Hot Jupiter Radii and
Spectroscopic Transits
PHY 688, Lecture 25
Mar 25, 2009

Outline
• Review of previous lecture:
– hot Jupiters
• surface temperature gradients
• winds
• phases and optical albedo
• Radii
• Spectroscopic transits
– the Rossiter-McLaughlin Effect
Mar 25, 2009 PHY 688, Lecture 25 2

Previously in PHY 688…
Mar 25, 2009 PHY 688, Lecture 25 3

Atmospheric Dynamics of Hot Jupiters
Mar 25, 2009 PHY 688, Lecture 25 4

Non-Uniform Planet Surface Brightness
• hot Jupiters are tidally locked to their host stars:
– orbital and rotation period are the same
(~1–5 days)
– sub-stellar point does not change
• however, peak planet brightness does not coincide with moment of secondary eclipse
– redistribution of heat
Mar 25, 2009 PHY 688, Lecture 25
HD 189733 at 8 µ m
(Knutson et al. 2007)
5

HD 189733b Brightness Map
• brightest spot is not at the substellar point
• brightest and faintest spot on
HD 189733b are on the same hemisphere!
• temperature difference is
~350 K
(Knutson et al. 2007)
Mar 25, 2009 PHY 688, Lecture 25 6

Non-Uniformity in Brightness
Depends on Incident Flux
• in fact, HD 189733b has a relatively homogenized daynight atmosphere
– ~350 K difference in temperature
– pL planet, no temperature inversion
• much larger day-night contrast inferred on υ And b,
HD 179949b
– ~1400 K at υ And b
– pM planets, temperature inversions
Mar 25, 2009 PHY 688, Lecture 25 7

Radiative
(Newtonian)
Cooling
• temperature disturbance relaxes toward radiative equilibrium exponentially, with time constant t rad
• for atmospheric P, T : t rad
~
P g c
P
4 " T 3
!
Mar 25, 2009 PHY 688, Lecture 25 (Fortney et al. 2008) 8

!
Winds:
Cooling vs.
Advection
• advection time scale t advec
– R
= p
R p
/ U
– planet radius
– U – wind speed
• balance of cooling vs.
advection decides wind speed U
" T day – night
" T rad
~ 1 # e # t advec
/ t rad
• winds of several km/sec
(~ sound speed) expected from 2D and 3D dynamical models
Mar 25, 2009 PHY 688, Lecture 25
U
(Fortney et al. 2008) 9

Winds: t rad
/ t advec
Ratio Depends
Also on Depth
!
• ratio is higher in the lower atmosphere
– especially in pM planets with stratospheres:
" T day – night
" T rad
~ 1 # e # t advec
/ t rad
• smaller day-night contrast (more redistribution of heat) in:
– deeper layers
– pL planets
Mar 25, 2009 PHY 688, Lecture 25 (Fortney et al. 2008) 10

Observations in Optical Reflected Light:
Phases of Hot Jupiters
Mar 25, 2009 PHY 688, Lecture 25 (Rowe et al. 2006) 11

HD 209458b: No Phase Variation Seen
MOST satellite data HD 209458: original time series standard star: original time series
HD 209458: folded to P = 3.52 d
0
0.02
0
5 × 10 –4
Mar 25, 2009 region of expected secondary eclipse
HD 209458: folded, binned and zoomed
PHY 688, Lecture 25
(Rowe et al. 2006)
12

Hot Jupiters are Very Dark in the Optical
• 500–800 nm opacity dominated by neutral alkali lines
Mar 25, 2009 PHY 688, Lecture 25 13

Outline
• Review of previous lecture:
– surface temperature gradients
– winds
– phases and optical albedo
• Radii
• Spectroscopic transits
– the Rossiter-McLaughlin Effect
Mar 25, 2009 PHY 688, Lecture 25 14

!
From Lecture 17 : Radius vs. Mass:
Comparison with Known Planets
• for polytropes
1 # n
R " M 3 # n
• n = 1.5 for brown dwarfs
• n = 0.5–1.0 for 0.1–1
M
Jup
planets
• ( n = 0: uniform density)
• icy/rocky cores in
Neptune, Uranus?
• the hot Jupiter HD
209458b has a larger radius than nonirradiated planets
H
2
O planet olivine (Mg,Fe)
2
SiO
4
planet
Mar 25, 2009 PHY 688, Lecture 25 (Guillot 2006) 15

Sizes and Structure of Giant Planets:
Very Hot Jupiters Are Larger pL planet pM planet
PHY 688, Lecture 25
(Charbonneau et al. 2007)
16 Mar 25, 2009

