Gamma-ray bursts (GRBs) are exceptionally bright electromagnetic events occurring daily on the sky. The prompt emission is dominated by X-/γ-rays. Since their discovery over 50 years ago, GRBs are primarily studied through spectral and temporal measurements. The properties of the emission jets and underlying processes are not well understood. A promising way forward is the development of missions capable of characterising the linear polarisation of the high-energy emission. For this reason, the SPHiNX mission has been developed for a small-satellite platform. The polarisation properties of incident high-energy radiation (50–600 keV) are determined by reconstructing Compton scattering interactions in a segmented array of plastic and Gd3Al2Ga3O12(Ce) (GAGG(Ce)) scintillators. During a two-year mission, ∼ 200 GRBs will be observed, with ∼ 50 yielding measurements where the polarisation fraction is determined with a relative error ≤ 10%. This is a significant improvement compared to contemporary missions. This performance, combined with the ability to reconstruct GRB localisation and spectral properties, will allow discrimination between leading classes of emission models.

Gamma-ray bursts (GRBs) are exceptionally bright electromagnetic events occurring daily on the sky. The prompt emission is dominated by X-/gamma-rays. Since their discovery over 50 years ago, GRBs are primarily studied through spectral and temporal measurements. The properties of the emission jets and underlying processes are not well understood. A promising way forward is the development of missions capable of characterising the linear polarisation of the high-energy emission. For this reason, the SPHiNX mission has been developed for a small-satellite platform. The polarisation properties of incident high-energy radiation (50-600 keV) are determined by reconstructing Compton scattering interactions in a segmented array of plastic and Gd3Al2Ga3O12(Ce) (GAGG(Ce)) scintillators. During a two-year mission, similar to 200 GRBs will be observed, with similar to 50 yielding measurements where the polarisation fraction is determined with a relative error <= 10%. This is a significant improvement compared to contemporary missions. This performance, combined with the ability to reconstruct GRB localisation and spectral properties, will allow discrimination between leading classes of emission models.

Black hole binary (BHB) systems comprise a stellar-mass black hole and a closely orbiting companion star. Matter is transferred from the companion to the black hole, forming an accretion disk, corona and jet structures. The resulting release of gravitational energy leads to the emission of X-rays¹. The radiation is affected by special/general relativistic effects, and can serve as a probe for the properties of the black hole and surrounding environment, if the accretion geometry is properly identified. Two competing models describe the disk–corona geometry for the hard spectral state of BHBs, based on spectral and timing measurements^2,3. Measuring the polarization of hard X-rays reflected from the disk allows the geometry to be determined. The extent of the corona differs between the two models, affecting the strength of the relativistic effects (such as enhancement of the polarization fraction and rotation of the polarization angle). Here, we report observational results on the linear polarization of hard X-ray emission (19–181 keV) from a BHB, Cygnus X-1⁴, in the hard state. The low polarization fraction, <8.6% (upper limit at a 90% confidence level), and the alignment of the polarization angle with the jet axis show that the dominant emission is not influenced by strong gravity. When considered together with existing spectral and timing data, our result reveals that the accretion corona is either an extended structure, or is located far from the black hole in the hard state of Cygnus X-1.

Polarimetry provides insights into the emission mechanisms of astrophysical sources by elucidating their magnetic field and geometry. Hard X-rays are produced in \mbox{regions} with strong magnetic fields or strong gravitational effects, which makes them a probe of extreme environments. This thesis describes the design, \mbox{calibration} and data analysis from the balloon-borne hard X-ray polarimeters the PoGOLite Pathfinder and its upgrade PoGO+. These instruments have measured the polari-zation from the Crab nebula and pulsar, and of the black hole binary Cygnus X-1.

Paper I explores to what extent the statistical uncertainties on the polarization parameters are non-Gaussian when the number of photons is low, as tends to be the case for balloon-borne instruments.With this in mind, a Bayesian method is used for data analysis in the subsequent papers. Paper II describes the measurement of the polarization of the Crab system in the 20-120 keV energy range conducted by the PoGOLite Pathfinder. Although the result is modest in its statistical significance it paves the way for the design of the upgraded instrument PoGO+.

The PoGO+ mission was conceived to remedy the shortcomings of the PoGOLite Pathfinder design and observation strategy, as well as the pre-flight calibration, which the focus of Paper III. Significant improvements are made to the detector response model, optimization of data acquisition thresholds, online veto system and to the general calibration procedure. When combined with interspersed target and background measurements, systematic uncertainties are significantly smaller for PoGO+ than for the PoGOLite Pathfinder.

The main scientific results are presented in Papers IV and V for the Crab (20-160 keV) and Cygnus X-1 (20-180 keV), respectively. For the Crab, PoGO+ does not support a rapid increase in the polarization fraction claimed previously. Additionally, the hard X-ray emission must be produced close to the pulsar and possibly in the fine structures of the nebula. This is in agreement with X-ray images from other instruments. For Cygnus X-1, the polarization measurements constrain the geometry by rejecting the model where the hard X-rays are produced in a compact corona close to the black hole and support the extended corona model.

The thesis demonstrates how balloon-borne instruments can be improved over the course of several campaigns and can contribute to the testing of detector design, development of analysis methods and provide new scientific results for bright X-ray sources.

