Planets-disc interactions and the early orbital evolution of planetary systems
Clément Baruteau Institute of Research in Astrophysics and Planetology, CNRS/University of Toulouse Protoplanetary Disk Dynamics and Planet Formation Workshop, Yokohama, 2 October 2015 1
Objectives and outline Give a practical overview of the physical processes that drive the orbital evolution of planets in their protoplanetary disc → low-mass (terrestrial) planets → massive (Jovian) planets
Discuss how models of planet-disc interactions can explain some of the properties of the exoplanets
2
Planets formation and orbital evolution planet formation planetesimal or pebble accretion?
disc collapse?
star
protoplanetary disc
3
Planets formation and orbital evolution planet-disc interactions
planet formation planetesimal or pebble accretion?
change planets semi-major axes (planetary migration) damp eccentricities and inclinations
disc collapse? ?
star
protoplanetary disc
4
Planets formation and orbital evolution planet-disc interactions change planets semi-major axes (planetary migration)
planet formation planetesimal or pebble accretion?
damp eccentricities and inclinations disc collapse?
planet-planet interactions also change semi-major axes! pump eccentricities and inclinations star
protoplanetary disc
5
Planets formation and orbital evolution disc dispersal
. interactions with the central star (tides, stellar evolution) or with nearby stars (e.g., Kozai cycles) . planet-planet interactions . planets-debris disc interactions (further formation of terrestrial planets and migration)
star
6
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Baruteau+ 14 in Protostars & Planets VI
-0.05
0.00
0.05
0.10
0.00
0.05
0.10
← gas density perturbation by a 5 Earth-mass planet
4
3
2
1
0
-0.05
1.5 protoplanetary gas disc
1.0 w
ak e
planet
-0.5 co-orbital perturbations
ke
star
0.0
wa
y / rp
0.5
-1.0 -1.5 -1.5
-1.0
-0.5
0.0 x / rp
0.5
1.0
1.5 7
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Baruteau+ 14 in Protostars & Planets VI
-0.05
0.00
0.05
0.10
0.00
0.05
0.10
← gas density perturbation by a 5 Earth-mass planet
4
3
2
1
0
-0.05
1.5 protoplanetary gas disc
1.0
The disc exerts a torque on the planet: w
0.5
ak e
planet
rp
-0.5 co-orbital perturbations
with Jp the planet’s angular momentum
For a planet on a circular and coplanar orbit, p Jp = Mp GM? rp [2]
-1.0 -1.5 -1.5
[1] + [2] →
-1.0
-0.5
0.0 x / rp
0.5
[1]
It changes the planet’s semi-major axis, eccentricity and inclination ke
0.0
wa
y / rp
= dJp /dt
1.0
1.5
drp /dt =
⇥ 2rp /Jp
8
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Baruteau+ 14 in Protostars & Planets VI
-0.05
0.00
0.05
0.10
0.00
0.05
0.10
← gas density perturbation by a 5 Earth-mass planet
4
3
2
1
0
-0.05
1.5
1.0 w
y / rp
0.5
ak e
Torque on planet by inner wake
rp
0.0
⇠ r p ⇥ F' > 0 → moves planet further out
-0.5
-1.0 -1.5 -1.5
-1.0
-0.5
0.0 x / rp
0.5
1.0
1.5 9
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Baruteau+ 14 in Protostars & Planets VI
-0.05
0.00
0.05
0.10
0.00
0.05
0.10
← gas density perturbation by a 5 Earth-mass planet
4
3
2
1
0
-0.05
1.5
1.0
rp
0.0
ke
-0.5
Torque on planet by outer wake
wa
y / rp
0.5
⇠ r p ⇥ F' < 0
-1.0
→ moves planet further in!
