Impact of magnetic field on circumstellar

disk formation

Yusuke Tsukamoto (Kagoshima U)

Shuichiro Inutsuka, Masahiro MachidaKazunari Iwasaki, Satoshi Okuzumi

Hajime Susa, Hideko Nomura

Outline

• Introduction

• Part1: Impact of dust size on formation and early evolution of YSOs with Ohmic and ambipolar diffusion (based on Tsukamoto+ submitted)

• Part2: Interplay of magnetic field-angular momentum misalignment of molecular cloud cores and Hall effect (based on Tsukamoto+17)

Kwon+18

BISTRO

From filament to circumstellar disk

Cloud core

Molecular cloud

Cloud core

Andre+17Andre+17

J flux

Magnetic field extracts angular

momentum from central

region→Magnetic braking

Disk formation is suppressed by

magnetic braking in idealized setup (ideal

MHD, coherent rotation, aligned B field)

→Magnetic braking catastrophe

(MBC;Mellon&Li+08)

落下速度Li+2011

vr

vφ

Radius

落下速度100 AU100 AU

Rotation stops

100AU

μ=5

μ=20

μ=100

Bate+ 14

Typical case

weak B field

strong B field

Magnetic braking and suppression of disk formation

Braiding+11

Mechanisms to solve magnetic braking catastrophe

• Realistic effect weakens magnetic braking– Turbulence diffusion (Santos-Lima+12

→Reinaldo talk)– Non-ideal MHD effect

(Machida+11,Tsukamoto+15, Tomida+15)– Misalignment of B and J (Hennebelle+09,

Joos+12, Tsukamoto+17,18)

• Many observations already find disks!→MBC is essentially solved

• We investigate more specific questions:1. How dust growth affects formation and

evolution of YSOs?2. How non-ideal effects work in misaligned

cloud core?

Santos-Lima2012

Yen+17

Part IImpact of dust size on formation and early evolution of circumstellar disk with Ohmic and ambipolar diffusion

Nakano+02

Why dust for non-ideal effect?

• Magnetic resistivity (ηO, ηH

ηA) depends on ionization state

• Ionization state is mainly determined by dust size and CR ionization rate

→dust size distribution is crucial to quantify the impact of non-ideal effect

Nakano+ 02

Okuzumi+09

Hall effectAmbipolar

diffusion

Ohmic

diffusion

Nakano+02

Ricci+10

Possible dust growth in the cloud core• Recent obs. suggest the dust growth

in very young YSOs– Dust size constraint from RAT theory

and polarized fraction (Valeska+19)– Optical index β decreases even in

Class 0 YSOs (Kwon+07)

• From theoretical point of view, dust can grow to <~1 μm in envelope and >>1 μm in disk of Class 0. (Hirashita+13)

Valeska+19

Hirashita+13

Kwon+07

Dust size dependence of resistivity• By dust growth

– ηA decreases in disk , ηA increases in envelope

– ηO decreases both in disk and envelope

→Complex dependence on dust size may introduce diversity of dynamics

diskenvelope

ηA

increases

ηA ,ηO

decreases

Gas density

Solid:ηA

Dashed:ηO

・μ=(M/Φ)/(M/Φ)crit~1

・r~104 AU

・B~10-5 G=10 μG

B

μfreeze~1

r~100 AU

⇒Bfreeze~ 100 mG

→β=0.1 !

• By dust growth, disk evolution is changed?

• Outflow evolution is changed?

• Magnetic flux accretion is changed?

– If all magnetic flux goes to disk, disk magnetic field is too large!

The questions addressed in this part

Setup of 3D simulations• Init cond.:Bonnor-Ebert sphere

– M=1 Msun, (M/Phi)=4 for const B

• Non-ideal effect: Ohmic, ambipolardiffusion

• Calculated untill Mstar~0.1Msun (>104

yr after protostar formation • Parameter: dust size distribution

– ISM like dust model– Large dust model

Time evolution of large dust model

Spiral arm formation by GI

1000AU 250AU

edgeon

faceon

Absence of outflow in early phase

Time evolution of ISM dust model

Disk begins to shrink after warp formation

1000AU 250AU

edgeon

faceon

Warp formation in later phase

Disk size evolution • Disk with large dust tends to be larger than with small dust

• Simulation results seems to consistent with disk size evolution of Class0 YSOs

■:Disk size from ALMA obs.

Fitting formula of Yen+17

Disk size evolution

Increases with dust size

Disk mass evolution• Disk with large dust tends to have

spiral arms by GI→ can explain recent obs of HH111 (Lee+20) or Elias 2-27 (Pérez+16)⇔Compared to obs. of Class 0 YSOs, disk tends to factor of 2-3 massive.

Lee+20

■:Disk mass from ALMA obs.

Disk mass evolution

Lee+20

Outflow evolution• The outflow mass decreases

as dust size increases• The outflow mass and

dynamical timescale are consistent with the observations of young outflow

Wu+04

Decreases with dust size

Outflow mass

Outward B field drift• Ambipolar diffusion induces outward B field drift in envelope

• We find B field drift happens with relatively large grain in later phase (Mstar>0.1 Msun)

→magnetic flux accretion to disk decreases with large grain

→disk formation is enhanced Large dust causes outward radial drift

ss

H2

H2

H2 i+

e-

vdrift

vdrift

Part II

• Interplay of magnetic field-angular momentum misalignment

and Hall effect (Tsukamoto+17)

J_ang

Bθ

Hull+19

Hull+14

Relative angle of magnetic field direction and outflows

Galmetz+18

• Observations reveal misalignment between disk Jang and B is common– Bimodal θ for Class O YSOs– Random θ for low-mass protostellar cores

→Does misalignment change disk formation process?

