Submit to this Journal Review for this Journal Propose a Special Issue

Article Menu

Share Help Cite Discuss in SciProfiles

Open AccessArticle

Peer-Review Record

Soft X-ray Spectrum Changes over the 35-Day Cycle in Hercules X-1 Observed with AstroSat SXT

Universe 2024, 10(7), 298; https://doi.org/10.3390/universe10070298

by Denis Leahy ^1,*

and Riddhiman Sharma ²

Reviewer 1: Anonymous

Reviewer 2: Anonymous

Reviewer 3: Anonymous

Universe 2024, 10(7), 298; https://doi.org/10.3390/universe10070298

Submission received: 15 May 2024 / Revised: 1 July 2024 / Accepted: 12 July 2024 / Published: 15 July 2024

(This article belongs to the Special Issue Universe: Feature Papers 2024 – Compact Objects)

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors In the paper, the authors analyse the soft X-ray spectra of the X-ray pulsar Her X-1 and their changes during a 35-day cycle. The data were obtained with the Astrosat SXT X-ray mission. The results presented by the authors are interesting because they cover the entire 35-day cycle and concern specifically the soft X-ray band. In the future these data will be useful for building theoretical models.
Nevertheless, I have a number of comments and suggestions that could improve the paper.
(1) The main result of the paper is to obtain soft X-ray spectra over a 35-day cycle. I would suggest that the authors change the title of the paper to highlight this feature of their work.

(2) Introduction, line 34: the abbreviation ‘EUV’ should be deciphered.
(3) Introduction, line 46: the authors mention scattering corona. I would mention the assumed temperature of the corona and that it is assumed to be optically thin.
(4) Resent detection of X-ray polarisation in Her X-1 by IXPE mission made it possible to determine parameters of neutron star rotation in this system, confirm the precession of a neutron star and get geometrical parameters of the precession. Does it help in understanding the spectral changes the authors report about? I would suggest discussing this at the end of the paper.
(5) There were reports of arguments towards the strong non-dipole magnetic field in Her X-1 based on pulse profile shape (see Postnov et al., 2013, https://ui.adsabs.harvard.edu/abs/2013MNRAS.435.1147P ), features of aperiodic variability (Mönkkönen et al., 2022, see https://ui.adsabs.harvard.edu/abs/2022MNRAS.515..571M ) and expected critical luminosity of a neutron star. Later, in section 4.2 (line 308), the authors provide an estimation for the inner disc radius: 400 km. Note, that this radius is small if one assumes a surface magnetic field ~4.e12G, accretion rate ~1.e17 g/s and neutron star magnetic field dominated by dipole component. I would suggest mentioning the possibility of a non-dipole magnetic field structure in Her X-1.

(6) In the Introduction I would mention the papers by Staubert et al., 2007 (https://ui.adsabs.harvard.edu/abs/2007A%26A...465L..25S ) and Vasco et al., 2011 (https://ui.adsabs.harvard.edu/abs/2011A%26A...532A..99V ) where the authors report the discovery of a positive cyclotron line energy/luminosity correlation in Her X-1, indicating the geometry of the emitting region on the neutron star surface (hot spots).
(7) First paragraph of Section 2: I would present the observational data as a table.

(8) The authors mention software tools they use in data processing. Probably the name of the tools should be given in a special font.

(9) The authors use a specific spectral model to quote spectra (formula 4). I would suggest to discuss for each fit spectra whether there are correlations between the model parameters found. Otherwise, it is not clear whether the fits proposed by the authors are the only possible.

(10) Table 1, columns 3,4,5: I suggest to use another format of number's representation. The same is related to some numbers represented in Table 2.

Author Response

Reviewer 1 report:

In the paper, the authors analyse the soft X-ray spectra of the X-ray pulsar Her X-1 and their changes during a 35-day cycle. The data were obtained with the Astrosat SXT X-ray mission. The results presented by the authors are interesting because they cover the entire 35-day cycle and concern specifically the soft X-ray band. In the future these data will be useful for building theoretical models.

