referee report for 1ES1011+496 EBL paper

[adiv.gonzalezmunoz]

28/09/2015

Dr Adiv Gonzalez Muñoz

vidadiv@gmail.com

Our Ref. : AA/2015/27256

Dear Dr. Gonzalez Muñoz,

Your paper "MAGIC observations of the February 2014 flare of 1ES 1011+496 and measurement of the EBL intensity" was submitted to a referee who recommends publication after substantial revision (see enclosed report).

Please take the referee's comments and suggestions into account in revising your work and send us the new version (in referee format and in printer format) at your earliest convenience.

Instructions for resubmission can be found at address https://mms-aanda.obspm.fr/is/aa/resubmit_a_paper.php. Your author ID number is 26551.

- In your cover letter, please indicate precisely all the changes made in the revised version. Please also include your detailed responses keyed to the items in the report.
- Mark all the changes clearly (using boldface) in your manuscript.

With best regards,

Sergio Campana
A&A Editor
-------------------
Referee Report

The manuscript "MAGIC Observations of the February 2014 flare of 1ES
1101+496 and measurement of the EBL density" by Ahnen et al. presents
observations of the BL Lac object 1ES 1101+496 with the MAGIC imaging
atmospheric Cerenkov telescope, and an attempt to measure the EBL
density with these observations, based on absorption of gamma rays by
the EBL photons. They do this using a technique previously used by
the HESS collaboration to "measure" the EBL by combining the HESS
spectra of several blazars (HESS Collaboration 2013, A&A, 550, A4).
Although I have no reason to doubt that the observations, calculations
and fits by Ahnen et al. are accurate, I do not think the results of
their likelihood fits can be interpreted as a "measurement" of the
EBL, although I am open to being persuaded otherwise. This also means
that, in my opinion, the previously published results of the HESS
Collaboration claiming a detection of EBL attenuation were not
correctly interpreted. I go into more detail on why I do not think
this interpretation is correct below. I think this criticism also
apply to the paper published by the HESS Collaboration in 2013.

All references to the manuscript below refer to the two-column A&A
format version.

Major comment:

The technique to "measure" the EBL compares a model fit to the
gamma-ray data with some model (Ahnen et al. use a log-parabola) with
parameter alpha=0, i.e., assuming no EBL, with a fit with the
parameter alpha left free, which controls the normalization of the EBL
absorption optical depth. The overall shape of the EBL is given by a
particular model, in this case the one by Dominguez et al. (2011).
They use Wilks' theorem to calculate the significance with which the
model with alpha left free is preferred over the model with alpha
fixed to 0, and claim this is the significance that the EBL is
"detected". However, it could also be interpreted as there being no
EBL absorption, and the model chosen (log-parabola) is just not a good
description of the data. Or, at least not as good a fit as the same
model with some amount of EBL absorption. Perhaps another function
would provide a better fit with alpha=0 than with alpha ~ 1. The
authors have obviously not exahausted every single possible function.
For example, what about a broken power-law, or smoothly broken
power-law?

I read the data points off of Figure 2 and fit them with a smoothly
broken power-law, with and without EBL opacity using the same method
as the authors. I found that the model with alpha set free was not
significantly preferred over the case where it was fixed to 0. I also
found that the smoothly broken power-law fit the observed data with
alpha=0 better than any of the functions listed in Table 1.

Putting upper limits on the EBL based on VHE gamma-ray observations is
well-established. I suggest the authors use their observations of 1ES
1011+496 to put upper limits on the EBL, rather than claiming a
detection. They could perhaps modify the likelihood fitting technique
to give upper limits or use a method outlined in one of the references
they mention in Section 1 (page 2, left column, 2nd full paragraph).


Other comments (minor):

The authors do not provide the values of their best fit parameters.
In any future version of the paper they should provide these
parameters if they do any sort of fitting.

According to the text after equation (1), a log-parabola fit to the
observed SED has 12 degrees of freedom. In Figure 2 I count 14 data
points, and the log-parabola model has 3 free parameters (Gamma, beta,
f_0) so shouldn't there be 14-3=11 degrees of freedom? Similarly,
shouldn't the power-law fit have 12 degrees of freedom, not 13, as
mentioned a few lines later?

Section 7, third line: "were" should be "where" ?

[abelardo.moralejo]

(Adiv has confimed the smoothly broken power-law fits better than any other function in the null EBL case, P=0.16)

First a technical issue, regarding the 50-60 GeV energy point used in the calculations, but not shown in the paper's SED. The missing point won't change anything, it is anyway a point with a negligible signal (<1sigma), though the large background statistics make it perfectly usable for the likelihood method. So we can either eliminate it from the paper and the calculations (but then numbers may change marginally - a mess at this stage), or just show it in the SEDs, the solution I prefer. It cannot be shown "as a point" because the error bar will go all the way to 0, so it must be an upper limit. Then, upon explaining the likelihood method or discussing the residuals plot, we must say in the paper that the method can use also the events in the 50-60 GeV bin which appears as an UL in the SED and that is why the point appears in fig. 7. Please let me know if you agree with this solution and if so go ahead with implementing it.

Regarding the fit: I just checked that in the test I did yesterday (fitting a smoothly broken PL which did not provide a good fit) I fitted all points in the flute output, including the last one at 4 TeV, which has really low statistics which did not fulfill the criteria we had set for bins to be used; therefore it is not used, nor shown in the paper. If I re-do the fit without that point, I reproduce very well your result, i.e. fit probability moves from 1e-3 to ~0.17 and the curve looks just the same as Adiv's. So much for the robustness of the method

All this said, the break in the "good fit" for alpha=0 is really sharp… shall we challenge the referee to come up with a physical modelling of the source (SSC or whatever) which makes something like that??

Of course, stating a maximum allowed rate of index vs. E change would be much harder to justify (if possible at all) than just stating that the spectra has to be concave, so I am afraid this is indeed quite a blow to the paper. Also, there is by now no doubt that alpha != 0, so the fit for the null hypothesis is not really the worrying case. The problem is that this function is probably bound to fit better also with e.g. alpha=0.5, and probably with not-clearly-unphysical parameters, so it is obvious that our lower bound is going to worsen. Let's wait for your full results and see (btw, I find some trouble in fit convergences, make sure the starting parameters make sense, e.g. for the spectral slopes you may use values obtained from fits in two sub-ranges of energy).
All this will certainly make the result be worse "at face value", but the paper may also become more interesting as a criticism of the method widely used in the past years.

As to the referee's argument that the likelihood method cannot be interpreted as a "measurement" of the EBL, I partly disagree. May be he is thinking in other works (e.g. Biteau et al) in which Power-laws are allowed, and hence all spectral curvature is attributed to the EBL. If instead the likelihood worsening when reducing alpha is not coming from the simple increase of curvature, but really from the "EBL-induced inflection feature", then one can interpret it as a measurement under the assumption that (1) the spectral template from EBL models is correct and (2) the source spectrum does not show an identical feature (Ockham's razor). It should be a must to show the residuals from the fits, as we did, to show that is really the case.

A final note of optimism: when you add the contemporaneous Fermi data, the model logparabola*EBL (4 parameters in total, if we include the free EBL scaling - we might as well fix alpha=1) fits nicely over >3 orders of magnitude in E, whereas you would need a rather complicated twice-broken power law with 7 parameters to do without the EBL.

[adiv.gonzalezmunoz]

(Adiv has confimed the smoothly broken power-law fits better than any other function in the null EBL case, P=0.16)

First a technical issue, regarding the 50-60 GeV energy point used in the calculations, but not shown in the paper's SED. The missing point won't change anything, it is anyway a point with a negligible signal (<1sigma), though the large background statistics make it perfectly usable for the likelihood method. So we can either eliminate it from the paper and the calculations (but then numbers may change marginally - a mess at this stage), or just show it in the SEDs, the solution I prefer. It cannot be shown "as a point" because the error bar will go all the way to 0, so it must be an upper limit. Then, upon explaining the likelihood method or discussing the residuals plot, we must say in the paper that the method can use also the events in the 50-60 GeV bin which appears as an UL in the SED and that is why the point appears in fig. 7. Please let me know if you agree with this solution and if so go ahead with implementing it.

I agree with the solution.

Regarding the fit: I just checked that in the test I did yesterday (fitting a smoothly broken PL which did not provide a good fit) I fitted all points in the flute output, including the last one at 4 TeV, which has really low statistics which did not fulfill the criteria we had set for bins to be used; therefore it is not used, nor shown in the paper. If I re-do the fit without that point, I reproduce very well your result, i.e. fit probability moves from 1e-3 to ~0.17 and the curve looks just the same as Adiv's. So much for the robustness of the method

All this said, the break in the "good fit" for alpha=0 is really sharp… shall we challenge the referee to come up with a physical modelling of the source (SSC or whatever) which makes something like that??

I guess that a model with more that 1 zone could create a spectral shape like that, although I'm talking from ignorance. Does any of you know a recent review of emission models for AGNs?

Of course, stating a maximum allowed rate of index vs. E change would be much harder to justify (if possible at all) than just stating that the spectra has to be concave, so I am afraid this is indeed quite a blow to the paper. Also, there is by now no doubt that alpha != 0, so the fit for the null hypothesis is not really the worrying case. The problem is that this function is probably bound to fit better also with e.g. alpha=0.5, and probably with not-clearly-unphysical parameters, so it is obvious that our lower bound is going to worsen. Let's wait for your full results and see (btw, I find some trouble in fit convergences, make sure the starting parameters make sense, e.g. for the spectral slopes you may use values obtained from fits in two sub-ranges of energy).

