Observability of HOFNARs at SRG/eROSITA

Round 1

Reviewer 1 Report

Referee opinion on Manuscript ID: universe-1735388

Title: Observability of HOFNARs at SRG/eROSITA

Authors: Alena D. Khokhriakova , Andrey I. Chugunov, Sergei B. Popov , Mikhail Gusakov, Elena Kantor

 

The paper relates to hypothetical new class neutron stars called “HOt and Fast Non-Accreting Rotators, HOFNARs” and their possible detection in observations. Unfortunately, the paper is badly prepared and written and is not suitable for publication. First, the very existence of such objects is speculation. Secondly, they should have such high temperatures that (as the authors themselves write) they should be easily observed, which is not the case. And the temperature range in which the analyzed objects could possibly have been much lower. Thus, the motivation of work is questionable.It is not clear from the paper how the authors calculate count rates (CR) of the modeled sources. So, it is not possible to validate this part of the work. What's worst, the very short section "Results" does not show how the described results were achieved or why the conclusions were drawn. The paper does not contain any statistical analysis, which is necessary in this type of work.  Section 3 and the next chapter look like a business presentation rather than a fair presentation of scientific results. For the above reasons, in my opinion, the paper is not suitable for publication

 

Comments for author File: Comments.pdf

Author Response

We strongly disagree with the report and note that the claims in it are not supported by other referees, who provided positive and constructive reports.
Anyway, the referee did not present any comments to which we can reply.

Reviewer 2 Report

 This paper is discussing the detection possibility of HOFNARs with eROSITA. They reasonably estimate it and discuss the identification method.

For the detection probability, the authors make several assumptions.  The important parameter for the estimation is the surface temperature of the 10-6K as a fiducial value.  The authors further  assume the temperature is constant during the whole life.  The validity of this value and assumption is not strong.   And if the detection rate is smaller than their prediction, the cause can  be considered to be un-suitable estimation of this temperature, as the authors point out this.   Then the discussion about the evolution of the LMXB or the URCA threshold might be meaningless.

  If the paper describes the physical importance of the negative detection well, the value of this paper becomes up.

 

I list up individual comments, which include very minor one like just my hope.

 

1. L118-121 The assumption of the temperature is very important. The author should explain more detail on the basis of temperature of 10^6 K.

 

2. Fig 1. I can not find the effective area in the web page of eRosita, written in the figure caption.

 

3. Equation (6)

The referring paper is a very old one.  Probably using the newer one (for example, Wilms, Allen and McCray 2000)　is better.  (I think this is a very minor comment,  considering the other assumptions).

 

4. L167-L174

It is better, if authors show a variance of the Nh values and a validity of the factor of 2, for example by showing the correlation between the author’s Nh and those obtained by FTOOLs.

 

5. L176

Please explain how to distribute  HOFNARs.　Do the authors use random numbers?

 

6. L191-L194

I can not understand what authors like to say. Do the authors like to say that factor of 1.5 is small enough comparing the other uncertainty,  Can the factor may be much larger than 1.5 ? If so, the treatment influences the conclusion.

 

7. Figure 3 “r” is not clear. I guess it is distance from the sun.  

 

8. L219 There is no period.

 

9.L225-L231 

This argument does not mean that the average number of density of XDINs is smaller than HOFNRs.

 

10.section 4.2  There are a lot of comparisons.  If the authors compile a kind of table of the characteristics (spectra, location) of the various objects (XDINS, CCO、HOFNAR, qLMXBs), the reader can easily understand the discussion. 

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

Author Response

We thank the referee for useful comments.
Please, note that the paper (in the revised version) is substantially expanded and modified. All changes are marked with bold face.

L118-121 The assumption of the temperature is very important. The author should explain more detail on the basis of temperature of 10^6 K.

The temperature distribution of HOFNARs is very model dependent and the fixed temperature distribution with the fiducial value 10^6 K is taken for simplicity to illustrate results, a set of other  HOFNAR temperatures is also considered.

