and The Cosmic Microwave Background

(Yamasaki etal, ApJL 625:L1=astro-ph/0410142 & astro-ph/0509xxx)

National Astronomical National Astronomical Observatory of JapanObservatory of Japan

The Primordial Magnetic Field

The University of Tokyo The University of Tokyo &&

D. G. Yamazaki D. G. Yamazaki ,,

K . Ichiki , T. Kajino, K . Ichiki , T. Kajino, && G. Mathews G. Mathews

COSMO 05COSMO 05

CMB SessionCMB Session

cmbast : U. Seljak, et al., 1997, CBI: B. S. Mason et al., 2003, WMAP: Bennett, et al., 2003, ACBAR: Kuo et al., 2004.

Background and MotivationBackground and Motivation

For higher l, the temperature anisotropy of CMB is not enough

There is the gap between observations and theoretical calculations for higher l

WMAP best fit cmbfast

We need some new physical process for higher l.Several semi-analytic studies point out that the effect of the primordial magnetic field (PMF) is very important in CMB for higher l. (Jedamzik et al. 2000: Durrer et al. 2000, Mack et al. 2002 Subramanian and Barrow, 1998, 2002)

The PMF is one of the new physical process for higher l

For higher l, our understanding of the temperature anisotropy of CMB is not enough.

Introduction 1Introduction 1

Those semi-analytic studies develop the CMB analysis. Their approximations are appropriate for lower l, however , their accuracy is not enough to compare theoretical CMB for higher l with observations.

We want to estimate the effect of the PMF on CMB accurately, So we construct new computation program which can calculate scalar and vector mode effects of magnetic fields on CMB.

We can solve these problems simultaneously by studying the effect of the PMF on the CMB.

A cluster of galaxies have magnetic field of 0.1-1 (T. E.

Clarke et. al. 2000). But the origin and evolution of magnetic field in the cluster of galaxies are not clearly understood. The study of the PMF at the last scattering surface of photons will provide important information to solve this problem.

Another interesting subject

The attractive point of our study

Introduction 2Introduction 2

1. We construct a new computation program which can calculate scalar and vector-mode effects of the PMF on CMB. 2. We estimate the PMF at 1Mpc by likelihood analysis with the Markov Chain Monte Carlo (MCMC) method, in order to solve the discrepancy between the theoretical primary CMB and observational data (WMAP: Verde et al. 2003, ACBAR: Kuo, C.L., et al., 2004, and CBI: Mason, B. S., et al., 2003) for higher l. 3. We then discuss the evolution of the PMF.

Purpose Purpose

Effect of PMFEffect of PMF

The Lorentz force changes only vectors of baryons

The magnetic field increases the fluid pressure

MF

baryonsLorentz force

Thomson scattering

Photon

Lines of magnetic force

MF

Repulsion between lines of magnetic force

Lines of magnetic force

magnetic pressure

Vector of photons is changed by Thomson scattering. (photons and baryons are tight-coupled before the last scattering surface ).

Eall = EPMF + Efluid All energy is the sum of the PMF and the fluid

Primordial Magnetic FieldPrimordial Magnetic Field

nnBB: power spectral index of the magnetic fieldBB: magnetic comoving mean-field amplitude (at 1Mpc)

We discard MHD back reaction onto the field itself within the linear approximation ( Durrer et al., 2000).

We consider the primordial stochastic magnetic field. The conductivity of the primordial plasma is very large, and it is “frozen-in” (Mack et al. 2002). So, Electric field is neglected

A time evolution of a magnetic field decouple from its spatial structure on sufficiently large scales: B(τ, x)=B (x)/a2, the power law:

,E 0

BnB kkP

Our cosmological magnetic field model on the early universe is a statistically homogeneous and isotropic random

Our purpose is to constraint these two parameters.Our purpose is to constraint these two parameters.

1. Combining Einstein equations with the fluid equations (Ma and Bertschinger 1995, Hu and White 1997), we obtain evolution equations of scalar and vector perturbations.

2. We evaluated the likelihood functions of WMAP, ACBAR, and CBI data sets in a wide range of the magnetic field strength B and power spectral index of the primordial magnetic field nB, with other cosmological parameters, h,bh2, ch2, ns,As, and in flat Universe models. To explore the parameter space, we make use of the Markov chain technique (Lewis 2002).

3. We also take account of the SZ effect in our analysis. For that, we follow an estimate of Komatsu and Seljak, with 8 = 0.9 (Spergel et at. 2003; Komatsu and Seljak 2002).

Estimation of Primordial magnetic field strengthEstimation of Primordial magnetic field strength

B=8nGB=6nG

500 1000 1500 25002000l

l(l+

1)C

l [

]

Result and Discussion IResult and Discussion I 　　 Numerical estimationsNumerical estimations

　 For higher l, the effect of a primordial magnetic field is much more important

　 The magnetic effect to CMB perturbation becomes strong for higher l

Excluded and allowed regions at 1 and 2 on two parameter plane |B| vs. nB , where |B| is the primordial magnetic field strength and nB is the power-law spectral index.

Result and Discussion IResult and Discussion I 　　 Numerical estimationsNumerical estimations

The upper limit of the magnetic field strength is |B| < 5.5 nG (1)

WMAP+ACBAR+CBI: %)

WMAP+ACBAR+CBI :1 (68%)

The multiple constraints on generation scenario of PMF The multiple constraints on generation scenario of PMF

③Limit from gravity wave (Caprini & Durrer 2002)

②Limit from the cluster of galaxiesBλ > 1.0 nG

①Our limit from WMAP + ACBAR + CBI date sets

Bλ < 5.5 nG(1Mpc)

1.0 nG < B < 5.5 nG

-3.0 < nB < -2.3 31 2+ +BBN:

QCD: 1 2+

inflation: 1

WMAP+ACBAR+CBI: %)

BBNQCD

inflation

WMAP+ACBAR+CBI :1 (68%)

Lower limit from Cluster of galaxies

BBN limits on B from the PMF generation epoch

Allowed region of the PMF from the multiple constraints categorized by the generation epochs

1 2 3

2. Likelihood analysis of WMAP data with MCMC method gives constraint on a primordial magnetic field, 　　　　 B < 5.5nG

SummarySummary

3. All constrains from the constraint of PMF by gravity wave and recent magnetic field strength in clusters of galaxies, 1 nG< B < 5.5 nG, -3.0 < nB < -2.3 in our estimated allowed parameter region.

1. We confirmed numerically (without approximation) that potential discrepancy of CMB at higher l between theory and observation is explained by the primordial magnetic field.

We considered only the isotropic collapse effect without other evolutions of the PMF after the LSS (the last scattering of photons).

If we include new effective evolution processes; cluster merger → shock driven Weidel instability, AGN 　 origin of magnetic field, the upper limit of the PMF may decrease from the present estimate.

We should research others effective evolutions of the cosmological primordial magnetic field after the last scattering of photons.

Discussion Discussion

Thank you very much for your attention