Origin of Cosmological magnetic ﬁelds: Primordial AND...

Origin of Cosmological magnetic fields: PrimordialAND dynamos?

Kandaswamy Subramanian

Inter-University Centre for Astronomy and Astrophysics,

Pune 411 007, India.

Nordita conference, Stockholm, June 23, 2015 – p.0/24

Summary

The universe is magnetized.

Planets, Stars, nearby and high Z Galaxies, Inter cluster

medium, Inter galactic medium in voids!

Early Universe Generation: Inflation?

Astrophysical dynamos: Coherence of fields?

A. Brandenburg & K. Subramanian, Physics Reports, 417, 1-205 (2005)

A. Brandenburg, D. Sokoloff & K. Subramanian, Space Science Reviews, 169, 123

(2012)

K. Subramanian, ”Magnetizing the Universe”, PoS proceedings, arXiv:0802.2804

K. Subramanian, Magneic fields in the early universe, Astron. Nacht., 331, 110

(2010)

K. Subramanian, The origin, evolution and signatures of primordial magnetic

fields, Rep. Prog. Phys., Submitted, arXiv: 1504:20311


Origin: Primordial? + Dynamos?

Primordial magnetic fields: Origin in an early universe phase

transition: Inflation, Electroweak, QCD.

Provide Seed for dynamo? Help induce coherence?

Inflation: Strength? EW/QCD transitions: Scale?

Detecting relic B fields can probe early universe physics?

Flux freezing: On large scales B(t)a2(t) = constant, So

B(z) = B0(1 + z)2. (ρB = ργ implies B ∼ 3µG).

B0 ∼ 10−9G on galactic scales, interesting for Galaxy

formation + galaxy/cluster B?

Fields decay unless maintained by Dynamos (Unless helical):Seed field + amplification by motions (turbulence/shear).

Can fluctuation dynamo generate coherent enough fields?

Can mean field dynamos generate coherent fields in presence of

rapidly growing fluctuations?Nordita conference, Stockholm, June 23, 2015 – p.2/24

Primordial fields origin during Inflation?

(Turner and Widrow, 1988; Ratra 1992; Gasperini et al. 1995)

Rapid expansion → vacuum fluctuations amplified andstretched to long wavelength ”classical” fluctuations

Negligible charge density breaks flux freezing.

BUT Need to break conformal invariance of ED (Couple to inflaton

φ, higer dimensional scale factor b(t), curvature R, axion θ ...)

S =

∫ √−g d4x b(t)[−f2(φ)

1

16πFµνF

µν −RA2 + gθFµν Fµν ]

EM wave amplified from vacuum fluctuations

After reheating E shorted out and B frozen in.

Exponentially sensitive to parameters, as need B ∼ 1/aǫ

Need huge growth of ’charge’: a Problem? (Demozzi et al, 2009)


Extra dimensional magnetogenesis

EM theory with Gauss-Bonnet gravity(Atmjeet, Pahwa, Seshadri, Subramanian, PRD, 2014; KA,TRS,KS 2015) :

S = − 116π

∫ √−g d4+Dx[

LEM + LMatt

]

=

− 116π

∫ √−g d4x (ΩDbD0 )(

b(t)b0

)D[LEM + LMatt]

define g = (bD0 ΩD)g, take LEM = [FµνFµν − FµνF

∗µν ].

Fix gauge: A0(t,x) = 0 and ∂jAj(t,x) = 0

To quantize, expand in terms of creation/anhilation operatorsAl(x, t) =√4π

∫

d3k(2π)3

∑2h,λ=1 ǫ

k

hl

[

cλ(k)Ah(k, η)eik·x + c†λ(k)A

∗h(k, η)e

−ik·x]

Using helicity basis: ǫkh = 1√2

(

ǫk1 + hiǫk2

)

Large class of solutions with a(t) ∝ eαt, b(t) ∝ eβt

Define A(η, k) ≡ a(η)(b(η))D/2A(η, k) (dη = dt/a(t))


Extra dimensional magnetogenesis

A′′(k, η) +[

k2 − ξ(ξ−1)η2 − 2ξhk

η

]

A(k, η) = 0; ξ = D2

(

−βα

)

For D = 4, α = β, γ = ξ = −2 → Scale invaraint spectrum.

If h = 0 and no parity breaking term:

(dρB/d ln k) =(

C(γ)/2π2)

H4(−kη)4+2γ ≈ (9/4π2)H4 (for γ = −2)

If parity breaking term is included much larger B0

(dρB/d ln k) =≈ 2.6× 102H4

B0 ∼ 0.7×10−10G(

H10−5Mpl

)

; B0 ∼ 2×10−9G(

H10−5Mpl

)

(helical)

Need mechanism for freezing b(t) evolution

Absorbing b0 which is outside all action into redefining the

metric could solve the strong coupling problem?


Helical Mode evolution

-10 - 8 - 6 - 4 - 2 00

2 ´ 106

4 ´ 106

6 ´ 106

8 ´ 106

kΗ

Ah

a2

k = 10−2, D = 4, βD/2α = 2. Positive helicity (red) Negative (blue).


Primordial fields versus Dynamos?

From one of Tanmay’s talk...200???

Dynamos required to maintain even primordial seed fields?Nordita conference, Stockholm, June 23, 2015 – p.7/24

Fluctation/Small scale turbulent dynamo

Turbulence common: Stars, galaxies, galaxy clusters: leads to

Random Stretching + ”Flux freezing” ⇒ Growth of B(BA = constant and ρAL = constant → B/ρ ∝ L, and A ∝ 1/(ρL))

Cancellation (Eyink, 2011) and Resistance limits growth.

