Halo Concentrations and the Fundamental Plane of Galaxy Clusters
, Megan Donahue 2, Stefano Ettori 3,4, Keiichi Umetsu 5, Elena Rasia 6, Massimo Meneghetti 3,4, Elinor Medezinski 7, Nobuhiro Okabe 8 and Marc Postman 9Round 1
Reviewer 1 Report
This paper represents a substantial step forward in confirming the existence of a fundamental parameter plane for galaxy clusters. It is excellent work and is well presented an clear. However it is very similar to their earlier paper "Discovery of a New Fundamental Plane Dictating Galaxy Cluster Evolution from Gravitational Lensing" (reference 23). This being the case I think they should include a statement in the introduction which indicates how this present paper extends that earlier work and what new insights it will provide, for example could be to include in the introduction an explanation of how they will show in the present work how the mass-temperature relation of clusters and the concentration-mas relation can be explained without assuming virialization. It's in the abstract but given the similarity of the papers, I think it is important for the reader to be made aware in the introduction of the new material to be presented.
On a more trivial note, in line 11 page 2, I think the sentence would read better as "Another commonly defined characteristic radius of clusters is that based on the critical density..."
Also, the use of the word "rather" on line 6, page 6 (my line numbers disappeared after page 4!) is a little awkward and the sentence could be rephrased.
Author Response
Our answers are written in ans_report1.pdf.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This article reviews interesting recent discovery of a new fundamental plane of galaxy cluster observables rs, Ms and Tx. The small scatter of the data around the discovered fundamental plane and the excellent match with simulation results are remarkable.
I have two main concerns about the scientific results:
(1) there is no mentioning of the errors associated with the determination of rs, Ms and Tx, nor the possible assumptions involved. This is especially a concern for the lensing-determined rs and Ms - how accurate are they? are they correlated?
(2) I personally find the similarity solution interpretation of the discovered fundamental plane not very convincing, mainly for two reasons. First, the physics leading to the existence of the character radius rs is not even included in the similarity solution. Second, the rho (gas density) ~ Ms / rs^3 relation assumed in the derivation of Eq (9) is very hand-waving.
Additionally, there is misusage of the term 'Virial theorem' in two places:
- Fig 2: It is Okay to present a comparison with the dimensional analysis Tx ~ Ms / rs, but it is not very proper to call it 'Virial theorem'. Even in the traditional misused concept of 'Virial theorem' for intracluster gas, Tx ~ Mvir / rvir rather than Ms / rs, and the difference between these two relations involves the concentration parameter, which is mass dependent.
- Page 7 "The similarity solution indicates that clusters are not in virial equilibrium": the Virial theorem defined as 2K + W =0 is not at all applicable to the intracluster gas. The correspondence of the Virial theorem for the intracluster gas is just the hydrostatic equilibrium (HSE) condition, as both HSE and Virial theorem result from the corresponding Euler equations.
Other suggestions:
(1) Could you please provide a mathematical description of the observational fundamental plane like Eq (9)?
(2) There should better be some description of all simulations used. Those for FB0 and FB1 are missing.
(3) Page 2, 2nd line, FB1 is for z=1 (instead of z=0)
Author Response
Our answers are written in ans_report2.pdf.
Author Response File: Author Response.pdf
