Changes between Version 6 and Version 7 of u/erica/AccretionModelingBlog


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Timestamp:
03/20/18 13:07:49 (7 years ago)
Author:
Erica Kaminski
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  • u/erica/AccretionModelingBlog

    v6 v7  
    1515From Bondi (1952) we have the following quantities (in order: Bondi radius, accretion rate, sonic radius, nondimensional density and velocity):
    1616
    17 $R_{BH}$
     17$R_{BH} = \frac{GM_*}{C_\infty^2}$
    1818
    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$\dot{M} = 4 \pi \lambda_{crit}(G M_*)^2c_\infty^{-3}\rho_{\infty}$
    2020
     21$R_s=\frac{5-3\gamma}{4}\frac{GM_*}{C_{\infty}^2}$
    2122
    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
     27In 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:
    2328
    2429|| $\lambda_{crit}$ || .2526 ||
     
    3035|| $T_{\infty}$ || 1.66 ||
    3136|| $M_*$ || ||
     37|| $R_{BH}$ || ||
     38|| $R_{s}$ || ||
     39|| ||  ||
     40
     41The case of $\gamma=5/3$ flow is an extreme limit for the solution space. This value of $\gamma$ has a few interesting features:
    3242
    3343