Review Reports

Round 1

Reviewer 1 Report (Previous Reviewer 2)

Comments and Suggestions for Authors

 Review of "The Shock Cone Instabilities and QPOs around the Hartle-Thorne Black Hole"

 

Abstract: much better written than previous version.

 

Introduction:

Bondi-Hoyle-Lyttleton (BHL) accretion is now introduced.

Hartle-Thorne black holes are now explained and references given.

 

Section 2.3: EGB gravity is now explained with references.

 

Section 4: the comment added about the Hartle-Thorne solution is helpful to physically distinguish it from Kerr solution.

 

Figure 1: last line of caption: Please change description: the influence of q is moderate (not strong) with change in density of ~136 to ~93 for q=0 to 5. Does q in the figure label mean q/M^3? if yes please change the figure label. Similarly for Fig.2 left and following figures. 

 

Section 4.3: the description is much improved.

 

Section 5.3: why is rapidly spinning Hartle-Thorne BH not possible (explain or give reference)?

 

Fig. 9: "Same as Fig.4.3 but for a/M=0.9" please correct the figure number reference (it is not 4.3)

 

page 16: "and causes a greater suppression of contour lines." it is not clear what you mean here; I think you mean smaller density, please explain clearly.

 

Author Response

The file is attached.

Author Response File: Author Response.pdf

Reviewer 2 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

The authors have corrected some parts of the manuscript previously

in response to my former review report. Especially it is appropriate

that the authors agree that the flow they study is not a disk flow.

 

Still it seems there are several points to be reconsidered in the

current version of the paper.

 

1. I still do not understand why the spacetime of "Hartle-Thorne gravity"

is mentioned as "black hole". Does it have an event horizon? Otherwise,

the solution contains a naked singularity and should not be called a

black hole.

 

2. I have suggested that vector arrows of fluid velocity should be plotted

to show clearly the structure of the flow. I think it would help reader to

understand the structure of accretion flow. I strongly recommend the

author to produce the plots.

 

3. The authors show figures of PSD and identified characteristic frequencies.

It seems that not all of the 'peaks' in PSD are identified as eigenmodes.

Why are some of the apparent peaks not identified as modes? How do they 

identify the frequencies? The authors should describe what are 

their criteria for the identification.

Author Response

The file is attached.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

Since the authors have responded appropriately to my former questions and made corrections to the manuscript, I now recommend the paper be accepted for publication.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In the current manuscript, the authors report their hydrodynamical simulations of accretion flows in several different metric theories of gravity, which are intended to contrast the differences in flow structure and their oscillations. Although it may have the potential to discriminate the theories of gravity, I found the presentation in the current version of the manuscript is not mature enough to be accepted for publication. Most importantly, I would point out that the authors may misunderstand the three-dimensional flow structures they study.

This is noticed in the right panels of Fig.3 and Fig.7.  From this plot of v^\phi, we see that this flow seems not circular (in the sense that the angular velocity is unidirectional),  but it converges to the shock cone which lies near \phi=0. Seemingly it is not a disk flow. However, the authors refer to "disk" everywhere  in the manuscript (actually, they have the word "disk" in the title of the manuscript). Are the authors sure that they see disk flow in the current study? I would suggest the authors make a velocity field plot overlayed in Fig.1 and Fig.13. Also, it would be helpful to make a density and velocity plot in the plane perpendicular to the equatorial plane, so that they grasp the three-dimensional structure of the flow.

 

As for the theories of gravity they compare, I found little description is provided in the manuscript, therefore a reader may have trouble in following the results. About the Hartle-Thorne metric (Eq.(1)). Is it an (approximate) solution of the vacuum Einstein equation, or a solution of some kind of gravity theory? It seems the solution has an angular momentum parameter a(=J/M^2) and a quadrupole q(=Q/M^3) as two independent parameters. If that is a solution of the vacuum Einstein equation, it is generally not a black hole, since from the no-hair theorem, a solution with q(=Q/M^3) parameter other than that of Kerr BH (q=(a/m)^2) has a naked singularity. Or is it a solution of some sort of modified gravity theory, whose vacuum solution admits a- and q- parameters to be independently specified? It seems very little background on this metric is provided in the current manuscript and a reader would expect more details on what this metric is. Also, Einstein-Gauss-Bonnet gravity is little explained in the manuscript. Some of the readers of the journal (including myself) are not familiar with the theory. It would be helpful to introduce the theory by stressing its difference from the Einstein's General Relativity.

