MHD planet simulations Owen & Adams

Dimensionless Parameters Single Body Λ≡ 2 𝑀 𝑣 𝐵 2 𝑟 2 - 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

Dimensionless Parameters Star-Planet Interactions Π 𝑊𝑊 = 𝑀 ∗ 𝑣 ∗ 𝑟 2 𝑀 𝑝 𝑣 𝑝 𝑎 2 - wind-wind interaction Π 𝑊𝐵 = 2 𝑀 ∗ 𝑣 ∗ 𝐵 𝑝 2 𝑎 2 - stellar wind-planet field interaction Π 𝐵𝐵 = 𝐵 ∗ 2 𝐵 𝑝 2 𝑟 6 𝑅 𝑝 6 𝑅 ∗ 6 𝑎 6 - field-field interaction Π 𝐵𝑊 = 𝐵 ∗ 2 𝑟 2 2 𝑀 𝑝 𝑣 𝑝 𝑅 ∗ 6 𝑎 6 - 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

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)

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

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

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

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

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

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)

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

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