Measuring the Spins of Accreting Black Holes

TL;DR

This work reviews two principal spin-measurement approaches for accreting black holes: the continuum-fitting (CF) method, which ties the inner disk edge to the ISCO via the thermal disk spectrum in thin accretion disks, and the Fe K$ m abla ext{α}$ reflection method, which uses relativistic line broadening to infer the ISCO radius. Focusing on stellar-mass black holes, the authors present spin measurements for eight systems that span $a_* oughly 0.12$ to $>0.98$, with uncertainties dominated by dynamical parameters and consistent cross-method checks where available (e.g., XTE J1550 ext{-}564). The results suggest natal spins for at least some high-spin BHs and indicate that relativistic jets are not solely governed by spin. The study underscores the need for more precise dynamical measurements, cross-validation between CF and Fe K$ m abla ext{α}$ methods, and future synergy with gravitational-wave observations to test the Kerr metric and the No Hair Theorem.

Abstract

A typical galaxy is thought to contain tens of millions of stellar-mass black holes, the collapsed remnants of once massive stars, and a single nuclear supermassive black hole. Both classes of black holes accrete gas from their environments. The accreting gas forms a flattened orbiting structure known as an accretion disk. During the past several years, it has become possible to obtain measurements of the spins of the two classes of black holes by modeling the X-ray emission from their accretion disks. Two methods are employed, both of which depend upon identifying the inner radius of the accretion disk with the innermost stable circular orbit (ISCO), whose radius depends only on the mass and spin of the black hole. In the Fe K method, which applies to both classes of black holes, one models the profile of the relativistically-broadened iron line with a special focus on the gravitationally redshifted red wing of the line. In the continuum-fitting method, which has so far only been applied to stellar-mass black holes, one models the thermal X-ray continuum spectrum of the accretion disk. We discuss both methods, with a strong emphasis on the continuum-fitting method and its application to stellar-mass black holes. Spin results for eight stellar-mass black holes are summarized. These data are used to argue that the high spins of at least some of these black holes are natal, and that the presence or absence of relativistic jets in accreting black holes is not entirely determined by the spin of the black hole.

Figures (6)

• Figure 1: Scale drawings of 21 black hole binaries. The size of the Sun and the Sun-Mercury distance (0.4 AU) are indicated at the top. The systems range in size from the giant GRS 1915+105 with an orbital period of 30.8 days to tiny XTE J1118+480 with an orbital period of 0.2 days. The shapes of the tidally distorted stars are accurately rendered, and the black hole is located at the center of the accretion disk (see key in inset). The inclination of the binary to our line of sight is indicated by the tilt of the accretion disk; an inclination angle of $i=0^{\circ}$ corresponds to a system whose accretion disk lies in the plane of the sky and is viewed face on (e.g., $i= 21^{\circ}$ for 4U 1543--47 and $i=75^{\circ}$ for SAX J1819.3-2525).
• Figure 2: Radius of the ISCO in units of $GM/c^2$ versus the black hole spin parameter. Negative values of $a_*$ correspond to retrograde motion, with the black hole spinning in the opposite sense of the disk. Stellar black holes are expected to have prograde spins ($a_*>0$) as a consequence of their formation in a binary system, whereas the spins of supermassive black holes, which are conditioned by galaxy merger events, may be either prograde or retrograde (e.g., gar+2010).
• Figure 3: $(top)$ Accretion-disk luminosity in Eddington-scaled units (for $M=10$$M_{\odot}$) versus time for all the 766 spectra considered in the study of LMC X-3 by ste+2010a. The downward arrows show RXTE data which are off scale. Data in the unshaded region satisfy our thin-disk selection criterion $L/L_{\rm Edd} < 0.3$ (Sec. 3). The dotted line indicates the lower luminosity threshold (5% $L/L_{\rm Edd}$) set to avoid confusion with strongly Comptonized data. $(bottom)$ Fitted values of the inner disk radius $r_{\rm in} \equiv R_{\rm in}/(GM/c^2)$ are shown for thin-disk data in the top panel that meet the selection criteria of the study (a total of 411 spectra). Despite large variations in luminosity, $r_{\rm in}$ remains constant to within a few percent over time. The median value for just the 391 selected RXTE spectra is shown as a red dashed line.
• Figure 4: Luminosity profiles from GRMHD simulations (solid lines) compared with those from the nov+1973 model (dashed lines) for $a_*=0$, $0.7$, $0.9$ and $0.98$ (bottom to top). The ISCO is located at the radius where the NT disk luminosity goes to zero.
• Figure 5: ($a$) Allowed values of black hole mass and distance for GRS 1915+105 fall within the shaded triangular region (see text). ($b$) Six estimates of the distance to GRS 1915+105 are shown. They range from below 7 to above 12 kpc. We are working toward a 10% trigonometric distance. Two hypothetical and possible outcomes of our VLBA observations, labeled VLBA1 and VLBA2, are indicated at the top of panel $a$. For references on distance estimates, see Figure 18 in mcc+2006.