Our results can be easily applied to analyze HOFNARs detectability for any given temperature by a linear combination of several fixed temperature log N-log S curves with appropriate weights.

To clarify it for the readers, we expand the first paragraph of Sec. 2.2. 

Fig 1. I can not find the effective area in the web page of eRosita, written in the figure caption.

We added the direct link:

https://wiki.mpe.mpg.de/eRosita/erocalib_calibration

 Equation (6).
The referring paper is a very old one.  Probably using the newer one (for example, Wilms, Allen and McCray 2000)　is better.  (I think this is a very minor comment,  considering the other assumptions).

 We agree that data from Wilms et al. (2000) might provide more precise results. However, for population studies (within all uncertainties) the older version we use works very satisfactory. So, we prefer not to introduce absorption from Wilms et al. now. We plan to use it in future modeling.

L167-L174
It is better, if authors show a variance of the Nh values and a validity of the factor of 2, for example by showing the correlation between the author’s Nh and those obtained by FTOOLs.

 In the revised version we make a direct comparison with UK-Swift (results are shown in a plot). The comparison demonstrates that the additional factor 2 is not necessary. So, it is removed in the revised version.

L176
Please explain how to distribute  HOFNARs.　Do the authors use random numbers?

 Yes, to generate positions of sources we use random numbers according to the distribution given in the section with the model description. A sentence about it is added at the very end of Sec. 2.1.

L191-L194
I can not understand what authors like to say. Do the authors like to say that factor of 1.5 is small enough comparing the other uncertainty,  Can the factor may be much larger than 1.5 ? If so, the treatment influences the conclusion.

 Taking into account usual uncertainties of population synthesis models we assume that the factor 1.5 is a small one, thus suggested modification of the Nh distribution does not seriously influence our main conclusions.
Still, in the revised version of the text modification of N_H is not used any more. So, that part of the text about additional test is deleted.

Figure 3 “r” is not clear. I guess it is distance from the sun.  

 Yes, this is a distance from the Sun. We added a phrase about it.

L219
There is no period.

 We agree. The text is corrected.

L225-L231
This argument does not mean that the average number of density of XDINs is smaller than HOFNARs.

 This is true. We just intended to say that known XDINS form a local population due a local enhancement in the number density of young NSs. Thus, on a larger scale the local enhancement of XDINSs cannot be just extrapolated.  We slightly modified this paragraph to make the message clearer.

10.section 4.2  There are a lot of comparisons.  If the authors compile a kind of table of the characteristics (spectra, location) of the various objects (XDINS, CCO、HOFNAR, qLMXBs), the reader can easily understand the discussion.

Generally, we agree with this comment. Still, we believe that before any HOFNARs are identified such detailed comparison is pre-mature. We hope to follow this advice later, when some observational data on HOFNARs in the Galaxy field become available.

Reviewer 3 Report

Referee report for Khokhriakova et al., “Observability of HOFNARs at SRG/eROSITA”.

 

The authors study the possibility of identifying neutron stars heated by the transformation of rotational energy into heat via r-modes, using the eROSITA sky survey. This is a very appropriate topic, as the survey, while unfortunately suspended at the moment, has completed ~half the intended depth, and should be the most sensitive soft X-ray sky survey ever.  The authors have made plausible assumptions, and for the most part I agree with their analyses and conclusions. I do have a few concerns and suggestions, which I detail below.

 

My largest concern is with comparison to the ROSAT Bright Survey. The authors say (p 7) that no objects which can be HOFNARs are identified in the RBS, but their preferred value of T=10^6 K predicts 6 (range of 3-10, which I infer is roughly a 90% probability range). Thus, formally, the detected value of 0 rules out T=10^6 K at 90% confidence (using Gehrels 1986 Table 1, I think 99.5% confidence is about right), and rules out T=8*10^5 K also at ~90% confidence (also using Gehrels’ Table 1). I think the authors are reluctant to embrace this constraint, understandably, but I think it allows a more robust upper estimate on the number of HOFNARs that are detectable under the authors’ assumptions (about 40, using 0.1 ct/s and the 8e5 K line in Fig. 2, though see below for caveats).

