Orbital Evolution of Planets
around Evolving Low- andIntermediate-Mass Stars
Masahiro IKOMA(Tokyo Tech, Japan)

INTRODUCTION
Planet Formation around Solar-Type Stars
observation

theoryIda & Lin (2004)

Obs.

1MSun star:
2-3MSun star:

Disks theory Planets<pre-MS>
DisksObs.

theoryPlanets <post-MS> Planets

INTRODUCTION

planet mass Mpsini (MJ)

Orbits of Planets around Evolved Stars▲low-mass giants (~1-1.5MSun)▲ clump giants (~2-3 MSun)○ solar-type dwarfs (0.8-1.2 MSun)

10?
1Detection Limit(Radial Velocity)~10-20 m/s0.1
0.01
0.01

0.1
1
semi-major axis (AU)10

Detection Limit(Time)~3 AU

No planet inside ~ 0.6AU around giants.

Data from: www. exoplanet.eu
Sato et al. (2008)

INTRODUCTION
Orbits of Planets around Evolved Stars▲low-mass giants (~1-1.5MSun)▲ clump giants (~2-3 MSun)○ solar-type dwarfs (0.8-1.2 MSun)--- periapsis = 0.04AU

1.0

eccentricity

0.8

Data from: www. exoplanet.eu
Sato et al. (2008)

0.6
0.4
0.2
0.0
0.01

0.1
1
semi-major axis (AU)10

Eccentricities of the planets around clump giants are
small relative to those around solar-type dwarfs.

INTRODUCTION
Post-Main-Sequence Evolution
4log L (Lsun)

321BAF GKM

Do such properties result
from the evolution of theirparent stars?

▲low-mass giants▲clump giants

3Evolution = Expansion

2.5
2

INFLATED PARENT STAR(1) engulf planets

1.50
Zi = 0.02

1Msun(2) exert a tidal force on planets-1
4.1 4.0 3.9 3.8 3.7 3.6 3.5 (3) lose its mass, which results
pushing planets outwardlog Te (K)(Stellar Data from Lejeune & Schaerer 2001)

INTRODUCTION
Fate of the Solar System (Previous Studies)

R*(t)/RSunlog R*/RSunEarthVenusage (Gyr)(Sackmann et al. 1993)

M*(t)/MSun(Rasio et al. 1996)

Orbital Evolution of Planets = Tide vs. Mass LossSIMULATION OF PLANETARY ORBIT EVOLUTION
Assumptions, Equations, etc.
MAJOR Assumptions:• equilibrium tide • fully convective envelope• stellar rotation << planetary revolution

EQUATIONS:mass loss

: convective friction time;: apsidal constant

STELLAR MODELS: Lejeune & Schaerer (2001)
PARAMETERS:• Stellar mass, Ms = 1.0, 1.5, 2.0, 2.5, 3.0 MSun
• Planetary mass, mp = 1, 10 MJup

• Metalicity, Z = 0.02

• Initial orbit, a = 0.1-2AU & e = 0.01-0.9

SIMULATION OF PLANETARY ORBIT EVOLUTION
Examples of Orbital Evolution
Ikoma et al. (in prep.)1

length (AU)observedsemimajor axis, a0.1

RGB

periapsis, a (1-e)

0.01

HB

stellar radius

0Ms = 2.5MSun
Z = 0.02
mp = 1MJupeinit = 0.5

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

age (Gyr)• Both a and e decrease in such a way that periapsis is kept constant.

• Stellar mass loss makes a negligible contribution.

SIMULATION OF PLANETARY ORBIT EVOLUTIONa & e in HB (2.5MSun Star)
1

Ikoma et al. (in prep.)

Ms = 2.5MSun
Z = 0.02
mp = 1MJup

eccentricity

0.8
0.6
0.4
0.2
00.1

0.2 0.3 0.5
12semimajor axis (AU)3

• Planets at a(1-e) > ~ 2x Rpeak survive RGB phase.

• Eccentricity ranges between 0 and 0.8 for a < 2 AU.

SIMULATION OF PLANETARY ORBIT EVOLUTIONa & e in HB: Sensitivity to Planet Mass
1eccentricity

0.8

Ikoma et al. (in prep.)○ mp = 1MJup, × mp = 10MJup
Ms = 2.5MSun Z = 0.02

1MJup
10 MJup

0.6
0.4
0.2
00.1

0.2 0.3 0.5
12semimajor axis (AU)3

Effect of stellar tide is somewhat stronger for more massive planets.

SIMULATION OF PLANETARY ORBIT EVOLUTION

a & e in HB: Sensitivity to Stellar Metalicity
1

Ikoma et al. (in prep.)○ Z = 0.001 ○ Z = 0.02
Ms = 2.5MSun, mp = 1MJup

eccentricity

0.8▲ detected planets

0.6
0.4
0.2
00.1

0.2 0.3 0.5
12semimajor axis (AU)3

Effects of different stellar metalicity seem to be small.

SIMULATION OF PLANETARY ORBIT EVOLUTION

a & e in HB: Sensitivity to Stellar Mass1

○ 3.0MSun ○ 2.5MSun ○ 2.0MSun

Ikoma et al. (in prep.)Z = 0.02, mp = 1MJup

eccentricity

0.8▲ detected planets

0.6
0.4
0.2
00.1

0.2 0.3 0.5
12 3
semimajor axis (AU)• Eccentricities of detected clump giants are low.  initially low?
• Measured semimajor axes are somewhat larger.  initially distant?

ORIGIN OF LOW ECCENTRICITIES AROUND CLUMP GIANTS
Widespread Idea forthe origin of eccentric planets
around solar-type stars

OrbitalInstability
Eccentric Planet
and/or
Hot Jupitere.g., Weidenschiling et al.

ORIGIN OF LOW ECCENTRICITIES AROUND CLUMP GIANTS
How can we explain it?
Formation of gas-giant planets is less frequent aroundintermediate-mass stars than around solar-type stars.
Multi-planet systems are rare, so that orbital instability
rarely happens around intermediate-mass stars.
Ikoma et al. (in prep.)

DISCUSSION: ORIGIN OF LOW-ECCENTRICITIESCorrelation between
Stellar Metalicity and Planetary Eccentricity
in the case of Solar-Type Stars

planet’s eccentricity

1.0

www.exoplanet.eu

0.5

0.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
parent star’s metalicity, [Fe/H]SIMULATION OF PLANETARY ORBIT EVOLUTION
Low-Mass Giants
1eccentricity

0.8○ 1MSun ○ 1.5MSun

Ikoma et al. (in prep.)Z = 0.02, mp = 10MJup▲ detected planets

0.60.40.2
00.1

1
semimajor axis (AU)10

• Two of them are consistent with our results• The other three seem not to have undergone RGB phases.

Summary and Conclusions
 I have simulated orbital evolution of planets aroundevolving low- and intermediate-mass stars.
 Clump giants

Planets of a < 0.5AU are likely to have been engulfed by theirparent stars, which is, however, not fully consistent withobservational results.
 Our theoretical model that assumes the planets’ eccentricities
in the MS phase range uniformly from 0 to ~1 does notaccount for low eccentricities of the detected planets, which
may means their eccentricities were originally low.
 Low-mass giantsSome of them seem not to have yet undergone the RGB phaseof their parent stars.

Need more samples!