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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 $R_{\rm g}$ size with the strong magnetic field, while the bremsstrahlung emission mainly originates in a distant region of 10 -- 20 $R_{\rm g}$ behind the oscillating shock, where $R_{\rm g}$ 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*.