Disk Formation and Jet Driving
in Collapsing Cloud Cores

Masahiro Machida(Kyushu University)

Star Formation Process
Observations have shown that
 Low-velocity outflows and high-velocity jets areubiquitous Circumstellar disk formation in the Class 0 stage(Tobin et al. 2012,2015, Murillo et al. 2013, Codella et al.. 2014,
Lee et al. 2014, Yen et al. 2015)

 Planet formation in the early stage (?)

Molecular Cloud Core

To understand star and disk formation process,we need to clarify
 Driving mechanism of low-velocity outflows
and high-velocity jets
 Circumstellar disk and planet formation
process
in collapsing cloud core

Protostar, Circumstellar , Disk,Jets

Star forms in Gravitationally Collapsing Cloud Is star formation simple ? Spherical symmetry?
 Magnetic field and rotation cause complexities Both are an anisotropic force⇒ Anisotropic structure formation (disk, jet and outflow) Both are conserved⇒ Magnetic flux and angular momentum problem

Arquilla&Goldsmith 86

Girart+ 09

 Disk formation, outflow and jet driving areclosely related to B and W
 We need to understand the star formation
process with B and W

Star Formation Process can be Divided into Two Stages
Molecular CloudCoreGas collapsing stage (before p.s. formation)

Protostar Formation
Gas accretion stage (after p.s. formation)

ProtostarPathway for Protostar Formation: Gas Collapsing Phase
Larson(1969), Winkler & Newman (1980), Tscharnuter(1987), Masunaga & Inutsuka(2000),Whitehouse & Bate(2006), Stematellos et al.(2007), Bate (2010), Tomida et al.(2010)

Schematic View of the Protostar Formation

ProtostarFormationin the collapsing gas until the protostar formation
Epoch
Protostar formation

Thermal evolution

104

Molecular cloudT (K)103

Temperature

Dissociation of H2102

10

Protostar (Second core)(~0.01AU)First adiabatic core formation
Tomidaet al.
(2013)FirstCore
Masunaga& Inutsuka(2000)
Gas temperature(~1-100AU)(~1-10AU)n (cm-3)

10 Cores10
Two10 Nested
Density
5

104

10100

1511020

Spatial Scale (AU)0.1

This Talk
1. Gas Collapsing Phase before theProtostar Formation

2. Early Gas Accretion Phase ~500
years after the Protostar Formation
3. Long-term Evolution ofCircumstellar Disk with Sink

1. Gas Collapsing Phase beforethe Protostar Formation

Gas Collapsing phase: 2D w/ B w/o non-ideal effects radiation

He could reproduced Low-velocity
outflow driven by the first core

Tomisaka (1998 , 2000, 2002)

Gas Collapsing phase: 3D w/ B w/o non-ideal effects w/ radiation
Bate (1998,2010, 2011)

First core is theorigin of the rotation
supported disk!!

 With rotation, the first core remains after the protostar formation (the remnant of) the first core is supported by the rotation and becomes tocircumstellar disk
Abstract…

…

Gas Collapsing phase: 3D w/ B w/o non-ideal effects w/o radiationn [cm-3]

1 AU

Without rotation, first core disappears in ~1 yr after the protostar formation
Gas behaves adiabatically at n≧1011 cm-3⇒ Adiabatic (or first core) formation

Dissociation of H2 at n≧1016 cm-3⇒ Rapid collapse again (second collapse)
Protostar formation⇒Collapse of the first core remnant⇒ Disappearance of F.C
Machida & Matsumoto’ 11

Gas Collapsing phase: 3D w/ B w/o non-ideal effects w/o radiation
With rotation, the first core evolves into the rotation supported diskn [cm-3]

Machida & Matsumoto’ 11

ProtostarFirst core remnant

Rotation supported disk

Gas Collapsing phase: 3D w/ B w/ non-ideal effects w/ radiation
Both non-ideal effect of B and radiation are considered
Jet

Protostar

Just after p.s. formation,
we can see the firstcore (remnant) or
nascent disk in density,temperature, andvelocity profiles

Rotation Color: density
supporteddisk

Density

Temperature

Velocity

Tomida et al. (2013)
The protostar formation process was successfully simulated
Protostar, nascent disk, low-velocity outflow, high-velocity jet were well reproducedBut, only 1 years after protostar formation

Recent Study of Gas Collapsing phase
Induction equation

OhmicHallAmbipolar

w/ non-ideal effects w/ radiation

Both radiation non-ideal MHD effect of Ohmic, ambipolar and Hall terms areconsidered Tomida et al. (2015): Ohmic + ambipolar diffusion, just before the protostar
formation epoch, Nested Grid

 Tsukamoto et al. (2015): Ohmic + ambipolar diffusion until the protostar formation,SPH
 Tsukamoto et al. in preparation: Ohmic + ambipolar diffusion + Hall term

Tomida + 15

Basic Equations (w/o div B cleaning)
MassConservation

Eq. of motion
Induction eq.
Gas Energy Eq.

div B=0
Poisson’s Eq.
Radiation Transfer+ Eq. of state+ AD & OD rates+ Opacities

Tomida + 15

Non-ideal MHD Models: First CoresOD Only

18AU

OD+AD

18AU

OD: Slow-rotating, vertical inflation by heating from second core
AD: Supported by rotation, non-axisymmetric (GI), but size is still small

Tomida + 15

Disk Formation after 2nd Collapse
OD Only, ρOD Only, Tg2AUA rotationally-supported disk is formed after protostellar core formation.

