Production of helical magneticnorosx52.nordita.org/~brandenb/programs/CMF/talks/Ferrer.pdf · 2015-06-25 · Magnetic ﬁelds are ubiquitous in the Universe Starting in 1949 ... I

Production of helical magneticfields during baryogenesisFrancesc FerrerWashington University in Saint LouisB [email protected]

NORDITA. June 23, 2015

Outline

Introduction: Observations of Magnetic Fields

B-field production during baryogenesisOne bubbleMany bubbles

Conclusions



Conclusions

Magnetic fields are ubiquitous in the Universe

Starting in 1949 . . .I Large scale magnetic fields have been detected in galaxies

and clusters (µG). Lyman-α systems at z ∼ 2.5 showevidence of B-fields in Faraday rotation measurements.

I B-fields appear to have similar magnitudes for the sametype of objects regardless of location in the universe.Common primordial seeds?

I Important to understand formation and evolution ofstructure.

I Could provide a window to processes in the EarlyUniverse.

How were these fields generated?

Small field seeds get amplified via dynamo mechanisms.I Seeds of astrophysical or cosmological origin?

Hoyle 1958

I Can we fit the observed intensity and coherence length?I How large should the initial seeds be for the B-fields to

have enough time to grow?Is there any observational support for this idea?



Hoyle 1958





Hoyle 1958



B-fields as a window to the Early Universe

Once generated, B-fields survive in the cosmologicalconducting plasma. There are plenty of opportunities in theearly stages of the evolution of the Universe!

I Breaking of conformal invariance during inflation.I During the QCD phase-transition.I At the time of matter-genesis.

B-fields as a window to the Early Universe

Once generated, B-fields survive in the cosmologicalconducting plasma. There are plenty of opportunities in theearly stages of the evolution of the Universe!

I Breaking of conformal invariance during inflation.I During the QCD phase-transition.I At the time of matter-genesis.



Conclusions

The electroweak phase transition

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Vachaspati & Ng 10

movies/animate.avi

B-fields and the electroweak phase-transition

Once electroweak fields become massive, they leave behindthe only massless field in the spectrum, the photon.At the time of the electroweak phase-transition, sphaleronprocesses occur that violate baryon number, CP violation isalso present.A sphaleron can be seen as two linked Z-strings. The leftovermagnetic field lines will be linked.

⇒ Magnetic Helicity

Why is helicity important?

h =1V

∫V

d3x A · B

I Discriminate astrophysical vs. cosmological seeds.I Provides a window to processes in the early universe.

I Leptogenesis vs ew baryogenesisLong, Sabancilar, Vachaspati, 2013

I Relate ρB to ρb.I For turbulent non-diffusive evolution, MHD studies show

that inverse cascade increases coherence length by η2/3.

Why is helicity important?

h =1V

∫V

d3x A · B

I Discriminate astrophysical vs. cosmological seeds.I Provides a window to processes in the early universe.

I Leptogenesis vs ew baryogenesisLong, Sabancilar, Vachaspati, 2013

I Relate ρB to ρb.I For turbulent non-diffusive evolution, MHD studies show

that inverse cascade increases coherence length by η2/3.

Evolution

Kahniashvili, Tevzadze, Brandenburg & Neronov 12; Saveliev, Jedamzik & Sigl 13

Evolution

Durrer & Neronov 13

Although the ew horizon is only ∼ 0.1pc, MHD evolution resultsin significant power at & 10 kpc scales.

Evolution

Durrer & Neronov 13

Although the ew horizon is only ∼ 0.1pc, MHD evolution resultsin significant power at & 10 kpc scales.



Conclusions

Helicity from sphaleron decay

Klinkhamer & Manton 82; Kuzmin, Rubakov & Shaposnikov 85


Vachaspati & Field 94


I A = sin θW W 3 + cos θW YI ∆NCS ∝ ∆nB

Sphaleron decays ⇔ Phase transition

h ∼ −nB

α

B 10−13r G ∼ 10−9 G




h ∼ −nB

α

B 10−13r G ∼ 10−9 G




h ∼ −nB

α

B 10−13r G ∼ 10−9 G




h ∼ −nB

α

B 10−13r G ∼ 10−9 G




h ∼ −nB

α

B 10−13r G ∼ 10−9 G

Simulations

Solve classical evolution equations on the lattice.

s s s ss s s ss s s ss s s s

-6

�

?

p- i6

j

Ambjorn, Askgaard, Porter & Shaposnikov 90; Rajantie, Saffin & Copeland 01

Simulations

C. Copi, FF, T. Vachaspati, A. Achucarro 08

movies/scalar_field.mp4



movies/sphaleron_64_0.2_double_v4_helicity2.avi


Yiyang Zahng, FF, Vachaspati

movieses/sphaleron_energy.mp4



movies/test_sphaleron1_04_helicity.swf



Helicity is conserved even though there is no plasma.



Helicity is conserved even though there is no plasma.


Manton 85


0 1 2 3 4

time

-0.1

-0.05

0he

licity

Yi-Zen Chu, J. Dent, T. Vachaspati 11



Conclusions

The electroweak phase transition

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Number of sphalerons

0 5 10 15 20 25

t

0

2000

4000

6000

8000

Nu

mb

er o

f sp

hal

ero

n e

xp

losi

on

s

MH(r)

0 50 100

r

0

0.0005

0.001

0.0015

0.002

M_H(r)



Conclusions

Conclusions

I Non-perturbative processes at the time of baryogenesiscan give rise to cosmologicaly relevant magnetic fields.

I The fields have left-handed helicity, and are coherent overtens of kpc.

I The study of astrophysical magnetic fields provides awindow to processes in the Early Universe.

I The detection of magnetic helicity can be linked to theepoch of matter-genesis.

Documents

Production of helical magneticnorosx52.nordita.org/~brandenb/programs/CMF/talks/Ferrer.pdf · 2015-06-25 · Magnetic ﬁelds are ubiquitous in the Universe Starting in 1949 ... I