Hydrodynamic Escape from Highly Irradiated Atmospheres

Ruth Murray-Clay Harvard-Smithsonian Center for Astrophysics Ruth Murray-Clay: Atmospheric Escape ~1% of stars host hot Jupiters

Earth Mercury 1 AU hot Jupiter 0.39 AU ~0.05 AU ~ 10 R*

Star

-6 Sun: LUV ~ 10 Lbol 3 x10 during T Tauri phase planets occupy a large phase space

Mp,Rp,a,L ,LUV, ,e,M˙ w,Bp ∗ ∗ initial atmosphere Ruth Murray-Clay: Atmospheric Escape Two classes of escape mechanisms: Each can be thermal or non-thermal

“kinetic” “hydrodynamic”

loss to space of bulk outflow of a individual atoms collisional fluid

exobase Ruth Murray-Clay: Atmospheric Escape Two classes of escape mechanisms: Each can be thermal or non-thermal

“kinetic” “hydrodynamic”

loss to space of bulk outflow of a individual atoms collisional fluid

exobase

limits of thermal escape Jeans escape hydrodynamic escape non-thermal processes, often Roche lobe overflow mediated by B-fields ram pressure stripping Ruth Murray-Clay: Atmospheric Escape UV photons heat the upper atmosphere by photoionization

Before: After:

UV photon collisions e- distribute energy from ejected electron

p+ H hot Jupiters cannot be evaporated, in spite of early results using “energy-limited escape” models meant for young Earth and Venus Ruth Murray-Clay: Atmospheric Escape What generates a Parker wind?

pressure @ ∞ > 0: bad! fluid, isothermal

hydrostatic Ruth Murray-Clay: Atmospheric Escape What generates a Parker wind?

pressure @ ∞ > 0: bad! fluid, isothermal accelerates the gas outward v energy for PdV work in outward flow comes from this assumption Ruth Murray-Clay: Atmospheric Escape Parker winds flow through a critical point T ↓:

2 rs = GMp/(2cs) ↑ sonic point: cs ~ vesc x M˙ =4πr2ρv ↓ De Laval Nozzle

rs exponential dropoff

Von Braun with the Saturn V rocket Ruth Murray-Clay: Atmospheric Escape Drop isothermal assumption still assume fluid (collisional)

heating from photoionization only photoionization heating sets lower boundary condition and pdV work deposited primarily 1 τ n ∼ at ~ 1 : 0 σH

P ~ nanobars, altitude set by lower atmosphere Ruth Murray-Clay: Atmospheric Escape Drop isothermal assumption still assume fluid (collisional)

heating from photoionization only photoionization heating sets lower boundary condition and pdV work deposited primarily 1 τ n ∼ at ~ 1 : 0 σH

For high UV flux: F P ~ nanobars, UV σ n ∼ n2 α ν0 0 + rec altitude set by lower atmosphere hν0 Ruth Murray-Clay: Atmospheric Escape Conduction

low UV flux regime

T

r Watson et al. 1981 Ruth Murray-Clay: Atmospheric Escape Radiative cooling

T ~ 10^4 K

EUV Ly α

τ~ 1

+ X-ray H3 T ~ 10^3 K

can kill flow altogether if too high Ruth Murray-Clay: Atmospheric Escape I haven’t cared about the exobase! If FUV low ⇒ many scale heights to sonic point; no longer collisional & model isn’t self-consistent

intermediate between modified Jeans hydrodynamic escape & escape Jeans escape:

fluid outflow v < cs

conduction Ruth Murray-Clay: Atmospheric Escape Hot Jupiter

1 bar surface of planet 10 Rp ~ 10 cm Teff ≈ 1300K Ruth Murray-Clay: Atmospheric Escape Hot Jupiter

hydrodynamic wind

Twind ≈ 10,000 K

Photoionization base (τUV = 1) 1.1 Rp

1 bar surface of planet 10 Rp ~ 10 cm Teff ≈ 1300K Ruth Murray-Clay: Atmospheric Escape Hot Jupiter

hydrodynamic wind

Sonic point 2-5 Rp Twind ≈ 10,000 K

Photoionization base (τUV = 1) 1.1 Rp

1 bar surface of planet 10 Rp ~ 10 cm Teff ≈ 1300K Ruth Murray-Clay: Atmospheric Escape Hot Jupiter

