Exploring Anisotropic Lorentz Invariance Violation from the Spectral-Lag Transitions of Gamma-Ray Bursts

Round 1

Reviewer 1 Report

The authors presented the constraints on a variety of isotropic 9 and anisotropic Lorentz-violating coefficients in the manuscript, based on the spectral-lag transition features of 32 GRBs. This is an interesting work concerning the basic physics. I have two comments below:

(1) Since the title is "Exploring Anisotropic Lorentz Invariance Violation....", however, I did not find a text to present the difference between "isotropic" and "anisotropic", the authors should describe it somewhere.

(2) The spectral-lag transition from positive to negative in this manuscript is for the power-law index when fitting the curve between the spectral lag and the photon Energy, the authors should stress it somewhere, otherwise the reader will be misled.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The authors present an analysis of previously published GRB spectral-timing
data in order to derive constraints on coefficients of the Lorentz-violating
Standard-Model Extension (SME). They do so by considering gamma-ray bursts
that exhibit a negative change in spectral lag indicating that some higher
energy photons arrive earlier than lower-energy ones. The authors fit a model
to the spectral lag that accounts for both intrinsic time lags and a lag due
to Lorentz invariance violation described in the framework of the SME. While
the constraints on coefficients with mass-dimiension d=6 presented in this
paper are (as the authors admit) not competitive, they do present an
interesting new approach with systematics that are very different from
previously reported results. Furthermore, there are very few constraints on
coefficients with mass-dimension d=8, and the results complement previous
constraints. Hence, these are important results. The paper is generally well
written. However, I do have some serious concerns about the presentation of the
analysis and the results that need to be addressed before I can recommend
publication.

The authors restrict their analysis negative-induced spectral lags. While they
don't specifically state how that is achieved, I must assume that this is done
by constraining the expansion of SME coefficients to positive values. It
appears that this constraint forces their analysis to always return positive
values, making it impossible to obtain uncertainty intervals that include zero.
In other words, the analysis is designed to exclude the null-hypothesis.
Indeed practically all best fit values of the linear combinations of
coefficients presented here are already excluded by previously reported
results. This limitation must be discussed in the paper.

Furthermore, the analysis measures the deviation of time-lag spectra from a
particular smoothly broken power-law model. There is no discussion of the
astrophysical motivation of this model. Must we assume that any deviation
from this model cannot be explained with source-intrinsic effects? What are
the systematic uncertainties introduced by making this model assumption?
Is it possible that making this assumption could either result in a bias
towards non-zero values of SME coefficients, or could it lead to artificially
low upper limits?

Even more concerningly, the authors report three results that exclude the
null-hypothesis with a high level of confidence. Estimating from the 95% levels
in Table 2, the results from GRB 090328, GRB 160625B, and GRB 200829A are
incompatible with zero at the 3.3σ, 11.8σ and 10.0σ confidence level,
respectively. Are the authors claiming to have discovered evidence of
Lorentz invariance violation? How can these results be reconciled with previous
upper limits? These questions need to be addressed explicitly in the paper.
Furthermore, it should be discussed how the limitation on values greater
than zero influenced the results, or how model-dependent the results are.


Minor comments:
- Line 18: "violated broken", remove one of the two words.

- Line 80: The authors should discuss the systematic uncertainty due to
  their choice of H₀ parameter given the tension between different
  measurements.
 
- Line 85: The SME coefficients are complex. Saying they're positive or
  negative makes no sense.
 
- Paragraph below line 107: What do you mean by "global fitting"? It seems
  that you still fit each GRB individually, treating the linear combination
  of SME coefficients for that GRB as a parameter. To me, your wording
  implies that all GRBs are fit simultaneously. At least in the d=6 case
  this would be possible (using the coefficients rather than their linear
  combinations as parameters). If you are indeed fitting all GRBs at the
  same time, it is unclear to me, what the connection between the different
  observations is. This needs a better explanation.
 
- Line 142: Your method relies on a particular model of the GRB lag
  transition. How can you claim that the results are more robust than
  previous, model independent results?

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

This paper can be considered a continuation of the previous work by Zi-Ke Liu et al (2022 ApJ 935 79) published this August. Zi-Ke Liu et al are indeed cited many times throughout the paper.

The 2 papers are very similar: they used the same GRB dataset, they make the same assumptions and they apply the same statistical analysis.

The main difference between the two papers is that Zi-Ke Liu et al considered vacuum dispersion with Taylor expansion, while in this work the authors focus on vacuum dispersion with Standard Model Extension.

The paper is easy to follow and clearly written, thus I recommend this paper for publication after implementing an important improvement that I describe below besides giving a list of typos that the author should correct.

--------------------------------------

Improvement:

The authors report limits on the LIV parameters for all the GRBs separately (table 2), but since the LIV parameters are global, it would be very useful to perform also a global fit on these parameters taking into account all GRBs, as it was done in Zi-Ke Liu et al (see Fig. 3 of their paper).

If otherwise, the authors think that such a global fit is not possible, they should explain it in the text. 

--------------------------------------

Typos:

line 4: of a GRB that displaying  --> of a GRB that displays

line 18: violated broken  -->  violated and broken

end of page 2: can be decomposed in a spherical-harmonic basis --> can be decomposed on a spherical-harmonic basis

line 74: represent spin-weighted --> represents spin-weighted

beginning of page 5: chain Mote Carlo (MCMC) technology --> chain Monte Carlo (MCMC) technique

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

I would like to thank the authors for the extensive changes made to the analysis and the description in the text in response to my previous comments. The paper has improved significantly. One aspect of the conclusions that I have been questioning has actually become worse with the new analysis, and has not been fully addressed.

The authors find a significant deviation from the null hypothesis of no LIV in 10 out of 32 Gamma-ray Bursts. As they acknowledge in the text, these deviations from the null hypothesis are inconsistent with constraints derived in previous works. Thus, clearly, in these cases the method did not work because the model assumption for the spectral lag behavior does not hold.
- To a degree, this undermines the argument made in section 3, that the broken power-law model is an accurate representation of the intrinsic time lag behavior. This needs to be discussed.
- The most important question this raises is: Why should one consider the upper limits derived for the other sources reliable, given the fact that for about 1/3 of the cases the astrophysical model does not work? Imagine the authors had found a significant non-zero spectral lag that is consistent with (i.e., below) existing upper limits. Would one claim a discovery of Lorentz invariance violation? This is, of course, hypothetical since no such discovery is claimed. However, given the limits reported here, the authors need to discuss whether or not the method they present could result in artificially low upper limits if the model does not correctly describe the intrinsic behavior of the GRB. Would it be possible to miss LIV due to the assumptions made in this paper? This certainly requires discussion, and may require some additional analysis to support the discussion. The limits reported here can only be considered reliable if the model assumption could at most result in limits that are higher than what one would achieve without assumptions about the GRB. In other words: can the limits derived in this paper be considered conservative?

Once these points have been addressed, I can recommend the paper for
publication.

Author Response

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Author Response File: Author Response.pdf