Chiral Matter and Topology in Astrophysics

Chiral Matter and Topology in Astrophysics

Naoki Yamamoto (Keio University)

“Recent Developments in Chiral Matter and Topology”

December 8, 2018

Main topics

• Core-collapse supernova

• Chiral hydrodynamics

• Chiral turbulence in supernovae

• Photonic chiral vortical effect in pulsars

Units: ~ = c = k

= e = 1

Core-collapse supernovae

explosions

• One of the most energetic phenomena in the Universe

• Transition to neutron stars & origin of heavy elements

• But explosion is difficult in conventional 3D hydrodynamic theory

Core-collapse supernova explosions

One of the puzzles in astrophysics

http://www.riken.jp/pr/press/2009/20091211/

Parity

Chirality of fermions

s

p

left-handed right-handed

mirror

s

p

Why is “God” left-handed?

W. Pauli

“God is just a weak left-hander. ”

The laws of physics are left-right symmetric except for the

weak interaction that acts only on left-handed particles.

From micro to macro

Macro Evolution of core-collapse supernovae (giant P violation) Chiral kinetic theory

Son, Yamamoto (2012); Stephanov, Yin (2012); J.

W. Chen, S. Pu, Q. Wang, X. N. Wang (2013), …

Micro

Microscopic parity violation is reflected in macroscopic behavior:

Chirality of fermions (e, ν) in Standard Model

Yamamoto (2016)

Supernova = Giant Parity Breaker

p + e ^L ! n + ⌫ _e ^L

e

e

e

e

supernovae

ν

ν

ν

ν

Ohnishi, Yamamoto (2014); Grabowska, Kaplan, Reddy (2015); Sigl, Leite (2016), …

supernovae

m

• Neutrino mean free path ~ 1cm at core (ρ

~10

g/cm

).

• Neutrino matter = Chiral liquid (μ

~200 MeV ≫ T~10 MeV) = 3D topological matter

Neutrino matter in supernovae

Chiral hydro

Chiral kinetic theory ν

~ 100 km

Chiral hydrodynamics

Chiral magnetic effect

Vilenkin (1980); Nielsen, Ninomiya (1983); Fukushima, Kharzeev, Warringa (2008), …

j = µ _R µ _L

4⇡ ² B ⌘ µ ₅

2⇡ ² B

j ₅ = µ _R + µ _L

4⇡ ² B ⌘ µ

2⇡ ² B

Chiral vortical effect

Vilenkin (1979); Erdmenger et al. (2009); Banerjee et al. (2011);

Son, Surowka (2009); Landsteiner et al. (2011)

j = µµ ₅

2⇡ ² !

j ₅ =

✓ µ ² + µ ² ₅

4⇡ ² + T ² 12

◆

!

! ⌘ r ⇥ v

vorticity

Lorentz covariant chiral hydro

@

T

= F

j

Energy-momentum conservation:

Anomaly relation:

Son, Surowka (2009); Sadofyev, Isachenkov (2011); Neiman, Oz (2011)

T

= (✏ + P )u

u

P g

+ (di↵usion) j

= nu

+⇠

B

+ ⇠!

+ (di↵usion)

B

= 1

2 ✏

u

F

, !

= ✏

u

@

u

@

j

= CE

B

j

= n

u

+⇠

B

+ ⇠

!

+ (di↵usion) (dissipation) (dissipation)

(dissipation)

Helicity conservation

@

j

= CE · B

Yamamoto (2016); see also Avdoshkin et al., (2016)

Helicity conservation

d dt

Z

d

x

✓

j

+ C

2 A · B

◆

= 0

Yamamoto (2016); see also Avdoshkin et al., (2016)

CVE CME

Helicity conservation

d dt

Z

d

x

✓

j

+ C

2 A · B

◆

= 0

j

= n

+⇠

v · ! + ⇠

v · B

Yamamoto (2016); see also Avdoshkin et al., (2016)

chiral charge magnetic helicity

fluid helicity mixed helicity

CVE CME

Helicity conservation

d

dt Q

= 0, Q

⌘ Q

+ Q

+ Q

+ Q

Q_mag = Z

d³x C

2 A · B

Q

= Z

d

x n

d

dt Z

d

x

✓

j

+ C

2 A · B

◆

= 0

Yamamoto (2016); see also Avdoshkin et al., (2016)

Q_flu = Z

d³x ⇠₅v · ! Q_mix = Z

d³x ⇠_B5v · B

j

= n

+⇠

v · ! + ⇠

v · B

B B

v v

B v

Neutrino chiral hydro

• Neutrino number + fluid helicity is conserved.

