Circumstellar Disk Formation around First Star: Effects of Magnetic Field Circumstellar Disk Without Magnetic Field With Magnetic Field Masahiro Machida (Kyushu Univ.) and Kentaro Doi (Konan-Univ.)
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Circumstellar Disk Formation around
First Star: Effects of Magnetic Field
Circumstellar Disk
Without
Magnetic Field
With
Magnetic Field
Masahiro Machida (Kyushu Univ.) and Kentaro Doi (Konan-Univ.)
Motivation
Present-day star formation
Binary is common
Most stars born in a stellar group or stellar cluster
Primordial star formation
Only single star appears in a single clump?
Most stars form in a stellar group or stellar cluster
But, Magnetic Effects have been ignored in primordial cloud
Magnetic field
can drive protostellar jet
can suppress disk formation and fragmentation
First collapse object
Before the protostar formation
After the protostar formation
Protostar
Circumstellar Disk
Gas collapsing (early) phase
(Main) Accretion (later) phase
~106 yr ~104-5 yr
Star Formation Process can be divided into Two Stages
(~0.01Msun)
(~104-5Msun)
To MS
Gas Collapsing Phase
Gas Accretion Phase
Star formation in primordial cloud (not present day case)
Fragmentation in Gas Collapsing Phase Fragmentation before the protostar formation
Rotational fragmentation (?)
Fragmentation does not always occurs
(fragmentation tends to occur in a rapidly rotating cloud)
Density H2 Fraction Temperature
3500 AU
Rotationally fragmentation?
Thermally unstable?
Turk et al. (2009)
Saigo, Umemura &
Matsumoto (2004)
Machida et al. (2008)
Before proto first
star formation
Global spiral can temporarily suppress fragmentation
in Gas collapsing phase?
Clark et al. (2011), Science
Tight multiple system (~AU)
Disk around the first star is unstable to
gravitational fragmentation
Sink radius = 1.5 AU, n<1016 cm-3
~100 yr after the first protostar formation
Stacy et al. (2010)
Binary (?), ~100 AU
Disk formation ⇒ spiral structure
⇒ fragmentation
Sink radius = 50 AU, n<1012 cm-3
~5000 yr after the first protostar formation
Fragmentation in Gas Accretion Phase
With Sink
Clark et al. (2011), Science
Tight multiple system (~AU)
Disk around the first star is unstable to
gravitational fragmentation
Sink radius = 1.5 AU, n<1016 cm-3
~100 yr after the first protostar formation
Stacy et al. (2010)
Binary (?), ~100 AU
Disk formation ⇒ spiral structure
⇒ fragmentation
Sink radius = 50 AU, n<1012 cm-3
~5000 yr after the first protostar formation
Fragmentation in Gas Accretion Phase
With Sink
Fragmentation in Gas Accretion Phase
Without Sink Greif et al. (2012)
Calculation ~10yr after the first protostar formation
Fragmentation occurs in a scale comparable to the protostellar radius
Effect and Limitation of Sink Fragmentation scale is determined by sink radius
We cannot use it with magnetic field due to divB=0 constraint
Sink
Magnetic field is incompatible
with sink treatment
Sink Treatment
We need sink cells or sink particles to calculate the evolution of the
circumstellar disk for a long duration
but, ignores the internal structure
Calculation Without Sink (This study)
~50AU ~2 AU
Clark et al. Rsink =1.5AU
~100 yr after the first
protostar formation
Stacy et al.; Rsink = 50 AU
Accretion Rate with Sink
OK
Magnetic Braking Catastrophe
Primordial Cloud
Magnetic dissipation is not so effective
(Maki & Susa 2004, 2007)
Magnetic braking Catastrophe is more serious
But, strength of magnetic field in the early
universe is highly controversial
Magnetic Braking
Angular momentum problem
Angular momentum is excessively transferred
No disk forms
Magnetic Dissipation
Magnetic flux problem
Ohmic dissipation
Disk Formation
角運動量輸送
Li et al. (2011)
This Study
This study investigates
Population III star formation in the gas accretion phase
without SINK
Especially, we focus on
Evolution of the circumstellar disk around Pop III star
Effects of magnetic field
Spherically Hydrostatic Core (Bonnor-Ebert Sphere)
B // W
Parameters: b0 and g0
密度
半径
Bonnor-Ebert Sphere
Rotation Axis
Ma
gn
eti
c F
ield
Lin
e
B0
14 pc
L=1 Ω0
Initial Values
Central density：n=104 cm-3
Temperature：T=230K
B.E. Radius: 1.3 pc
Mass： Mcloud =103 Msun
b0≡Erot / Egrav,
g0≡Emag / Egrav
W0 = 10-15 [s-1] at n=104 cm-3
(W0 and B0)
Cloud Rotation
Magnetic Field
b0 =10-4
g0 =3×10-3
B0 =10-7 at n=104 cm-3
Bromm et al. 2002
As the initial state,
we mimicked results
of the cosmological
simulations
Initial Settings
Not Cosmological Simulation!!!
