GLOBAL EVOLUTION OF DUST
IN
PROTOPLANETARY DISKS
MICHAŁ RÓŻYCZKA
KACPER KORNET, PETER BODENHEIMER & TOMEK STEPINSKI
JENAM 2004
SESSION 3
GRANADA,
16.09.2004
GLOBAL EVOLUTION OF DUST IN PROTOPLANETARY DISKS
• INTRODUCTION
• DISK EVOLUTION CODE
• DISK MODELS
• DUST EVOLUTION IN DISKS
WITH DIFFERENT METALLICITIES
JENAM 2004
SESSION 3
GRANADA,
16.09.2004
INTRODUCTION:
EVOLUTION OF SOLIDS IN PPDs
1km
Protostars & Planets IV; Beckwith et al.
INTRODUCTION:
EVOLUTION OF SOLIDS IN PPDs
1km
109
Protostars & Planets IV; Beckwith et al.
INTRODUCTION:
EVOLUTION OF SOLIDS IN PPDs
1km
planetesimal
swarm
108
10 µm
Protostars & Planets IV; Beckwith et al.
INTRODUCTION:
VKepl
DUST IN A GASEOUS DISK
V<VKepl
PRESSURE GRADIENT
INTRODUCTION:
DUST IN A GASEOUS DISK
V relative to the gas
DRAG
DRIFT Vmax ~0.1 km/s
tdrift : 1 AU/100 yr
DISK EVOLUTION CODE
initial conditions:
M0, R0, α, Z
type of solids
coagulation
.
accretion evaporation
.
sedimentation ..
gas drag .
final swarms:
Mf, Rf, Σs(r), a(r)
EVOLUTION OF A TYPICAL MODEL
M0 = 0.16 M~
R0 = 40 AU
α = 0.01
Z = solar
color: size
(10-3 ÷ 106 cm)
height: Σs
M0 = 0.16 M~; R0 = 40 AU
α=0.01
FINAL Σs
INITIAL Σs
47 UMa: INNER PLANET
47 UMa OUTER PLANET
FINAL Σs
INITIAL Σs
DISK MODELS:
CONCLUSIONS
DUST DRIFT IS THE MAJOR PROCESS
SHAPING PLANETESIMAL SWARMS
SURFACE DENSITY OF SOLIDS
MAY BE SIGNIFICANTLY ENHANCED
DUE TO THE DRIFT,
PROMOTING THE FORMATION
OF GIANT PLANET CORES
DUST EVOLUTION IN DISKS WITH DIFFERENT
METALLICITIES
α = 0.01; lg Z = 0
α = 0.01; lg Z = 0
Colored area:
giant planet formation
completed in 3×106 yr
color: outer radius
(AU)
contours: inner radius
(AU)
α = 0.01; lg Z = 0
Colored area:
giant planet formation
completed in 3×106 yr
at R < 5 AU
S1
S2
Pp = S2/S1
α = 0.01; lg Z = 0
Colored area:
giant planet formation
completed in 3×106 yr
at R < 5 AU
S1
S2
ASSUMPTION 1:
M0 - Lg R0 plane
is uniformly populated
by real protoplanetary
disks
α = 0.01; lg Z = 0
Colored area:
giant planet formation
completed in 3×106 yr
at R < 5 AU
S1
S2
ASSUMPTION 2:
migration from R > 5 AU
to
R < 5 Au
is insignificant
α = 0.01; lg Z = 0
Colored area:
giant planet formation
completed in 3×106 yr
at R < 5 AU
S1
(1,2) ⇒
S2
Pp
can be compared
directly to the
observational data
Fischer & Valenti
with dust redistribution
no redistribution
FINAL CONCLUSIONS
OPTIMISTIC:
THE RADIAL DRIFT OF SOLIDS,
ASSOCIATED WITH COLLISIONAL COAGULATION,
IS THE MOST IMPORTANT PROCESS GOVERNING
THE EVOLUTION OF SOLIDS IN REAL PP DISKS
PESIMISTIC:
THE AGREEMENT BETWEEN OUR RESULTS
AND OBSERVATIONS IS PURELY COINCIDENTAL;
IT DOES NOT HAVE ANY PHYSICAL MEANING
NEEDED:
MORE SOPHISTICATED MODELS OF PP DISKS
EUROPEAN RESEARCH-TRAINING NETWORK „PLANETS”
NETWORK NODES
STOCKHOLM
LONDON
LEIDEN
PARIS
GENEVA
WARSAW
HEIDELBERG
