Does magnetic-field-angular-momentum
misalignment strengthens or weakens
magnetic braking ?
Yusuke Tsukamoto
Kagoshima University

S. Okuzumi, K. Iwasaki, M. N. Machida,
S. Inutsuka

BJang

Outline Introduction:
 Observation of magnetic field and turbulence of thecloud core
 Magnetic braking and its anisotropic impact
 Discrepancy among the previous studies
 Results
 Dependency of central angular momentum evolution

on the initial condition and magnetic resistivity
 Strong magnetic braking in isothermal collapse phasein perpendicular cloud cores Summary and discussion

Strong magnetic field and weak turbulence in cloud cores Magnetic field of thecloud cores is strong.
OH Zeeman Obs.
M/Φµ== 2−4(M/Φ)crit

Troland+08

μ=1

μ~4.8

 Turbulence is weak

Mturb < 1
Ward-Tompson+06
Taurus:○,ρOph:▲

Lada+07
Pipe NebulaMagnetic braking and its anisotropic impact
 In the core with observed B

and subsonic turbulence,magnetic braking is
dynamically important.

100AUweak B field
μ=100

Bate+ 14
μ=20J flux

μ=5strong B field

Magnetic braking and its anisotropic impact
 What kind of structure does the magnetic braking

imprint to the rotation structure?
→it introduces anisotropy of the angular momentum!
 Matsumoto+04 showed that magnetic braking
enforces J and B to be aligned.

JangJ⊥J⊥selectively
decreases

θ=0゜

BJ||

θ=45゜

Solid: J||
Dashed: J⊥
Matsumoto+04

θ=90゜

Magnetic braking and its anisotropic impact
 What kind of structure does the magnetic braking

imprint to the rotation structure?
→it introduces anisotropy of the angular momentum!
 Matsumoto+04 showed that magnetic braking
enforces J and B to be aligned.

JangJ⊥J⊥selectively
decreases

θ=0゜

BJ||

θ=45゜

Solid: J||
Dashed: J⊥
Matsumoto+04

θ=90゜

Dependence of magnetic braking timescale on B direction
 Timescale of magnetic braking→is given as the time in which Alfven wave sweeps the region whose inertia
equals to the central inertia

 The magnetic

drrdr 𝑅𝑐2 − 𝑅2t b,⊥ = ∫=∫=vA (𝑟)Bc
2 𝐵𝑐

ρext (𝑅4 − 𝑅𝑐4 ) = 𝜌𝑐 𝑅41(4 𝜋𝜌𝑒𝑥𝑡 )1/2 𝑅𝑐
1𝜌𝑐 2t b,⊥ = ()1 +0 −132𝜌𝑒𝑥𝑡𝐵𝑐

braking isstrong in thecore with B⊥Jwith simple B
geometry(Moschouvias+85)

Random distribution of magnetic field andoutflow directionThis suggests:
1.
2.

The magnetic braking is dynamicallyimportant but it does not enforce J || B.
The magnetic field is dynamicallyunimportant at the observed
scale(turbulence is strong or magnetic fieldis weak)

Hull+17
Serpens SMM1

Hull+14magnetic braking timescale of hourglass B field
エンベロープ内では磁場配位は砂時計型→広がった分「腕」が稼げる→より効率的な磁気ブレーキ
 Rc/Rextは解析から決めるのは困難(Joos+12ではRext=Rcore→過大評価)→シミュレーションしてみる必要がある

2

12t∥
𝑅𝑐
𝜌𝑐=&+ &+𝑡⊥
𝑅𝑒𝑥𝑡
𝜌𝑒𝑥𝑡

Girart+06
NGC 1333 IRAS 4A

Does magnetic braking really enforce B || J?
Ideal MHD studies
 Magnetic braking is efficient when B||J→J⊥B tends to realized (Hennebell+09, Joos+12).
⇔ B||J tends to be realized (Mouschovias+85,Matsumoto+04)


J_ang

θ

B

Resistive MHD study Magnetic braking efficiency is almost unchanged(non-ideal MHD:Masson+16)

θ=0゜
θ=90゜

θ=0゜
θ=90゜Joos+12

Matsumoto+04

Does magnetic braking really enforce B || J?
Ideal MHD studies
 Magnetic braking is efficient when B||J→J⊥B tends to realized (Hennebell+09, Joos+12).
⇔ B||J tends to be realized (Mouschovias+85,Matsumoto+04)
Resistive MHD study Magnetic braking efficiency is almost unchanged(non-ideal MHD:Masson+16)

Masson+16
θ=0゜

θ=40゜J_angθBPurpose of this study
 Resolve the discrepancy of the previous studies
 Reveal the nature of the magnetic braking in cloudcore collapse We particularly focus on
 The Initial conditions○ Matsumoto+04: Bonnor-Ebert sphere, α=0.5○ Joos+12:

α=E$%𝐸'()*, α=0.25

 Magnetic diffusion(ohm, ambipolar diff.)○ Matsumoto+04, Joos+12:ideal MHD○ Masson+: resistive MHD (uniform sphere, α=0.25)

Numerical methods and models

methods: non-ideal Godunov SPMHD (Iwasaki+11,YT13) with FLD (Whitehouse+05)
 Initial condtions: uniform cloud cores with M = 1 Msolar(β=0.03) Both ideal and resistive (Ohm+ambipolar diff.) MHD
simulations are conducted.