L = 1
L = 2
L = 3 L = 31 L=4
Schematic view of Nested Grid
3D Resistive MHD Nested Grid Method Grid size: 256 x 256 x 32 Grid level: lmax=21 (l : Grid Level)
Total grid number: 256 x 256 x 32 x 21
Grid generation: Jeans Condition
l =21: Lbox = 21 AU, Δxl=21 ~ 1.8 Rsun
Numerical Method
P=P(r)
Resistive MHD eq.
One-zone calc.
Resistivity h is given by one-zone
calculation
Protostar Model
To model protostellar evolution (mass and radius) & To suppress further contraction of the
protostar
Eos is artificially changed in high-density region (Tomisaka 2002)
n [cm-3]
Protostellar mass and radius relation
(Omukai & Palla) is well reproduced!
Test Calculation
Without Rotation (and without magnetic field)
r-1.5
Without Magnetic Field
660 yr after the first
protostar formation
Vigorous fragmentation
Ejection of low-mass
protostar
Nine protostars with mass
of 0.001-0.1 are ejected
No stable disk
Animation
Mass Exchange
between Protostars
Disk Destruction
Event at ~6 years after the first protostar
formation
Event at ~165 years after the first protostar
formation
Protostellar Orbits Some protostars are
ejected from the center of
the cloud
Black: Primary protostar
Red: other protostars
Number of Fragments and Protostellar Mass
Number of fragment can decrease
because of merger between
protostars
11 protostars at the maximum
Primary star reaches M~10Msun
Secondary star has a mass of
0.1-1Msun
With Magnetic Field (relatively strong)
B=2x10-8 G at n=1 cm-3 B=2x10-9 G at n=1 cm-3
Interchange instability Early fragmentation
MRI
B=2x10-12 G at n=1 cm-3
MRI
Single star Single star Single star
B ~ nano G B ~ pico G B ~ 10 nano G
With Magnetic Field (relatively weak)
B=2x10-14 G at n=1 cm-3 B=2x10-15 G at n=1 cm-3
MRI Multiple fragmentation
Binary star Multiple stars
Cluster
B ~ femto G
Star formation
mode changes
with B ~ femto Gauss
B ~ 10 femto G
With Magnetic Field
1st column: 2x10-8 G
2nd column: 2x10-9 G
3rd column: 2x10-10 G
4th column: 2x10-12 G
5th column: 2x10-14 G
6th column: 2x10-15 G
Each column: time sequence image
for each model
Color: density (on the equatorial plane)
Amplification of Magnetic Field
Gas Collapsing Phase
Gas Accretion Phase
B∝r2/3
b∝(0.1-0.001)bps,0
⇒ B=10-106 Bps,0
Jet Driving
Strong jet appears
when B > 10-9 G
Summary
No circumstellar disk forms around Population III stars both with
and without magnetic field
Without magnetic field
A high mass accretion rate induce vigorous fragmentation
Disk destruction, mass exchange, ・・・
With magnetic field
Disk formation is suppressed by the magnetic braking
Jet driving
Star formation mode is controlled by magnetic field
B0<10-15 G: Population III cluster
10-12 G < B0 < B-15 G: Population III binary
B0 >10-12 G: Single Population III star
Critical magnetic field strength: B ~ femto (10-15) G !!
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