hydrodynamic wind

Sonic point 2-5 Rp Twind ≈ 10,000 K

H, H+, He

Photoionization base (τUV = 1) 1.1 Rp

H2 1 bar surface of planet 10 Rp ~ 10 cm Teff ≈ 1300K Ruth Murray-Clay: Atmospheric Escape Hot Jupiter

hydrodynamic wind

Roche lobe radius 4.5 Rp Sonic point 2-5 Rp Twind ≈ 10,000 K

H, H+, He

Photoionization base (τUV = 1) 1.1 Rp

H2 1 bar surface of planet 10 Rp ~ 10 cm Teff ≈ 1300K Ruth Murray-Clay: Atmospheric Escape Hot Jupiter

hydrodynamic wind exobase mean free path = scale height

Roche lobe radius 4.5 Rp Sonic point 2-5 Rp Twind ≈ 10,000 K

H, H+, He

Photoionization base (τUV = 1) 1.1 Rp

H2 1 bar surface of planet 10 Rp ~ 10 cm Teff ≈ 1300K Ruth Murray-Clay: Atmospheric Escape Hydrodynamic Escape Equations

∂ 2 Mass continuity: (r ρv)=0 ∂r

∂v ∂P GM ρ 3GM∗ρr Momentum: ρv = − − p + ∂r ∂r r2 a3

Energy: ∂ kT kTv ∂ρ −τ ρv = + $Fν e aν n0 +Λ ∂r !(γ − 1)µ" µ ∂r 0 0

Ionization equilibrium: F e−τ ∂ n ν0 a n2 α 1 r2n v 0 ν0 = + rec + 2 ( + ) hν0 r ∂r Solved using a relaxation code Ruth Murray-Clay: Atmospheric Escape Hydrodynamic Escape Equations

∂ 2 Mass continuity: (r ρv)=0 ∂r

∂v ∂P GM ρ 3GM∗ρr Momentum: ρv = − − p + ∂r ∂r r2 a3

Energy: ∂ kT kTv ∂ρ −τ ρv = + $Fν e aν n0 +Λ ∂r !(γ − 1)µ" µ ∂r 0 0 Photoionization heating Ionization equilibrium: + Lyα cooling F e−τ ∂ n ν0 a n2 α 1 r2n v 0 ν0 = + rec + 2 ( + ) hν0 r ∂r Solved using a relaxation code Ruth Murray-Clay: Atmospheric Escape Hydrodynamic Escape Equations

∂ 2 Mass continuity: (r ρv)=0 ∂r Tidal Gravity

∂v ∂P GM ρ 3GM∗ρr Momentum: ρv = − − p + ∂r ∂r r2 a3

Energy: ∂ kT kTv ∂ρ −τ ρv = + $Fν e aν n0 +Λ ∂r !(γ − 1)µ" µ ∂r 0 0 Photoionization heating Ionization equilibrium: + Lyα cooling F e−τ ∂ n ν0 a n2 α 1 r2n v 0 ν0 = + rec + 2 ( + ) hν0 r ∂r Solved using a relaxation code Ruth Murray-Clay: Atmospheric Escape Hydrodynamic Escape Equations

∂ 2 Mass continuity: (r ρv)=0 ∂r Tidal Gravity

∂v ∂P GM ρ 3GM∗ρr Momentum: ρv = − − p + ∂r ∂r r2 a3

Energy: ∂ kT kTv ∂ρ −τ ρv = + $Fν e aν n0 +Λ ∂r !(γ − 1)µ" µ ∂r 0 0 Photoionization heating Ionization equilibrium: + Lyα cooling F e−τ ∂ n ν0 a n2 α 1 r2n v 0 ν0 = + rec + 2 ( + ) hν0 r ∂r Solved using a relaxation code Consistently solves ionization and energy equations. Can be used for different regimes. Ruth Murray-Clay: Atmospheric Escape

General boundary conditions

• Critical (sonic) point of transsonic wind (2 conditions) • ionization fraction at depth is small • density at depth is large enough that τ>> 1 • temperature at depth is < 104 K • self consistent optical depth to ionization Ruth Murray-Clay: Atmospheric Escape Solution for the current HD 209458b Murray-Clay et al. 2009

Mp = 0.7 MJ

Rp = 1.4 RJ

hν0 = 20eV

-13 ρbase = 4x10 g

Tbase = 1000 K -5 fbase = 10

τsp = 0.0046

2 FUV = 450 erg/cm /s Ruth Murray-Clay: Atmospheric Escape Energy and ionization balance

Solar FUV T Tauri FUV Ruth Murray-Clay: Atmospheric Escape Mass-Loss Rates: Dependence on UV Flux Murray-Clay et al. 2009

