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Black Hole Spin via Continuum Fitting and the Role of Spin in Powering Transient Jets

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Abstract

The spins of ten stellar black holes have been measured using the continuum-fitting method. These black holes are located in two distinct classes of X-ray binary systems, one that is persistently X-ray bright and another that is transient. Both the persistent and transient black holes remain for long periods in a state where their spectra are dominated by a thermal accretion disk component. The spin of a black hole of known mass and distance can be measured by fitting this thermal continuum spectrum to the thin-disk model of Novikov and Thorne; the key fit parameter is the radius of the inner edge of the black hole’s accretion disk. Strong observational and theoretical evidence links the inner-disk radius to the radius of the innermost stable circular orbit, which is trivially related to the dimensionless spin parameter a ∗ of the black hole (|a ∗|<1). The ten spins that have so far been measured by this continuum-fitting method range widely from a ∗≈0 to a ∗>0.95. The robustness of the method is demonstrated by the dozens or hundreds of independent and consistent measurements of spin that have been obtained for several black holes, and through careful consideration of many sources of systematic error. Among the results discussed is a dichotomy between the transient and persistent black holes; the latter have higher spins and larger masses. Also discussed is recently discovered evidence in the transient sources for a correlation between the power of ballistic jets and black hole spin.

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Notes

  1. Spin is commonly expressed in terms of the dimensionless parameter a ∗≡cJ/GM2, where J and M are respectively the angular momentum and mass of the black hole.

  2. Apart from H1743–322, our selection is based on firm dynamical evidence, and we therefore exclude some important systems for which there is significant evidence that the primary is a black hole, e.g., Cyg X-3 (Zdziarski et al. 2013), or a strong presumption that it is, e.g., SS433 (Begelman et al. 2006) and 4U 1957+11 (Nowak et al. 2012).

  3. For alternatives, see Gierliński et al. (2001), Kolehmainen and Done (2010), and Straub et al. (2011).

  4. In contrast, Noble et al. (2010) find that the stress profile is almost completely independent of disk thickness.

  5. While thin disks are subject to warping, thick disks are not (Dexter and Fragile 2011).

  6. Unfortunately the continuum-fitting method cannot fit for the inclination of the inner disk because there is a degeneracy between the inclination and spin parameter (Li et al. 2009).

  7. In the case of a fifth transient, 4U1543–47, radio observations did not include the peak of the light curve, so one could only deduce a lower limit to the jet power. Note that the radio peak can be very narrow in time, e.g., ≈1-day in the case of XTE J1859+226 (Fig. 2), so one requires dense radio monitoring to catch the peak.

  8. The scaling by mass is sensible because the sources are near the Eddington luminosity limit, which is proportional to mass. However, since the masses of the black holes differ little (Table 1), the results would be virtually identical if the mass scaling were eliminated.

  9. None of the results change if one chooses a different reference frequency, e.g., 1.4 GHz or 15 GHz.

  10. The two scalings agree for small values of a ∗, but differ as a ∗→1.

  11. The lower level of confidence reported by Russell et al. (2013) is largely attributable to their use of radio data for a flare of H1743–322 that is unrelated to the ballistic jet, namely a flare event that occurred 28 days before the X-ray flux peaked (McClintock et al. 2009). We focus solely on post-Eddington radio flares. The relevant radio flare event, which we consider, occurred 2.6 days after X-ray maximum (Steiner et al. 2013).

  12. The ejection apparently shuts off, coincidentally, as the jet becomes optically thin.

  13. Using somewhat different assumptions, (Willott et al. 1999) estimated that kinetic jet kinetic luminosities of radio galaxies should vary as (νL ν )6/7, i.e., a slope again close to but less than unity.

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Acknowledgements

The authors thank S. W. Davis for important input on Sect. 5.3. We also thank C. Brocksopp, E. Kuulkers, M. L. McCollough, C. Sánchez-Fernández and C. Zurita for help in preparing Fig. 2; J. García and T. Fragos for their comments on a version of the manuscript; R. Fender for discussions on MeerKAT; and an anonymous referee for several important criticisms. JEM was supported in part by NASA grant NNX11AD08G and RN by NASA grant NNX11AE16G. JFS was supported by NASA Hubble Fellowship grant HST-HF-51315.01.

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  1. Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA, 02138, USA

    Jeffrey E. McClintock, Ramesh Narayan & James F. Steiner

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  1. Jeffrey E. McClintock
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Correspondence to Jeffrey E. McClintock.

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McClintock, J.E., Narayan, R. & Steiner, J.F. Black Hole Spin via Continuum Fitting and the Role of Spin in Powering Transient Jets. Space Sci Rev 183, 295–322 (2014). https://doi.org/10.1007/s11214-013-0003-9

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  • DOI: https://doi.org/10.1007/s11214-013-0003-9

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