Version 16 (modified by 9 years ago) ( diff ) | ,
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Defining the parameter space for stellar-planetary wind interactions
Ignoring magnetic fields, and assuming circular orbits, we can define the problem using these 9 primary variables
Mass of planet | |
Radius of planet | |
Temperature at planet surface | |
Density at planet surface | |
Mass of star | |
Radius of star | |
Temperature at stellar surface | |
Density at stellar surface | |
orbital separation |
Time and length symmetry allows us to fix the total mass and separation without loss of generality. In addition, the actual densities don't matter - just their ratios, so we can also fix the planetary density without loss of generality. So we can reduce the list of 9 primary variables to the following six dimensionless variables that define the interaction
mass ratio | |
ratio of densities at surfaces | |
dimensionless planetary radius | |
dimensionless stellar radius | |
characterizes planetary wind | |
characterizes stellar wind |
Now instead of those 6, we may want to define the following 5 length scales, and density ratio at the bow shock
Ratio of Hill radius to orbital radius | |
Ratio of bow shock radius to orbital radius | |
Ratio of planetary radius to orbital radius | |
Ratio of sonic radius to planetary orbital radius | |
Density ratio at bow shock. | |
Ratio of bondi-hoyle radius to orbital radius |
Using the following relations,
orbital angular velocity | |
Hill radius | |
stellar sound speed | |
planetary sound speed | |
Bondi-Hoyle radius | |
bow shock standoff distance |
and the dimensionless solution to the Parker Wind
which gives us the following solutions for the stellar and planetary winds
We can directly calculate
and numerically solve the following 3 equations for
, , andMatsakos 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 | |
II | |
III | |
III | |
IV | |
IV |
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
Now
, , , so in generalHowever, 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.
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.
different
As a side note, we have
planetary escape speed | |
dimensionless radius at which coriolis forces bend planetary wind - not independent |
Planetary Atmospheres
Profiles
- Density
- Enclosed Mass
- Pressure - and rho*R*T mismatch
Module supports
- Global simulation in a fixed frame
- Global simulation in a rotating frame
- Local simulation in a rotating frame
- Spatial based Refinement of planet
- Stellar envelope in HSE
- Source code problem.f90
- Data file problem.data
- Uses Particles, Ambients, Clumps, and Refinement Objects
Still working on
- Basic testing of hydrostatic equilibrium for planet
- Line transfer for stellar heating
- Second AMR implicit solve may need to be added later (ie Howell and Greenough 2002)
Results
Working on getting stable planetary atmosphere using profile without a core. Turning on characteristic limiting seems to cause numerical artifacts which lead to 'explosion'. See ticket #
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