Extrasolar Planets

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Tidal interactions of close-in extrasolar planets with their host stars

Ludmila Carone

Institut für Geophysik und Meterologie

Universität zu Köln, Cologne, Germany

5th Corot Week, 11. December 2003 in Berlin

Extrasolar Planets

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Very close-in extrasolar planets

2,414HD 49674 G5 0,12 0,057 4,948 0 27,757 1 0,981

2,3520,9563,971 0 27,757 1HD 76700 G6 0,197 0,049

2,952HD 209458 G0 0,69 0,045 3,525 0 15,7 1,05 1,2

2,4751,0063,487 0 27,757 1,1BD -10 3166 G4 0,48 0,046

2,721OGLE-TR-58 G0 1,6 0,052 4,345 0 27,757 0,99 1,106

2,7211,1063,101 0 27,757 1OGLE-TR-10 G0 0,7 0,042

2,721OGLE-TR3 G0 0,5 0,023 1,19 0 27,757  1,000 1,106

2,7061,11,212 0 18,399 1,04OGLE-TR56 G0 1,45 0,023

Stellar radius [Ro]

Roche zone [Ro]

revolution period [days]

Orbit excentricity

Stellar rotation [days]

Stellar mass [Mo]

Stellar name

Spectral type

Planetary mass [Mj]

Semi major axis [AU]

Extrasolar Planets

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Tides raised by the star on the planet

• Close-in extrasolar planets (a < 0.05 AU) experience extreme gravitational interaction

• ->Tidal bulge on planet

-> synchronous rotation (rotation = revolution)

Extrasolar Planets

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Time to reach synchronous rotation

• Tides raised by the star on the planet

• -> synchronous rotation of the planet

0

322

3

3

2

p

p

p p

p p p p

n

k RM GMQ a aM M M

sinp pM M i-> depends on planetary mass and radius

Extrasolar Planets

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Time to reach synchronous rotation all planets a < 0.20 AU

0.00 0.05 0.10 0.15 0.2010-510-410-310-210-1100101102103104105106

semi major axis [AU]

stellar rotationplanetary rotationsolar rotation by JupiterJupiter´s rotation by Sun

tim

e re

qu

ired

to

syn

chro

niz

e ro

tati

on

[G

y]

Z:exocalculationsrot_slow-down.sgr/Z14

tau Boo

Extrasolar Planets

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Tides raised by the planet on the star

• Tidal bulge on the host star

-> increase/decrease of semi major axis

-> decrease/increase of stellar rotation

Extrasolar Planets

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Tidal evolution

• Tides raised by the planet on the star decrease/increase of

semi major axis

Spin-up/decrease of star rotation

depends on planetary mass and star radius

213 13

5* P 2* * * 0

* *

13 3 k Ma(t) sign( n) R GM t a

2 Q M

113 13

* P 5* P2* *0 0 * * * 0

* * *

GM M 13 3 k M(t) a sign( n) R GM a

2 C 2 Q M

Extrasolar Planets

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The parameters k* and Q*

• Evolution time scale depends strongly on stellar love number k* and the stellar tidal dissipation factor Q*

6 7*

*

10 Q 3 10

0.02 k 0.17

6 9*

*

Q5 10 1.5 10

k

• Pätzold & Rauer (2002) favor: 8*

*

Q1 10

k

Extrasolar Planets

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OGLE-TR-56b (an extreme planet)

• OGLE-TR-56b was discovered during the OGLE-survey (Konacki et al, 2003)

• Parameters:

P J

P J

true J

M sin i 1.45 0.23 M

R 1.23 0.16 R

a 0.0225 0.0004 AU

e 0 Inclination 81 2.2 deg

M 1.47 0.25 M

• extremly close distance to its host star & large mass -> very strong tidal interactions

Extrasolar Planets

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OGLE-TR-56b: Evolution of semi major axis

0 1 2 3 4 5 60.01

0.015

0.02

evolution time [Gyr]

sem

i m

ajor

axi

s [A

U]

