Changes between Version 6 and Version 7 of u/erica/AccretionModelingBlog
- Timestamp:
- 03/20/18 13:07:49 (7 years ago)
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u/erica/AccretionModelingBlog
v6 v7 15 15 From Bondi (1952) we have the following quantities (in order: Bondi radius, accretion rate, sonic radius, nondimensional density and velocity): 16 16 17 $R_{BH} $17 $R_{BH} = \frac{GM_*}{C_\infty^2}$ 18 18 19 In addition, the Bondi solution requires a numerical constant, $\lambda$, which controls the strength of the accretion flow. At its critical value, $\lambda=\lambda_{crit}$, $\dot{M}$ is strongest. The case of $\gamma=5/3$ flow is an extreme limit for the solution space. This value of $\gamma$ has a few interesting features: 19 $\dot{M} = 4 \pi \lambda_{crit}(G M_*)^2c_\infty^{-3}\rho_{\infty}$ 20 20 21 $R_s=\frac{5-3\gamma}{4}\frac{GM_*}{C_{\infty}^2}$ 21 22 22 In the code, $\lambda_{crit}$ is solved for numerically for given value of $\gamma$. In this simulation, these parameters are: 23 $z\_=\frac{\rho}{\rho_{\infty}}$ 24 25 $y\_=\frac{v_r}{C_\infty}$ 26 27 In the above, $\lambda$ is a numerical coefficient which controls the strength of the accretion flow. At its critical value, $\lambda=\lambda_{crit}$, $\dot{M}$ is strongest. In the code, $\lambda_{crit}$ is solved for using Eqn. 18 in Bondi's paper. In this simulation, these parameters are: 23 28 24 29 || $\lambda_{crit}$ || .2526 || … … 30 35 || $T_{\infty}$ || 1.66 || 31 36 || $M_*$ || || 37 || $R_{BH}$ || || 38 || $R_{s}$ || || 39 || || || 40 41 The case of $\gamma=5/3$ flow is an extreme limit for the solution space. This value of $\gamma$ has a few interesting features: 32 42 33 43