Changes between Version 7 and Version 8 of u/adebrech

Timestamp:

05/26/16 15:22:01 (9 years ago)

Author:

adebrech

Comment:

—

u/adebrech

@@ -2 +2 @@
 [[PageOutline]]
 
+= Change in Bow Shock with Magnetic Field =
+If sigma,,*,, and sigma,,p,, are equal, the bow shock radius is unchanged with or without magnetic field - ratio of radius to orbital separation, chi,,bow,, = 0.240468. With sigma,,*,, = 1, sigma,,p,, = 0.1, chi,,bow,, = 0.148204; sigma,,*,, = 0.5, sigma,,p,, = 0.1, chi,,bow,, = 0.187300; sigma,,*,, = 0.1, sigma,,p,, = 0.5, chi,,bow,, = 0.302483; sigma,,*,, = 0.1, sigma,,p,, = 1, chi,,bow,, = 0.363674; and with sigma,,*,, = 0.5 and sigma,,p,, = 1, chi,,bow,, = 0.297793 ≈ chi,,Coriolis,,.
+
 = [http://arxiv.org/pdf/1206.5003v3.pdf Tremblin & Chiang], Computational Charge Exchange =
-Followup to 2008 and 2010 studies of charge exchange between planetary and stellar winds, which used Monte Carlo simulations of 'meta-particles' that were computationally obstructed by bow shocks. Here they use the hydrodynamic equations (no magnetism, Coriolis and centrifugal forces, or tidal gravity). A slow stellar wind (130 km/s) was chosen to approximate the solar wind, and the isothermal planetary wind was initialized as 80% ionized, following Murray-Clay et al. The planetary wind incorporated photoionization/recombination and advection. To incorporate charge exchange, the hydrodynamic code was augmented with chemical reaction solvers - 4 equations relate x,,i,,, i=1-4 representing each possible combination of hot or cold and neutral or ionized hydrogen, and n,,H,, with beta, the reaction rate. These equations take reverse exchange into account, so as not to overestimate neutral hydrogen too greatly (still slightly overestimated). x,,i,, is also included in the hydrodynamic equations.
+Followup to 2008 and 2010 studies of charge exchange between planetary and stellar winds, which used Monte Carlo simulations of 'meta-particles' that were computationally obstructed by bow shocks. Here they use the hydrodynamic equations (no magnetism, Coriolis and centrifugal forces, or tidal gravity). A slow stellar wind (130 km/s) was chosen to approximate the solar wind, and the isothermal planetary wind was initialized as 80% ionized, following Murray-Clay et al. The planetary wind incorporated photoionization/recombination and advection. To incorporate charge exchange, the hydrodynamic code was augmented with chemical reaction solvers - 4 equations relate x,,i,,, i=1-4 representing each possible combination of hot or cold and neutral or ionized hydrogen, and n,,H,, with beta, the reaction rate. These equations take reverse exchange into account, so as not to overestimate neutral hydrogen too greatly (still slightly overestimated). x,,i,, is also included in the hydrodynamic equations. The simulations appear to reproduce the observed absorption curves well, with asymmetry between the two sides of the Doppler shift. 
 
-[[Image(TremblinEqns.jpg)]]
+[[Image(simabs.jpg, width=300)]]
 
+[[Image(TremblinEqns.jpg, width=400)]]
+
+Compare these with the equations used by Christie et al (see below) for incorporating charge exchange:
+
+[[Image(ChristieEqns.jpg,width=400)]]