******** Author response:
We would like to thank the reviewer for the very helpful requests for changes to the manuscript.
*********************
Nevertheless, I have a number of comments and suggestions that could improve the paper.
(1) The main result of the paper is to obtain soft X-ray spectra over a 35-day cycle. I would suggest that the authors change the title of the paper to highlight this feature of their work.
******** Author response:
done
************************
(2) Introduction, line 34: the abbreviation ‘EUV’ should be deciphered.
******** Author response:
EUV has been spelled out in the text, and also added to the list of abbreviations at the end.
************************
(3) Introduction, line 46: the authors mention scattering corona. I would mention the assumed temperature of the corona and that it is assumed to be optically thin.
******** Author response:
done
************************
(4) Resent detection of X-ray polarisation in Her X-1 by IXPE mission made it possible to determine parameters of neutron star rotation in this system, confirm the precession of a neutron star and get geometrical parameters of the precession. Does it help in understanding the spectral changes the authors report about? I would suggest discussing this at the end of the paper.
******** Author response:
The new text has been added at the end of section 4.3 (comparison with previous work), referencing the results published by Garg et al. 2023.
************************
(5) There were reports of arguments towards the strong non-dipole magnetic field in Her X-1 based on pulse profile shape (see Postnov et al., 2013, https://ui.adsabs.harvard.edu/abs/2013MNRAS.435.1147P ), features of aperiodic variability (Mönkkönen et al., 2022, see https://ui.adsabs.harvard.edu/abs/2022MNRAS.515..571M ) and expected critical luminosity of a neutron star. Later, in section 4.2 (line 308), the authors provide an estimation for the inner disc radius: 400 km. Note, that this radius is small if one assumes a surface magnetic field ~4.e12G, accretion rate ~1.e17 g/s and neutron star magnetic field dominated by dipole component. I would suggest mentioning the possibility of a non-dipole magnetic field structure in Her X-1.
******** Author response:
A footnote has been appended to the paragraph where the disk radius is mentioned, and the relevant references have been added.
************************
(6) In the Introduction I would mention the papers by Staubert et al., 2007 (https://ui.adsabs.harvard.edu/abs/2007A%26A...465L..25S ) and Vasco et al., 2011 (https://ui.adsabs.harvard.edu/abs/2011A%26A...532A..99V ) where the authors report the discovery of a positive cyclotron line energy/luminosity correlation in Her X-1, indicating the geometry of the emitting region on the neutron star surface (hot spots).
******** Author response:
done
************************
(7) First paragraph of Section 2: I would present the observational data as a table.
******** Author response:
The observational data is summarised in Table 1. A pointer has been added to the mentioned paragraph.
************************
(8) The authors mention software tools they use in data processing. Probably the name of the tools should be given in a special font.
******** Author response:
The font of the names of software tools has been changed to \textit{} and that of the spectral models to \textit{}.
************************
(9) The authors use a specific spectral model to quote spectra (formula 4). I would suggest to discuss for each fit spectra whether there are correlations between the model parameters found. Otherwise, it is not clear whether the fits proposed by the authors are the only possible.
******** Author response:
We add further text just before equation for to address this question.
************************
(10) Table 1, columns 3,4,5: I suggest to use another format of number's representation. The same is related to some numbers represented in Table 2.
******** Author response:
All numbers with exponential notation (E+0n) have been changed to the standard scientific format (x10^n).

**************************

Reviewer 2 Report

Comments and Suggestions for Authors

I think that the results in this manuscript are to be open to the public but it should be done after responding to the following comments.

Major comments:

1. On the results in Table 2

1.1) The value of PL norm in SH is the same as that in MH but disagrees with those plotted in Fig.6.

1.2) Values of N_H and f_c of eclipse are presented in the table but it seems inconsistent with the statement in Line 225 - 227.

1.3) Units of "norm"s should be indicated.

2. On the partial covering situation

The authors introduce the partial covering model to reproduce the spectral variation over the 35-day cycle, in which an X-ray emission region as viewed from an observer is supposed to be partially covered by absorbers with N_H less than 10^24 cm^-2. However, the results of the spectral fits show that the flux before the partial covering still significantly varies over the 35-day cycle. This indicates that another area should exist in the intrinsic X-ray emission region as viewed from us and be completely blocked by some material on the line of sight, if we premise that properties of the intrinsic X-rays in the present analysis do not so largely change from phase to phase of the 35-day cycle. Namely, we need another partial covering situation due to the X-ray blocker with N_H >>10^24 cm^-2 than that due to the X-ray absorber. It should be mentioned in the paper.