Previous studies with misaligned cloud cores(ideal MHD)• Hennebelle+09, Joos+12 with ideal MHD

simulations showed misalignment weakens magnetic braking (MB)

θ=0゜

θ=90゜Joos+12

Joos+12

Previous studies with misaligned cloud cores(ideal MHD)

B

B

Small disk with θ=0 large disk with θ=90

Joos+12

• Hennebelle+09, Joos+12 with ideal MHD simulations showed misalignment weakens magnetic braking (MB)

gas rotation induced by Hall effect• Hall effect induces the left-handed screw rotation

around the local magnetic field (JH : Purple arrow)

At midplane,

left-handed

screw rotation

is inducedBJH

toroidal current at midplane

→toroidal magnetic field

→toroidal magnetic tension

Hall induced rotation in misaligned core• Jang is vector sum of initial Jang and Hall induced Jang

• Acute angle and obtuse angle cause different resultalthough it can not distinguish from polarized emission

B

Jini

Jini+JH

B

JiniJH

Jini+JH

JH

Question for Part II:

How Hall effect modifies disk formation in misaligned core?

B

Jini

Jini+JH

B

JiniJH

Jini+JH

JH

Simulaiton setup

Okuzumi+09

Simulations starting from cloud core

θ

• Init condition– M=1 Msun, (M/Phi)=4

• Non-ideal effect: Ohmic, ambipolar diffusion and Hal effect

• Calculated untill the protostarformation

• Parameter: relative angle between initial J and B

Density structures with various θ

• pseudo-disk along B field direction (r~500AU) forms

800AU

Initial B direction

200AU

Disk normal is neither parallel to B and initial J !

Disk size ↑ as θ ↑Intial B directionJ direction

Density structures with various θ

• Jang(θ=0)< Jang(θ=90) < Jang(θ=180)

→Disk in parallel core can be larger or smaller than perpendicular (θ=0 and θ=180 are not distinguishable)

180deg=anti-parallel

90deg

=perpendicular

0deg= parallel

~1000AU ~100AU <=10AU

Angular momentum profile with Hall effect

B

B

B small disk with θ=0

Medium sized disk with θ=90

large disk with θ=180

Angular momentum profile with Hall

Observation of disk in parallel cores• Hall effect may assist disk and binary formation in

anti-parallel cloud core

→Kwon+19 pointed out that the relatively large disk (and binaries) can form even in parallel cloud cores

Comparison between ηturb

with free-fall timescale

• In collapsing cloud core, turbulence is trans- to sub-sonic

vturb < cs < vff → vff /vturb>1• Comparison with free-fall timescale

(Magnetic Reynolds number)

Re =vffλJ

𝜂𝑅𝐷=

vff 𝜆𝐽𝑣𝑡𝑢𝑟𝑏𝜆𝐽

=𝑡difftff

> 1

ηRD = vturb 𝐿min 1,𝑣𝑡𝑢𝑟𝑏𝑣𝑎

𝑎

< 𝑣𝑡𝑢𝑟𝑏 𝐿

Comarison between ηturb and ηO, ηA

ηturb=cs λJ

Zhao+ 18

ηturb=cs λJ

Important region is here!Lam+19 does not include this increase by dust

ηO ηA

Summary

• Part I :– Disk size positively depends on

dust size

– Outflow mass negatively depends on dust size

– Outward magnetic field drift happens only with large dust grain

→Dust growth in star forming region changes disk evolution!

• Part II:– With Hall effect, central angular

momentum of acute/obtuse angle differs

→(Apparent) misalignment not always enhances the disk formaiton

Backup slide

Formation of warped pseudo-diskand negative impact on disk growth• The warp of pseudo-disk develops in ISM dust

models and not in large dust models• Due to the warp formation, the magnetic flux

tube contracts→magnetic field in the disk is enhanced→stronger magnetic braking →Disk begins to shrink

Flux tube contracts

Magnetic field increases

Disk begins to shrink

中心角運動量の向き

ホールあり

ホールなし

180deg=anti-parallel135deg

90deg

0deg= parallel

45deg

70deg

110deg

90deg

0deg= parallel

45deg

70deg

• 中心領域の角運動量の向きは10-15<ρ<10-13で急激に変化

→中心付近(数100AUスケール)で回転がゆがんだ構造が実現

• 磁場/初期角運動量の向きと大きく異なる

When Hall effect becomes important ?• Magnetic resistivity strongly depends on the CR

ionization rate and dust size• Koga+19 investigate how characteristic disk size by Hall

effect depends on grain size and CR ionization rate• Hall effect becomes important when

1. cosmic ray ionization rate is low (ζ<~10-17 s-1)2. dust grain is sub-micron (a~ 0.05 μm)3. Magnetic field is strong (μ~1)

Turbulent diffusion rate

ηturb~𝑣𝑙 𝜆𝐽 ~1018

𝑣𝑙200 𝑚 𝑠−1

𝜌

10−13𝑔 𝑐𝑚−3

−12

𝑐𝑚2 𝑠−1