Fragmentation and Evolution of the First Core

1
Fragmentation and Evolution of the First Core

• Kohji Tomisaka
• and
• Kazuya Saigo (NAOJ)

2
Star Formation of M8 stars
consensus of scenarios of
Dynamical Contraction of Cores
Starless Cores
Prestellar Cores
Protostars
Main-sequence Stars
Pre-main-sequence Stars (T Tau. Stars)
Protostellar Cores
IR Sources
Accretion Energy
Hydrogen Nuclear Fusion
Opt, Near IR Sources
Gravitational Energy of Stars
3
Spherical Collapse
Gas ( ) contracting under the
self-gravity

• (1) isothermal g 1 rltrA10-13 g cm-3
• run-away collapse
• first collapse (dynamical collapse)
• central density increases greatly
• in a finite time-scale.
• (2) adiabatic g 7/5 rA ltrlt rB 5.6 10-8 g cm-3
• first core a nearly hydrostatic
• core forms at the center
• (outflow and fragmentation)
• (3) H2 dissociation g 1.1 rB ltrlt rC 2.0 10-3g
  cm-3
• second collapse dynamical collapse begins at the
  center of the 1st core.

Larson (1969)
Temp-density relation of gas _at_ cloud center.
(Tohline 1982)
First Collapse ? 1
rC
rC
First Collapse ? 1
rB
rB
First Core g7/5
Second Collapse ? 1.10
Second Collapse ? 1.10
rA
rA
log nc (cm-3)
cf. Masunaga Inutsuka (2000)
4
Runaway Collapse
First core
Isothermal spherical collapse shows
(1)Convergence to a power-law structure
(2)Divergence of central density in a finite
time.
(3)Only a central part contracts.
??
This is called runaway collapse.
Larson 1969, MNRAS, 145,271
5
How about a rotating magnetized cloud?
1. In case with B and W, a contracting disk is
made in the runaway collapse phase. As a
consequence, (a) A flat first core is born.
(b) Outflow is driven by the effect of twisted
B-field and a rotating disk. (c) B-field
transfers the angular momentum from the
contracting disk to the envelope. 2. Star
formation process is controlled by the rotation
speed of the first core. Evolution is
classified into three types. (a) A slow
rotator evolves similarly to the BW0 cloud.
(b) An intermediate rotator forms a bar and
spiral arms, which transfer the angular momentum
from the center. Owing to this, collapse
proceeds. (c) A bar or spiral arms of fast
rotator finally fragments. This leads to the
binary formation.
6
Initial Condition
Numerical Method
To achieve high resolution near the center of the
cloud.
B
W
Nested grid
periodic boundary
(1) We assume a hydrostatic balance between
pressure, Lorentz force, centrifugal force and
gravity.
(2) We added both axisymmetric and
nonaxisymmetric r perturbations.
7
The coarsest grid
Nested 4-times finer grid
r
r
W
W
a1,W0.5
8
First Core Phase Evolution
Nested 28-times finer grid
r
W

• Just after the central
• density exceeds rA
• (first core formation),
• outflow begins to blow.
• (2) In this case, gas is
• accelerated by the
• magnetocentrifugal wind
• mechanism.
• (3) 10 of gas in mass
• is ejected with almost all
• the angular momentum.

9
Angular Momentum Redistribution in Dynamical
Collapse

• In outflows driven by magnetic fields
• The angular momentum is transferred effectively
  from the disk to the outflow.
• If 10 of inflowing mass is outflowed with
  having 99.9 of angular momentum, j would be
  reduced to 10-3 jcl.

10
Angular Momentum Problem

• Specific Angular Momentum of a New-born Star
• Orbital Angular Momentum of a Binary System
• Specific Angular Momentum of a Parent Gas
• Centrifugal Radius

Tomisaka 2000 ApJL 528 L41--L44
11
Angular Momentum Transfer
Specific Angular Momentum of gas ltM
Initial
Core Formation
7000 yr after Core Formation
Accumulated Mass
12
Molecular Outflow
Saito, Kawabe, KitamuraSunada 1996
L1551 IRS5
Optical Jets
13
Evolution of a Rotating First Core
Saigo Tomisaka (2006, ApJ, 645, 381-394)
Saigo, Matsumoto, Tomisaka (2006, in prep.)

• I have showed that B-field controls the angular
  momentum of the first core.
• Fragmentation develops quickly in a hydrostatic
  state (first core) rather than in a contracting
  circumstance (runaway phase)
• Fragmentation in a first core brings binary or
  multiple stars.
• ?binaries are more popular than single stars.
• ?We study the fragmentation of the 1st core using
  a nested grid hydrocode.