Context. One of the difficulties with performing polarization analysis is that the mean polarization fraction of sub-divided data sets is larger than the polarization fraction for the integrated measurement. The resulting bias is one of the properties of the generating distribution discussed in this work. The limitations of Gaussian approximations in standard analysis based on Stokes parameters for estimating polarization parameters and their uncertainties are explored by comparing with a Bayesian analysis. The effect of uncertainty on the modulation factor is also shown, since it can have a large impact on the performance of gamma-ray burst polarimeters. Results are related to the minimum detectable polarization (MDP), a common figure of merit, making them easily applicable to any X-ray polarimeter. Aims. The aim of this work is to quantify the systematic errors induced on polarization parameters and their uncertainties when using Gaussian approximations and to show when such effects are non-negligible. Methods. The probability density function is used to deduce the properties of reconstructed polarization parameters. The reconstructed polarization parameters are used as sufficient statistics for finding a simple form of the likelihood. Bayes theorem is used to derive the posterior and to include nuisance parameters. Results. The systematic errors originating from Gaussian approximations as a function of instrument sensitivity are quantified here. Different signal-to-background scenarios are considered making the analysis relevant for a large variety of observations. Additionally, the change of posterior shape and instrument performance MDP due to uncertainties on the polarimeteric response of the instrument is shown.

The PoGO mission, including the PoGOLite Pathfinder and PoGO+, aims to provide polarimetric measurements of the Crab system and Cygnus X-1 in the hard X-ray band. Measurements are conducted from a stabilized balloon-borne platform, launched on a 1 million cubic meter balloon from the Esrange Space Center in Sweden to an altitude of approximately 40 km. Several flights have been conducted, resulting in two independent measurements of the Crab polarization and one of Cygnus X-1. Here, a review of the PoGO mission is presented, including a description of the payload and the flight campaigns, and a discussion of some of the scientific results obtained to date. 

The linear polarization fraction (PF) and angle of the hard X-ray emission from the Crab provide unique insight into high-energy radiation mechanisms, complementing the usual imaging, timing, and spectroscopic approaches. Results have recently been presented by two missions operating in partially overlapping energy bands, PoGO+ (18-160 keV) and AstroSat CZTI (100-380 keV). We previously reported PoGO+ results on the polarization parameters integrated across the light curve and for the entire nebula-dominated off-pulse region. We now introduce finer phase binning, in light of the AstroSat CZTI claim that the PF varies across the off-pulse region. Since both missions are operating in a regime where errors on the reconstructed polarization parameters are non-Gaussian, we adopt a Bayesian approach to compare results from each mission. We find no statistically significant variation in off-pulse polarization parameters, neither when considering the mission data separately nor when they are combined. This supports expectations from standard high-energy emission models.

Polarimetric observations of celestial sources in the hard X-ray band stand to provide new information on emission mechanisms and source geometries. PoGO+ is a Compton scattering polarimeter (20-150 keV) optimised for the observation of the Crab (pulsar and wind nebula) and Cygnus X-1 (black hole binary), from a stratospheric balloon-borne platform launched from the Esrange Space Centre in summer 2016. Prior to flight, the response of the polarimeter has been studied with polarised and unpolarised X-rays allowing a Geant4-based simulation model to be validated. The expected modulation factor for Crab observations is found to be M-Crab = (41.75 +/- 0.85)%, resulting in an expected Minimum Detectable Polarisation (MDP) of 7.3% for a 7 day flight. This will allow a measurement of the Crab polarisation parameters with at least 5 sigma statistical significance assuming a polarisation fraction similar to 20% - a significant improvement over the PoGOLite Pathfinder mission which flew in 2013 and from which the PoGO+ design is developed.

We have measured the linear polarization of hard X-ray emission from the Crab in a previously unexplored energy interval, 20-120 keV. The introduction of two new observational parameters, the polarization fraction and angle stands to disentangle geometrical and physical effects, thereby providing information on the pulsar wind geometry and magnetic field environment. Measurements are conducted using the PoGOLite Pathfinder - a balloon-borne polarimeter. Polarization is determined by measuring the azimuthal Compton scattering angle of incident X-rays in an array of plastic scintillators housed in an anticoincidence well. The polarimetric response has been characterized prior to flight using both polarized and unpolarized calibration sources. We address possible systematic effects through observations of a background field. The measured polarization fraction for the integrated Crab light curve is 18.4(-10.6)(+9.8) per cent, corresponding to an upper limit (99 per cent credibility) of 42.4 per cent, for a polarization angle of (149.2 +/- 16.0)degrees.

Polarimetric studies of astrophysical sources can make important contributions to resolve the geometry of the emitting region and determine the photon emission mechanism. PoGOLite is a balloon-borne polarimeter operating in the hard X-ray band (25-240 key), with a Pathfinder mission focussing on Crab observations. Within the polarimeter, the distribution of Compton scattering angles is used to determine the polarisation fraction and angle of incident photons. To assure an unbiased measurement of the polarisation during a balloon flight it is crucial to characterise the performance of the instrument before the launch. This paper presents the results of the PoGOLite calibration tests and simulations performed before the 2013 balloon flight. The tests performed confirm that the polarimeter does not have any intrinsic asymmetries and therefore does not induce bias into the measurements. Generally, good agreement is found between results from test data and simulations which allows the polarimeter performance to be estimated for Crab observations.