 

Comments on the Quality of English Language

I have noticed many, though not serious, errors in English. I would suggest the authors use a service to check grammatical errors in the manuscript. As an example, let me just point out some of the errors in the abstract. In square brackets '[ ]', I have made corrections. The vacant bracket means the word preceding it should be omitted.

"In order to explain the observed X-ray data in [a] black hole-disk system and understand the physical mechanics behind QPOs are important attempt[attempts] to unraveling[unravel] the mystery of the universe. In this paper, we are[] numerically revealed the dynamical and oscillation properties of the shock cone formed around the slowly and fastly rotating Hartle-Thorne black hole as a result of Bondi-Hoyle-Lyttleton (BHL). According to the numerical simulations, it is found that the increase of the quadrupole parameter (q/M^3) causes in[] the decreasing[decrease] of the shock cone opening angle around the black hole. q/M^3 is the[] one of the parameter[parameters] which alters the geometry around the black hole. The bigger the quadrupole parameter causes the more matter falling[falls] into black hole[the black hole] within the cone. The effect of the quadrupole parameter along with black hole rotation have[has] caused the matter inside the cone to exhibit chaotic motion. The dynamical changes and chaotic behavior of the shock cones have excited the fundamental oscillation modes. On the other hand, new frequencies have also been formed due to [the] nonlinear coupling of the fundamental modes. Conversely, we have numerically studied the behavior of cones formed around fastly rotating Hartle-Thorne black holes and showed similarities to those obtained from slowly rotating cases. It is believed that it is theoretically impossible but producing numerical result[results] for rapidly rotating Hartle-Thorne black holes would contribute [to] the literature and opening[open] a new discussion area. Finally, The comparison between the results from the Hartle-Thorne models and Kerr and EGB gravities has been made to reveal the impact of the quadrupole parameter on the shock cone and QPOs."

 

Author Response

In accordance with the suggestions and criticisms made by the reviewers, significant changes have
been highlighted in red throughout the manuscript. Additionally, detailed responses have been provided
separately for each reviewer’s reports. Summarizing the changes made in the article under general headings:

1) A comprehensive grammar check was conducted, and substantial corrections were made. Some sections
were rewritten.
2) Situations leading to misunderstandings, such as ’Disk,’ were corrected.
3) Figures 5 and 9 were redrawn and explanations were provided to understand whether the QPOs are persistent/
transient.
4) PSD plots in Figures 10, 11, 12, and 14 were redrawn.
5) Table 1 was updated to indicate the time each model reaches a steady state.
6) Detailed clarifications requested by the reviewers were provided.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

 Review of "Disk Instabilities and QPOs around the Hartle-Thorne Black Holes"

 

Generally, needs editing of English grammar, especially the abstract.

The calculations look to be done very well.

 

Abstract:

 

Line 8-9 sentence does not make sense: 

"In order to explain the observed X−ray data in black hole-disk system and understand the 

physical mechanics behind QPOs" is OK. The rest "are important attempt to unraveling the mystery of the universe" is not sensible and should be removed; instead start the sentence with something like: "We report work done in order to". 

 

Line 10-12 sentence does not make sense: suggest rewrite

"In this paper, we  calculate dynamical and oscillation properties of the shock cone formed around both slowly and rapidly rotating Hartle-Thorne black holes as a result of Bondi-Hoyle-Lyttleton (BHL) accretion."