-1.5 -1.5
-1.0
-0.5
0.0 x / rp
0.5
1.0
1.5 10
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
-0.05
Baruteau+ 14 in Protostars & Planets VI
0.00
0.05
0.10
0.05
0.10
4
3
2
1
0
-0.05
0.00
0.05
0.10
0.00
0.05
0.10
-0.05
0.00
4
3
2
1
0
-0.05
0.3
1.0
0.2
ke
wa
1.5
0.1
y / rp
y / rp
0.5
0.0
0.0
-0.1
wake
-0.5 -0.2
-1.0 -0.3
-1.5 -1.5
-1.0
-0.5
0.0 x / rp
0.5
1.0
1.5
0.85 0.90 0.95 1.00 1.05 1.10 1.15 x / rp
The total wake torque is (generally) negative and favors inward migration
e.g., Tanaka+ 02
11
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
-0.05
Baruteau+ 14 in Protostars & Planets VI
0.00
0.05
0.10
0.05
0.10
4
3
2
1
0
0.00
0.05
0.10
0.00
0.05
0.10
0.00
4
3
2
1
-0.05
1.0
0.2
0.1
0.5
U-turn
y / rp
0.0
0.0 U-turn
-0.1
-0.5 co-orbital perturbations
e re
-1.0 -0.3
-1.5 -1.5
gion
-0.2
-1.0
-0.5
0.0 x / rp
0.5
1.0
1.5
esho
y / rp
gion e re
0.3
esho
1.5
Hors
0
Hors
-0.05
-0.05
0.85 0.90 0.95 1.00 1.05 1.10 1.15 x / rp
The horseshoe region exerts a torque on the planet called corotation torque
12
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
-0.05
0.00
0.05
0.10
0.05
0.10
4
3
2
1
0
0.3
esho gion e re
0.2
⇠ P⌃
0.1 U-turn
0.0 U-turn
-0.1
-0.3
esho
e re
gion
-0.2
Hors
y / rp
(r ⇥ v) · ez /⌃
0.00
Hors
The angular momentum of the horseshoe region evolves due to the advection-diffusion of the disc’s potential vorticity and specific entropy in that region
-0.05
0.85 0.90 0.95 1.00 1.05 1.10 1.15 x / rp
13
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
-0.05
0.00
0.05
0.10
0.05
0.10
4
3
2
1
0
0.3
gion e re
0.2
⇠ P⌃
0.1 U-turn
0.0 U-turn
-0.1
-0.3
esho
e re
gion
-0.2
Hors
y / rp
The sign and magnitude of the corotation torque thus depend on: - the density and temperature gradients across the horseshoe region, - diffusion processes there (turbulence?)
esho
(r ⇥ v) · ez /⌃
0.00
Hors
The angular momentum of the horseshoe region evolves due to the advection-diffusion of the disc’s potential vorticity and specific entropy in that region
-0.05
0.85 0.90 0.95 1.00 1.05 1.10 1.15 x / rp
14
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
-0.05
0.00
0.05
0.10
0.05
0.10
4
3
2
1
0
0.3
gion e re
0.2
⇠ P⌃
0.1 U-turn
y / rp
The sign and magnitude of the corotation torque thus depend on: - the density and temperature gradients across the horseshoe region, - diffusion processes there (turbulence?)
esho
(r ⇥ v) · ez /⌃
0.00
Hors
The angular momentum of the horseshoe region evolves due to the advection-diffusion of the disc’s potential vorticity and specific entropy in that region
-0.05
0.0 U-turn
-0.1
e.g., Masset & Casoli 10, Paardekooper, Baruteau & Kley 11 -0.3
esho
e re
gion
-0.2
Hors
The corotation torque is generally positive and favors outward migration
0.85 0.90 0.95 1.00 1.05 1.10 1.15 x / rp
15
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
-0.05
0.00
0.05
0.10
0.05
0.10
4
3
2
1
0
0.3
gion e re
0.2
⇠ P⌃
0.1 U-turn
y / rp
The sign and magnitude of the corotation torque thus depend on: - the density and temperature gradients across the horseshoe region, - diffusion processes there (turbulence?)