Well, I ran the scan for alpha (from 0 to 2.5) and the curve(s) is a mess. I guess, as happened before, it is quite sensitive to the starting parameters and in this cases is worse since are 5 of them. It looks as if there were 3 different curves (or families of solutions). See the plots I'm attaching

TS_BPL.pdf

(14.65 KiB) Downloaded 107 times

Chi2_BPL.pdf

(14.68 KiB) Downloaded 110 times

. Maybe HESS people found similar problems and that's why they excluded the smooth broken power-law. What I can try to do is a coarse scan checking the initial parameters on each step.

All this will certainly make the result be worse "at face value", but the paper may also become more interesting as a criticism of the method widely used in the past years.

As to the referee's argument that the likelihood method cannot be interpreted as a "measurement" of the EBL, I partly disagree. May be he is thinking in other works (e.g. Biteau et al) in which Power-laws are allowed, and hence all spectral curvature is attributed to the EBL. If instead the likelihood worsening when reducing alpha is not coming from the simple increase of curvature, but really from the "EBL-induced inflection feature", then one can interpret it as a measurement under the assumption that (1) the spectral template from EBL models is correct and (2) the source spectrum does not show an identical feature (Ockham's razor). It should be a must to show the residuals from the fits, as we did, to show that is really the case.

A final note of optimism: when you add the contemporaneous Fermi data, the model logparabola*EBL (4 parameters in total, if we include the free EBL scaling - we might as well fix alpha=1) fits nicely over >3 orders of magnitude in E, whereas you would need a rather complicated twice-broken power law with 7 parameters to do without the EBL.

[daniel.mazin]

Hi,

I think it is clear that we do not exclude all possible concave functions.
We should/could argue that Fermi-LAT spectra + close by AGNs at VHE
are perfectly fit by a power law, by a log parabola or any of these with a cut-off over 2 orders of magnitude in energy.
If we have an exception we should mention it but I think these are really rare.
Smoothly broken power law (is referee Rolf? he bugged me about doable broken power law for Crab) was not seen for BLLacs yet
and not predicted by the standard models yet. Yes, we agree it's a caveat of the method to measure the EBL
but on the other hand it would be a conspiracy that a logparabola (3 free parameters) + EBL
should be in reality replaced by a smoothly broken power law with 5 free parameters and a sharp intrinsic change of the slope.

Daniel

[abelardo.moralejo]

Hi,

regarding the instability of the fits. I think this is very likely a consequence of the complexity and perhaps also the "unnaturalness" of the function. A power-law and a log-parabola are (in log-log scale) linear in their parameters, and they change in a continuous and monotonical way upon changing any of the parameters. With those functions you cannot get two "similar" curves in distant regions of the parameter space. Things get a bit more complex with exponential cut-offs (no longer linear in the parameters), and even more so with the Smoothly Broken PL: your fit and the one I obtained (with the extra point) in my first attempt both match the points more or less ok, yet have very different parameters. All this is made even messier by the fact that with alpha=1 de-absorption, the points actually follow nearly a power-law, so there are as many as 3 "useless" parameters in the SBPL, and even more degeneracy.


Did you try to fit simple power-laws in the <300 GeV and >300 GeV ranges to obtain the starting values for the slopes? We might even fix the slopes in the final fit to the values obtained in the limited-range PL fits. Perhaps we can obtain a decent TS curve in that way. Also, try to set bounds to the break energy, otherwise things can get crazy with it when the points get close to being a pure PL around alpha=1 : for example, the function can "use" one of the slopes to fit all but one of the points, and the other one to fit better just the first or the last point. Of course, such a fit will not necessarily have a good probability (because of the 5 params), but it is clear why the scan of fits you made is completely crazy. On the other hand, the bounds to parameters always made a mess because they effectively reduce the # of degrees of freedom hence e.g. fit probability will not be correct.


About the unnaturalness of the fit with the too-sharp break: probably with 2-zone models and/or complicated electron spectra one could achieve similar shapes, as you say. But again, that is not the biggest of our problems, because we are not trying to exclude the alpha=0 case (despite we quote a significance for it; there is by now no doubt there is quite some EBL). And for the case, say alpha=0.5 the Smoothly-Broken PL will not look unphysical, I guess. So our lower constrain is bound to worsen. We need to have the curve for the SBPL so that we can quote a number. Then we can make the argumentation outlined by Daniel, I also think for BL Lacs (unlike for FSRQs) broken power-laws are not, empirically, good fits. The bad side is that most of that evidence comes from Fermi - lower energies and not a large energy range per source.
I also think that exponential cut-offs are quite "physically justified" - at least they are good parametrizations of the effect of an internal absorption (same as they are quite good parametrizations of EBL absorption at large distances). To my knowledge the broken power law does not have such justification. We may argue that adding non-linear parts in the fitting functions (with the added complication in the Likelihood maximization process) is only done if there is some justification behind. I also think like you Adiv that those complications are almost certainly the reason why SBPL is not considered by other authors.

I propose the following approach:

1.- Try to obtain the TS curve for the SBPL by finding suitable initial slopes (or even fixing them) through PL fits to the <300 and >300 GeV ranges, and limiting the range of break energies.

2.- If (1) succeeds, include it in the paper with a discussion about the "unnaturalness" of the parametrization. We will have to moderate the claim about the lower constraint, perhaps in an extreme case state we can set none.

2b.- Else, if (1) fails, explain that some concave functions like SBPL which are non linear in their parameters can't be properly used because of multiple Likelihood maxima etc. Still, include the discussion that there may exist concave intrinsic spectra that fit better, even with alpha=0, than those we have used. Say that is also the case for other published results.

3.- In any case, change the claims (if any) that we only request the function to be concave, which is obviously not correct. State that we try a given set of concave functions which have shown to yield good fits to intrinsic BL Lac spectra (cite Fermi EBL paper - read also what they may say about this in their latest AGN catalog paper)

[adiv.gonzalezmunoz]

1.- Try to obtain the TS curve for the SBPL by finding suitable initial slopes (or even fixing them) through PL fits to the <300 and >300 GeV ranges, and limiting the range of break energies.

I try first putting limits in the break energy between a several values. Then I fixed the break energy at 300 GeV. In all cases I got the (kind off) two bump structure in the TS, that is, without a clear maximum. Then I put limits to the slopes, and still got the two bumps. And actually when I try to make a fine scan, the minimization hangs. I think that the fact that we have to put constrains or limits to try to produce a reasonable TS curve, somehow shows that the method is limited to "smooth" functions, that is, with not so many parameters.

2.- If (1) succeeds, include it in the paper with a discussion about the "unnaturalness" of the parametrization. We will have to moderate the claim about the lower constraint, perhaps in an extreme case state we can set none.

2b.- Else, if (1) fails, explain that some concave functions like SBPL which are non linear in their parameters can't be properly used because of multiple Likelihood maxima etc. Still, include the discussion that there may exist concave intrinsic spectra that fit better, even with alpha=0, than those we have used. Say that is also the case for other published results.

3.- In any case, change the claims (if any) that we only request the function to be concave, which is obviously not correct. State that we try a given set of concave functions which have shown to yield good fits to intrinsic BL Lac spectra (cite Fermi EBL paper - read also what they may say about this in their latest AGN catalog paper)

I guess we can go with solution 2b with the arguments that you say. In the part where we describe the observed spectrum I guess we should include that it can be well fitted with the SBPL, but remarking that it was necessary to go as "high" as 5 parameters, which is reasonable to assume that is the consequence of having the intrinsic spectrum + the EBL.
I'll produce a draft as soon as possible.

[abelardo.moralejo]

Hi,

good, that is ok for me. In my talk at TeVPa I plan to discuss in some depth that this particular observation raises several issues with the widely used likelihood procedure for EBL constraining: one is this problem with the SBPL (or other complex concave functions), and the other one is the fact that with the approach of previous "compilation" papers, our 1011 observation (included in such compilation studies) would be fitted with a power-law as intrinsic spectrum, and dominate (TS-wise) the overall results - with a resulting lower EBL constraint which would rely on the unreasonable assumption that the intrinsic spectrum "must be" a power law - and the EBL result will have some bias towards too high density. The same thing is at work in all those compilation papers which use the power-law abundantly, though it is not so obvious because of the many low-statistics spectra.

[adiv.gonzalezmunoz]

Hi

First of all, I'm sorry for the long delay, unfortunately now I have to dedicate more time to my activities with HAWC putting aside this paper. Please find in the attachment a new version of the paper, where the fit to the broken power-law is discussed. I understand that this is just a first version of the reply to the journal. I still haven't include any correction or discussion related to the problem with the numbers of points in the fit, but I think we can already start the discussion. Abelardo suggested to show the first point as an upper limit, so here is my technical question: I'm reading the Status file as
TGraphErrors* SED = (TGraphErrors*) MStatusDisplay->FindCanvas("SED")->FindObject("SED");

in which I only load the points and use them to make all the fits an so on, so, how can I load also the upper limits?
Thanks

[abelardo.moralejo]

Hi,

I reply here to the technical question, so that you can go on with the work. Inside the Output*root file you have an object of type MHFlux which is called FluxUL.
You can obtain a graph of the SED upper limits by doing TGraphErrors* SEDULs = FluxUL->DrawSED()

And obtain the values with SEDULs->GetY()

Note that you will get ULs for all points, but obviously need only the one between 47 and 63 GeV for which no significant point exists. Note also that the ULs look pretty high, the reason is that in the calculation of upper limits we conservatively assume a 30% gaussian (systematic) uncertainty in the overall efficiency (= collection area) which is not included in the (statistical) error bars of the significant spectral points.
Actually, for the sub-threshold upper limits (like the one we want to show) that is pretty ok: because of the steeply rising Aeff vs. E, the systematic uncertainty in Aeff is large. For the very high energies that 30% is quite an overconservative choice, but we are not going to show those upper limits in this paper, so its is not an issue here.