 

line 13: replace "causes in the decreasing of" by "decreases"

 

line 14: omit "q/M3 is the one of the parameter which alters the geometry around the black hole." (it is obvious)

 

line 15: "The  bigger the quadrupole parameter causes the more matter falling into black hole within the cone."

replace by: "A larger quadrupole parameter causes more matter falling into black hole within the cone."

 

line 16: "The effect of the quadrupole parameter along with black hole rotation have caused the matter inside the 

cone to exhibit chaotic motion." Not correct, as shown in Fig.10,11,12 here. Omit.

 

Line 17: "The dynamical changes and chaotic behavior of the shock cones have excited the fundamental oscillation modes." rewrite: the authors demonstrate changes in dM/dt do this, not shock cones.

 

line 18: "On the other hand, new frequencies have also been formed due to nonlinear coupling of the fundamental modes."

This remains to be demonstrated, see comment on Fig.5 in general comments.

 

line 19-20: " Conversely, we have numerically studied the behavior of cones formed around fastly rotating Hartle-Thorne black holes and showed similarities to those obtained from slowly rotating cases. "

The authors are referring to Fig.2 through 8. What similarities? Do you mean accretion cone angle, v_r, v_phi? dM/dt looks very different.

 

line 21-22: "It is believed that it is theoretically impossible but producing numerical result for rapidly rotating Hartle-Thorne black holes would contribute the literature and opening a new discussion area."

Please omit this general remark, it does not describe results here.

 

line 23-23: "Finally, The comparison between the results from the Hartle-Thorne models and Kerr and EGB gravities has been made to reveal the impact of the quadrupole parameter on the shock cone and QPOs." 

The authors are referring to Fig.10,11,12 for Kerr and EGB to Fig.2 through 9 for Hartle-Thorne case, but quadrupole parameter applies only to Hartle-Thorne case, so this sentence doesn't make sense. Need to replace with a correct statement.

 

For introduction:

 

Mentioned in abstract: need brief description (and a reference) to explain Hartle-Thorne black hole

Need brief description (and a reference) to explain the term Bondi-Hoyle-Lyttleton (BHL) (here, rather than at start of section 3).

 

Please explain how a Hartle-Thorne black hole is more general than the Kerr Black hole (and give a reference).

 

line 98 need to explain here briefly what is an EGB black hole

 

line 147: "unlike in Kerr gravity" what is Kerr gravity? do you mean General Relativity?

 

line 150: "higher curvature" I think you mean adding terms that are higher order in curvature than for GR.

 

line 174: Do you mean axially symmetric (r, phi, with no theta dependence) or do you mean in 2-D spacetime with 2_D hydro? I think the former.

 

line 235: I think Hartle-Thorne is only useful if there is significant mass exterior to the BH, please explain.

 

Fig.1: to my eye these all look the same but you state the influence of q is clearly visible (not true)

 

Fig.5 and Fig.9: describe how power spectrum was taken: did you omit the initial transient period (shown in Fig.4 right)?; did you split your simulation into 2 halfs and compare power spectrum of each half to verify that some frequencies are persistent/others transient?

 

Fig.13: to my eye these all look the same but you state the influence of q is clearly visible (not true)

 

Discussion and conclusion: these may need to be rewritten after the above corrections are done.

 

Comments on the Quality of English Language

These are included in the above report.

Author Response

In accordance with the suggestions and criticisms made by the reviewers, significant changes have
been highlighted in red throughout the manuscript. Additionally, detailed responses have been provided
separately for each reviewer’s reports. Summarizing the changes made in the article under general headings:

1) A comprehensive grammar check was conducted, and substantial corrections were made. Some sections
were rewritten.
2) Situations leading to misunderstandings, such as ’Disk,’ were corrected.
3) Figures 5 and 9 were redrawn and explanations were provided to understand whether the QPOs are persistent/
transient.
4) PSD plots in Figures 10, 11, 12, and 14 were redrawn.
5) Table 1 was updated to indicate the time each model reaches a steady state.
6) Detailed clarifications requested by the reviewers were provided.

Author Response File: Author Response.pdf