abelardo.moralejo wrote:(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.
abelardo.moralejo wrote: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??
abelardo.moralejo wrote: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).
abelardo.moralejo wrote: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.
abelardo.moralejo wrote: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.
abelardo.moralejo wrote: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 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?
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.
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.
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 wrote:
hypothetical, and the quotation marks in "detection" are there to show we would not consider that a reasonable statement.
Adiv
adiv.gonzalezmunoz wrote:- " 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
adiv.gonzalezmunoz wrote:We disagree. It is a measurement which ...
Adiv
adiv.gonzalezmunoz wrote: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
adiv.gonzalezmunoz wrote:We are confused. How can that be a problem for us? PWL is a particular case of log-parabola.
Adiv
adiv.gonzalezmunoz wrote:No, it is not circular reasoning. We explicitly talk of measurements in the optically-thin regime:
Adiv
adiv.gonzalezmunoz wrote: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
adiv.gonzalezmunoz wrote: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.
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