A statistical hardness classification of ultraluminous X-ray sources using long-term Swift /XRT monitoring
- 1Institut für Astronomie und Astrophysik
Abstract
We present a homogeneous statistical framework to characterize observed long-term hardness behavior in 29 ultraluminous X-ray sources using over 3500 archival Swift X-Ray Telescope (XRT) observations. Observations were classified as soft-band dominated, hard-band dominated, or uncertain using the hardness ratio and its confidence bounds. We defined HR as the ratio of the 1.5−10 to 0.3−1.5 keV count rates. We derived f soft and f hard and introduced the crossing index (CI), defined as the fraction of consecutive pairs of confidently classified observations that fall on opposite sides of the HR = 1 boundary. These descriptors were analyzed with rule-based classification and unsupervised hierarchical clustering. The rule-based analysis identifies eight soft-band-dominated, five hard-band-dominated, and 16 mixed-band systems, while clustering reveals a similar three-group structure. Sources with known or candidate accretor types typically occupy band-dominated groups, whereas unknown accretors are more common in the mixed-band group. All four sources with reported long-term X-ray modulations discussed in an orbital or super-orbital context belong to the rule-based mixed-band class. The three-cluster solution is preferred in 25 of 29 leave-one-out trials, while bootstrap tests reveal the band-dominated groups to be more stable than the mixed-band group. Because the classification uses observed count rates, these groups represent Swift /XRT signatures rather than intrinsic spectral states. Response-folding tests show that the modeled hardness ratio depends on absorption column density and photon index. Bayesian reanalysis of a representative low-count source reduced CI from 56.3% to 38.5% but preserved its mixed-band classification. Random downsampling produced no systematic shift in CI, using half of the observations changed median CI by at most ∼10% across four sources. Larger samples with independent absorption constraints can test links between these observational classes, accretor type, long-term periodic modulation, and other X-ray properties.
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BibTeX
@article{allak2026statistical,
title = {{A statistical hardness classification of ultraluminous X-ray sources using long-term Swift /XRT monitoring}},
author = {Sinan Allak and Wei Yu and Menglei Zhou and Honghui Liu and Andrea Santangelo},
journal = {Astronomy \& Astrophysics},
year = {2026},
month = oct,
doi = {10.1051/0004-6361/202662175},
url = {https://www.aanda.org/10.1051/0004-6361/202662175},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A statistical hardness classification of ultraluminous X-ray sources using long-term Swift /XRT monitoring
AU - Sinan Allak
AU - Wei Yu
AU - Menglei Zhou
AU - Honghui Liu
AU - Andrea Santangelo
PY - 2026
DA - 2026/10/28
JO - Astronomy & Astrophysics
DO - 10.1051/0004-6361/202662175
UR - https://www.aanda.org/10.1051/0004-6361/202662175
AB - We present a homogeneous statistical framework to characterize observed long-term hardness behavior in 29 ultraluminous X-ray sources using over 3500 archival Swift X-Ray Telescope (XRT) observations. Observations were classified as soft-band dominated, hard-band dominated, or uncertain using the hardness ratio and its confidence bounds. We defined HR as the ratio of the 1.5−10 to 0.3−1.5 keV count rates. We derived f soft and f hard and introduced the crossing index (CI), defined as the fraction of consecutive pairs of confidently classified observations that fall on opposite sides of the HR = 1 boundary. These descriptors were analyzed with rule-based classification and unsupervised hierarchical clustering. The rule-based analysis identifies eight soft-band-dominated, five hard-band-dominated, and 16 mixed-band systems, while clustering reveals a similar three-group structure. Sources with known or candidate accretor types typically occupy band-dominated groups, whereas unknown accretors are more common in the mixed-band group. All four sources with reported long-term X-ray modulations discussed in an orbital or super-orbital context belong to the rule-based mixed-band class. The three-cluster solution is preferred in 25 of 29 leave-one-out trials, while bootstrap tests reveal the band-dominated groups to be more stable than the mixed-band group. Because the classification uses observed count rates, these groups represent Swift /XRT signatures rather than intrinsic spectral states. Response-folding tests show that the modeled hardness ratio depends on absorption column density and photon index. Bayesian reanalysis of a representative low-count source reduced CI from 56.3% to 38.5% but preserved its mixed-band classification. Random downsampling produced no systematic shift in CI, using half of the observations changed median CI by at most ∼10% across four sources. Larger samples with independent absorption constraints can test links between these observational classes, accretor type, long-term periodic modulation, and other X-ray properties.
SN - 0004-6361
SN - 1432-0746
ER -