1. Muduleye L. HUANG @GCWorkshop2009,Shanghai 1 Polarized Emission And Black Hole Shadow Image of Sagittarius A* Lei Huang Center for Astrophysics, USTC Institute of Astronomy & Astrophysics, Academia Sinica Collaborators: Siming Liu, Rohta Takahashi, Mike J. Cai, Zhi-Qiang Shen, Ye-Fei Yuan.

2. Muduleye L. HUANG @GCWorkshop2009,Shanghai 2 Outline 1. Radiative transfer 2. Results based on accretion flow with plasma wave heating mechanism 3. Accretion Flow Structure Estimation with 1.3mm VLBI 4. Black Hole Spin Estimation with 1.3mm VLBI

3. Muduleye L. HUANG @GCWorkshop2009,Shanghai 3 1. Radiative Transfer North East North B B Line of sight

4. Muduleye L. HUANG @GCWorkshop2009,Shanghai 4 1. Radiative Transfer North East North B B Line of sight The four-vectors of reference coordinates (a µ, b µ ) are calculated according to the parallel transport in general relativistic theory (Chandrasekhar 1983). Rotation matrix:

5. Muduleye L. HUANG @GCWorkshop2009,Shanghai 5 1. Radiative Transfer North East North B B Line of sight

6. Muduleye L. HUANG @GCWorkshop2009,Shanghai 6 1. Radiative Transfer North East North B B Line of sight 0 RM RRM

7. Muduleye L. HUANG @GCWorkshop2009,Shanghai 7 1. Radiative Transfer North East Decomposition on LP modes

8. Muduleye L. HUANG @GCWorkshop2009,Shanghai 8 1. Radiative Transfer North East Decomposition on LP modes Decomposition on CP modes

9. Muduleye L. HUANG @GCWorkshop2009,Shanghai 9 1. Radiative Transfer North East Decomposition on LP modes Decomposition on CP modes Decomposition on Natural modes where are solved from (Melrose 1997)

10. Muduleye L. HUANG @GCWorkshop2009,Shanghai 10 1. Radiative Transfer Relationship between modes: Emissivity: implying

11. Muduleye L. HUANG @GCWorkshop2009,Shanghai 11 2. Results based on accretion flow with 2. Results based on accretion flow with plasma wave heating mechanism Heating mechanism by turbulent plasma wave – (Pseudo-Newtonian potential adopted, r in = 6M)

12. Muduleye L. HUANG @GCWorkshop2009,Shanghai 12 2. Results based on accretion flow with 2. Results based on accretion flow with plasma wave heating mechanism Huang et al. (2009) Relativistic birefringence effects

13. Muduleye L. HUANG @GCWorkshop2009,Shanghai 13 2. Results based on accretion flow with 2. Results based on accretion flow with plasma wave heating mechanism Huang et al. (2009) RM = n. B Degeneracy between T e and  p Smaller  p, larger RM (Flare-dominated)

14. Muduleye L. HUANG @GCWorkshop2009,Shanghai 14 2. Results based on accretion flow with 2. Results based on accretion flow with plasma wave heating mechanism Kerr Metric adopted r in =r + Small  p leads to large RM to decrease CP in sub-mm band.

15. Muduleye L. HUANG @GCWorkshop2009,Shanghai 15 H: Hawaii, including JCMT and SMA, S: SMTO, C: CARMA, L: LMT, A: Chilean, including ASTE and ALMA, P: PdBI, M: MT-COOK 3. Accretion Flow Structure Estimation with 1.3mm VLBI

16. Muduleye L. HUANG @GCWorkshop2009,Shanghai 16 H: Hawaii, including JCMT and SMA, S: SMTO, C: CARMA, L: LMT, A: Chilean, including ASTE and ALMA, P: PdBI, M: MT-COOK 3. Accretion Flow Structure Estimation with 1.3mm VLBI Huang, Takahashi, & Shen (2009) Potential to detect valley points on baselines between Hawaii and Western U.S. Compactness and symmetry of the emission region would be measured with ALMA joined. More information comes from detections along more directions. Flares may happen !!

17. Muduleye L. HUANG @GCWorkshop2009,Shanghai 17 Plasma wave heating mechanism Classical RIAF 4. Black Hole Spin Estimation with 1.3mm VLBI Huang, Takahashi, & Shen (2009), VLBI data from Doeleman et al. (2008) Model-dependent Model-independent: Shadow shape; Periodicity

18. Muduleye L. HUANG @GCWorkshop2009,Shanghai 18 Summary We consider the effects of relativity and birefringence self-consistently in the radiative transfer. LP and CP observations can give constraints on orientation, mass accretion rate, and plasma  p. The structure of the accretion flow, including the central black hole shadow, can be detected by potential 1.3mm- VLBI stations. The black hole spin parameter cannot be well-estimated without imaging, or periodicity detection.