3. On the discussions

3.2) The drop of the blackbody area from MH and SH to during dips is argued to be caused by increased covering factor of the absorber (from Line 311). However, the BB norm is estimated as the value before the partial covering and thus the increased covering factor cannot be the origin of the area drop. The increased covering factor of the blocker should cause it.

3.3) The 1 keV line norm is mentioned to have similar behavior to the power law norm (from Line 322), from which it is discussed that the 1 keV line emission region is compact (from Line 325). However, such a discussion is not done for the blackbody component and should be added. We see from Table 2 and by comparing Fig.6 and 9 that the ratio of BB norm to power law norm also changes only a small amount between MH, SH and LS. If so, in spite of the similar behavior between the 1 keV line and the BB, the 1 keV component is discussed to originate in an inner region than the BB component (from Line 378). What is the significant evidence to claim the inner position of the 1 keV line emitter ?

Minor comments:

1. "KeV line width", "KeV line center energy" and "KeV line norm" from Line 242 to 244 would be better to be replaced to "1 KeV line ....".

2. "many times" is repeated in the sentence from Line 260.

3. It would be better to include the recent work by Inoue (2019, PASJ, 71, 36) in the references for the model to reproduce the 35 day cycle.

4. References for the model of the hard X-rays from the polar cap (Line 38) are recommended to include Inoue (2020, PASJ, 72, 12) which proposes a different model from that by Ref[7}.

Author Response

Reviewer 2 report:

I think that the results in this manuscript are to be open to the public but it should be done after responding to the following comments.
******** Author response:
We would like to thank the reviewer for the very helpful requests for changes to the manuscript.
*************
Major comments:

1. On the results in Table 2
1.1) The value of PL norm in SH is the same as that in MH but disagrees with those plotted in Fig.6.
******** Author response:
I checked again the output of the fits from XSPEC and found that I had copied the wrong number for powerlaw norm into Table 2 for spec19_SH. The correct value has now been entered into Table 2.
************************
1.2) Values of N_H and f_c of eclipse are presented in the table but it seems inconsistent with the statement in Line 225 - 227.
******** Author response:
Because N_H and f_c could not be constrained by the fits of eclipse spectra, the values were set to be identical to those of spec3_MH.
This is a special case of the statement on (old) line number 190. The statement on lines 225-229 was reworded to avoid confusion.
************************
1.3) Units of "norm"s should be indicated.
******** Author response:
The units of the norms have been added to Table 2 and to the captions of Figures 6, 9 and 10.
************************
2. On the partial covering situation
The authors introduce the partial covering model to reproduce the spectral variation over the 35-day cycle, in which an X-ray emission region as viewed from an observer is supposed to be partially covered by absorbers with N_H less than 10^24 cm^-2. However, the results of the spectral fits show that the flux before the partial covering still significantly varies over the 35-day cycle. This indicates that another area should exist in the intrinsic X-ray emission region as viewed from us and be completely blocked by some material on the line of sight, if we premise that properties of the intrinsic X-rays in the present analysis do not so largely change from phase to phase of the 35-day cycle. Namely, we need another partial covering situation due to the X-ray blocker with N_H >>10^24 cm^-2 than that due to the X-ray absorber. It should be mentioned in the paper.
******** Author response:
Text of explanation is added just below the spectral model equation (4), and a reference is given to Mihara et al 1991, who were the first to use a partial covering absorber for the spectrum Her X-1.
**********************
3. On the discussions
3.1) The statement from Line 295 is difficult to understand. If the blackbody is extended more than the PL emitter, the rise of the BB should be more smeared than that of the PL but the sharp rise from the first blue point to the second blue point in Figure 9 looks inconsistent with it. From the beginning, is the statical significance assured on the hypothesis that the light curve shapes of the first seven blue points are different between Figure 6 and 9 ?
******** Author response:
Re the first point: The statement in (old) line 295 was not clear, so has been reworded.
Re the second point: The powerlaw source is smaller than the blackbody based on the variability of powerlaw norm (Fig. 6, except first point of TO) while the blackbody norm is constant (Fig.9).
************************
3.2) The drop of the blackbody area from MH and SH to during dips is argued to be caused by increased covering factor of the absorber (from Line 311). However, the BB norm is estimated as the value before the partial covering and thus the increased covering factor cannot be the origin of the area drop. The increased covering factor of the blocker should cause it.
******** Author response:
The reviewer is correct here- it is caused by optically thick matter not covering factor. The description has been corrected (old line 311).

