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Update 9/13

Determining parameters for magnetic fields of planet and star for HD209458b simulations:

Matsakos et al. use the plasma \beta = \frac{8 \pi P}{B^2} = \frac{8 \pi \rho c_s^2}{B^2} at the base of the outflows (surfaces) to define the magnetic field strength. With \beta_s = 5, the magnetic field at the surface is 11.5 G, or ~10 B_s.

The magnetic field of HD209458b was estimated to be ~10% that of Jupiter (Ref), or ~0.5 G. This gives \beta_p = 0.25, which is right in the middle of the range used in Matsakos (0.002 - 400).

Currently, calculations of the bow shock radius use \sigma. Will need to convert this to using \beta by relating magnetic field:

r_{bow}=\mbox{solve} \left [\rho_s(a-r_{bow}) v_s(a-r_{bow})^2 + P_s(a-r_{bow} ) +\frac{B_s^2}{(a-r_{bow})^6} = \rho_p(r_{bow}) v_p(r_{bow})^2 +P_p(r_{bow}) + \frac{B_p^2}{r_{bow}^6} \right ]

Or, in terms of knowns,

\rho_p c_p^2 \left\{ \phi(\frac{\xi_{bow}}{\xi_p},\lambda_p) [\psi(\frac{\xi_{bow}}{\xi_p}, \lambda_p) + 1] + \frac{8 \pi \xi_p^6}{R_p^6 \beta_p \xi_{bow}^6}\right \}=\rho_s c_s^2 \left\{\phi(\frac{1-\xi_{bow}}{\xi_s},\lambda_s)[\psi(\frac{1-\xi_{bow}}{\xi_s}, \lambda_s) + 1] + \frac{8 \pi \xi_s^6}{R_s^6 \beta_s (1-\xi_{bow})^6}\right\}

With the \beta values above, this gives a bow shock distance of 0.155 (in computational units).

(What does \beta from PlanetaryAtmospheres represent? \neq to plasma \beta)

The other parameter that needs to be set is the cutoff radius for the fields. Currently planning on large (essentially infinity) for the star and near the edge of the box for the local simulations (0.125 orbital radii).

Once these are set, I'll be ready to start running simulations. Plan to begin with isotropic temp profile and no rotation, then jumping to anisotropic with rotation (& the global model) if it works - are we interested in the intermediate models still?

Also beginning to look at simulating WASP-12b, to attempt to reproduce the observed absorption lines of Mg II and Ca II. Physically, this requires that a fairly dense (10⁹/cm³ of H) and stable torus be created by the capture of the planetary wind. Will possibly require inclusion of radiative transfer, depending on level of ionization of torus.

astrobear

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Update 9/13

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