Further Development of Event-based Analysis of X-Ray Polarization Data
An event-based maximum likelihood method for handling X-ray polarimetry data is extended to include the effects of background and nonuniform sampling of the possible position angle space. While nonuniform sampling in position angle space generally introduces cross terms in the uncertainties of polar...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2024-01-01
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| Series: | The Astrophysical Journal |
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| Online Access: | https://doi.org/10.3847/1538-4357/ad0897 |
| _version_ | 1797257213439377408 |
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| author | Herman L. Marshall |
| author_facet | Herman L. Marshall |
| author_sort | Herman L. Marshall |
| collection | DOAJ |
| description | An event-based maximum likelihood method for handling X-ray polarimetry data is extended to include the effects of background and nonuniform sampling of the possible position angle space. While nonuniform sampling in position angle space generally introduces cross terms in the uncertainties of polarization parameters that could create degeneracies, there are interesting cases that engender no bias or parameter covariance. When including background in Poisson-based likelihood formulation, the formula for the minimum detectable polarization has nearly the same form as for the case of Gaussian statistics derived by Elsner et al. in the limiting case of an unpolarized signal. A polarized background is also considered, which demonstrably increases uncertainties in source polarization measurements. In addition, a Kolmogorov-style test of the event position angle distribution is proposed that can provide an unbinned test of models where the polarization angle in Stokes space depends on event characteristics such as time or energy. |
| first_indexed | 2024-04-24T22:34:04Z |
| format | Article |
| id | doaj.art-c4876fbf4acc41c0a61bef66349979b1 |
| institution | Directory Open Access Journal |
| issn | 1538-4357 |
| language | English |
| last_indexed | 2024-04-24T22:34:04Z |
| publishDate | 2024-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | The Astrophysical Journal |
| spelling | doaj.art-c4876fbf4acc41c0a61bef66349979b12024-03-19T13:57:57ZengIOP PublishingThe Astrophysical Journal1538-43572024-01-0196418810.3847/1538-4357/ad0897Further Development of Event-based Analysis of X-Ray Polarization DataHerman L. Marshall0Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology , 77 Massachusetts Ave., Cambridge, MA 02139, USA hermanm@space.mit.eduAn event-based maximum likelihood method for handling X-ray polarimetry data is extended to include the effects of background and nonuniform sampling of the possible position angle space. While nonuniform sampling in position angle space generally introduces cross terms in the uncertainties of polarization parameters that could create degeneracies, there are interesting cases that engender no bias or parameter covariance. When including background in Poisson-based likelihood formulation, the formula for the minimum detectable polarization has nearly the same form as for the case of Gaussian statistics derived by Elsner et al. in the limiting case of an unpolarized signal. A polarized background is also considered, which demonstrably increases uncertainties in source polarization measurements. In addition, a Kolmogorov-style test of the event position angle distribution is proposed that can provide an unbinned test of models where the polarization angle in Stokes space depends on event characteristics such as time or energy.https://doi.org/10.3847/1538-4357/ad0897PolarimetryX-ray astronomyAstronomical methodsAnalytical mathematics |
| spellingShingle | Herman L. Marshall Further Development of Event-based Analysis of X-Ray Polarization Data The Astrophysical Journal Polarimetry X-ray astronomy Astronomical methods Analytical mathematics |
| title | Further Development of Event-based Analysis of X-Ray Polarization Data |
| title_full | Further Development of Event-based Analysis of X-Ray Polarization Data |
| title_fullStr | Further Development of Event-based Analysis of X-Ray Polarization Data |
| title_full_unstemmed | Further Development of Event-based Analysis of X-Ray Polarization Data |
| title_short | Further Development of Event-based Analysis of X-Ray Polarization Data |
| title_sort | further development of event based analysis of x ray polarization data |
| topic | Polarimetry X-ray astronomy Astronomical methods Analytical mathematics |
| url | https://doi.org/10.3847/1538-4357/ad0897 |
| work_keys_str_mv | AT hermanlmarshall furtherdevelopmentofeventbasedanalysisofxraypolarizationdata |