************************
3.3) The 1 keV line norm is mentioned to have similar behavior to the power law norm (from Line 322), from which it is discussed that the 1 keV line emission region is compact (from Line 325). However, such a discussion is not done for the blackbody component and should be added. We see from Table 2 and by comparing Fig.6 and 9 that the ratio of BB norm to power law norm also changes only a small amount between MH, SH and LS. If so, in spite of the similar behavior between the 1 keV line and the BB, the 1 keV component is discussed to originate in an inner region than the BB component (from Line 378). What is the significant evidence to claim the inner position of the 1 keV line emitter ?
******** Author response:
The paragraph has been reworded: the evidence is the considerable variability in powerlaw norm (known to be from the neutron star) and 1 keV line norm in contrast to the blackbody norm near constancy.
************************
Minor comments:
1. "KeV line width", "KeV line center energy" and "KeV line norm" from Line 242 to 244 would be better to be replaced to "1 KeV line ....".
******** Author response:
this change has been made
************************
2. "many times" is repeated in the sentence from Line 260.
******** Author response:
the redundance has been removed.
************************
3. It would be better to include the recent work by Inoue (2019, PASJ, 71, 36) in the references for the model to reproduce the 35 day cycle.
******** Author response:
This reference has been added to the introduction.
************************
4. References for the model of the hard X-rays from the polar cap (Line 38) are recommended to include Inoue (2020, PASJ, 72, 12) which proposes a different model from that by Ref[7}.
******** Author response:
This reference has been added to the introduction.
************************

Reviewer 3 Report

Comments and Suggestions for Authors

Comments for author File: Comments.docx

Author Response

Reviewer 3 report:

Review of “Astrosat SXT X-ray Spectrum Changes over the 35-day Cycle in Hercules X-1”, by Denis Leahy and Riddhiman Sharma

