Constraining the Thickness of the Galactic Halo through Cosmic-Ray Anisotropy Using the Spatial-Dependent-Propagation Model

Round 1

Reviewer 1 Report

This paper discusses the use of the spatial-dependent propagation model with a nearby source to simultaneously study the cosmic ray spectra and its anisotropy in the energy range 10^2 – 10^7 GeV and the Solar offset from the galactic disk. The model describes properly the CR spectra and anisotropy, however, the thickness of the halo should increase linearly with the displacement of the Sun from the Galactic disk because a thicker halo is needed to counterbalance the vertical anisotropy that would be induced by the solar offset. 

From the experimental point of view, this is an interesting model result that could help understanding the origin of the variations in the spectral index and anisotropy of CR as a function of energy which indicates a more complex scenario that what was hypothesized in the past decades. The authors suggest that the currently operating LHAASO experiment could test the proposed model with higher accuracy thanks to the data collected in the TeV – PeV range both for the anisotropy and CR spectra. This would be extremely important to prove the correctness of the model.

From my perspective the paper is well written and deserves publication. The bibliography is rich and appropriate providing a good summary of the current experimental results and model interpretations and predictions.

 

Before publications I have a few small recommendations:

a)     Line 33: reference [19] belongs to IceCube, not to EAS-TOP therefore it has to be changed with 'EAS-TOP[18], IceCube/IceTop [19,20]'.

b)    Line 94: ‘The’ repeated twice. 

c)     Line 126-127: ‘It was found that….’. If possible I would suggest to provide a reference or a more quantitative result that supports this statement.

d)    Figure 6: Experimental points should have their own legend to understand to which experiments they refer to.

e)     Line 200: substitute ‘solar’ with ‘Sun’

f)     Line 211: remove ‘the’ in front of ‘constrain’

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Dear Author

The manuscript "Evidence of thick halo obtained by cosmic ray anisotropy for spatial-dependent propagation model" the study of the combined effect of the solar offset, the nuclei spectra, and the cosmic ray anisotropy to investigate spatial dependent propagation models.
This is potentially a very interesting topic.

However the manuscript is not very clear and should be improved.

Question 1)
Please improve the sentence:
"the propagation parameters under various Z_IH are determined by fitting the ratio B/C, and the background component of proton spectra are obtained with the DRAGON package".
In particular Fig.3 Fig.4 and Fig.5 captions are describing "Model predictions" but some of these data points should be used in the fit.
I require section 3 must be improved with a clear list of data that are used in the fits.

Question 2)
Fig.4 must be improved
(PAMELA ATIC NUCLEON)
but mainly DAMPE and CALET measurements of proton flux at "low energy" are missing.
IceTop measurement of proton flux at higher energy is missing.
(See. e.g. https://doi.org/10.1016/j.astropartphys.2020.102441)
If proton flux information is used in the results, these data should be considered.

Question 3)
Please comment why Helium and p+He data are not included in this analysis.

Question 4)
Please quantify/comment how much robust are the results against systematics in the flux measurements (see e.g. the different proton flux measured by KASKADE and IceTop)

Question 5)
Please quantify/comment how much robust are the results against the assumption of the local source hypothesis. Different explanations of the proton flux behavior are possible.

Question 6)
"The goodness of model fitting [...] are 0.81, 0.43, 4.84, 10.16 and 16.92"
Please give the explicit description of the "goodness of model fitting" adopted (and the number    of parameters and data points in the fit).

Question 7)
The title of the manuscript is:    
"Evidence of thick halo obtained by cosmic ray anisotropy for spatial-dependent propagation model"
However the Fig. 7 suggests that this manuscript would provide an upper limit to the halo thickness.
Please clarify this point.
If this analysis provides an upper limit, this limit should be stated in the conclusion (and in the abstract) with an indication of the confidence level.
Moreover I also suggest improving the title accordingly since the "Evidence" term is usually related to a measurement and not to a limit.

