the interplay between planet growth and migration · the interplay between planet growth and...
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The interplay between planet growth and migration
Bertram Bitsch
Lund Observatory
May 2017
Bertram Bitsch (Lund) The interplay between planet growth and migration 1 / 13
Exoplanet observations
(Winn & Fabrycky 2015)
Bertram Bitsch (Lund) The interplay between planet growth and migration 2 / 13
Exoplanet observations
super Earths
cold Jupitershot Jupiters
(Winn & Fabrycky 2015)
Bertram Bitsch (Lund) The interplay between planet growth and migration 2 / 13
Period ratios of super-Earths
Simulations with migration predict planet trapping in resonances) Systems become unstable and we can re-produce the period ratios by
mixing 90% unstable with 10% stable systems (Izidoro et al. 2017)
) Can we avoid parking the planets in resonance somehow?
Bertram Bitsch (Lund) The interplay between planet growth and migration 3 / 13
Period ratios of super-Earths
Simulations with migration predict planet trapping in resonances) Systems become unstable and we can re-produce the period ratios by
mixing 90% unstable with 10% stable systems (Izidoro et al. 2017)
) Can we avoid parking the planets in resonance somehow?
Bertram Bitsch (Lund) The interplay between planet growth and migration 3 / 13
Period ratios of super-Earths
Simulations with migration predict planet trapping in resonances) Systems become unstable and we can re-produce the period ratios by
mixing 90% unstable with 10% stable systems (Izidoro et al. 2017)
) Can we avoid parking the planets in resonance somehow?Bertram Bitsch (Lund) The interplay between planet growth and migration 3 / 13
Type-I Migration
Waves carry energy and angular momentum
) Lindblad torques drive strong inward migration: a / q
a Horseshoe movement of gas causes corotation torque (barotropic & entropy)
a Corotation torque can drive outward migration, but depends on gradients in⌃g and T (Paardekooper & Mellema, 2006; Baruteau & Masset, 2008)
Bertram Bitsch (Lund) The interplay between planet growth and migration 4 / 13
Type-I Migration
Waves carry energy and angular momentum
) Lindblad torques drive strong inward migration: a / q
Horseshoe movement of gas causes corotation torque (barotropic & entropy)
a Corotation torque can drive outward migration, but depends on gradients in⌃g and T (Paardekooper & Mellema, 2006; Baruteau & Masset, 2008)
Bertram Bitsch (Lund) The interplay between planet growth and migration 4 / 13
Type-I Migration
Waves carry energy and angular momentum
) Lindblad torques drive strong inward migration: a / q
Horseshoe movement of gas causes corotation torque (barotropic & entropy)
a Corotation torque can drive outward migration, but depends on gradients in⌃g and T (Paardekooper & Mellema, 2006; Baruteau & Masset, 2008)
Bertram Bitsch (Lund) The interplay between planet growth and migration 4 / 13
Type-I Migration
Waves carry energy and angular momentum
) Lindblad torques drive strong inward migration: a / q
Horseshoe movement of gas causes corotation torque (barotropic & entropy)
Corotation torque can drive outward migration, but depends on gradients in⌃g and T (Paardekooper & Mellema, 2006; Baruteau & Masset, 2008)
Bertram Bitsch (Lund) The interplay between planet growth and migration 4 / 13
Pebble accretion in the Hill regime
(Ormel & Klahr 2010; Lambrechts & Johansen 2012; Bitsch et al. 2015b)
Pebbles are accreted fromthe entire Hill sphere
) Accretion much moree�cient than planetesimals
Accretion rate by pebbleaccretion in Hill regime
Mc = 2⇣ ⌧f0.1
⌘2/3rHvH⌃Peb
Bertram Bitsch (Lund) The interplay between planet growth and migration 5 / 13
Dust gaps in discs: Pebble isolation mass
Gaps in dust disc are wider than in the gas disc (Paardekooper & Mellema, 2006)
Pebble isolation mass:
Miso
= 20
✓H/r
0.05
◆3
MEarth
(Lambrechts et al., 2014)
) Pebble accretion self-terminates: no accretion of solids any more!) super-Earth fully formed in our model
Bertram Bitsch (Lund) The interplay between planet growth and migration 6 / 13
Growth vs. migrationTemperature profile: T / r�b, Surface density profile: ⌃ / r�(3/2�b)
(Brasser, Bitsch & Matsumura, 2017)
Bertram Bitsch (Lund) The interplay between planet growth and migration 7 / 13
Growth vs. migration