The submission contains some interesting results and may in principle be publishable after substantial revision. However, the writing is quite cumbersome, the information could be presented more elegantly and efficiently – even in less space. In addition, the preparation of the manuscript is quite sloppy, multiple corrections are necessary, and some fundamental questions in regard to the interpretation of the data analysis results need to be answered. The work appears to be a report of a students project, the student is not the first author (!?). The first author identifies his contribution, e.g., as “writing” and “supervision”, but fails to produce concise text that contains all the necessary information. Finally, the authors neglect previously published work, the first author tends to just cite his own work, even does not give references for adopted quantities from other work.
******** Author response:
We would like to thank the reviewer for the very helpful requests for changes to the manuscript.
Regarding the student (second author): part of the work was carried out by the student, all during a 12 week period; the rest of the work (lasting ~4 years) was carried out by D. Leahy. For the list of contributions, the guidelines of "Universe" were followed.
We agree that several references are missing and add these.
************************
Here is a list of necessary corrections / additions (following the flow of the submission):
- Abstract, line 13: change “rotation” to “precession”
******** Author response:
done.
************************
- Abstract, lines 14 and 15: the terms “turn-on, MH, rise …” are not defined. Here it may be just stated that there is the flux modulation with a period of about 35 days with different intensity levels at various phases (“states”), and that observations were done at most of these states.
******** Author response:
This has been rewritten.
************************
- Introduction: a description of the 35-d flux modulation needs to be given with a clear definition of the various “states”.
******** Author response:
A paragraph has been added.
************************
- Introduction, line 36: it is not the accretion disk which is “Roche-lobe filling”!
******** Author response:
The wording has been changed to convey the correct meaning (the star is Roche lobe filling).
************************
- Introduction, line 36: say “… of the rotation neutron star.”
******** Author response:
The request doesn't seem to make sense, please reword.
************************
- Introduction, line 49: “co-pointed”  “co-pointing”
******** Author response:
done
************************
- Introduction, line 51-53: give the full names, plus abbreviations in parenthesis for NUV, …. (or at least point to the list of abbreviations at the end).
******** Author response:
done
************************
- 2. Data and Analysis, lines 64-67: point to Table 1, in which the MJDs are given.
******** Author response:
done
************************
- 2. Data and Analysis, lines 77: state the duration of one satellite orbit.
******** Author response:
done
************************
- 2. Data and Analysis, lines 85: “relativistic effects …”: give magnitude of these effects, in case they are significant, explain.
******** Author response:
A footnote has been added.
************************
- 2.1 Lightcurve Analysis, line 98: say what orbital phase zero is.
******** Author response:
This has been added.
************************
- 2.1 Lightcurve Analysis, lines 98, 100, 102: give references for the adopted values for T0, P(T0) and P_dot.
******** Author response:
The reference to Staubert et al 2009 has been added.
************************
- 2.1 Lightcurve Analysis, lines 113: give conversion factor between BAT and SXT count rates.
******** Author response:
The scaling constant is given.
************************
- 2.1 Lightcurve Analysis, lines 125-132: very useful statement – unfortunately, the opportunity is missed to change to the generally used definition of 35-day-phase-zero, namely the turn-on.
******** Author response:
Text has been added which includes the generally used definition of 35-day phase 0. The discussion of determination of phases using the RXTE\PCA data is not central to the paper, thus is moved to a footnote.
************************
- 2.2 X-ray Spectrum Analysis, line 144: again, how are “turn-on” and “rise” defined? From Table 1 it appears that rise is about 0.3 day after turn-on: why does one need to have two terms for the initial increase in flux? See also lines 298-299.
******** Author response:
The state definitions are based on the shape of the lightcurve vs. time over a 35-day period. The definitions of turn-on and rise are added to section 2.1 (Lightcurve Analysis), to the text on Fig. 2, which illustrates MH turn-on and rise.
************************
- 2.2 X-ray Spectrum Analysis, line 179 / 185-186: bring the information of lines 186-186 up right after formula (4).
******** Author response:
done
************************
- 2.2 X-ray Spectrum Analysis, line 179-186: repeat in the text the notation of the various spectral components, like <1>, <2>, …
******** Author response:
done
************************
- 2.2 X-ray Spectrum Analysis: strangely, there is no reference to Fig. 5 anywhere in the text.
******** Author response:
The reference to this example spectrum fit in Fig. 5 has been moved from the text referring to Table 2 to just after the paragraph introducing the model.
************************
- 2.2 X-ray Spectrum Analysis, Fig. 5: should’nt that be spec3MH (not spec7MH)? spec3MH appears to be the reference!?
******** Author response:
spec7MH was chosen because it is more typical of the signal-to-noise of MH spectra.
************************
- 2.2 X-ray Spectrum Analysis, line 187: give reference to Fig. 5 here, possibly also at other places.
******** Author response:
as noted (2 responses above), the reference to Fig.5 was moved to after the (old) line 187.
************************
- 2.2 X-ray Spectrum Analysis, line 200: say “… that it is not …”
******** Author response:
This has been reworded: splitting 1 keV and 6.4 keV line discussion into 2 paragraphs, including
a clarification (use Fe line rather than 6.4 keV line) and fix of a typographical error "6.4 keV" was changed to "Fe keV line"

************************
- 2.2 X-ray Spectrum Analysis, Fig. 10: what are the units at the y-axis? Also, explain in the text.
******** Author response:
This has been added to the figure caption and to the text.
************************
- 2.4 Spectrum of Her X-1, line 275: “… the first to do so…”: this appears to be a strong statement: see e.g. Kuster et al. 2005, Brumback et al. 2021, Fürst et al. 2013, …
******** Author response:
References to Kuster et al. 2005, Brumback et al. 2021, Fürst et al. 2013
have been added with brief summaries.
************************
- 4.2 X-ray Spectrum Analysis, lines 285-292 and 4.3 Comparison with previous work, lines 329-349, related to the earlier description of the data analysis: It needs to be shown that the data are really good enough to uniquely measure the covering factor and the column density, simultaneously. Please demonstrate that the spectral analysis can do this, e.g. by showing a corresponding correlation plot.
******** Author response:
For lines 285-292 a footnote with short description of the significance of the column density and covering factor is added. An extra figure with a correlation plot of column density and covering factor is not added because of a request not to add more plots by another reviewer.
************************

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Thanks to the authors for the updated version of the article. The article is much improved. However, I have an additional comment concerning the polarisation of X-rays detected in Her X-1.

