Download Inti didn`t form in the X wind (and neither did most CAIs)

Mass Distribution and Planet
Formation in the Solar Nebula
Steve Desch
School of Earth and Space Exploration
Arizona State University
Planet Formation Conference, Tubingen
March 2, 2009
Outline
•Minimum Mass Solar Nebula
•Nice Model of Planet Migration
•Updated MMSN Model
of Desch (2007)
•Implications for Disk Evolution,
Particle Transport, and Planetary
Growth
•Summary
What Is A
Minimum Mass Solar Nebula?
It's essential to constrain the mass distribution in the solar nebula:
•To know pressures, etc., in region where meteoritic components
like chondrules and CAIs formed
•To know the surface densities of solids and gas in regions where
giant planets formed
•To know how gradients in the disk led to mass transport and disk
evolution.
Many authors developed Minimum Mass Solar Nebula (Edgeworth
1949; Kuiper 1956; Safronov 1967; Alfven & Arrhenius 1970; Weidenschilling
1977; Hayashi 1981; Hayashi et al. 1985)
The model of Weidenschilling (1977) is well developed...
MMSN: H and He are added to
planet masses until they have
solar composition,
The augmented mass then
spread out over the annuli in
which they orbit.
Surface density roughly
(r) ~ r-1.5
Hayashi et al. (1985) widely
used:
(r) = 1700 (r / 1AU)-1.5 g cm-2
= 54 (r / 10 AU)-1.5 g cm-2
Weidenschilling (1977)
A Few Problems with the MMSN
Densities in MMSN model are routinely thought to be too low:
•Can't account for mass lost during planet formation, as entrained
dust or ejected planetesimals (it's a minimum mass!)
•Chondrule formation models (Desch & Connolly 2002) require higher
pressures.
•Models of formation of Jupiter’s core routinely have to increase
solids densities from canonical value (1 - 2 g cm-2) to ~ 10 g cm-2
(e.g., Pollack et al. 1996)
•Can't form Uranus and Neptune cores within lifetime of disk,
while H and He gas are available to accrete (Lissauer & Stewart 1993).
Underlying assumption of MMSN - planets formed where we find
them today - is wrong! Planets migrated! (Fernandez & Ip 1984;
Malhotra 1993). They migrated a lot!! (Tsiganis et al. 2005)
Planetary Migration
The ‘Nice’ Model (Tsiganis et al. 2005; Gomes et al. 2005; Morbidelli et al.
2005; Levison et al. 2007, 2008) explains:
•The timing and magnitude of Late Heavy Bombardment
•Giant planets' semi-major axes, eccentricities and inclinations
•Numbers of Trojan asteroids and irregular satellites
•Structure of Kuiper Belt, etc.
IF
•Planets formed at 5.45 AU (Jupiter), 8.18 AU (Saturn), 11.5 AU
(Neptune / Uranus) and 14.2 AU (Uranus / Neptune)
•A 35 M Disk of Planetesimals extended from 15 - 30 AU
•Best fits involve encounter between Uranus and Neptune; in 50% of
simulations they switch places
Planetary Migration
2:1 resonance crossing occurs about 650 Myr
after solar system formation
r (AU)
5
10
15
20
25
30
New Minimum Mass Solar Nebula
Starting
positions
from
Nice
model
Latest
planetary
models
Dust lost
when gas lost
Desch (2007)
New Minimum Mass Solar Nebula
Disk much denser!
Disk much more
massive: 0.092 M
from 1-30 AU; vs.
0.011 M
Density falls steeply
(as r-2.2) but very
smoothly and
monotonically!
Matches to < 10%!!
Consistent with
many new
constraints
Desch (2007)
New Minimum Mass Solar Nebula
Mass distribution is
not smooth and
monotonic if Uranus
and Neptune did not
switch orbits.
Very strong, if
circumstantial
evidence that
Neptune formed
closer to the Sun
than Uranus
Desch (2007)
Why So Steep A Profile?
Steep profile (r) = 343 (r / 10 AU)-2.17 g cm-2 is not consistent
with steady-state alpha accretion disk (Lynden-Bell & Pringle 1974)
zero-torque condition
near r = R
If (r)  r-p, T(r)  r-q, implies p = 3/2 - q < 3/2
Why So Steep A Profile?
