Linearized iterative least-squares (LIL): A parameter fitting algorithm for component separation in multifrequency CMB experiments such as Planck

We present an efficient algorithm for the least squares parameter fitting optimized for component separation in multi-frequency CMB experiments. We sidestep some of the problems associated with non-linear optimization by taking advantage of the quasi-linear nature of the foreground model. We demonstrate our algorithm, linearized iterative least-squares (LIL), on the publicly available Planck sky model FFP6 simulations and compare our result with the other algorithms. We work at full Planck resolution and show that degrading the resolution of all channels to that of the lowest frequency channel is not necessary. Finally we present results for the publicly available Planck data. Our algorithm is extremely fast, fitting 6 parameters to 7 lowest Planck channels at full resolution (50 million pixels) in less than 160 CPU-minutes (or few minutes running in parallel on few tens of cores). LIL is therefore easily scalable to future experiments which may have even higher resolution and more frequency channels. We also naturally propagate the uncertainties in different parameters due to noise in the maps as well as degeneracies between the parameters to the final errors on the parameters using Fisher matrix. One indirect application of LIL could be a front-end for Bayesian parameter fitting to find the maximum of the likelihood to be used as the starting point for the Gibbs sampling. We show for rare components, such as the carbon-monoxide emission, present in small fraction of sky, the optimal approach should combine parameter fitting with model selection. LIL may also be useful in other astrophysical applications which satisfy the quasi-linearity criteria.Comment: Accepted versio

Time of primordial Be-7 conversion into Li-7, energy release and doublet of narrow cosmological neutrino lines

One of the important light elements created during the big bang nucleosynthesis is Be-7 which then decays to Li-7 by electron capture when recombination becomes effective but well before the Saha equilibrium recombination is reached. This means that Be-7 should wait until its recombination epoch even though the half-life of the hydrogenic beryllium atom is only 106.4 days. We calculate when the conversion from primordial Be-7 to Li-7 occurs taking into account the population of the hyperfine structure sublevels and solving the kinetic equations for recombination, photoionization and conversion rate. We also calculate the energies and the spectrum of narrow neutrino doublet lines resulting from Be-7 decay.Comment: Minor typos correcte