Measuring the Spins of Stellar-Mass Black Holes

TL;DR

This white paper argues that measuring spins of stellar-mass black holes is a central frontier because spin informs jet production, GRBs, and compact-object evolution. It reviews two proven spin-diagnostic methods, continuum-fitting of the thermal disk spectrum and modeling of relativistically broadened Fe K lines, and discusses two promising avenues—high-frequency QPOs and X-ray polarimetry—as complementary probes. Current results include precise spins for several BHs via CF and a near-extreme spin for GRS 1915+105, with the CF method yielding $a_* > 0.98$ in that system, and the Fe K method enabling SMBH spin measurements for active galaxies. To advance through 2010–2020, the paper calls for a next-generation X-ray timing/spectral mission, advances in 3D GRMHD simulations with radiation, and a dedicated X-ray polarimetry mission, positioning BH spin studies as a cornerstone of future high-energy astrophysics and IXO-era science.

Abstract

In astronomy, the problem of black holes is arguably second in importance only to the problem of cosmology. A current frontier in black hole research is the measurement of spin. During the past three years, the spins of several stellar-mass black holes in X-ray binaries have been measured via two techniques: fitting the X-ray continuum spectrum and modeling the profile of the Fe K line. This fledgling enterprise motivates the following decadal goals: (1) Firmly establish the continuum-fitting and Fe K methods; obtain precise values of spin for 10-20 black holes, several using both methods; (2) use the derived masses and spins to test models of jets, GRBs, supernovae, black hole formation, black hole binary evolution, etc.; (3) serve the IXO mission by securing the Fe K methodology, which is currently the only means to measure the spins of supermassive black holes in AGN; (4) identify the correct model of high-frequency QPOs, thereby opening a third channel for measuring spin; (5) pursue X-ray polarimetry as a means of securing the continuum-fitting and Fe K methods, and also as a possible fourth avenue to spin; and (6) develop and test MHD models of thin disks in strong gravity. Achieving these goals requires the establishment of an RXTE follow-on mission dedicated to the study of bright and transient compact objects, as well as strong support for theoretical work on 3D MHD simulations of accretion flows in the Kerr metric of a spinning black hole.

Figures (2)

• Figure 1: Spin results for the BH primary in M33 X-7 obtained by fitting Chandra spectra (filled/open circles) and XMM spectra (crosses) to the relativistic disk model kerrbb2 (ref. 10); the data are ordered by total counts. The four "gold" Chandra spectra with $\gtrsim 5000$ counts each (filled circles) yield spin estimates that agree with the mean value (dotted line) to within their $\approx 2$% statistical uncertainties, which is remarkable stability given that the observations span years (see dates). Meanwhile, this mean value agrees with the mean spin for the 11 low-quality spectra with $<3000$ counts to within $\approx 1$%. Including all observational uncertainties (e.g., BH mass), one obtains $a_* = 0.77 \pm 0.05$.
• Figure 2: Spin results versus time for the BH primary in LMC X-1 obtained by fitting RXTE spectra to the relativistic disk model kerrbb2 (ref. 11). The spectra were selected as minimally Comptonized from a complete sample of 55 RXTE spectra. As indicated, the scatter about the mean value of $a_*$ is small. Including all model-parameter and observational uncertainties (e.g., $\alpha$-viscosity and BH mass), one obtains $a_* = 0.90_{-0.09}^{+0.04}$. Virtues of RXTE are its good coverage of the Compton power-law component above 10 keV and the many independent observations it provides (typically hundreds); drawbacks are its poor low-energy response and spectral resolution.