[Paper Review] Determining the spin of two stellar-mass black holes from disk reflection signatures

R. C. Reis, A. C. Fabian+2 more|ArXiv.org|Feb 10, 2009

Astrophysical Phenomena and Observations4 citations

TL;DR

This paper determines the spin parameters of two stellar-mass black holes, SWIFT J1753.5-0127 and GRO J1655-40, using XMM-Newton X-ray data and a self-consistent relativistic reflection model that includes disk blackbody emission and Comptonization. The method independently constrains spin without relying on mass or distance, yielding a spin of $0.76^{+0.11}_{-0.15}$ for J1753.5-0127 and a lower limit of $a > 0.90$ for J1655-40, with strong evidence for disk misalignment.

ABSTRACT

We present measurements of the dimensionless spin parameters and inner-disk inclination of two stellar mass black holes. The spin parameter of SWIFT J1753.5-0127 and GRO J1655-40 are estimated by modelling the strong reflection signatures present in their XMM-Newton observations. Using a newly developed, self-consistent reflection model which includes the blackbody radiation of the disk as well as the effect of Comptonisation, blurred with a relativistic line function, we infer the spin parameter of SWIFT J1753.5-0127 to be 0.76 +0.11-0.15. The inclination of this system is estimated at 55+2-7 degrees. For GRO J1655-40 we find that the disk is significantly misaligned to the orbital plane, with an innermost inclination of 30+5-10 degrees. Allowing the inclination to be a free parameter we find a lower limit for the spin of 0.90, this value increases to that of a maximal rotating black hole when the inclination is set to that of the orbital plane of J1655-40. Our technique is independent of the black hole mass and distance, uncertainties in which are among the main contributors to the spin uncertainty in previous works.

Motivation & Objective

• To determine the spin parameters of two stellar-mass black holes, SWIFT J1753.5-0127 and GRO J1655-40, using X-ray reflection signatures.
• To overcome uncertainties in black hole mass and distance that plague previous spin measurements.
• To test whether the accretion disk extends to the innermost stable circular orbit (ISCO), a direct indicator of spin.
• To assess the physical consistency of alternative spectral models that do not require disk truncation at ISCO.

Proposed method

• Modeling XMM-Newton X-ray spectra using a self-consistent relativistic reflection model (REFHIDEN) that includes disk blackbody emission and Comptonization effects.
• Convoluting the reflection spectrum with a relativistically blurred line function to account for Doppler shifts and gravitational redshifting near the black hole.
• Using a spectral grid (REFHIDEN) to compute reflection features across a range of spin parameters, ionization parameters, and inclinations.
• Fitting the observed X-ray spectra with a combination of disk thermal emission and reflection components to constrain the inner disk radius and spin.
• Evaluating competing models, including those with highly ionized, truncated disks, by comparing $χ^2$ statistics and physical consistency.
• Assessing disk geometry by calculating the ratio of disk half-thickness to inner radius ($t/r$) to test for physical plausibility of high-ionization, truncated disk solutions.

Experimental results

Research questions

• RQ1 What is the dimensionless spin parameter of SWIFT J1753.5-0127, and does its accretion disk extend to the innermost stable circular orbit?
• RQ2 What is the spin parameter and inner-disk inclination of GRO J1655-40, and is the disk misaligned relative to the orbital plane?
• RQ3 Can a high-ionization, truncated disk model explain the X-ray spectrum without requiring emission from the ISCO?
• RQ4 How does the inclusion of Comptonization and disk blackbody emission improve the physical consistency of spin measurements?
• RQ5 Is the observed broad Fe-Kα line in these systems better explained by relativistic reflection or Compton broadening in a truncated disk?

Key findings

• The spin parameter of SWIFT J1753.5-0127 is measured at $0.76^{+0.11}_{-0.15}$ at 90% confidence, indicating a rapidly spinning black hole.
• The innermost disk inclination for J1753.5-0127 is estimated at $55^{+2}_{-7}$ degrees, consistent with a moderately inclined system.
• For GRO J1655-40, the best-fit model requires a disk misaligned with the orbital plane, with an innermost inclination of $30^{+5}_{-10}$ degrees.
• The spin of GRO J1655-40 is constrained to a lower limit of $a > 0.90$ at 90% confidence, increasing to maximal spin ($a=1$) if the disk inclination matches the orbital plane.
• A competing model with a highly ionized, truncated disk at $\sim 255\ r_{\rm g}$ is physically inconsistent, as it predicts a disk thickness-to-radius ratio ($t/r$) exceeding unity, violating thin-disk assumptions.
• A physically consistent solution requires the disk to extend to the ISCO ($\sim 6\ r_{\rm g}$) with a lower ionization parameter ($\xi \sim 500\ \rm{erg\ cm^2\ s^{-1}}$), yielding a $\chi^2$ improvement of -7.7 for two additional degrees of freedom.