I ran the isotropic wind simulation in 2.5D for lambda = 5.3, 2*Jupiter-mass planet and t = 250 days.

*The density profile agrees well with the curves given in S&P for the symmetric case.

• At r = 4R, S&P shows that the density drops to ~0.01 of the initial value. The simulation gives 0.03

*At r~2R, S&P shows ~0.1 of initial rho. The simulation gives 0.10

*The velocity profile shows a transition from subsonic to supersonic flow at higher distances. The only difference is that my simulation gives a sonic surface much closer to the planet as compared to S&P result. They see one at r = 2R. I got one at approximately r = 1.2.

Movie here. ​http://www.pas.rochester.edu/~mehr/wikistuff/2.gif

*I ran the simulation again with four times the box size and 30 days. The sonic surface can be seen moving outwards now and there is no inflow from the boundaries.

​http://www.pas.rochester.edu/~mehr/wikistuff/symbox.gif

*No temperature variation wrt angle. Temperature stays constant at the base of the wind.

​http://www.pas.rochester.edu/~mehr/wikistuff/symmetrical.gif

*Still failing to get supersonic outflow at the edges, and therefore the inflow at the end.

*Temperature profile

​http://www.pas.rochester.edu/~mehr/wikistuff/symmtemp.gif

*Working on including radial ambient outflow to match with the initial conditions.

• As discussed earlier, I removed the temperature asymmetry from the problem by commenting out the function we wrote to vary it as a function of angle.

Problem As the image from the initial cycle shows, the right side is still colder than the left.

*Also, after cycle 10 the color bars at the base of the wind do not change, which means the temperature is being maintained as we need, but the contrast between the day and the night is unclear. I am using the unedited version of outflows.f90 for this and I still get the contrast.

Subsonic flow problem *We were not getting supersonic outflow at the boundary. I tried various fixes including increasing the box-size, ambient temperature and density but the mach number continues to stay below one for one side and supersonic for the other. Below curve A is for the left side.

Later on we do see supersonic speeds but it's mostly rightward inflow as shown by the contours below.

Initial Conditions I ran these simulations for lambda=5.3 as done in the paper. The only part where my initial conditions differ from the paper are the direction of the ambient velocity. I gave it a y-directed initial sound speed. I am looking into how to make it radial by modifying the code.

Movie ​http://www.pas.rochester.edu/~mehr/wikistuff/movie.gif

• Got rid of the inflow from the left and the unexpected bow-shock.

Movie ​http://www.pas.rochester.edu/~mehr/wikistuff/movieb.gif

Density

Mach number -Still seeing higher values on the wrong side

Ran the original simulation for a longer time (25 days) and wider bounds. Inflow from the boundaries persists.

​http://www.pas.rochester.edu/~mehr/wikistuff/movietime.gif

Gravity Only

Testing whether the point gravity is working correctly.

​http://www.pas.rochester.edu/~mehr/wikistuff/movie_go.gif

New Initial Condition

Ambient has a fixed outward radial velocity. No difference from the original.

One problem is that the outflow speed does not seem to be exceeding the escape speed.

Wind Only

I keep getting the following error if I comment out the ambient to look at a strong wind only.

Here's a review of everything that has been accomplished up till now on the S&P problem.

*Introduced asymmetry wrt initial temperature in the outflow module.

*Initialized the ambient at low density and sound speed to allow for a thermally driven wind.

*Ran the simulations for a period of 10 days, temperature values of the order of 10,000K and planetary sizes of 1-2 Jupiter masses. *All having to do with different values of the hydrodynamic escape parameter

*Best results seen in the range of lambda 4-6. Robustness issues.

Following are some plots and a comparison with the S&P results.

lambda = 5.67 Density

*In steady state the pattern matches well with S&P results; purely radial flow at large distances and circulation at small distances.

*Major difference is the position of the shock. I do not see a discontinuity in the theta direction. Instead it's visible between the ambient and the planetary outflow. S&P get a shock discontinuity at about theta = 3pi/4

*Cuts at theta = 0 (K) , pi/2 (L) and pi (M). As expected.

Temperature *Day-night temperature ratio 20,000:200K. S&P kept a ratio of 100:1.

*The position of sonic surface is well in agreement with the S&P result occuring at almost 2*planetary_radius.