esho
(r ⇥ v) · ez /⌃
0.00
Hors
The angular momentum of the horseshoe region evolves due to the advection-diffusion of the disc’s potential vorticity and specific entropy in that region
-0.05
0.0 U-turn
-0.1
e re
-0.3
esho
e.g., Masset & Casoli 10, Paardekooper, Baruteau & Kley 11
The wake torque + the corotation torque drive the migration of low-mass planets (type I migration)
gion
-0.2
Hors
The corotation torque is generally positive and favors outward migration
0.85 0.90 0.95 1.00 1.05 1.10 1.15 x / rp
16
Low-mass planets in a disc
cs 2 ⌃r6 ⌦4 /
0 , with
0
=
✓
Mp M?
◆2
Total torque on planet
water ice line
silicate evaporation line
(typically up to ~ 10 Earth masses)
Bitsch+ 13
regions of outward migration
17
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
cs 2 ⌃r6 ⌦4 /
0 , with
0
=
✓
Mp M?
◆2
Total torque on planet
water ice line
silicate evaporation line
migration stalls (“planet traps”)
Bitsch+ 13
regions of outward migration
18
Low-mass planets in a disc
cs 2 ⌃r6 ⌦4 /
0 , with
0
=
✓
Mp M?
◆2
Total torque on planet
water ice line
silicate evaporation line
(typically up to ~ 10 Earth masses)
Bitsch+ 13
❗ This picture is viscosity- and time-dependent e.g., Bitsch+ 15 19
Low-mass planets in a disc
cs 2 ⌃r6 ⌦4 /
0 , with
0
=
✓
Mp M?
◆2
Total torque on planet
water ice line
silicate evaporation line
(typically up to ~ 10 Earth masses)
Bitsch+ 13
Planets below a few Earth masses should still migrate inwards! For an Earth-mass planet at 5 AU, the migration timescale is only ~0.7 Myr. 20
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
/
0 , with
0
=
✓
Mp M?
◆2
cs 2 ⌃r6 ⌦4
planetesimal accretion
Total torque on planet
water ice line
silicate evaporation line
pebble fast accretion
Bitsch+ 13 Lambrechts & Johansen 12
Planets below a few Earth masses should still migrate inwards! For an Earth-mass planet at 5 AU, the migration timescale is only ~0.7 Myr. 21
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Some recent developments on type I migration: additional corotation torque with a weak azimuthal magnetic field Guilet, Baruteau & Papaloizou 13 4
3
2
1
0
-0.10
-0.05
-0.10
-0.05
0.00
0.00
0.05
0.10
0.05
0.10
Density perturbation (laminar model) 1.0
azimuth
ke
wa
0.5
planet
0.0
ke
wa
-0.5
-1.0 0.6
0.8
1.0 radius
1.2
3D laminar disc (viscosity+resistivity)
1.4
22
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Some recent developments on type I migration: additional corotation torque with a weak azimuthal magnetic field Guilet, Baruteau & Papaloizou 13 4
3
2
1
0
-0.10
-0.05
-0.10
-0.05
0.00
0.00
0.05
0.10
0.05
0.10
Density perturbation (laminar model) 1.0
→ magnetic flux & magnetic pressure increase downstream of the U-turns,
0.5
azimuth
U-turn
→ thermal pressure decreases,
0.0
→ 𝜌 decreases at constant T U-turn
-0.5
-1.0 0.6
Magnetic field lines are bent by the horseshoe motion of the gas:
0.8
1.0 radius
1.2
3D laminar disc (viscosity+resistivity)
1.4
23
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Some recent developments on type I migration: additional corotation torque with a weak azimuthal magnetic field Guilet, Baruteau & Papaloizou 13 4
3
2
1
0
-0.10
-0.05
-0.10
-0.05
0.00
0.00
0.05
0.10
0.05
0.10
Density perturbation (laminar model) 1.0
→ magnetic flux & magnetic pressure increase downstream of the U-turns,
0.5 U-turn
azimuth
Magnetic field lines are bent by the horseshoe motion of the gas:
→ thermal pressure decreases,
0.0
→ 𝜌 decreases at constant T U-turn
-0.5
Azimuthal asymmetry of the U-turns makes this new corotation torque positive -1.0 0.6
0.8
1.0 radius
1.2
3D laminar disc (viscosity+resistivity)
1.4
24
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Some recent developments on type I migration: additional corotation torque with a weak azimuthal magnetic field Guilet, Baruteau & Papaloizou 13 4
4
3
3
2
2
1
1
-0.10
-0.05
0.00
0.05
0.10
0
-0.10
-0.05
0.00
0.05
0.10
-0.4
-0.2
0.0
0.2
0.4
-0.4
-0.2
0.0
0.2
0.4
Instantaneous density perturbation
1.0
1.0
0.5
0.5
Azimuth
azimuth
Density perturbation (laminar model)
0.0
-0.5
-1.0 0.6
0.0
Baruteau+ 11a,14
0
-0.5
0.8
1.0 radius
1.2
3D laminar disc (viscosity+resistivity)
1.4
-1.0 0.6
0.8
1.0 Radius
1.2
3D MRI-turbulent disc (ideal MHD)
1.4
25
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Some recent developments on type I migration: additional corotation torque with a weak azimuthal magnetic field Guilet, Baruteau & Papaloizou 13 4
4
3
3
2
2
1
1
-0.10
-0.05
0.00
0.05
0.10
0
-0.10
-0.05
0.00
0.05
0.10
0.5
0.5
Azimuth
1.0
-0.5
-1.0 0.6
-0.05
0.00
0.00
0.05
0.10
0.05
0.10
Density perturbation averaged over 35 orbits
1.0
0.0
-0.05
-0.10
Density perturbation (laminar model)
azimuth
-0.10
0.0
Baruteau+ 11a,14
0
-0.5
0.8
1.0 radius
1.2
3D laminar disc (viscosity+resistivity)
1.4
-1.0 0.6
0.8
1.0 Radius
1.2
3D MRI-turbulent disc (ideal MHD)
1.4
26
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Some recent developments on type I migration:
azimuth
0.04 rad
additional torque due to accretion heating released by planet Benítez-Llamblay, Masset et al. 15 → “heating torque”
-0.04 rad
Hill radius
5.0 AU
radius
5.4 AU 27
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Some recent developments on type I migration:
azimuth
0.04 rad
additional torque due to accretion heating released by planet Benítez-Llamblay, Masset et al. 15 → “heating torque”
Hill radius
-0.04 rad
The heating torque may reverse the migration of 1-3 Earth-mass planets 5.0 AU
radius
5.4 AU 28
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Some recent developments on type I migration: additional corotation torque when the planet actually migrates → “dynamical corotation torque”
Masset & Papaloizou 03 Paardekooper 14 Pierens 15
← gas density perturbation by a 20 Earth-mass planet migrating in a massive disc (Σ ~ 10ΣMMSN)
29
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Some recent developments on type I migration: additional corotation torque when the planet actually migrates → “dynamical corotation torque”
Masset & Papaloizou 03 Paardekooper 14 Pierens 15
The corotation torque is generally the sum of: (i) the torque due to orbit-crossing gas + feedback on migration
30
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Some recent developments on type I migration: additional corotation torque when the planet actually migrates → “dynamical corotation torque”
Masset & Papaloizou 03 Paardekooper 14 Pierens 15
The corotation torque is generally the sum of: (i) the torque due to orbit-crossing gas + feedback on migration
(ii) the torque due to trapped co-orbital gas - feedback on migration
31
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Some recent developments on type I migration: additional corotation torque when the planet actually migrates → “dynamical corotation torque”
