The interplay between planet growth and migration · The interplay between planet growth and migration Bertram Bitsch Lund Observatory May 2017 Bertram Bitsch (Lund) The interplay

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?





) Can we avoid parking the planets in resonance somehow?





) 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)



Type-I Migration






Type-I Migration




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



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?


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








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








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 migration Bertram Bitsch Lund Observatory May 2017 Bertram Bitsch (Lund) The interplay

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