Proto-Brown Dwarf Disks as Products of Protostellar Disk Encounters
Sijing Shen & Dr. James Wadsley
McMaster University Hamilton, Ontario, Canada
Brown Dwarfs: Observational Facts
Encounter-Induced BD formation
A non-coplanar encounter by two prograde rotating disks is depicted in Fig. 4, and a coplanar encounter by two
retrograde disks is depicted in Fig. 5. New objects are produced mainly via instabilities and fragmentation of the
inner disks (r < 400 AU, see Fig. 4 c; Fig 5, panel 5 & 6). The disks were destabilized by enhancing the inner disk
density via angular momentum cancellation (retrograde disks) or via tidal filamentary structures (prograde disks, Fig.
4 b). This is quantitatively reflected in a decrease of the Toomre Q parameter. The stability criterion (Q≥0.9) still
holds during the encounter. For the disks which were initially very stable (Q>1.1), no fragmentation happens. The
tidal structure fragmented occasionally if the gas was relatively cold (Fig. 4, panel 4). Shocks were produced in
every physical encounter (Fig. 4, a; Fig. 5, a). However, fragmentation of the shocked gas only happened in the
coplanar encounters also with low initial Q (Fig. 5, b).
Many brown dwarfs (0.013 Msun < M < 0.075 Msun) have been
found in both field and star clusters (Chabrier 2002; Martin et al.
2001). The flatness of the substellar initial mass function (IMF)
indicates that BDs are as common as normal stars. Observations
of young brown dwarfs in star-forming regions such as Rho Oph
have revealed that a large percentage of BDs are surrounded by
disks (Fig.1)(Pascucci et al. 2003; Muench et al. 2001). Accretion
was also detected in some of the disks by Hα profile analyses
(e.g., Natta et al. 2004), sometimes associated with outflows
(Whelan et al, 2005).
Fig. 1 IR Excess in a brown dwarf
Spectral energy distribution (SED) –
Existence of a surrounding Disk.
Adapted from Pascucci et al. (2003)
a
b
Origin of Brown Dwarfs: Protostellar Disk Encounters
The formation mechanism of BDs is unclear . The main difficulty in forming a BD by direct collapse is that the
mass of BD (<0.075 Msun) is too small compared to the expected mass scale – the Jeans Mass (~ 1 Msun) in
molecular cloud cores (MCC). Mechanisms to solve this problem often seek to lower the local Jeans mass, by
finding regions that are extra cold (Elmegreen 1999), or enhancing the local density via turbulent flows
(“Turbulent Fragmentation” , Padoan & Nordlund 2004).
In this poster, we examine another mechanism of BD formation: encounters of protostellar disks. When cores
first collapse to form stars they have extended protostellar disks. In young star clusters at least one encounter
is likely during this phase and the disks can be induced to fragment. Since disks have much higher densities
than MCCs, the Jeans mass in disks is in the substellar mass scale. Previous studies of this mechanism using
SPH simulations (Lin et al. 1998; Watkins et al. 1998) did find BD mass objects forming during the encounters.
However, it was not clear whether the fragmentation was physical or numerical, because the Jeans mass was
not resolved in those simulations and simplified models of the vertical structure were used, both of which can
enhance artificial fragmentation (Truelove et al. 1997; Kim et al. 2002).
Here we present an high resolution study of protostellar disk encounters. The aims of this study mainly
include: 1. Investigate the conditions that allow encounter induced BD formation; 2. Characterize the nature
of any objects produced via this mechanism and discuss the observational implications.
Fig. 4 A prograde-prograde non-coplanar disk encounter.
The disk moving from top right to bottom left is tiled π/4
relative to the encounter plane. The color bars give the
logarithmic density in code units (solar masses per cube
AU). Panel 6 shows the fragmented disk at the bottom left of
panel 5.
Fig. 5 A retrograde- retrograde coplanar protostellar disk encounter.
The color bars under each panel indicate the logarithmic density in code
unit (solar masses per cube AU). Panel 3 shows the boxed region in
panel 2 with different zoom and density scale. Panel 5 & 6 show the
objects formed in the left & right box of panel 4, respectively.
The Nature of the Objects & Observational Implications
Modeling the Protostellar Disk & Encounters
The simulations used the Gasoline TreeSPH code (Wadsley et al. 2004). We modeled a 0.6 Msun protostellar
disk with 200, 000 SPH particles (1MEarth per particle), which ensured that the disks vertical structure and the
local Jeans Mass was resolved well after the fragmentation happened. The disk structure was built selfconsistently assuming hydrostatic equilibrium in the vertical direction. The disk was initially stable against
spontaneous fragmentation. We performed a convergence study to identify real vs. artificial instability (Fig. 3).