Masset & Papaloizou 03 Paardekooper 14 Pierens 15
The corotation torque is generally the sum of: (i) the torque due to orbit-crossing gas + feedback on migration
(ii) the torque due to trapped co-orbital gas - feedback on migration
(iii) the horseshoe drag due to co-orbital gas No feedback on migration
32
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Some recent developments on type I migration: additional corotation torque when the planet actually migrates → “dynamical corotation torque”
Masset & Papaloizou 03 Paardekooper 14 Pierens 15
The corotation torque is generally the sum of: (i) the torque due to orbit-crossing gas + feedback on migration
(ii) the torque due to trapped co-orbital gas - feedback on migration
dynamical corotation torque (iii) the horseshoe drag due to co-orbital gas No feedback on migration
static corotation torque 33
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Some recent developments on type I migration: additional corotation torque when the planet actually migrates → “dynamical corotation torque”
Masset & Papaloizou 03 Paardekooper 14 Pierens 15
Semi-major axis
→ large in massive low-viscosity discs, where it either slows down inward migration (- feedback) or leads to runaway outward migration (+ feedback)
* Pierens 15
*qd = Mdisc / Mstar
34
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Some recent developments on type I migration: additional corotation torque when the planet actually migrates → “dynamical corotation torque”
Masset & Papaloizou 03 Paardekooper 14 Pierens 15
Semi-major axis
→ large in massive low-viscosity discs, where it either slows down inward migration (- feedback) or leads to runaway outward migration (+ feedback)
* Pierens 15
→ analogous to type III migration of massive planets
*qd = Mdisc / Mstar
35
Massive planets in a disc (typically beyond Saturn masses)
4
3
2
1
0
-5.0
-4.5
-5.0
-4.0
-4.5
-4.0
-3.5
-3.0
-3.5
-3.0
Log (Surface density) at t = 100.0Torb
1.5
← gas surface density (log scale) of a protoplanetary disc perturbed by a 3 Jupiter-mass planet
1.0 0.5
w
planet
star
0.0
ke
-0.5
wa
y / rp
ak e
gap
-1.0 -1.5 -1.5
-1.0
-0.5
0.0 x / rp
0.5
1.0
1.5 36
Massive planets in a disc (typically beyond Saturn masses)
4
3
2
1
0
-5.0
-4.5
-5.0
-4.0
-4.5
-4.0
-3.5
-3.0
-3.5
-3.0
Log (Surface density) at t = 100.0Torb
1.5
← gas surface density (log scale) of a protoplanetary disc perturbed by a 3 Jupiter-mass planet
1.0 0.5
w
planet
star
0.0
e.g., Dürmann & Kley 15
ke
-0.5
wa
y / rp
ak e
Jupiter-like planets thus migrate inward, on timescales > 104-5 yr.
gap
-1.0 -1.5 -1.5
Massive planets deplete their co-orbital region: → corotation torque largely suppressed → wake torque weakened; still is main driver of migration (type II migration)
-1.0
-0.5
0.0 x / rp
0.5
1.0
1.5 37
Massive planets in a disc (typically beyond Saturn masses)
← gas surface density (log scale) of a protoplanetary disc perturbed by a Saturn-mass planet in a massive disc
Intermediate-mass planets only partly deplete their co-orbital region. The corotation torque can still be large: → possible runaway in massive and/or low-viscosity discs (type III migration) → otherwise, intermediate regime between type I & II migration Masset & Papaloizou 03 Lin & Papaloizou 10
38
Massive planets in a disc (typically beyond Saturn masses)
4
3
2
1
0
-5.0
-4.5
-5.0
