The LIRA-Ising model: estimating the boundaries of irregularly shaped X-ray sources
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Published version
Author(s)
Type
Journal Article
Abstract
Mapping the boundary of an extended source is a key step in the study of its morphology. The background contamination and statistical fluctuations of typical astronomical images make this a challenging statistical task, particularly for X-ray images with low surface brightness. We develop a three-step Bayesian procedure to identify the boundaries of irregularly shaped sources. We first apply a Bayesian multiscale reconstruction algorithm known as LIRA to obtain posterior pixelwise probability distributions of the source intensity that properly account for known structures, astrophysical
background, and the effect of the telescope point spread function. Next, we adopt an Ising model to group pixels with similar intensities into cohesive regions corresponding to background and source. Finally, the boundary is derived on the basis of the most likely aggregation of pixels into the source region. Because the overall model combines LIRA and the Ising model, we call it LIRA-Ising. We verify the proposed method using a set of simulation studies. We then apply it to the Chandra X-ray Observatory images of two high redshift quasars, PKS J1421−0643 and 0730+257, to determine the extent and morphology of X-ray jets. Our method shows a uniform X-ray surface brightness of PKS J1421−0643 jet, and identifies knotty structure in the X-ray jet of 0730+257.
background, and the effect of the telescope point spread function. Next, we adopt an Ising model to group pixels with similar intensities into cohesive regions corresponding to background and source. Finally, the boundary is derived on the basis of the most likely aggregation of pixels into the source region. Because the overall model combines LIRA and the Ising model, we call it LIRA-Ising. We verify the proposed method using a set of simulation studies. We then apply it to the Chandra X-ray Observatory images of two high redshift quasars, PKS J1421−0643 and 0730+257, to determine the extent and morphology of X-ray jets. Our method shows a uniform X-ray surface brightness of PKS J1421−0643 jet, and identifies knotty structure in the X-ray jet of 0730+257.
Date Issued
2026-03-01
Date Acceptance
2026-01-07
Citation
Astrophysical Journal Supplement Series, 2026, 283 (14), pp.1-15
ISSN
0067-0049
Publisher
IOP Publishing
Start Page
1
End Page
15
Journal / Book Title
Astrophysical Journal Supplement Series
Volume
283
Issue
14
Copyright Statement
© 2026. The Author(s). Published by the American Astronomical Society. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
License URL
Identifier
10.3847/1538-4365/ae3716
Subjects
Interdisciplinary astronomy (804)
Algorithms (1883)
Astrostatistics (1882)
Computational methods (1965)
Deconvolution (1910)
Bayesian statistics (1900)
Publication Status
Published
Date Publish Online
2026-02-18