Revisiting the Earth’s atmospheric scattering of X-ray/$\gamma$–rays and its effect on space observation: Implication for GRB spectral analysis

X-ray/$\gamma$–ray astrophysical observations are primarily conducted from space-based platforms as the Earth’s atmosphere does not transmit these high energy photons. While most photons are absorbed, a fraction of the X-ray/$\gamma$–ray photons from any extra-terrestrial sources undergoes Compton scattering in the upper layers of the atmosphere. In the Earth’s atmosphere, which has a mass column density of $\sim 10^{3}~{}\mathrm{g~{}cm}^{-2}$ at sea level, some of the scattered photons travel upwards having an appearence of reflection of X-ray/$\gamma$–ray by the atmosphere. Any space borne measurement of those high energy photons from astrophysical sources will be affected by simultaneous detection of the reflected photons.

The topic of interaction of extra-terrestrial high energy photons with the atmosphere is not new. Various studies have been performed to determine the spectrum of reflected Cosmic X-ray Background (CXB)¹¹1Alternately termed as Cosmic Diffused Gamma ray Background (CDGRB). photons from the Earth’s atmosphere and their effects on observations by various space-based high-energy instruments (e.g. Churazov $et~{}al$., 2008). Such works are often done in conjugation with studies determining the X-ray/$\gamma$–ray spectrum arising from the interaction of Cosmic ray particles (e.g. Sazonov $et~{}al$., 2007) with the molecules in Earth’s atmosphere. Together these two components constitute the X-ray/$\gamma$–ray albedo contribution and add up to the total background noise in high energy space detectors.

Apart from such studies in the context of Earth’s atmosphere, the main motivation of research related to the Compton reflection of high energy photons has been of purely astrophysical nature. This includes mainly the study of the scattering during the passage and interaction of cool electrons in relatively cooled plasma, such as the corona above a relatively cool, optically thick accretion disk (e.g. Bisnovatyi-Kogan & Blinnikov, 1977). In such studies one usually calculates a Green’s function describing the reflection of monochromatic radiation (White $et~{}al$., 1988), and convolves the incident spectrum with this function to calculate the reflected spectrum.

From the studies of Earth’s atmospheric scattering of high energy photons it is estimated that a moderate fraction of the incoming X-ray/$\gamma$–ray photons is reflected or back-scattered in the upper atmospheric layers of the Earth. Some studies estimate that in the $\sim$ 30 – 300 keV energy range (hereafter referred to as “intermediate energy”) of X-rays/$\gamma$–rays, as many as $\sim 30$% of the incident photons can be scattered back (see for instance Churazov $et~{}al$., 2008). The scattered fraction decreases outside this energy range, but remains non-negligible over a much broader X-ray/$\gamma$–ray band.This suggests that Low Earth Orbit (LEO) satellites observing energetic photons from Gamma Ray Bursts (GRBs) and other astrophysical transients detect significant flux reflected from the Earth’s atmosphere as well. The magnitude and spectrum of the contribution should vary largely based on the relative angular position (viewing angle) of the GRB with respect to the instrument, as well as to the line joining the instrument to the geo-center, relative orientation of the instrument with the ground, and the source spectral properties. Whether this is considered as an interpretable addition to the source signal or merely as an addition to the background noise detected by the instrument like the CXB and albedo photons, any analysis of properties of the transients should correctly account for the contribution.

Till date, the contribution of Earth’s reflection of X-rays and $\gamma$–rays in prompt GRB observation has mainly been studied from the standpoint of its application in study of firstly, polarization in those wavelengths (e.g. Willis $et~{}al$., 2005) and secondly in the process of localization of transient source (e.g. Pendleton $et~{}al$., 1999). The fact that the angular distribution of Compton scattered flux from Earth’s atmosphere should be dependent on the direction of polarization of the incoming photon beam from a distant GRB sources, has been exploited to find the polarization characteristics from measurement of the reflected X-ray flux. There has been rigorous investigation (Pendleton $et~{}al$., 1999) for estimating the atmospheric scattering contribution to accurately determine transient source location by CGRO/BATSE and Fermi missions. They mainly concentrate on Monte Carlo simulation studies and some observations with solar flares.

