Chemical modeling of the complex organic molecules in the extended region around Sagittarius B2

The chemical differentiation of seven COMs in the extended region around Sgr B2 has been observed: CH$_2$OHCHO, CH$_3$OCHO, t-HCOOH, C$_2$H$_5$OH, and CH$_3$NH$_2$ were detected both in the extended region and near the hot cores Sgr B2(N) and Sgr B2(M), while CH$_3$OCH$_3$ and C$_2$H$_5$CN were only detected near the hot cores. The density and temperature in the extended region are relatively low. Different desorption mechanisms have been proposed to explain the observed COMs in cold regions but fail to explain the deficiency of CH$_3$OCH$_3$ and C$_2$H$_5$CN. We explored under what physical conditions the chemical simulations can fit the observations and explain the different spatial distribution of these species. We used the Monte Carlo method to perform a detailed parameter space study. We investigated how different mechanisms affect the results. All gas-grain chemical models based on static physics cannot fit the observations. The results based on evolving physical conditions can fit six COMs when $T\sim30-60$ K, but the best-fit temperature is still higher than the observed dust temperature of 20 K. The best agreement at $T\sim27$ K is achieved by considering a short-duration $\sim 10^2$ yr X-ray burst with $\zeta_{\mathrm{CR}}=1.3\times10^{-13}$ s$^{-1}$ when the temperature is 20 K. The reactive desorption is the key mechanism for producing these COMs and inducing the low abundances of CH$_3$OCH$_3$ and C$_2$H$_5$CN. The evolution of the extended region around Sgr~B2 may have begun with a cold, $T\le10$ K phase followed by a warm-up phase. When its temperature reached $T\sim20$ K, an X-ray flare from Sgr A* with a short duration of no more than 100 years was acquired, affecting strongly the Sgr B2 chemistry. The observed COMs retain their observed abundances only several hundred years after such a flare, which could imply that such short-term X-ray flares occur relatively often.