Steep profile (r) = 343 (r / 10 AU)-2.17 g cm-2 is not consistent
with steady-state alpha accretion disk (Lynden-Bell & Pringle 1974)
.
If steady state disk, M = uniform in r (or else mass would build up).
Alpha disk implies  =  C H  T / 
If T(r)  r-q then (r)  r-p, where p = 3/2 - q.
Typically q ≈ 0.4 - 0.75, so p ≈ 0.75 - 1.1
Even the MMSN was inconsistent with steady-state alpha accretion
disk, and new profile definitely is inconsistent.
Why So Steep A Profile?
In fact, if  ~ r-p and T ~r-q and p + q > 2, mass must flow
outward (Takeuchi & Lin 2002)
Desch (2007) solved steady-state equations for alpha disk (LyndenBell & Pringle 1974) with an outer zero-torque boundary condition.
Found a steady-state alpha disk solution if solar nebula was a
decretion disk
zero-torque condition
near r = rd
Why So Steep A Profile?
There are only two free parameters to this steady-state alpha
decretion disk solution:
•location of disk outer edge, rd
•surface density at some radius, (r0)
Why So Steep A Profile?
Steady-state alpha
decretion disk fits
even better!
Best fits involve
rd ≈ 40 - 100 AU
Beyond rd, mass
must be removed.
Disk profile is so
steep because mass is
constantly removed
from the outer edge
of the disk.
A New MMSN: Some Numbers
Once steady-state flow is established, it persists as long as mass
exists inside a few AU to feed it.
Mass flows outward from a few AU, through outer solar system, to
disk edge at ≈ 60 AU.
If. T(r) follows Chiang & Goldreich (1997) and  = 3 x 10-4 then
M = 5 x 10-9 M yr-1. Small particles and gas move out in ≈ 5 Myr
A New MMSN: A Few Caveats
Steady-state decretion disk solution only applies in the outer solar
nebula, beyond a few AU, where we have constraints.
Presumably a reservoir of mass inside a few AU radially spread,
and both dumped mass onto star and fed the decretion flow.
Inferred surface densities are those of planetesimals when they
could accrete into planetary cores = densities of planetesimals
when they grew large enough to dynamically decouple from the
gas. Steady state presumed reached within ~ 105 years.
Assumes planets formed in disk at same locations where they
started in the Nice model. Implies no significant migration after
cores formed.
Why Is There An Outer Edge?
External Photoevaporation!
External UV radiation
with G0 = 1000 (several
pc from O6 star) causes
photoevaporation that
can remove mass at disk
edge at 60 AU at rate
5 x 10-9 M yr-1
Self-regulating: keeps
disk edge where photoevaporation mass loss
rate = mass flux through
disk.
Adams et al. (2004)
Why Is There An Outer Edge?
External photoevaporation imposes a zero-torque boundary
condition at outer edge: d / dr = 0 at disk edge!
UV
T ~ 104 K
T ~ 102 K
 decreases
 increases
∆r
Why Is There An Outer Edge?
External photoevaporation prevents disk from viscously
spreading! Takes mass away from disk, but also forces remaining
mass into more compact configuration.
UV
T ~ 104 K
T ~ 102 K
High pressure
Gas must gain angular
momentum to escape through
outer edge of disk!
Evolution of New MMSN Disk
Total mass in disk <
10 AU = 0.10 M
Roughly 0.05 M
dumped onto star,
0.05 M fed into
outer disk.
Mass lost onto star
depletes inner disk.
Steady-state solution
in outer solar system
can be maintained for
(0.05 M) / (5 x 10-9
M yr-1) = 10 Myr
time
Evolution of New MMSN Disk
Compare to viscously
spreading disk
Mass in outer solar
system allowed to
spread out to several
x 100 AU.
Consistent with disks
in Taurus (Hartmann
1998)
Surface density at 10
AU falls by more
than a factor of 10.
time
Consequence #1: Radial Transport
Steady-state alpha decretion disk, like steady-state alpha accretion
disk, experiences radial diffusion on timescales ~ (r/H)2 ()-1
In accretion disks, outward radial diffusion still occurs, on same
timescale as net flow of gas inward: crystalline silicates (Gail 2001)
or CAIs (Cuzzi et al. 2003). But outward radial diffusion is always
"upstream" and limited (Cuzzi & Hogan 2003; Cuzzi et al. 2003).