We investigated how various missions have incorporated the Earth reflection effect in their data processing. We have been particularly interested in digging into the CGRO/BATSE and Fermi/GBM spectral data processing and distribution, as these two have been the main workhorses in providing the spectral observation of GRB prompt emission from hard X-rays up to soft $\gamma$–ray part of the spectrum. In case of CGRO/BATSE the atmospheric contribution is evaluated during burst localization using EGS electromagnetic cascade Monte Carlo code with a spherical geometry of concentric shells representing an atmosphere with exponential density. Subsequent iterative $\chi^{2}$ minimization technique is followed (Pendleton $et~{}al$., 1999) to differentiate the scattering contribution from the total observed spectra consisting of photons both directly detected from the source and those scattered from atmosphere.

The analyses presented by Pendleton $et~{}al$. (1999) show us the extent to which the atmospheric scattering of source photons can contaminate observation of transients. In Figure 3 of the article demonstrating the distribution of number of GRBs detected by the detectors of different viewing angles (with respect to the burst) as function of the ratio of the detected atmospheric scattered flux to that of directly detected flux, it seems that for the detector with large viewing angles for a significant number of cases the detected scattered counts are well above the direct counts (by as much as an order). For moderate viewing angles the scattering rate is between 20% and 50% of that of the direct count rate. Figure 4 of the same article is also significant, depicting how the detected scattered to direct photon ratio can vary with zenith angle (i.e., the angle between the direction from instrument to the geo-center and the direction to the GRB), the viewing angle (w.r.t the burst) of detector and the orientation of the detector normal respective to the ground normal. The bottom-left plot showing the variation of the ratio with the source zenith angle for large viewing angle of the downward-facing detectors demonstrates the highest contribution of atmospheric scattering and its sharp dependence on photon incidence angle.

For Fermi/GBM, according to Meegan $et~{}al$. (2009), the atmospheric scattering response estimation has been performed following the same method as described for BATSE in the GEANT4 based GBM Response Simulation System (GRESS; Hoover $et~{}al$., 2005; Kippen $et~{}al$., 2007) and validated with BATSE simulation results. This is then used to form a source-specific total response function for a particular set of earth-spacecraft viewing conditions, to be calculated in the IODA DRMGEN software in stand alone mode. Whereas, Connaughton $et~{}al$. (2015) directly use the atmospheric response database established for BATSE (Pendleton $et~{}al$., 1999) in their study.

The problem of unwanted contribution of atmospheric scattering of X-ray/$\gamma$–ray is well addressed and steps have been followed to mitigate it, albeit, seemingly, there has been no quantitative, comprehensive and generalized description on how this should manifest in the estimation of the source characteristics, such as photon spectrum and polarization. These studies have been highly focused on specific instruments, and the final products are often deeply integrated with the instrument response function. Instead, in this work we take a generalized approach by concentrating on the Monte Carlo simulation of the interaction of energetic astrophysical source photon at atmosphere, completely devoid of any specific instrument interactions and characteristics. Thus, our goal is to calculate the distribution of atmospheric Compton scattered photons for a plane–parallel photon beam incident upon the Earth’s atmosphere and how it should manifest on the outcome of the spectral and polarization characteristics of the cumulative photon detection. Here we are presenting our findings only on the spectral front and intend to address the same on polarization elsewhere.

