A Model for the Accretion Disk of Hercules X-1 from 35-Day Cycle Lightcurves
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors constructed a 3D disk+corona model of Her X-1. They extended their original model, which was based on MAXI observations, by incorporating Swift/BAT data and compared the results. Their methods and results are clearly presented, and the paper is suitable for publication.
I only have minor comments.
- Page 3 line 87: We note than -> We note that
- Page 4 line 131: "30 minutes to run" If possible, provide details about the machine or computing environment used to perform the runs.
- Page 5 line 153: several several energy bands -> several energy bands
- Page 5 line 182
- The disk is required to have to an atmosphere -> The disk is required to have an atmosphere
- gradient rise to and fall -> gradient rise and fall
- Main Heigh state whis is observed -> Main Heigh state which is observed
Author Response
Authors response to the report by reviewer 1. Reviewers comments are in " ", followed by our responses.
"The authors constructed a 3D disk+corona model of Her X-1. They extended their original model, which was based on MAXI observations, by incorporating Swift/BAT data and compared the results. Their methods and results are clearly presented, and the paper is suitable for publication.
I only have minor comments."
"Page 3 line 87: We note than -> We note that"
The correction has been made.
"Page 4 line 131: "30 minutes to run" If possible, provide details about the machine or computing environment used to perform the runs."
This has been added as a footnote.
"Page 5 line 153: several several energy bands -> several energy bands"
The correction has been made.
"Page 5 line 182
The disk is required to have to an atmosphere -> The disk is required to have an atmosphere
gradient rise to and fall -> gradient rise and fall
Main Heigh state whis is observed -> Main Heigh state which is observed"
These corrections have been made.
Reviewer 2 Report
Comments and Suggestions for AuthorsSee attached file.
Comments for author File: 
Comments.pdf
Author Response
Authors response to the report by reviewer 2. Reviewers comments are in " ", followed by our responses.
"Review of Her X-1 paper by Leahy & Frost
This paper performs a comprehensive investigation of the parameters describing the accretion
disk and corona in the famous Hercules X-1 neutron star binary. The first author has written
many previous papers on this system and this paper is an interesting and clearly useful
improvement on the model presented most recently in Leahy & Mendelsohn (2025), thanks to
incorporation here of data from both the Swift/BAT and MAXI instruments. The modeling used
the Shape code to examine many possible parameters for both a twisted disk and a corona in
order to yield the best values of both direct and scattered emission in matching the overall 35
day X-ray brightness cycle.
The data, procedure, and results were all described clearly and the conclusions certainly
appear to be sound. Fundamentally, the results and conclusions are similar to earlier studies
but this paper produces more precise values for the inclination angle, masses of the neutron
star and companion as well as the companion radius because two complementary sets of
observations were fit in conjunction.
This approach and results are important and in this reviewer’s opinion, this paper should be
published in essentially the current form. All the minor corrections of typos and a couple of
comments given below can be dealt with easily."
The response to each comment below is given, and the text marked in boldface.
"line 17: … eachother…. Should be … each other."
this is corrected
"line 35: … a significant to the … Presumably is: … a significant contribution to the … but
maybe some other word is missing"
The word contribution has been inserted.
"line 41: … carried by [9]…. should be … carried out by [9]."
this is corrected
"line 81: … Figure 2 show the … should be … Figure 2 shows the …"
this is corrected
"line 83: scale should be scaled"
this is corrected
"line 149: … has low ionization … should be … has a low ionization …"
this is corrected
"line 183: … state whis is … … should be … state which is …"
this is corrected
"It would be nice if ($\alpha_{cor}$) was added following the BAT and MAXI Corona Powerlaw
Index parameter names in Table 1."
this has been done
"line 241: … obtained the … should be … obtained using the … OR … obtained via the …"
this is corrected
"line 245: …. Their … should be …. There …"
this is corrected
"line 251: … softness ration…. should be … softness ratio…."
this is corrected
"line 274: … (r) that … should be … (r), that …"
this is corrected
"line 306: … errors bars.… should be … error bars…."
this is corrected
"line 308: … for far … should be … for a far …"
this is corrected
"line 332: … center of mas of … should be … center of mass of …"
this is corrected
"line 333: The units of $a_x$ should be specified".
This has been added (light-s).
"line 363: … region, and … should be … regions, and …"
this is corrected.
We thank the referee for pointing out these various corrections.
Reviewer 3 Report
Comments and Suggestions for AuthorsThis paper studies the 35-day average lightcurves of Her X-1 are from Swift/BAT observations and from observations, and then shows a model to fit the curves, which can constrain the binary parameters. This work is still interesting for the super-orbital curve origin and accreting neutron star properties. Before the publication, some problems should be resolved. Some comments are shown below.
Main issues:
1) In the present version, the innovation of this work is not so clear for me. The paper is very similar to the previous work by the similar authors, then what are the significant change and improvements by this work? The authors should claim them more clearly. The same model and same source, same light curves, would make this work less scientific implication.
2) Fig 1 shows the light curves of two detectors, and also hardness ratio with two different mission. I think that the hardness ratio would be more important compared with the light curves in this work. Anyway, in the present plots, they are not clear or correct. First, the direct ratio by two different missions may not so suitable. Second, if you have the reasons that the ratio is ok, then you should improve the plots, like how to reduce some plots with small errors. I would like to see the spectral evolution of the source with the 35-day circle.
3) Then would the present model explain the possible spectral evolution of Her X-1 over the 35-day circle, like with the software SHAPE? Some previous RXTE results have show the spectral variation during the Main High State.
