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					    Extrasolar Planets




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




                                            Z:\exo\presentations\EGS2001_exo.ppt, 08.05.2013 08:53AM, 1
              Extrasolar Planets

                       Very close-in extrasolar planets

                                                revolution                 Stellar
Stellar     Spectral   Planetary     Semi major period        Orbit        rotation          Stellar         Stellar     Roche zone
name        type       mass [Mj]     axis [AU]  [days]        excentricity [days]            mass [Mo]       radius [Ro] [Ro]

OGLE-TR56 G0                  1,45         0,023      1,212              0      18,399               1,04               1,1           2,706

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

OGLE-TR-10 G0                  0,7         0,042      3,101              0      27,757                   1           1,106            2,721

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

BD -10 3166 G4                0,48         0,046      3,487              0      27,757                1,1            1,006            2,475

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

HD 76700    G6               0,197         0,049      3,971              0      27,757                   1           0,956            2,352

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




                                                                              Z:\exo\presentations\EGS2001_exo.ppt, 08.05.2013 08:53AM, 2
       Extrasolar Planets

        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)
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      Extrasolar Planets

        Time to reach synchronous rotation
• Tides raised by the star on the planet
      • -> synchronous rotation of the planet

                                    n   p0
               p                                      3
                        3k2 p       M
                                      2
                                                Rp  GM
                                                   
                       2 pQp M p  M p  M   a  a3


         -> depends on planetary mass and radius
                               Mp  Mp sin i



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Extrasolar Planets

  Time to reach synchronous rotation
                                                                 all planets a < 0.20 AU



         time required to synchronize rotation [Gy]
                                                      106
                                                      105
                                                      104
                                                      103
                                                      102
                                                      101
                                                                         tau Boo
                                                      100
                                                      10-1
                                                      10-2                         stellar rotation
                                                      10-3                         planetary rotation
                                                                                   solar rotation by Jupiter
                                                      10-4                         Jupiter´s rotation by Sun
                                                      10-5
                                                          0.00    0.05      0.10       0.15                                 0.20
   Z:exocalculationsrot_slow-down.sgr/Z14                            semi major axis [AU]
                                                                                   Z:\exo\presentations\EGS2001_exo.ppt, 08.05.2013 08:53AM, 5
      Extrasolar Planets

       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
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        Extrasolar Planets

                             Tidal evolution

• Tides raised by the planet on the star
       decrease/increase of
            semi major axis
                                                                                2
        13           3  k* M P 5
                                                13
                                                                              13
a(t)   sign(*  n)           R * GM*  t  a 0 
                                                 2

       2              Q* M*                       
        Spin-up/decrease of star rotation
                          13                                       1
                                                                          
               GM*  M P  2 13                3  k* M P 5      13
* (t)  *0               a 0  sign(*  n)           R * GM*   a 0 
                2  C*                                                   
                                2              Q* M*                   
                                                                         
           depends on planetary mass and star radius

                                             Z:\exo\presentations\EGS2001_exo.ppt, 08.05.2013 08:53AM, 7
        Extrasolar Planets

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

                     10  Q*  3 10
                         6               7


                      0.02  k*  0.17
                            Q*
                5 10      6
                                  1.5 10 9

                            k*
   •   Pätzold & Rauer (2002) favor: Q*
                                           1 10 8

                                      k*
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      Extrasolar Planets

         OGLE-TR-56b (an extreme planet)

• OGLE-TR-56b was discovered during the OGLE-survey
  (Konacki et al, 2003)
• Parameters:
              M P  sin i  1.45  0.23 M J
              R P  1.23  0.16 R J
              a  0.0225  0.0004 AU
              e  0 Inclination  81  2.2 deg
              M true  1.47  0.25 M J

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


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


                                                                                                      Qstar                    9
                                                                                                                1.5  10
                            0.02                                                                     kst ar
  sem i m ajor axis [AU]




                                                                                    Qstar             8
                                       Qstar            6                                     10
                           0.015                 5  10                           kst ar
                                       kst ar




                                           roche limit

                            0.01
                                   0             1          2               3                 4                   5                    6
                                                                evolution tim e [Gy r]


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  Extrasolar Planets


OGLE-TR-56b: Evolution of stellar rotation
                              20
                              19

                              18
                              17

                              16
                              15                                                              Qstar                   9
                                                                                                        1.5  10
    stellar rotation [days]




