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Pitfalls of statistics-limited X-ray polarization analysis
KTH, School of Engineering Sciences (SCI), Physics, Particle and Astroparticle Physics.ORCID iD: 0000-0002-5742-7553
2018 (English)In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 615, article id A54Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
EDP Sciences, 2018. Vol. 615, article id A54
Keywords [en]
polarization; methods: data analysis; methods: statistical
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
URN: urn:nbn:se:kth:diva-228211DOI: 10.1051/0004-6361/201731971ISI: 000438418300002000438418300002OAI: oai:DiVA.org:kth-228211DiVA, id: diva2:1208699
Funder
Swedish National Space Board
Note

QC 20180521

Available from: 2018-05-18 Created: 2018-05-18 Last updated: 2018-07-31Bibliographically approved
In thesis
1. Measurements of hard X-ray polarization from the Crab and Cygnus X-1
Open this publication in new window or tab >>Measurements of hard X-ray polarization from the Crab and Cygnus X-1
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2018. p. 110
Series
TRITA-SCI-FOU ; 2018:14
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Physics; Physics
Identifiers
urn:nbn:se:kth:diva-228216 (URN)978-91-7729-780-2 (ISBN)
Public defence
2018-05-31, FB42, Roslagstullsbacken 21, AlbaNova Universitetscentrum, Stockholm, 14:00 (English)
Opponent
Supervisors
Note

QC 20180521

Available from: 2018-05-21 Created: 2018-05-18 Last updated: 2018-05-21Bibliographically approved

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