Time delays between radio and X-ray and between narrow radio bands of Sgr A flares in the shock oscillation model

We examine the time delay between radio and X-ray and between narrow radio frequency flares in Sagittarius A* (Sgr A*), from analyses of the synchrotron, bremsstrahlung and monochromatic luminosity curves. Using the results of 2D relativistic radiation magnetohydrodynamic (MHD) simulations based on the shock oscillation model, we find three types of time delay between the synchrotron and bremsstrahlung emissions: Type A with a time delay of 2 -- 3 h on the shock descending branch, Type B with no time delay and Type C with an inverse time delay of 0.5 -- 1 h on the shock ascending branch. The time delays in Types A and C are interpreted as a transit time of Alfv\'{e}n and acoustic waves between both emission dominant regions, respectively. The delay times between 22 and 43 GHz flares and between 8 and 10 GHz flares are \(\sim\) 13 -- 26 min and 13 min, respectively, while the inverse delay also occurs dependently on the shock location branch. These time delays between the narrow radio bands are interpreted as the transit time of the acoustic wave between the frequency-dependent effective radii \(R_{\tau_{\rm \nu=1}}\), at which the optical depth \(\tau_{\rm \nu}\) at the accretion disc surface becomes \(\sim\) unity. The shock oscillation model explains well the observed delay times of 0.5 -- 5 h between radio and X-ray, 20 -- 30 min between 22 and 43 GHz and \(\sim\) 18 min between 8 and 10 GHz in Sgr A*.