Yusuke Tsukamoto RIKEN

Formation and early evolution of

circumstellar discs

50 AU

To be formed or not to be formed. That is the question.

Formation and evolution of protostars and disks

Planet formation

Formation and evolution of protostars and disks

Planet formation

This phase is

theoretically very

interesting and

challenging because

the complicated

physical processes

interplay.

Cloud core PS formation Jet Protostar (PS)

Disk formation

Angular mometnum transfer via B field

Non-ideal effect: Ohmic diffusion Hall term Ambipoloar difusion

Important processes for disk formation

Turbulence and misalignment

• The angular momentum transfer by the magnetic field • Turbulence and misalignment change the accretion flow • Non-ideal effects change the strength of magnetic field

B

The effect of magnetic braking on the disk formation

The disk size becomes small as

the magnetic field strength

increases.

The observation shows that the

cloud cores are strongly

magnetized (Troland+ 08).

The magnetic braking completely

suppresses the disk formation in

Class 0 YSOs(Mellon+ 08)

→Magnetic braking catastrophe

(MBC)

100AU

μ=5

μ=20

μ=100

Bate+ 14

Typical case

weak B field

strong B field

μ =M/Φ

M/Φ crit= 2 − 4

The disk is observed in the Class 0 YSOs

Observations suggest

that some of Class 0

YSOs have the disk with

the size of ~ 100 AU. (Ohashi+14, Sakai+ 14

Tobin+15, Yen+15)

→There must be physical

mechanisms which solve

MBC.

Ohashi+14

Yen+15

Misalignment between magnetic field and the rotation axis.

Misalignment reduces the efficiency of the magnetic braking (Hennebell+09, Joos+12) In general case, the magnetic field and the rotation axis are

mutually misaligned.

The disk is formed in their simulations

The difference of specific angular momentum is a factor of 2-3.

→Misalignment cannot completely solve MBC (Li+13)

Joos+12

Mean specific angular

momentum

Turbulence in the cloud core

The magnetic braking is weakened by turbulence Turbulent reconnection provides the effective resistivity (Santos-Lima+11,

12)→the magnetic field becomes weak.

In turbulent cloud core, the large disk is formed (Seifried+ 12)

The diffusion rate strongly depends on the numerical resolution. →Convergence check is required.

Complex shear flow is important ? (Seifrield+ 12) →Dr. Seifried talks.

Seifried+12

Santos-Lima+ 11

Non-ideal MHD effects are fundamental physical processes in

the cloud core.

The ionization degree of cloud cores is quite low and the gas has the

finite conductivity.

→The finite conductivity causes the non-ideal MHD effects.

However, the most of simulations employed the ideal MHD

approximation.

Machida+2007

The importance of non-ideal MHD effect

Ideal MHD term

Non-Ideal terms

Magnetic diffusions

Ohmic diffusion: Effective in high density region (ρ>10-12 g/cm3)

Independent on B

Ambipolar diffusion: Effective in low density region (ρ<10-12 g/cm3)

𝛈𝐀 ∝ 𝑩𝟐

Ideal MHD term

Ohmic diffusion Ambipolar diffusion

Non-ideal MHD simulation with large sink

Li+ 11 claimed that non-ideal MHD effects can not solve MBC. Even with all non-ideal effects, the rotation is suppressed by magnetic

braking and the disk is not formed.

Their simulations employed relatively large sink (or outgoing inner boundary, r~7 AU) and did not resolve the disk with a size of r<~10 AU. The gas dynamics within several times of sink radius may be affected.

Furthermore, they neglected the first core phase.

Rotation is suppressed

Li+ 11 Infa

ll and r

ota

ion v

elo

city

radius

The importance of first core

Although the first core is transient object, it has a large impacts on the protostar and disk formation.

The molecular outflows are launched from the first cores.

The magnetic diffusion is effective inside it and the diffusion timescale becomes much smaller than the lifetime of first core.

→The magnetic flux would be largely removed in the first core phase.

Inutsuka+10

Inutsuka12

Ohmic resistivity

Decoupled region

The effect of magnetic diffusion

YT+15a investigated the effect of magnetic diffusions

without sink and resolving protostar formation.

Magnetic flux is largely removed in the first core

phase.