The authors cite the paper by Gary et al. 2023, which gives values for the degree of linear polarisation and polarisation angle, but makes no conclusions about the rotation geometry of the neutron star. There are two papers that reproduce the rotation geometry of the neutron star in Her X-1 based on measured polarisation: Doroshenko et.al, 2022, Nature Astronomy, 6, 1433 and Heyl et al, 2023, arXiv:2311.03667. In the latter, it is possible to determine changes in the rotational geometry during the 35-day cycle. I would suggest the authors of the paper to discuss how their results on the observation of spectral variability agree with the already known rotation geometry of the neutron star in Her X-1.

Author Response

Reviewer 1:

Thanks to the authors for the updated version of the article. The article is much improved. However, I have an additional comment concerning the polarisation of X-rays detected in Her X-1.

Author response:

We now reference the two papers in the discussion section 4.3: in short, the spectral study is not sensitive to the rotational geometry or to small changes in it.

(Doroshenko, Victor; Poutanen, Juri; Tsygankov, Sergey S. et al. Determination of X-ray pulsar geometry with IXPE polarimetry; 2022 Nature Astronomy, Volume 6, p. 1433-1443;
and
Heyl, Jeremy ; Doroshenko, Victor ; González-Caniulef, Denis et al. X-ray Polarization Reveals the Precessions of the Neutron Star in Hercules X-1; (unpublished) eprint arXiv:2311.03667.)

The added text is in bold in section 4.3.

Reviewer 2 Report

Comments and Suggestions for Authors

I am sorry but the responses to the following two items are not satisfactory.

==== Referee comment to the previous manuscript

3.1) The statement from Line 295 is difficult to understand. If the blackbody is extended more than the PL emitter, the rise of the BB should be more smeared than that of the PL but the sharp rise from the first blue point to the second blue point in Figure 9 looks inconsistent with it. From the beginning, is the statical significance assured on the hypothesis that the light curve shapes of the first seven blue points are different between Figure 6 and 9 ?
******** Author response:
Re the first point: The statement in (old) line 295 was not clear, so has been reworded.
Re the second point: The powerlaw source is smaller than the blackbody based on the variability of powerlaw norm (Fig. 6, except first point of TO) while the blackbody norm is constant (Fig.9).

===== Referee comment to the previous manuscript

== Referee comment to the revised manuscript

The remaining point is only one, common to the above two items. It is that no statistical significance of the difference in the time variability between the power-law norm and the blackbody norm has not been presented in the paper. To my understanding, the authors insist that the 6 points (except the first one) around the MH of the power-law norm are variable but those of the blackbody norm are constant. However, if we taking account of the errors, the difference between the two looks not so convincing to me. I request the authors to perform a chi-square test on a hypothesis that ratios between the two norms from the same spectral data are the same over the 6 points. If the hypothesis is rejected, it becomes possible to say that the both light-curve shapes are significantly different from each other. Then, the same thing should be done for the ratios between the power-law norm and the 1 keV line norm.

In relation to the above issue, I would like to add two minor comments.

1) There is a statement that the power law norm changes during MH and SH (from line 319 in the revised manuscript). However, the three points in the SH look constant within errors.

2) It should be indicated somewhere which points in Fig 6 - 10 correspond to MH-TO and MH-rise. It is also unclear why the TO is separately treated from the rise.

Author Response

Reviewer 2:

I am sorry but the responses to the following two items are not satisfactory.

==== Referee comment to the previous manuscript

===== Referee comment to the previous manuscript

== Referee comment to the revised manuscript

Two comments on this issue:

1. "less variable" is more correctly described as "smaller decrease from MH to SH implying a more extended blackbody region than powerlaw region or 1 keV line region".
In particular, the ratio of blackbody norm for SH (3 points average) to MH (6 points average) 1.5+-1.5, but for powerlaw norm the SH to MH ratio is 0.46+-0.11 and for 1 keV line norm the SH to MH ratio is 0.44+-0.12.

2. We have carried out the chi^2 test (parameters compared to a constant) for the "normal" spectra (14 of them) which all have powerlaw norm, blackbody norm, and 1keV line norm. The results are: the chi^2 for powerlaw norm is 940.1, for blackbody norm is 99.4 and for the 1 keV line norm is 281.5; thus all 3 are variable but the powerlaw is most variable, 1 keV line next most variable and blackbody norm least variable.
For only the 6 points in MH: the chi^2 for powerlaw norm is 49.6, for blackbody norm is 2.13 and for the 1 keV line norm is 54.5.
This information has been added in Section 4.2.

