Magnetic fields in the universe. Chiara Caprini, CEA Saclay

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1 Magnetic fields in the universe Chiara Caprini, CEA Saclay

2 The problem: cannot explain the origin of magnetic fields observed in astrophysical objects Outline Observations and amplification by structure formation Possible generation mechanisms Model and evolution Primordial magnetic fields Constraint and observational effects (CMB)

3 Observations: observational techniques Zeeman splitting: direct measure from hydrogen emission lines, only for the Milky Way ν = eb/(2πm e ) Synchrotron radiation: plane of the sky component, needs independent measure of the electron density I(ν) B (1+α)/2 ν (1 α)/2 n e (E) = n 0 E α Faraday rotation: widely used - line of sight component, independent measure of electron density, several λ φ zs λ 2 = B µg ( ) n e l(z) rad cm 3 d kpc m 2 (Grasso and Rubinstein 2001, Giovannini 2003)

4 Observations: galactic magnetic fields General characteristics: B 2 tot = B 2 u + B 2 r B u µg B r several µg l corr kpc Structure: Axisymmetric or bisymmetric? Equipartition holds? Follows optical spiral arms? Dynamically important and not yet understood M51 (Zweibel and Heiles 1997, Han )

Observations: cluster magnetic fields General characteristics: B µg l corr 1 100 kpc Examples: Synchrotron emission of cluster-wide diffuse sources: COMA Average value: B 0.

5 Observations: cluster magnetic fields General characteristics: B µg l corr kpc Examples: Synchrotron emission of cluster-wide diffuse sources: COMA Average value: B 0.1 1µG Faraday rotation of radio sources inside or behind the cluster + X-ray observation of the hot gas + simulations (Carilli and Taylor 2002) Abell 2382 (Guidetti et al 2007)

Observations: cluster magnetic fields B 3.3µG Kolmogorov spectrum Λ max 35kpc Hydra A: B 7µG Λ max 3kpc (Vogt and Ensslin 2005) M:!MM 0"I""$0+! ' J:76K25"""L M:!M* C@6D:;E2"F4G:7"H1:2;7<5"48" =>?

6 Observations: cluster magnetic fields B 3.3µG Kolmogorov spectrum Λ max 35kpc Hydra A: B 7µG Λ max 3kpc (Vogt and Ensslin 2005) M:!MM 0"I""$0+! ' J:76K25"""L M:!M* C@6D:;E2"F4G:7"H1:2;7<5"48" =>?7@"A"B-<9;: :2;7<5 M:!M'!"#"$%&'"(")&*"("*+"""", µ -""#"$*&."(")&*"(")&/+"012! M:!MN )&M M!M M) M)) 0""J012""L Very detailed MHD simulations (Dolag 2005, Dubois and Teyssier )

7 High redshift objects: (Athreya et al 98, Pentericci et al 02...) Faraday rotation in radio proto-galaxies and quasars at z>2 B µg l corr kpc Observations: summary Magnetic fields of order microgauss in all observed objects Correlated on scales of the order of the object size Probably grown in short times (or present previously) Ω B h 2 B2 8πρ c 0.06 Ω rad h 2 E gal B M EB ns M (R = 10 5 ly, h = 10 3 ly) (R = 10 6 cm, B = Gauss) ( ) 2 B 10 6 Gauss B 10 9 Gauss contributes 1% in the CMB (Durrer et al 99, Dolgov 03)

8 High electrical conductivity Observations: amplification Conservation of magnetic flux Amplification by structure collapse: B fin = B in ( Lin L fin ) 2 = B in ( ) 2/3 ρfin ρ in { Bgal in Bin clu Gauss 10 8 Gauss Amplification by galactic dynamo: INGREDIENTS: high conductivity, differential rotation, turbulence RESULTS: exponential growth up to equipartition, axisymmetric PROBLEMS: needs many rotations, reaches saturation? B gal in Gauss (t gal 10Gy) (Brandenburg and Subramanian 2005)

9 Possible generation mechanisms B 10 9 Gauss or Gauss at about 100 kpc Generation after recombination good: known physics bad: non-linear physics, correlation scale too small Generation prior to recombination CAUSAL: ACAUSAL: good: quite easy to get bad: correlation scale too small good: generated at any scale bad: not very predictive more than 100 primordial mechanisms but no preferred one (no amplitudes: depend on average method, evolution, parameters of the model...)

