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Fred Adams, Univ. Michigan
Extreme Solar Systems II
Jackson, Wyoming, September 2011
Hot Jupiters can Evaporate
• HD209458b (Vidal-Madjar et al. 2003,
2004; Desert et al. 2008; Sing et al. 2008;
Lecavelier des Etangs et al. 2008)
• HD189733b (Lecavelier des Etangs et al.
2010)
dM
10
11
 10 10 g /s
dt
The Planetary System
M  1M SUN
FUV  100 1000 (cgs)
M P  1M JUP
RP  1.4RJUP
B  1 Gauss
BP  1 Gauss
 orb  0.05AU Porb  4day
 orb  10R  100RP
e 0
 orb  R  RP
Basic Regime of Operation
dM
RP3 FUV
10
1
4
1

 10 g s  10 M J Gyr
dt
GM P
B
2
8v
 10 10 (magnetically  controlled)
4
2
6
C
qB
4

 10 (well  coupled)
 cmnv
B
2
2
4
 8v /B   10 (current  free)
B
TWO COUPLED PROBLEMS
• LAUNCH of the outflow from planet
• PROPAGATION of the outflow in the
joint environment of star and planet,
including gravity, stellar wind, stellar
magnetic field
• Matched asymptotics: Outer limit of the
inner problem (launch of wind) provides
the inner boundary condition for the outer
problem (propagation of wind)
This Work Focuses on Launch of the Wind
The Coordinate System
 

r
B  BP  3 3cos  rˆ  zˆ  B (R / ) 3 zˆ
p    
2
cos
q    2 /  sin 
where   (B R / ) /BP  10
3

1/ 2
2
3
3
and   r /R
ˆ
p  f ()cos  rˆ  g()sin  


1/ 2
ˆ
ˆ
q  g()sin  r  f ()cos   g ()
where f    2 3 and g     3
Magnetic Field Configuration
OPEN FIELD LINES
CLOSED FIELD LINES
Magnetic field lines
are lines of constant
coordinate q.
The coordinate p
measures distance
along field lines.
Field lines are open
near planetary pole
and are closed near
the equator. Fraction
of open field lines:
 3 
f  1  1 

 2   
1/ 3 1/ 2
Equations of Motion
Steady-state flow along field-line direction:
Fluid fields are functions of coordinate p only.
u

u 
 u

hq h
p
p
hq h p
 
u 1 

 
u 


p  p
p
 p
v
u
aS


1

b
 2 
aS

GMP
b
2
RP aS
Two parameters specify the
dimensionless problem
GM P
b
2  10
RP aS
B R / 

 0.001
BP
3
Solutions
b

3
2 f 2  g 2 / f  2g  2 f q 2 /  2
Sonic point
f 3 2  g 2  f 2 q 2
2



H
b
1
  qH S1/ 2 exp  21   b  
S
2 
 2q
Continuity eq.
constant
f    2 , g     , and
2
3
H  f cos   g sin  , sin   q /(   2 / )
2
2
2
2
2
2
2
Sonic Surface
OUTFLOW
DEAD ZONE
Fluid Field Solutions
Mass Outflow Rates
qX
dm
 4    dq
dt
0
  (B R / ) /BP
3



b  GMP /a RP
2
S
3
Mass Outflow Rates
  (B R / ) /BP
3

3
dm
1/ 3
3
 A0 b exp b 

dt
where A0  4.8  0.13
b  GMP /a RP
2
S
Physical Outflow Rate vs Flux
MP  0.5, 0.75, 1.0MJ

Column Density
UV 1

Observational Implications
The Extreme Regime
In systems where the stellar outflow
and the stellar magnetic field
are both sufficiently strong, the
Planet can Gain Mass from the Star
Ý 105 M
ÝP 1015 g /s 1000 M
ÝSUN
M

The ZONE of
EVAPORATION
Summary
• Planetary outflows magnetically controlled
• Outflow rates are moderately *lower*
• Outflow geometry markedly different:
Open field lines from polar regions
Closed field lines from equatorial regions
• In extreme regime with strong stellar
outflow the planet could gain mass from the
star
• Outflow rates
sensitive
3
1/ 3 to planetary mass:
2
Ý
m  b exp b  ,
b  GM P /(aS RP )
Reference: F. C. Adams, 2011, ApJ, 730, 27
see also: Trammell et al. (ApJ); Trammell Poster