Hadronic Energy Scale Calibration of Calorimeters in Space Using the Moon’s Shadow

Round 1

Reviewer 1 Report

The paper "Energy Scale Calibration of Calorimeters in Space using Moon's shadow" (instruments-2702756) describes a method to determine the energy scale of the calorimeter of a space-based experiment from the displacement of Moon's shadow due to the bending of charged cosmic rays (CRs) in Earth's magnetic field. The method is simulated for protons detected in a calorimeter based on the design of the HERD experiment, using the orbit of the China Space Station (CSS). For these assumptions, the calibration procedure is shown to be sensitive to shifts of the global energy scale of 10% with a measurement time of 5 years.

The method to use Moon's shadow to demonstrate the capabilities of experiments measuring CRs has been proposed a long time ago, and has been used by many experiments measuring the extensive air showers produced by CRs. This is correctly described in the introduction of the paper. It is also mentioned that Imaging Atmospheric Cherenkov Telescopes (IACTs) like L3+C, Tibet-III, ARGO-YBJ and HAWC have used the deflection of charged particles in Earth's magnetic field to determine the ratio of anti-protons to protons and the positron fraction. However, at least some of these experiments have also used a method similar to the one described in this paper for an "Absolute rigidity scale calibration" (ARGO-YBJ, arXiv:1107.4887) or the "Calibration of the air shower energy scale of the water and air Cherenkov techniques in the LHAASO experiment" ([9] in the paper). This is not explicitly mentioned in the paper.

The simulation of this method for the energy calibration of calorimeters in space based experiments shows that with realistic assumptions, it is applicable and leads to a sensitivity of 10% or better for an observation time of 5 years. This makes it an interesting option for HERD, and possibly other experiments with comparable large field of view, pointing and energy resolution. 

The description of the method and the discussion of the results is well structured, and mostly clear. However, I have some general questions and comments. Some smaller comments are listed below.

General:

- description of the effect, definition of the angles: since Earth's magnetic field can be approximated well by a dipole, the deflection of the charged particles happens nearly exactly in one plane. This is not mentioned in the paper, and it is not clear to me if the angles alpha and beta are defined in that plane, or if they are solid angles.

- in the analysis, it is not clear to me if only CRs in a narrow strip around the expected deflection direction are used, or if the full field of view is used

- the simulation uses protons to study the sensitivity to the energy calibration. Why? Why not electrons?

- the paper simulates an isotropic CR distribution from outer space by back-propagating CRs that are isotropically distributed at the detector location. Since Earth's magnetic field changes the directions of the particles, this is not necessarily true. Please give some indication why this is a valid assumption (or for which kind and energy of particles it is valid)

- analysis, figure 4: are all energy bins combined to get the result in the lower plot of figure 4? If yes, would it make sense to split the data sample into energy ranges to be able to detect not only a global mis-calibration, but also energy-dependent effects?

- the analysis combines data corresponding to a measurement time of 5 years. Is it realistic to assume that the calorimeter is stable on such long time scales? Could the method be used to monitor variations with time? Or are there other methods foreseen to monitor these?

- since the uncertainties on the CR energy spectrum are not small, it would be interesting to know if a variation of the spectrum has a significant effect on the result of the calibration procedure

- the analysis shows clearly that a mis-calibration of 10% in either direction could be detected. But it also shows a small bias for these values. It would be interesting to know what is the smallest mis-calibration that would lead to a significant detectable effect.

Smaller:

- figure 2: since the satellite polar passages cause relatively large asymmetric tails, could one gain in sensitivity by excluding these data in the later analysis?

- l. 91: inverting its sign -> inverting the sign of its electric charge

- l. 125: Heavside -> Heaviside

- l. 130: proton spectrum -> proton energy spectrum

- l. 131: is the spectrum weighted such that the true energy spectrum follows the parametrisation, or such that the measured spectrum follows it?

- l. 162: are 4 billion protons realistic for 5 years data taking?

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript proposes the observation of the Moon's shadow displacement in cosmic rays, due to their deflection in the geomagnetic field, as an innovative method for the calibration of calorimeters in space.
A simplified simulation of a realistic case has been developed to demonstrate that this effect can be exploitable for the energy scale calibration of calorimetric instruments in orbit in Earth’s proximity.

I think the proposed technique is potentially interesting for the whole cosmic rays community, especially for whom that work in actual and future calorimetric experiments for cosmic rays detection.
The manuscript is well organized and clearly written, the analysis presented in this work is explained clearly and sounds technically correct, except for one major point that in my opinion must be clarified before to recommend the manuscript for publication.

