The Formation and Longterm Evolution of Circumstellar Disks

1
The Formation and Long-term Evolution of
Circumstellar Disks

• Shantanu Basu
• The University of Western Ontario, Canada
• Eduard Vorobyov (ICA, St. Marys U., Canada)

Isaac Newton Institute DDP Program
seminar September 24, 2009
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The Envelope-Disk Connection
Calvet, Hartmann, Strom (1999)
FU Ori
C. Briceno
FUors are YSOs with significant circumstellar
material.
Typical disk accretion FU Ori
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Empirical Inference of YSO Accretion History
Hartmann (1998), based on Kenyon et al. (1990)
New evidence from Spitzer (very low luminosity
objects VeLLOs Enoch et al. 2008) also
reveals need for episodic accretion
Observed frequency of FU Ori eruptions (last 50
years) is several times greater than the low-mass
star formation rate within 1 kpc ? It is thought
that all YSOs undergo multiple eruptions.
4
Gravitational instability of a gaseous disk

• The stability properties of gas disks are often
  expressed in terms of the Toomre Q-parameter
  (Toomre 1964)
• If Q gt 2 the disk is stable (but still may have
  low-amplitude non-axisymmetric density
  perturbations).
• If 1 lt Q lt 2 the disk is unstable and can
  develop observationally meaningful
  non-axisymmetric structure.
• If Q lt 1 the disk is vigorously unstable and can
  fragment into self-gravitating clumps.

Fragment formation ultimately depends also upon
cooling and heating rates (Gammie 2001 also,
Lodato, Rice, Durisen, Pickett, Boss, and others)
and/or upon mass accretion onto the disk
(Vorobyov, Basu)
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Global Core ? Disk Formation/Accretion
Simulations
We Employ the Thin-Disk Approximation Vorobyov
Basu (2006)

• Our model is global, nonaxisymmetric, and
  includes disk self-gravity.
  Outer boundary at 104 AU, i.e. prestellar core.
• Integrate vertically (in z-direction) through
  cloud. Solve time-dependent equations for
  profiles in (r,f) directions. ICs from
  self-similar core collapse calculations.
• With nonuniform mesh, can study large dynamic
  range of spatial scales, 104 AU down to
  several AU
• Allows efficient calculation of long-term
  evolution even with very small time stepping due
  to nonuniform mesh. Can study disk accretion for
  106 yr rather than 103 yr (for 3D)
• Can run a very large number of simulations for
  statistics and parameter study
• Last two still not possible for 3D simulations

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Whats not included in this model (for now)

• Magnetic braking
• Ambipolar diffusion, Ohmic dissipation, Hall
  term
• Model for inner disk ( 5 AU) inside central
  sink cell
• Magnetorotational instability (cant occur in
  thin-disk model)
• Stellar irradiation effects on disk
• Radiative transfer in disk - we use P P(r),
  barotropic relation
• Photoevaporation of outer disk

Schematic from Armitage, Livio, Pringle (2001)
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Basic Equations
2D convolution theorem (Binney Tremaine,
Galactic Dynamics) very
useful to model isolated objects
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Core initial conditions
These profiles represent best analytic fits (Basu
1997) to axisymmetric models of magnetically
supercritical core collapse (e.g. Basu
Mouschovias 1994).
All scale as r -1 at large radii.
Pick r0, W0, a, so that core is mildly
gravitationally unstable initially.
Basic qualitative results are independent of
details of initial profiles.
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Self-consistent formation of the protostellar
disk and envelope-induced evolution
Evolution of the protostellar disk
Mass infall rate onto the protostar
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Early (Burst Mode) Disk Evolution
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Mass accretion bursts and the Q-parameter
Black line - mass accretion rate onto the central
sink Red line the Q-parameter
Smooth mode
Burst mode
Vorobyov Basu (2006)
The disk is strongly gravitationally unstable
when the bursts occur
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Accretion history of young protostars
Burst mode
Residual accretion , self-regulated mode
FU Ori outburst
disk accretion
envelope accretion
VeLLOs?
Vorobyov Basu (2007)
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Disk mass stays well below central mass
M 1 M8, rout 0.05 pc, b 0.275
disk formation at 10 AU
Gravitational instability and clump formation can
occur in low-mass
protostellar disks.
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Azimuthally Averaged Spatial Profiles Into the
Late Phase
Keplerian
W
Accretion and instability help to self-regulate
disks to a near-uniform Q distribution
Sharp edge!
S
Slope of MMSN
?
Disk weakly nonisothermal
T
Nonaxisymmetry is essential for this result.
Vorobyov Basu (2007)
Q
Self-regulation
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Two Modes of Disk Accretion
Late self-regulated mode Gravitational torque
driven accretion, Q 1, not GI Diffuse spiral
structure
Early burst mode Episodic vigorous gravitational
instability (GI). Distinct spiral modes Clumps
form and accreted inward Binary formation may
occur here
VB06
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The Swing Amplifier why fluctuations persist in
self-regulated mode
Leading spiral waves can be unwound into trailing
spiral waves. During the process, a transient
instability feeds energy into the spiral
mode. For the process to work continuously, need
a feedback loop, i.e. fresh sources of leading
waves in the system. Where from??
Toomre (1981), based on work by Zang and Toomre.
Also, Goldreich Lynden-Bell (1965).
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Compile accretion rates for various initial core
masses
Solid circles time-average (class II phase, 0.5
to 3 Myr) values from models with differing
initial mass. Bars represent variations from mean
during same time period.
All other symbols data from Muzerolle et al.
(2005) and Natta et al. (2006).
Blue line best fit to simulation averages.
Black line best fit to all data points. Red
lines best fits to low and higher mass regimes
of data.
Blue line
Vorobyov Basu (2008)
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Some key results

