fgas+paper

Referee Report
toc

Major comments:
(1) One of the main interests of the cluster community lies in extending such analysis to higher redshift clusters, in order to characterize the cluster gas evolution and to gain better leverage on cosmological parameters. It is therefore critical to demonstrate that the new model is applicable for interpreting high-z clusters (z>>0.3). I suggest the authors to include high-z clusters in this work to demonstrate the applicability of the model to higher-z systems (e.g., CL1226 at z=0.89 for which both X-ray and SZA data in Mroczkowski et al. 2009 might be useful).

(2) In the present text, it was unclear why the authors have selected A2631 and A2204 for this work. Please clarify the motivations for choosing these two clusters.

For example, I noticed in Figure 2 that A2631 and A2204 are non-cool core (NCC) and cool core (CC) clusters, respectively. This would be one good reason for selecting these two clusters.

I also noticed that there are even better X-ray and SZA data on A1835 (z=0.25) (Bulbul et al. 2010; Mroczkowski et al. 2009), in terms of the exposure time and dataset quality. It seems that A1835 would be a better testbed for the new model. Why not use A1914, A1835, and CL1226 instead or at least in addition?

(3) In Table 3, I recommend to report the best-fit Ysph, which is more robustly measured and interesting quantity than the central pressure normalization. It would then be useful to compare the best-fit Ysph values derived using the generalized NFW technique (Mroczkowski et al. 2009) for A1914, A1835, and CL1226. More generally and importantly, I would like to ask the authors to demonstrate how the new model improves upon the previous approach, in terms of determining the Ysph, Mgas, Mtot, and fgas profiles.

Note that the central pressure normalization is degenerate with other parameters including r_s, n, and beta. I suggest the authors to investigate the degeneracy among their model parameters in more details as well.

(4) The best-fit values of ne_0 and r_s for A2631 reported in Table 4 and 5 are strongly inconsistent. D_A measurements for A2631 is only marginally consistent with the LCDM value as well. Please comment on these offsets.

(5) The model assumes the polytropic gas at all radii. This is a strong assumption which have been called into question recently. For example, recent Chandra observations of nearby clusters provides the evidence against the polytropic model (Vikhlinin et al. 2006). Recent theoretical work further supports the idea that the polytropic index varies with radius, due to the radially-dependent non-thermal pressure (e.g., Lau et al. 2009, Battaglia et al. 2010; Shaw et al. 2010). This is what is responsible for the radially-dependent bias in the hydrostatic mass in Lau et al. (2009) discussed in Section 4.5.5, and the same effect will be a source of systematic bias associated with the present model. I suggest the authors to assess this effect and include it as part of the model assumption in Table 6.

(6) In Equation 11, the mean molecular weight depends on the assumed abundance. Please report the abundance model used in this work. The mean molecular weight also depends on the assumed He abundance in clusters. This could be additional sources of systematic uncertainties in the interpretation of X-ray data (Markevitch 2007, Peng & Nagai 2009), including X-ray derived pressure. I suggest to comment on the possible systematic uncertainty associated with this effect.

Minor comments:
(1) alpha, beta, gamma need to be defined. I recommend to elaborate on the analytical model and define key parameters more clearly.

(2) The best-fit values of ne_0 and r_s for A2631 reported in Table 4 and 5 are strongly inconsistent. D_A measurements for A2631 is only marginally consistent with the LCDM value as well. Please comment on these offsets.

(3) The best fit parameters from the X-ray analyses presented in Table 5 in the present work and Table 4 in Balbul et al. (2010) differ slightly, although the analyses were based on the same data and analyses techniques. Please clarify what has changed?

Major comments:
1 & 2. This paper demonstrates the joint analysis method on two clusters, A2631 and A2204. We chose a non-cool core cluster (A2631) and a cool core cluster (A2204) to demonstrate this method and validate the model, and clarify the motivation for selecting them in Section 2. The Bulbul et al. (2010) model accurately describes the X-ray data using the density and temperature profile as well as the SZ data using the pressure profile. For this methods paper we therefore limit our analysis to these two clusters; the analysis of the full sample of 25 clusters (including CL1226 and A2204) will published in a subsequent paper.

3. We now also report the value of Y(r500) in Table 3. Their ratio is the same as that of the normalization constants of the pressure, since in this analysis we linked the shape parameters (rs, n, and beta) allowing only the normalization parameters to vary (neo,Teo, and Peo) between the two datasets. This results in the X-ray and SZ pressure profiles to have the same shape, therefore the ratio of the SZ to X-ray pressure is constant at all radii. Bonamente et al. (2011) reports the Ysph values for a sample of 25 relaxed clusters (including A2204, CL1226, and A1835) using the Bulbul et al. (2010) and Arnaud et al. (2009) models.

In the introduction we now explain the difference between our method for measuring masses versus the Mroczkowski et. al 2009 approach as well as the models used in the analysis.

We discuss degeneracy among parameters in Section 3, and explain that we use a singular-value decomposition (SVD) method to reduce the effects of parameter correlation, and improve computational time. We also added an Appendix with further details on parameter correlations and the SVD method.

4. The Abell 2631 joint chain was not fully converged. We re-ran the chain and confirmed that the parameters are now converged. Table 4 and Figure 4 has been updated to reflect the changes. We find better agreement between the parameters r_s, n, beta, and Tx0 in Tables 4 and 5. The parameter neo in Table 4 is not identical to that in Table 5 because D_A is allowed to vary in the joint analysis and the parameters neo and D_A are anti-correlated; this is a known feature when D_A is allowed to vary in the analysis.

The measurement of the angular diameter distance for a given cluster is affected by a number of systematic effects (Bonamente et al. 2006), and the agreement of D_A with the LCDM value is expected for a large sample but not necessarily for individual clusters, although we now find agreement with the LCDM model for both clusters. This explanation has now been added to Section 4.2.

5. The model assumes polytropic at large radii, but this polytropic relation is modified in the cluster core. To determine the systematic effect associated with assuming a polytropic relationship at large radii, we compared our X-ray masses with those calculated using the Vikhlinin et al. (2006) model. From this comparison, we found that the gas mass fraction varies by 10%. Section 4.5.7 discusses the polytropic assumption at large radii.

6. We report the abundance model used in the analysis after Equation 11. We also added a section (4.5.8) discussing the systematic uncertainties associated with helium sedimentation.

Minor comments:
1. All parameters are clearly defined in Section 3.

2. See comment #4.

3. Bulbul et al. (2010) uses a different calibration software, CALDB4.1.1 whereas we use CALDB4.3. The new calibration results in a different measurement of the temperature profile in the clusters and therefore different measurements of the masses.