Constraining primordial magnetic fields with observations Kerstin Kunze (University of Salamanca and IUFFyM) KK PRD 83 (2011) 023006; PRD 85 (2012) 083004; PRD 87 (2013) 103005; PRD 89 (2014) 103016, arxiv:1703.03650 (PRD (2017) accepted for publication) KK, E. Komatsu, JCAP 1506 (2015) 06, 027 KK, E. Komatsu, JCAP 1401 (2014) 01, 009
Overview Observations of large scale magnetic fields Effects of primordial magnetic fields on the CMB and LSS
Observations: Methods Galactic and extra galactic magnetic fields Synchrotron radiation Diffuse Synchrotron radio emission NASA equipartition of energy between relativistic particles and magnetic fields allows estimate of magnetic field strength cosmic rays σ N 0 ν (γ 1)/2 B (γ+1)/2 γ 2.75 for galactic radio emission ρ CR B2 8π ρu2 2 kinetic energy Estimate of magnetic field component perpendicular to line of sight σ ν B N 0 emissivity frequency magnetic field perpendicular to line of sight n u m b e r o f re l a t i v i s t i c electrons per unit energy Faraday rotation Estimate of magnetic field component parallel to line of sight Faraday rotation measure RM = 812 L 0 n e B dl radians m 2 χ =RMλ 2 n e thermal electron density B magnetic field in μg wavelength Kronberg AIP 2002
M51 Observations Total synchrotron intensity around the galaxy cluster Abell 2255 (Neininger 1992) Total magnetic field strength B t =(13.7 ± 2)µG Galactic magnetic field Polarised emission from Milky Way dust ESA and the Planck Collaboration (2015) Magnetic field strength: near sun: 2 μg halo (north/south): 4 (2) μg Kronberg, Newton-McGee (2011) All-sky map of rotation measures in the Milky Way, using data of 2257 sources. (Govoni et al. 2006) Magnetic field strength at center ~2.5 μg.
Observations: Methods Void magnetic fields / cosmological magnetic fields scattering of starlight with dust Extended emission due to deviation of electrons/ positrons in a magnetic field Interaction with EBL (Extragalactic background light) Energy of primary γ-ray: E γ m2 e ϵ Energy of EBL soft photon 250 ( ϵ ) 1 GeV 1 ev Interaction with CMB: inverse Compton scattering E IC = 4ϵ CMBE 2 e 3m 2 e Energy of CMB photon 3 ( ) 2 Ee GeV 1 TeV direct starlight emission EBL direct measurement σ NCMB 0 ν (γ 1)/2 B (γ+1)/2 Blazar Artist s impression. Image Credit: NASA/JPL B B limit Color code: Fraction of total energy emitted in this region Durrer, Neronov (2013)
Observations Spectral energy distribution of 1ES 0229+200 Fermi/lat HESS B(G) HESS Veritas Tavecchio et al. (2010) B 5 10 15 G Assuming mean blazar TeV flux constant on large time scales Dermer et al. (2011) B 10 18 G Assuming mean blazar TeV flux constant over 3-4 years of observations
Cosmological magnetic fields and the CMB Assumptions Origin of magnetic fields in the very early universe Stochastic magnetic field Bi ( k)b j ( q) = k,q P S (k) Most general form: helical magnetic field ij k i k j k 2 + kk 0P A (k)i ijmˆkm where P M (k, k m,k L )=A M k M = S, A k L nm W (k, k m ) pivot scale Example of helical magnetic field structure: Filament eruption in solar corona modelled by twisted flux rope window function W (k, k m )= 3 2 k 3 m e (k/k m) 2 damping scale upper cut-off Torok & Kliem (2005)
Cosmological magnetic fields and the CMB effects of magnetic field survival magnetic field effects of magnetic field decay contribution to perturbations of energy density, anisotropic stress and to baryon velocity via Lorentz force plasma interactions induce partly decay/damping energy injection CMB temperature anisotropies and polarisation CMB spectral distortions
Primary CMB anisotropies and polarisation induced by contribution of helical magnetic field ANGULAR POWER SPECTRA FOR SCALAR,VECTOR AND TENSOR MODES distinctive signature of helical magnetic field 2 TE 2 TT T 0 l(l+1)cl /(2π)[µK 2 T 0 l(l+1)cl /(2π)[µK 2 ] ] 10 4 10 2 10 0 10-2 10-4 10-6 10 2 10 0 10-2 10-4 10-6 B=5 ng, n S =-2.9, β=0 Scalar n A =-2.9 Scalar n A =-1.9 Vector n A =-2.9 TT Vector n A =-1.9 Tensor n A =-1.9 Tensor n A =-1.9 10 100 1000 l B=5 ng, n S =-2.9, β=0 Scalar n A =-2.9 Scalar n A =-1.9 Vector n A =-2.9 TE Vector n A =-1.9 Tensor n A =-2.9 Tensor n A =-1.9 T 0 2 l(l+1)cl EE /(2π)[µK 2 ] T 0 2 l(l+1)cl BB /(2π)[µK 2 ] 10 1 10 0 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10 0 10-2 10-4 10-6 B=5 ng, n S =-2.9, β=0 Scalar n A =-2.9 Scalar n A =-1.9 Vector n A =-2.9 Vector n A =-1.9 Tensor n A =-2.9 Tensor n A =-1.9 EE 10 100 1000 l B=5 ng, n S =-2.9, β=0 Vector n A =-2.9 Vector n A =-1.9 Tensor n A =-2.9 Tensor n A =-1.9 BB T 0 2 l(l+1)cl EB /(2π)[µK 2 ] T 0 2 l(l+1)cl TB /(2π)[µK 2 ] 10 0 10-2 10-4 10-6 10-8 10-10 10-12 10-14 10-16 10 0 10-5 10-10 B=5 ng, n S =-2.9, β=0 Vector n A =-2.9 Vector n A =-1.9 Tensor n A =-2.9 EB Tensor n A =-1.9 10 100 1000 B=5 ng, n S l =-2.9, β=0 Vector n A =-2.9 Vector n A =-1.9 Tensor n A =-2.9 TB Tensor n A =-1.9 10-8 10-10 10 100 1000 l MODIFIED VERSION OF CMBEASY 10-8 10 100 1000 l 10-15 10 100 1000 l KK 12
Bulk motions of electrons along the line of sight induce secondary temperature fluctuations in the postdecoupling, reionized universe. Fluctuations in baryon energy density along line-of-sight change number density of potential scatterers for CMB photons, thus change scattering probability and visibility function. Secondary CMB anisotropies In the presence of a magnetic field not only the scalar mode but also the vector mode source bulk motions.
