Radiative shock oscillation model for the long-term flares of Sgr A*

We examine time-dependent 2D relativistic radiation MHD flows to develop the shock oscillation model for the long-term flares of Sgr A*. Adopting modified flow parameters in addition to the previous studies, we confirm quasi-periodic flares with periods of $\sim$ 5 and 10 days which are compatible with observations by Chandra, Swift, and XMM-Newton monitoring of Sgr A*. Using a simplified two-temperature model of ions and electrons, we find that the flare due to synchrotron emission lags that of bremsstrahlung emission by 1 – 2 hours which are qualitatively comparable to the time-lags of 1 – 5 hours reported in several simultaneous observations of radio and X-ray variability in Sgr A*. The synchrotron emission is confined in a core region of 3 $R_{\mathrm{g}}$ size with the strong magnetic field, while the bremsstrahlung emission mainly originates in a distant region of 10 – 20 $R_{\mathrm{g}}$ behind the oscillating shock, where $R_{\mathrm{g}}$ is the Schwarzschild radius. The time lag is estimated as the transit time of the acoustic wave between the above two regions. The time-averaged distribution of radiation shows a strong anisotropic nature along the rotational axis but isotropic distribution in the radial direction. A high-velocity jet with $\sim 0.6c$ along the rotational axis is intermittently found in a narrow funnel region with a collimation angle $\sim {15}^{\circ }$. The shock oscillating model explains well the flaring rate and the time lag between radio and X-ray emissions for the long-term flares of Sgr A*.