αE$%
α=𝐸'()*M/Φ
= 4.0(M/Φ)012$.6.4.2
04590

θ

Simulations start from cloud core

α=0.4, θ=0α=0.6, θ=0α=0.2, θ=45α=0.4, θ=45α=0.6, θ=45α=0.2, θ=90α=0.4, θ=90

α=0.6, θ=90α=0.2, θ=0600 AU

Matsumoto+17

Evolution of central J (ρ>10-12g/cc Ideal simulaiton) As α of initial core decreases, J of θ=90 increases quickly We obtained the consistent results with previous studies

α=0.6

θ=0
θ=45
θ=90α=0.4
α=0.2

Central densitylargeαsmall

consistentconsistentMatsumoto+04Joos+12

Evolution of central J (ρ>10-12g/cc, resistive)In all simulations with magnetic diffusion, J of the central region
decreases as θ increases. (consistent with Matsumoto+04)
Difference between θ=0, 45 is quite small and roughly consistent with
Masson+16
α=Eth/Egrav=0.6 θ=0
ρ>10-12 g/cc region θ=45
θ=90

α=0.2
α=0.4

central density

Masson+16

Roughly
consistentconsistentWhy do the results depend on the initial condition?
 When and how themagnetic braking
changes the gas angularmomentum have been
ambiguous because
previous studies only
investigate the J evolutionof the central disk
 To reveal the physicalmechanism, we should
investigate the angularmomentum evolution offluid elements.

We follow J evolution offluid elements→We can answer whenand how J is changed

Previous studies
investigate howmean J of diskchanges under themass accretionNon-spherical collapse and apparent enhancement ofmagnetic braking

BCollapse is
not sphericalsymmetric !
Shell with M(r)=0.01 Msun

Fluid elementswith small/large J
selectively
accretes to thecentral region incore with θ=0, 90

Shell with M(r)=0.1 Msun

Angular momentum evolution of the spherical shell


B



In isothermal collapse phase:magnetic braking is stronger inmodel with θ=90
Ideal: strong magnetic braking in
adiabatic/rotationally supported
phase.
Non-ideal: magnetic braking is
suppressed in adiabatic/rotationally
supported phase.

Shell with M(r)=0.01 Msun

Ideal:α=0.4
θ=45゜
θ=0゜
θ=90゜

isothermal

resistive

isothermalAngular momentum evolution of the spherical shell
In isothermal collapse phase:magnetic braking is stronger inmodel with θ=90Tomisaka00
 Ideal: strong magnetic braking in
B adiabatic/rotationally supported
phase.
 Non-ideal: magnetic braking issuppressed in adiabatic/rotationally
supported phase.
Shell with M(r)=0.01 Msun
Angualr momentum
Ideal:α=0.4
distribution at first
θ=45゜
coreformation

θ=0゜
θ=90゜

isothermal

Angualr momentum
distribution after
first core formation

resistive

isothermalComparison between ideal and resistive Evolution in isothermal

phase is essentially thesame.
 Magnetic resistivity (Ohmand ambipolar) changes
the angular momentum
evolution in ρ>10-13g cm-3

resistive
ideal

resistive
ideal

θ=45゜

θ=0゜
resistive

ideal

θ=90゜

Summary and discussion

We investigated the magnetic
braking in misaligned cloud cores
and almost all previous results arereproduced.
Results
 In isothermal collapse phase,magnetic braking is strong when B⊥J→If magnetic filed is dynamicallyimportant in isothemal phase orenvelope (r~1000AU scale), B || Jrealizes!
 Once magnetic diffusion is included(more realistic simulation), thecentral angular momentum (or disksize) is always larger in B||J caseDiscussion With multiscale observationof polarization, we candetermine the scale atwhich the magnetic braking
is dynamically important !

Summary and discussion
Hull+13 showed that B of core scale is notaligned with outflow direction (J direction)
 This suggests : The magnetic braking is efficient but it does notenforce J || B.
 The magnetic field is dynamically unimportant at
the observed scale(turbulence is strong or
magnetic field is weak)

Hull+13

Hull+17

Remaining questions
 Magnetic field is weak in the core scale?
 How can we explain the Zeeman obs?
 Turbulence in cloud core is strong?
 Simulations tends to produce the cores with strong

turbulence(supersonic, Klessen+05)
 Observation does not show supersonic line width. i.e.,
subsonic turbulence (Andre+06, Lada+07). Angularmomentum problem also becomes serious.
OH Zeeman Obs.
Troland+08

μ=1

Hull+13μ~4.8Remaining questions
 Magnetic field is weak in the core scale?
 How can we explain the Zeeman obs?
 Turbulence in cloud core is strong?
 Simulations tends to produce the cores with strong

turbulence(supersonic, Klessen+05)
 Observation does not show supersonic line width. i.e.,
subsonic turbulence (Andre+06, Lada+07). Angularmomentum problem also becomes serious.
Klessen+05