1. Proto-BD disks – Accretion times, Outflows, Planetary companions?
The simulations produced bound objects with masses ranging from 2 to 73 Jupiter Masses. All the objects spin rapidly
and have a highly flattened shape (Fig.6). The size of these disks varies from 0.3 to 18 AU. A large portion of mass
of a clump should then contract to form a proto-BD, leaving rest of the material (%1-5% Scholz et al. 2006) residing in
the disk and accreting onto the central object on a viscous time scale. Adopting a medium accretion rate for a young
& ~ 10−10 M / yr, the lifetime of a 1 Jupiter mass disk is about 5 Myrs, comparable to a protostellar disks.
BD: M
sun
Also, to shed its angular momentum, the proto-BD disk should launch a small scale outflows and/or form planets, both
of which were observed. (Fig. 7 & Fig. 8 ).
Fig. 2 Vertical structure of the protostellar
disk. Left: HST/NICMOS image of a disk
around a young stellar object. Adapted from
Padgett et al. (1999). Right: The simulated
optical image of our disk model viewed
edge-on. The increase of scale height with
radius can be seen.
Fig. 3 Resolution convergence
study. The disk was physically
stable against spontaneous
fragmentation. Left: Disk
modeled with 2000 particles with
unresolved Jeans mass and scale
height. Middle: Same disk with
20000 particles with Jeans mass
resolved but not the scale height.
Right: The disk used in our
encounter simulations. Both the
left and the middle show strong
instability and fragmentation
(indicated by the box) within one
dynamical time scale.
OR
Fig. 6 A typical object formed from encounters. Left: the
object projected to the x-z plane; Right: the object projected
in the x-y plane.
Fig 7 An outflow in a
young BD disk indicated
by the P Cygni-like dip in
the H α profile. Adopted
from Whelan et al. (2005)
Fig 8 A giant planet
companion to a nearby
BD (2M1207). Adopted
from Chauvin et al.
(2005)
2. Hierarchical Star-BD Multiples
In one of our simulations, a binary brown dwarf pair was made via a secondary fragmentation of a disk-shape
clump. The two components have separation ~ 3 AU and orbital period ~13 years. Both of them are surrounded
with small disks. The pair in turn orbits the star with separation ~100 AU (Fig. 9). This hierarchical system was
observationally inferred for GL 569, a recently-observed BD triple (GL 569 B) around a M2.5V star (GL 569 A)
(Gorlova et al. 2003; Simon et al. 2006). It is also consistent with recent observation of accretion signature
around each components of some BD multiples (Kraus et al. 2006)
Parameter Space of Encounters
We explored a parameter space consisting of: 1. The initial stability property of the disks – the Toomre Q
parameter ; 2. The initial configuration of the two disks -- coplanar vs. non coplanar; prograde (angle
between spin & orbit < 90 deg. ) vs. retrograde (angle between spin & orbit > 90 deg.); 3. The encounter
velocity.
1.The Toomre Q parameter
Q ≡
c sκ
πG Σ
Cs Sound Speed
Epicycle Frequency
G Gravitational constant
Σ Surface Density
κ
Toomre Q stability criterion for linear, axisymmetric perturbation: Q > 1.0 (Toomre 1964). For non-linear
perturbation Q is still around 1.0. But finite thickness disks are more stable than thin disks (Q > 0.7; Kim et al.
2002)
The criterion for our disk against spontaneous fragmentation: Q ≥ 0.9.
2. Disk Configurations
In our simulation Q = 0.9, 1.1, 1.3
A retrograde disk.
Prograde disks
A coplanar encounter
A prograde disk.
A non-coplanar encounter
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Mass Distribution of the Objects
(Preliminary)
The mass distribution of objects from all the simulations is plotted
in Fig. 10. A total of 32 clumps were produced in 14 encounters.
The encounters produce more objects at the low mass end, which
is consistent with the observed substellar IMF. The turnover in
planetary mass (M< 5 MJupiter) may be due to the scale of the
gravitational softening. However, all the planetary mass objects
are also surrounded with disks. The recent discovery of planetary
mass objects exhibiting disks and a T-Tauri phase (Mohanty et al.
2005) thus supports this mechanism. As part of our future work,
better statistical study will be nundertaken to compare the mass
−α
distribution with the observational power-law IMF dN / dm ∝ m .
Fig. 10 The mass distribution of 32
objects produced by 14 simulations.
The data were binned in every 5
Jupiter masses.