Changes between Version 1 and Version 2 of u/JCMar2212

Timestamp:

03/21/12 15:02:23 (13 years ago)

Author:

Jonathan

Comment:

—

u/JCMar2212

@@ -2 +2 @@
 
 = The Star Formation Rate of Supersonic MHD Turbulence (Padoan and Nordlund 2011) =
+Attempt to determine [[latex($SFR(\alpha_{vir}, M_S, \beta)$)]] for isothermal self-gravitating MHD turbulence.
+
 [[Image(JCMar1.png)]]
 
-Attempt to determine [[latex($SFR(\alpha_{vir}, M_S, \beta)$)]] for isothermal self-gravitating MHD turbulence.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+== The Model ==
+
 
 === Post shock density ===
@@ -11 +59 @@
  and if [[latex($v_l \propto l^{1/2}$)]] then
   [[latex($\rho_l \propto l$)]]
+
+
+
+
 
 === Shock thickness ===
@@ -24 +76 @@
  So flows on all scales will produce shocks of the same thickness, but the post shock densities will increase with scale.
 
+
+
+
+
+
+
 === Shock instability ===
  If [[latex($\lambda_{HD} > \lambda_J(\rho_{cr,HD})$)]] then the shocked layer will be unstable to collapse so we can define a critical density based on the shock layer thickness
@@ -35 +93 @@
  [[Image(JCMar3.png)]]
 
- We can calculate the amount of gas above the critical density [[latex($M_{>\rho_{cr}} = \displaystyle \int_{x_{cr}}^\infty {x p(x) dx}$)]] and the characteristic time for that mass to form stars as [[latex($\tau_{ff,cr}$)]] with some efficiency [[latex($\epsilon$)]] giving a star formation rate of [[latex($\epsilon \frac{M_{\rho_{>cr}}}{\tau_{ff,cr}}$)]] or the standard "star formation rate per free fall time" [[latex($SFR_{ff}=\epsilon \frac{\tau_{ff,0}}{\tau_{ff,cr}} M_{\rho_{>cr}}$)]]
-
- 
 
 
 
 
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ We can calculate the amount of gas above the critical density [[latex($M_{>\rho_{cr}} = \displaystyle \int_{x_{cr}}^\infty {x p(x) dx}$)]] and the characteristic time for that mass to form stars as [[latex($\tau_{ff,cr}$)]] with some efficiency [[latex($\epsilon$)]] giving a star formation rate of [[latex($\epsilon \frac{M_{\rho_{>cr}}}{\tau_{ff,cr}}$)]] or the standard "star formation rate per free fall time" [[latex($SFR_{ff}=\epsilon \frac{\tau_{ff,0}}{\tau_{ff,cr}} M_{\rho_{>cr}}$)]]
+
+ They assumed that in the hydro case [[latex($\epsilon \approx 1$)]]
+
+=== MHD? ===
+  For MHD a similar analysis can be carried out although the post shock [[latex($\beta$)]] must be measured.  The main modification is that the post shock magnetic pressure must also be taken into account.  
+
+== The setups ==
+
+[[Image(JCMar2.png)]]
+
+
+== The results ==
+
+[[Image(JCMar4.png)]]
+
+----
+
+[[Image(JCMar5.png)]]
+
+----
+
+[[Image(JCMar6.png)]]
+