Stability of multiplanet systems in and around habitable zones

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Stability of multiplanet systems in and around
habitable zones

• Ravi kumar Kopparapu (CGWP, Penn State)
• Rory Barnes (LPL, University of Arizona)

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Packed Planetary systems (PPS)

• Many known systems are found near instability
  (Barnes Quinn2004)
• Does this mean that they are packed ? (Barnes
  Raymond 2004)
• If regions of stability are available in
  between two known planets, then it will
  harbor an unseen planet.
• 3 out of 4 systems predicted to have planets by
  PPS have been confirmed HD 74156, HD 37124 and
  55 Cnc

3
Hill Lagrange stability

• Two kinds of stability
• Hill stability Ordering of planets is
  conserved, outer planet may escape for two
  planet system
• Lagrange stability Ordering of planets is
  conserved, planets (and their a and e ) remain
  bounded.
• Previous studies have shown that, for a two
  planet non-resonant systems, these boundaries are
  almost identical. Barnes Greenberg (2006,
  2007)

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Stability of planetary systems in HZs
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Stability of single planet systems in HZs
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Stability of two planet systems
Planet a 1 Jup, a0.6 AU, e 0 Planet b 3
E, a 1.0 AU, e 0 Planet c 1 Jup,
a1.4-4.0 AU, e 0, 0.6
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Stability of two planet systems
Planet a 1 Jup, a0.6 AU, e 0 Planet b 30
E, a 1.0 AU, e 0 Planet c 1 Jup,
a1.4-4.0 AU, e 0, 0.6
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Stability of two planet systems
Planet a 1 Jup, a0.6 AU, e 0 Planet b
300 E, a 1.0 AU, e 0 Planet c 1 Jup,
a1.4-4.0 AU, e 0, 0.6
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Summary/Future work

• Hill-stability can easily identify stable,HZ
  orbits.
• Hill-stability can also determine if a two planet
  system is packed (PPS)
• A stable region may harbor a planet with any
  mass.
• Dependence on m e of inner planet for single
  planet systems.
• Current RV limits can constrain companion mass
  orbital parameters that are stable in EHZ

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END
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Summary/Future work

• Large regions of stability in HZ of single
  planet systems gt More hidden planets (PPS)
• Current RV limits can constrain companion mass
  orbital parameters that are stable in EHZ
• It appears that for two-planet systems, the
  stability boundary is independent of the mass of
  the hypothetical planet.
• Dependence on m e of inner planet for single
  planet systems.
• Successful prediction of a companion in single
  planet systems ?

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Observed extrasolar planets (DELETE)

• 329 planets (www.exoplanet.eu)
• 281 planetary systems (www.exoplanet.eu)
• 34 multi-planet systems
• Likely more multi-planet
• Systems will be observed.

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Stability of multi-planet systems

• Whats the point ? To find more planets.
• Look for any signs of hidden planet
• Studying long term stability may uncover hidden
  planets, followed up by observations.
• Long term stability ? A stable orbit,
  without an ejection in 106 years.
• Goal A stable habitable planet
• DELETE

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Stability of single planet systems in HZs (DELETE)

• Hill stability
• Stability criterion ß gt ßcrit

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Stability of single planet systems in HZs
(DELETE)

• EHZ Barnes et al.(2008)
• The range of orbits for which a planet
  receives as much flux over an orbit as a planet
  on a circular orbit in a HZ Kasting et
  al.(1993)
• Delete eqution
• Dele

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Stability of single planet systems in HZs
(Delete)

• Hill stability
• Stability criterion ß gt ßcrit

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Stability of single planet systems in HZs
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Stability of two planet systemsDELETE
10 Earth mass
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Packed Planetary systems (PPS)

• Barnes Quinn(2004) found that several systems
  are near instability, meaning slight perturbation
  results in ejections (they are packed to the
  limit).
• This led to PPS, which proposes that systems
  tend to form dynamically packed planets (Barnes
  Raymond(2004))
• If regions of stability are available in
  between two known planets, then it will
  harbor an unseen planet.
• Observational evidence for 3 out of 4 systems
  predicted to have planets by PPS HD 74156, HD
  37124 and 55 Cnc, Bean et al. (2007), Fisher et
  al.(2007)

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Stability of single planet systems in HZs
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Stability of single planet systems in HZs