Gas+Mass+Fraction+for+the+Dahle-BCS+sample+from+X-ray+Observations

Cluster Sample
David Landry is calculating masses for all of the Dahle clusters, using both Polytropic and Vikhlinin models. The Dahle (2006) sample is made up of 34 of the brightest (//L// X,0.1-2.4keV > 6x10 44 erg/s) clusters taken from the BCS in the redshift range 0.15 < //z// < 0.30. The sample is about 90% complete and has X-ray, SZ, and weak lensing data available. The cooling times have been calculated for the clusters in which we calculated masses and 3 Gyr was chosen as the cutoff for a cool-core cluster.



Mass Calculations
One method used to determine the mass of a cluster is by using the hot gas as tracer of gravitational potential, assuming hydrostatic equilibrium between the gas and dark matter (Sarazin 1988). Hydrostatic equilibrium (HSE) is given by the following equation:



Using the equation for HSE along with the equation of state for an ideal gas, the total mass of the cluster can be obtained by



and the mass of the gas is calculated by



Vikhlinin Model
The models used to describe the density and temperature profiles of the hot plasma in clusters is the Vikhlinin et al. (2006) model and the Bulbul et al. (2010) model (Polytropic). The Vikhlinin model is modeled as a generalization of the //β//-model and is given by



which uses a total of ten free parameters. These parameters are correlated and their values are degenerate. The Vikhlinin temperature profile is given by the phenomenological function



which has nine free parameters and can model nearly any smooth temperature distribution. The second term in the temperature profile describes the region outside of the cool-core as a broken power law with a transition region. Therefore, the Vikhlinin model has a total of 19 free parameters.

Polytropic Model
The Bulbul et al. (2010) model gives analytic functions for temperature, density, and gas pressure, assuming a polytropic equation of state. The poly temperature profile is given by



where //τ cool //is

has been adopted from Vikhlinin et al. (2006) that measures the amount of central cooling. The first term in parentheses is derived from analytically integrating the gravitational potential and assuming the gas is in hydrostatic equilibrium. With this temperature profile, the gas density profile can be determined from the polytropic equation of state. This yields



which has a total of 8 free parameters.

Radial Profile of fgas
The gas mass fraction is defined as //f// gas =//M// gas ///M// total, where //M// gas is the mass of the hot gas. Many of the previous studies of the gas mass fraction provided measurements only out to small radii and indicated that fgas is constant with radius (LaRoque et al. 2006; Allen et al. 2008). A study by Vikhlinin et al. (2006), on the other hand, reports that fgas actually increases with radius. Given that there is no consensus on the radial distribution of fgas, or its value at large radii, at present we do not know whether the baryon content of clusters really tracks the cosmic baryonic fraction. My goal is to measure the radial profile of fgas(r) to large radii and determine whether the cluster baryon fraction is equal to //Ω b /////Ω M //.

I have measured the gas mass fraction at r500 for all 15 of the cool-core clusters in the BCS/Dahle sample and found that fgas increases with radius. The figure below shows the distribution of fgas as a function of r500 using the Vikhlinin model. This plot shows the median fgas value at r/r500=0.1,0.2,0.3,...,1.0. I fit the average fgas profile using linear regression and using the equation //y//=//a//+//bx//, the best fit parameters are given by //a//=0.068+-0.003 and //b//=0.075+-0.004. Note: Correlation has not been taken into account.



Plots showing the radial profile of the gas mass fraction for each individual cluster using the Vikhlinin model can be found here: fgas profiles.

Model Comparison of X-ray Masses using models by Vikhlinin et al. (2006) and Bulbul et al. (2010)
More information about the model comparison can be found at model comparison.

Fits to X-ray Data
An example of the fit to the temperature and surface brightness profile using both models is given below





To see more plots showing fits to the data and a table with masses, please go here: model comparison

Here are some plots showing the model comparison between the Vikhlinin and Poly model. Red shows measurements at r2500 and blue is at r500.



The weighted averages for both models are given below (note: errors are statistical only):

fgas:
 * Weighted average at r2500: [[image:Fgas_r2500.jpg]]


 * Weighted average at r500: [[image:Fgas_r500.jpg]]

At r2500, the two models are consistent at the 4-//σ// level and there is a 10% systematic uncertainty between the two models.

At r500, the two models are consistent at the 1-//σ// level. Since both models are statistically consistent at r500, then there is no evidence for a systematic difference between them at large radii.

Ysph-Mtot
Below is a plot showing the Ysph-Mtot scaling relation for 15 clusters at r500. The red data points correspond to the Poly model and the blue data points correspond to the Vikhlinin model. Previous results from Nagai (2006), Arnaud et al. (2010), Andersson et al. (2010), and Marrone et al. (2010) using the "free slope" for all clusters and "self-similar" slope for undisturbed clusters are also shown. The slopes of each line are given by //B//. These are taken from the following equation:



Here is the Ysph-Mtot plot for 15 clusters at r500.



Pressure Profiles
The study of pressure profiles of clusters scaled by mass has been limited. The gravitational potential of a cluster is related to the gas pressure and this pressure can provide information about the intracluster medium. Using the ideal gas law, the pressure can be measured from the density and temperature obtained through X-ray observations. Here is a plot showing the pressure as a function of radius. This is only for five clusters and has not been scaled by mass. The red lines are the pressure profiles obtained from the Poly model and the blue lines are from the Vikhlinin model. We want to get the average pressure profile scaled by mass for all the cool-core clusters and compare our average pressure profile with Arnaud et al. (2010).