Download Disk Instability Models

Disk Instability Models: What Works
and What Does Not Work
Alan P. Boss
The Formation
of
Carnegie Institution of Washington
Planetary Systems
Heretic’s Approach to
Solar System
FormationFForm
From
Protostellar Disks to Planetary Systems
University of Western Ontario, London, Ontario, Canada
May 18, 2006
Outline:
 Recent work on disk instability models:
•Vertical convective fluxes
•Survival of virtual protoplanets
•Disks in binary G dwarf star systems
•200-AU-scale disks around G dwarfs
•Disks around M dwarf stars
•Formation of super-Earths around M dwarfs
3
Disk Instability?
In order for disk instability to be able to form giant
protoplanets, there must be a means of cooling the disk on
the time scale of the instability, which is on the order of the
orbital period.
Radiative cooling in an optically thick disk is too inefficient
to cool the disk’s midplane, as its characteristic time scale is
of order 30,000 yrs for the solar nebula at 10 AU.
The only other possible mechanism for cooling the disk
midplane is convective transport – can it do the job?
2 AU
Temperature contours
at 339 yrs
Vertical
scale
expanded
by 10
Inner
edge
4 AU
^
^ ^^ ^
^ 20 AU
2 AU
339 yrs
Superadiabatic vertical temperature gradients
(Schwarzschild criterion for convection)
Vertical scale
expanded by
10
4 AU
^
^ ^ ^ ^
^ 20 AU
Velocity vectors at 339 yrs
2 AU
8 AU
^
^
^ 14 AU
Vertical Convective Energy Flux
1. For each hydrodynamical cell, calculate the vertical
thermal energy flux:
Fconv = - vq A E r
where vq = vertical velocity, A = cell area
perpendicular to the vertical velocity, E = specific
internal energy of cell, and r = cell density.
2. Sum this flux over nearly horizontal surfaces to find
the total vertical convective energy flux as a function
of height in the disk.
339 yrs
Peak flux is high enough to
remove all thermal energy
from this ring of gas in 50 yrs.
Rapid Convective Cooling? (Boss 2004)
• Radiative transfer is unable to cool disk midplanes on the
dynamical time scale (a few rotational periods).
• Convective transport appears to be capable of cooling
disk midplanes on the dynamical time scale.
• Evidence for convective transport includes Schwarzschild
criterion for convection, convective cells seen in velocity
vector fields, and calculations of the total vertical
convective energy flux.
• Assuming that the surface can radiate away the disk’s
heat on a comparable time scale, marginally
gravitationally unstable disks should be able to form giant
protoplanets.
Mayer et al. (2002)
disk instability
model after 800 yrs
[SPH with simple
thermodynamics]
time evolution of
clump orbits
Boss (2005)
Virtual protoplanet orbits for at least 1000 years, at least 30 orbits
Gas Giant Planets in Multiple Star Systems
• Hierarchical triple star systems (planet orbits the single
member of the triple):
16 Cygni B – about 850 AU separation
HD 178911 B – about 640 AU separation
HD 41004 A – about 23 AU separation
• Binary star systems:
HD 195019 – about 150 AU separation
HD 114762 – about 130 AU separation
HD 19994 – about 100 AU separation
Gamma Cephei – about 20 AU separation
Gl 86 – about 20 AU separation
[ At least ~ 29 multiple stars have planets to date (M. Mugrauer, 2004)]
Q = cs W/(p G s)
marginally
gravitationally
unstable disk
Q=2 as in Nelson (2000)
Q=1 highly unstable
20 AU
radius
disk
no binary
245 years
to binary ^– at apastron
20 AU
radius
disk
after one
binary
rotation
period:
239 years
Ms= 1 Msun
Md= 0.09 Msun
a = 50 AU
e = 0.5
Differences between Nelson (2000) and Boss (2006)
• Nelson (2000) used (2D)
60,000 SPH particles
• Thin disk so adiabatic
gradient assumed in
vertical direction, as if
cooled by convection
• Surface T > 100 K means
higher midplane T
• Artificial viscosity
converts KE into heat in
shock fronts and
elsewhere (a = 0.002 to
0.005)
• Cooling time ~ 10 P
• Boss (2006) used over
1,000,000 grid points (3D)
• Fully 3D so vertical
convection cools disk
midplane in optically thick
regions, radiation cools in
optically thin regions
• Surface T = 50 K means
lower midplane T
• No artificial viscosity so
no irreversible heating in
shock fronts and a =0
assumed
• Cooling time ~ 1-2 P
GQ Lup b – 1 Myr-old gas giant planet at 100 AU? (Neuhauser et al. 2005)
200 AU radius disk with 0.16 Msun orbiting a 1Msun protostar after 20000 yrs (Boss 2006)
=> SIM!
Extrasolar Planet Census: Low-mass Host Stars
* Most planet-host stars are G dwarf stars like the Sun, while
most nearby stars are M dwarfs, less massive than the Sun.
* M4 dwarf star Gl876 (0.32 MSun) has two known gas giant
planets and one sub-Neptune-mass planet.
* Microlensing surveys appear to have found two Jupiter-mass
planets orbiting M dwarfs.
* Two M dwarfs with known planets (Gl 876, Gl 436) both
have solar metallicity – neither is metal-rich.
* Another M dwarf with a known planet (Gl 581) is metal-poor
([Fe/H] = -0.25) compared to the Sun.
* While the frequency of giant planets around M dwarfs is
uncertain, it is clearly not zero.
Surface density needed for Q = 1 disk instability
Initial disk surface density: Qmin = 1.5
0.5 MSun protostar
0.065 MSun disk
20 AU
radius
disk
20 AU
radius
disk
0.5 MSun protostar
0.065 MSun disk
Disk surface density at 208 yr
0.5 MSun protostar
0.065 MSun disk
0.93 MJupiter clump
gas density at 208 yr
Clump formation by disk instability after 445 yrs in a
0.02 MSun disk orbiting a 0.1 MSun star (Boss 2006).
Jupiter-mass
clump at 7 AU
0.065 MSun disk with Qmin= 1.5 orbiting a 0.5 MSun protostar after 215 yrs
with
latest M
discoveries
added
DiscoveryDiscovery
space withspace
planets
around
dwarf stars
highlighted
Gl 876
OGLE-2003-BLG-235
OGLE-2005-BLG-071
Gl 876
Gl 436
Gl 581
Gl 876
OGLE-2005-BLG-169
OGLE-2005-BLG-390
Heretical Explanation for Microlensing Planets
• Most stars form in regions of high-mass star formation (e.g.,
Orion, Carina) where their protoplanetary disks can be
photoevaporated away by nearby O stars.
• Photoevaporation converts gas giant protoplanets into ice
giants if the protoplanet orbits outside a critical radius, which
depends on the mass of the host star.
• For solar-mass stars, the critical radius is > 5 AU, while for a
0.3 MSun M dwarf star, the critical radius is > 1.5 AU.
• If M dwarfs have disks massive enough to undergo disk
instability, then their gas giant protoplanets orbiting outside
~1.5 AU will be photoevaporated down to super-Earth mass,
for M dwarfs in regions of high-mass star formation.
• In low-mass star formation regions (e.g., Taurus), their gas
giant protoplanets will survive to become gas giant planets.