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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
€
M0 = Md (t = 0) = 0.05 M∗
Passive, flat disk with isothermaltemperature profile in z-direction
New!
Mass
(Eart
h
mass
)
Time (Myr)
€
M∗ =1.0Msun
€
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∗
€
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)
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