Stellar Modeling via the Tolman IV Solution: The Cases of the Massive Pulsar J0740+6620 and the HESS J1731-347 Compact Object

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Tolman solutions have been got by Tolman more than 80 years ago. Qualitatively the Tolman IV solution can describe compact object well. In the current paper the author refine the Tolman IV solution with specific solution expression. Especially three free parameters are introduced by assumption. In principle we can also introduce other kind of assumption to introduce a different specific solution expression. As a theoretical model of J0740+6620 and J1731-347, comparison between theoretical prediction and observation is wanted. Unfortunately all analysis presented in the current paper are pure theoretical prediction.

 

But anyhow the present paper is an interesting investigation based on GR of observed compact objects. It is also a usful reference for afterword research. According to this consideration, I suggest to accept the current paper for publication.

Author Response

Dear Editor,

I wish to thank the referee for a positive report. 

Sincerely,

The author

 

 

Reviewer 2 Report

Comments and Suggestions for Authors

This paper deals with the use of exact solutions to describe some astrophysical compact objects. The overall goal and conclusions are however unclear, and it is difficult to understand what the result is. The author mentions the use of exact solutions, without mentioning how, in general, the equations can be solved (and are generally solved) numerically for a microphsycial EoS. It can still be very useful to use exact solutions, as is e.g. the Toleman VII solution, which can also be used to interpret EoS independent results. The use of Toleman IV is not new to describe quark stars, and I do not understand what additional analysis is introduced in this manuscript, other than a fit to two particular objects. It is also unclear what to make of the initial discussion on non isotropic objects. In conclusion, I regret to say that this does not satisfy the requirements of novelty or interest, for publication.

Comments on the Quality of English Language

The paper is written in good English.

Author Response

Dear Editor,

I wish to thank the referee for taking the time to review the manuscript as well as for his/her feedback.

Finding exact analytic solutions to Einstein's field equations has always been interesting and at the same time challenging due to the complexity of the system of nonlinear coupled differential equations. As a matter of fact modeling of stars has kept scientists busy for decades. One must always bear in mind that an exact analytic solution per se does not say much, unless it is shown that it is a well behaved, realistic solution capable of describing astrophysical configurations. Although the Tolman IV solution was obtained a long time ago, the analysis performed here is not as trivial as it may look at first sight. To the best of our knowledge, in the present work recently observed astronomical objects of known stellar mass and radius are modeled via the Tolman solution, while at the same time it is demonstrated that all well established criteria for realistic solutions are met. Furthermore, a comparison has been made between the Tolman solution, which does not rely on any equation-of-state, and the numerical solution of the TOV equations assuming two analytic equations-of-state, namely the Extended Chaplygin Gas as well as the Color Flavor Locked equations-of-state.

Sincerely,

The author

Reviewer 3 Report

Comments and Suggestions for Authors

1. Why is the unphysical Kohler-Chao solution included in the paper? Was it known in advance to be inappropriate for the description of stellar interior in hydrostatic equilibrium ?

2. The method in which the unphysical Kohler-Chao solution was obtained is explicitly given in the paper. Why has the obtaining of the more physical solution used in the paper - the Tolman IV - not being presented? 

3. The formulas which described the radial dependence of Cs and Gamma are given for the in unphysical solution but not for the physical one. Why is this so? 

4. Gamma increases steeply as as r increases from 0 to 1. Does it remain finite at the surface? This has been only vaguely commented in the Conclusion but not in the body of the paper. 

5. The equation of state can be obtained in permetric form and in principle it could be studied in a future work, probably. (I expect only a brief comment here, not changes in the text)

6. The considerations given in Lines 204 to 207 are unclear. How were these plots produced and how do they compare to Figures 3 and 4? Plot them together so that one could compare.

Author Response

Dear Editor,

Please see the attachment.

Sincerely,

The author

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

I would like to thank the author for the sincere answer. The presentation has been improved significantly. My opinion is that the paper is interesting and can be published after minor revision. 

I have one more concern about the physical soundness of the solution. Divergent index Gamma seems unphysical. Is this problem shared by other interior solutions which are applied to model real objects? Can this problem be alleviated? A comment on this issue and a clear statement in the  Conclusion and the Abstract must be added. Currently, the Conclusion states that " the quantities of interest were found to be finite at the center of the star and at the same time smooth, continuous functions of the radial coordinate throughout the pulsar".

 

Author Response

Dear Editor,

Please see the attachement.

Sincerely,

Grigoris Panotopoulos

Author Response File: Author Response.pdf