 

My other significant concern is that the authors are rather vague about the reference point that should be used (page 6, lines 187-190, and p. 4, lines 154-155). It’s reasonable to say that 0.01 ct/s is the detection limit for eROSITA, but such sources will be barely detected. The authors suggest 0.1 cts/s as a better reference point. I think this deserves a little more discussion; the authors could reference the expected average (vignetted) exposure value from the survey to underpin their estimates. As a rough estimate, I see from Predehl+21 that the all-sky average after 4 years should be 2.5 ks; with vignetting (factor 1.88) and reduction of survey time (factor 2), that gives ~650 s, so that a 0.1 ct/s source will provide of order 65 counts. This is perhaps plausible as a lower limit for the number of counts needed to distinguish the hardness ratios of HOFNARs from the majority of X-ray sources (not to distinguish them from XDINS etc, but just to make a candidate catalog). I invite the authors to make their own estimate in this spirit.

 

A third significant concern, though I do not think it ends up mattering significantly, is the extinction calculation (section 2.4). The model for the ISM used here is rather oversimplified, and inaccurate (though the inaccuracy is the fault of the prior modelers, not the current authors). The oversimplification is the distribution of molecular H_2 as a simple double exponential. This is a reasonable model for atomic H (with caveats) and for stars, but molecular H_2 is very clumpy—at the least this point should be acknowledged in the text.  The inaccuracy is the distribution of HI; the radial scale and scale height quoted do not look reasonable. I referred to Kalberla and Kerp (2009, ARAA), an appropriate review, where I see that a more appropriate radial scale would be about 3 kpc, and a more appropriate scale height (at our galactocentric distance, this varies) would be about 0.15 kpc. However, atomic H does very little extinction, so changing these values is unlikely to make large changes to the authors’ results.

   The FTOOLS (Colden) calculator is known to underestimate extinction values for many X-ray sources, due to the fact that it is constructed solely from atomic gas maps, omitting H_2. However, this tends to cause problems only at large distances in the Galactic plane, which is not really relevant for the authors’ purposes, as systems beyond (say) 3 kpc in the Galactic plane are already too obscured to be detectable.

   The advent of Gaia along with many other surveys has enabled much better three-dimensional extinction maps. I would encourage the authors to try using the Bayesmap to estimate extinction to ~1-2 dozen of their simulated objects; this tool is available at argonaut.skymaps.info, and published by Green et al. 2019, ApJ, 887, 93. If they find broadly similar results (at least within ~3 kpc) as their model, then just adding such a check to their paper should be sufficient. As mentioned above, I doubt the final results will be dramatically different, so I would not insist that the authors redo their full simulations.

 

Below, I list smaller points, in order through the document.

 

Abstract; as mentioned above, the ROSAT Bright Survey makes the 10^6 K surface temperature (with assumed total population) implausible. It would seem appropriate to use the T=8e5 K scenario as a fiducial  upper limit, stating the assumption that HOFNARs are 10% as numerous as MSPs; and to mention that T=1e6 K (or higher) is possible if the relative frequency is smaller than this 10% assumption.

 

Model, section 2.1, line 63 on; the authors here imply that HOFNARs are typically bright for 10^10 years. My reading of reference 7 is that the fiducial lifetime is more typically 10^9 years. I would suggest the authors make clear that such a shorter lifetime is quite possible—as I will explain below, it doesn’t change their results, though it injects some uncertainty.

 

Same paragraph; “reasonable to assume they should have similar spatial distribution.” —this also depends on the HOFNAR lifetime, and to a lesser extent on spin-up. If HOFNARs have lifetimes ~10^9 years (which seems plausible), they may have slightly less extended spatial distributions than MSPs.  I doubt this will dramatically affect the conclusions, but is worth briefly mentioning. (MSPs can also be produced with less spin-up than seems necessary for HOFNARs, which could conceivably create differences in their distribution, but this is even less likely to give substantial differences.)