πF R 3 12 M˙ UV(3 P) M˙ ∼ 3 × 10 g/s = GM p HD 209458b: T Tauri ~ 0.1% loss

HD 209458b: main sequence ~ 1% loss M˙ ∼ 1010 g/s Ruth Murray-Clay: Atmospheric Escape Mass-Loss Rates: Dependence on UV Flux Murray-Clay et al. 2009 !FUV πF R 3 12 M˙ xUV(3 P) M˙ ∼ 3 × 10 g/s = GM p HD 209458b: T Tauri ~ 0.1% loss

ionization energy

HD 209458b: main sequence ~ 1% loss M˙ ∼ 1010 g/s Ruth Murray-Clay: Atmospheric Escape Mass-Loss Rates: Dependence on UV Flux Murray-Clay et al. 2009 !FUV 1RP πF R 3 12 M˙ xUV(3x P) M˙ ∼ 3 × 10 g/s = GM p HD 209458b: T Tauri ~ 0.1% loss

ionization energy

ionization HD 209458b: radius main sequence ~ 1% loss M˙ ∼ 1010 g/s Ruth Murray-Clay: Atmospheric Escape Mass-Loss Rates: Dependence on UV Flux Murray-Clay et al. 2009 !FUV 1RP 3 πFUV(3RP) M˙ ∼ × 12 M˙ = x x 3 10 g/s GMp Lyα cooling HD 209458b: T Tauri ~ 0.1% loss

ionization energy

ionization HD 209458b: radius main sequence ~ 1% loss M˙ ∼ 1010 g/s Ruth Murray-Clay: Atmospheric Escape The wind cannot directly generate enough absorption at ±100 km/s to reproduce measurements of HD 209458b.

-100 km/s 100 km/s

Velocity (km/s) ï400 ï200 0 200 400 3 ) 1 ï Å 1 ï s 2

ï 2 erg cm 14 ï 1 Flux (10 0 1214 1215 1216 1217 Wavelength (Å)

Vidal-Madjar et al. 2003 Murray-Clay, Chiang, & Murray 2009 Ruth Murray-Clay: Atmospheric Escape What about the stellar wind and the planetary magnetic field?

NASA NASA Ruth Murray-Clay: Atmospheric Escape

Stone & Proga 2009 Possibilities to explain the observations: • charge-exchange in the shock or planetary magnetosphere generates high-velocity neutrals • 3D effects increase the neutral column Ruth Murray-Clay: Atmospheric Escape Both the stellar wind ram pressure and magnetic fields can reduce and/or shape mass loss

wind

star hot Jupiter Ruth Murray-Clay: Atmospheric Escape Low mass gas giants and the atmospheres of solid planets can be significantly depleted

planet is 0.05AU from a solar mass star 0.10

0.08 ice giants gas giants 0.06

0.04

Neptune 0.02 HD 209458b

Fraction of Mass Lost Over 10 Gyr 0.00 0.0 0.2 0.4 0.6 0.8 1.0 “super Earth” Planet Mass (MJ) Ruth Murray-Clay: Atmospheric Escape

Atmospheric escape is crucial to characterization of planetary atmospheres

Charbonneau et al. 2009 Ruth Murray-Clay: Atmospheric Escape

Super-Earths or Atmospheric escape mini-Neptunes? is crucial to characterization of planetary atmospheres

Charbonneau et al. 2009 Ruth Murray-Clay: Atmospheric Escape

Super-Earths orvs. Atmospheric escape mini-Neptunes?mini-Neptunes: is crucial to characterization of primordial atmosphere vs. ongoing outgassing planetary and loss atmospheres

Charbonneau et al. 2009 Ruth Murray-Clay: Atmospheric Escape

Summary

• Given UV fluxes typical of hot Jupiters orbiting Sun-like stars, atmospheric escape is ~ hydrodynamic and “energy limited” with r = Rp for observed exoplanets if they have hydrogen-dominated atmospheres, but for smaller radii, beware. • At lower UV fluxes, beware! • At higher UV fluxes, beware! • A practical guide to estimating Mdot for hydrogen- dominated atmospheres given FUV, Rp, and Mp will be available soon.