Afterglow Light Curves from Off-Axis GRB Jets in Stratified Circumburst Medium
Round 1
Reviewer 1 Report
In the manuscript, the authors consider the afterglows of gamma-ray bursts and derive analytical expressions for the same in the stratified external circumburst medium for off-axis light curves. They determine the temporal indices of the coasting phase, the Newtonian phase, and the deep Newtonian phase for various viewing angles and power-law indices of medium density. The afterglow flux evolution is then plotted for various off-axis angles.
I believe the findings of the papers will be useful in classifying GRBs and their possible use as standard candles. I would like authors to explore this angle to make the paper of interest to cosmologists.
I strongly recommend acceptance of the paper for publication in Universe.
Author Response
Response to Reviewer 1 Comments
In the manuscript, the authors consider the afterglows of gamma-ray bursts and derive analytical expressions for the same in the stratified external circumburst medium for off-axis light curves. They determine the temporal indices of the coasting phase, the Newtonian phase, and the deep Newtonian phase for various viewing angles and power-law indices of medium density. The afterglow flux evolution is then plotted for various off-axis angles.
I believe the findings of the papers will be useful in classifying GRBs and their possible use as standard candles. I would like authors to explore this angle to make the paper of interest to cosmologists.
Re: We thank the referee for good comments on our paper.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments for author File: Comments.pdf
Author Response
Response to Reviewer 1 Comments
Point 1: according to my estimates, Eq.~(6) of the subsection 2.1 for fast cooling in the coasting phase contains an error: it should be $\nu_a \propto T^{(8 – 9s)/ 5}$ but not $T^{(23 – 9s)/ 5}$ as it is written in Eq.~(6). In any case, such a discrepancy requires an explanation: any reader can produce these simple estimations.
Re: We thank the referee for their carefully reviewing the paper. We indeed made a stupid mistake. We have corrected the index from $T^{(23 – 9s)/ 5}$ to $T^{(8 – 9s)/ 5}$. We also have double checked other scalings to guarantee no other errors.
Point 2: This error (as it seems to me) leads to an error in Eq.~ (7) for the same phase, namely: it should be $F_\nu \propto \nu^2 T^{1+s}$ at $ \nu < \nu_a$ , but not $F_\nu \propto \nu^2 T^{-4+s}$ as it is written in Eq.~(7).
Re: The wrong light curve index in $\nu_a$ indeed led to the error in Eq. (7). We have corrected the index from $F_\nu \propto \nu^2 T^{-4+s}$ to $F_\nu \propto \nu^2 T^{1+s}$.
Point 3: This in turn leads to errors in the second column of Table 1 for fast cooling in the coasting phase at $\nu < \nu_a$.
Re: We have correct the error in Table 2 (old Table 1). We thank the referee again for pointing out this error.
Point 4: Such errors, if the authors will not refute the proposed estimates, may lead to changes in the early stages (relatively small $T$) of Fig. 1, 2, 3.
Re: We thank the referee for raising this point. The errors will not affect the light curves and the slopes in Fig. 1, 2, 3, because the light curves are calculated with the numerical method, which is different from the analytical estimation. And for the cases of $s=0$ and $s=2$ in Fig. 2 and 3, the three frequencies we considered are not in the segment of $\nu<\nu_a$ in the early stage (coasting phase).
Point 5: Regarding figures 4, 5, 6:
(a) In my opinion, the authors should explain just in the text a quite visible fact,
that in the left and right panels, the light curves corresponding to the same set of
variables $\theta_\nu$ and $s$ do not match as in maximum amplitudes, as in
peak positions. These discrepancies are not too great, but quite noticeable. For
example, the authors can compare two red curves in the third left and right panels from the top in Fig.~4 at $ s=1.0, \theta_\nu = 0.4,$ (left) and $\theta = 0.4, \s= 1.0$ (right).
(b) One can also wish that units of measurement have also been entered in the
right panels, since the scales of the left and right panels in all three figures are
mutually shifted.
Re:
(a) We indeed made a mistake when plotting the figures. The mistakes in the plotting code lead to disagreement between the figures and the captions. We have corrected the errors. We thank the referee for pointing out this mistake.
(b) We thank the referee for their suggestion. To be more clear, we add the y ticks (flux) in the right panels. See the new Figures 4, 5, 6.
We also corrected other typos.
Reviewer 3 Report
This is a high-quality paper that deserves to be published in its present form. The only comment is that the characters in both figures and tables should have been somewhat larger.
Author Response
Point 1: This is a high-quality paper that deserves to be published in its present form. The only comment is that the characters in both figures and tables should have been somewhat larger.
