Planetesimal formation at water snow lineJoanna Drążkowska (University of Zurich)

joannad@physik.uzh.ch

collaboration:Yann Alibert (University of Bern)Kees Dullemond (Heidelberg University)

Why is the snow line a good place to form planetesimals?

Context• the connection between dust evolution and planetesimal formation represents a major gap in the state-of-the-art planet formation models • direct growth from dust to planetesimals is inefficient because of fragmentation and radial drift • streaming instability is efficient in turning pebbles to planetesimals but it only happens under special conditions • I make 1-D models of dust evolution in a global protoplanetary disk to predict where and when planetesimals form

Icy dust is more sticky than dry dust, so the pebbles outside of the snow line grow to larger sizes than inside. Because of their size, the icy pebbles drift inward quickly.

refractory dust

Part of the water vapor released by evaporating icy pebbles is returned outside of the snow line by diffusion and recondenses locally enhancing the density of solids (this is called the "cold finger" effect).

solid icewater vapor

The small aggregates inside of the snow line are well coupled to the gas and they do not drift fast. A "traffic jam" appears in the inner part of the disk, leading to significant dust-to-gas ratio increase, which propagates outwards thanks to diffusion and collective drift effect.

Models

distance to the star [AU]

MMSN10-2

100

102

100 101 102

5 ⋅105 yrs10-2

100

1023 ⋅105 yrs

Σ[g

cm-2

]

10-2

100

1022 ⋅105 yrs

10-2

100

102105 yrs

10-2

100

102104 yrs

gasdustplanetesimalswater icewater vapor10-2

100

1021 yr

Can planetesimals already form during the disk infall?

10-2

100

102

Σplts[g/cm2]

MMSN

100 101 102

r [au]

105

106

107

t[years]

cold finger

traffic jam+ cold finger

build

up s

tage

clas

s II

stag

e

33

32

31

30

29

28

27

26

logΣ̇plts[gcm

−2s−1]

10-2

100

102

Σplts[g/cm2]

MMSN

100 101 102

r [au]

105

106

107

t[years]

build

up s

tage

clas

s II

stag

e

32

31

30

29

28

27

26

25

logΣ̇plts[gcm

−2s−1]

Most of dust coagulation models start when the protoplanetary disk is already fully-formed. At the same time, observational studies suggest that planetesimal formation should start very early. In our models, we found that planetesimal formation during the disk buildup is only possible if the gas and water vapor redistribution is efficient (αv ≥ 10-3) but the dust resides in a quiescent midplane (αt ≤ 10-4 ). This favours the cold finger effect, which is the only way to create pile-up of pebbles during disk infall. The plausibility of such a setup in a realistic protoplanetary disk is unclear.

standard model αv = αt = 10-3 "dead zone" model αv = 10-3, αt= 10-5

Setup• the gas disk model is from Bitschet al. (2015), the initial mass of the disk is 0.1 M⊙

• the initial dust-to-gas ratio is 0.03

• the dust evolution algorithm is based on the two-population model of Birnstiel et al. (2012)

• planetesimal formation criterion is based on the midplane density ratio ρdust(St ≥ 10-2) / ρgas ≥ 1

• fragmentation velocity outside of the snow line is vf = 10 m/s and inside of the snow line vf = 1 m/s

Results• dust evolution is driven by radial drift in the outer part of the disk and by fragmentation in its inner part

• the radial drift shifts mass inwards and the dust-to-gas ratio in the inner disk is enhanced

• the "traffic jam" is more efficient than the "cold finger" effect

• the maximum dust-to-gas ratio enhancement always occurs directly outside of the snow line and it spreads outwards thanks to the collective drift

• planetesimal formation only takes place directly outside of the snow line• typical outcome is a massive annulus of planetesimals(Σplts > ΣMMSN)

Further reading: Drążkowska & Dullemond "Can dust coagulation trigger streaming instability?", 2014, A&A 572, A78Drążkowska, Alibert & Moore "Close-in planetesimal formation by pile-up of drifting pebbles", 2016, A&A 594, A105Drążkowska & Alibert "Planetesimal formation starts at the snow line", 2017, A&A 608, A92Drążkowska & Dullemond "Planetesimal formation during protoplanetary disk buildup", 2018, A&A under review

Conclusions• planetesimal formation needs large pebbles and enhanced dust-to-gas ratio: pebble pile-ups

• planetesimal formation is hindered by the growth barriers – even if it happens via the streaming instability, large enough pebbles need to grow first

• it is very hard to trigger planetesimal formation in the outer part of the disk during its gas-rich phase

• planetesimals do not form everywhere in the disk, the water snow line is one favorable place to trigger planetesimal formation both when the disk is already fully formed and during its buildup

• a significant redistribution of solids must take place before the conditions necessary for planetesimal formation are met

• solids-to-gas ratio is increased at the location where planetesimals form, which should facilitate faster accretion of the final planets

• if planetesimals are formed already in the disk infall stage, their mass is much lower than the mass of planetesimals formed during the subsequent disk evolution, but due to their early occurrence they may be important for planet formation