DETERMINATION OF THE PRIMORDIAL MAGNETIC-FIELD POWER SPECTRUM BY FARADAY-ROTATION CORRELATIONS

This paper introduces the formalism which connects between rotation me asure (RM) measurements for extragalactic sources and the cosmological magnetic field power spectrum. It is shown that the amplitude and sha pe of the cosmological magnetic held power spectrum can be constrained by using a few hundred radio sources, for which Faraday RMs are avail able. This constraint is of the form B-rms less than or similar to 1 x (26 x 10(-7) cm(-3)/(n) over bar(b)]) h nG on similar to 10-50 h(-1) Mpc scales, with (n) over bar(b) the average baryon density and h the Hubble parameter in units of 100 km s(-1) Mpc The constraint is superi or to and supersedes any other constraint that comes from either cosmi c microwave background (CMB) fluctuations, baryonic nucleosynthesis, o r the first two multipoles of the magnetic held expansion. The most ad equate method for the constraint calculation uses the Bayesian approac h to the maximum likelihood function. I demonstrate the ability to det ect such magnetic fields by constructing simulations of the field and mimicking observations. This procedure also provides error estimates f or the derived quantities. The two main noise contributions due to the Galactic RM and the internal RM are treated in a statistical way foll owing an evaluation of their distribution. For a range of magnetic fie ld power spectra with power indices -1 less than or equal to n less th an or equal to 1 in a flat cosmology (Omega(m) = 1) we estimate the si gnal-to-noise ratio, Q, for limits on the magnetic held B-rms on a sim ilar to 50 h(-1) Mpc scale. Employing one patch of a few square degree s on the sky with source number density n(src), an approximate estimat e yields Q similar or equal to 3(B-rms/1 nG)(n(src)/50 deg(-2))(2.6 x 10(-7) cm(-3)/(n) over bar(b)) h. An all-sky coverage, with a much spa rser but carefully tailored sample of similar to 500 sources, yields Q similar or equal to 1 with the same scaling. An ideal combination of small densely sampled patches and sparse all-sky coverage yields Q sim ilar or equal to 3 with better constraints for the power index. All of these estimates are corroborated by the simulations.