Issue |
A&A
Volume 693, January 2025
|
|
---|---|---|
Article Number | A75 | |
Number of page(s) | 11 | |
Section | Astrophysical processes | |
DOI | https://doi.org/10.1051/0004-6361/202451798 | |
Published online | 03 January 2025 |
A simplified approach for reproducing fully relativistic spectra in X-ray binary systems: Application to Cygnus X-1
1
Department of Physics, University of Ioannina, GR-45110 Ioannina, Greece
2
Department of Informatics, University of Western Macedonia, GR-52100 Kastoria, Greece
⋆ Corresponding authors; th.papavasileiou@uowm.gr; hkosmas@uoi.gr
Received:
5
August
2024
Accepted:
22
November
2024
Context. General relativistic effects are strong near the black hole of an X-ray binary and significantly impact the total energy released in the innermost accretion disk’s region. The simple pseudo-Newtonian solution in the standard disk model cannot replenish for effects such as light-bending, gravitational redshift, and Doppler boost. These can heavily affect the observed spectra depending on the rotation of the black hole and the disk’s inclination.
Aims. A proper relativistic treatment would be troublesome, unappealing, or require more advanced computational tools (e.g., the kerrbb code). Our goal is to fully incorporate the black hole’s spin and all the general relativistic effects on the observed spectra coming from X-ray binary systems while maintaining the simplicity of the standard Shakura-Sunyaev disk model.
Methods. We propose a way to replicate general relativistic spectra as predicted by the Novikov-Thorne model and the kerrbb numerical code by assuming a standard accretion disk with a shifted inner boundary that depends on the black hole spin and the source’s viewing angle. An essential aspect in employing this approach for a broader range of disk inclinations is the derivation of spin-dependent temperature profiles for the accretion disk, obtained from some of the most efficient pseudo-Newtonian potentials around Kerr black holes. We then applied this method to Cygnus X-1, fitting the observational data obtained during its soft and hard spectral states.
Results. The fully relativistic spectra are reproduced to an excellent approximation, with an error margin of 0.03–4%, by a standard disk model with a modified innermost radius within the range Rin = (0.2 − 2)RISCO, depending on the source’s viewing angle and black hole spin. This approach produces observed spectra as predicted by general relativity without the need for the ray-tracing method and complex numerical calculations. Thus, it emerges as a more straightforward alternative way of estimating black hole spins through the continuum-fitting method by successfully blending the general relativity properties with the Newtonian simplicity in a more complete way than the pseudo-Newtonian solutions. Relativistic effects near the black hole make an otherwise standard accretion disk with inclination θ < 60° seem truncated to larger radii to a distant observer. On the other hand, an edge-on view of the disk gives the perspective of being pulled closer to the central object than the respective innermost radius of the stable circular orbit. In addition, we show that the observational data of Cygnus X-1 can be satisfactorily fitted by employing a reasonably simple lepto-hadronic jet model and a hybrid thermal–nonthermal corona along with the relativistic-equivalent standard thin accretion disk.
Key words: accretion, accretion disks / black hole physics / gravitation / radiation mechanisms: non-thermal / radiation mechanisms: thermal / relativistic processes
© The Authors 2025
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This article is published in open access under the Subscribe to Open model. Subscribe to A&A to support open access publication.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.