Numerical simulations of winds driven by radiation force from the corona above a thin disk

Observations show that winds can be driven from the innermost region (inside a 50 Schwarschild radius) of a thin disk. It is interesting to study the winds launched from the innermost region. A hot corona above the black hole (BH) thin disk is irradiated by the disk. We perform two-dimensional hydrodynamical simulations to study the winds driven by radiation force from the corona in the innermost regions. The hard X-ray spectrum from active galactic nuclei (AGNs) suggests that the corona temperature is about $10^9$ K, so that we mainly analyze the properties of winds (or outflows) from the $10^9$ K corona. The disk luminosity plays an important role in driving the outflows. The more luminous the disk, the stronger the outflows. Mass outflow rate ($\dot{M}_{\rm out}$) at a 90 Schwarschild radius depends on disk luminosity, which can be described as $\dot{M}_{\rm out}\propto 10^{3.3 \Gamma}$ ($\Gamma$ is the ratio of the disk luminosity to the Eddington luminosity). In the case of high luminosity (e.g. $\Gamma=0.75$), the supersonic outflows with maximum speed $1.0 \times 10^4$ Km s$^{-1}$ are launched at $\sim17^{o}$ --$30^{o}$ and $\sim50^{o}$ --$80^{o}$ away from the pole axis. The Bernoulli parameter keeps increasing with the outward propagation of outflows. The radiation force keeps accelerating the outflows when outflows move outward. Therefore, we can expect the outflows to escape from the BH gravity and go to the galactic scale. The interaction between outflows and interstellar medium may be an important AGN feedback process.Comment: 9 pages, 12 figures, accepted for publication in Ap

Two dimensional numerical simulations of Supercritical Accretion Flows revisited

We study the dynamics of super-Eddington accretion flows by performing two-dimensional radiation-hydrodynamic simulations. Compared with previous works, in this paper we include the $T_{\theta\phi}$ component of the viscous stress and consider various values of the viscous parameter $\alpha$. We find that when $T_{\theta\phi}$ is included, the rotational speed of the high-latitude flow decreases, while the density increases and decreases at the high and low latitudes, respectively. We calculate the radial profiles of inflow and outflow rates. We find that the inflow rate decreases inward, following a power law form of $\dot{M}_{\rm in}\propto r^s$. The value of $s$ depends on the magnitude of $\alpha$ and is within the range of $\sim 0.4-1.0$. Correspondingly, the radial profile of density becomes flatter compared with the case of a constant $\dot{M}(r)$. We find that the density profile can be described by $\rho(r)\propto r^{-p}$, and the value of $p$ is almost same for a wide range of $\alpha$ ranging from $\alpha=0.1$ to $0.005$. The inward decrease of inflow accretion rate is very similar to hot accretion flows, which is attributed to the mass loss in outflows. To study the origin of outflow, we analyze the convective stability of slim disk. We find that depending on the value of $\alpha$, the flow is marginally stable (when $\alpha$ is small) or unstable (when $\alpha$ is large). This is different from the case of hydrodynamical hot accretion flow where radiation is dynamically unimportant and the flow is always convectively unstable. We speculate that the reason for the difference is because radiation can stabilize convection. The origin of outflow is thus likely because of the joint function of convection and radiation, but further investigation is required.Comment: 16 pages, 13 figures, accepted for publication in Ap

Computing resource allocation in three-tier IoT fog networks: a joint optimization approach combining Stackelberg game and matching

Fog computing is a promising architecture to provide economical and low latency data services for future Internet of Things (IoT)-based network systems. Fog computing relies on a set of low-power fog nodes (FNs) that are located close to the end users to offload the services originally targeting at cloud data centers. In this paper, we consider a specific fog computing network consisting of a set of data service operators (DSOs) each of which controls a set of FNs to provide the required data service to a set of data service subscribers (DSSs). How to allocate the limited computing resources of FNs to all the DSSs to achieve an optimal and stable performance is an important problem. Therefore, we propose a joint optimization framework for all FNs, DSOs, and DSSs to achieve the optimal resource allocation schemes in a distributed fashion. In the framework, we first formulate a Stackelberg game to analyze the pricing problem for the DSOs as well as the resource allocation problem for the DSSs. Under the scenarios that the DSOs can know the expected amount of resource purchased by the DSSs, a many-to-many matching game is applied to investigate the pairing problem between DSOs and FNs. Finally, within the same DSO, we apply another layer of many-to-many matching between each of the paired FNs and serving DSSs to solve the FN-DSS pairing problem. Simulation results show that our proposed framework can significantly improve the performance of the IoT-based network systems

Thermal wind from hot accretion flows at large radii

We study slowly rotating accretion flow at parsec and sub-parsec scale irradiated by a low luminosity active galactic nuclei. We take into account the Compton heating, photoionization heating by the central X-rays. The bremsstrahlung cooling, recombination and line cooling are also included. We find that due to the Compton heating, wind can be thermally driven. The power of wind is in the range $(10^{-6}-10^{-3}) L_{\rm Edd}$, with $L_{\rm Edd}$ being the Eddington luminosity. The mass flux of wind is in the range $(0.01-1) \dot M_{\rm Edd}$ ($\dot M_{\rm Edd}= L_{\rm Edd}/0.1c^2$ is the Eddington accretion rate, $c$ is speed of light). We define the wind generation efficiency as $\epsilon = P_W/\dot {M}_{\rm BH}c^2$, with $P_W$ being wind power, $\dot M_{\rm BH}$ being the mass accretion rate onto the black hole. $\epsilon$ lies in the rage $10^{-4}-1.18$. Wind production efficiency decreases with increasing mass accretion rate. The possible role of the thermally driven wind in the active galactic feedback is briefly discussed.Comment: 9 pages, 6 figures, accepted by MNRA