The polarized mm/sub-mm radiation from Sgr A* is apparently produced by a Keplerian structure whose peak emission occurs within several Schwarzschild radii ( r _ { S } \equiv 2 GM / c ^ { 2 } ) of the black hole .
The Chandra X-ray counterpart , if confirmed , is presumably the self-Comptonized component from this region .
In this paper , we suggest that sub-mm timing observations could yield a signal corresponding to the period P _ { 0 } of the marginally stable orbit , and therefore point directly to the black hole ’ s spin a .
Sgr A* ’ s mass is now known to be ( 2.6 \pm 0.2 ) \times 10 ^ { 6 } M _ { \odot } ( an unusually accurate value for supermassive black hole candidates ) , for which 2.7 \hbox { min } < P _ { 0 } < 36 min , depending on the value of a and whether the Keplerian flow is prograde or retrograde .
A Schwarzschild black hole ( a = 0 ) should have P _ { 0 } \approx 20 min .
The identification of the orbital frequency with the innermost stable circular orbit is made feasible by the transition from optically thick to thin emission at sub-mm wavelengths .
With stratification in the emitter , the peak of the sub-mm bump in Sgr A* ’ s spectrum is thus produced at the smallest radius .
We caution , however , that theoretical uncertainties in the structure of the emission region may still produce some ambiguity in the timing signal .
Given that Sgr A* ’ s flux at \nu \sim 1 mm is several Jy , these periods should lie within the temporal-resolving capability of sub-mm telescopes using bolometric detectors .
A determination of P _ { 0 } should provide not only a value of a , but it should also define the angular momentum vector of the orbiting gas in relation to the black hole ’ s spin axis .
By analogy with low-mass X-ray binaries and Galactic black hole candidates , Sgr A* may also display quasi-periodic oscillations , which can reveal additional features in the geometry of the accreting gas .
In addition , since the X-ray flux detected by Chandra appears to be the self-Comptonized mm to sub-mm component , these temporal fluctuations may also be evident in the X-ray signal .