I'll check the other changes and comment soon.

[abelardo.moralejo]

Aside from the latest changes, I cannot understand how is it possible that we still have such a terrible confusion about concaveness and convexness in the submitted draft - having people to check it during August holidays is possibly one of the reasons.

Functions are:
CONCAVE if their slope decreases as x increases (negative second derivative)
CONVEX is their slope increases as x increases (positive second derivative)

In other words, you have to look at them "from below".

So the VHE BL Lac SEDs are expected to be CONCAVE : hardness decreasing with energy. Our fitting functions are forced to be concave. The spectra cannot be convex.

Please, check for all occurrences of "concav*" and "conve*" in the draft, and fix them.

[abelardo.moralejo]

Hi,

attached are my comments. I am sorry to say that I think we have not advanced much with respect to one month ago when the referee report arrived.

For the justification of the used functions etc, see my comments inside the attached pdf.

Besides adding the UL in the plot, you still have to explain in the text why fits to the shown spectra have one fewer point (and hence one fewer degree of freedom) than the log-likelihood fits and residuals plots.

Perhaps the LP, second-best fit to the observed spectrum, should be shown also in fig. 2 as a dashed red line.

[adiv.gonzalezmunoz]

Hi

Please find in the attachment an updated version of the draft. I already fixed the mix up with the concave and convex definitions and also included the corrections and comments by Abelardo. The draft is still missing the SED plot with the upper limits and the fit to a LP, and the corresponding explanation of why the difference in the degrees of freedom. I already ask help to Abelardo to produce the plot. I would do it myself but I haven't had the time to install mars in my computer, and working in the PIC from here is quite painstaking. Meanwhile we can make some progress with the main text. The referee also asked to include the values of the parameters of the fitting. I think that does not add any to purpose of the paper, but just to make him happy, should we include only the parameters of the best fit? that is, the parameters of the LP for alpha=1.07? or for all the funtions and for alpha=0 and alpha=1.07, or only for the latest?

By the way, my claim that only in the paper of PKS2155 a broken power law is used, is based on a search that I made in the TeVCat, in which I checked all the HBLs and the IBLs and that was the only case I found.

Sorry for the delay.

[abelardo.moralejo]

Hi,

I already sent to Adiv the Fig. 2 (SED) with upper limits. I put back the log-parabola as the function shown in the plot, we do not want to highlight it as a good 5-parameter "empirical fit" to the observed spectrum - since a simple power-law times the Domínguez nomimal EBL (i.e. 2 parameters in total) is better.

Below are comments to the current version, with very specific suggestions for whole paragraphs, in order to make things faster.
I have read the whole paper again, so some of the comments do not refer to the recent changes - but they are important (the referee will not be the last person to read the paper, I hope).


Abstract:

"including a scale factor" => "including a normalization factor" (for consistency with the next section of the abstract).

"from which the EBL imprint could be measured with a significance of 4.6 sigma for an opacity normalization factor…" =>

" … with a significance of 4.6 sigma, corresponding to an opacity normalization factor $\alpha_0$ = 1.07…. with respect to the nominal one in the assumed EBL template (Domínguez et al 2011)"

Results

"After background suppression cuts, 3219 gamma-like ON events above 60 GeV" => you do not provide the estimated background, so this is not very informative. Write either the excess events or both ON and OFF (the former is preferred). MORE IMPORTANT: is the number a typo?? I checked by chance your flute outputs and I see many more events! Post-cuts we have ~6200 EXCESS events after all cuts (including hadronness & theta2), i.e. those which go into the spectrum! PLEASE CHECK! We should put the number of excess events which go into the spectral calculation, especially because you say "above 60 GeV", I can guess your number comes from some Odie "FR" or something like that, but that is obviously wrong!

All the paragraph starting "In order to find an acceptable fit..." and ending in "in the literature has been used to fit the observed data from an HBL at VHE (Aharonian & et al. 2007)" has to be much reduced and simplified. And as we discussed already in this thread, it makes no sense to argue about fits to observed spectra to justify that the intrinsic spectrum must be this or that... (if anything, we should argue from BL Lac spectra in the optically-thin regime, like those of Fermi-LAT).

Here is my proposed version to replace that part:

"The average observed spectral energy distribution is shown in fig. 2. The estimated {\it intrinsic} spectrum, assuming the EBL model by Domínguez et al. (2011), can be fitted with a simple power-law function (PWL) with a probability of 0.23 (Chi2/d.o.f.= 16.3/13), a photon index Gamma = 2.0 +/- 0.1 and a normalization factor at 250 GeV f0 = (5.4 +/- 0.1) * 10^-11 cm-2 s-1 TeV-1. The {\it observed} spectrum is clearly curved. Several functions were tried to parametrize it: power-law with an exponential cut-off (EPWL), log-parabola (LP), log-parabola with exponential cut-off (ELP), power-law with a sub/super-exponential cutoff (SEPWL) and a smoothly-broken power-law (SBPWL). Of these, only the SBPWL (with 5 parameters), achieves an acceptable fit (P = 0.16), though with a sharp change of photon index by Delta_Gamma = 1.35 within less than a factor 2 in energy. Among the other, smoother functions, the next-best fit is provided by the LP (shown in fig. 2), with P = 2.2*10^-3. This non-trivial shape of the observed spectrum, and its simplification when the expected effect of the EBL is corrected, strongly suggests this observation has high potential for setting EBL constraints."

BUT PLEASE CHECK: You state 12 d.o.f. for the LP, but we have 14 points so it should be 11 for the log-parabola. I am afraid you are still including the next point (>4 TeV, with only 3 events, which we are not considering since the beginning). Please fix this, this inconsistency was also pointed out by the referee. Put the right P & Chi2 values for the 11 d.o.f. in the new paragraph above.



The last paragraph of the Results section should also be simplified:

"The night-wise estimated intrinsic spectra could all be fitted with power-laws, and the evolution of the resulting photon indices is shown in figure 3. In the latter part of the observed period, the activity of the source was lower, resulting in larger uncertainties for the fits. There is no evidence for significant spectral variability in the period covered by MAGIC observations, despite the large variations in absolute flux."


EBL measurement

"These arguments put serious constrains to the photon index of the energy spectrum of VHE photons" => "constraints"

In the paragraph "For the modeling of the intrinsic..." I would replace the part right after "...nor has it been observed in any BL Lac in the optically-thin regime."

by the following:

"... in the optically-thin regime. In particular, the un-absorbed part of BL Lac spectra measured by Fermi-LAT are well fitted by log-parabolas (Ackermann et al 2102).
\par
The PWL and the LP are functions that are linear in their parameters in the log flux - log E representation (hence well-behaved in the fitting process), and both can model pretty well the de-absorbed spectrum found in Sect. 3. The EPWL, ELP and SEPWL have additional (non-linear) parameters which are physically motivated, e.g. to account for possible internal absorption at the source. Note that these functions (except the PWL) can also mimic the {\it overall} spectral curvature induced by the EBL over a wide range of redshifts, but will be unable to fit the inflection point (in the optical depth vs. log E curve) that state-of-the-art EBL models predict around 1 TeV. We therefore expect an improvement of the fit quality as we approach the true value of the scaling factor $\alpha$, hence providing a measurement of the actual EBL density. The chosen spectral functions, however, do not exhaust {\it all possible} concave shapes. Therefore the EBL constraints we will obtain are valid under the assumption that the true intrinsic spectrum can be well described (within the uncertainties of the recorded fluxes) by one of those functions. As we saw in section 3, the 5-parameter smoothly-broken power-law (not included among the possible spectral models) provides an acceptable fit to the {\it observed} spectrum; if considered a plausible model for the intrinsic spectrum, it would severely weaken the lower EBL density constraint. On the contrary, the upper constraint (arguably the most interesting one VHE observations can contribute) from this work would be unaffected, as we will see below."


"To apply the TS we decided to use an average spectrum" => "For the calculation of the TS we decided to use the average flare spectrum"

The changes also require to modify this part of the same paragraph:

"Despite changing the flux level, the EBL determination method should work properly as long as the average intrinsic spectrum in the observation period can be described with one of the tested parameterizations. This would of course be the case if the spectral shape is stable, or changes moderately.
A varying spectral shape would in any case need quite some fine tuning to reproduce, in the average spectrum, a feature like the one expected to be induced by the EBL. A simple way to check the stability of the spectral shape is fitting the points on the Fig. 3 to a constant value. The Chi2/d.o.f. of this fit is 23.5/16 and the probability is 10%."

Instead, I suggest:

"Despite changing the flux level, the EBL determination method should work properly as long as the average intrinsic spectrum in the observation period can be described with one of the tested parameterizations. Assuming that is the case for the different states of the source, it will also hold for the average spectrum if the spectral {\it shape} is stable through the flare. A simple way to check the stability of the spectral shape is fitting the points on Fig. 3 to a constant value. The Chi2/d.o.f. of this fit is 23.5/16 and the probability is 10%, so there is no clear signature of spectral variability - beyond a weak hint of harder spectra in the second half of the observation period. A varying spectral shape would in any case need quite some fine tuning to reproduce, in the average spectrum, a feature like the one expected to be induced by the EBL."



Right after this:

"Then the Poissonian likelihood of the actual observation (the post-cuts number of recorded events vs Eest, in both the ON and OFF regions) was computed, after maximizing it in a parameter space which includes, besides the intrinsic spectral parameters, the Poisson parameters of the background in each bin of Eest."