Qstar

kstar1.5 109

Qstar

kstar

Qstar

kstar108

Qstar

kstarQstar

kstar5 106

Qstar

kstar

roche limit

Extrasolar Planets

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OGLE-TR-56b: Evolution of stellar rotation

0 1 2 3 4 55

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

evolution time [Gyr]

stel

lar

rota

tion

[da

ys]

Qstar

kstar1.5 109

Qstar

kstarQstar

kstar108

Qstar

kstar

Qstar

kstar5 106

Qstar

kstar

Extrasolar Planets

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OGLE-TR-56b: Evolution of stellar rotation(only in convection envelope)

0 1 2 3 4 50

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

evolution time [Gyr]

stel

lar

rota

tion

[da

ys]

Qstar

kstar1.5 109

Qstar

kstarQstar

kstar108

Qstar

kstar

Qstar

kstar5 106

Qstar

kstar

Extrasolar Planets

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Time to reach roche limit

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.0550.1

1

10

100

1 103

1 104

1 105

1 106

semi major axis [AU]

tim

e to

rea

ch r

oche

lim

it [

Gyr

]

Extrasolar Planets

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Conclusion

• OGLE-TR-56b may reach the roche limit within the lifetime of its host star

• Tidal effects could lead to a considerable spin up in stellar rotation

• Even more so, when only spin-up in convection envelope is considered (no friction between core and envelope)

• The strength of tidal effects depends strongly on the planet‘s mass and the semi major axis

• But for a better prediction the geophyisical properties Q* and k* have to be determined -> we need more data

Extrasolar Planets

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Very close-in extrasolar planets

2,414HD 49674 G5 0,12 0,057 4,948 0 27,757 1 0,981

2,3520,9563,971 0 27,757 1HD 76700 G6 0,197 0,049

2,952HD 209458 G0 0,69 0,045 3,525 0 15,7 1,05 1,2

2,4751,0063,487 0 27,757 1,1BD -10 3166 G4 0,48 0,046

2,721OGLE-TR-58 G0 1,6 0,052 4,345 0 27,757 0,99 1,106

2,7211,1063,101 0 27,757 1OGLE-TR-10 G0 0,7 0,042

2,721OGLE-TR3 G0 0,5 0,023 1,19 0 27,757  1,000 1,106

2,7061,11,212 0 18,399 1,04OGLE-TR56 G0 1,45 0,023

Stellar radius [Ro]

Roche zone [Ro]

revolution period [days]

Orbit excentricity

Stellar rotation [days]

Stellar mass [Mo]

Stellar name

Spectral type

Planetary mass [Mj]

Semi major axis [AU]

Extrasolar Planets

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OGLE-TR-3b: Evolution of semi major axis

0 1 2 3 4 5 60.012

0.014

0.016

0.018

0.02

0.022

0.024

evolution time [Gyr]

sem

i m

ajor

axi

s [A

U]

Qstar

kstar1.5 109

Qstar

kstar

Qstar

kstar108

Qstar

kstar

Qstar

kstar5 106

Qstar

kstar

roche limit

Extrasolar Planets

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OGLE-TR-3b: Evolution of stellar rotation

0 1 2 3 4 5 618

20

22

24

26

28

evolution time [Gyr]

stel

lar

rota

tion

tim

e [d

ays]

Qstar

kstar1.5 109

Qstar

kstar

Qstar

kstar108

Qstar

kstar

Qstar

kstar5 106

Qstar

kstar

Extrasolar Planets

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OGLE-TR-3b: Evolution of stellar rotation(only in convection envelope)

0 1 2 3 4 5 65

10

15

20

25

30

evolution time [Gyr]

stel

lar

rota

tion

tim

e [d

ays]

Qstar

kstar1.5 109

Qstar

kstar

Qstar

kstar108

Qstar

kstar

Qstar

kstar5 106

Qstar

kstar