Neutrino eigenstates and flavour, spin and spin-flavour oscillations in a constant magnetic field

We further develop a recently proposed new approach to the description of the relativistic neutrino flavour $\nu_e^L \leftrightarrow \nu_{\mu}^L$, spin $\nu_e^L \leftrightarrow \nu_{e}^R$ and spin-flavour $\nu_e^L \leftrightarrow \nu_{\mu}^R$ oscillations in a constant magnetic field that is based on the use of the exact neutrino stationary states in the magnetic field. The neutrino flavour, spin and spin-flavour oscillations probabilities are calculated accounting for the whole set of possible conversions between four neutrino states. In general, the obtained expressions for the neutrino oscillations probabilities exhibit new inherent features in the oscillation patterns. It is shown, in particular, that: 1) in the presence of the transversal magnetic field for a given choice of parameters (the energy and magnetic moments of neutrinos and the strength of the magnetic field) the amplitude of the flavour oscillations $\nu_e^L \leftrightarrow \nu_{\mu}^L$ at the vacuum frequency is modulated by the magnetic field frequency, 2) the neutrino spin oscillation probability (without change of the neutrino flavour) exhibits the dependence on the mass square difference $\Delta m^2$. It is shown that the discussed interplay of neutrino oscillations in magnetic fields on different frequencies can have important consequences in astrophysical environments, in particular in those peculiar for magnetars.Comment: 7 pages and 3 figures. arXiv admin note: text overlap with arXiv:1803.0575

Astrokit -- an Efficient Program for High-Precision Differential CCD Photometry and Search for Variable Stars

Having a need to perform differential photometry for tens of thousands stars in a several square degrees field, we developed Astrokit program. The software corrects the star brightness variations caused by variations of atmospheric transparency: to this end, the program selects for each star an individual ensemble of reference stars having similar magnitudes and positions in the frame. With ten or more reference stars in the ensemble, the differences between their spectral types and the spectral type of the object studied become unimportant. Astrokit searches for variable stars using Robust Median Statistics criterion, which allows candidate variables to be selected more efficiently than by analyzing the standard deviation of star magnitudes. The software allows very precise automatic analysis of long inhomogeneous sets of photometric observations of a large number of objects to be performed, making it possible to find "hot Jupiter" type exoplanet transits and low-amplitude variables. We describe the algorithm of the program and the results of its application to reduce the data of the photometric sky survey in Cygnus as well as observations of the open cluster NGC188 and the transit of the exoplanet WASP-11 b / HAT-P-10 b, performed with the MASTER-II-URAL telescope of the Kourovka Astronomical Observatory of the Ural Federal University.Comment: to be published in Astrophysical Bulletin, Vol. 69, No.