Please include the following footnote, which addresses one of the referee's concerns:

"Note that in the Poissonian likelihood approach we have included the point at E ~ 55 GeV which was shown just as an upper limit in fig. 2, since it has an excess of just around 1 standard deviation above the background. The fits performed with the Poissonian likelihood approach have therefore one more degree of freedom than the Chi2 fits reported in section 3, and the 55 GeV point is included in fig. 7"




"Fig. 4 shows the -2 logL probabilities..." : although I think I suggested this wording myself, I now think that the proper way of saying it is "Chi2 probabilities". Although it is a poissonian likelihood, in the end in order to calculate probabilities we have to trust that -2log(L/Lmax) is Chi2-distributed in the null hypothesis (and in the asymptotic limit). PLEASE NOTE that this has to be changed also in Fig.4: y-axis should be "Fit Chi2 probability".


Actually, fig. 5 y-axis label is also wrong. What is plotted is not the "raw" poisonian L, but actually -2 log (L/Lmax), where Lmax is the "absolute maximum" likelihood, i.e. that of a model which would get exactly the number of Non and Noff events in all bins. This is asymptotically, and again thanks to the Wilks theorem, a Chi2 with the number of d.o.f. of the fit (points-parameters) because the alternative hypothesis (=perfect prediction) has 0 degrees of freedom - as many parameters as points, obviously. Either we explain it properly, or we just put on the y-axis "fit Chi2"



Then, replace the (still outdated) part starting "Following the approach by Abramowski et al. (2013) would lead us...", until the end of the paragraph, by:

"Following the approach in Abramowski et al. (2013) would lead us to choose the PWL as model for the intrinsic spectrum, as the next models in complexity (LP and EPWL) are not preferred at the 2-$\sigma$ level. However, choosing the PWL is rather questionable, since it does not allow for any intrinsic spectral curvature, meaning that all curvature in the observed spectrum will be attributed to the EBL absorption. If this procedure is applied to a large number of spectra, as in in Biteau & Williams (2015), individual < 2-$\sigma$ hints of intrinsic (concave) curvature might be overlooked and accumulate to produce a bias in the EBL estimation. In our case, the assumption of power-law intrinsic spectrum would result in an EBL “detection” at the 13-$\sigma$ level. We prefer to adopt a more conservative approach, choosing the next-best function, the LP. Note however that at the best-fit $\alpha$, all the tested functions become simple power-laws, hence the fit probabilities at the peak depend only on the number of free parameters.


At the end of section 4, add this paragraph:

"We again remark that allowing for other concave spectral shapes, like the SBPWL, would severely affect our lower EBL bound. This would also be the case for earlier published EBL lower constraints based on gamma-ray data - especially those in which the PWL is among the allowed models for the intrinsic spectrum. For the observations discussed in the present paper, the SBPWL would achieve an acceptable fit even in the no-EBL assumption. This and earlier "detections" of the EBL through its imprint on gamma-ray spectra hence rely on somewhat tentative assumptions on the intrinsic spectra - but assumptions which, as far as we know, are not falsified by any observational data available on BL Lacs. On the other hand, the upper bounds we have obtained are robust, since they are driven by the fact that convex spectral shapes (completely unexpected for BL Lacs at VHE) would be needed to fit our observations if EBL densities above the best-fit value are assumed."


Systematic uncertainty

I would remove:

"with the difference that in our case the scaling factors were applied to the data, whereas in Aleksi´c et al. (2015b), the light scale was artificially shifted in the MC simulations."

(the difference is not so relevant and it is actually not easy to understand)


Remove also:

"With this procedure, the accuracy of the light scale is determined, and since the number of photoelectrons is related to the energy of the shower, then a shift in the light scale is equivalent to a shift in the energy scale."

Sorry I did not catch the above earlier, but it is not correct. We do not determine here the accuracy of the light scale, we use the +/-15% to see how much the EBL results vary. And it is not equivalent to a shift in the energy scale.


For the part starting "Comparing the profiles, we looked..." until the end of the paragraph I suggest:

"From the 1-$\sigma$ uncertainty ranges in $\alpha$ obtained for the different shifts in the light scale, we determine the largest departures from our best-fit value $\alpha_0$, arriving to the final result $alpha_0 = 1.07 (-0.20, +0.24)_{stat+sys}$"



Conclusions

"The intrinsic spectrum of 1ES 1011+496, apart of being quite hard, apparently does not have intrinsic curvature, which makes it a good candidate for observations, unlike other sources at similar redshifts (z=0.212)."

Change to

"The spectrum of 1ES 1011+496 during this flare displays little intrinsic curvature over > 1 order of magnitude in energy, which makes this an ideal observation for constraining the EBL."


"the EBL was detected" => I would put "detected" in quotation marks, given the discussion with the referee.


"About the most constraining measurement of the EBL..." => how about HESS' PKS2155? at least the TS of one of the HESS samples in their EBL paper was larger. Did we discuss that statement? - I can't remember now.

PLEASE add in the acknowledgements the standard sentence thanking the anonymous referee for his fruitful suggestions etc.

[adiv.gonzalezmunoz]

Please find in the attachment the new version of the draft in which all the comments, corrections and text suggested by Abelardo has been included. With his suggestions the draft I think has improved a lot. Some numbers has been updated in which the fit now really correspond to the number of points shown in the plot of the SED. The changes in the plots are also included.

[abelardo.moralejo]

Hi,

thanks a lot. I would like to read it once more, but I am in a meeting until Saturday so likely unable to do it before that. Just going fast through the plots I realised y-axis of fig.5 unchanged - strictly speaking it should be "-2 log L/Lmax" (but would require some explanation of what Lmax is - in the HESS paper they did it with a footnote).

Can you meanwhile prepare the reply to the referee? We should also briefly discuss it.

Ciao,

A.

[adiv.gonzalezmunoz]

Hi

I'm attaching a new version. I fixed the title in the axis and also corrected something that happened in the previous version where the legend in the plots 4 and 5 were showing the same lines and colors. Also corrected some minor details in the text.

[adiv.gonzalezmunoz]

I'm re-posting the comments of the referee to work on it

...I do not think the results of
their likelihood fits can be interpreted as a "measurement" of the
EBL, although I am open to being persuaded otherwise. This also means
that, in my opinion, the previously published results of the HESS
Collaboration claiming a detection of EBL attenuation were not
correctly interpreted. I go into more detail on why I do not think
this interpretation is correct below. I think this criticism also
apply to the paper published by the HESS Collaboration in 2013.

Major comment:

The technique to "measure" the EBL compares a model fit to the
gamma-ray data with some model (Ahnen et al. use a log-parabola) with
parameter alpha=0, i.e., assuming no EBL, with a fit with the
parameter alpha left free, which controls the normalization of the EBL
absorption optical depth. The overall shape of the EBL is given by a
particular model, in this case the one by Dominguez et al. (2011).
They use Wilks' theorem to calculate the significance with which the
model with alpha left free is preferred over the model with alpha
fixed to 0, and claim this is the significance that the EBL is
"detected". However, it could also be interpreted as there being no
EBL absorption, and the model chosen (log-parabola) is just not a good
description of the data. Or, at least not as good a fit as the same
model with some amount of EBL absorption. Perhaps another function
would provide a better fit with alpha=0 than with alpha ~ 1. The
authors have obviously not exahausted every single possible function.
For example, what about a broken power-law, or smoothly broken
power-law?

I read the data points off of Figure 2 and fit them with a smoothly
broken power-law, with and without EBL opacity using the same method
as the authors. I found that the model with alpha set free was not
significantly preferred over the case where it was fixed to 0. I also
found that the smoothly broken power-law fit the observed data with
alpha=0 better than any of the functions listed in Table 1.

Putting upper limits on the EBL based on VHE gamma-ray observations is
well-established. I suggest the authors use their observations of 1ES
1011+496 to put upper limits on the EBL, rather than claiming a
detection. They could perhaps modify the likelihood fitting technique
to give upper limits or use a method outlined in one of the references
they mention in Section 1 (page 2, left column, 2nd full paragraph).

Other comments (minor):

The authors do not provide the values of their best fit parameters.
In any future version of the paper they should provide these
parameters if they do any sort of fitting.

According to the text after equation (1), a log-parabola fit to the
observed SED has 12 degrees of freedom. In Figure 2 I count 14 data
points, and the log-parabola model has 3 free parameters (Gamma, beta,
f_0) so shouldn't there be 14-3=11 degrees of freedom? Similarly,
shouldn't the power-law fit have 12 degrees of freedom, not 13, as
mentioned a few lines later?

Well, my reply could be like this:

"First of all, thank you for a comprehensive review of our work, your comments lead us to a deep reviewing of our numbers and arguments.
Your major comment is centered in the fact that you do not think that the method we applied to study the imprint of the EBL in the observed spectrum of 1ES 1011+496 can be interpreted as a measurement. Lets start with the fit to the average observed spectrum. Following your suggestion we indeed found that a fit to a smooth broken power-law (SBPWL) gives a much better probability than a log-paraboa, and we haved decided to include it as part of our results of the analysis of the observations. However, such fit is just a parameterization for what has been observed by the MAGIC telescopes and includes a sharp break in the spectral index. In order to apply the method described in the paper for measuring the imprint of the EBL in the observed spectra, we need to make assumptions for the shape of the intrinsic spectrum and this assumptions has to be motivated by what it is known of the physics of the sources and supported by observation in the optically-thin regime. As noted in the manuscript, 1ES 1011+496 its a very particular case since the de-absorbed spectrum seems to be quite flat, then, in the method, the model for the intrinsic spectrum when reaches the maximum likelihood (normalization around 1) will become a power-law, and since we are restricting that the functions do not become convex, it will stay as power-law for higher normalizations. It is these feature that give us a good upper limit in our measurement. Now, the 5 functions that we used comply with the requirements of concavity and that have been supported by observations of HBLs. Including the SBPWL will not improve or worsen that upper limit since it will also converge into a power-law after de-absorption. The SBPWL also has the problem of hyper-degeneration around the maximum since it has 3 more parameters than the power-law, finding the true maximum is not trivial and depends heavily in the initial parameters. Due to this fortunate flat shape of the intrinsic spectrum, is that we think that we can "detect" the imprint of the EBL in the observed spectrum.
Regarding your minor comment, it was a mistake of a mismatch of points shown in the plot and the ones taken for the fit. That problem has been corrected and the corresponding numbers has been updated in the manuscript."

