1. MHD planet simulations
Owen & Adams

2. Dimensionless Parameters Single Body
Λ≡ 2 𝑀 𝑣 𝐵 2 𝑟 ratio of ram to magnetic pressure
Λ < 1, magnetic field dominates
For star, this means field will be primarily in the z direction
For planet, outflow will be constrained to follow field lines
Λ > 1, wind dominates
Stellar field will be mostly radial
Planetary magnetic field also blown out near the planet
4 divisions of parameter space

3. Dimensionless Parameters Star-Planet Interactions
Π 𝑊𝑊 = 𝑀 ∗ 𝑣 ∗ 𝑟 2 𝑀 𝑝 𝑣 𝑝 𝑎 wind-wind interaction
Π 𝑊𝐵 = 2 𝑀 ∗ 𝑣 ∗ 𝐵 𝑝 2 𝑎 stellar wind-planet field interaction
Π 𝐵𝐵 = 𝐵 ∗ 2 𝐵 𝑝 2 𝑟 6 𝑅 𝑝 6 𝑅 ∗ 6 𝑎 field-field interaction
Π 𝐵𝑊 = 𝐵 ∗ 2 𝑟 𝑀 𝑝 𝑣 𝑝 𝑅 ∗ 6 𝑎 planet wind-stellar field interaction
Assuming Mdot*/Mdotp = 100, v*/vp = 10, and a/Rp = 100, equality at 3.2 Rp, 5.5 Rp, 10 Rp, 14 Rp

4. Simulation Setup
2D analysis (ZEUS) on spherical grid – labeled in x (towards star) and z (perpendicular to orbital plane)
Include radiative transfer
Dipole field from planet
Linear background field from star
Neglect planet rotation and stellar gravity
Stellar field is dipole, have parameter that accounts for whether field is blown out by stellar wind or not (beta star)

5. Simulation Assumptions
Λ* < 1, so that stellar magnetic field is in z direction
𝐵= 𝛽 ∗ 𝐵 𝑝 , where 𝛽 ∗ = 𝐵 ∗ 𝐵 𝑝 𝑅 ∗ 3 𝑎 3
Stellar magnetic field protects planet from stellar wind
Π 𝑊𝑊 ≪1
Fix mass and radius of planet
𝑀 𝑝 = 𝑀 𝐽
𝑅 𝑝 =1.4 𝑅 𝐽
Choice of calculation scheme restricts to radiation-recombination regime (high UV flux)
Magnetic field from star at planet location
Don’t include any stellar wind
Symmetry boundary conditions at angular bounds, outflow in r

6. Parameters to Explore
This leaves 𝐵 𝑝 , 𝛽 ∗ , and 𝐹 𝑈𝑉 as free parameters
Attempt to determine under what conditions flow is controlled by field

7. No Field Case
Effects of flux only – outflow circles around planet, very similar to our temperature profile

8. Weak Field, High Flux Bp = 0.3 G
Even small magnetic field completely suppresses night-side outflows (reduces mdot by ~2x)

9. These simulations are limited to the day side
Bp of 0.5, 1, 4, 10
Beta star of 0, 3*10^-3 (corresponds to orbit of ~8x R* w/ B* 15x Bp, so pretty close)
At larger planetary field strengths, field line opening depends fairly strongly on background field

10. Effect on Mass Loss Rate
Overall, suppressed by ~1 order of magnitude (due to lack of nightside flow and fraction of dayside surface due to closed field lines)

11. High Stellar Field Strength
At lower stellar field strengths, increasing leads to higher mass loss due to more open field lines
As you pass 10-2, higher field strength leads to more difficulty making smooth transition to supersonic flow, sharply decreasing mass loss rate

12. Ref
Owen, J.E & Adams, F.C. 2014, MNRAS, 444, 3761