Problems Facing Planet Formation around M Stars

Fred C. AdamsUniversity of Michigan

From work in collaboration with: P. Bodenheimer, M. Fatuzzo, D. Hollenbach, G. Laughlin, P. Myers, and E. Proszkow

OUTLINE

• Planet formation via the core accretion paradigm a function of stellar mass

• Photoevaporation of circumstellar disks due to external FUV radiation

• Scattering interactions between newly formed solar systems and binary stars

Overarching question: How does planetformation proceed differently in disks surrounding low mass (M type) stars?

Phase 1: Growing planet consists mostly of solid material. Planet experiences runaway accretion until the feeding zone is depleted. Solid accretion occurs much faster than gas accretion during this phase. Phase 2: Solid and gas accretion rates are both small and nearly independent of time. This phase dictates the overall time-scale.Phase 3: Runaway gas accretion occurs after the solid and gas masses are roughly equal.

Core Accretion ParadigmPerri & Cameron 1974,

Mizuno et al 1978, Mizuno 1980, Bodenheimer & Pollack 1986, Pollack et al 1996

“Standard model” (Pollack et al.1996) issues:1. Central core mass of the planet seems too high2. Time to reach runaway gas accretion is too long

Recent work refines the core accretion scenario:1. Improved physics:

equation of state ( Saumon & Guillot 2004)envelope opacity (Ikoma et al 2000, Podolak 2003)

2. Additional physics:migration of the cores (Papaloizou & Terquem 1999,

Alibert et al 2004, Ida & Lin 2004)

turbulence in the disk (Rice & Armitage 2003)competition between embryos (Hubickyj et al 2005)time evolution of the disk (Alibert et al 2004,

Ida & Lin 2004, LBA2004)

A Brief History of Core Accretion

** the earliest phase -- dust to rocks -- still under study **

During Phase 1, mass increase of the planet depends on its radius, and the ratio of the gravitational to geometric cross section:

Core Accretion Paradigm

Escape velocity from the planetary surface is much larger than relative velocity of planetesimals. Phase I is characterized by runaway growth of the solid core which ends when the core depletes its feeding zone.

Hill Radius

Phase 2: As solid accretion proceeds to several Earth masses, gas envelope becomes increasingly significant. Modeling this stage requires computation of the hydrodynamic structure of the gas envelope.1. Stellar Evolution code for

the quasi-equilibrium envelope:

2. Planetesimal dissolution routine:

- numerical integration in envelope- energy deposition into envelope

Benchmark model of Jupiter formation (Pollack et al. 1996)

Core Mass

Gas Mass

Total Mass

Millions of Years

Earth

Masses

isolation mass reached

Disk Properties

€

σ(r) =σ d∗(rin /r)3 / 2 , T(r) = Td∗(rin /r)

3 / 4

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M0 = Md (t = 0) = 0.05 M∗

Passive, flat disk with isothermaltemperature profile in z-direction

New!

Mass

(Eart

h

mass

)

Time (Myr)

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M∗ =1.0Msun

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M∗ = 0.4Msun

Forming Planets at a = 5.2 AU

2.03

15.3

10.8 Me

time

Planet mass vs semimajor axis a (AU)

Stellar mass = 0.4 Msun

Planet Inhibiting FactorsOrbits are slower: Surface density of solids is lower:

If M stars form in groups/clusters:Gas is more easily evaporated in disks around M stars (by factor 10-100)Passing binaries and tides disrupt disks

€

σ d ∝Md ∝M∗ , Γearly ∝M∗2 , Γlate ∝M∗

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Γorbit =Ω∝M∗1/ 2

Photoevaporation from External FUV

Subcritical Disk, Spherical flow, PDR heating (Adams, Hollenbach, Laughlin, Gorti 2004)

Composite Distribution of FUV Fluxes

Composite Distribution includes:1. Distribution of cluster sizes N (from Lada/Lada 2003)2. Distribution of FUV luminosity per cluster from sampling IMF3. Distribution of radial positions within the cluster

Results from PDR Code

Lots of chemistry and many heating/cooling linesdetermine the temperatureas a function of G, n, A

Solution for Fluid Fields

outer disk edge

sonic surface

Evaporation Time vs FUV Field

-----------------------

(for disks around solar mass stars)

Evaporation Time vs Stellar Mass

Evaporation is much more effective for disks around low-mass stars:Giant planet formation can be compromised

Over time span 10 Myr FUV Flux of G = 3000truncates disk at radius

€

Rdisk ≈ 34AU (M∗ /Msun )

Evaporation vs Accretion

Disk accretion aids and abetsthe disk destruction process by draining gas from the inside, while evaporation removes gas from the outside . . .