→Magnetic braking is no longer important inside the

first core when the magnetic diffusion is included.

YT+15a

20 AU Large plasma β

inside the first core !

Plasma β

Ideal MHD

MHD w diffusion weak B field

strong B field

β =P𝑔𝑎𝑠

Pmag

The disk formation inside the first core The disk is formed just after

the protostar formation ! The magnetic flux is largely

removed inside the first core

→The disk formation becomes possible within it.

However, disk size is small (r~ 1AU) at its formation epoch.

1.5 AU

YT+15a

Machida+11

Ohm

Radius (AU)

Infa

ll vel (k

m/s

)

Ideal MHD

Ohm+ambi

Disk !

Non-ideal MHD

Long term evolution with Ohmic diffusion and sink

time

Dis

k r

adiu

s

Disk grows in later phase !

Machida+12

Disk quickly grows when the envelope mass becomes smaller than the disk mass. The magnetic braking is an angular momentum transfer process from the

disk to the envelope

When the mass of envelope becomes small, it is no longer important.

Large disk formation (r~100 AU) is possible at the end of Class 0 phase even in the strongly magnetized cloud core.

4000 AU

Long term evolution with Ohmic diffusion and sink

Disk quickly grows when the envelope mass becomes smaller than the disk mass. The magnetic braking is an angular momentum transfer process from the

disk to the envelope

When the mass of envelope becomes small, it is no longer important.

Large disk formation (r~100 AU) is possible at the end of Class 0 phase even in the strongly magnetized cloud core.

Disk size is limited by the

size of dead zone

Disk quickly grows !

Inutsuka+12

How about the effect of the Hall current term ?

Ideal MHD term

Hall current term

Hall current term directly changes the gas rotation Hall current term generates toroidal magnetic field from poloidal

magnetic field.

Directly changes the magnetic tension and affects the magnetic braking

The effect differs depending on the relative angle of B and rotation vector (Wardle+99) When B and rotation vector are

parallel: spin-down the gas rotation

anti-parallel: spin-up the gas rotation

How about the effect of the Hall current term ?

Hall current term directly changes the gas rotation Hall current term generates toroidal magnetic field from poloidal

magnetic field.

Directly changes the magnetic tension and affects the magnetic braking

The effect differs depending on the relative angle of B and rotation vector (Wardle+99) When B and rotation vector are

parallel: spin-down the gas rotation

anti-parallel: spin-up the gas rotation

B Rotation

vector

Parallel cloud core

B Rotation

vector

Anti-parallel cloud core

How about the effect of the Hall current term ?

Hall current term directly changes the gas rotation Hall current term generates toroidal magnetic field from poloidal

magnetic field.

Directly changes the magnetic tension and affects the magnetic braking

The effect differs depending on the relative angle of B and rotation vector(Wardle+99) When B and J_ang are

parallel: spin-down the gas rotation

anti-parallel: spin-up the gas rotation

B Rotation

vector

Parallel cloud core

B Rotation

vector

Anti-paralell cloud core

Last weak, we submitted new paper which describes the effect of Hall term (arxiv1506.07242v1) →The first 3D simulations with all non-ideal terms and radiation transfer !

How about the effect of the Hall current term ?

Hall current term directly changes the gas rotation Hall current term generates toroidal magnetic field from poloidal

magnetic field.

Directly changes the magnetic tension and affects the magnetic braking

The effect differs depending on the relative angle of B and rotation vector(Wardle+99) When B and J_ang are

parallel: spin-down the gas rotation

anti-parallel: spin-up the gas rotation

B Rotation

vector

Parallel cloud core

B Rotation

vector

Anti-paralell cloud core

Last weak, we submitted new paper which describes the effect of Hall term (arxiv1506.07242v1) →The first 3D simulations with all non-ideal terms and radiation transfer ! Yesterday, Dr Wurster gave me an e-mail and he also did the simulations with the Hall term. →Please check Dr Wurster’ s poster too!