Best Regards

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

This paper is interesting and attempts to find a global understanding of a combination of measured cosmic ray anisotropies and composition, essentially at energies below the cosmic ray knee.  Its ideas will be of interest to the cosmic ray community although, in my opinion, model oversimplifications in the paper will require much more work before the results can be truly acceptable.  However, the ideas in the paper make its publication worthwhile.  Its assumptions are generally simple but serve to point ways forward in the field and can be topics for further discussion.

The paper uses ideas of cosmic ray diffusion from both local and distant sources to fit features of the cosmic ray energy spectra and composition.  Those observational data are now sufficiently detailed that it is truly time for the addition of detailed galactic structure to propagation modelling.  This is begun in this paper in terms of the dimensions of the galactic halo and the location of the solar system within the structure of our galaxy.  This is currently oversimplified for truly fitting models to real data.  We are dealing with radii of gyration (highest for protons) which are substantially sub-pc in dimensions.  However, it is well-known that the heliosphere resides in a complex local matter/ magnetic field structure which has dimensions of many pc, often called the local bubble, which must be an important contributor to the cosmic ray anisotropy at sub-PV rigidities.

So, my feeling is that this paper is worthwhile but it does not contain THE answer.

As general comments on the paper, it would be  better if specific rigidities are identified with various phenomena (e.g. lines 63, 64).  this is often done in the paper but it could be done more since we are dealing with a rigidity range which is much more than 1000x and physical phenomena change appreciably from TV to PV.

As I noted above, there is a problem with using straightforward diffusion ideas in a galactic volume out to 0.2 kpc (line 100), even assuming some form of general (Kolmogorov) turbulence.

Figure 1 would be better re-drawn with larger fonts.  The current fonts are not easy to read if a printed page is used.

In Figure 4, as I understand it, there is a large jump in the figure structure from 0.75 to 1 kpc.  This seemed strange to me and a comment in the paper would be welcome.

Rigidity is crucial in this work so it would be helpful to know when the composition under study is protons (Fig 4) or maybe mixed in some unclear way (Figure 6).

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Dear Author

As I said, this manuscript is potentially a very interesting.

I appreciate your effort in improving the manuscript, however four points must be solved:

 

1) as requested in the previous report i cannot see “A clear list of data used in the fits” 

2) From the improvements in line 171-175 I understood you are fitting only the 4 points of the green area in fig.6.  I cannot understand the reason and I found this is unfair. A fair approach would be the evaluation of the overall chisquare using ALL the data points you show in fig.6, fig.5,fig.4 (both P and He plots), fig.3.

3) P-values are puzzling, the quoted limit seems not reliable to me.

As far I understand (in this deprecated 4 points approach) you have 4 data points and 1 free parameter,

The minimum of chisquare you found is near to 1 (but a chisquare minimum of 3 is typically expected with 4 points and 1 parameter) however in this 1 parameter case the evaluation of the P-value should be straightforward from the simple 1 parameter gaussian probability.

I understand you assign 1 sigma to chisquare=14.5, 2sigma to 30.5 and 3sigma to 50.5.

Please explain to me why the P values are not 3.8sigma=sqrt(14.5) and 5.5sigma=sqrt(30.5) and 7.1sigma=sqrt(50.5) ad expected for 1 parameter.

Moreover I suggest you to include all the data points of all the figures in the chisquare evaluation, paying attention to evaluate the systematic errors of P flux at high energy, as I suggested you in previous report. Then you could/should face the problem of comparing a minimum of chisquare that is much larger with respect to the number of data points, that is evidence of systematics or a not "fully-reliable" model.

 

4) The chisquare obtained for Z_IH = 0.75 is not very high. It is not clear to me if lower Z_IH are still compatible with data points or not. You should evaluate also the model with Z_IH=0.5 (you could obtain a Z_IH measurement and not a limit). I suggest you to show the plot chisquare vs Z_IH (and possibly to provide a quadratic fit to find a minimum and evaluate the confidence interval). At the end you must comment with a warning that your limit/measurement is obtained considering the model you assumed for the local source and you should be fair in citing also the possibility a different model considering complex cosmic ray propagation.

 

best regards.

 

 

Author Response

please see the attached file

Author Response File: Author Response.pdf