The interplay between planet growth and migration · The interplay between planet growth and...

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)


Exoplanet observations

super Earths

cold Jupitershot Jupiters

(Winn & Fabrycky 2015)


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?


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)


Type-I Migration



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)


Type-I Migration



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)


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


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


Growth vs. migrationTemperature profile: T / r�b, Surface density profile: ⌃ / r�(3/2�b)

(Brasser, Bitsch & Matsumura, 2017)


Growth vs. migration



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


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)


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


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


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


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


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?


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


The interplay between planet growth and migration · The interplay between planet growth and...

Documents

Transcript of The interplay between planet growth and migration · The interplay between planet growth and...