Re: We thank the referee for their positive comment and suggestion on our paper. We have changed the font in Figures 4, 5, 6 and Tables 2, 3, 4, 5 (old Tables 1, 2, 3, 4) to make them more clear.
Reviewer 4 Report
The paper analyzes o-axis light curves of GRB afterglows in the stratified external medium and summarizes the scaling.
The authors do not analyze other works in the literature compared to the proposed work; thus making it difficult to verify the differences and the contributions of the proposed work with other works in the literature. I suggest writing a section of related works, in which it describes the main works in the area and what the difference between them and this work is.
The authors used the FORTRAN programming language which is a very old language from 1957. Using a more modern language can be more effective and beneficial.
The algorithms need to be better detailed in the text so as to make the paper clearer.
The paper needs a table of acronyms to facilitate the search for their definition. Some acronyms may have more than one definition, so it is necessary to have a consistency of the terms.
Although the authors have achieved good results, a more detailed description of why these results have been obtained is important, especially in comparison with other works in the literature.
The references are written in an uncommon standard.
Finally, what is the novelty of the algorithm? Why do not the authors put into the spotlight with more strength the potential of the method? Is the method novel enough? What are its differences with other similar methods? Why do they select this method and do not select other methods?
Author Response
Response to Reviewer 1 Comments
Point 1: The authors do not analyze other works in the literature compared to the proposed work; thus making it difficult to verify the differences and the contributions of the proposed work with other works in the literature. I suggest writing a section of related works, in which it describes the main works in the area and what the difference between them and this work is.
Re: We thank the referee for their good suggestion. We have added some sentences to compare our results with other works. See the last part in subsection 2.1 (P3, in bold), the last second sentence in subsection 2.2 (P4, in bold), and the sentences below Eq. 15 (P4, in bold) and the last second sentence in subsection 2.3 (P5, in bold). We want to emphasize that previous works gave the light curve slopes of two special cases of s=0 and s=2, while we gave the general case with arbitrary s.
Point 2: The authors used the FORTRAN programming language which is a very old language from 1957. Using a more modern language can be more effective and beneficial.
Re: We thank the referee for raising this point. Fortran is indeed an old language. But it is still useful in numerical calculation. Sometimes it is even faster than the c language in calculation.
Point 3: The algorithms need to be better detailed in the text so as to make the paper clearer.
Re: We thank the referee for this requirement. We have provided more details of the algorithms in the first paragraph in subsection 3.3 (P6, in bold).
Point 4: The paper needs a table of acronyms to facilitate the search for their definition. Some acronyms may have more than one definition, so it is necessary to have a consistency of the terms.
Re: We thank the referee for this good suggestion. We have made a table of acronyms. See Table 1 (P2) in the new version.
Point 5: Although the authors have achieved good results, a more detailed description of why these results have been obtained is important, especially in comparison with other works in the literature.
Re: We thank the referee for the positive comment on the paper. As we presented before, we gave general light curves for arbitrary power-law circumburst medium density. One can be used to qualitatively identify the circumburst environment from the observed spectral and multi-wavelength light curves and find the density profile (wind, ISM, or other cases). The numerically light curves are also a display of the temporal morphology of the GRB afterglow for different view angles and different circumburst density profiles, which can be used to identify GRB sources from future survey data and fit the multi-wavelength light curves. We have added a paragraph in section 4 (P11 in bold) to give a more detailed description of this question.
Point 6: The references are written in an uncommon standard.
Re: We thank the referee for noting this. We have double checked the references and corrected the errors.
Point 7: Finally, what is the novelty of the algorithm? Why do not the authors put into the spotlight with more strength the potential of the method? Is the method novel enough? What are its differences with other similar methods? Why do they select this method and do not select other methods?
Re: We thank the referee for raising these points. The basic algorithms we used are not novel, like the Runge-Kutta method, Gaussian integration, iteration method, and so on. We used some techniques to improve the integral precision and speed up the numerical calculation so that we can use the code to make the data fit with multi-wavelength light curves. To our knowledge, the 2 or 3 dimension hydrodynamic simulations, although more accurate, are not efficient to do the data fit because they are time-consuming. In subsection 3.3, we have provided more details of the algorithms (P6, in bold).
Round 2
Reviewer 2 Report
I have no comments or suggestions to the vertion 2 of the manuscript.
To my mind the article can be published.
Comments for author File: Comments.pdf
Reviewer 4 Report
The authors did only some superficial amendments and do not agree with me. They believe their paper is publishable although the paper is almost the same and the problems are almost the same. Let the editor decide what to do with this paper.