Random B grows if RM = vL/η > Rcrit ∼ 30− 100 (Kazantsev 1967)

Single scale random flow: Growth rate ∼ v/L (107 yr: Galaxies;

108 yr clusters), field concentrated in scales ∼ lη ∼ L/R1/2m

Magnetic ’Kazantsev’ spectrum M(k) ∝ k3/2 till k < kη ∼ 1/lη;

Persists for finite τ ! (Pallavi Bhat, KS, 2014/15)

How does it saturate? Important for young galaxy/cluster/IGM

Faraday RM and mean field dynamos?


The fluctuation dynamo Simulations

Simulations by Haugen, Brandenburg, Dobler, 2004; Pallavi Bhat, 2012, Pm = ν/η = 1

1 10 100k

10-12

10-10

10-8

10-6

10-4

10-2

k-5/3

k3/2

M(k)

K(k)


Faraday RM from Fluctuation dynamo

(Pallavi Bhat, KS, MNRAS, 429, 6429, 2013)

RMS Faraday RM σRM by shooting lines of sight through the

simulation box. Normalize by σ0 = Kne(Brms/√3)√Ll

σRM ≈ 0.4− 0.5 σ0 for various Rm and Pm explored.Rare structures contribute < 20% to σRM

50 100 150 200 250 300

Eddy turn over time

0.0

0.2

0.4

0.6

Rota

tion M

easure

: − σ R

M

nocutoff

2Brmscutoff

1Brmscutoff

5123, Pm=1


Turbulent Mean-Field Dynamo: Galactic

U = U+ u, B = B+ b: Mean + Stochastic fields

Mean field satisfies DYNAMO equation

∂B

∂t= ∇×

(

U×B+ E − η(∇×B))

;

Finding E = u× b is a closure problem: E = αB− ηturb(∇×B)

α = −(τ/3)〈u · ω〉+ (τ/3ρ)(4π/c)〈j · b〉; ηturb = (τ/3)〈u2〉(Pouquet et al. 1976)

Galactic Shear generates Bφ from Br

Supernovae drive HELICAL turbulence (Due to Rotation +

Stratification)

Helical motions generate Br from Bφ

Exponential growth of B, tgrowth ∼ 108 − 109 yr

Can also ’explain’ magnetic spiral correlated with optical (Luke

Chamandy, KS/AS, 2013,14 ...Nordita conference, Stockholm, June 23, 2015 – p.11/24

Galactic Shear and α effect

Kinematic Limit?

Helicity (links) conservation? Mean field versus fluctuations?


Helicity and dynamo quenching

Anvar and Natasha Shukurov 2009

Helical motions transfer helicity between WRITHE AND TWIST Helicities

Lorentz force of small-scale twist Helicity grows to kill the dynamo

Unless one has helicity fluxes.


Helical B resilient to turbulent diffusion

Even sub equipartition Helical fields decay on slow resistive rate(EB,KS, 2013; Pallavi Bhat, EB, KS, MNRAS, 2014)

k

Power spectra with turbulent forcing at kf=5

10-5

10-4

10-3

10-2

M(k

)

1 10 100

10-3

10-2

10-1

1.0

kH

(k)/

(2*M

(k))


Can MFD work in presence of FD?

Subramanian and Brandenburg, MNRAS, 2014, 445, 2930

Helically forced turbulence with kf = 4

Consider various helicity, Pm and Rm.

Expect α2 LS dynamo + Fluctuation dynamo

Check k dependent growth rate for magnetic energy and

normalized magnetic helicity spectra.

EM (k, t) = EM0(k)eλ(k)t, HM (k, t) = HM0(k)e

λ(k)t

Spectrum of positively and negatively polarized contributions

E±M0 =

1

2

[

EM0(k)±1

2kHM0(k)

]

.

Mean/large scale field will show up as excess of E−M0

Is there an evidence for a mean field in Kinematic stage?


Pm = 0.1, Rm = 160, fully helical


Pm = 0.1, Rm = 330, fully helical


Mean B/fluctuations decreases with Rm

Magnetic energy spectrum peaks at small resistive scale even

when turbulence helical. Understood Via Kazantsev model.

Brms/Brms decreases strongly with Rm at kinematic stage


Does Saturation Save LSD?

Pallavi Bhat, Axel Brandenburg, Kandaswamy Subramanian (2015?)

Power shifts to larger scales on saturation:-)

1 10 100k

10-10

10-8

10-6

10-4

10-2

EM(k)

EK(k)


Unified Large/Small scale dynamo?



Evolution of M(k) for different k, 10243, RM=330, PM=0.1

200 400 600 800 1000t

10-12

10-10

10-8

10-6

10-4

10-2

M(k

) fo

r dif

fere

nt

k

k=1

k=4

k=50

k=200

k=500


Does Saturation Save LSD?



EM±, 10243, PM=0.1

1 10 100k

10-12

10-10

10-8

10-6

10-4

10-2

EM

±

1 10 100

k

−0.01

0.00

0.01

0.02

0.03

0.04

λ


Unified dynamo Saturation


Large-scale field significant on Saturation:-)


Final Thoughts?

Universe is Magnetized!

Origin during inflation in early universe?

Helical magnetic fields particularly interesting.

Strong coupling problem? Extra dimensional magnetogenesis

potential solution?

Dynamos needed to maintain even primordial fields

Need to understand their saturation better.


THANK YOU!


Origin of Cosmological magnetic ﬁelds: Primordial AND...

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