10 Generation after recombination BIERMANN BATTERY: B t = v B B 4πσ n e P e en 2 e galactic: shocks by SN explosions in proto-galaxies (problem: scale) both: radiation pressure at reionisation + density fluctuations EJECTION: galactic: from stars (problem: mean to zero) cluster: from galaxies and/or AGN (open questions: mix? amplitude?) CLUSTER: SMALL SCALE TURBULENT DYNAMO open questions: what generates it (mergers)? scale (reversal of the field, Faraday rotation)? (Hanaya et al 2005, Biermann and Galea 2003, Langer et al 2005, Colgate and Li 2000, Subramanian 2008, Schekochihin and Cowley )

11 Generation prior to recombination INFLATION: one needs to break conformal invariance of EM coupling of em field with the metric Turner and Widrow 1988 Bamba and Sasaki 2007 Campanelli et al 2008 coupling directly to the inflaton 1 4m 1 ( 2 (RF µνf µν + R µν F µα Fα ν + R µναβ F µν F αβ ) ) n R 4 m 2 F µνf µν, 1 ( ) α η F µνf µν 4 e αφ F µν F µν Ratra 1992, Bamba and Yokoyama introducing a charged scalar field (D µ φ) D µ φ m 2 φ φ 1 4 F µνf µν Turner and Widrow 1988, Calzetta et al 1998, Giovannini and Shaposhnikov 2000, Dimopoulos et al 2002, Prokopec et al 2004, Diaz-Gil et al inflation in string theory context Martin and Yokoyama 2007 f(φ)f µν F µν pre big bang, dynamical extra dimensions, non-linear em... Gasperini et al 1995, Kunze η 1

12 Generation prior to recombination PRIMORDIAL PHASE TRANSITIONS FIRST ORDER: charge separation at bubble walls + amplification by MHD turbulence (both EW and QCD) Hogan 1983, Quashnock et al 1989, Cheng and Olinto 1994, Baym et al 1996, Sigl et al 1996, Ahonen and Enqvist SECOND ORDER EW: generated by the symmetry breaking Vachaspati 1991, Davidson 1996, Grasso and Riotto 1997, Hindmarsh and Everett 1997, Tornkvist HELICITY GENERATION: H = 1 V EW baryogenesis: decay of EW strings V d 3 x A B h n b α Cornwall 1997, Vachaspati 2001, Copi et al coupling with a pseudoscalar φf µν F µν Field and Carroll 1998, Campanelli and Giannotti

13 Generation prior to recombination GENERATION BY VORTICITY t B + E = 0 B t E = 4πJ J = en(v p v e ) B = 4πen(Ω p Ω e ) electrons do Thomson scattering (Harrison 1973) vorticity by wiggly strings, superconducting strings or string loops Vachaspati and Vilenkin 1991, Davis and Dimopoulos 2005, Battefeld et al vorticity by second order perturbations Berezhiani and Dolgov 2003, Gopal and Sethi 2004, Matarrese et al 2004, Takahashi et al

14 Primordial magnetic fields: model break FRW symmetries π ij = (B 2 /3)h ij B i B j weak background field B 2 = O(0) ρ π ij, D i B j,... = O(1) Barrow, Maartens and Tsagas order 1/2 in perturbation B 2, π ij = O(1) Durrer et al homogeneous (Barrow et al ) or stochastic B i = 0 Power spectrum: B 2 0 B i (k)bj (q) = δ(k q)[ (δ ij ˆk iˆkj )S(k) + iɛ ijmˆkm A(k) ] Gaussian, homogeneous, isotropic and divergence free

15 Primordial magnetic fields: model energy density E B = 0 dk k 2 S(k) helicity density H = 0 dk ka(k) S(k) B + (k)b + ( k) + B (k)b ( k) A(k) B + (k)b + ( k) B (k)b ( k) parity even parity odd S(k) A(k) power spectra: Volume average: S(k) (λ n+3 B 2 λ)k n B λ (x) = 1 λ 3 B 2 λ = B 2 L d 3 y B(y)e (x y) 2 2λ 2 ( ) n+3 L λ A(k) (λ m+2 H λ )k m Hindmarsh and Everett 1997 line average: Bλ 2 = BL(L/λ) 2 surface average: Bλ 2 = BL(L/λ) 2 2

Primordial magnetic fields: model CONSTRAINT FOR A CAUSAL SPECTRUM: B i (x)b j (x + r) = 0 for r > L correlation function compact support L horizon power spectrum analytic B i (k)bj (q) = δ(k q)[ (δ

16 Primordial magnetic fields: model CONSTRAINT FOR A CAUSAL SPECTRUM: B i (x)b j (x + r) = 0 for r > L correlation function compact support L horizon power spectrum analytic B i (k)bj (q) = δ(k q)[ (δ ij ˆk iˆkj )S(k) + iɛ ijmˆkm A(k) ] k 0 : S(k) k 2, k 4... A(k) k, k 3... DIVERGENCE FREE IMPLIES NO WHITE NOISE λ Hogan 1973 B 2 λ = B 2 L ( ) n+3 L λ L no random walk leads to extra suppression at large scales

17 Primordial magnetic fields: evolution MHD: one relativistic fluid + em field (T µν f + T µν em) ;ν = 0 F µν ;ν = j µ F [µν;α] = 0 j µ + u ν j ν u µ = σf µν j ν conformal invariance in FRW flat spacetime induction equation: B t = (v B) + B 4πσ dφ dt = 1 4πσ S B ds dh dt = 1 4πσ V d 3 x B ( B) IDEAL MDH limit σ : flux and helicity are conserved B 2 a 4