 

Page 3, lines 86-97; as mentioned above, HOFNARs may have shorter lifetimes (~1 Gyr?) than MSPs. As globular clusters are older than the Galaxy as a whole, this may mean that the relative abundance of HOFNARs vs. MSPs could be higher in the Galaxy as a whole than in globular clusters. Again, this is only worth a brief mention, the author’s fiducial assumption here of 10% the MSP population is reasonable.

 

Section 2.2, p 3, lines 116-118; I might suggest a brief comment on how another temperature distribution (e.g. a power-law) would affect their overall findings (my initial assumption would be; not dramatically).

 

p. 5, equation 5, and line 152; since the normalization by 4*pi*r^2 is carried out within the integration, the numerator should contain L(E), not F(E), signifying luminosity rather than flux.

 

Fig. 3; I would suggest plotting two histograms, one for >0.1 ct/s as well as one for >0.01 cts/s, as the >0.1 ct/s sources are those which can be identified, and where estimates of distances would help in estimating feasibility of multiwavelength follow-up. Assuming the authors follow my suggestions above, it would be appropriate to change the distribution to T=8e5 K instead.

 

page 8, lines 263-264; there is a serious weakness here in that newly detected sources will be fainter than those previously known, thus making it harder to detect pulsations.

 

Fig. 4; this figure is somewhat hard to read, especially when printed out (as some readers will do). It attempts to convey, I think, too much information, and fails to get the key information across. I recommend that the authors remove the sources with ctrate <0.01 cts/s (which won’t be detected at all), and have only two kinds of points—sources with >0.1 cts/s, and those with 0.01–0.1 cts/s. This will enable the reader to find the points with >0.1 cts/s much more easily (I believe these are the truly interesting points).

 

page 9, line 274, and footnote 2; X-ray polarization could be a signature, though it would take some work to come up with clear predictions on differences between HOFNARS and other objects. However, the authors should be aware that IXPE is unlikely to be useful in the study of such faint sources; its area is only a few hundred cm^2 (perhaps a factor 2-3 larger than ROSAT), but to detect 1% polarization (as typical), the limiting flux must therefore increase by a factor of ~100, so IXPE is only designed to look at the brightest X-ray sources (not the faint sources discussed in this paper).

 

page 9, line 278-279; although rapid rotation alters the X-ray spectrum, the effect upon blackbody-like spectra is degenerate with other parameters, and cannot be identified clearly from a single spectrum. (See the NICER papers, and the relevant preceding papers by e.g. Bogdanov.) So I would suggest cutting this line.

 

Conclusions; the second sentence should be altered, following comments above. I am more pessimistic than the authors that numerous HOFNARs will be discovered by eROSITA, but I share their confidence that detecting any would be a dramatic scientific finding.

Author Response

We thank the referee for useful comments.
Please, note that the paper (in the revised version) is substantially expanded and modified. All changes are marked with bold face.

My largest concern is with comparison to the ROSAT Bright Survey. The authors say (p 7) that no objects which can be HOFNARs are identified in the RBS, but their preferred value of T=10^6 K predicts 6 (range of 3-10, which I infer is roughly a 90% probability range). Thus, formally, the detected value of 0 rules out T=10^6 K at 90% confidence (using Gehrels 1986 Table 1, I think 99.5% confidence is about right), and rules out T=8*10^5 K also at ~90% confidence (also using Gehrels’ Table 1). I think the authors are reluctant to embrace this constraint, understandably, but I think it allows a more robust upper estimate on the number of HOFNARs that are detectable under the authors’ assumptions (about 40, using 0.1 ct/s and the 8e5 K line in Fig. 2, though see below for caveats).

 In the revised version we change normalization to 5% instead of 10%. Also we modified slightly the model of the ISM distribution (removed an extra coefficient 2 in N_H). This changed numbers. 