Secondary CMB anisotropies Induced temperature anisotropies Future observations with ALMA might reach Credit: ALMA (ESO/NAOJ/NRAO) KK 14 Atacama Large Millimeter/submillimeter Array (ALMA): ALMA - the largest astronomical project in existence- is a single telescope of revolutionary design, composed of 66 high precision antennas located on the Chajnantor plateau, 5000 meters altitude in northern Chile.
Cosmological magnetic fields and the CMB Damping of magnetic fields There is also damping around neutrino decoupling at around z~ 10 10 when a black body spectrum is always restored. (no spectral distortions) Before decoupling of photons viscous damping energy injection After decoupling of photons decaying MHD turbulence ambipolar diffusion change in thermal and ionisation history
Damping in the pre-decoupling era Subramanian, Barrow 1998 (nonlinear treatment) In a magnetized plasma: 3 additional modes Jedamzik, Katalinic, Olinto 1998 Fast magnetosonic modes: damp similarly to sonic waves (Silk damping) damping wave number k d = k γ Slow magnetosonic and Alfvén modes: overdamped limit damping wave number k d = k γ v A cos θ inverse of usual photon diffusion scale Alfvén velocity v A B 0 / ρ + p ( ) v A =3.8 10 4 B0 1nG a n g l e b e t w e e n background field direction and wave vector
Damping in the post-decoupling era Ambipolar diffusion After decoupling radiative viscosity dramatically drops. However magnetic fields can still be damped. Decaying MHD turbulence After decoupling turbulence no longer suppressed, nonlinear interactions transfer energy to smaller scales, dissipating magnetic field on large scale, inducing MHD turbulence to decay. non helical (open debate on inverse cascade for non helical fields: Kahniashvili et al. 13, 14, 15)
radiative viscosity decaying MHD turbulence ambipolar diffusion z>z dec z dec >z>100 z<100 Evolution of electron temperature T e = 2ȧ a T e + x e 1+x e 8ρ γ σ T 3m e c (T γ T e )+ x eγ 1.5k B n e KK, Komatsu 15
Effect of post-decoupling magnetic field damping on CMB anisotropies tot = reio + high z determined by (B 0,n B ) C EE ` at low l not affected magnetic field dissipation contributes C TT `! C TT ` e 2 tot KK, Komatsu 15
TT EE magnetic field parameters TE B =3nG n B = 1.5, 2.5, 2.9 Planck13+WP KK, Komatsu 15
The 95% CL upper bounds are B0 < 0.63, 0.39, and 0.18 ng for nb = 2.9, 2.5, and 1.5, respectively. y distortion y < 10 9, 4 10 9, and 10 9 for nb = 2.9, 2.5, and 1.5, respectively modified version of CLASS + montepython KK, Komatsu 15
Effect of pre-decoupling magnetic field damping on CMB anisotropies 6000 B=0.05 ng, n B =-2.9 60 B=0.05 ng, n B =-2.9 5000 B=0.01 ng, n B =-2.5 B=0.005 ng, n B =-1.5 50 B=0.01 ng, n B =-2.5 B=0.005 ng, n B =-1.5 T 0 2 l(l+1)cl TT /(2π)[µK 2 ] 4000 3000 2000 1000 B=0 WMAP 9 T 0 2 l(l+1)cl EE /(2π)[µK 2 ] 40 30 20 B=0 0 10-1000 10 100 1000 0 200 400 600 800 1000 1200 1400 l l magnetic field parameters 200 B=0.05 ng, n B =-2.9 B =0.05 ng,n B = 2.9 B =0.01 ng,n B = 2.5 B =0.005 ng,n B = 1.5 T 0 2 l(l+1)cl TE /(2π)[µK 2 ] 150 100 50 0-50 B=0.01 ng, n B =-2.5 B=0.005 ng, n B =-1.5 B=0-100 -150-200 200 400 600 800 1000 1200 1400 l KK 17
10 0 10-2 10-4 B=5 ng, n S =-2.9, β=0 Vector n A =-2.9 Vector n A EB =-1.9 Tensor n A =-2.9 Tensor n A =-1.9 Summary T 0 2 l(l+1)cl EB /(2π)[µK 2 ] 10-6 10-8 10-10 10-12 10-14 10-16 CMB anisotropies Direct contribution of magnetic field 10 100 1000 l Linear matter power spectrum KK 11? primordial magnetic fields
Summary CMB anisotropies Indirect contribution: energy injection from decay of magnetic field? primordial magnetic fields CMB spectral distortions