Basic ResultFormation of Jupiter mass planets isseriously inhibited around M stars

however: Formation of Neptune mass planetstakes place readily around M stars

Planets around M stars are smaller and rockier than for solar type stars

Solar System Scattering

Many Parameters +Chaotic Behavior

Many Simulations Monte Carlo

Monte Carlo Experiments

• Jupiter only, v = 1 km/s, N=40,000 realizations• 4 giant planets, v = 1 km/s, N=50,000 realizations• KB Objects, v = 1 km/s, N=30,000 realizations • Earth only, v = 40 km/s, N=100,000 realizations • 4 giant planets, v = 40 km/s, Solar mass, N=100,000 realizations• 4 giant planets, v = 1 km/s, varying stellar mass, N=100,000 realizations

Ecc

en

t ric

ity

e

Semi-major axis a

JupiterSaturn Uranus

Neptune

Scattering Results for our Solar System

Red Dwarf saves the Earth

sun red dwarf

earth

moon

20 AU1601350±≈C

Cross Sections

2.0 M1.0 M

0.5 M0.25 M

2/1

*0

−

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛≈

MMa

C p

AUejσ

Summary• Planet Formation is inhibited around M dwarfs• The core accretion paradigm predicts that Jovian

planets should be rare around M dwarfs • Neptune-like planets predicted to be more common• Photoevaporation model for external FUV radiation• Disks around M stars are more easily evaporated• Calculation of planet scattering cross sections• Planets around M stars are more easily scattered

All of these effects scale with stellar mass:

€

∝M∗p

References

2. Photoevaporation of Circumstellar Disks due to external FUV Radiation 2004, ApJ, 611, 360

1. Core Accretion Model Predicts Few Jovian Planets Orbiting Red Dwarfs 2004, ApJ, 612, L73

3. Early Evolution of Stellar Groups and Clusters 2006, ApJ, 641, 504

• Grain opacities are a key issue. Original studies (Pollack et al. 1996) used envelope opacities with an interstellar size distribution.

• Material that enters a giant planet envelope has been modified from the original interstellar grains by coagulation and fragmentation.

• When grains enter the protoplanetary envelope, they coagulate and settle out quickly into warmer regions where they are destroyed. True opacities are ~50x smaller than interstellar (Podolak 2003).

log T

QuickTime™ and aGraphics decompressor

are needed to see this picture.

non-ideal gasideal gas

interstellar opacity

envelope opacity

-2

2

0

4

3.5 2.03.0 2.54.0

A key (well established) result of standard core accretion theory is the extraordinary sensitivity of the time of onset of rapid gas accretion to the surface density of solids in the disk.

Recent calculations (Hubickyj et al. 2005), show that decreasing solid surface density from 10 to 6 g/cm^2 causes a 12 Myr delay in the onset of rapid gas accretion. This density decrease corresponds to a ~0.2 dex decrease in metallicity.

Time (Millions of Years)

1 32 54

1

876

10

20

30

Mass (Earth

Masses)

Competition between embryos can introduce a cutoff to solid body accretion prior to obtaining isolation mass. If this occurs at core masses of order 10 Earth masses, onset of rapid gas accretion can occur much earlier. This effect also leads to an acceptably decreased core mass.

5 earth mass cutoff slows down onset of rapid gas accretion

no embryo competitio

n

10 earth mass cutoff

(Hubickyj et al. 2005)

30

40

10

20

total mass

core mass

gas mass

321time (millions of years)

21 3time (millions of years)

mass (earth

masses)

log L/Lsun

-10

-8

-6

-4

-2

Reduced grain opacity greatly speeds up the gas accretion

timescale.

(Hubickyj et al. 2005)