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Linear polarization measurements provide access to two quantities, the degree (DOP) and the angle of polarization (AOP). The aim of this work is to give a complete and concise overview of how to analyze polarimetric measurements. We review interval estimations for the DOP with a frequentist and a Bayesian approach. Point estimations for the DOP and interval estimations for the AOP are further investigated with a Bayesian approach to match observational needs. Point and interval estimations are calculated numerically for frequentist and Bayesian statistics. Monte Carlo simulations are performed to clarify the meaning of the calculations. Under observational conditions, the true DOP and AOP are unknown, so that classical statistical considerations-based on true values-are not directly usable. In contrast, Bayesian statistics handles unknown true values very well and produces point and interval estimations for DOP and AOP directly. Using a Bayesian approach, we show how to choose DOP point estimations based on the measured signal-to-noise ratio. Interval estimations for the DOP show great differences in the limit of low signal-to-noise ratios between the classical and Bayesian approach. AOP interval estimations that are based on observational data are presented for the first time. All results are directly usable via plots and parametric fits.

HERMES-Pathfinder is a space-borne mission based on a constellation of six nano-satellites flying in a low-Earth orbit. The 3U CubeSats, to be launched in early 2025, host miniaturized instruments with a hybrid Silicon Drift Detector/scintillator photodetector system, sensitive to both X-rays and gamma-rays. A seventh payload unit is installed onboard SpIRIT, an Australian-Italian nano-satellite developed by a consortium led by the University of Melbourne and launched in December 2023. The project aims at demonstrating the feasibility of Gamma-Ray Burst detection and localization using miniaturized instruments onboard nano-satellites. The HERMES flight model payloads were exposed to multiple well-known radioactive sources for spectroscopic calibration under controlled laboratory conditions. The analysis of the calibration data allows both to determine the detector parameters, necessary to map instrumental units to accurate energy measurements, and to assess the performance of the instruments. We report on these efforts and quantify features such as spectroscopic resolution and energy thresholds, at different temperatures and for all payloads of the constellation. Finally we review the performance of the HERMES payload as a photon counter, and discuss the strengths and the limitations of the architecture.

Soft protons are a potential threat for X-ray missions using grazing incidence optics, as once focused onto the detectors they can contribute to increase the background and possibly induce radiation damage as well. The assessment of these undesired effects is especially relevant for the future ESA X-ray mission Athena, due to its large collecting area. To prevent degradation of the instrumental performance, which ultimately could compromise some of the scientific goals of the mission, the adoption of ad-hoc magnetic diverters is envisaged. Dedicated laboratory measurements are fundamental to understand the mechanisms of proton forward scattering, validate the application of the existing physical models to the Athena case and support the design of the diverters. In this paper we report on scattering efficiency measurements of soft protons impinging at grazing incidence onto a Silicon Pore Optics sample, conducted in the framework of the EXACRAD project. Measurements were taken at two different energies, ~470 keV and ~170 keV, and at four different scattering angles between 0.6 deg and 1.2 deg. The results are generally consistent with previous measurements conducted on eROSITA mirror samples, and as expected the peak of the scattering efficiency is found around the angle of specular reflection.

The High Energy Rapid Modular Ensemble of Satellites (HERMES) instrument is a compact X/\\(\\gamma\\)-ray spectrometer operating on board the 6U (11 kg) SpIRIT CubeSat. The payload is particularly well suited for the observation of cosmic transients such as Gamma-Ray Bursts and bright pulsars thanks to its unique broadband sensitivity from a few keV to a few MeV and the temporal resolution down to half a microsecond. We report here the detection of the \\(\\sim\\)33~ms Crab pulsar double-peaked pulse profile obtained by considering the canonical Crab ephemerides as provided by the Jodrell Bank catalog. We collected approximately 5.7\\(\\cdot\\)10\\(^4\\) photons from 730~s of observations, in the 3 keV -- 2 MeV energy band, during a single operation, and achieved a 5\\(\\sigma\\) pulse profile significance in the 3--11.5 keV energy band with binning at the ms scale. The results demonstrate that SpIRIT/HERMES can achieve millisecond timing accuracy at high energies and, thanks to its wide field of view and broad energy band, has the potential to contribute to GRB monitoring in the near future. Such capabilities were previously the domain of flagship observatories, underscoring the performance of the HERMES instrument with its compact form factor.

