The Rotation Measure and 3.5mm Polarization of Sgr A*

We report the detection of variable linear polarization from Sgr A* at a wavelength of 3.5mm, 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 +/- 2 deg with rms scatters of 0.4% and 9 deg over the five epochs. We also detect polarization variability on a timescale of days. Combined with previous detections over the range 150-400GHz (750-2000 microns), 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 ~0.2 - 4 x 10^-8 Msun/yr 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 10 R_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 inter-day 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