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...

Weidenschilling (1977)

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

A Few Problems with the MMSNDensities 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)

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

Planetary Migration

r (AU) 5 10 15 20 25 30

2:1 resonance crossing occurs about 650 Myr after solar system formation

New Minimum Mass Solar Nebula

Desch (2007)

Starting positions from Nice model

Latest planetary models

Dust lost when gas lost

New Minimum Mass Solar NebulaDisk 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 constraintsDesch (2007)

New Minimum Mass Solar NebulaMass 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)

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)

Why So Steep A Profile?

If (r) r-p, T(r) r-q, implies p = 3/2 - q < 3/2

zero-torque condition near r = R

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)

Why So Steep A Profile?

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?

Desch (2007) solved steady-state equations for alpha disk (Lynden-

Bell & Pringle 1974) with an outer zero-torque boundary condition. Found a steady-state alpha disk solution if solar nebula was a decretion disk

In fact, if ~ r-p and T ~r-q and p + q > 2, mass must flow outward (Takeuchi & Lin 2002)

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 NumbersOnce 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 CaveatsSteady-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!

Adams et al. (2004)

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 photo-evaporation mass loss rate = mass flux through disk.

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

∆ r

decreases increases

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

Gas must gain angular momentum to escape through outer edge of disk!

High pressure

Evolution of New MMSN DiskTotal 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 DiskCompare 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.

Comet 81P/Wild 2Scattered into present orbit in 1974; was previously a member of the Kuiper Belt Scattered Disk

Probably formed at 10-30 AU

Stardust Sample Track 25 called ‘Inti’. It’s a CAI, formed (by condensation) at > 1700 K.

Zolensky et al (2006)

Explains presence of CAIs in comets!

Consequence #2: Planet GrowthNew 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).

Desch (2007)

•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

Uranus and Neptune would not form in a viscously spreading, Taurus-style 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 Outside 15 AU,

planets cannot grow before gas dissipates; no gas = no damping of eccentricities

Desch (2007)

Some ConclusionsThe 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 ConclusionsLikely 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

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).

Radius of disk, mass loss rate, consistent with environment with G0 ~ 103, equal to being a few pc from an O6 star.

Some ConclusionsSteady-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!