Magnetic Fields

Calculated with Matlab script (not final):

Dimensionless Parameters

\xi_p	0.013893	ratio of planet radius to orbital separation
\xi_s	0.117818	ratio of stellar radius to orbital separation
\xi_H	0.057598	ratio of Hill radius to orbital separation (from planet)
\xi_{bow}	0.240468	ratio of bow shock radius to orbital separation (from planet)
\xi_{Mp}	0.074592	ratio of planet sonic radius to orbital separation (from planet)
\xi_{\Omega}	0.074592	ratio of coriolis radius to orbital separation (from planet)
\chi_{bow}	22.853798	ratio of densities at bow shock
\lambda_s	22.088202	stellar lambda
\lambda_p	10.738334	planetary lambda
\sigma_p	0.100000
\sigma_s	0.100000

Physical Parameters

Orbital separation	0.047470	AU
Mass of Star	1.148000	solar masses
Mass of Planet	0.690396	Jupiter masses
Radius of Star	1.203000	solar radii
Radius of Planet	1.380000	Jupiter radii
Temperature of Star	999999.671375	Kelvin
Temperature of Planet	10005.732583	Kelvin
Density of Star	3.211200e-13	g/cc
Density of Planet	3.211200e-15	g/cc
Orbital period	3.523762	days
Magnetic field of Star	0.059783 Gauss
Magnetic field of Planet	0.052956 Gauss
Mass loss from Star	5.680185e-16	solar masses per yr
Mass loss from Planet	1.000014e+10	g/s
Mach number of Stellar wind at shock	6.926105e-01
Mach number of Planetary wind at shock	1.448805e+00
lScale for sim	7.097443e+11	cm
TimeScale	3.044531e+05	s
rScale	3.211200e-15	g/cc
Location of planet in units of lscale	1.000000e+00
predicted bow shock radius in units of lscale	2.406060e-01

Magnetic radii are cutoff distances (where dipole field drops to zero). Set stellar to large and planetary to < orbital radius. Need to figure out difference between beta formulae.

Mass Loss Rates

Value	Mdot (g/s)
Aniso	6.1x109
lambda=5	5.6x1011	(doesn't reach steady state)	5.5x1011
lambda=15	3x107
Mp = MJ	9.9x109
Mp = 0.5MJ	1.5x109
Mp = 0.25MJ	> 1.67x109	(not well resolved)	3.7x108
Tp = 5x104 K	Negative throughout	(not resolved)	3.4x108
Tp = 5x103 K	1.4x109
Tamb = 3 K	4.5x109
Tamb = 25 K	4.5x109
Tamb = 50 K	4.5x109

Compare Aniso with net value from planet paper:

I find it suspicious that all three values for T_amb are the same (to 6 decimal places), but less than T_amb = 100 K (for Aniso).

Calculations with VisIt

Focusing on mass loss rate at the moment. Testing on Run5 (Aniso) so I can compare to Jonathan's paper. Created all the expressions I believe are required (see attachment​), with the mass flux defined as density times radial velocity² (properly scaled). When I perform a weighted query on the mass flux over a spherical isosurface (defined in terms of distance from origin), however, I get a value about 3 magnitudes too large (1.14*10¹³). Also tried calculating flux with the mesh flux operator, but velocity times density doesn't seem to be the appropriate quantity. It does make nice pictures, though:

First is at r = 0.1, second is at r = 0.05 (Plot is pseudocolor of operator/Flux/Mesh, SphericalSlice centered at origin). Note that values are negative because the normals of the spherical slice point inwards.

Fixed scaling of expressions. Now summing over an isosurface gives the expected values; it would be easy enough to use min/max to calculate inward and outward flux separately, if desired.

Parameter Space for Planet Sims

Successfully recreated Run 5 (Aniso) from Jonathan's simulations, after meeting and fixing some of the code. Most runs are taking 5-8 hours with 1 level AMR (did check, optimization flag is set to level 3 in makefile). Used momenta to compare relative strength of outflows, made density movies.

In comparison to Aniso, changing lambda performs as expected - with lambda = 5, there is a marked increase in the strength of the wind, and with lambda = 15 there is very little to no wind (size of planet changes as well).

Increased size of the domain to capture sonic radius; bigger outflow, as expected (note that the density scale is different than the rest of the plots, in order to discern the planet):

Run longer (1.5x almost reaches steady state):

Changing the mass of the planet wasn't quite as clear. Overall, it doesn't appear to have affected the wind very much. Again, the planet size is related to the mass (since density is also specified). It is hard to see a wind on the smallest (.25 M_J) planet, but momentum plots appear to support its existence.

Decreased size of domain to better resolve near planet; weaker outflow:

Changing the temperature of the planet also affects the radius (through lambda). A 5x hotter planet appears to have a stronger outflow at the end, although it takes a significant amount of time to gain significant size (perhaps should run this simulation for longer). A planet with .5 T doesn't appear to be very different, qualitatively, from the original run.

Decreased size of domain to resolve planet; actually has weaker outflow (mass loss rate 1 order of magnitude smaller):

Finally (for the moment), changed ambient temperature to lower values. Would also like to explore higher values to see if they have much effect. The 50K, 25K, and 3K runs all have similar maximum momenta, approx. 2x the Aniso run, which seems to suggest a stronger outflow, but the density plots look nearly identical.

What parameters are best to plot?

Sonic Radii

For a few of the parameters, I also plotted contours on the sonic radius. Respectively, Run5 (original), lambda=5 with larger domain, M_p=.25M_J with smaller domain, T_p=5x10⁴ K with smaller domain, and T_amb=50K.

Added lambda=5, run longer (1.5x):

Experimenting with AstroBEAR

Ran OutflowWind simulations with varying parameters. Thickness and wind velocity don't appear to have any effect - perhaps an effect of rescaling? Velocity speeds up the simulation as a whole. The rest are as follows:

Reference (default parameters, 100 frames, 2 units computational time (conversion?)):

Radius increases size of wind, but otherwise has little effect, at least at small values (expected).

Radius of 2:

Increasing density appears to decrease relative density at the center of the front of the outflow (slightly counter-intuitive, but makes sense).

Density of 5: Density of 10: Density of 20:

Increasing temp. creates a more diffuse cloud at the end (predictably). Temp = 0 appears to cause buggy behavior.

Temp = 0: Temp = 1: Temp = 5:

Also tried a run at 1000 frames, but definitely overkill for time.