Download The Role of the Galaxy in the Dynamical Evolution of

The Role of the Galaxy in the Dynamical
Evolution of Transneptunian Objects
Martin Duncan
Queen's University at Kingston, Canada
In collaboration with
Ramon Brasser
Observatoire de Nice, France
&
Harold Levison and Luke Dones,
Southwest Research Institute, Boulder, USA
Outline
• Brief background on Inner and Outer Oort cloud
• Brief background on embedded star clusters
• Numerical simulations
• Results of computations
• Ongoing work and Summary
Oort cloud
- Oort cloud is cloud of comets surrounding the
Sun (Oort, 1950).
- Isotropic beyond a~10 000 AU, but there may
exist massive inner region (Hills 1981)
from which long-period comets are rare.
-
Inner part (likely flattened) may be related
to current scattered disk (Duncan &
Levison 1997) and/or a population
produced in putative primordial star cluster
environment (Gaidos 1995, Fernandez
1997, Eggers 1999, Fernandez & Brunini
2000, Morbidelli & Levison 2004, Kenyon
& Bromley 2004, Brasser et al 2005 - this
talk)
- Several simulations done in the past to form
the Oort cloud, yet none incorporating both
embedded star cluster environment and gas
drag from primordial solar nebula.
Early Model of Oort Cloud formation (Duncan, Quinn and Tremaine 1987)
Assumed current
giant planet orbits
and masses with
comets started on
very eccentric orbits
(a ~ 2000 AU) with
pericentres (q)
distributed from just
inside Jupiter to just
outside Neptune.
Included tidal field
from Galactic plane
and passing stars
representative of
current solar
neighbourhood
Torquing due to Galactic Tides
Galactic Disc
(slab of constant density ρG)
r
F = -4π G ρG z
Torque dJ/dt = r X F
For high eccentricity J α q1/2, where q is
pericentric distance.
Thus tidal torque will change q and can define tidal
torquing time = Δq/(dq/dt) for say Δq = 10 AU.
Example of
evolution of
perihelion
distance, q,
versus
semimajor
axis, a, for a
comet
reaching
Oort cloud in
current Solar
environment
(Dones et al
2004)
Tidal torque
evolves q at
constant a
Diffuse in a at constant q
Oort Cloud Dynamics
In current Galactic
environment (upper red
curve) Jup & Sat
(lower 2 blue curves) tend to
eject comets with peris in
their vicinities.
Comets with peris in Ura Nep zone and beyond (top 2
blue curves) can have peris
lifted by tides before
ejection.
Origin of The Oort Cloud
Dones, Levison,
Duncan & Weissman
2004 (DLDW04)
integrated the orbits
of several thousand
test particles.
Initial orbits were
uniform in semimajor
axis between 4 &40
AU with small
eccentricities &
inclinations (unlike
DQT87)
Forces included Sun
and 4 giant planets,
Galactic tides (both
disk and radial
components) &
passing stars.
Origin of Oort Cloud
(DLDW04)
Scattered Disk
a) By 4 Gyr, equal
numbers (2.5% of
original) in outer
cloud (a > 20,000
AU) vs. inner cloud
Outer Cloud
b) Scattered disk
population is ~1/10
of outer cloud
Inner Cloud
Mass Estimates of Outer Oort Cloud (DBDL08)
Mass Estimates of Outer Oort Cloud (part 2)
Oort cloud: Formation in “Standard Model”
(DLDW04)
Outer OC formation efficiency only ~3%
after 4 Gyr in current environment
and inner cloud comparable to outer
cloud in mass.
May be problematic:
1) Mass of protoplanetary disk may have
been low ( as current migration
theory suggest it was - Gomes et al
2004). If so, is Standard Model too
inefficient, especially since stripping
by Giant Molecular Clouds was not
included? Then again, mass of typical
comet is unknown, so estimates of
mass vary greatly ( ~ 1 - 60 Earth
masses: Francis 2004).
2) Ratio of # of scattered objects to
# in OC seems too high in
simulations (but there are large
observational uncertainties).
3) Does not produce Sedna-like orbits
(a ~ 500, q ~ 75)
2003 VB12: “SEDNA” (Brown, Trujillo & Rabinowitz)
R magnitude: 20.5, H=1.7
Extremely red
Not detected in IR by Spitzer or IRAM ->
D < 1800 km, so it's smaller than Pluto.
Probably bigger than Quaoar (D = 1250 km).
a = 530 AU (3 oppositions)
q = 76 AU !!
i = 12 degrees
Now at 90 AU --> will reach
perihelion in 2076!) Would only be
detectable in survey over ~ 2% of orbit
Origin? Probably early encounter with
passing star (cf. Morbidelli & Levison
2004; Kenyon & Bromley 2004)
Possible Chronology of Oort Cloud Formation
• (THIS WORK):
First few million years: Sun forms in embedded star cluster (discussed
next), Jupiter and Saturn cores (and possibly Uranus and Neptune
close in) form. Jupiter and Saturn accrete gas, rapidly approaching
current masses, and such large masses very quickly scatter
planetesimals in their vicinities. Passing stars and cluster tidal field
lift pericentres ⇒ inner Oort Cloud.
