Constraining primordial magnetic fields with distortions of the black-body spectrum of the cosmic microwave background: pre- and post-decoupling contributions

Kerstin E. Kunze; Eiichiro Komatsu

doi:10.1088/1475-7516/2014/01/009

paper

Constraining primordial magnetic fields with distortions of the black-body spectrum of the cosmic microwave background: pre- and post-decoupling contributions

arXiv:1309.7994 · doi:10.1088/1475-7516/2014/01/009

Abstract

Observational limits on $y$ - and $μ$ -type distortions can constrain properties of magnetic fields in the early universe. For a Gaussian, random, and non-helical field, $μ$ and $y$ are calculated a function of the present-day strength of the field, $B_{0}$ , smoothed over a certain Gaussian width, $k_{c}^{- 1}$ , and spectral index, $n_{B}$ , defined by $P_{B} (k) \propto k^{n_{B}}$ . For $n_{B} = - 2.9$ and $k_{c}^{- 1} = 1 Mpc$ , the COBE/FIRAS limit on $μ$ yields $B_{0} < 40$ nG, whereas the projected PIXIE limit on $μ$ would yield $B_{0} < 0.8$ nG. For non-scale-invariant spectra, constraints can be stronger. For $B_{0} = 1$ nG with $k_{c}^{- 1} = 1 Mpc$ , the COBE/FIRAS limit on $μ$ excludes a wide range of spectral indices given by $n_{B} > - 2.6$ . After decoupling, energy dissipation is due to ambipolar diffusion and decaying MHD turbulence, creating a $y$ -type distortion. The distortion is completely dominated by decaying MHD turbulence, and is of order $y \approx 1 0^{- 7}$ for a few nG field smoothed over the damping scale at the decoupling epoch, $k_{d, d ec} \approx 290 (B_{0} /1 nG)^{- 1} Mpc^{- 1}$ . This contribution is as large as those of the known contributions such as reionization and virialized objects at lower redshifts. The projected PIXIE limit on $y$ would exclude $B_{0} > 1.0$ and 0.6 nG for $n_{B} = - 2.9$ and -2.3, respectively, and $B_{0} > 0.6$ nG for $n_{B} \geq 2$ . The current limits on the optical depth to Thomson scattering restrict the predicted $y$ -type distortion to be $y ≲ 1 0^{- 8}$ . (Abridged)

26 pages, 36 figures

Constraining primordial magnetic fields with distortions of the black-body spectrum of the cosmic microwave background: pre- and post-decoupling contributions

Abstract

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