Transcript The End of the Main Sequence - University of Western Ontario

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
Overarching question: How does planet
formation proceed differently in disks
surrounding low mass (M type) stars?
• 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
Core Accretion Paradigm
Perri & Cameron 1974, Mizuno et al
1978, Mizuno 1980, Bodenheimer &
Pollack 1986, Pollack et al 1996
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.
A Brief History of Core Accretion
“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
time evolution of the disk (Alibert et al 2004,
2005)
** the earliest
phase -- dust to rocks -- still under study **
Ida & Lin 2004, LBA2004)
Core Accretion Paradigm
During Phase 1, mass increase of
the planet depends on its radius,
and the ratio of the gravitational to
geometric cross section:
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 quasiequilibrium envelope:
2. Planetesimal dissolution routine:
- numerical integration in envelope
- energy deposition into envelope
Earth
Masses
Benchmark model
of Jupiter formation
Total Mass
(Pollack et al. 1996)
Gas Mass
isolation mass
reached
Millions of Years
Core Mass
New!
Disk Properties
Passive, flat disk with isothermal
temperature profile in z-direction
 (r)   d (rin /r)
3/ 2
, T(r)  Td (rin /r)
M0  Md (t  0)  0.05 M
3/ 4
Mass (Earth mass)
Forming Planets at a = 5.2 AU
M  1.0M sun

M  0.4 M sun
 Time (Myr)
2.03
15.3
10.8 Me
Stellar mass = 0.4 Msun
Planet mass vs semimajor axis a (AU)
Planet Inhibiting Factors
Orbits are slower: orbit   M
Surface density of solids is lower:
1/ 2

 d  Md  M , early  M2 , late  M

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
Photoevaporation from External FUV
Subcritical Disk, Spherical flow, PDR heating
(Adams, Hollenbach, Laughlin, Gorti 2004)
Composite Distribution of FUV Fluxe
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
sonic surface
outer disk edge
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
Rdisk  34AU (M / M sun )
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
Scattering Results for our Solar System
Jupiter
Saturn
Uranus
Neptune
Semi-major axis a
Red Dwarf saves the Earth
moon
red dwarf
sun
earth
Cross Sections
2.0 M
0.5 M
 a p  M * 

 ej  C 0  
 AU  M  
1 / 2
C 0  1350  160AU
2
1.0 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:
M
p

References
1. Core Accretion Model Predicts Few
Jovian Planets Orbiting Red Dwarfs
2004, ApJ, 612, L73
2. Photoevaporation of Circumstellar
Disks due to external FUV Radiation
2004, ApJ, 611, 360
3. Early Evolution of Stellar Groups
and Clusters 2006, ApJ, 641, 504
non-ideal gas
ideal gas
4
Q u ic k T im e ™ a n d a
G r a p h ic s d e c o m p r e s s o r
a r e n e e d e d t o s e e t h is p ic t u r e .
2
interstellar opacity
0
envelope opacity
-2
4.0
3.5
3.0
2.5
2.0
log T
•
•
•
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).
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.
Mass (Earth Masses)
10 earth
mass
cutoff
(Hubickyj et al. 2005)
30
no embryo
competition
20
5 earth mass cutoff
slows down onset of
rapid gas accretion
10
1
1
2
3
4
5
6
7
8
Time (Millions of Years)
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.
40
Reduced grain opacity greatly speeds up the
gas accretion timescale.
-2
30
-4
gas mass
log L/Lsun
mass (earth masses)
total mass
20
-6
core mass
10
-8
1
2
3
time (millions of years)
-10
1
2
3
time (millions of years)
(Hubickyj et al. 2005)