(Brasser, Bitsch & Matsumura, 2017)
Bertram Bitsch (Lund) The interplay between planet growth and migration 8 / 13
The disc model
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.1 1 10
H/r
r [AU]
α=0.001α=0.005
α=0.01
(Brasser, Bitsch & Matsumura, 2017)
Simple 2 component power law disc, T / r�b
Mdisc
= 3⇡⌫⌃g = 3⇡↵H2⌦K⌃g ; M decreases in time
Viscous heated inner part (b = 0.9, or b = 1.2)
Viscous part depends on accretion rate and viscosity
Stellar heated outer part (b = 3/7)
Bertram Bitsch (Lund) The interplay between planet growth and migration 9 / 13
Growth Tracks
0
1
2
3
4
5
6
0.1 1
M [
ME]
r [AU]
α=0.01, r0=0.5 AUα=0.005, r0=0.5 AUα=0.001, r0=0.5 AU
α=0.01, r0=2.5 AUα=0.005, r0=2.5 AUα=0.001, r0=2.5 AU
b=0.9
0
1
2
3
4
5
6
0.1 1
M [
ME]
r [AU]
α=0.01, r0=0.5 AUα=0.005, r0=0.5 AUα=0.001, r0=0.5 AU
α=0.01, r0=2.5 AUα=0.005, r0=2.5 AUα=0.001, r0=2.5 AU
b=1.2
0
0.5
1
1.5
2
2.5
1 1.5 2 2.5 3
r [A
U]
time [Myr]
α=0.01, r0=0.5 AUα=0.005, r0=0.5 AUα=0.001, r0=0.5 AU
α=0.01, r0=2.5 AUα=0.005, r0=2.5 AUα=0.001, r0=2.5 AU
Inner Edge
b=0.9
0
0.5
1
1.5
2
2.5
1 1.5 2 2.5 3
r [A
U]
time [Myr]
α=0.01, r0=0.5 AUα=0.005, r0=0.5 AUα=0.001, r0=0.5 AU
α=0.01, r0=2.5 AUα=0.005, r0=2.5 AUα=0.001, r0=2.5 AU
Inner Edge
b=1.2
Bertram Bitsch (Lund) The interplay between planet growth and migration 10 / 13
Dependency on ↵ and r0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
α
r0 [AU]
0
1
2
3
4
5
6
7
8
9
MP [
ME]
b=0.9
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
α
r0 [AU]
0
1
2
3
4
5
6
7
8
9
MP [
ME]
b=1.2
(Brasser, Bitsch & Matsumura, 2017)
Disc evolution for 2 Myr (Disc initial age = 1 Myr)
Planets always migrate to inner edge of disc, for shallow temperaturegradients (b=0.9)
Steep temperature gradient needed (b=1.2) to keep planets awayfrom the inner edge of the disc
Higher ↵ needed to prevent more massive planets to stay out
Bertram Bitsch (Lund) The interplay between planet growth and migration 11 / 13
Timing matters
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
α
r0 [AU]
0
1
2
3
4
5
6
7
8
9
MP [
ME]
b=0.9
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
α
r0 [AU]
0
1
2
3
4
5
6
7
8
9
MP [
ME]
b=1.2
(Brasser, Bitsch & Matsumura, 2017)
Disc evolution for 1 Myr (Disc initial age = 2 Myr)
Planets do not have enough time to grow and migrate all the way tothe inner edge, even for b=0.9
Higher ↵ still preferred
) Do the super Earths form late?
) or do discs have short lifetimes?
Bertram Bitsch (Lund) The interplay between planet growth and migration 12 / 13
Timing matters
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
α
r0 [AU]
0
1
2
3
4
5
6
7
8
9
MP [
ME]
b=0.9
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
α
r0 [AU]
0
1
2
3
4
5
6
7
8
9
MP [
ME]
b=1.2
(Brasser, Bitsch & Matsumura, 2017)
Disc evolution for 1 Myr (Disc initial age = 2 Myr)
Planets do not have enough time to grow and migrate all the way tothe inner edge, even for b=0.9
Higher ↵ still preferred
) Do the super Earths form late?
) or do discs have short lifetimes?
Bertram Bitsch (Lund) The interplay between planet growth and migration 12 / 13
Timing matters
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
α
r0 [AU]
0
1
2
3
4
5
6
7
8
9
MP [
ME]
b=0.9
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
α
r0 [AU]
0
1
2
3
4
5
6
7
8
9
MP [
ME]
b=1.2
(Brasser, Bitsch & Matsumura, 2017)
Disc evolution for 1 Myr (Disc initial age = 2 Myr)
Planets do not have enough time to grow and migrate all the way tothe inner edge, even for b=0.9
Higher ↵ still preferred
) Do the super Earths form late?
) or do discs have short lifetimes?
Bertram Bitsch (Lund) The interplay between planet growth and migration 12 / 13
Summary / Discussion
The negative temperature gradient needs to exceed approximately 0.9for outward migration to occur
A critical scale height hcrit
exists below which planets at the pebbleisolation M
iso
mass are trapped in the outward migration region,preventing them from reaching the central star
Planets at Miso
can be prevented to reach the central star, as long as↵ and the temperature gradient are large enough. Typically b > 0.9and ↵ > 0.004 are needed
Formation time is important: shorter time in disc: less migration
More information: Brasser, Bitsch & Matsumura, 2017
Bertram Bitsch (Lund) The interplay between planet growth and migration 13 / 13