Main issue with code *Only gives sensible results for carefully chosen parameter values. Compare the movies below for lambda=5.67 and lambda=6.11 ​http://www.pas.rochester.edu/~mehr/wikistuff/movienew.gif

​http://www.pas.rochester.edu/~mehr/wikistuff/bad.gif

Next Tasks *Finish the write-up. *Owens Adams Paper *Move to 3D regime

I ran the simulation again for lambda=5.67 for a longer time (10 days, turning off outflow at day 5). The strange box-like artifact seems to have gone away and the steady state looks very close to the original paper.

​http://www.pas.rochester.edu/~mehr/wikistuff/movienew.gif

-Here are some scaled plots for values of lambda between 3 and 10. I initialized the ambient outflow as done in the paper and turned it off after 0.5 days, so that the dominant thermally driven results are visible. In the paper, they refer to it as the steady state.

The plots here are the density profile, temperature and density with the velocity/soundspeed contours. The transition from subsonic speeds at small distances to supersonic speeds can be seen.

Lambda = 3.67

Lambda = 5.5

​http://www.pas.rochester.edu/~mehr/wikistuff/movie5.gif

Lambda = 8

Will add cuts at different values of theta to determine the exact position of the shock discontinuity

• Added the hydrodynamic escape parameter to the code.

• Tested for several cases. Agrees with the values used by S&P.(Lambda = 14.82 for solar corona).

-Case for lambda = 10.6, 1 Jupiter mass, 10,000K. The ratio of rho-wind to rho-ambient was 100.

Movie here.​http://www.pas.rochester.edu/~mehr/wikistuff/gamma10.gif

Whereas the S&P case for lambda=5 looks like this

• Included point gravity source in the simulation. Refer to Sonny's post here.​https://astrobear.pas.rochester.edu/trac/blog/ceh528610092014

• S&P also track the subsonic to supersonic wind profile against radius. Need to investigate that.

-Included the extrapolative BC's on both sides in 2D.

​http://www.pas.rochester.edu/~mehr/wikistuff/movie.gif

-Comparison with S&P results.

• Did a 2d run including the anisotropy and gamma = 1.01
• Code screen shots and (nonsensical) movie below.

-WindOutflow Module first run and debugging.

-B.C's can be replicated from the Stone/Proga paper.

-Working on incorporating the non-radial component of the velocity in the code.

• Modified the outer boundary condition to introduce stellar wind.

-Fixed the density, internal energy and velocity in both directions at the boundary.

-Planet inside the wind acceleration region. Non-MHD model.

-Planetary wind swept back into parabolic shape.

-Discontinuity separating shocked planet and stellar winds

-Shock diverts the stellar wind around the outflow

-Constant density at terminal velocity*

-Nearly isothermal

Sonic Surfaces:

-At 0.5R fort the planetary wind. Same as the case without stellar wind

-At 2.5R planetary wind termination shock. Decelerates the wind.

-At 4.75R stellar wind termination shock.

-Exact location depends on the assumed momentum flux in the stellar wind. Confines the planetary wind close to the surface.

-Mass loss rate is nearly identical to the case with no stellar wind.

Comparison of Column density: -With stellar wind, viewing from the night side the column density is enhanced as the planetary wind is confined.

• Cometary tail at a different angle.

Limitations: -No modelling of thermal processes, fixed parameters. -Non-MHD -Orbital motion of the planet and gravitation from the star not included. -Valid for low values of lambda.

Anisotropic Windflows from close in Exo-planets (Stone & Proga 2009)

• Close-in EGP's: a < 0.1 AU. Because of tidal locking and irradiation on only one side, the assumption of spherical symmetry no longer holds.

• The paper investigates the effect of anisotropic heating on winds in 2D.

Method: Take hydrodynamic equations in polar coordinates. Introduce anisotropy by making internal energy a function of theta on the surface of the planet.

• Hydrodynamic escape parameter.

-Adiabatic Index.

Some results:

-Evidence of non-radial outflow.

-Inflow on the night side

-Shock front as the wind flows from the day side to night side.

-Only radial outflow at large radii.

-Nearly isothermal.

-Sonic surface at 0.5R. Decelerating wind on the night side?

-Density variations b/w opposite sides are only significant very close to the planet.

-Polar velocity increasing as you go from day to night side; discontinuity at the shock.

-Effect of increasing gamma. Cooling.

-Mass loss rate decreased by a factor of 2.

-Model not valid at very large distances. Effect of including stellar winds?

-Met Jonathan for a walk-through of the 3D outflow routine.