Heating or Cooling: Study of Advective Heat Transport in the Inflow and the Outflow of Optically Thin Advection-dominated Accretion Flows

Advection is believed to be the dominant cooling mechanism in optically thin advection-dominated accretion flows (ADAF's). When outflow is considered, however, the first impression is that advection should be of opposite sign in the inflow and the outflow, due to the opposite direction of radial motion. Then how is the energy balance achieved simultaneously? We investigate the problem in this paper, analysing the profiles of different components of advection with self-similar solutions of ADAF's in spherical coordinates ($r\theta\phi$). We find that for $n < 3\gamma/2-1$, where $n$ is the density index in $\rho \propto r^{-n}$ and $\gamma$ is the heat capacity ratio, the radial advection is a heating mechanism in the inflow and a cooling mechanism in the outflow. It becomes 0 for $n = 3\gamma/2-1$, and turns to a cooling mechanism in the inflow and a heating mechanism in the outflow for $n > 3\gamma/2-1$. The energy conservation is only achieved when the latitudinal ($\theta$-direction) advection is considered, which takes an appropriate value to maintain energy balance, so that the overall effect of advection, no matter the parameter choices, is always a cooling mechanism that cancels out the viscous heating everywhere. For the extreme case of $n=3/2$, latitudinal motion stops, viscous heating is balanced solely by radial advection, and no outflow is developed.Comment: 9 pages, 4 figures, accepted by Ap

Study of advective energy transport in the inflow and the outflow of super-Eddington accretion flows

Photon trapping is believed to be an important mechanism in super-Eddington accretion, which greatly reduces the radiative efficiency as photons are swallowed by the central black hole before they can escape from the accretion flow. This effect is interpreted as the radial advection of energy in one-dimensional height-integrated models, such as the slim disc model. However, when multi-dimensional effects are considered, the conventional understanding may no longer hold. In this paper, we study the advective energy transport in super-Eddington accretion, based on a new two-dimensional inflow-outflow solution with radial self-similarity, in which the advective factor is calculated self-consistently by incorporating the calculation of radiative flux, instead of being set as an input parameter. We found that radial advection is actually a heating mechanism in the inflow due to compression, and the energy balance in the inflow is maintained by cooling via radiation and vertical ($\theta$-direction) advection, which transports entropy upwards to be radiated closer to the surface or carried away by the outflow. As a result, less photons are advected inwards and more photons are released from the surface, so that the mean advective factor is smaller and the emergent flux is larger than those predicted by the slim disc model. The radiative efficiency of super-Eddington accretion thus should be larger than that of the slim disc model, which agrees with the results of some recent numerical simulations.Comment: 7 pages, 3 figures, submitted to MNRA

How Does the Low-Rank Matrix Decomposition Help Internal and External Learnings for Super-Resolution

Wisely utilizing the internal and external learning methods is a new challenge in super-resolution problem. To address this issue, we analyze the attributes of two methodologies and find two observations of their recovered details: 1) they are complementary in both feature space and image plane, 2) they distribute sparsely in the spatial space. These inspire us to propose a low-rank solution which effectively integrates two learning methods and then achieves a superior result. To fit this solution, the internal learning method and the external learning method are tailored to produce multiple preliminary results. Our theoretical analysis and experiment prove that the proposed low-rank solution does not require massive inputs to guarantee the performance, and thereby simplifying the design of two learning methods for the solution. Intensive experiments show the proposed solution improves the single learning method in both qualitative and quantitative assessments. Surprisingly, it shows more superior capability on noisy images and outperforms state-of-the-art methods