-4.0
-4.5
-4.0
-3.5
-3.0
-3.5
-3.0
Log (Surface density) at t = 100.0Torb
1.5 1.0 0.5
w
planet
“Criterion” for gap-opening depends on planet-to-star mass ratio (q) and disc’s aspect ratio (h) through q/h3, and on disc viscosity Crida+ 06
star
0.0
ke
-0.5
wa
y / rp
ak e
← gas surface density (log scale) of a protoplanetary disc perturbed by a 3 Jupiter-mass planet
gap
-1.0 -1.5 -1.5
-1.0
-0.5
0.0 x / rp
0.5
1.0
1.5 39
Massive planets in a disc (typically beyond Saturn masses)
4
3
2
1
0
-5.0
-4.5
-5.0
-4.0
-4.5
-4.0
-3.5
-3.0
-3.5
-3.0
Log (Surface density) at t = 100.0Torb
1.5 1.0 0.5
w
planet
“Criterion” for gap-opening depends on planet-to-star mass ratio (q) and disc’s aspect ratio (h) through q/h3, and on disc viscosity Crida+ 06
star
0.0
❗ Crida et al’s criterion is for when the co-orbital surface density drops to 10% its initial value
ke
-0.5
wa
y / rp
ak e
← gas surface density (log scale) of a protoplanetary disc perturbed by a 3 Jupiter-mass planet
gap
-1.0 -1.5 -1.5
-1.0
-0.5
0.0 x / rp
→ partial gaps (dips) expected for planets > 5-10 Earth masses 0.5
1.0
1.5
e.g., Dong+ 11 40
Massive planets in a disc (typically beyond Saturn masses)
Jovian planet
← gas surface density (log scale) of a protoplanetary disc perturbed by a 3 Jupiter-mass planet
“Criterion” for gap-opening depends on planet-to-star mass ratio (q) and disc’s aspect ratio (h) through q/h3, and on disc viscosity Crida+ 06
❗ Crida et al’s criterion is for fixed planets. Modified by migration! Malik+ 15
← e.g., planets formed by gravitational Baruteau+ 11b
instability —> talk by D. Stamatellos 41
Massive planets in a disc (typically beyond Saturn masses)
“Criterion” for gap-opening depends on planet-to-star mass ratio (q) and disc’s aspect ratio (h) through q/h3, and on disc viscosity Crida+ 06
❗ Crida et al’s criterion is for the gas. Its application to gaps observed in sub-mm interferometric imaging is highly uncertain… © ESO
42
Massive planets in a disc
Y [AU]
(typically beyond Saturn masses)
X [AU]
X [AU]
X [AU] Zhu, Nelson et al. 12 43
Objectives and outline Give a practical overview of the physical processes that drive the orbital evolution of planets in their protoplanetary disc → low-mass (terrestrial) planets → massive (Jovian) planets
Discuss how models of planet-disc interactions can explain some of the properties of the exoplanets
44
Planets-disc interactions and the observed exoplanets data extracted from exoplanets.org
1.0
1.0
Jupiter
0.8
0.8
102 0.6
0.6
10 0.4
0.4
Eccentricity
Planet mass [Earth mass]
103
Earth
1
0.2
0.2
10-1
07/2014
Mercury
1
10
102 103 104 Orbital period [days]
105 0.0 0
1
2
3
4
0.0
45
Planets-disc interactions and the observed exoplanets data extracted from exoplanets.org
hot Jupiters
1.0
1.0
150
100
50
Jupiter
0.8
0.8
102 0.6
0.6
10 0.4
0.4
Earth
1
0.2
0.2
0 4500
10-1 5000 5500 6000 6500 Effective temperature [Kelvin]
Eccentricity
Planet mass [Earth mass]
| Projected spin-orbit misalignment | [deg.]
103
07/2014
Mercury
7000
1
10
102 103 104 Orbital period [days]
105 0.0 0
1
2
3
4
0.0
46
Planets-disc interactions and the observed exoplanets data extracted from exoplanets.org
hot Jupiters
1.0
1.0
150
100
50
Jupiter
0.8
0.8
102 0.6
0.6
10 0.4
0.4
Earth
1
0.2
0.2
0 4500
10-1 5000 5500 6000 6500 Effective temperature [Kelvin]
Eccentricity
Planet mass [Earth mass]
| Projected spin-orbit misalignment | [deg.]