Outflows by radiation+shock heating -> magnetic pressure driven jets

Tomida + 15

Force Balance
Ideal MHDOD OnlyOD+AD• Ideal MHD model is essentially not rotating, and is totallysupported by the gas pressure.
• OD model has considerable rotation, but not enough to
support the first core and it is still pressure supported.
• Rotation is dominant, but not by far, in OD+AD model. The
gas pressure is still contributing.

SPH: Non-Ideal (Ohmic + Ambipolar diff.) Radiation MHDTsukamoto+ 15

Angular Momentum J

Rotation supported disk forms at the same epochof the protostar formation with B diffusion
Density

Temperature

Ohm + Ambipolar

Plasma b
IdealIdeal MHDDensity

 Disk is massive andgravitationally unstable+ Ohmic+ Ohmic+ Ambipolar

 G.I. is expected to play animportant role in a further
evolutionary stage

2. Early Gas Accretion Phase~500 years after theProtostar Formation

Ω0 w/o radiation
Gas Accretion phase: 3D w/ B w/o non-ideal effectResistive MHD eqs.

Initial ConditionΩ  (,T )P  P(  ),(Barotropic eos + Protostellar Model)

Magnetic Field

Rotation Axis

Bonnor-Ebert Sphere

4.6x104 AU

Molecular Cloud core

In this study, Both protostar (h<0.01AU) and molecular cloud core >105 AU are
spatially resolved Cloud evolution was calculated for >500 years after the protostar
formation

 Without Sink
 With huge computational time (~10 months (wall clock time))

Gravitational Instability & Magnetic Effects
Plasma bb>103(very weak B)

b<10(Strong B)

Jet

Non-axisymetricstrcuture due to G.I.
Equatorial planeKeplerianDiskhigh bregion

low b Protostar
regiony=0 planecolor：Plasma b
contour: density (left)、b (right)

Magnetic field dissipates in a high density gas region
>~3 AU (magnetic coupling region): magnetic braking, low-velocity outflow

 ~0.5 < r < 3 AU (magnetic decoupling region): non-axisymmetric structure by G.I
<~0.5 AU (magnetic coupling region): (tower) jet, magnetic braking, MRI (disk surface)Time variability of Outflow and Jet
Episodic Jets cause Episodic Accretion(a) Mass (b) Momentum(c) Kinetic energy (d) Outflow and inflow rates

Jets, Outflow, Disk and Protostar
Schematic view High-velocity jet is driven near the protostar
 Low-velocity outflow is driven by the outer disk region

 High-velocity jet is enclosed by the low-velocity
outflow

Large scale

Simulation

Small scale

We cannot calculate this phase for a long time
without cheating (sink)

Sink？
Gas Collapsing Stage
Molecular
Cloud

F.C. formation

Gas Accretion Stage
P.S. formation

Disk formation?

Class 0Class IClass IITo calculate the disk formation processserious calculation without sink⇒ an impracticably huge CPU time (power) is requiredeasy calculation with sink⇒ we can easily acquire outcomes!
(However, we donot know whether the outcomes are correct or not)

Sink method (there are many prescriptions)
A high-density gas region requires a short time step which
impedes a long time disk evolution
 a high density region is masked and is removed

 an inner boundary is imposed around the protostar

Serious Caution?

Machida, Inutsuka, Matsumoto (2014)

Starting from the same initial condition, the disk formation was calculated with different sink sizes
Results dramatically and qualitatively differ with different sink treatment (or sink radius)

Sink radius of <1AU and spatial resolution of <0.1 AU are inevitably needed
racc=6.7 AUlarge sinkSame settings asin Seifried et al.

Uniform
SphereNo disk forms

racc = 12.6AU

completely different
outcome!

ntrh=3x1011 cm-3
No disk forms

racc = 1AU

small sink
Disk forms!

racc = 1 AU
ntrh = 1013 cm-3
Large disk appears!

Long-term evolution of disk
with rsink < 1 AU
Even with strong magnetic field, therotation supported disk forms in very earlyphase of star formation (Class 0 phase)ratio of vf to Keplerian vel.

Machida, Inutsuka, Matsumoto (2014)
See also Dapp & Basu ‘10, 12

Exponential Disk Growth
The disk rapidly grows as the infalling envelope dissipates.

disk radius

Disk-to-envelope mass ratio
Slowly rotating massive
infalling envelope

magnetic field lines

rapidly rotating lessmassive disk

Evolution of Outflow

 As the disk grows, the outflow also grows
 As the infalling envelopes dissipates, theoutflow weakens and finally disappears

Star forming cloud(Molecular cloud core)Gravitational Instability andPlanet Formation
Disk gravitational instability without sink
 Fragmentation occurs in the disk But, fragments falls onto the protostar

Gravitational instability inevitably
occurs during the early phase ofstar formation
Machida & Nakamura’ 15

Inutsuka et al.
2010
See also Vorobyov,
Basu et al.

Summary The star formation process from prestellar cloud until protostar and circumstellar
disk formation have been investigated using numerical simulations
 Recent theoretical studies indicates that
 The first core forms before the protostar formation and evolves into theprotostar formation: the first core is the origin of circumstellar disk
 The low-velocity outflow is driven by the first core or outer disk region, while
jets are driven near the protostar: the magnetic dissipation region causes two
distinct flows

 The dissipation of magnetic field occurs in the first core or nascent disk andalleviates the angular momentum transfer due to magnetic braking
 To accurately investigate the disk formation, sink radius of < 1AU and spatial
resolution of ~0.1AU are inevitably needed The size of rotation disk is within ~10 AU during the Class 0 stage, while thedisk size exponentially grows as the infalling envelope dissipates and reaches~100 AU Gravitational instability occurs and tends to form planetary mass objects
during the (early) gas accretion phase