Update 7/7

  • Solving parker wind equation,

psi − ln(psi) = 4 ln(xi) + 4/xi − 3, where psi = (v/vs)2 and xi = r/rs.

There are 4 types of solutions - combinations of sub/supersonic at the surface and v → 0/vf as xi → infinity. The only physical solution is subsonic at the surface and has a nonzero velocity infinitely far away, and passes through xi = 1, psi = 1.

Attempts at solutions using approximations and a single solve:

Alternate implementation of approximation from Jonathan's code; works for r > rs, but not r < rs.

Pertinent line is: yy(i)=vpasolve(y - log(y) == -3 + 4*log(xx(i))+4/xx(i),y,(xx(i) > 1) * xx(i) + (xx(i) ⇐ 1)*exp(3-4*log(xx(i))-4/xx(i)))

Interpreted as:

if xx(i) ≥ 1

yy(i)=vpasolve(y - log(y) == -3 + 4*log(xx(i))+4/xx(i));

else

yy(i)=vpasolve(y - log(y) == exp(3-4*log(xx(i))-4/xx(i)));

end

Correct & incorrect plots:

  • Calculated mass loss rate in VisIt. Used a scalar expression for the radial mass (momentum) flux and summed over isosurfaces (can also use spherical slices) to get mass loss rate. Plots were unfortunately uniform in display; however, in experimenting, discovered the flux operator makes plots that appear qualitatively correct for the flux:

Mass loss rates for the various simulations from last time:

Value Mdot (g/s)
Aniso 6.1x109
lambda=5 5.6x1011
lambda=15 3x107
Mp = MJ 9.9x109
Mp = 0.5MJ 1.5x109
Mp = 0.25MJ > 1.67x109 (not well resolved)
Tp = 5x104 K Negative throughout (not resolved)
Tp = 5x103 K 1.4x109
Tamb = 3 K 4.5x109
Tamb = 25 K 4.5x109
Tamb = 50 K 4.5x109

Aniso appears correct, based on plot from planet paper.

Working on calculating the sound speed to get the sonic radius.

  • Started working through occasional prelim problems, as well.

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