We suspect that reporting precise percentage, as in the example suggested by the referee, can lead to a misleading feeling of high precision which is never a property of population synthesis studies when many different uncertainties are in the game. Still, we modify the text. 

My other significant concern is that the authors are rather vague about the reference point that should be used (page 6, lines 187-190, and p. 4, lines 154-155). It’s reasonable to say that 0.01 ct/s is the detection limit for eROSITA, but such sources will be barely detected. The authors suggest 0.1 cts/s as a better reference point. I think this deserves a little more discussion; the authors could reference the expected average (vignetted) exposure value from the survey to underpin their estimates. As a rough estimate, I see from Predehl+21 that the all-sky average after 4 years should be 2.5 ks; with vignetting (factor 1.88) and reduction of survey time (factor 2), that gives ~650 s, so that a 0.1 ct/s source will provide of order 65 counts. This is perhaps plausible as a lower limit for the number of counts needed to distinguish the hardness ratios of HOFNARs from the majority of X-ray sources (not to distinguish them from XDINS etc, but just to make a candidate catalog). I invite the authors to make their own estimate in this spirit.

We agree with the referee. The text is modified to give more details about the limiting count rate. In the revised version we add a discussion for both values (0.1 and 0.01 cts/s).

A third significant concern, though I do not think it ends up mattering significantly, is the extinction calculation (section 2.4). The model for the ISM used here is rather oversimplified, and inaccurate (though the inaccuracy is the fault of the prior modelers, not the current authors). The oversimplification is the distribution of molecular H_2 as a simple double exponential. This is a reasonable model for atomic H (with caveats) and for stars, but molecular H_2 is very clumpy—at the least this point should be acknowledged in the text.  The inaccuracy is the distribution of HI; the radial scale and scale height quoted do not look reasonable. I referred to Kalberla and Kerp (2009, ARAA), an appropriate review, where I see that a more appropriate radial scale would be about 3 kpc, and a more appropriate scale height (at our galactocentric distance, this varies) would be about 0.15 kpc. However, atomic H does very little extinction, so changing these values is unlikely to make large changes to the authors’ results.

   The FTOOLS (Colden) calculator is known to underestimate extinction values for many X-ray sources, due to the fact that it is constructed solely from atomic gas maps, omitting H_2. However, this tends to cause problems only at large distances in the Galactic plane, which is not really relevant for the authors’ purposes, as systems beyond (say) 3 kpc in the Galactic plane are already too obscured to be detectable.

We thank the referee for this comment as it stimulated us to make additional checks. We hope that this helped to make the paper better.
We directly confronted N_H calculated in the model we used (without additional factor 2) with UK Swift. A figure is added to the manuscript. As we see, the ISM model we used fits well with data from UK Swift for N_H through the whole Galaxy.
Thus, in the revised version we do not use the additional factor we introduced to double N_H in our model. 

   The advent of Gaia along with many other surveys has enabled much better three-dimensional extinction maps. I would encourage the authors to try using the Bayesmap to estimate extinction to ~1-2 dozen of their simulated objects; this tool is available at argonaut.skymaps.info, and published by Green et al. 2019, ApJ, 887, 93. If they find broadly similar results (at least within ~3 kpc) as their model, then just adding such a check to their paper should be sufficient. As mentioned above, I doubt the final results will be dramatically different, so I would not insist that the authors redo their full simulations.

We thank the referee for this link to the 3D dust map. We hope to use it in future in more detailed population studies, as comparison of X-ray absorption due to hydrogen with the dust absorption in optics is a rather complicated task involving additional uncertainties. At the moment, we are quite satisfied that an absorption model we have (on the basis of a recent ISM distribution) successfully passed comparison with UK Swift. 

Abstract; as mentioned above, the ROSAT Bright Survey makes the 10^6 K surface temperature (with assumed total population) implausible. It would seem appropriate to use the T=8e5 K scenario as a fiducial  upper limit, stating the assumption that HOFNARs are 10% as numerous as MSPs; and to mention that T=1e6 K (or higher) is possible if the relative frequency is smaller than this 10% assumption.

