We present a new model to calculate reflection spectra of thin accretion
disks in Kerr spacetimes. Our model includes the effect of returning radiation,
which is the radiation that is emitted by the disk and returns to the disk
because of the strong light bending near a black hole. The major improvement
with respect to the existing models is that it calculates the reflection
spectrum at every point on the disk by using the actual spectrum of the
incident radiation. Assuming a lamppost coronal geometry, we simulate
simultaneous observations of NICER and NuSTAR of bright Galactic black holes
and we fit the simulated data with the latest version of RELXILL (modified to
read the table of REFLIONX, which is the non-relativistic reflection model used
in our calculations). We find that RELXILL with returning radiation cannot fit
well the simulated data when the black hole spin parameter is very high and the
coronal height and disk’s ionization parameter are low, and some parameters can
be significantly overestimated or underestimated. We can find better fits and
recover the correct input parameters as the value of the black hole spin
parameter decreases and the values of the coronal height and of the disk’s
ionization parameter increase.

Future Roadmap: Challenges and Opportunities


  • High Black Hole Spin Parameter: The study finds that when the black hole spin parameter is very high, it becomes challenging to fit the simulated data using RELXILL with returning radiation. This indicates a need for further research and development of improved models or modifications to address this challenge.
  • Low Coronal Height: The simulated data also shows difficulties in fitting when the coronal height is low. This suggests that understanding the interaction between the accretion disk and the black hole in such conditions requires further investigation and refinement of the models.
  • Low Disk’s Ionization Parameter: Similar to the previous challenge, the study highlights difficulties in fitting the data when the disk’s ionization parameter is low. This limitation calls for exploring better approaches to accurately consider the effects of ionization in the calculations.


  • Varying Parameters: The research shows that as the value of the black hole spin parameter decreases and the values of the coronal height and the disk’s ionization parameter increase, better fits can be obtained, and the correct input parameters can be recovered. This opens up opportunities to explore a wider range of parameter values to improve the accuracy of future simulations.
  • Expanded Dataset: With simultaneous observations from NICER and NuSTAR, it is now possible to gather more comprehensive data on bright Galactic black holes. This expanded dataset provides an opportunity to further refine and validate models by comparing them with real observations.
  • Model Development: The study introduces a new model that calculates reflection spectra at every point on the disk using the actual spectrum of the incident radiation. This innovative approach opens up opportunities for further development and refinement of models to better account for returning radiation near black holes.

In conclusion, while there are challenges in accurately fitting the simulated data when dealing with high black hole spin parameters, low coronal height, and low disk’s ionization parameter, there are also promising opportunities to improve the understanding and modeling of accretion disks in Kerr spacetimes. Conducting further research, expanding observational datasets, and refining the models will be crucial in overcoming these challenges and capitalizing on the opportunities presented by the latest advancements in observational technology and theoretical modeling.

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