Context: Environmental soft protons have affected the performance of the X-ray detectors on board Chandra and XMM-Newton, and they pose a threat for future high energy astrophysics missions with larger aperture, such as ATHENA. Aims: We aim at estimating soft proton fluxes at the ATHENA detectors independently of any modelisation of the external fluxes in the space environment.We analysed the background data measured by eROSITA on board SRG, and with the help of simulations we defined a range of values for the potential count-rate of quiet-time soft protons focused through the mirror shells. We used it to derive an estimate of soft proton fluxes at the ATHENA detectors, assuming ATHENA in the same L2-orbit as SRG. Results: The scaling, based on the computed proton transmission yields of the optics and optical/thermal filters of eROSITA and ATHENA, indicates that the soft proton induced WFI and X-IFU backgrounds could be expected close to the requirement. Conclusions: No soft proton fluxes detrimental to the observations have been suffered by eROSITA during its all-sky survey in orbit around L2. Regardless of where ATHENA will be placed (L1 or L2), our analysis suggests that increasing somewhat the thickness of the WFI optical blocking filter, e.g. by 30%, would help to reduce the soft proton flux onto the detector, in case the planned magnetic diverters perform worse than expected due to soft proton neutralisation at the mirror level.

JEM--EUSO is an international program for the development of space-based Ultra-High Energy Cosmic Ray observatories. The program consists of a series of missions which are either under development or in the data analysis phase. All instruments are based on a wide-field-of-view telescope, which operates in the near-UV range, designed to detect the fluorescence light emitted by extensive air showers in the atmosphere. We describe the simulation software ESAFin the framework of the JEM--EUSO program and explain the physical assumptions used. We present here the implementation of the JEM--EUSO, POEMMA, K--EUSO, TUS, Mini--EUSO, EUSO--SPB1 and EUSO--TA configurations in ESAF. For the first time ESAF simulation outputs are compared with experimental data.

Astronomical X-ray observatories with grazing incidence optics face the problem of pseudo-focusing of low energy protons from the mirrors towards the focal plane. Those protons constitute a variable, unpredictable component of the non X-ray background that strongly affects astronomical observations and a correct estimation of their flux at the focal plane is then essential. For this reason, we investigate how they are scattered from the mirror surfaces when impacting with grazing angles. We compare the non-elastic model of reflectivity of particles at grazing incidence proposed by Remizovich et al. (1980) with the few available experimental measurements of proton scattering from X-ray mirrors. We develop a semi-empirical analytical model based on the fit of those experimental data with the Remizovich solution. We conclude that the scattering probability weakly depends on the energy of the impinging protons and that the relative energy losses are necessary to correctly model the data. The model we propose assumes no dependence on the incident energy and can be implemented in particle transport simulation codes to generate, for instance, proton response matrices for specific X-ray missions. Further laboratory measurements at lower energies and on other mirror samples, such as ATHENA Silicon Pore Optics, will improve the resolution of the model and will allow us to build the proper proton response matrices for a wider sample of X-ray observatories.

The High Energy Rapid Modular Ensemble of Satellites (HERMES) Technological and Scientific pathfinder is a space borne mission based on a constellation of LEO nanosatellites. The payloads of these CubeSats consist of miniaturized detectors designed for bright high-energy transients such as Gamma-Ray Bursts (GRBs). This platform aims to impact Gamma Ray Burst (GRB) science and enhance the detection of Gravitational Wave (GW) electromagnetic counterparts. This goal will be achieved with a field of view of several steradians, arcmin precision and state of the art timing accuracy. The localization performance for the whole constellation is proportional to the number of components and inversely proportional to the average baseline between them, and therefore is expected to increase as more. In this paper we describe the Payload Data Handling Unit (PDHU) for the HERMES-TP and HERMES SP mission. The PDHU is the main interface between the payload and the satellite bus. The PDHU is also in charge of the on-board control and monitoring of the scintillating crystal detectors. We will explain the TM/TC design and the distinct modes of operation. We also discuss the on-board data processing carried out by the PDHU and its impact on the output data of the detector.

THESEUS, one of the two space mission concepts being studied by ESA as candidates for next M5 mission within its Comsic Vision programme, aims at fully exploiting Gamma-Ray Bursts (GRB) to solve key questions about the early Universe, as well as becoming a cornerstone of multi-messenger and time-domain astrophysics. By investigating the first billion years of the Universe through high-redshift GRBs, THESEUS will shed light on the main open issues in modern cosmology, such as the population of primordial low mass and luminosity galaxies, sources and evolution of cosmic re-ionization, SFR and metallicity evolution up to the \"cosmic dawn\" and across Pop-III stars. At the same time, the mission will provide a substantial advancement of multi-messenger and time-domain astrophysics by enabling the identification, accurate localisation and study of electromagnetic counterparts to sources of gravitational waves and neutrinos, which will be routinely detected in the late '20s and early '30s by the second and third generation Gravitational Wave (GW) interferometers and future neutrino detectors, as well as of all kinds of GRBs and most classes of other X/gamma-ray transient sources. In all these cases, THESEUS will provide great synergies with future large observing facilities in the multi-messenger domain. A Guest Observer programme, comprising Target of Opportunity (ToO) observations, will expand the science return of the mission, to include, e.g., solar system minor bodies, exoplanets, and AGN.