Giant Planet Interiors

PHY 688, Lecture 17Mar 6, 2009

Mar 6, 2009 PHY 688, Lecture 17 2

Outline• Review of previous lecture

– the hydrogen burning limit– lithium and deuterium burning– atmospheric lithium as an age/mass indicator

• Giant planet interiors– comparison to brown dwarfs

• NASA’s Kepler Telescope launches tonight!– in search for other habitable worlds

Mar 6, 2009 PHY 688, Lecture 17 3

Previously in PHY 688…

Mar 6, 2009 PHY 688, Lecture 17 4

The Minimum Main-Sequence Mass

• Derive by equating nuclear energy generation toenergy loss through cooling.

• Have expression for L(M, κR, η)• Find expression for!

dE

dt+ P

dV

dt= T

dS

dt= ˙ " #

$L

$M= 0

!

˙ " (M,#)

Mar 6, 2009 PHY 688, Lecture 17 5

p-p Chain Reaction Rate in Low-MassStars Is Decided by the First Step (p+p)

take into accountCoulomb coupling

Mar 6, 2009 PHY 688, Lecture 17 6

Minimum Main Sequence Mass

• MMMSM depends on:– opacity κR (i.e., metallicity Z)– He content Y (through α(Y))

• MMMSM = 0.075 MSun at solar Y (25%), Z (1.6%)– lower for higher Y, Z

!

MMMSM = 0.0865MSun

10"2g cm"2

#R

$

% &

'

( ) I *( )I *min( )

I *( ) =* ++( )

1.509

*1.325

Mar 6, 2009 PHY 688, Lecture 17 7

Lithium and Deuterium Burningstarsbrown dwarfs“planets”

Li and H burning: at > 2.7 × 106 K

D burning: at > 4 × 105 K

(Burrows et al. 2001)

LiH

Mar 6, 2009 PHY 688, Lecture 17 8

starsbrown dwarfs“planets”

(Burrows et al. 2001)

Li and D: Depleted within Few 100Myr

50% Li depletion50% D depletion

Mar 6, 2009 PHY 688, Lecture 17 9

Lithium is Observable in the Photosphere

(Kirkpatrick et al. 1999)

Mar 6, 2009 PHY 688, Lecture 17 10

The Lithium Test for Age/Substellarity

(Basri 1997)

presence of Li:

• youth

and / or

• substellarmass

Teide 1,Calar 3

Mar 6, 2009 PHY 688, Lecture 17 11

Outline

• Review of previous lecture– the hydrogen burning limit– lithium and deuterium burning– atmospheric lithium as an age/mass indicator

• Giant planet interiors– comparison to brown dwarfs

• NASA’s Kepler Telescope launches tonight!– in search for other habitable worlds

Mar 6, 2009 PHY 688, Lecture 17 12

From Lecture 13: H Phase Diagram

(Burrows & Liebert 1993)

T

Mar 6, 2009 PHY 688, Lecture 17 13

H Phase Diagram: Revisited

• compared tobrown dwarfs, theinteriors of giantplanets are:– more strongly

degenerate (θ ≡ ηin this diagram)

– more stronglyCoulomb-coupled

(Guillot 2006)

Mar 6, 2009 PHY 688, Lecture 17 14

Polytropic Index n for Giant Planets

• brown dwarfs arepressure-supportedby degenerate non-relativistic electrongas:Pe ∝ ρ 5/3, i.e,n =1.5

• stronger electronscreening inCoulomb plasmain planetaryinteriors weakensP(ρ) dependence

(Guillot 2006)

Mar 6, 2009 PHY 688, Lecture 17 15

From Lecture 13: Radius vs. Mass

(Burrows & Liebert 1993)

Mar 6, 2009 PHY 688, Lecture 17 16

Radius vs. Mass:Comparison with Known Planets

• for polytropes

• n = 1.5 for browndwarfs

• n = 0.5–1.0 for0.1–1 MJup planets

• (n = 0: uniformdensity)

• icy/rocky cores inNeptune, Uranus?

(Guillot 2006)

!

R"M

1#n

3#n

olivine (Mg,Fe)2SiO4 planetH2O planet

Mar 6, 2009 PHY 688, Lecture 17 17

Solar System Giant Planets• Accurate masses from observations of natural satellite motions:

– Jupiter: M = 317.834 MEarth– Saturn: M = 95.161 MEarth

– Uranus: M = 14.538 MEarth

– Neptune: M = 17.148 MEarth

• Rapid rotation (~10 hrs for J+S, ~17 hrs for U+N) distortsgravitational field:– Requatorial / Rpolar = 1.02 (Neptune) to 1.11 (Saturn)– non-zero gravitational moments Ji

• Ji obtained from analysis of spacecraft trajectories during flybys– Pioneer 10+11, Voyager 1+2, Ulysses, Galileo, Cassini– axial moments of inertia substantially less than those for uniform-density

spheres– indicate central dense regions: rocky cores (?)

