What influences the pebble isolation mass?kuiper... · 10 M E 15 M E 20 M E 25 M E 30 M E 50 M E...
Transcript of What influences the pebble isolation mass?kuiper... · 10 M E 15 M E 20 M E 25 M E 30 M E 50 M E...
What influences the pebbleisolation mass?
Bertram Bitsch
Bertram Bitsch What influences the pebble isolation mass? 1 / 11
Giant planet formation
0.001
0.01
0.1
1
10
100
1000
0.1 1 10
MP [
ME]
r [AU]
r0=15 AUr0=25 AUr0=30 AU
⇒ When does solid accretion stop?
Bertram Bitsch What influences the pebble isolation mass? 2 / 11
Remember radial drift
P
v η(1− )Kep
FFG
Disc is hotter and denser close to the star: radial pressure gradient
Radial pressure gradient force mimics decreased gravity⇒ gas orbits slower than Keplerian:
vgas = vKep −∆v = vKep − ηvKep, η = −1
2
(H
r
)2∂ ln(P)
∂ ln(r)
Particles do not feel the pressure gradient force and want to orbit Keplerian
Headwind from sub-Keplerian gas drains angular momentum from particles, sothey spiral in through the disc
Bertram Bitsch What influences the pebble isolation mass? 3 / 11
Pebble accretion
Most planetesimals aresimply scattered by theprotoplanet
Pebbles spiral in towardsthe protoplanet due to gasfriction
⇒ Pebbles are accretedefficiently
Accretion rate by pebbleaccretion in Hill regime
Mc = 2( τf
0.1
)2/3
r2HΩKΣPeb
(Ormel & Klahr 2010; Lambrechts & Johansen,
2012, 2014; Johansen & Lambrechts, 2017)
Bertram Bitsch What influences the pebble isolation mass? 4 / 11
Gaps in discs: Pebble isolation mass
-0.006
-0.004
-0.002
0
0.002
0.004
0.006
1 1.1 1.2 1.3 1.4 1.5 1.6
η
r [rp]
10 ME15 ME20 ME25 ME30 ME50 ME
Pebble isolation mass(vgas = (1− η)vkep):
⇒ Pebble accretion self-terminates:no accretion of solids any more!
(Lambrechts et al., 2014; Bitsch et al. (2018))
Pebble isolation mass: What does it depend on?
⇒ H/r , ν, dlnP/dln r and τf !
Bertram Bitsch What influences the pebble isolation mass? 5 / 11
Gaps in discs: Pebble isolation mass
-0.006
-0.004
-0.002
0
0.002
0.004
0.006
1 1.1 1.2 1.3 1.4 1.5 1.6
η
r [rp]
10 ME15 ME20 ME25 ME30 ME50 ME
Pebble isolation mass(vgas = (1− η)vkep):
⇒ Pebble accretion self-terminates:no accretion of solids any more!
(Lambrechts et al., 2014; Bitsch et al. (2018))
Pebble isolation mass: What does it depend on?
⇒ H/r , ν, dlnP/dln r and τf !
Bertram Bitsch What influences the pebble isolation mass? 5 / 11
Pebble isolation mass
1
10
100
0.0001 0.001 0.01
Mis
o [
ME]
α
H/r=0.03H/r=0.05H/r=0.07
fit
25
18
20
22
24
26
28
30
32
-4 -3.5 -3 -2.5 -2 -1.5 -1
Mis
o [
ME]
dln P/dln r
Misofit
(Bitsch et al. 2018)
The pebble isolation mass without diffusion M†iso is given by
M†iso = 25ffitME , (1)
ffit =
(H/r
0.05
)3(
0.34
(log(α3)
log(α)
)4
+ 0.66
)1−d ln(P)d ln(r) + 2.5
6
, (2)
with α3 = 0.001.Bertram Bitsch What influences the pebble isolation mass? 6 / 11
Diffusion of dust particles
radial advection vs. turbulentdiffusion:
vr,pρp − Dρgdε
dr= 0
vr,p = −2τf∆v , D = αcsHg
Maximum loading:Hd ∼ Hb ∼ Hg
(Bitsch et al. 2018)
Estimating Hb:D
2τf∆v∼ Hg ⇒ τf ∼
α
2Π
where Π = ∆v/cs
⇒ Pebbles with τf > α/(2Π) are trapped in the pressure bump!
Bertram Bitsch What influences the pebble isolation mass? 7 / 11
Implications for pebble isolation mass
10-4
10-3
10-2
10-1 1
|∆v / cs|
10-4
10-3
10-2
α
0.0001
0.001
0.01
0.1
1
10
Sto
ke
s n
um
be
r
0.0010.010.11.0
503025
5030
503020
5035
50
0.0010.010.11.0
503025
5030
503020
5035
50
0.0010.010.11.0
503025
5030
503020
5035
50
0.0010.010.11.0
503025
5030
503020
5035
50
0.0010.010.11.0
503025
5030
503020
5035
50
0.0010.010.11.0
503025
5030
503020
5035
50
0.0010.010.11.0
503025
5030
503020
5035
50
0.0010.010.11.0
503025
5030
503020
5035
50
(Bitsch et al. 2018)
Pebble isolation mass with diffusion:
Miso = M†iso +
Πcrit
λME (3)
Πcrit = α2τf
and λ ≈ 0.00476/ffit
Bertram Bitsch What influences the pebble isolation mass? 8 / 11
Implications for the solar system formation
(Kruijer et al. 2017, see also Gerber et al. 2017)
Bertram Bitsch What influences the pebble isolation mass? 9 / 11
Planet blocking the flux
(Pinilla et al. 2016)
⇒ How much mass can drift through?
Bertram Bitsch What influences the pebble isolation mass? 10 / 11
Summary
The pebble isolation mass depends on: H/r , ν, and d lnP/d ln r
⇒ Larger core masses in discs with larger viscosity
Pebbles can diffuse through pressure bump if τf < α/(2∆v/cs)
⇒ Increase of pebble isolation mass in high viscosity discs
⇒ Blocking very small pebbles is difficult!
Jupiter’s core can explain the difference in formation between NC andCC iron meteorites
⇒ exact mass of the core depends on disc structure and τf !
Bertram Bitsch What influences the pebble isolation mass? 11 / 11