Problems Facing Planet Formation around M Stars Fred C. Adams University 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 planet formation 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 Paradigm Perri & 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 high 2. 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 Passive, flat disk with isothermal temperature profile in z-direction New!

Mass (Earth mass) Time (Myr) Forming Planets at a = 5.2 AU

Me time Planet mass vs semimajor axis a (AU) Stellar mass = 0.4 Msun

Planet Inhibiting Factors Orbits 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 ) Passing binaries and tides disrupt disks

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 IMF 3. Distribution of radial positions within the cluster

Results from PDR Code Lots of chemistry and many heating/cooling lines determine the temperature as 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 = 3000 truncates disk at radius

Evaporation vs Accretion Disk accretion aids and abets the disk destruction process by draining gas from the inside, while evaporation removes gas from the outside...

Basic Result Formation of Jupiter mass planets is seriously inhibited around M stars however: Formation of Neptune mass planets takes 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

Eccentricity e Semi-major axis a Jupiter SaturnUranus Neptune Scattering Results for our Solar System

Red Dwarf saves the Earth sun red dwarf earth moon

Cross Sections 2.0 M  1.0 M  0.5 M  0.25 M 

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:

References 2. Photoevaporation of Circumstellar Disks due to external FUV Radiation 2004, ApJ, 611, 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 non-ideal gas ideal gas interstellar opacity envelope opacity

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) 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 competition 10 earth mass cutoff (Hubickyj et al. 2005)

total mass core mass gas mass 321 time (millions of years) 213 mass (earth masses) log L/Lsun Reduced grain opacity greatly speeds up the gas accretion timescale. (Hubickyj et al. 2005)