•(ONGOING WORK):
Subsequent evolution involves evolution on longer timescales of
scattered disk from current Uranus and Neptune zone and the early
inner Oort cloud as perturbed by Giant Molecular Clouds and
evolving stellar background. Also investigating extent of capture of
comets from disks of passing stars during embedded phase.
Embedded star clusters
Embedded clusters
•Young (1-5 Myr) star-forming regions, fraction of mass in stars ~1030%
• Difficult to observe in the visible; most done in the IR
•Very dense environment (typically 102-103 Msun pc-3 in stars; but
Trapezium and others have >104 Msun pc-3 in stars
- e.g. Gutherman et al 2005 find 24-91% of stars in 3 clusters are in
regions denser than 104 Msun pc-3 )
• Residual gas ultimately blown away, most likely by massive stars (O
& B-type)
• Open clusters are not the normal evolutionary outcome - most
embedded cluster dissolve (Lada & Lada 2003) and most stars are
thought to have formed in embedded clusters of 100-1000 stars.
Plummer potential arises from
ρ(r) = ρ0 / (1 + r 2/ rc2) 5/2
1)
Construct N-body
realization (including
realistic mass spectrum and
assumed star formation
efficiency ~ 10-25%.)
2) Integrate all stars in chosen
fixed potential (NOT
including star-star
scattering). Two examples
at right.
3) For each ~ solar-mass star,
record encounter
parameters as other stars
enter ‘sphere of influence’
influence’
of fixed radius (~ 0.5-1
Plummer radius) centred on
chosen star. Encounter
parameters are later used in
SWIFT integrations to
compute stellar
perturbations on comets.
Cluster simulations
Numerical simulations
• Planets: Jovians: pre-LHB orbits (the ‘Nice model’) but current masses;
parameters: either only Jup+Sat or J+S+U+N
• Cluster: Plummer potential produces tidal field;
parameters: central density ρ0 , core radius, lifetime (~5 Myr)
• Sun: Orbit in cluster simulated simultaneously to get time-varying tides;
parameters: inclination, eccentricity, semi-major axis
• Stars: Introduced via previously determined ‘catalog’ of encounters from
N-body realization, integrated directly while in ‘sphere of influence’, then
removed.
• Gas (if present): Drag formula using local density ; parameters: density
profile, inner/outer cutoff
Dense cluster, just Jup+Sat, no gas drag
Dense cluster, just Jup+Sat, no gas drag
Positions of 2000 CR105 and (90377) Sedna
Comet Clouds for different cluster densities
Example of models for the “Sedna region”
Gas Drag
Deceleration due to drag
∝ (ρg/rc)
vr2
where ρg is gas density and vr
is relative velocity. We
often assume comet size rc =
1.7 km (derived from recent
long-period comet
observations) but compare
with runs with larger sizes.
For low inclination eccentric
orbits orbiting in Hayashi
profile gas disk, angular
momentum roughly
conserved. This leads to
increase of pericentre! and
may lift comets away from
scattering planets.
Gas drag added: minimum mass gas disk, dissipation time 2 Myr
Gas drag added: minimum mass gas disk, dissipation time 2 Myr
Gas drag added: minimum mass gas disk, dissipation time 2 Myr
5 x minimum mass gas but truncated at 10 AU; decay time = 2 Myr
Different configurations at 3 Myr (typical cluster lifetime)
Puffing Up the Inner Cloud (BDL08)?
Start with inner
clouds of BDL06
(recall ρ0 is central
density of initial
embedded star
cluster).
Subject them to 4
Gyr of passing stars
in current Galactic
environment.
Only small fraction
of comets evolve
from inner to outer
cloud, especially in
systems that
originally produced
a Sedna-like
population.
Capture of inner cloud objects from passing stars?
(Morbidelli & Levison 2004; Kenyon & Bromley 2004)
Capture of inner cloud objects from passing stars?
(Morbidelli & Levison 2004; Kenyon & Bromley 2004)
Capture of inner cloud objects from passing stars?
(Morbidelli & Levison 2004; Kenyon & Bromley 2004)
Summary on Origins of Oort Cloud in Early Solar Environment
• Standard Model:
Model: Planetesimal clearing without gas and using existing planetary
orbits/Galactic tidal field is very inefficient (~2.5%) at creating the outer Oort Cloud, does not
produce “Sednas”
Sednas” and produces a [scattered disk / Oort cloud] mass ratio probably larger than
inferred from observations.
•Within a Dense Embedded Star Cluster the efficiency of populating the (mostly inner) Oort
cloud is 5-20%, depending on the cluster density and stellar orbit. A dense embedded star
cluster can reproduce orbits of Sedna and CR105.
• Protoplanetary Gas drag produces a size-sorting: large objects like Sedna are relatively
unaffected while km-sized bodies tend to be deposited interior and exterior to the scattering
planets. The mass, extent and duration of gas disk determine the efficiency of Oort cloud
formation.
•“Puffing -up”
-up” of an inner cloud to replenish outer cloud in 4 Gyr in current Galactic
environment is inefficient (1-10%). However, we are currently investigating the effects of Giant
Molecular Clouds, especially early on when Sun’
Sun’s velocity relative to GMCs (including its birth
GMC) is only 1-5 km/s.
km/s.
•Capture of icy bodies from passing stars in early embedded phase may cumulatively add
significantly to inner/outer cloud and is being investigated.