of $10^{-4}-10^{-6}$, for sources at a distance of 3 Gpc. The problem of parameter estimation of massive nonspinning binary black holes using post-Newtonian (PN) phasing formula is studied in the context of LISA. Specifically, the performance of the 3.5PN templates is contrasted against its 2PN counterpart using a waveform which is averaged over the LISA pattern functions. The improvement due to the higher order corrections to the phasing formula is examined by calculating the errors in the estimation of mass parameters at each order. The estimation of the mass parameters ${\cal M}$ and $\eta$ are significantly enhanced by using the 3.5PN waveform instead of the 2PN one. For an equal mass binary of $2\times10^6M_\odot$ at a luminosity distance of 3 Gpc, the improvement in chirp mass is $\sim 11$ and that of $\eta$ is $\sim 39$. Estimation of coalescence time $t_c$ worsens by 43%. The improvement is larger for the unequal mass binary mergers. These results are compared to the ones obtained using a non-pattern averaged waveform. The errors depend very much on the location and orientation of the source and general conclusions cannot be drawn without performing Monte Carlo simulations. Finally the effect of the choice of the lower frequency cut-off for LISA on the parameter estimation is studied.Comment: 12 pages, 5 figures (eps) significant revision, accepted for publication in Phys. Rev. D. Matches with the published versio

Using member galaxy luminosities as halo mass proxies of galaxy groups

Reliable halo mass estimation for a given galaxy system plays an important role both in cosmology and galaxy formation studies. Here we set out to find the way that can improve the halo mass estimation for those galaxy systems with limited brightest member galaxies been observed. Using four mock galaxy samples constructed from semi-analytical formation models, the subhalo abundance matching method and the conditional luminosity functions, respectively, we find that the luminosity gap between the brightest and the subsequent brightest member galaxies in a halo (group) can be used to significantly reduce the scatter in the halo mass estimation based on the luminosity of the brightest galaxy alone. Tests show that these corrections can significantly reduce the scatter in the halo mass estimations by $\sim 50\%$ to $\sim 70\%$ in massive halos depending on which member galaxies are considered. Comparing to the traditional ranking method, we find that this method works better for groups with less than five members, or in observations with very bright magnitude cut.Comment: ApJ accepte