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