In the revised version we use fiducial normalization to 5% of MSPs. The text is modified accordingly.
Uncertainties in the normalization do not allow us to make solid conclusions about small differences in temperature. 

Model, section 2.1, line 63 on; the authors here imply that HOFNARs are typically bright for 10^10 years. My reading of reference 7 is that the fiducial lifetime is more typically 10^9 years. I would suggest the authors make clear that such a shorter lifetime is quite possible—as I will explain below, it doesn’t change their results, though it injects some uncertainty.

Same paragraph; “reasonable to assume they should have similar spatial distribution.” —this also depends on the HOFNAR lifetime, and to a lesser extent on spin-up. If HOFNARs have lifetimes ~10^9 years (which seems plausible), they may have slightly less extended spatial distributions than MSPs.  I doubt this will dramatically affect the conclusions, but is worth briefly mentioning. (MSPs can also be produced with less spin-up than seems necessary for HOFNARs, which could conceivably create differences in their distribution, but this is even less likely to give substantial differences.)

 Thank you for this comment. We fully agree with it and added a passage in the modified version of the paper (the second passage of Sec. 2.1)

Page 3, lines 86-97; as mentioned above, HOFNARs may have shorter lifetimes (~1 Gyr?) than MSPs. As globular clusters are older than the Galaxy as a whole, this may mean that the relative abundance of HOFNARs vs. MSPs could be higher in the Galaxy as a whole than in globular clusters. Again, this is only worth a brief mention, the author’s fiducial assumption here of 10% the MSP population is reasonable.

 We agree. We add a corresponding statement (see the last but one paragraph of section 2.1)

Section 2.2, p 3, lines 116-118; I might suggest a brief comment on how another temperature distribution (e.g. a power-law) would affect their overall findings (my initial assumption would be; not dramatically).

The temperature distribution of HOFNARs is very model dependent, but, hopefully, detectability of HOFNARs can be easily analyzed for any given distribution by staking our results for different temperatures with appropriate weights. We clarify it in the updated version (the first paragraph of Sec. 2.2)

1. 5, equation 5, and line 152; since the normalization by 4*pi*r^2 is carried out within the integration, the numerator should contain L(E), not F(E), signifying luminosity rather than flux.

 We did not suspect that such notation can lead to confusion, as the quantity is explicitly described. Indeed, formally this quantity can be called “luminosity measured in photons”. However, notation “L” is used in the paper in a different sense (as the usual luminosity). We change notation to N_{ph}.   

Fig. 3; I would suggest plotting two histograms, one for >0.1 ct/s as well as one for >0.01 cts/s, as the >0.1 ct/s sources are those which can be identified, and where estimates of distances would help in estimating feasibility of multiwavelength follow-up. Assuming the authors follow my suggestions above, it would be appropriate to change the distribution to T=8e5 K instead.

We plotted these two histograms, but for T=1e6 K and new normalization (our argumentation for this choice is given in the revised version of the manuscript).

page 8, lines 263-264; there is a serious weakness here in that newly detected sources will be fainter than those previously known, thus making it harder to detect pulsations.

 We agree. This part is re-written. We note in the new version that only dedicated observations with future X-ray observatories can identify pulsations in most of newly detected XDINSs.

Fig. 4; this figure is somewhat hard to read, especially when printed out (as some readers will do). It attempts to convey, I think, too much information, and fails to get the key information across. I recommend that the authors remove the sources with ctrate <0.01 cts/s (which won’t be detected at all), and have only two kinds of points—sources with >0.1 cts/s, and those with 0.01–0.1 cts/s. This will enable the reader to find the points with >0.1 cts/s much more easily (I believe these are the truly interesting points).

