Spin-induced disk precession in the supermassive black hole at the Galactic center

Sagittarius A* is a compact radio source at the Galactic center that is thought to be the radiative manifestation of a 2.6 × 10⁶ M_⊙ supermassive black hole. At least a portion of its spectrum-notably the millimeter/submillimeter "bump"-appears to be produced within the inner portion (r < 10r_s) of a hot, magnetized Keplerian flow, whose characteristics are also consistent with the ∼10% linear polarization detected from this source at millimeter wavelengths. (The Schwarzschild radius, r_s, for an object of this mass M is 2GM/c ² ≈ 7.7 × 10¹¹ cm, or roughly 1/20 AU.) 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 timescale near the marginally stable orbit around an object with this mass is ≈20 minutes. 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 ∼30r_s, for which a ≈ (M/10)(r_o/30r _s)_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 nonthermal (∼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 r_o ∼ 30r_s. Such a small disk size is also suggested by earlier hydrodynamical simulations and is implied by Sgr A*'s spectral and polarimetric characteristics.