Optical Measurements of Black Hole Masses

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Scientific paper

Sixteen Galactic X-ray binaries are known to contain massive compact X-ray sources with masses that range from about 5 to 14 solar masses. These compact objects are widely believed to be black holes, since the maximum mass of a neutron star allowed by general relativity is only about 3 solar masses. A firm minimum mass for each black hole has been determined to a typical accuracy of a few percent by simply measuring the orbital radial velocity curve of the black hole's binary companion. This one straightforward measurement alone is sufficient to establish that 11 of the 16 binaries contain black holes (i.e. compact objects more massive than 3 solar masses). Determining the actual mass of a black hole is less clear-cut. It requires measuring and modeling the orbital light curve to determine the inclination of the orbital plane, and also measuring the rotational velocity of the companion to determine its mass relative to the mass of the black hole. Presently, the masses of the 16 black holes are uncertain by about 20-60%; however, it is now possible to improve substantially on these results. The mass of a black hole is of fundamental importance because mass and spin completely define an astrophysical black hole, according to the `no-hair' theorem. Knowledge of black hole masses is important currently for several reasons including the following: (1) The black-hole mass distribution constrains theoretical distributions of black hole masses derived in supernova calculations. (2) The leading models for the fast QPOs (40-450 Hz), which have been observed for five Galactic black holes, invoke general relativistic effects and depend on both the mass and spin of the black hole; thus a secure dynamical measurement of the mass is a crucial first step in determining the spin of a black hole.

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