• Generation of fluid helicity is numerically observed.

• Chiral hydrodynamic equations for pure neutrino matter:

CVE CVE

@

(n + ⇠v · !) + r · j = 0, j = nv + ⇠!

Kobayashi, Okuno, Yamamoto, in preparation

• When coupled to charged sector, fluid helicity ~ μ

for electrons

j ⇠ (v · !)B

Chiral MHD turbulence

in supernovae

Turbulence and cascade

https://doi.org/10.1515/htmp-2016-0043

• The structure becomes smaller, and eventually dissipates (direct cascade)

• Similar in magneto-hydrodynamics (MHD)

………

Direct cascade

(3D usual matter) Inverse cascade

(2D usual matter)

explosion difficult explosion easier

F. Hanke (2014)

2D

3D

Cascade and explosion

What about 3D chiral matter?

Chiral MHD for supernovae

Masada, Kotake, Takiwaki, Yamamoto, arXiv:1805.10419

Proto-neutron star (PNS)

Chiral MHD for supernovae

“CME”

chiral anomaly

• Chiral MHD w/o vorticity at the core (proton, e

, e

):

@

B = r ⇥ (v ⇥ B) + ⌘r

B + ⌘ r ⇥ (⇠

B)

• Setup for proto-neutron stars (100 MeV = 1) :

Masada, Kotake, Takiwaki, Yamamoto, arXiv:1805.10419

@

n

= ⌘

2⇡

( r ⇥ B ⇠

B) · B

⇢

= 5.0, P

= 1.0, ⇠

= 4.2 ⇥ 10

, ⌘ = 100.0

+(di↵usion) (dissipation)

Movies of 3D simulations are available at:

http://www.kusastro.kyoto-u.ac.jp/~masada/movie.mp4

Masada, Kotake, Takiwaki, Yamamoto, arXiv:1805.10419

Energy spectra

• As time passes, energy in small-k and large-k regions grows

• Eventually, ε

~k

, ε

~k

Masada et al., arXiv:1805.10419; see also Brandenburg et al., arXiv:1707.03385

ε

ε

Neutrino chiral radiation hydro

r ^↵ (T _hyd ^↵ + T _⌫ ^↵ ) = 0

Yamamoto, work in progress

Stress tensor for ν Stress tensor for N & e

(Hydro) (Chiral kinetic theory)

T

= Z

p

|p|

✓ ˆ

p

p ˆ

n

1

2 p

✏

⌦

@

n

1

2 p

✏

⌦

@

n

◆

⌦

= p ˆ 2 |p|

Berry curvature of ν :

Photonic chiral vortical effect

Avkhadiev-Sadofiev (2017); Yamamoto (2017); V. A. Zyuzin (2017);

Chernodub, Cortijo, Landsteiner (2018), …

Helicity and Berry curvature

• Spin-momentum locking ⇄ helicity λ

• chiral fermions (λ=±1/2)

• photons (λ=±1)

• gravitons (λ=±2)

• Berry curvature (adiabatic approximation): ⌦

= p ˆ

|p|

• Semi-classical equations of motion in a rotating frame:

• Photonic chiral current along a rotation:

˙x = ˆ p + p ˙ ⇥ ⌦

p = 2 ˙ |p| ˙x ⇥ ! + O(!

) Coriolis force

j

= 2!

Z d

p

(2⇡)

|p|( ˆ p · ⌦

)n

= ± T

6 ! equilibrium non-equilibrium

Yamamoto, arXiv:1702.08886

Photon gas under rotation

X-ray pulsars

Pulsars → Polarized photon flux:

R

L

T ⇠ 10 keV, ! ⇠ 10

Hz

cf) photon flux from sun: f ⇠ 10

/s · cm

f

⇠ 10

/s · cm

Conclusion

• Chiral effects of e & ν may help the supernova explosion

• Photonic chiral vortical effect in pulsars

• Quantum correction to gravit. lensing of gravit. waves

~ Berry curvature