The broader goal of this work is two-fold. The first is to replicate the work that has been performed for other missions, and apply it directly to analysis of sources in AstroSat-CZTI (Singh $et~{}al$., 2014; Bhalerao $et~{}al$., 2017b; Rao $et~{}al$., 2017). Since its launch 5 years ago CZTI has detected more than 400 GRBs (Sharma $et~{}al$., 2020). CZTI has been used for some GRB localization studies (Bhalerao $et~{}al$., 2017a), and has also been very successful in detection of polarization in them (see Chattopadhyay $et~{}al$., 2019). Inclusion of the process of evaluation and deduction of atmospheric scattered contribution from prompt GRB spectra will be a significant step towards accurate analysis of all the above characteristics.

The second goal of the work is to publicly release all source codes and simulation data in a format that will be easy to adapt to any other mission. This goal stems from the plurality of upcoming and proposed missions to study high energy transients and gravitational wave high-energy electromagnetic counterpart detection, such as large instruments like SVOM (Cordier $et~{}al$., 2015), GECAM (Zhang $et~{}al$., 2019); as well as cubesat class instruments like BurstCube (Racusin $et~{}al$., 2017), HERMES (Fuschino $et~{}al$., 2019), BlackCAT (Chattopadhyay $et~{}al$., 2018), and Camelot (Werner $et~{}al$., 2018). There are also proposed missions, which are scientifically oriented towards hard X-ray/gammma ray polarimetry, such as POLAR-2 (Hulsman $et~{}al$., 2020) on-board Chinese space station and a Large Area GRB Polarimeter (LEAP) (McConnell $et~{}al$., 2017) on-board ISS. Rather than each of these missions developing their own atmospheric scattering databases, a single open database will serve the purpose well. It will also make it possible for comparisons between any other atmospheric scattering simulations, thus arriving at a quantitative estimate of systematic errors that may be present in the responses.

The organization of the paper is as follows. In Section 2, we discuss our simulation setup including detector geometry of Earth’s atmosphere and photon collecting detector, the physics of interaction and photon generation and run execution process. In Section 3 we presents our simulation outcome for mono-energetic photons and a hypothetical GRB spectrum, represented by Band function (Band $et~{}al$., 1993). In this section we will also investigate how the scattered photon contribution may change the spectral characteristics and possibly contribute artefacts in the exact evaluation of the spectral slope, if they are not accounted for correctly. We conclude in Section 4 by discussing about the outcome of our study and describing our future plan of work.

We have used GEometry ANd Tracking 4 (GEANT4) for simulating the Compton reflection of X-rays from Earth’s atmosphere. GEANT4 is a well known Monte Carlo detector simulation package (Agostinelli $et~{}al$., 2003) written in C++, initially developed for the simulation of high energy physics and gradually got enhanced, in order to be applied to lower energies also. Currently, it is used extensively in high energy detector and instrument simulation (mass model) of most of the astronomical missions including AstroSat-CZTI (Mate $et~{}al$., 2021). Below we describe the construction of the simulation geometry including the Earth’s atmosphere, the generic detector at LEO height, the physics models used in the simulation, and the methods for particle generation, data extraction, and analysis.

As discussed in the previous section, we undertake simulations only for mono-energetic beams with different incidence angles. The outcome, with suitable interpolation can easily be converted into response matrix and the spectrum for any realistic astrophysical source has to be synthesized by using a weighted sum of the simulated mono-energetic responses. The weights are to be determined by the number of source photons expected at that incident energy. The exercise of starting with mono-energetic incident beams has two main advantages. Firstly, it is helpful in better understanding of the exact nature of the atmospheric scattering response and how it varies over the incident photons at different ranges of X-ray/$\gamma$–ray energies. Secondly, this allows us to re-use our simulation results for any incident spectrum, without resorting to computationally expensive runs for each of them.

In this study, we have presented some of our simulation outcomes helpful in better understanding the nature of the Earth’s atmospheric reflection of X-ray/$\gamma$–ray photons from transient space objects and how can it affect the observation. We are in the process of developing a comprehensive and open-source simulation framework for estimating the atmospheric scattered component to be used in the construction of a publicly available database on Atmospheric Response Matrix (ARM). This particular study concentrates on contemplating the significance of proper evaluation of the atmospheric reflection component in terms of its effect on prompt GRB spectral analysis. In some upcoming studies we intend to perform simulations to find out the influence of Earth’s atmospheric scattering on the determination of polarization of high energy photons from such sources.