We removed the sources with count rate <0.01 cts/s. Now the figure gives a better representation of bright sources. 

page 9, line 274, and footnote 2; X-ray polarization could be a signature, though it would take some work to come up with clear predictions on differences between HOFNARS and other objects. However, the authors should be aware that IXPE is unlikely to be useful in the study of such faint sources; its area is only a few hundred cm^2 (perhaps a factor 2-3 larger than ROSAT), but to detect 1% polarization (as typical), the limiting flux must therefore increase by a factor of ~100, so IXPE is only designed to look at the brightest X-ray sources (not the faint sources discussed in this paper). 

 We agree. We added a comment that only future missions can succeed. 

page 9, line 278-279; although rapid rotation alters the X-ray spectrum, the effect upon blackbody-like spectra is degenerate with other parameters, and cannot be identified clearly from a single spectrum. (See the NICER papers, and the relevant preceding papers by e.g. Bogdanov.) So I would suggest cutting this line.

We removed this statement. 

Conclusions; the second sentence should be altered, following comments above. I am more pessimistic than the authors that numerous HOFNARs will be discovered by eROSITA, but I share their confidence that detecting any would be a dramatic scientific finding.

In the revised version we made the statement softer. 

Reviewer 4 Report

I have carefully read the manuscript of Khokhriakova et al. and I found it very interesting. The authors describe the possible existence of a new family of neutron stars, dubbed HOFNARs, together with number simulations based on population synthesis models and search strategies. Although no HOFNAR has been firmly identified yet, some candidates have been found, which encourages to pursue their search. Finding new HOFNAR candidates would be important to consolidate a new evolutionary path of LMXBs.

Both the population synthesis models and their applications are clearly explained and the assumptions are reasonable. I have no major point on this section but I have more on the detectability.

The predicted low number of HOFNARs suggests that finding good candidates is like searching for a needle in a haystack.  As the authors explain, this requires access to large X-ray surveys to detect the thermal emission from the neutron star surface, and the eROSITA survey is the natural choice.

- Hot thermal sources without radio emission could be a starting point, as explained, to distinguish HOFNAR candidates from MSPs, although the radio beam angle could explain the non detection. A further discriminant from MSPs would be the temperature and size of the emitting region. While the first can be determined from the X-ray spectrum, the second requires the knowledge of the distance, which cannot be directly obtained without a radio detection. What method do the authors assume as distance indicator?

• According to the authors, HOFNARs can be both in binary systems and isolated. In both cases, optical observations are useful to distinguish the former from the latter. However, given the eROSITA error circle what would the chance coincidence probability be to detect a possible HOFNAR companion? What would be the required limiting magnitude? What would be the typical magnitude for an isolated HOFNAR,  given its 10^6 K BB spectrum and for an hypothetical distance of 100 pc? If an isolated HOFNAR is detected in the optical, would proper motion studies useful to support the identification?

-         Lack of surface cooling would be useful to support an HOFNAR identification but is it feasible in the eROSITA lifetime?

- Since all the authors are affiliated to Russian institutes, they should have already  access to the proprietary eROSITA data for one half of the sky. Do They have some plans to access these data and start they search from now?

Author Response

We thank the referee for useful comments.
Please, note that the paper (in the revised version) is substantially expanded and modified. All changes are marked with bold face.

 

- Hot thermal sources without radio emission could be a starting point, as explained, to distinguish HOFNAR candidates from MSPs, although the radio beam angle could explain the non detection. A further discriminant from MSPs would be the temperature and size of the emitting region. While the first can be determined from the X-ray spectrum, the second requires the knowledge of the distance, which cannot be directly obtained without a radio detection. What method do the authors assume as distance indicator?

• According to the authors, HOFNARs can be both in binary systems and isolated. In both cases, optical observations are useful to distinguish the former from the latter. However, given the eROSITA error circle what would the chance coincidence probability be to detect a possible HOFNAR companion? What would be the required limiting magnitude? What would be the typical magnitude for an isolated HOFNAR,  given its 10^6 K BB spectrum and for an hypothetical distance of 100 pc? If an isolated HOFNAR is detected in the optical, would proper motion studies useful to support the identification?
  
