Spin-Induced Disk Precession in the Supermassive Black Hole at the Galactic Center

Sgr A* is a compact radio source at the Galactic Center, thought to be the radiative manifestation of a 2.6 × 106 M⊙ supermassive black hole. At least a portion of its spectrum—notably the mm/sub-mm “bump”—appears to be produced within the inner portion (r < 10 rS) of a hot, magnetized Keplerian flow, whose characteristics are also consistent with the ∼ 10% linear polarization detected from this source at mm wavelengths. (The Schwarzschild radius, rS , for an object of this mass M is 2GM/c2 ≈ 7.7 × 1011 cm, or roughly 1/20 A.U.) The recent detection of a 106-day cycle in Sgr A*’s radio variability adds significant intrigue to this picture, since it may signal a precession of the disk induced by the spin a of the black hole. The dynamical time scale near the marginally stable orbit around an object with this mass is ≈ 20 mins. Thus, since the physical conditions associated with the disk around Sgr A* imply rigid-body rotation, a precession period of 106 days may be indicative of a small black hole spin if the circularized flow is confined to a region ∼ 30 rS , for which a ≈ (M/10) (ro/30 rS) 5/2. The precession of a larger structure would require a bigger black hole spin. We note that a small value of a/M (< 0.1) would be favored if the non-thermal (∼ 1 − 20 cm) portion of Sgr A*’s spectrum is powered with energy extracted via a Blandford-Znajek type of process, for which the observed luminosity would correspond to an outer disk radius ro ∼ 30 rS . Such a small disk size is also suggested by earlier hydrodynamical simulations, and is implied by Sgr A*’s spectral and polarimetric characteristics. Subject headings: accretion—black hole physics—Galaxy: center—gravitation— radiation mechanisms: non-thermal—relativity