4) There are no any detailed (mathematical and logical ) description of the model, so it is a little difficult to read the parts of the model and methods. The authors can improve these parts.
5) line 44, you state that a warped accretion disk is required to be present in Her X-1. Is it correct or confirmed by all research work? In a work by IXPE, e.g., Heyl et al. 2024, NA, they suggest the magnetic pole precession would lead to the 35-day circle, and they donot need the warped disk. The authors may confirm their statement or update some physical scenario.
There are some typos and grammar errors, the authors should check them in the revised version. Here I show some examples:
line 17: are consistent with eachother
line 23: This results is significantly improved binary system parameters
line 28: the first paragraph. In addition, you may give more intrducion to the source Her X-1, so the paragraph can be extended.
line 35: there is a significant to the cycle by X-rays scattered from near the inner part of the accretion disk
......
The authors can examine the whole paper.
Author Response
Authors response to the report by reviewer 3. Reviewers comments are in " ", followed by our responses.
"This paper studies the 35-day average lightcurves of Her X-1 are from Swift/BAT observations and from observations, and then shows a model to fit the curves, which can constrain the binary parameters. This work is still interesting for the super-orbital curve origin and accreting neutron star properties. Before the publication, some problems should be resolved. Some comments are shown below."
"Main issues:
1) In the present version, the innovation of this work is not so clear for me. The paper is very similar to the previous work by the similar authors, then what are the significant change and improvements by this work? The authors should claim them more clearly. The same model and same source, same light curves, would make this work less scientific implication."
Authors response:
The main changes are: fitting both Swift/BAT and MAXI observations with the same model (previous Leahy& Mendelsohn work fit only MAXI observations). In the current work, we derive the scaling of model disk radius to physical disk radius as a function of radius, and thus apply this to determine the physical corona inner radius. We have reworded the abstract and the summary section.
"2) Fig 1 shows the light curves of two detectors, and also hardness ratio with two different mission. I think that the hardness ratio would be more important compared with the light curves in this work. Anyway, in the present plots, they are not clear or correct. First, the direct ratio by two different missions may not so suitable. Second, if you have the reasons that the ratio is ok, then you should improve the plots, like how to reduce some plots with small errors. I would like to see the spectral evolution of the source with the 35-day circle."
Authors response: The MAXI and Swift/BAT 35-day cycle light curves were created with approximately 10 years (each) of data. Both MAXI and BAT are all-sky monitor instruments and have relatively low sensitivity. Thus even combining the 10 years of data gives the error bars of Fig. 1. For the ratio of MAXI to BAT count rate (the softness ratio), the errors are large whenever the count rates are low, just by error propagation. We now give the error calculation formula in the text of Section 2. The large errors in the softness ratio occur when the relative error in BAT or MAXI count rate are large, which occurs when the count rate is low.
"3) Then would the present model explain the possible spectral evolution of Her X-1 over the 35-day circle, like with the software SHAPE? Some previous RXTE results have show the spectral variation during the Main High State."
Authors response:
Thank you for pointing this out.
The observed spectral evolution of Her X-1 has been observed for turn-on to Main High using RXTE observations by Kuster et al. 2005, who show that the spectral changes can be explained by changing contribution of absorbed and scattered X-rays (their schematic diagram is in their Fig. 13). Leahy & Abdallah 2022 measure spectral evolution of Her X-1 with RXTE over Main High (results in their Figs. 8 to 13) but do not present an interpretation in terms of a schematic model.
Thus explaining the spectral evolution of Her X-1 with 35-day phase is a good suggestion for future work and would be a major project involving two parts: i) a full analysis of RXTE spectra over 35-day phase, and ii) improvements to the SHAPE model to allow it to compute spectra.
We add text to the summary section (last sentence).
"4) There are no any detailed (mathematical and logical ) description of the model, so it is a little difficult to read the parts of the model and methods. The authors can improve these parts."
Authors response: We add a short description at the beginning of section 4 and have expanded sections 4.2 (disk) and 4.3 (corona) with more description.
"5) line 44, you state that a warped accretion disk is required to be present in Her X-1. Is it correct or confirmed by all research work? In a work by IXPE, e.g., Heyl et al. 2024, NA, they suggest the magnetic pole precession would lead to the 35-day circle, and they donot need the warped disk. The authors may confirm their statement or update some physical scenario."
Authors response:
In Heyl et al 2024, changing polarization of Her X-1 is reported, summarized in their Table 1 by RVM parameters for 5 different 35-day phases. They "suggest" that magnetic pole precession could lead to this result, but they present no model to support that as the cause the polarization changes. Polarization changes are expected in the disk plus corona model because of changing contribution of direct plus scattered components.
We add an explanatory footnote to the end of the paragraph stating the need for the warped disk.
"There are some typos and grammar errors, the authors should check them in the revised version. Here I show some examples:
line 17: are consistent with eachother"
this has been corrected.
"line 23: This results is significantly improved binary system parameters"
results is has been changed to results in.
"line 28: the first paragraph. In addition, you may give more intrducion to the source Her X-1, so the paragraph can be extended.
****(need to extend the introduction)
"line 35: there is a significant to the cycle by X-rays scattered from near the inner part of the accretion disk"
significant has been changed to significant contribution
....
"The authors can examine the whole paper."
we have proofread the paper again for typos and grammar corrections and made these.
Round 2
Reviewer 3 Report
Comments and Suggestions for AuthorsThe authors have almost resolved my previous questions. Thus, the paper can be published.