Please comment and fix

[abelardo.moralejo]

Hi,

attached my very few comments to the latest version. mostly on small grammar issues. From my side, green light for submission once implemented.
I'll send now comments on the reply to the referee.

A.

[abelardo.moralejo]

Hi,
I have edited the reply (see below). On doing so I realized we are not fulfilling one of the requests of the referee, i.e. providing all the fit parameters. Adiv, you can find what is needed written in uppercase in the response below. Sorry for this, but it is an explicit request that we have overlooked in this last version, and I am afraid that he does not accept it.

Ciao,

A.

----

Dear reviewer,

first of all, thank you for a comprehensive review of our work; your comments have led us to a thorough reevaluation of our numbers and arguments.

Your major comment is centered in the fact that you do not think that the method we applied to study the imprint of the EBL in the observed
spectrum of 1ES 1011+496 can be interpreted as a measurement. We partially agree to this, in the sense that the "measurement" is indeed dependent
of the considered models for the intrinsic spectrum. We cannot claim that we only need to assume the spectrum to be concave, at least in what regards the
lower constraint to the EBL density. On the other hand, the upper constraint is quite robust, since assuming high EBL densities results in a
clearly convex de-absorbed spectrum, completely unexpected for this type of object. It is besides a quite good (1-sigma) upper constraint due to the
lucky fact that nominal EBL density (from Domínguez'11) already results in a de-absorbed spectrum very close to a pure power-law - which
then becomes a convex spectrum when assuming higher densities. This is a very nice feature of this observation, which we think is quite unprecedented
in VHE spectra of such high-quality.

We have tried to make these points clear in the new version of the manuscript.

Following your suggestion, we indeed checked that a fit to a smooth broken power-law (SBPWL) gives a much better probability than a log-paraboa,
and we have decided to include it in the paper as part of our results of the analysis of the observations. We present it as an empirical parameterization
of the observed spectrum, and note that it features a rather sharp break in the spectral index, which hints at it not being an intrinsic feature
of the source. Although we cannot make a likelihood ratio test with two models that are non-nested, it is at least indicative that a 5-parameter
function fits the observed spectrum worse than a simple 2-parameter function (PWL) times the transmission factor predicted by the nominal Domínguez EBL.

For the same reason, the SBPWL has the problem of being very degenerate around the likelihood maximum (having 3 redundant parameters). On top of it,
the function is non-linear in most of its parameters. These features lead to trouble in finding the absolute likelihood maximum for the different
values of alpha, i.e. a strong dependence on initial parameters and convergence on local maxima. Actually, we think this is probably the reason
for which in earlier works the simplest function was chosen unless the next one in complexity achieved (in the scanned range of alpha) a fit which
was better at the >= 2 sigma level (e.g. in Biteau & Williams arXiv:1502.04166). Note that in our case such a procedure would have resulted in
choosing the power-law, which we explicitly rejected because it would lead to attribute all observed spectral curvature to the EBL, denying any
possibility of intrinsic curvature.

We are aware that some of the functions we use have also parameters on which the functions are non-linear (the sub/super/exponential cut-offs), but
they are justified physics-wise, because they can model an internal absorption feature (as well as mimic the overall curvature induced by the EBL).
Besides, we did not notice any relevant convergence or initial-parameters problems with these functions.


Regarding your minor comments:

ADIV, PLEASE INCLUDE BEST-FIT PARAMETERS AS THE REFEREE REQUESTED. I THINK THESE ARE NEEDED:
- THE LOG PARABOLA IN FIG. 2
- THE BEST-FIT POWER-LAW OF FIG. 4 (LP AND OTHERS WOULD BE JUST THE SAME, SO NO NEED) WHICH IS NOT IDENTICAL TO THE POWER-LAW FIT TO THE DE-ABSORBED SPECTRUM
REPORTED EARLIER (BOTH BECAUSE OF THE METHOD AND BECAUSE OF DIFFERENT DEABSORPTION).
- SBPL, I AM AFRAID THE REFEREE MAY WANT TO HAVE ALL 5 PARAMETERS AND THE FUNCTION ALSO WRITTEN DOWN.

Regarding the issue with the number of degrees of freedom, the difference is due to the fact that fig. 2 does not feature a point at ~55 GeV which has
just ~1 sigma significance (an upper limit is displayed now). The point is not shown because of its low significance, and consequently it does not participate in
the fits reported in section 3. In the Poissonian likelihood method, on the other hand, there is no reason to exclude this low-significance point (you can
see it in fig. 7), therefore there is one more degree of freedom in all fits reported on section 4. This is now clarified in a footnote.

[adiv.gonzalezmunoz]

Hi

Thanks for fixing the reply to the referee. I have included your corrections and also the values of the parameters for the LP, the SBPWL in the Results section, and the PWL at the best-fit alpha=1.07 in the EBL measurement section.

For that part in the reply to the referee I would say:
We have included the values of the parameters of the fitted functions in Section 3. In Section 4 we have included the parameter values only of the PWL at the best-fit alpha=1.07. All the other functions will have the same values for those parameters (photon index and normalization) and since all become power-laws (as explained in the manuscript), quoting the values of the extra parameters will not add useful information.


The updated version is in the attachment

[abelardo.moralejo]

Hi Adiv,

perfect, thanks a lot for prompt response. If nobody replies today, please go ahead with resubmission on Thursday morning. Let's hope the referee finds the modifications acceptable.

Best regards,

Abelardo

[adiv.gonzalezmunoz]

Hi

I just found out that in the resubmition form theres is one mandatory field called "Cover letter to the editor". I though it was only a reply to the referee. It says that in the "cover letter" we had to specify the changes made to the paper. So, my reply would be like this (please comment and fix):

Dear Sergio Campana, A&A Editor

Thanks for considering our paper "MAGIC observations of the February 2014 flare of 1ES 1011+496 and measurement of the EBL intensity" for publication in your journal. We have reviewed all comments issued by the referee and we have address them all, as you can see in the reply to the referee.

Major changes to the manuscript includes (modification are in boldface in the manuscript as requested):
Section 3. We have updated Fig. 2. The spectral points are the same as in the previous version but we have included upper limits that are useful to clarify the likelihood computation in section 4, and also we add a grid to the figure. also we have included the fit to a smooth broken power-law as suggested by the referee.
Section 4 has been deeply reviewed and re-written. We have addressed the concerns of the referee about our method for the measurement of the EBL imprint in the VHE data and interpretation of the results. We give arguments supporting our interpretation of the results and the method that we followed. The numerical results presented in this section (the opacity normalization and the significance of the measurement) have not changed.
Also in section 4, we have included a footnote to clarify the apparent discrepancy between the number of spectral points taken for the computation of the likelihood and the ones taken for the fit in section 3.

Minor changes include the modification of the axis labels in figures 4 and 5. Previously they were labeled as "-2log L probability" and "-2log L" respectively. Now they are labeled as "Chi^2 probability" and "Fig Chi^2". In both cases we are referring to the same quantity but we think that the later is clearer to the reader. Also Section 7 has been slightly re-written to add support to our conclusions.

Best regards

The corresponding authors.

[abelardo.moralejo]

Hi,

fine with me. You may also add that we have included a discussion on the fact that the lower EBL density constraint is indeed dependent on the allowed models for the intrinsic spectrum, and as such it is less robust than the upper constraint.

Ciao,

A.

[adiv.gonzalezmunoz]

I have resubmitted the paper

Just for bookkeeping I'm attaching the pdf files that I sent to the journal. Our reference number is still AA/2015/27256

Lets see how it goes.

[adiv.gonzalezmunoz]

Here it is the complete second referee report from A&A

21/12/2015

Dr Adiv Gonzalez Muñoz

vidadiv@gmail.com

Our Ref. : AA/2015/27256

Dear Dr Gonzalez Muñoz,

Your paper "MAGIC observations of the February 2014 flare of 1ES 1011+496 and measurement of the EBL intensity" was submitted to a referee who recommends publication after revision (see enclosed report).

Please take the referee's comments and suggestions into account in revising your work and send us the new version (two pdf files: one in referee format and the other in printer format) at your earliest convenience.

Instructions for resubmission can be found at address https://mms-aanda.obspm.fr/is/aa/resubmit_a_paper.php. Your author ID number is 26551.

- In your cover letter, please indicate precisely all the changes made in the revised version,
- Mark all the changes clearly (using boldface) in your manuscript.

With best regards,

Sergio Campana
A&A Editor
--------------------
Referee Report

The authors have modified the manuscript based on my comments. They
have clearly thought about the issues I brought up in my first report,
and I appreciate their effort, but I am not entirely satisfied. I do
have a major comment (below), which might be considered semantic, but
I do think it is important. As with my first report, all references
to the paper below refer to the two column version. The manuscript
does present a nice piece of work and deserves to be published in A&A.
My objection aside, it is well-written.