We find that the Earth’s atmosphere is quite effective at scattering incident X-rays and $\gamma$–rays, creating an overall reflected spectrum that is usually strong in the 30–300 keV region. The GRB fireball model (Paczynski, 1986; Goodman, 1986; Lundman $et~{}al$., 2012) predicts thermal components in GRB spectra. Such components have been identified in a multitude of GRBs (for instance Ryde, 2005; Guiriec $et~{}al$., 2011, 2013; Iyyani $et~{}al$., 2013, 2015; Axelsson $et~{}al$., 2012; Burgess $et~{}al$., 2014; Nappo, F. $et~{}al$., 2017), and their temperatures are similar to the ones obtained in our fits above. The simplified example in §3.2 demonstrates how Earth’s reflection can mimic such a thermal component. While this component is typically modelled in analysis, §3.3 shows how even small systematic errors in the estimation of atmospheric reflection can alter our interpretations of GRB data.

The problem may be further exacerbated when accounting for the direction-dependent sensitivity of the detector instrument. For instance, the effective area of AstroSat-CZTI varies by more than two orders of magnitude over the entire sky (Mate $et~{}al$., 2021). If the GRB were to be incident from a low-sensitivity direction while the scattered radiation arrives from a high-sensitivity direction for the satellite, the scattered component can be an order of magnitude larger than the incident component — further magnifying the effect of any uncertainties in the scattering model.

For typical observations for which one needs smaller contribution of thermal (blackbody) flux to account for the hump in the intermediate range of prompt GRB spectra, extra care should be taken to exclude any contribution from atmospheric scattering. For example, for GRB110721A (Axelsson $et~{}al$., 2012; Iyyani $et~{}al$., 2013), blackbody is found to contribute maximum of $\sim$ 10% of total flux, for GRB1000724B (Guiriec $et~{}al$., 2011) this is found to be $\sim$4%. In these cases a slight over/under estimation of the scattering contribution may impose considerable artefacts in the analysis leading to wrong estimation of the thermal component.

This underscores the need for having robust ARM calculations that can be used in any spectral analysis. Likewise, such calculations are also needed for localisation and polarisation analyses. The calculation of the reflected spectrum from the Earth involves several complexities like creating an accurate description of the atmosphere, accounting for all physical effects, and generating a large number of incident photons to get good statistics. Approximations have to be made at each stage to make the problem tractable, and each approximation may introduce systematic errors in the final answer, which can have significant impacts on the scientific outcomes.

It is not feasible for each mission to dedicate significant resources and undertake simulations to calculate the ARM, nor should it be necessary. Instead, it is important that a few groups independently develop response matrices, and compare their results to quantify accuracy and reliability of the answers. Further, end users should be made aware of these limitations, and inclusion of appropriate systematic errors in analysis may be recommended.

Going further, there are several improvements we intend to undertake. Firstly, there is a direct trade-off between using a large detector for collecting sufficient number of photons, and the resultant large differences in the scattering angles of photons that are incident on opposite ends of the detector. We will explore more simulation geometries, including multiple-detector scenarios, that will allow us to more effectively utilise all data generated in a simulation.

Second, the current simulations were carried out over a relatively coarse energy grid, at a certain incidence angle, with a modest number of photons. We plan to undertake convergence studies to determine the step sizes required in energies and angles to ensure reliable simulation results. We will also quantify the relationship between the number of photons in each monochromatic beam and the statistical uncertainty in the final reflected spectrum. Once these requirements are clearly defined, we will undertake simulations to create a database that can be re-used for all further calculations.

The final source codes and outputs of our simulations will be made available publicly for scrutiny and reuse, in a format that may be easily repurposed for other missions.