(The new discussion is in bold text in the last few paragraphs of section 4.2)

************
In relation to the above issue, I would like to add two minor comments.

1) There is a statement that the power law norm changes during MH and SH (from line 319 in the revised manuscript). However, the three points in the SH look constant within errors.

2) It should be indicated somewhere which points in Fig 6 - 10 correspond to MH-TO and MH-rise. It is also unclear why the TO is separately treated from the rise.
*********************
(new) Author response:
Re point 1) the second value of powerlaw norm in SH has large error. The other two points in SH show declining powerlaw norm (point 3 is lower than point 1 by 1.8 sigma). We have rewritten the first part of the 4th paragraph of section 4.2 (in bold)

Re point 2) this information has now been added in figure captions.

Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

I am sorry but cannot help saying that the responses are not to the point yet. Major comments are as follows

1) To my understanding, if we report that two observed values are significantly different from each other, the statistical significance of the difference should be as large as 3 sigma at least. I believe it is the common sense in our field.

Hence, I cannot accept the argument from line 320, claiming that the values of 1.5 +- 0.9 and 0.46 +- 0.06 are different. The statistical difference looks a little larger than 1 sigma only.

In the sentence from line 316, 1.8 sigma is used as the evidence for the difference, which contradicts to the usual sense too.

2) Sentences from line 324 to 332 (and from liine 366 to 368) seem to insist that the deviation from the constant with the larger chi^2 value indicates the stronger time variation. However, this argument is wrong. The chi^2 value is calculated from the data normalized by the errors, and thus the data with the relatively smaller errors presents the larger chi^2 value even if the two data have intrinsically the same amplitude of the variation.

I would like to request again to perform a chi^2 test to see whether the light curves of the 6 points in MH have the same shape between the power-law norm and the blackbody norm.

Unless the difference between the two light curves is statistically proved, the authors should weaken the discussions on the difference of the emission size between the 1 keV line and the blackbody.

Author Response

Reviewer comment:
I am sorry but cannot help saying that the responses are not to the point yet. Major comments are as follows

1) To my understanding, if we report that two observed values are significantly different from each other, the statistical significance of the difference should be as large as 3 sigma at least. I believe it is the common sense in our field.
Hence, I cannot accept the argument from line 320, claiming that the values of 1.5 +- 0.9 and 0.46 +- 0.06 are different. The statistical difference looks a little larger than 1 sigma only.
In the sentence from line 316, 1.8 sigma is used as the evidence for the difference, which contradicts to the usual sense too.
******************
Author response:
re line 316:
We agree that the 1.8 sigma is weak evidence for the significance of decline, so that line is reworded. The point was that count rate and powerlaw norm have similar shape.

re line 320:
The reviewer is correct: the difference between ratio of blackbody norm SH to MH compared to ratio of powerlaw norm SH to MH is significant only at 1.3 sigma.
The argument was that the blackbody norm is less variable than powerlaw norm. Thus we rewrite the text around line 320 to weaken our argument.

******************
2) Sentences from line 324 to 332 (and from liine 366 to 368) seem to insist that the deviation from the constant with the larger chi^2 value indicates the stronger time variation. However, this argument is wrong. The chi^2 value is calculated from the data normalized by the errors, and thus the data with the relatively smaller errors presents the larger chi^2 value even if the two data have intrinsically the same amplitude of the variation.
I would like to request again to perform a chi^2 test to see whether the light curves of the 6 points in MH have the same shape between the power-law norm and the blackbody norm.
Unless the difference between the two light curves is statistically proved, the authors should weaken the discussions on the difference of the emission size between the 1 keV line and the blackbody.
******************
Author response:

It seems we previously misunderstood the chi^2 test to perform. Thus the previous chi^2 test result has been omitted, and the new chi^2 test, directly comparing shapes of powerlaw norm and blackbody norm, was carried out, and is now discussed.
We also add a figure which directly compares PL norm, blackbody norm, and 1 keV line norm; and split the rather long paragraph containing line 320 into 2 parts.
We have also rewritten the text lines 366-368 which discusses 1 keV line norm.
Finally we have rewritten the conclusion section to be consistent with the other changes in Section 4.2. The new text is in bold font.

******************

Article Menu

Soft X-ray Spectrum Changes over the 35-Day Cycle in Hercules X-1 Observed with AstroSat SXT

Further Information

Guidelines

MDPI Initiatives

Follow MDPI