Major comment:

I agree with the authors statements regarding the upper limit on the
EBL (top of the first column of page 4, top of the first column of
page 6), namely that it is a robust, reliable result. The authors now
state in several places that the lower limit on the EBL is not robust.
I would go further than this, I think the lower-limit is basically
meaningless, since (as the authors now state in the text) they cannot
exhaust every possible concave model. My main concern with the text
at this point is therefore the description of the result as a
"measurement" or "detection". Perhaps this is a matter of semantics,
but I do think the distinction is important. A measurement implies
both an upper and lower limit. Since I do not believe the authors
have found a reliable lower limit, I do not think characterizing the
result as a "measurement" is accurate. Therefore, everywhere the
authors use the phrase "measurement of the EBL" or "the EBL was
detected" (e.g., bottom of second column of page 6), or something
similar, they need to change to "constraint" or "upper limit" (or
something similar). This includes the title of the paper.

Other comments:

Authors (from their reply): "We present it as an empirical
parametrization of the observed spectrum, and note that it features a
rather sharp break in the spectral index, which hints at it not being
an intrinsic feature of the source."

Why would this imply it is not an intrinsic feature of the source?
Many LAT spectra of blazars show sharp breaks (e.g. Abdo et al. 2009,
ApJ, 699, 817; Abdo et al. 2010, ApJ, 710, 1271) and several authors
have thought of theoretical ways to create them.

Authors (top of first column of page 6): "[The detections of the EBL]
rely on somewhat tentative assumptions of the intrinsic spectra--but
assumptions which, as far as we know, are not falsified by any
observational data available on BL Lacs."

These assumptions need to be stated explicitly. I guess the main
assumption is that the intrinsic spectrum must be a log-parabola
(bottom of first column on page 4). But I do not agree with this
assumption. First of all, many BL Lacs do not have their intrinsic
LAT spectra fit preferentially by a log-parabola over a power-law.
Second, this seems to be circular reasoning. The authors are using
the gamma-ray spectra deabsorbed with a particular EBL model to argue
that the intrinsic spectra are log-parabolas, and then using a
log-parabola gamma-ray spectrum to claim a "detection" of the EBL.

Authors (from their reply): "Although we cannot make a likelihood
ratio test with two models that are non-nested, it is at least
indicative that a 5-parameter function fits the observed spectrum
worse than a simple 2-parameter function (PWL)"

I think the SBPWL and PWL models are nested. If E_b in Equation (1)
goes to infinity it will be a PWL. If You aren't allowed
to allow a parameter to go to infinity for it to be nested, you
could rewrite Equation (1) as
dF/dE = f_0 (E/E_0)^(-Gamma_1)*( 1 + (E*beta)^g)^( (Gamma_2-Gamma_1)/g )
Let beta --> 0 and it will be a PWL. If this equation isn't nested
with a PWL, then a PWL with exp(-alpha*tau_gg) wouldn't be nested with
a PWL either, right?

Authors (from their reply): "For the same reason, the SBPWL has the
problem of being very degenerate around the likelihood maximum (having
3 redundant parameters). On top of it, the function is non-linear in
most of its parameters. These features lead to trouble in finding the
absolute likelihood maximum for the different values of alpha, i.e. a
strong dependence on initial parameters and convergence on local
maxima."

Some of these problems might be resolved by using a "Band function",
often used in the analysis of gamma-ray bursts. See Band et
al. (1993), ApJ, 413, 281, Equation (1). At least, it would have one
less free parameter than the broken power-law model the authors use.

[adiv.gonzalezmunoz]

Post on behalf of Abelardo

Hi,

below are some suggestions for the reply to the referee.

Have a nice eve!

A.

--------

On Wed, Dec 23, 2015 at 9:29 PM, Adiv Gonzalez <vidadiv@gmail.com> wrote:

I agree with the authors statements regarding the upper limit on the
EBL (top of the first column of page 4, top of the first column of
page 6), namely that it is a robust, reliable result. The authors now
state in several places that the lower limit on the EBL is not robust.
I would go further than this, I think the lower-limit is basically
meaningless, since (as the authors now state in the text) they cannot
exhaust every possible concave model.

Even if one could exhaust all possible concave models, the measurement (including the upper constraint) would still depend on the assumption that BL Lac VHE spectra must be concave. Currently it depends on the intrinsic spectrum to be not just concave, but also describable by one of the considered simple concave functions. It is indeed an assumption-dependent constraint, but we do not think it is meaningless.

My main concern with the text
at this point is therefore the description of the result as a
"measurement" or "detection". Perhaps this is a matter of semantics,
but I do think the distinction is important. A measurement implies
both an upper and lower limit. Since I do not believe the authors
have found a reliable lower limit, I do not think characterizing the
result as a "measurement" is accurate.

In principle, the goal is not to detect the EBL, since there is no doubt that some level of EBL must exist at least from the resolved galaxies. In this sense the lower constraint is of no big interest as long as it does not go significantly above the lower limits from galaxy counts (and it doesn't).
In any case, what we currently have in the paper about "detection" is the following:

- "we aim at detecting the imprint of the EBL... " : no problem there, we hope.

- "the assumption of power-law intrinsic spectrum would result in an EBL “detection” at the 13 level." : hypothetical, and the quotation marks in "detection" are there to show we would not consider that a reasonable statement. Yet, that is what others would have done with this data sample (i.e. assume intrinsic PL), had it been included in their compilations to study the EBL with VHE spectra.

- "This and earlier claims of detections of the EBL through its imprint on gamma-ray spectra hence rely on somewhat tentative assumptions on the intrinsic spectra" : precisely the point at stake is clearly stated there, so we do not see a problem. But we may replace "claims of detections of the EBL through" by "lower constraints on the EBL density obtained through" if it sounds better.

- "In the approach that we followed along this work, for the description of the intrinsic spectrum at VHE we restricted ourselves to smooth concave functions which have shown in the past to provide good fits to BL Lac spectra whenever the expected EBL absorption was negligible. Under this assumption, the EBL was “detected” with a significance of 4.6 sigma" => Again, we think that the quotation marks and the explanation makes it clear the "detection" relies on spectral assumptions. Yet since the assumptions are the same used by different authors, the number is useful to show the quality of these data (rather exceptional for a source at this distance).

Therefore, everywhere the
authors use the phrase "measurement of the EBL" or "the EBL was
detected" (e.g., bottom of second column of page 6), or something
similar, they need to change to "constraint" or "upper limit" (or
something similar). This includes the title of the paper.

We disagree. It is a measurement which depends on some assumptions. We do not think any of the assumptions is particularly outrageous, and they are actually more conservative than those in earlier papers on the same topic (i.e. Log-Par vs. Power-Law). All the information is available in the paper for the reader to judge.

Other comments:

Authors (from their reply): "We present it as an empirical
parametrization of the observed spectrum, and note that it features a
rather sharp break in the spectral index, which hints at it not being
an intrinsic feature of the source."

Why would this imply it is not an intrinsic feature of the source?
Many LAT spectra of blazars show sharp breaks (e.g. Abdo et al. 2009,
ApJ, 699, 817; Abdo et al. 2010, ApJ, 710, 1271) and several authors
have thought of theoretical ways to create them.

The first reference is about 3C 454.3, an FSRQ, and the second reference mentions that and another clear case of sharp break, which is an LSP BL Lac. Besides, the paper states that the curvature (let alone a sharp break) is absent in all HSP-BLLacs, the class to which 1ES1011 belongs. Therefore we do not think this is a valid objection.

Authors (top of first column of page 6): "[The detections of the EBL]
rely on somewhat tentative assumptions of the intrinsic spectra--but
assumptions which, as far as we know, are not falsified by any
observational data available on BL Lacs."

These assumptions need to be stated explicitly. I guess the main
assumption is that the intrinsic spectrum must be a log-parabola
(bottom of first column on page 4).

They are stated explicitly in the paper, there is no need to guess. And it is not just the log-parabola, all other tested shapes count as well - the lower constraint if we had used any of them would have gone up, so they are included in our result.

But I do not agree with this assumption. First of all, many BL Lacs do not have their intrinsic
LAT spectra fit preferentially by a log-parabola over a power-law.

We are confused. How can that be a problem for us? PWL is a particular case of log-parabola.

Second, this seems to be circular reasoning. The authors are using
the gamma-ray spectra deabsorbed with a particular EBL model to argue
that the intrinsic spectra are log-parabolas, and then using a
log-parabola gamma-ray spectrum to claim a "detection" of the EBL.

No, it is not circular reasoning. We explicitly talk of measurements in the optically-thin regime:

"...nor has it been observed in any BL Lac in the optically-thin regime. In particular, the un-absorbed part of BL Lac spectra measured by Fermi-LAT are well fitted by log-parabolas (Ackermann et al. 2012)."

Authors (from their reply): "Although we cannot make a likelihood
ratio test with two models that are non-nested, it is at least
indicative that a 5-parameter function fits the observed spectrum
worse than a simple 2-parameter function (PWL)"

I think the SBPWL and PWL models are nested. If E_b in Equation (1)
goes to infinity it will be a PWL.

This is a misunderstanding, what we wrote is "...than a simple 2-parameter function times the transmission factor predicted by the nominal Domínguez EBL model". Of course, SBPL and PWL are nested... we meant that "SBPL" and "PWL*EBL" are not nested, so we can not compare them via a LRT. Yet, it is interesting to see that a quite complex spectrum (fitted by a 5-parameter function) becomes nearly a pure power-law upon correcting for EBL absorption using the Domínguez model.

Authors (from their reply): "For the same reason, the SBPWL has the
problem of being very degenerate around the likelihood maximum (having
3 redundant parameters). On top of it, the function is non-linear in
most of its parameters. These features lead to trouble in finding the
absolute likelihood maximum for the different values of alpha, i.e. a
strong dependence on initial parameters and convergence on local
maxima."

Some of these problems might be resolved by using a "Band function",
often used in the analysis of gamma-ray bursts. See Band et
al. (1993), ApJ, 413, 281, Equation (1). At least, it would have one
less free parameter than the broken power-law model the authors use.