In a decretion disk, outward radial diffusion goes "with the flow":
the majority of material can be transported outward.
Enables outward transport of crystalline silicates and even CAI-like
materials produced in inner solar system, out to regions > 10 AU
where comets form.
Explains presence of CAIs in comets!
Comet 81P/Wild 2
Scattered into present orbit in
1974; was previously a member
of the Kuiper Belt Scattered Disk
Probably formed at 10-30 AU
Zolensky et al (2006)
Stardust Sample Track 25
called ‘Inti’. It’s a CAI,
formed (by condensation)
at > 1700 K.
Consequence #2: Planet Growth
New MMSN model much more favorable for planetary growth:
•Planets form closer to Sun in Nice model: orbital timescales faster
•Density of solids higher than in traditional MMSN
•Higher gas densities damp eccentricities of planetesimals,
facilitating accretion
Desch (2007) calculated growth rate of planetary cores using
formulism of Kokubo & Ida (2002).
Tidal disruption considered; assumed mass of planetesimals
~ 3 x 1012 g (R = 0.1 km, i.e., comets).
•Cores grow in 0.5 Myr (J), 2 Myr (S), 5-6 Myr (N) and 9-11 Myr (U)
•Even Uranus and Neptune reach 10 M before H, He gas gone
Desch (2007)
Uranus and Neptune would not form in a viscously spreading, Taurusstyle disk. Photoevaporation aids planet growth!
Desch (2007)
Masses of Solids in Planets
Inside 15 AU, planets
limited by availability
of solids; they achieve
isolation masses
Desch (2007)
Outside 15 AU,
planets cannot grow
before gas dissipates;
no gas = no damping
of eccentricities
Some Conclusions
The traditional MMSN is wrong. (1) Planets did not form where we
find them today: solar nebula must have been more compact. (2)
Mass was lost during planet formation as dust and/or ejected
planetesimals: solar nebula must have been more massive.
Using Nice model positions, Desch (2007) found new MMSN
model. Mass ~ 0.1 M, (r) ~ r-2.2. Strongly implies Uranus and
Neptune switched orbits.
Cannot be in steady-state accretion; but (r) is consistent with outer
solar system as a steady-state alpha decretion disk with an outer
edge ≈ 60 AU.
Consistent with observed outer edge in Kuiper
Belt at 47 AU (Trujillo & Brown 2001)
Some Conclusions
Likely cause of outer edge is external photoevaporation due to
nearby massive stars.
External photoevaporation naturally imposes zero-torque outer
boundary condition because of intense heating.
Photoevaporation
removes gas from disk,
but prevents it from
viscously spreading
outward.
Radius of disk, rate of
mass loss, consistent
with environment with
G0 ~ 103, equivalent to
a few pc from O6 star.
Some Conclusions
Radius of disk, mass loss rate, consistent
with environment with G0 ~ 103, equal to
being a few pc from an O6 star.
Formation of Sun in massive star-forming region also consistent
with injection of short-lived radionuclides like 60Fe from nearby
core-collapse supernova (Hester et al. 2004).
Formation of Sun in massive star-forming region also consistent
with stellar encounter to explain orbits of Sedna and other KBOs
(Kenyon & Bromley 2004).
Mass independent fractionation of oxygen isotopes observed in
meteoritic inclusions, if due to self-shielding of CO isotopomers
against photodissociation, also requires G0 ~ 103 (Lyons et al. 2009).
Some Conclusions
Steady-state decretion disk profile assists outward radial
transport.
Crystalline silicates and Inti-like objects formed in the inner solar
system are more easily transported outward to comet-forming zone.
For  = 3 x 10-4, outward transport takes no more than 5 Myr.
Steady-state decretion disk profile aids planet growth by keeping
mass in more compact configuration.
Starting with cometesimals, cores of even Neptune & Uranus could
form within 10 Myr while H/He gas remains.
Consistent with Saturn formation within 2 Myr (Castillo et al. 2007)
Star-forming environment matters to planet formation!