• Can fit mean observed T Tauri star (TTS)
  accretion rates using a model of gravitational
  torque driven accretion
• Model also produces near-Keplerian rotation and
  r -3/2 surface density profile in disk
• However, disk masses and disk-to-star mass
  ratios are a factor 10 greater than
  observational estimates for TTSs and BDs (Andrews
  Williams 2005 Scholz et al. 2006)

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Observed disk masses underestimated?

• Grain growth in disks already significant.
  Standard opacity requires grain growth to 1 mm at
  100 AU, but what if they grow further? Larger
  grains would lead to higher disk mass estimates
  (Andrews Williams 2007 Hartmann et al. 2006)
• Upper envelope of TTS accretion rate dM/dt
  10-7 Msun/yr implies Mdisk dM/dt x 1 Myr 0.1
  Msun
• MMSN contains 0.01 Msun material, barely
  enough to make Jupiter. Extrasolar systems with M
  sin i up to several Jupiter masses imply Mdisk gtgt
  0.01 Msun
• Chondrule formation models (Desch Connolly
  2002 Boss Durisen 2005) require a high density
  and Mdisk 0.1 Msun

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Basic Equations with Viscosity
unit tensor
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The Additional Effect of a-viscosity
Red lines, a 0. Solid black lines, a 0.01.
Vorobyov Basu (2009, MNRAS, 393, 822)
Distances on horizontal axis in AU.
Density drops and disk is larger in viscous disk.
Self-regulated disk structure is lost, and it is
clearly gravitationally stable.
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An effective alpha for models
Vorobyov Basu (2009)
at inner sink
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Can viscous approach model gravitational
instability/torques?
In Burst mode No! Global (mostly m1) mode
dominates
Burst mode
Self-regulated mode ? many higher order modes
dominate
Vorobyov Basu (2009)
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Viscous approach may be useful for self-regulated
mode
In self-regulated mode, many high order spirals,
lots of mode-mode interaction ? a local
approximation more suitable, e.g., Lin Pringle
(1987,1990), Lodato Rice (2004), Vorobyov
(2010).
Lodato Rice 2004 a self-regulated disk, Q 1
Vorobyov Basu (2007) evolution of a ring
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Summary

• Circumstellar disks that form self-consistently
  enter an early burst mode of episodic vigorous
  gravitational instability ? formation of clumps ?
  FU Ori-type bursts. Very low accretion states may
  correspond to VeLLOs.
• At late ( Myr) stages, disks enter a
  self-regulated mode, have a sharp edge and
  maintain persistent nonaxisymmetric density
  fluctuations ? non-radial gravitational forces ?
  torques that drive accretion at rates comparable
  to that of TTSs
• Self-regulation of disk in late phase leads to Q
  const. and to surface density profile S r
  -3/2 same slope as MMSN
• For models with 0.5 Msun and above, can fit
  observed dM/dt vs. M relation.
• Disk mass stays well below central mass, but
  factor 10 larger than observational estimates.
  Observed disk masses systematically
  underestimated?
• Addition of a-viscosity increasingly undermines
  all of the above effects, and dominates even for
  a 10-2 . Other parametrizations of viscosity (Q
  -dependent) may provide a reasonable
  approximation to the self-regulated mode.