A magnetohydrodynamic model for multi-wavelength flares from Sagittarius~A⋆^\star (I): model and the near-infrared and X-ray flares

Flares from the supermassive black hole in our Galaxy, Sagittarius~A$^\star$ (Sgr A$^\star$), are routinely observed over the last decade or so. Despite numerous observational and theoretical efforts, the nature of such flares still remains poorly understood, although a few phenomenological scenarios have been proposed. In this work, we develop the Yuan et al. (2009) scenario into a magnetohydrodynamic (MHD) model for Sgr A$^\star$ flares. This model is analogous with the theory of solar flares and coronal mass ejection in solar physics. In the model, magnetic field loops emerge from the accretion flow onto Sgr A$^\star$ and are twisted to form flux ropes because of shear and turbulence. The magnetic energy is also accumulated in this process until a threshold is reached. This then results in a catastrophic evolution of a flux rope with the help of magnetic reconnection in the current sheet. In this catastrophic process, the magnetic energy is partially converted into the energy of non-thermal electrons. We have quantitatively calculated the dynamical evolution of the height, size, and velocity of the flux rope, as well as the magnetic field in the flare regions, and the energy distribution of relativistic electrons in this process. We further calculate the synchrotron radiation from these electrons and compare the obtained light curves with the observed ones. We find that the model can reasonably explain the main observations of near-infrared (NIR) and X-ray flares including their light curves and spectra. It can also potentially explain the frequency-dependent time delay seen in radio flare light curves.Comment: 17 pages, 13 figures, accepted by MNRA

Distributed Stochastic Optimization over Time-Varying Noisy Network

This paper is concerned with distributed stochastic multi-agent optimization problem over a class of time-varying network with slowly decreasing communication noise effects. This paper considers the problem in composite optimization setting which is more general in noisy network optimization. It is noteworthy that existing methods for noisy network optimization are Euclidean projection based. We present two related different classes of non-Euclidean methods and investigate their convergence behavior. One is distributed stochastic composite mirror descent type method (DSCMD-N) which provides a more general algorithm framework than former works in this literature. As a counterpart, we also consider a composite dual averaging type method (DSCDA-N) for noisy network optimization. Some main error bounds for DSCMD-N and DSCDA-N are obtained. The trade-off among stepsizes, noise decreasing rates, convergence rates of algorithm is analyzed in detail. To the best of our knowledge, this is the first work to analyze and derive convergence rates of optimization algorithm in noisy network optimization. We show that an optimal rate of $O(1/\sqrt{T})$ in nonsmooth convex optimization can be obtained for proposed methods under appropriate communication noise condition. Moveover, convergence rates in different orders are comprehensively derived in both expectation convergence and high probability convergence sense.Comment: 27 page