Basic equations for the simulations in YT+ 15b Dρ

Dt= −𝜌𝜕μ𝑣μ

ρDvμ

Dt= 𝜕𝜈Tμν +

χFρ

cFμ

𝜌De

Dt= 𝜕𝜈𝑇𝜇𝜈v𝜇 − 4𝜋𝜅𝑝𝜌𝐵 + 𝑐𝜅𝐸𝜌

2𝜉

　　　　　　　　　　　　− 𝛻 ⋅ [ 𝜂𝑂 𝛻 × 𝐵 + 𝜂𝐻 𝛻 × 𝐵 × 𝐵 −𝜂𝐴 𝛻 × 𝐵 × 𝐵 × 𝐵 × 𝐵]

𝜌Dξ

Dt= 𝜕𝜈𝐹𝜈 − 𝜕𝜇𝑣𝜈𝑷rad

𝜇𝜈− 4𝜋𝜅𝑝𝜌𝐵 + 𝑐𝜅𝐸𝜌

2𝜉

D

Dt

𝐵𝜇

𝜌=

𝐵𝜈

𝜌𝜕𝜈𝑣𝜇

　　　　　　　　　　　　　　　　　　　　　　　 −1

𝜌𝛻 × {𝜂𝑂 𝛻 × 𝐵 + 𝜂𝐻 𝛻 × 𝐵 × 𝐵 −𝜂𝐴 𝛻 × 𝐵 × 𝐵 × 𝐵 }

Tμν = − 𝑝 +

𝐵2

2𝛿𝜇𝜈 + 𝐵𝜇𝐵𝜈 e =

1

2𝑣2 + 𝑢 +

𝐵2

2𝜌

u =p

γ−1 ρ:specific internal energy

ξ :specific radiative energy

Equation of continuity

Equation of motion

Energy equation of matter

Equation of radiation energy

Induction equation

ち

RHD

MHD

ち Non-ideal

Ohm+ambipolar+Hall (parallel case) Ohm+ambipolar+Hall (anti-parallel case)

Large disk is formed!

50 AU

B: ⊗ B: ◉

Formation of large disk in the early Class 0 phase

YT+15b

B Rotation

vector

Parallel

B Rotation

vector

Anti-paralell

50 AU

The difference of specific angular momentum

Time evolution

Mean specific angular momentum of the region of ρ > 10−13 𝑔 𝑐𝑚−3

an order of magnitude different

Parallel

Anti-paralell

Central density

Q value and plasma β of the massive disk

The disk is massive enough to develop the

gravitational instability (GI).

The magnetic flux is largely removed from the

disk by the magnetic diffusions.

→GI will play the important role in the

subsequent evolution of disk !

Q value

plasma β

Q =Ωcs

𝜋𝐺Σ∼ 1 β =

P𝑔𝑎𝑠

Pmag≫ 1

Formation of anti-rotating envelope

Spin-up at the center causes the anti-rotation in the

envelope due to the angular momentum conservation.

This structure has a scale of >~200 AU and expands in

subsequent evolution stage →It would be observable !

300 AU

Rotation velocity

Anti-paralell

Discussions (1)

The disk formation is enabled by magnetic diffusions just after the protostar formation The magnetic flux is largely removed in the first core phase and

magnetic braking is no longer important.

→Disk is formed just after the protostar formation !

However, the size of the disk is r~ 1 AU in the strongly magnetized cloud cores.

The disk quickly grows when the mass of envelope becomes smaller than the disk mass. Because the magnetic braking weakens as the envelope disappears.

The Hall current term crucially assists the early formation of the large and massive disk in the strongly magnetized cloud core. Spin-up effect of the Hall term becomes strong as the magnetic field

strength increases.

→Large disk can form even in the strongly magnetized core.

Crucially important for the disk fragmentation !

𝛈𝑯 ∝ 𝑩

Discussion (2) Bimodality of disk size in Class 0 phase

~50 %

~50 %

~50 %

~50 %

Hall current term induces

bimodality of disk size

Half of cloud core may have

the parallel configuration

→About half of Class 0 YSOs

have the relatively large disk and

the others do not.

B

Parallel

B

Anti-paralell

The anti-rotating envelope is formed due to the angular momentum conservation.

It has a relatively large scale of r>200 AU and vrot ~ 1 km

→It would be observable (though it is challenging).

If such structures are observed, they provide clear evidence that the Hall current term plays an important role in the disk formation.

Discussion (3) Formation of anti-rotating envelope

P-V