Changes between Version 15 and Version 16 of PlanetaryAtmospheres

Timestamp:

08/28/15 17:46:38 (11 years ago)

Author:

Jonathan

Comment:

—

PlanetaryAtmospheres

@@ -3 +3 @@
 == Defining the parameter space for stellar-planetary wind interactions ==
 
-Ignoring MHD for the moment, and assuming circular orbits, we can define the problem using these 9 primary variables
+Ignoring magnetic fields, and assuming circular orbits, we can define the problem using these 9 primary variables
 
 || $M_p$ || Mass of planet ||
@@ -69 +69 @@
 
 
+
+Matsakos et al, compare the ordering of the Hill radius, the bow radius, and the magnetic radius which give 6 different possible orderings.  They lump them into 4 different types.
+
+|| I || $\xi_H > \xi_\beta > \xi_{bow}$ ||
+|| II || $\xi_H > \xi_{bow} > \xi_{beta}$ ||
+|| III || $\xi_{bow} > \xi_\beta > \xi_H$ ||
+|| III || $\xi_{bow} > \xi_H > \xi_\beta$ ||
+|| IV || $\xi_\beta > \xi_{bow} > \xi_H$ ||
+|| IV || $\xi_\beta > \xi_H > \xi_{bow}$ ||
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+
+
+In general, the planet radius will always be the smallest.  You can probably argue that the Hill radius will in general be larger than the Bondi Hoyle radius, since
+
+$\frac{r_{H}}{r_{BH}}=\frac{v_s(a)^2+(a\Omega)^2+c_s^2}{2 G M_p} a\left ( \frac{q}{3} \right ) ^ {1/3} $
+$ = \frac{v_s(a)^2+G(M_s+M_p)/a+c_s^2}{2 G M_p} a\left ( \frac{q}{3} \right ) ^ {1/3} =\left ( \frac{ \left ( \psi(\frac{1}{\xi_s})+1 \right )}{2\xi_s \lambda_s q}+\frac{1+q}{2q} \right )\left ( \frac{q}{3} \right ) ^ {1/3} $ 
+
+Now $\psi \approx< 5$, $q \approx 1/1000$, $\xi_s \approx 1/100$, so in general $r_H >> r_{BH}$
+
+However, the location of the stellar sonic radius compared to a can be used to constrain the velocity of the stellar wind - and would presumably have more bearing on the dynamics of the bow shock.
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+The planet radius probably does not matter to much (as long as it is small enough), but if you include the sonic radius and the bondi-hoyle radius, you could have 120 different orderings possible.  You could also just focus on the dominant radius (and have 5 types), or the dominant 2 and have 20 sims.  In addition you could modify the density contrast at the bow shock to double the number of runs.
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+ different 
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 As a side note, we have 
 || $\frac{v_{esc}}{c_p}=\sqrt{2 \lambda_p}$ || planetary escape speed ||