                              14                            Qstar        8
                                                                                              kst ar
                                                                      10
                              13                            kst ar
                              12
                              11

                              10

                              9

                              8        Qstar            6
                                                 5  10
                              7        kst ar
                              6

                              5
                                   0                1         2                    3                       4                        5
                                                              evolution time [Gyr]



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           Extrasolar Planets

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

                            20
                            19
                            18
                            17
                            16
                            15
                            14
                                                                                                 Qstar                    9
                            13                                                                             1.5  10
  stellar rotation [days]




                            12                                Qstar        8
                                                                                                 kst ar
                            11                                          10
                                                              kst ar
                            10
                             9
                             8
                            7
                            6
                            5
                            4        Qstar             6
                            3                  5  10
                                     kst ar
                            2
                            1
                            0
                                 0                1             2                    3                        4                         5
                                                                evolution time [Gyr]
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Extrasolar Planets


                                                   Time to reach roche limit
                                   1 10
                                           6




                                   1 10
                                           5




                                   1 10
                                           4
 time to reach roche limit [Gyr]




                                   1 10
                                           3




                                      100



                                           10



                                               1



                                       0.1
                                          0.02      0.025   0.03   0.035          0.04          0.045         0.05           0.055
                                                                        sem i m aj or axis [AU]


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      Extrasolar Planets

                           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


                                     Z:\exo\presentations\EGS2001_exo.ppt, 08.05.2013 08:53AM, 14
              Extrasolar Planets

                       Very close-in extrasolar planets

                                                revolution                 Stellar
Stellar     Spectral   Planetary     Semi major period        Orbit        rotation          Stellar         Stellar     Roche zone
name        type       mass [Mj]     axis [AU]  [days]        excentricity [days]            mass [Mo]       radius [Ro] [Ro]

OGLE-TR56 G0                  1,45         0,023      1,212              0      18,399               1,04               1,1           2,706

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

OGLE-TR-10 G0                  0,7         0,042      3,101              0      27,757                   1           1,106            2,721

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

BD -10 3166 G4                0,48         0,046      3,487              0      27,757                1,1            1,006            2,475

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

HD 76700    G6               0,197         0,049      3,971              0      27,757                   1           0,956            2,352

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




                                                                              Z:\exo\presentations\EGS2001_exo.ppt, 08.05.2013 08:53AM, 15
                   Extrasolar Planets


OGLE-TR-3b: Evolution of semi major axis
                          0.024


                                                                                                      Qstar                      9
                          0.022                                                                                   1.5  10
                                                                                                      kst ar

                                                                                       Qstar             8
                           0.02                                                                    10
 sem i m ajor axis [AU]




                                                                                       kst ar

                          0.018
                                      Qstar           6
                                                5  10
                                      kst ar
                          0.016



                          0.014
                                      roche limit

                          0.012
                                  0       1               2               3                   4                     5                    6
                                                              evolution tim e [Gy r]
                                                                                       Z:\exo\presentations\EGS2001_exo.ppt, 08.05.2013 08:53AM, 16
 Extrasolar Planets


OGLE-TR-3b: Evolution of stellar rotation
                                 28


                                                                                                             Qstar               9
                                                                                                                       1.5  10
                                                                                                             kst ar
                                 26

                                                                                         Qstar           8
                                                                                                       10
                                                                                         kst ar
  stellar rotation time [days]




                                 24




                                 22
                                          Qstar           6
                                                    5  10
                                          kst ar

                                 20




                                 18
                                      0        1              2              3                    4                   5                 6
                                                                  evolution time [Gyr]


                                                                                     Z:\exo\presentations\EGS2001_exo.ppt, 08.05.2013 08:53AM, 17
 Extrasolar Planets

OGLE-TR-3b: Evolution of stellar rotation
                                                     (only in convection envelope)
                                 30




                                 25
                                                                                                         Qstar                   9
                                                                                                                   1.5  10
                                                                                                         kst ar
  stellar rotation time [days]




                                 20

                                                                                  Qstar             8
                                                                                              10
                                                                                  kst ar
                                 15
                                          Qstar           6
                                                    5  10
                                          kst ar

                                 10




                                  5
                                      0        1              2              3                  4                    5                    6
                                                                  evolution time [Gyr]
                                                                                         Z:\exo\presentations\EGS2001_exo.ppt, 08.05.2013 08:53AM, 18

				
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