Mar 6, 2009 PHY 688, Lecture 17 18

A Brown Dwarf’s and Jupiter’sInteriors

(1 bar)

(4×109 bar)0.05 MSunbrown dwarf

(Guillot 2006)

Mar 6, 2009 PHY 688, Lecture 17 19

Solar System Giant Planet Interiors

• sizes of rockycores in Jupiterand Saturn arevery uncertain

• interior structureof Uranus andNeptune is evenmore uncertain

(Guillot 1999)

Mar 6, 2009 PHY 688, Lecture 17 20

The Existence of a Rocky/Icy Core inJupiter’s is Uncertain

(Guillot 2006)

• solutions for thetwo EOS’s aremutuallyinconsistent

• middle ground ispossible

• regardless:– Mcore < 10 MEarth

• < 3% by mass– Mcore could be 0

EOS discontinuous across PPT

EOS smoothly interpolated between molecular and metallic fluids

Mar 6, 2009 PHY 688, Lecture 17 21

Saturn’s Core Mass is BetterConstrained

• EOS’s that arediscontinuousor interpolatedacross PPTagree

• core mass is6–17 MEarth

– 6–18% oftotal mass

(Guillot 2006)

Mar 6, 2009 PHY 688, Lecture 17 22

Evolution of Planets and BrownDwarfs on the H-R Diagram

Evolution of brown dwarfs and planets on the H-R diagram

(Burrows et al. 1997)

Mar 6, 2009 PHY 688, Lecture 17 23

Outline

• Review of previous lecture– the hydrogen burning limit– lithium and deuterium burning– atmospheric lithium as an age/mass indicator

• Giant planet interiors– comparison to brown dwarfs

• NASA’s Kepler Telescope launches tonight!– in search for other habitable worlds

Mar 6, 2009 PHY 688, Lecture 17 24

The following slides are from Gibor Basri(UC Berkley, Kepler Co-PI)

Mar 6, 2009 PHY 688, Lecture 17 25

THE HABITABLE ZONE BYSTELLAR TYPES

The Habitable Zone (HZ) in green is the distance from a star where liquid water is expected toexist on the planets surface (Kasting, Whitmire, and Reynolds 1993).

Mar 6, 2009 PHY 688, Lecture 17 26

SEARCH RESULTS

The first 50 known extrasolar planets are also shown along with the planets in oursolar system.

The limit for planet detection using Doppler spectroscopy is shown.The range of habitable planets (0.5 to 10 M⊕) in the HZ is shown in green.

Solar planets

Extrasolar

pulsar planets

Doppler 3m/s

Semi-major Axis (AU)

Pla

ne

tary

Ma

ss (

M!

)

Orbital Period (years)

0.1

1

10

100

1000

10000

0.01 0.1 1 10 100

1 10 1000.10.01

Mar 6, 2009 PHY 688, Lecture 17 27

PHOTOMETRY CAN DETECT EARTH-SIZED PLANETS

• The relative change in brightness (ΔL) is equal to the relative areas(Aplanet/Astar)

• To measure 0.01% must get above the Earth’s atmosphere

• Method is robust but you must be patient:Require at least 3 transits, preferably 4 with same brightness change, duration and temporal separation

(the first two establish a possible period, the third confirms it)

Jupiter: 1% area of the Sun (1/100)

Earth or Venus0.01% area of the Sun (1/10,000)

Mar 6, 2009 PHY 688, Lecture 17 28

Detecting Planets withTransit Photometry

Mar 6, 2009 PHY 688, Lecture 17 29

Kepler MISSIONCONCEPT

• Kepler is the first mission optimized for findinghabitable planets ( 0.5 to 10 M⊕ )in the HZ ( near 1 AU ) of solar-like stars

• Continuously and simultaneouslymonitor 100,000 main-sequence stars

• Use a one-meter Schmidt telescope:FOV >100 deg2 with an array of 42 CCD

• Photometric precision:Noise < 20 ppm in 6.5 hours V = 12 solar-like star=> 4σ detection for one Earth-sized transit

• Mission:Heliocentric orbit for continuous viewing > 4 year duration

Mar 6, 2009 PHY 688, Lecture 17 30

Kepler Field of View

Mar 6, 2009 PHY 688, Lecture 17 31

Potential for Detections

Expected # of planets found, assuming one planet of a given size &semi-major axis per star and random orientation of orbital planes.

# of PlanetDetections

Orbital Semi-major Axis (AU)

10000

1000

100

10

10.2 10 1.40.4 1.20.80.6 1.6

Mar 6, 2009 PHY 688, Lecture 17 32

Kepler Mission LaunchMar 6, 2009

10:49pm EST

Mar 6, 2009 PHY 688, Lecture 17 33