If my understanding is correct, the measured energy of the incoming protons is obtained with a simple Gaussian smearing of 30% (line 118), this is in my opinion too simplistic.
In fact, in a calorimetric instrument the measured energy does not correspond to the "true" energy of the incoming particle with some uncertainty due to the resolution,
but is a fraction of the incoming particle energy, often called deposited energy, that we can assume is related to the electromagnetic part of the shower.
This energy deposit is event dependent, and as far as I know there is not a way to measure the "true" particle energy on an event-by-event basis.
The deconvolution process adopted in calorimetric experiments to reconstruct the measured particle energy from the deposited one is a statistical process, that given a certain distribution of deposited energy returns the distribution of the particle energy, but not the measured particle energy of each event.
What is not clear to me is how the author thinks to solve this problem and manage to back-propagate the measured particle and build the distributions of "observed measured angle" in each measured energy bin.
One can think to use the deposited energy instead of the "measured energy", but this would have an impact on the results, that could be huge, due to the fact that particles of different energy sometimes deposit almost the same amount of energy in the calorimeter. The feasibility of this must be assessed.

Other minor details to review are listed below:

1) No considerations are made about particle detection efficiency (e.g. lines 81-84), but since penetrating particle cannot be used for this measurement (all MIPs would deposit almost the same amount of energy) the let say "trigger" efficiency is relevant, and could decrease a lot the statistics of the measurement.

2) Only the proton is considered in this manuscript. Maybe considering the helium nuclei could provide a benefit in terms of statistics (this is just a suggestion).

3) About the possible sources of systematic error (line 176), as stated by the author at line 212 "deviations in the understanding of resolutions may cause biases in the energy scale evaluation".
I think that if the author could understand from the simulations the magnitude of this kind of systematics this would a further improvement of the article results.

4) I think that also the contamination of the measured sample from other nuclear species (for example helium nuclei) could have a relevant impact on the systematic of the measurement, the author could add a comment on that.

5) Line 208, for current missions (like CALET), the acceptance is a fraction of the one supposed here (roughly ~1/20 for CALET, ~1/5 for DAMPE) and maybe the situation is even worse if we consider the detection efficiency.
Could the author have a comment on how much this reduction of statistics would affect the results of the proposed analysis?

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

This paper proposes the use of the Moon-Earth spectrometer technique for the calibration. It would be interesting for the astroparticle community because the absolute energy calibration is one of the essential issues for the calorimetric experiments. The manuscript is well described about the motivation, simulation method, and analysis. However, before granting publication, I would like the following point to be addressed for the improvement of the manuscript.

As a realistic test, authors have appropriately considered about an angular resolution and energy resolution of the detector responses. On the other hand, the discussion about the statistics is not enough, which is my only concern. Unlike the ground-based experiments which have a huge acceptance, the space missions have much smaller acceptance. In the paper, authors introduce the case of HERD which has a geometrical factor of 10 m²sr for a 5-year operation. However, according to the reference paper of L. Pacini et al. [PoS(ICRC2021) 66], the geometrical factor of HERD for protons is only 1 m²sr. The ten times larger acceptance is too optimistic. Also, authors propose a possibility to the current mission like CALET, but the geometrical factor of CALET is ~0.1 m²sr [PRL 129, 101102 (2022)]. The lack of the statistics should make an impact in the calibration accuracy. Before the publication, I need to request authors to have a discussion and/or revise the manuscript about the statistics more carefully, especially the relation to the calibration accuracy. For instance, it would be helpful for readers that authors could suggest an exposure enough to achieve the 5% accuracy of the energy calibration by this simulation.

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

The submitted manuscript presents a very interesting and peculiar method to calibrate the energy scale of a calorimeter used  for astroparticle experiments in space using the Moon's shadow.  The manuscript presented shows a very interesting and peculiar method to calibrate the energy scale of a calorimeter for astroparticle experiments in space using the shadow of the moon. The manuscript is written in a very clear way, the topic has been exposed in a complete and comprehensive way. The provided example is based on the simulation of the new cosmic rays detector to be used in low Earth orbit , similar to that of the Herd mission. The results of the simulation are very encouraging and the author also traced the path for a further improvement of the method using the shadow of the sun, keeping in mind the necessary introduction of a model for the interplanetary magnetic field between Earth and Sun.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

All my comments to the previous version have been taken into account.

Author Response

Thank you. Please note that the bibliography has been revised following a comment from another referee and the editor.

Reviewer 2 Report

A minor comment. There are many citations that refer to proceeding papers, not subject to review. Where is possible would be better to put a more recent reference possibly from a referred journal. For example reference 29 refers to an old ICRC conference, the same results has been recently published in PRL.

Author Response

Thank you. I modified the bibliography following your suggestion and some comments from the editor.

Reviewer 3 Report

In the resubmitted paper, my concerns have been appropriately addressed. I have no further comments and recommend it for publication.

Author Response

Thank you. Please note that the bibliography has been revised following a comment from another referee and the editor.