  Optical identification and study of an isolated HOFNAR might be an extremely difficult task, as such sources are not expected to be near-by objects (our estimates show that all HOFNARs might be at distances >> 100 pc). Thus, we do not discuss this in the paper.
  
  For sources in binaries optical identification can serve as a distance indicator. Otherwise, we have just a poor estimate based on the interstellar absorption in X-rays.

-         Lack of surface cooling would be useful to support an HOFNAR identification but is it feasible in the eROSITA lifetime?

According to theoretical estimates, there are no chances to detect HOFNARs cooling during the eROSITA lifetime as all time scales are too long. Also, till eROSITA operates in the survey mode it is impossible to collect enough photons to obtain a high-quality spectrum for any candidate. Dedicated observations with larger observatories (Chandra< XMM-Newton, in future - ATHENA) are necessary.

- Since all the authors are affiliated to Russian institutes, they should have already  access to the proprietary eROSITA data for one half of the sky. Do They have some plans to access these data and start they search from now?

The situation with direct access to the “russian” data is not so simple. Authors of this paper are currently not members of the consortium. Thus, we cannot easily access the data. However, we plan (after the paper is published) to discuss with colleagues from the consortium the possibility to dig the data in order to identify HOFNARs.   

Reviewer 5 Report

The report is written in the file report112.pdf

Comments for author File: Comments.pdf

Author Response

We thank the referee for useful comments.
Please, note that the paper (in the revised version) is substantially expanded and modified. All changes are marked with bold face.

However, there are two theoretical aspects that are just mentioned but not discussed in the

manuscript that in my opinion require a more detailed explanations. On the one hand, the

existence of HOFNARs require that the candidate NS lie in the region of of r-mode instability.

This, of course, depends on the underlying EOS of the NS and on the damping mechamnism

involved in the spin-down evolution, which nally determine the instability region. In addition,

direct URCA processes also play a role during the cooling of newborn NS. More details about

these topics can be found in S.P. Pattnaik et al, J. Phys. G Nucl. Part. Phys. 45 055202 (2018) and T.R. Routray et al Phys. Scr. 96 045301 (2021) and references therein. Thus to point out the minimal conditions that EoS of NS should fulll in order to the possible existence of HOFNARs seems to me an essential information that should be given in the manuscrpt. On the other hand, the authors claim that if there is no detection of HOFNARs from eROSITA X-ray all-sky survey, important constraints can be put on the properties and origin of these objects. More specic and detailed discussions about these constraints seem to me absolutely necessary.

We added a paragraph  (the first one in Section 2.2.) to clarify that  a realistic study of HOFNAR formation is a very complicated problem. Solution of this problem  essentially depends on several processes for which models are not enough certain, yet.  We  provide a list of  references on this topic, including the one suggested by the referee. We also add a footnote with a reference to a paper where it was stated  that r-mode heating can be important for newborn neutron stars.

 

Finally, let me point out a possible misprint. At the begining of Section 4.2 it is written "As

shown in Sec. 3 for our fiducial parameters (see Sec. 2) we expect detection of  600 HOFNARs by eROSTA X-ray all-sky survey and 120 of them (2.5-3% of the total HOFNARs population) are expected...". If the total population is  600, the 2.5-3% should be 12 and not 120. If I am wrong, please clarify the seentence,

We tried to re-write this part in a more clear way. Note also, that due to modifications in the model numbers are slightly changed.

Round 2

Reviewer 1 Report

 

Second Referee opinion on Manuscript ID: universe-1735388

Title: Observability of HOFNARs at SRG/eROSITA

Authors: Alena D. Khokhriakova , Andrey I. Chugunov, Sergei B. Popov , Mikhail Gusakov, Elena Kantor

The authors did not take my comments into account in any way.
They were also not included in the revised version of the work.
Thus, I do not see any grounds for revising my previous negative opinion.
I maintain the opinion that the paper is not suitable for publication.