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

Abstract

Sgr A* is a compact radio source at the Galactic Center, thought to be the radiative manifestation of a $2.6\times 10^6 M_\odot$ supermassive black hole. At least a portion of its spectrum--notably the mm/sub-mm ``bump''--appears to be produced within the inner portion ($r< 10 r_S$) of a hot, magnetized Keplerian flow, whose characteristics are also consistent with the $\sim 10%$ linear polarization detected from this source at mm wavelengths. (The Schwarzschild radius, $r_S$, for an object of this mass $M$ is $2GM/c^2\approx 7.7\times 10^{11}$ 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 $\approx 20$ 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 $\sim 30 r_S$, for which $a\approx (M/10) (r_o/30 r_S)^{5/2}$. 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 non-thermal ($\sim 1-20$ 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 $r_o\sim 30 r_S$. Such a small disk size is also suggested by earlier hydrodynamical simulations, and is implied by Sgr A*'s spectral and polarimetric characteristics.