Abstract.We have developed a high-precision code which solves the kinematic dynamo problem both for given rotation law and meridional flow in the case of a low eddy diffusivity of the order of 10 11 cm 2 s −1 known from the sunspot decay. All our models work with an α-effect which is positive (negative) in the northern (southern) hemisphere. It is concentrated in radial layers located either at the top or at the bottom of the convection zone. We have also considered an α-effect uniformly distributed in all the convection zone. In the present paper the main attention is focused on i) the parity of the solution, ii) the form of the butterfly diagram and iii) the phase relation of the resulting field components. If the helioseismologically derived internal solar rotation law is considered, a model without meridional flow of high magnetic Reynolds number (corresponding to low eddy diffusivity) fails in all the three issues in comparison with the observations. However, a meridional flow with equatorial drift at the bottom of the convection zone of few meters by second can indeed enforce the equatorward migration of the toroidal magnetic field belts similar to the observed butterfly diagram but, the solution has only a dipolar parity if the (positive) α-effect is located at the base of the convection zone rather than at the top. We can, therefore, confirm the main results of a similar study by .

Abstract.We have investigated the turbulent mean-field dynamo action in protoneutron stars that are subject to convective and neutron finger instabilities during the early evolutionary phase. While the first one develops mostly in the inner regions of the star, the second one is favored in the outer regions, where the Rossby number is much smaller and a mean-field dynamo action is more efficient. By solving the mean-field induction equation we have computed the critical spin period below which no dynamo action is possible and found it to be ∼1 s for a wide range of stellar models and for both axisymmetric and non-axisymmetric magnetic fields. Because this critical period is substantially longer than the characteristic spin period of very young pulsars, we expect that a mean-field dynamo will be effective for most protoneutron stars. The saturation dipole field estimated by making use of the model of "global" quenching fits well the pulsar magnetic fields inferred from the spin-down data. Apart from the large-scale magnetic field, our model also predicts a generation of small-scale fields which are typically stronger than the poloidal field and can survive during the lifetime of pulsars. Extremely rapidly rotating protoneutron stars (P ∼ 1 ms) may have a dipole field ∼(3−6) × 10 14 G.

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We discuss the mean-field dynamo action in protoneutron stars that are subject to instabilities during the early evolutionary phase. The mean field is generated in the neutron-finger unstable region where the Rossby number is ∼1 and mean-field dynamo is efficient. Depending on the rotation rate, the mean-field dynamo can lead to the formation of three different types of pulsars. If the initial period of the protoneutron star is short, then the generated large-scale field is very strong (>3 × 10 13 G) and exceeds the small-scale field at the neutron star surface. If rotation is moderate, then the pulsars are formed with more or less standard dipole fields (<3 × 10 13 G) but with surface small-scale magnetic fields stronger than the dipole field. If rotation is very slow, then the mean-field dynamo does not operate, and the neutron star has no global field. Nevertheless, strong small-scale fields are generated in such pulsars, and they can manifest themselves as objects with very low spin-down rate but with a strong magnetic field inferred from the spectral features.

In this paper, in the framework of the secondary infall model, the correlation between the central surface density and the halo core radius of galaxy, and cluster of galaxies, dark matter haloes was analyzed, this having recently been studied on a wide range of scales. We used Del Popolo (2009) secondary infall model taking into account ordered and random angular momentum, dynamical friction, and dark matter (DM) adiabatic contraction to calculate the density profile of haloes, and then these profiles are used to determine the surface density of DM haloes. The main result is that r * (the halo characteristic radius) is not an universal quantity as claimed by Donato et al. (2009) and Gentile et al. (2009). On the contrary, we find a correlation with the halo mass M 200 in agreement with Cardone & Tortora (2010), Boyarsky at al. (2009) and Napolitano et al. ( 2010), but with a significantly smaller scatter, namely 0.16 ± 0.05. We also consider the baryon column density finding this latter being indeed a constant for low mass systems such as dwarfs, but correlating with mass with a slope α = 0.18 ± 0.05. In the case of the surface density of dark matter for a system composed only of dark matter, as in dissipationless simulations, we get α = 0.20 ± 0.05. These results leave little room for the recently claimed universality of (dark and stellar) column density.