The rotation measure and 3.5 millimeter polarization of Sagittarius A

We report the detection of variable linear polarization from Sgr A* at a wavelength of 3.5 mm, the longest wavelength yet at which a detection has been made. The mean polarization is 2.1% +/- 0.1% at a position angle of 16 degrees +/- 2 degrees with rms scatters of 0.4% and 9 degrees over the five epochs. We also detect polarization variability on a timescale of days. Combined with previous detections over the range 150-400 GHz (750-2000 mm), the average polarization position angles are all found to be consistent with a rotation measure of -(4.4 +/- 0.3) x 10(5) rad m(-2). This implies that the Faraday rotation occurs external to the polarized source at all wavelengths. This implies an accretion rate similar to(0.2-4) x 10(-8) M-circle dot yr(-1) for the accretion density profiles expected of ADAF, jet, and CDAF models and assuming that the region at which electrons in the accretion flow become relativistic is within 10R(S). The inferred accretion rate is inconsistent with ADAF/Bondi accretion. The stability of the mean polarization position angle between disparate polarization observations over the frequency range limits fluctuations in the accretion rate to less than 5%. The flat frequency dependence of the interday polarization position angle variations also makes them difficult to attribute to rotation-measure fluctuations and suggests that both the magnitude and position angle variations are intrinsic to the emission.