Please Adiv check that, although the Band function parametrizations I was able to find are of the type
f = blabla if x < x0
f = sth.else if x > x0

and do not seem to be linear in the parameters either. Besides, I have never heard of the Band function being used to fit blazar spectra, but I may be wrong.

I hope this helps to have the reply to the referee ready before end of the year. Let's continue discussion in the forum once you post the referee's comments and a draft of the counter-reply.

Best regards,

Abelardo

[adiv.gonzalezmunoz]

Hi

I concur with most of the comments from Abelardo for the reply to the referee. Only a couple of remarks

I don't want to sound as trying to be compliant with the referee, but maybe for the sake of trying to avoid more delays with the publication we could give up on this matter and make the changes from "measurement" to "limits". Most likely this guy will be hard in changing his mind. Actually I received the same complain from Stecker (the guy from the EBL model and other ebl-related papers) when I gave a kind of informal talk about this in NASA-Goddard, although Pepa says that he recently complains just about everything. But I agree that does not mean that our lower limit (although not so robust) is meaningless. Then the title would be: MAGIC observations of the February 2014 flare of 1ES 1011+496 and limits to the EBL density. Or we can take advantage on his acknowledgment of our upper limits and put something like: MAGIC observations of... and robust upper limit to the EBL density.

Indeed this guy is wrong in citing those sources as being examples of spectra with sharp breaks that can be applied to our case. As I claimed before, I made a check in ALL HBLs and IBLs cited in TeVCat to see if any was described with a broken power law and I only found one (PKS 2155-304). Moreover, in the latest Fermi catalog they only use, power laws, log parabolas and superexponential cut-off power laws for the description of all their sources.

Well I checked the reference that this guy sent and it is what Abelardo say, a function divided in two regions depending on the energy but still not linear in the parameters and I think this will only make things more complicated, because the fitting procedure will have to be divided between the spectral points that are in one region and the rest of the points in the other region. Actually I don't see how that would be different than fitting two power laws for each part of the spectrum before and after the break.

Tomorrow and maybe the day after I'll be checking my e-mail, but after that until January 3th, I'll have limited access to internet.

Cheers

Adiv

[abelardo.moralejo]

Hi,

ok, I am not fixed on the "measurement" word, so we can try to please the referee a bit. But if we replace "measurement", I prefer to use "constraint" rather than "limit".
Also: I do not know if our internal referees are getting notifications about all of this. If they are not, they should. Adiv, can you check and make sure they are aware of all the modifications?

Ciao,

A.

[david.paneque]

Hi there,
I agree with the tentative reply to the referee.
You were quite unfortunate and got a really picky referee...

As for measurements vs constraints, I think it is fine to keep measurements based on the fact that previous publications also use the word "measurement"./
And then, to comply to the referee, you can add few sentences with the clear caveat that this measurmeent is based on a set of assumptions, and that the lower limits need to be taken with a grain salt. But here you could also mention that you will keep using the word measurement for the sake of comparison with previous papers. I think such reply to the referee would work. But well... ultimately it is your choice. The easiest thing (to get it accepted) is to comply with the referee, but then it looks as "if our paper is worse" than other papers with similar (even less significant studies).

And I agree that nobody uses a band function to describe the spectra of blazars. I am not aware of any case and hence, at the very least, we can claim that it is not common or standard practice.

cheers,
D.

[adiv.gonzalezmunoz]

Hi David, thanks for joining to the discussion.

Well, the caveat that our "measurement" has is already stated in the paper, and in more than one place we say that our best result is the "upper bound". We could rephrase it to make it more evident, but I think that is not necessary. The problem (or at least the impression that I have) is that the referee do not like the word "measurement", particularly because it is in the title. I agree that using the word "measurement" lead the reader to compare our work with the previous ones... maybe that is a good argument to sell to the referee.

Ok, then, the reply to the editor and the referee could be like:

------------------------------------------------------------------------------------------------------------------------------------------------
Dear Sergio Campana, A&A Editor

In this version of our paper "MAGIC observations of the February 2014 flare of 1ES 1011+496 and measurement of the EBL intensity" we keep the last modifications submitted in the previous version. We have reviewed all comments issued by the referee and we have prepared a reply.

Best regards

The corresponding authors.

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

Dear referee

Thanks for reviewing again our work and sending us your comments. For this reply and for a better understanding we quote your comments

Referee: "I agree with the authors statements regarding the upper limit on the
EBL (top of the first column of page 4, top of the first column of
page 6), namely that it is a robust, reliable result. The authors now
state in several places that the lower limit on the EBL is not robust.
I would go further than this, I think the lower-limit is basically
meaningless, since (as the authors now state in the text) they cannot
exhaust every possible concave model. "

Even if one could exhaust all possible concave models, the measurement (including the upper constraint) would still depend on the assumption that BL Lac VHE spectra must be concave. Currently it depends on the intrinsic spectrum to be not just concave, but also describable by one of the considered simple concave functions. It is indeed an assumption-dependent constraint, but we do not think it is meaningless.

Referee: "My main concern with the text
at this point is therefore the description of the result as a
"measurement" or "detection". Perhaps this is a matter of semantics,
but I do think the distinction is important. A measurement implies
both an upper and lower limit. Since I do not believe the authors
have found a reliable lower limit, I do not think characterizing the
result as a "measurement" is accurate. "

In principle, the goal is not to detect the EBL, since there is no doubt that some level of EBL must exist at least from the resolved galaxies. In this sense the lower constraint is of no big interest as long as it does not go significantly above the lower limits from galaxy counts (and it doesn't).
In any case, what we currently have in the paper about "detection" is the following:

- "we aim at detecting the imprint of the EBL... " : no problem there, we hope.

- "the assumption of power-law intrinsic spectrum would result in an EBL “detection” at the 13 level." : hypothetical, and the quotation marks in "detection" are there to show we would not consider that a reasonable statement. Yet, that is what others would have done with this data sample (i.e. assume intrinsic PL), had it been included in their compilations to study the EBL with VHE spectra.

- "This and earlier claims of detections of the EBL through its imprint on gamma-ray spectra hence rely on somewhat tentative assumptions on the intrinsic spectra" : precisely the point at stake is clearly stated there, so we do not see a problem. But we may replace "claims of detections of the EBL through" by "lower constraints on the EBL density obtained through" if it sounds better.

- "In the approach that we followed along this work, for the description of the intrinsic spectrum at VHE we restricted ourselves to smooth concave functions which have shown in the past to provide good fits to BL Lac spectra whenever the expected EBL absorption was negligible. Under this assumption, the EBL was “detected” with a significance of 4.6 sigma" => Again, we think that the quotation marks and the explanation makes it clear the "detection" relies on spectral assumptions. Yet since the assumptions are the same used by different authors, the number is useful to show the quality of these data (rather exceptional for a source at this distance).

Referee: "Therefore, everywhere the
authors use the phrase "measurement of the EBL" or "the EBL was
detected" (e.g., bottom of second column of page 6), or something
similar, they need to change to "constraint" or "upper limit" (or
something similar). This includes the title of the paper."

We disagree. It is a measurement which depends on some assumptions. We do not think any of the assumptions is particularly outrageous, and they are actually more conservative than those in earlier papers on the same topic (i.e. Log-Par vs. Power-Law). We believe that is better to keep the word "measurement" since it will be better for the reader to compare our work with previous papers that use the same or similar techniques and also interpret them as measurements. All the information is available in the paper for the reader to judge.

Referee: "Many LAT spectra of blazars show sharp breaks (e.g. Abdo et al. 2009,
ApJ, 699, 817; Abdo et al. 2010, ApJ, 710, 1271) and several authors
have thought of theoretical ways to create them."

The first reference is about 3C 454.3, an FSRQ, and the second reference mentions that and another clear case of sharp break, which is an LSP BL Lac. Besides, the paper states that the curvature (let alone a sharp break) is absent in all HSP-BLLacs, the class to which 1ES1011 belongs. Therefore we do not think this is a valid objection.

Referee: "These assumptions need to be stated explicitly. I guess the main
assumption is that the intrinsic spectrum must be a log-parabola
(bottom of first column on page 4)."

They are stated explicitly in the paper, there is no need to guess. And it is not just the log-parabola, all other tested shapes count as well - the lower constraint if we had used any of them would have gone up, so they are included in our result.

Referee: "But I do not agree with this assumption. First of all, many BL Lacs do not have their intrinsic
LAT spectra fit preferentially by a log-parabola over a power-law."

We are confused. How can that be a problem for us? PWL is a particular case of log-parabola.

Referee: "Second, this seems to be circular reasoning. The authors are using
the gamma-ray spectra deabsorbed with a particular EBL model to argue
that the intrinsic spectra are log-parabolas, and then using a
log-parabola gamma-ray spectrum to claim a "detection" of the EBL."

No, it is not circular reasoning. We explicitly talk of measurements in the optically-thin regime:

"...nor has it been observed in any BL Lac in the optically-thin regime. In particular, the un-absorbed part of BL Lac spectra measured by Fermi-LAT are well fitted by log-parabolas (Ackermann et al. 2012)."

Referee: "I think the SBPWL and PWL models are nested. If E_b in Equation (1)
goes to infinity it will be a PWL. "

This is a misunderstanding, what we wrote is "...than a simple 2-parameter function times the transmission factor predicted by the nominal Domínguez EBL model". Of course, SBPL and PWL are nested... we meant that "SBPL" and "PWL*EBL" are not nested, so we can not compare them via a LRT. Yet, it is interesting to see that a quite complex spectrum (fitted by a 5-parameter function) becomes nearly a pure power-law upon correcting for EBL absorption using the Domínguez model.