Temp-density relation of IS gas. (Tohline 1982)
First Collapse ? 1
rC
rB
First Core ? 7/5
Second Collapse ? 1.10
rA
14
Hydrostatic Equilibrium

• Hydrostatic Axisymmetric Configuration for
  Barotropic Gas
• Angular Momentum Distribution
• same as a uniform-density sphere with rigid-body
  rotation
• total mass and total ang. mom.
• Self-consistent Field Method (SCF)
  Hachisu(1986), Tohline, Durisen
• to understand the evolution of first core

dissociation density
15
Examples of Hydrostatic Configuration for
Rotating Barotropes
Mass and simultaneous angular momentum accretions
drives an evolution like this
Three models have the same central density
rc4rdiss, but different angular momenta as 2.25
1049 (left), 4.18 1049 (middle), and 9.99
1049 g cm2 (right), and masses as 2.77 1031
(left), 3.45 1031 (middle), and 4.97 1031 g
(right).
16
Mass-Density Relation ( )

• Below , mass increases with central
  density .
• Mass is prop. to Jeans mass
• (Chandrasekhar 1949)
• Mass accretion drives the core
• from lower-left to upper-right.
• Above mass
• decreases due to soft EOS.
• Further accretion destabilizes
• the cloud and drives dynamical contraction (2nd
  collapse).
• Maximum mass of the 1st core is 0.01 M8.

17
Hydrodynamical Simulation

• run-away (1st collapse)? 1st core
• 1st core grows by mass accretion from contracting
  envelope.
• Initial Condition
• Bonnor-Ebert sphere ( envelope (R50,000AU))
• nc104H2cm-3, T10K
• Rotation wWtff00.3
• increase the BE density
• by 1.18 times
• Perturbations m2 and m3
• dr/r10
• Numerical method
• HD nested grid
• barotropic EOS

hydrostatic sphere
Increase the mass by 1.1-8 times
Add m2 and m3 perturbation
18
Non-rotating cloud

• density rcltrdis,Mcl increases with rc.
• Jeans mass
• Evolution is driven by accretion.
• At rcgt2rdis, soft EOS makes Mcl decrease.
• dynamical contraction (2nd collapse)
• maximum mass of a 1st core is equal to 0.01 M8.

19
Non-rotating model

• Unless the cloud is much more massive than the
  B-E mass, the first core evolves to follow a path
  expected by quasi-hydrostatic evolution.
• Maximum mass of a first core is small 0.01M8.
• Quasi-static evolution gives a good agreement
  with HD result.

max.mass
20
Mass-Density Relation ( )

• rotation rate of parent cloud
• wlt0.015
• similar to non-rot. case.
• second collapse
• wgt0.015
• Mass increases much
• well below

21
Rotating Cloud (w0.05)

• First, the 1st core increases its mass (upwardly
  in Mcl-rc plane).
• follows a hydrostatic evolution path.
• Shape round spherical disk.
• Then, the first core begins to contract
  (rightward in the plane)
• This phase, spiral arms appear.
• J is transferred outwardly.
• Coredisk continues to contract.

22
Comparison with previous simulations

• Bate (1998)
• SPH simulation
• w0.08
• spiral ? transfer J
• Matsumoto, Hanawa (2003)
• Nested Grid Eulerian Hydrodynamics
• w0.03
• spiral
• w0.05
• spiral
• fragmentation

23
Nonaxisymmetric instability

• Rotational-to-gravitational energy ratio T/W
• A polytropic disk with T/Wgt0.27 (g5/3) is
  dynamically unstable under a wide range of
  conditions (g5/3 Pickett et al. 1996 g7/5,
  9/5, 5/3 Imamura et al. 2000 )
• T/W increases with mass accretion.
• After T/W exceeds the critical value,
• nonaxisymmetric instability grows.
• Angular momentum is transferred outwardly.
• This may stabilize the disk again.

24
Rotating Cloud (w0.05)

• Evolution depends on the initial mass.
• MMBE
• Follow quasihydrostatic evolution
• MgtgtMBE
• evolution depends on its initial condition.

25
Fragmentation

• In a fast rotating cloud, fragmentation (more
  than 2 fragments) is observed in the 1st core.
• This occurs after non-axisymmetric instability is
  triggered.

26
Typical Rotation Rate

• NH3 cores (n3 104cm-3) Goodman et al (1993)
• N2H cores ( 2 105cm-3) Caselli et al. (2002)

27
Luminosity of the First Core
3D simulation
Quasi-static evolution
second collapse
second collapse
Lbol
Lifetime of 1st core is not short !
t(yr)
Absolute value L and timescale are obtained
after is given.
L is a decreasing function of w.
28
Mass Accretion Rate

• Mass accretion rate is between the LP solution
  and a SH disk solution.
• Much higher than that expected for SIS.

(Whitworth Summers 1985)
29
(No Transcript)
30
Summary

• The evolution of a 1st core is well described
  with the quasi-static evolution.
• Slow (or no) rotation model exhibits the second
  collapse (wlt0.015).
• Maximum mass of the 1st core 0.02 M8 (w0.015).
• Rotating cloud with wgt0.015, the 1st core
  contracts slowly.
• After T/Wgt0.27, a dynamical nonaxisymmetric
  instability grows and spiral pattern appears.
• Gravitational torque transfers the angular
  momentum outwardly.
• The 1st core contracts further.
• In a rotating cloud with wgt0.1, we found
  fragmentation of the 1st core.