Analytical Constraints on the Radius and Bulk Lorentz Factor in the Lepto-Hadronic One-Zone Model of BL Lacs
Round 1
Reviewer 1 Report
The paper is dedicated to restriction of parameters of neutrino-emitting blazar based on multi-wavelength observations. It provides analytical expression for boundaries of parameter space and therefore can be adjusted for future observations. The downside is that the strongest limit on parameter space comes from observed neutrino flux, which value is extremely unreliable at present moment. Yet, it cannot be considered as a weak point of the paper, since future observations could improve the available information on neutrino fluxes.
Therefore, I suggest this paper to be accepted after a few minor corrections:
1)Page 2, line 68. \tau_{flfl} is later called \tau_{\gamma\gamma}
2)Page 2, line 89 - page 3, line 92. It is stated that t'_{var} ~ R'/c, but later it is stated that t'_{var} <= R'/c. Could you please clarify it? The second condition seems excessive, since expression for t'_{var} is already introduced.
3)Page 3, line 100. Limitations, based on the gamma-ray flux from SSC and hadronic processes are introduced as L_{ssc} <= L_{\gamma} AND L_{p\gamma} <= L_{\gamma}. Would it be possible to introduce a stronger limitation that L_{ssc} + L_{p\gamma} <= L_{\gamma}?
4)Page 5, Eq. (16). This expression relates gamma-ray spectrum to proton spectrum. Should it be expressed through q instead of \alpha?
5)Page 5, line 147, Eq. (18), Eq. (19). L_{pfl} was never introduced. Is it L_{p\gamma}?
6)Fig. 2. In the legend I suggest replacing 10L^*_p with 10L_{\rm Edd} and same for factors 10^2 and 10^3
7)Fig. 2. and Fig. 3. The green regions are too small and are almost impossible to see. You can, probably place them in front of the curves to make them visually larger.
Author Response
Dear Editor,
Thank you for forwarding us the referee’s report. We have studied this helpful report carefully and revised our manuscript accordingly based on the report. Please find our reply to the referee’s comments below.
Best regards,
Zhi-Peng Ma and Kai Wang
The paper is dedicated to restriction of parameters of neutrino-emitting blazar based on multi-wavelength observations. It provides analytical expression for boundaries of parameter space and therefore can be adjusted for future observations. The downside is that the strongest limit on parameter space comes from observed neutrino flux, which value is extremely unreliable at present moment. Yet, it cannot be considered as a weak point of the paper, since future observations could improve the available information on neutrino fluxes.
Re: We thank the referee very much for reading our paper carefully and providing this helpful report, which allows us to improve the manuscript. The comments below are replied from point to point.
Therefore, I suggest this paper to be accepted after a few minor corrections:
- Page 2, line 68. \tau_{flfl} is later called \tau_{\gamma\gamma}
Re: Thanks. It is \tau_{\gamma\gamma}. We have revised it.
- Page 2, line 89 - page 3, line 92. It is stated that t'_{var} ~ R'/c, but later it is stated that t'_{var} <= R'/c. Could you please clarify it? The second condition seems excessive, since expression for t'_{var} is already introduced.
Re: We have modified the expression for avoiding confusion in Line 89.
- Page 3, line 100. Limitations, based on the gamma-ray flux from SSC and hadronic processes are introduced as L_{ssc} <= L_{\gamma} AND L_{p\gamma} <= L_{\gamma}. Would it be possible to introduce a stronger limitation that L_{ssc} + L_{p\gamma} <= L_{\gamma}?
Re: Thanks for the comment. The constraint from gamma-rays produced by hadronic processes is actually much weaker than that from SSC (See Fig. 1). A significant stronger limitation cannot be derived by combining L_{ssc} + L_{p\gamma}<= L_{\gamma} than SSC alone.
4)Page 5, Eq. (16). This expression relates gamma-ray spectrum to proton spectrum. Should it be expressed through q instead of \alpha?
Re: Actually, Eq. (16) represents the interaction efficiency of photomeson production process for a single proton with Lorentz factor of \gamma’_p, which is related with the low-energy photon distribution, e.g., the spectral index of low-energy photon, \alpha. We consider the proton spectrum in Eq. (17) and combining both equations, Eq. (18) is derived, which contains the proton distribution, e.g. the proton index q.
- Page 5, line 147, Eq. (18), Eq. (19). L_{pfl} was never introduced. Is it L_{p\gamma}?
Re: Thanks for reminding us. It should be L_{p\gamma}. We have modified it.
- 2. In the legend I suggest replacing 10L^*_p with 10L_{\rm Edd} and same for factors 10^2 and 10^3
Re: Thanks for the suggestion. We have revised it.
- 2. and Fig. 3. The green regions are too small and are almost impossible to see. You can, probably place them in front of the curves to make them visually larger.
Re: We agree with the referee. For visually distinguishable to the green region, we have added the zoom-in panels for Fig. 2 and Fig. 3, respectively.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This paper presents a clear discussion of the much-studied emission of neutrinos by blazar jets. My understanding is that the interpretation of the IC170922 event is consistent with previous conclusions that the predicted flux is too low to explain the flux-level corresponding to one event. This is not surprising; jets are transparent to high energy photons and thus do not contain the target density to produce neutrinos ( the p-gamma opacity is 10-3 times the gamma-gamma opacity). The failure is turned into a success by invoking Eddington bias. The authors propose an interesting twist on this idea introduced by equations 19-21. The way this referee understands the approach is that, if neutrinos are produced in a very large number of sources, one special source can stand out and produce a 3-sigma event, even when the typical flux of the sources is 3x10^-3 times smaller on average. They assume 100 Eddington proton beam producing a flux that that is more than a hundred times smaller than the flux corresponding to one neutrino. This would be possible except that the neutrino was accompanied by an optical flash and emission of this source has been observed in the 10-year IceCube data, mostly concentrated in a 100-day flare in 2014-15. That is not consistent with observing a single statistical fluctuation of many weak sources in 2017.
Author Response
Dear Editor,
Thank you for forwarding us the referee’s report. We have studied the report carefully. Please find our reply to the referee’s comments below.
Best regards,
Zhi-Peng Ma and Kai Wang
This paper presents a clear discussion of the much-studied emission of neutrinos by blazar jets. My understanding is that the interpretation of the IC170922 event is consistent with previous conclusions that the predicted flux is too low to explain the flux-level corresponding to one event. This is not surprising; jets are transparent to high energy photons and thus do not contain the target density to produce neutrinos (the p-gamma opacity is 10-3 times the gamma-gamma opacity). The failure is turned into a success by invoking Eddington bias. The authors propose an interesting twist on this idea introduced by equations 19-21. The way this referee understands the approach is that, if neutrinos are produced in a very large number of sources, one special source can stand out and produce a 3-sigma event, even when the typical flux of the sources is 3x10^-3 times smaller on average. They assume 100 Eddington proton beam producing a flux that that is more than a hundred times smaller than the flux corresponding to one neutrino. This would be possible except that the neutrino was accompanied by an optical flash and emission of this source has been observed in the 10-year IceCube data, mostly concentrated in a 100-day flare in 2014-15. That is not consistent with observing a single statistical fluctuation of many weak sources in 2017.
Re: We thank the referee for this comment. We agree with the referee. It may be possible to observe a single high-energy neutrino event from an individual source due to the statistical fluctuation of many weak blazar source. Therefore, as you mentioned, a 3x10^-3 times smaller neutrino flux is also involved in the manuscript for a conservative parameter constraint.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
I receommend publication of the paper in its revised form.