Referee: "Some of these problems might be resolved by using a "Band function",
often used in the analysis of gamma-ray bursts. See Band et
al. (1993), ApJ, 413, 281, Equation (1). At least, it would have one
less free parameter than the broken power-law model the authors use."

We have checked the "Band function". Although indeed has less free parameters than the smooth broke power-law, it is still a function that is not linear in its parameters. Using such function wouldn't be much different than using a broken power-law, that is, with a sharp change defined by the intervals in the function, which would go in the same direction of our argument of the "unnaturalness" of the smooth broken power-law used for describing the VHE emission from a blazar.


Best regards

The corresponding authors

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


Please feel free to modify or comment on the reply.

On the other hand, as I said, I think the draft based on this reply does not need modification. If you think it does, please tell me in which part is needed.

Cheers

Adiv

[abelardo.moralejo]

Hi Adiv,

fine from my side!

Best regards,

A.

[david.paneque]

Posted on behalf of Stefano Covino


Green light, David. With pleasure!

S.

[david.paneque]

Hi there,
I went over it.
It looks good. I only have few minor remarks to smooth out and/or improve clarity in some of the statements.
I have not yet heard from Ulisses. But the report is relatively minor, I think we can go ahead. No need to wait further.
cheers,
D.

hypothetical, and the quotation marks in "detection" are there to show we would not consider that a reasonable statement.
Adiv

hypothetical, and the quotation marks in "detection" are there to show that it is not a formal detection from the strictly point of view.

- " But we may replace "claims of detections of the EBL through" by "lower constraints on the EBL density obtained through" if it sounds better.
Adiv

In any case, following the journal referee suggestion, we replaced XXX by YYY

Note for Adiv et al:
do it, better than waiting for referee confirmation. We do not want to have another iteration with him/her.

We disagree. It is a measurement which ...
Adiv

We respectfully disagree. It is a measurement which ...

Besides, the paper states that the curvature (let alone a sharp break) is absent in all HSP-BLLacs, the class to which 1ES1011 belongs. Therefore we do not think this is a valid objection.
Adiv

The sharp breaks mentioned by the referee are absent in HSP-BLLacs (this is actually mentioned in the paper cited). The blazar 1es1011 is an HSP-BLL Lac and hence we do not think the referee’s objection can be applied to this case.

We are confused. How can that be a problem for us? PWL is a particular case of log-parabola.
Adiv

This is not a problem for the results reported in this paper because the PWL is a particular case of a log-parabola.

remark for Adiv et al:
better NOT to ask questions to the referee, because this invites the referee to answer us… there are some people that love to have these kind of discussions… I really do not, and hope you do not want either. Better NOT to have any other iteration with the referee.

No, it is not circular reasoning. We explicitly talk of measurements in the optically-thin regime:

Adiv

We think it is not a “circular reasoning” because we explicitly mention that the log-parabola measurements are performed in the optically-thin regime:

Referee: "I think the SBPWL and PWL models are nested. If E_b in Equation (1)
goes to infinity it will be a PWL. "

This is a misunderstanding, what we wrote is "...than a simple 2-parameter function times the transmission factor predicted by the nominal Domínguez EBL model". Of course, SBPL and PWL are nested... we meant that "SBPL" and "PWL*EBL" are not nested, so we can not compare them via a LRT. Yet, it is interesting to see that a quite complex spectrum (fitted by a 5-parameter function) becomes nearly a pure power-law upon correcting for EBL absorption using the Domínguez model.
Adiv

We naturally agree with the referee that the SBPL and the PWL are nested models. What we meant is that “SBPL” and “PWL*EBL” are not nested, and hence cannot be compared via a LRT. We believe that the sentence we have in the manuscript (i.e. “… than a 2-parameter function times the transmission factor predicted by the nominal Dominguez EBL model”) is clear on this respect.

We have checked the "Band function". Although indeed has less free parameters than the smooth broke power-law, it is still a function that is not linear in its parameters. Using such function wouldn't be much different than using a broken power-law, that is, with a sharp change defined by the intervals in the function, which would go in the same direction of our argument of the "unnaturalness" of the smooth broken power-law used for describing the VHE emission from a blazar.

broke power-law
—>
broken power law

3 instances in total.

Note that it is “broken power-law function “, but a “broken power law”
(subtle difference)

[adiv.gonzalezmunoz]

Hi all

I just re-submitted the draft to A&A. I have included in the reply (and the manuscript) all the suggestions made by David.

Let's hope this time the referee shows some flexibility


Adiv

[adiv.gonzalezmunoz]

Hi

For the record, attached are the manuscript versions that I sent to the journal

Adiv

[adiv.gonzalezmunoz]

Hi all

The referee has sent his reply. He basically insist that we should change "measurement" to "constraint" or "upper limit" in the title and the text. Please see his reply in the following lines

Referee Report

I feel rather strongly that the results of this manuscript should not
be described as a "measurement" or "detection" of the EBL, as I
discussed in my previous report. If the authors insist on
characterizing their results this way, I think at this point it will
save everybody time if they ask the scientific editor to overrule my
objection, or ask for another referee. Otherwise, I think we will
just go around in circles. Rather than the standard format of quoting
the authors followed by my response, I give a summary of both the
authors' position and my position. I hope the authors will think the
summary is fair to them. I think this summary will be more useful to
the editor and/or future referee.

I would like to say once again that, aside from this disagreement, the
authors present an interesting, well-written paper that should be
published in A&A.

The authors' position:

1) The authors put an upper limit on the EBL based on MAGIC
observations of the source 1ES 1011+496 and the primarily assumption
that its gamma-ray spectrum is concave. This upper limit is reliable
and robust.

2) Their lower limit on the EBL depends strongly on the assumed form
for the intrinsic gamma-ray spectrum of 1ES 1011+496, and so the
lower-limit is not particularly robust. It their response to my first
report, the authors modified the manuscript in several places to say
this.

3) Despite the fact that it is not robust, the authors think the lower
limit is still meaningful. This is because the intrinsic spectrum is
"describable by one of the simple concave function" they use (listed
in Table 1 of the manuscript, and described in a previous paper by the
HESS Collaboration).

4) The authors put the word "detection" in quotation marks in several
places as an indication that it is "not a formal detection". In at
least one instance they replaced the word "detection" with
"constraint" in response to my last report.

5) Previous papers have used similar techniques and referred to the
result as a "detection". It is not completely clear which papers the
authors are referring to in their last response, but I assume they
mean the paper by the HESS Collaboration (2013, A&A, 550, A4).
Keeping the phrase "measurement" in the title and other places will
allow readers to compare this result with the previous results by the
HESS Collaboration.

6) All of the assumptions are clearly spelled out in the manuscript.
The readers can read the details of the technique for themselves and
determine for themselves whether or not the phrases "measurement of
the EBL" or "detection of the EBL" are justified.

7) The lower limit on the EBL is not particularly interesting. The
authors' exact words: "the goal is not to detect the EBL, since there
is no doubt that some level of EBL must exist at least from the
resolved galaxies. In this sense the lower constraint is of no big
interest as long as it does not go significantly above the lower
limits from galaxy counts (and it doesn't)."

The referee's position/response:

1) The authors put an upper limit on the EBL based on MAGIC
observations of the source 1ES 1011+496 and the primarily assumption
that its gamma-ray spectrum is concave. This upper limit is reliable
and robust. I completely agree with the authors about the upper
limit.

2) The lower limit on the EBL depends strongly on the assumed form for
the intrinsic gamma-ray spectrum of 1ES 1011+496, and so the
lower-limit is not particularly robust. The authors and I seem to be
in agreement about this also, at least to a certain extent.

3) I do not think the lower limit is meaningful because of this lack
of robustness. Unlike the upper limit, the lower limit does not
depend only on the assumption that the intrinsic spectrum is concave,
but depends on the particular choice of function to model the
intrinsic spectrum. I think there are many possibilities for the
intrinsic spectrum that are not adequately described by one of their
simple functions. The intrinsic spectrum could have peculiarities due
to the (poorly understood) particle acceleration process, or cutoffs
from internal absorption, or cutoffs in the electron distribution, or
turnover in the Klein-Nishina cross-section at high energies (the
latter two assume the gamma-rays are produced by Compton scattering).
If the gamma-rays are produced by a hadronic process, the shape of the
gamma-ray spectrum is even less well-understood.

4) Because the lower limit is not meaningful, I do not think the
result should be characterized as a "detection of the EBL" or a
"measurement of the EBL". Instead phrases like "constraint" or "upper
limit" should be used. I do not think putting "detection" in
quotation marks is an adequate substitute for using the phrase
"constraint". Also I note their are many instances of the phrase
"measurement of the EBL" without quotation marks. This includes in
the title of the paper, the abstract, the last paragraph of Section 1,
the title of Section 4, etc. I disagree with all of these uses.

5) I also disagree with the HESS Collaboration's characterization of
their result as a "measurement". I stated this in my first report.

6) Let's face it, most readers are not going to dig into the details
of this paper. If they read the title of the paper, where a
"measurement" is claimed, they are going to think there is a robust,
meaningful, upper AND lower limit on the EBL. Words matter, and I
think the title of the manuscript gives a misleading impression.

7) In none of my reports have I given an opinion on how interesting
the lower limit is relative to the upper limit.

Final thoughts from the referee: The fact that the authors "partially
agree" with me about the lower limit, and that they do not think the
lower limit is particularly interesting, indicates that this is mostly
a semantics argument. But, I do feel that the semantics are important
in this case. Consider if MAGIC put only an upper limit on the
gamma-ray flux from a particular source. This would not be
characterized as a "detection" or "measurement". If an upper limit on
gamma-ray flux was described as a measurement in the title and
abstract of a paper, a referee would certainly object.

[Brianvaf]

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