Possibility of the formation ofhigh-mass close binary systems
by magnetic braking
Naoto Harada1, Shingo Hirano1, Masahiro Machida1 &Takashi Hosokawa2
1 : Kyushu University, 2 : Kyoto University

Observations of High-Mass Close Binaries
Duchene & Kraus (2013)

Frequency

Most massive stars
are in binary systems.
Most high-mass binarysystems are close.

1 [AU]Log Binary separation [AU]but the mechanism of the formation of HMCB is unclear.

Expression of the separation• Assume that eccentricity = 0.
• Equation of motion𝑠𝑚%𝑚$𝑥• Orbital angular momentum around the center of gravity

1+𝑞 *𝐽+
𝑠=𝑞+ 𝐺 𝑚 + 𝑚$𝑞 ≡ 𝑚% ⁄𝑚$%.

… Bate & Bonnell (1997)

Difficulty of the formation of close systems• Assume the equal mass binary (q = 1)
16 𝐽+
𝑠=.
𝐺 𝑀343→ Angular Momentum transfer isnecessary to form close systems!

• How to transfer the angularmomentum?
We paid attention to magnetic braking
during the collapse of a molecular cloud core. Machida+ 2007

Previous works on the formation of binaries
Accretion

Collapse

Cloud corefragmentation

protostar

Simulation

pre-mainsequenceKuruwita+ (2017) : Ideal MHD, Low-mass, 1 model
3000 yr since sink particle formation
Modeling the magnetic braking effectSemi Analysis

Lund & Bonnell (2018)

Overview of this work
Accretion

Collapse

Cloud coreThis work︓

fragmentation

protostarpre-mainsequence

3D non-ideal MHD simulation + analytical model, 8 models~5×10* yr since sink formation

We investigated the magnetic braking effect on
the long-time evolution of the separation!

Methods : Outline of this work
Simulation
Set one sink at the centerTwo sink thresholds

𝑛%:;< = 10=> 𝑐𝑚@. , 𝑟%:;< ≈ 21 𝑎𝑢Analysis
Estimate the separation
by sink data
Calculate how much M & J are
brought into the center withmagnetic braking working.

Assumption

Simulation set up• Basic equation• Initial condition
Critical Bonnor-Ebert sphere
𝑀GH4IJ = 100 𝑀⨀
𝑛GL;3LM = 3.9×10* 𝑐𝑚@.
𝛽 ≡ 𝐸M43 ⁄𝐸SMT = 0.02𝜇≡• Simulation codeV⁄W
= ∞ 𝑜𝑟 3V⁄W XYZ[T = 10 K 𝑖𝑠𝑜𝑡ℎer𝑚𝑎𝑙𝑛%:;< = 10=> [𝑐𝑚@.]

Nested Grid Code (Machida & Hosokawa 2013)
Stellar evolution（Hosokawa+ 2011）

Parameter
We studied 𝛼, 𝜃 dependence of the separation evolution.
𝛼 ≡ 𝐸3j ⁄𝐸SM＝＞ Accretion rate is depend on α.
𝜃 ≡ Inclination b/t B0 direction & rotation axis＝＞ Efficiency of angular momentum transfer is depend on θ.

Ω

𝛼 = 0.2= 0.6

Non-Mag𝜃 = 00°
= 45°
= 90°

𝜃

B0

Assumption & Analytical model• Assumption
Binary system formed in sink region and𝑀343 = 𝑀%:;< , 𝐽343 = 𝐽%:;<
𝑀343 ︓Binary’s total mass,
𝐽343 ︓Binary’s total J• Calculate the separation+16 𝐽343
𝑠=.
𝐺 𝑀343zzzz

Results︓Time evolution of the separation
Green︓Separation ＞ sink diameter

Grey︓Separation＜ Stellar diameterWith B field, systems became much closer.

Formation of the Contact Binarysr*s < 2×r*

α dependence

Large α ＝＞ Close separation← Angular momentum is more transferredbecause the collapse time became longer.

Discussion︓Why the separation fluctuated?
xz plane of α=0.6, θ=0° at M={1,3,5,10}

Red regions :𝑃VTS ⁄𝑃MTo > 1 … 𝑃VTS ≡ 𝐵+⁄2𝜇>, 𝑃MTo ≡ 𝜌𝑣 +The change of this configuration caused the separation
fluctuations?

Summary
By MHD simulation + Analytical model,
we investigated long-time evolution of the separation.
• Angular momentum transfer by magnetic braking isnecessary to form high-mass close binaries!
• α dependence…
Larger α model evolved closer system.
• θ dependence…
The relationship is reversed several times.
• Separation fluctuation
It is caused by the change of 𝑃VTS ⁄𝑃MTo > 1 region?

Appendix

Origins of Binary-BH, NS
LIGO-Virgo/
Frank Elavsky/
NorthwesternUniversity

High-Mass Close Binary can evolve to Binary-BH or NS.

Sink setting• Set two thresholds, 𝑛%:;< & 𝑟%:;< .
• Renew the sink parameters every step based on…

• In this work, 𝐶TGG = 0.03, 𝑟%:;< ===𝜆=+ x+y𝑐z{o| ;}Z~• %Previous works on the formation of binaries
Accretion

Collapse

Cloud corefragmentation

Simulation
Matsumoto & Hanawa (2003)
Machida+ (2008)

protostar

Semi Analysis
Lund & Bonnell (2018)

Mass-Time plotAngular momentum-Mass plot

Mdot-Mass plotAngular momentum transfer

Separation[AU]
Separation [AU]

θ dependence100(a) α=0.2(b) α=0.6410

3.513radius
Non-Mag
θ=0o
θ=45o
θ=90o0.1

0.01
0.1

2.5

1210 0.1
Mass [M[𝑀⊙]Total Mass1.5⊙]110Non-Magθ=0o
θ=45ooθ=901-10 closer-5 the separation
05 is. 10
Early stage︓The larger 𝜃 is, theLate stage︓The relationship is reversed several times.