MUNICH
(M0, j0) plane; with dust redistribution
DISK EVOLUTION CODE
GLOBAL EVOLUTION OF DUST IN PROTOPLANETARY DISKS
JENAM 2004, SESSION 3; GRANADA, 16.09.2004
DISK EVOLUTION CODE
• evolution of gas :
- one-dimensional α-disks
- semi-analytical description
- not influenced by the dust
• evolution of solids:
- single-type solids
- spherical grains
- non-destructive collisions
- instantaneous evaporation
- single-valued distribution of grain sizes a(r)
• models are followed for 107 yr
(unless all solids are accreted prior to that time)
GASEOUS DISK EVOLUTION
M0 = 0.16 M~
J0 = 7×1052 g cm2 s-2
R0 = 40 AU
PARTICLE SIZE DISTRIBUTION
WEIDENSCHILLING 1997,
Icarus 127, 290
M1
M2
M1 ≈ M2
DRIFT VELOCITY
APPROXIMATE FORMULAE VS. ACCURATE CALCULATIONS
THIS WORK
WEIDENSCHILLING 1977
(MNRAS 180, 57)
MODELS
GLOBAL EVOLUTION OF DUST IN PROTOPLANETARY DISKS
JENAM 2004, SESSION 3; GRANADA, 16.09.2004
SAMPLE MODEL, GAS
M0 = 0.16 M~
J0 = 7×1052 g cm2 s-2
α=0.01
R0 = 40 AU
colour: T
(max 3200 K)
height: Σg
SAMPLE MODEL, GAS AND SOLIDS
α = 10-3
α = 10-2
α = 10-3
α = 10-2
CONCLUSIONS
• redistribution
• there is a rather sharp transition between
models that lose all solids and models that
almost do not lose any solids
• solids are entirely lost from disks that are
initially massive and/or compact, i.e. hot
• for the same M0 and j0 less viscous disks retain
more solids
• for the same M0 and j0 less viscous disks
produce more extended swarms
FORMATION OF PLANETS
IN 47 UMa
GLOBAL EVOLUTION OF DUST IN PROTOPLANETARY DISKS
JENAM 2004, SESSION 3; GRANADA, 16.09.2004
47 UMa:
G0V;
M = 1.03M~
[Fe/H] = -0.08
d = 13.3pc
PLANETS:
2.54 MJ
0.76 MJ
2.09 AU
3.73 AU
FORMATION OF THE INNER PLANET
IN A STATIC DISK
BODENHEIMER et al. 2000, Icarus 143,2
FORMATION POSSIBLE, IF
Σg = 1-2×104 g cm-2
(20 times more than in the MMSN)
PROBLEMS:
GRAVITATIONAL INSTABILITY OF THE OUTER DISK
DISK ACCRETION RATE TOO HIGH (10-5 M~ yr-1)
CORE TOO MASSIVE (69 MJ)
INNER PLANET
CORE MASS
ENVELOPE MASS
Σd IN THE FEEDING ZONE
OUTER PLANET
CORE MASS
ENVELOPE MASS
Σd IN THE FEEDING ZONE
A NEW LOOK
AT THE SNOWLINE
GLOBAL EVOLUTION OF DUST IN PROTOPLANETARY DISKS
JENAM 2004, SESSION 3; GRANADA, 16.09.2004
Ruden 1999
NATO ASIC
540, 643
RSL = Revap
Revap : T(Revap) = Tevap
RSL
M0 = 0.02 M~
R0 = 52 AU
α = 0.1
SNOWLINE –
A MORE GENERAL DEFINITION
RSL : Σd(RSL + δR) >> Σd(RSL - δR)
δR/R<<1
„KEPLERIZATION RADIUS”:
Rk
:
Rk / vr(Rk) > 107 yr
CONSEQUENCE:
RSL ≠ Revap !
RSL = max (Revap, Rk )
Revap :
T(Revap) = Tevap
1
2
3
4
5
6
7 RfSL [AU]
CONCLUSIONS
• snowline, defined as before, originates due to
the redistribution of solids
• the location of the snowline is fixed in < 105 yr
• min RSL : 0.1 AU
• locally, Σd in the final swarm may be much
higher than in the initial disk