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On the inclination of planetary orbits! !

Caroline Terquem! University of Oxford!


Planets on inclined orbits

Higher inclinations for planets around stars with Teff>6250K?


Planet formation, Hot Jupiters and misalignments
1. If planets form by the core accretion scenario and migrate in: Hot Jupiters But no eccentricity and no misalignment (if the disc is in the star's equatorial plane) With further planet/planet scattering and/or Kozai cycles: Eccentricity and misalignment But companions required...


2. If planets form through fragmentation of a disc or protostellar envelope on a scale of 100 AU Population of massive planets (a few Jupiter masses) on randomly inclined orbits Dynamical relaxation (105-106 yrs) may produce hot Jupiters

(Papaloizou & Terquem 2001)


Possible explanation for misaligned orbits around hotter stars « Perhaps more massive stars are more likely to form systems of massive planets in unstable configurations, leading to an enhanced rate of gravitational scattering in comparison to cooler stars. »
(Winn et al. 2010)


Can orb it's in c lin ation s b e main tain ed in th e presence of a disc?


Kozai cycles with a disc
L' L I Planet's orbit

Disc

Kozai cycles if most of the disc mass is beyond the planet orbit Ic may be much smaller than 39o (Terquem & Ajmia 2010)


50 40

I (deg)

30 20 10 0 0.8 0.6

Planet: a=7 AU I=50o
10 MJu
p

1 MJu

Mp = 1 M
p

Nept

e

Disc: Mdisc=10-2 M Rin=1 AU Rout=100 AU

0.4 0.2 0 7

a (au)

6 5 4 0 time (years)

t (yr)

10

6

(Teyssandier, Terquem & Papaloizou 2013)


How to incline an orbit initially in the disc?
Wa r p e d induced

either by a perturber or by accretion from an envelope Gravitational interaction between the disc's outer parts and the planet inclination of the orbit (Terquem 2013)


Precession of the orbit
Lorb Disc ring

Ld

Planet

Circular orbits: L

orb orb

and Ld precess around L precesses around L
d

orb+Ld

Since Lorb ї Ld, L

! Inclination of the orbit varies between 0 and 2®


Evolution of the orbit's inclination
=55o When I ' 90±, no longer circulates and e grows. I: inclination of the orbit : longitude of ascending node : argument of pericentre


Evolution of the orbit's inclination
=70o The orbit becomes retrograde and e reaches very high values ! tidal circularization ! hot Jupiter on inclined orbit


How to incline an orbit initially in the disc?
Migrating planets locked in 2:1 resonance: possibility of an inclination-type resonance that pumps up the inclination of the orbit.

Requires the eccentricity of the inner planet to reach a threshold ei,res : · Numerical simulations (Thommes & Lissauer 2004) ei,res0.6 · Analysis (Teyssandier & Terquem 2014) ei,res0.3


(Teyssandier & Terquem 2014)


Conclusions
Planets up to 1 Jupiter mass could survive on inclined orbits in the presence of a disc Material with randomly oriented angular momentum may induce orbital inclination Inclination-type resonance for planets in 2:1 commensurability does not occur in general