Radii of Very
Hot Jupiters
• some large radii cannot be explained by coreless planet models with high-altitude stratospheres:
– extra internal power source?
• stratospheric heat trap
• tidal heating
• damping or orbital eccentricity and apparent resetting of planet age?
– host stars are giga-years old
Mar 25, 2009 PHY 688, Lecture 25
(Fortney et al. 2007)
17

Are Very Hot Jupiters Younger?
Mar 25, 2009 PHY 688, Lecture 25
(Fortney et al. 2007)
18

Jupiter’s Evolution in the Solar System
Mar 25, 2009 PHY 688, Lecture 25 19

Radii of Very
Hot Jupiters
• some large radii cannot be explained by coreless planet models with high-altitude stratospheres:
– extra internal power source?
• stratospheric heat trap
• tidal heating
• damping or orbital eccentricity and apparent resetting of planet age?
– host stars are giga-years old
– preferential evaporation of neutral helium?
Mar 25, 2009 PHY 688, Lecture 25
(Fortney et al. 2007)
20

Larger Radii through Evaporation of
Neutral Helium
• material evaporated form planet carries both H and He
• H is ionized, He is not
– this depends strongly in strength of
EUV emission from host star
– 10,000K temperature is in between ionization points
• strong planetary magnetic field could limit loss of charged H ions without affecting neutral He loss
• decrease of mean molecular weight at constant entropy: larger radius
Mar 25, 2009
(Hansen & Barman 2007)
PHY 688, Lecture 25 21

Outline
• Review of previous lecture:
– surface temperature gradients
– winds
– phases and optical albedo
• Radii
• Spectroscopic transits
– the Rossiter-McLaughlin Effect
Mar 25, 2009 PHY 688, Lecture 25 22

Rossiter-McLaughlin Effect
• change of apparent radial velocity of host star during transit of secondary companion
• Rossiter (1924), McLaughlin (1924): “rotational” effect
Mar 25, 2009 PHY 688, Lecture 25 23

Rossiter-McLaughlin Effect
• first detected in eclipsing binary stars
– as in bottom panel
• effective Doppler shift of (absorption) line changes depending on the part of the host star that is occulted
Mar 25, 2009 PHY 688, Lecture 25 (Gaudi & Winn 2007) 24

RM Effect Geometry
• seek to measure angle λ between projected stellar rotation axis and planetary orbital axis
Mar 25, 2009
(Ohta et al. 2005)
• note: Ω
S and V
sin I
S sin I s
here is the same as V s
sin I s
in the following slides: the projected stellar spin rate
PHY 688, Lecture 25 25

RM Effect Geometry
• shape of deviation from normal radial velocity signature depends on λ
Mar 25, 2009 PHY 688, Lecture 25
(Gaudi & Winn 2007)
26

RM Effect Geometry
• shape of deviation from normal radial velocity signature depends on λ
– differentiate prograde vs. retrograde planetary orbits
Mar 25, 2009 PHY 688, Lecture 25
(Ohta et al. 2005)
27

RM Effect Magnitude
• depends on stellar rotation rate and planet-star radius ratio γ = R p
/ R s
– photometric measurements of transit give precise and independent measure of γ
Mar 25, 2009 PHY 688, Lecture 25
(for γ << 1)
(Gaudi & Winn 2007) 28

Observations of RM Effect Due to
Planet Transits
• first observed in
HD 209458b in
2000
• shown here for
TrES-1
– only third such observation
– independent
I s
V shape of stellar spectral lines s sin
constrain from
Mar 25, 2009 PHY 688, Lecture 25
(Narita et al. 2007)
29

RM Effect in TrES-1
Mar 25, 2009 PHY 688, Lecture 25
(Narita et al. 2007)
30

Summary of RM Effect Observations for Transiting Planets
• measure projected spin-orbit angle λ
•
• infer constraints on actual spin-orbit angle ψ
ψ peak
< 22º at 95% confidence
• broadly consistent with planet formation in a disk, no major orbital disturbance
(Fabrycky & Winn 2009) 31 Mar 25, 2009 PHY 688, Lecture 25

The RM Effect: Other Applications
• very sensitive to
– V sin I s
(projected stellar rotation velocity)
– R p
, R s
– a (orbital semi-major axis)
– i (orbital inclination)
• shown is plot of for various parameters p
• useful for
– studying planet atmospheres
– detecting/confirming wide planets
Mar 25, 2009 PHY 688, Lecture 25 (Ohta et al. 2005) 32

Using the RM Effect to Probe
Atmospheric Composition
• employ the strong R p
/R s
dependence
Mar 25, 2009 PHY 688, Lecture 25 (Dreizler et al. 2009) 33

Detecting Exo-Earth’s through the
RM Effect
Earth’s r.v. and
RM signature
• note: i and I are the same variable in the top equation above
Mar 25, 2009 PHY 688, Lecture 25 (Gaudi & Winn 2007) 34