18 Primordial magnetic fields: evolution 100 GeV 1 MeV 0.32 ev TURBULENT PHASE ν l νe Re = vl ν 1 VISCOUS PHASE σ T ν l γe σ T 3/2 Re 1 ReM Re 103 ( 100GeV T ) 4 ReM Re 1010 ( m e T ) 3/2 Turbulent cascade Alfvén waves in viscous fluid: damping of magnetic energy L > V A L Silk 20 ΩB Ω rad Mpc Jedamzik et al 1996, Ahonen and Enqvist 1996 Jedamzik et al 1996, Subramanian and Barrow 1997, Banerjee and Jedamzik 2004

19 Primordial magnetic fields: evolution TURBULENT PHASE non-helical field: DIRECT CASCADE E B (t) t 2(n+3)/(n+5) L B (t) t 2/(n+5) helical field: INVERSE CASCADE Magnetic energy is transferred to larger scales E B (t) t 2/3 L B (t) t 2/3 Christensson et al 2002, Banerjee and Jedamzik 2004, Campanelli

20 Primordial magnetic fields: constraint CONSTRAINT FROM GRAVITATIONAL WAVES AND NUCLEOSYNTHESIS GW spectrum always blue: bound on the integrated spectrum stronger than large scales (CMB) GW production takes place before dissipation: magnetic energy stored in GW GW production very efficient CAUSAL GENERATION AT 100 GeV: n = 2 B 0.1Mpc Gauss INFLATIONARY GENERATION AT 10^15 GeV: n = 0 n 3 B 0.1Mpc Gauss B 0.1Mpc 10 9 Gauss CC and Durrer 2001

21 Primordial magnetic fields: constraint δg µν = 8πGT B µν H 2 h GT B ḣ GT B /H ρ GW ḣ2 8πG Ω GW Ω2 B Ω rad S(k) (λ n+3 B 2 λ)k n Ω B (t) B2 λ ρ c (λk (t)) n+3 GW generated since the beginning: Ω GW Ω2 B (k ) Ω rad B 2 λ < ρ c (λk ) n+3 Ω rad NON HELICAL FIELD

22 Primordial magnetic fields: CMB effects l 2 C l ( ΩB Ω rad ) ( ) 4 B 10 9 Gauss MF energy momentum tensor: scalar, vector, tensor modes δg µν = 8πG(T µν + T B µν) (T µν + T Bµν ) ;ν = 0 MF + baryons: MHD waves (magnetosonic, Alfvén) (n 3) Vector mode (Alfvén waves) survives at scales: L V A L Silk V A ΩB Ω rad Subramanian and Barrow 2002 Temperature and B polarisation at high multipoles

23 Primordial magnetic fields: CMB effects Yamakazi et al 2008, Finelli et al 2008, Giovannini and Kunze 2007, Kahniashvili and Ratra 2006, Lewis 2004, Mack et al 2002, Koh and Lee

24 Primordial magnetic fields: CMB effects Parity odd cross-correlations from helical field l 2 C T B l l 2 C EB l at l = 50 Faraday rotation of CMB polarisation average rotation angle: Φ 2 ( B 10 9 Gauss ) ( 30GHz Pogosian et al 2001, CC et al ν ) 2 rotation of E in B: l 2 C B l at l = 10 4, ν = 30GHz Kosowsky and Loeb 1996, Campanelli et al 2004, Kosowsky et al Homogeneous field breaks isotropy a l+1,m a l 1,m Durrer et al 1998, Naselsky et al 2004 Stronger B polarisation from Faraday rotation, TB cross-correlation Scoccola et al 2004, Kristiansen and Ferreira

25 Conclusions The origin of MF observed in astrophysical objects is still unclear Observations: SKA radiotelescope: all-sky rotation measure survey evolution of magnetised structure from z>3 detect MF in the IGM? PLANCK: detect B polarisation and large multipoles parity-odd cross-correlations? non-gaussianity? LISA: GW signal from EW primordial fields Theory: deeper understanding of small scale dynamo processes are helical fields the solution? (not mentioned structure formation, cosmic rays...)

26 The alpha-omega mean field dynamo induction equation B t = (V B) B mean and random components = B + b V = V + v substituting and further averaging B t = ( V B ) + v b quasi-linear approximation + homogeneity and isotropy v b = α B β B β = τ α = τ v v 3 v2 3 field with poloidal and toroidal components α = α 0 z h B φ t B r t B e γt γ = α0 Ω = Ω B r = α B φ z h 2Gy 1 omega: poloidal into toroidal alpha: toroidal into poloidal B gal in Gauss (Brandenburg and Subramanian 2005)

Effects of primordial kinetic and magnetic helicity

Effects of primordial kinetic and magnetic helicity Tina Kahniashvili 1. T. Kahniashvili and B.Ratra, 2005, PRD, 71, 103006 2. T. Kahniashvili, G. Gogoberidze, and B. Ratra, astro-ph/0505628, Phys. Rev.