103
07/2014
Mercury
7000
1
10
102 103 104 Orbital period [days]
105
Aligned hot Jupiters most likely result from disc migration rather than from high-eccentricity migration followed by star-planet tidal re-alignment
see Rogers & Lin 13, Lai 12
0.0 0
1
2
3
4
0.0
47
Planets-disc interactions and the observed exoplanets data extracted from exoplanets.org
hot super Earths
1.0
1.0
in-situ formation or disc migration? 103 Jupiter
0.8
0.8
102 0.6
0.6
10 0.4
0.4
Eccentricity
Planet mass [Earth mass]
e.g., Hansen & Murray 13, Raymond & Cossou 14, Ogihara+ 15
Earth
1
+: planets detected only by transit (mass is inferred from the massradius diagram of planets with both mass and radius determined)
10-1
0.2
0.2
07/2014
Mercury
1
10
102 103 104 Orbital period [days]
105 0.0 0
1
2
3
4
0.0
48
Planets-disc interactions and the observed exoplanets data extracted from exoplanets.org
hot super Earths
1.0
1.0
in-situ formation or disc migration?
Number
2:1
5:3
3:2
25
5:4 4:3
30
20 15
Jupiter
102
0 1.0
10
3.0
❗ disc migration of super-Earths doesn’t necessarily lead to resonant systems! Baruteau & Papaloizou 13
0.4
0.4
Earth
1
+: planets detected only by transit (mass is inferred from the massradius diagram of planets with both mass and radius determined)
10-1 1.5 2.0 2.5 Orbital period ratio
0.6
0.6
10 5
0.8
0.8
Eccentricity
hints through the period ratio distribution of confirmed multiplanetary systems?
103 Planet mass [Earth mass]
e.g., Hansen & Murray 13, Raymond & Cossou 14, Ogihara+ 15
0.2
0.2
07/2014
Mercury
1
10
102 103 104 Orbital period [days]
105 0.0 0
1
2
3
4
0.0
49
Any questions?
© ESO
Essential points Planet-disc interactions lead to inward or outward migration, depending on the planets mass and, crucially, on the disc’s physical properties near the planets’ radial location (𝞺, T, B field, turbulence). Predictive scenarios of planetary migration require more knowledge of protoplanetary disks in regions of planet formation (observations & theory). While disk migration is certainly inevitable, it is one among many mechanisms that shape the architecture of planetary systems.
Suggested references Baruteau et al. 2014 (Protostars & Planets VI): Planet-disc interactions and the early evolution of planetary systems, http://arxiv.org/abs/1312.4293 Kley & Nelson 2012 (ARA&A): Planet-Disk Interaction and Orbital Evolution, http:// arxiv.org/abs/1203.1184 50
Back-up slides
51
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Some recent developments on type I migration: additional corotation torque with a weak azimuthal magnetic field
52
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Some recent developments on type I migration: additional corotation torque with a weak azimuthal magnetic field torque due MHD waves
strong
ke
planet
wak e MHD waves
Uribe+ 15
wa
Gas mass density
Terquem 03, Fromang+ 05, Uribe+ 15, Comins+ 15
53
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
2π
Some recent developments on type I migration: additional corotation torque with a weak azimuthal magnetic field strong vertical
Muto+ 08, Uribe+ 15
Uribe+ 15
Azimuth
planet
Gas mass density
torque due MHD waves
0 0.8
Radius
1.2
54
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Some recent developments on type I migration: additional corotation torque with a weak azimuthal magnetic field torque due MHD waves
strong vertical & weak? Zhu+ 13
planet
55
Low-mass planets in a disc (typically up to ~ 10 Earth masses)
Some recent developments on type I migration: the corotation torque depends on the planet’s eccentricity!
Fendyke & Nelson 14
numerical results fit
planet’s horseshoe region shrinks 56
