Accounting for Selection Bias and Redshift Evolution in GRB Radio Afterglow Data
Round 1
Reviewer 1 Report
I have read carefully the manuscript, "Accounting for Selection Bias and Redshift Evolution in GRB Radio Afterglow Data", by authors Dainotti, Levine, Fraija, and Chandra.
The work shows the evolution in the GRB population parameters with redshift, as found via an Efron Petrosian method, and includes the evolution in parameters for the radio afterglow for a small (15 burst) sample of relevant GRBs.
I find the paper to be interesting, well written, and highlights the importance of including parameter evolution with redshift when GRB correlations are used.
I have some minor comments that the authors should consider.
In order of appearance:
It would be nice to see more diverse citations in the introduction. Many/all of the listed examples are self-citations e.g., high redshift GRBs at z~9.4 should include Cucchiara ea 2011... and maybe other examples of high-z GRBs -- Tanvir ea 2009, Tanmoy ea 2014, Littlejohns ea 2013, McGuire ea 2016, Salvaterra ea 2009, Tanvir ea 2018, and so on.
Similarly, the listed review papers are all by the same authors -- are there any other examples?
Lloyd-Ronning's recent work is noted towards the end of the Introduction -- the following paragraph starts, "In this study..." and describes the aim as being to seek if evolution in z "...is still true..." -- it is not clear o me if the evolution with redshift here is that found by Lloyd-Ronning, or Dainotti, or both? This could be more clearly written.
The broken power law index, alpha_1 -- is this alpha_1 the pre-break index? If so, it should be clearly defined as such. Also, as the sample is selected by the plateau, surely alpha_1~0? What is the range for alpha_1 in the sample?
The limiting duration for T90* is stated as negative, -0.54 s and -0.3 s.
Why is T90* a negative value? It is not clear to me what a negative T90 duration means/is, as T90 is the arrival time for 90% of the energy at the detector?
The requirement for a limit is introduced, however, it is not instantly clear what e.g., a "fluence limit" means here?
For the fluence, how is the limit chosen? Is this some artificial lower-limit? Is it motivated by detector sensitivity? Is it found by some vague statistical method?
This should be more clearly described and explained.
For the flux cuts -- does this mean cut above or below the limit?
"...as well as the distance between the two samples..." -- it is not immediately obvious what "distance" means here, please clarify in the text.
The log flux limit of -17.2, what unit is the flux in here? Please state it.
In the Results, the functional form for each parameter is given -- the primed quantities need to be clearly defined.
In Discussion & Conclusion, the \delta value should be re-described i.e., the index for the parameter redshift evolution.
Fig 3; Add a more complete description of the plots in the caption -- red line, blue dots... what are these?
Isn't Tmin = -0.54, or -0.3 s (negative times!)? It appears that Tmin ~ 4.5s at z=0 here?
Can we not plot the parameter trend +/- 1-sigma lines on here also?
Final point 3 re EP and small samples.
I'm not sure point 3 is shown -- The authors should remove this from the listed conclusions and keep the general discussion i.e., that the small sample size does not appear to be an issue. "Appear" is the key word here, a larger sample size could well change the result, as discussed for X-ray/optical data.
Author Response
Please see the attachment
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This paper report the study of redshift evolution of physical
quantities for gamma-ray bursts whose radio afterglow was detexted.
The resdhift evolution of the rest time and luminosity of radio afterlow
plateau end was a new result, but the paper presentation should be
updated for publication.
Major comments
First of all, the main subject of this paper is unclear. In the introduction,
bias correction is explained in detal, while the main result is to obtain
the redshift evolution using EP methed.
If the main subject is to derive redshift evolution, authors should
explain why end time and luminosity of radio afterglow plateau is important
to understand GRB physics or evolution. Whey the past study using optical and X-rasy data is not enough ?
If you develope a new method following EP method, you should describe it but
I do not find any discription about it.
In summaty, the introduction should be updated so as to describe the importance of study of redshift evolution of GRB quantities and radio properties. EP method is just a method to apply in this paper.
ALso, what you can say about GRB science from obtained redshift evolution of radio perperties should be discussed
minor comments
line 149-151
SHow an equiation you used in the fitting of light curve.
line 165-166
What is the minimum observed time ?
line 169-170
It is not clear the relation of 0.54 and 0.30.
line 186
Unit or definition of this quantity should be shown for -17.2.
line 197^109
The meaning and definition of tau should be shown.
line 254-260
It seems that the results compared with the result in this paper are
not published and not presented anywhere, so should not be used.
Author Response
Please see the attachment
Author Response File: Author Response.pdf
Reviewer 3 Report
This manuscript reports on the correction of the GRB variables due to the selection bias using the Efron-Petrosian method. The correction is crucial for exploring the potential correlations between these variables and using them as cosmological tools. Especially, the radio afterglow data are analyzed for the first time in this work. I think this manuscript is worth publishing after the authors address the points I raise below.
1. It could be understood that Eiso presents a strong evolution with redshift in view of the different characteristics of GRB progenitors at different redshifts. However, the correlation of La,radio with redshift is a bit confusing. The GRB sample that has radio afterglow data is small. It may be due to the truncation from detector limits, or most commonly the subjective and objective issues on the follow-up observations in the radio band after a GRB trigger. The radio light curves showing a “plateau” feature is a subsample of this “biased” sample. It is hard to relate La,radio with the redshift. Thus it would be fine for readers if possible brief reasons for the La,radio vs redshift correlation are given.
2. In line 85 on page 3, when “model discriminators” are mentioned, references using relations (e.g., E_p vs E_iso) to discriminate the prompt emission models (synchrotron or photosphere) of GRB should be added.
3. In line 151 on page 4, radio light curves showing a “plateau” feature are collected as the sample. Is it possible to determine/give the explicit criteria for this feature in the text, e.g., the critical value for the temporal indices of light curves?
Author Response
Please see the attachment
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Manuscript has been revised accordingly.
Just one comment on conclusion.
line356: "all present strong correlation with redshift"; but Eiso does not show a significant evolution in the author's result 0.39+/-0.88, so this should be "T90, La,radio, Ta,radio show a strong correlation....."
Author Response
Dear Referee,
We thank you very much for your last comment which we have fully addressed.
We have put in bold the changes.
Thank you,
The authors
