MaNGA (Mapping Nearby Galaxies at Apache Point Observatory) is a 6-year SDSS-IV survey that will obtain spatially resolved spectroscopy from 3600Å to 10300Å for a representative sample of over 10000 nearby galaxies. In this paper we present the analysis of nebular emission line properties using observations of 14 galaxies obtained with P-MaNGA, a prototype of the MaNGA instrument. By using spatially resolved diagnostic diagrams we find extended star formation in galaxies that are centrally dominated by Seyfert/LINER-like emission, which illustrates that galaxy characterisations based on single fibre spectra are necessarily incomplete. We observe extended LINER-like emission (up to 1R e ) in the central regions of three galaxies. We make use of the EW(Hα) to argue that the observed emission is consistent with ionisation from hot evolved stars. We derive stellar population indices and demonstrate a clear correlation between D n (4000) and EW(Hδ A ) and the position in the ionisation diagnostic diagram: resolved galactic regions which are ionised by a Seyfert/LINER-like radiation field are also devoid of recent star formation and host older and/or more metal rich stellar populations. We also detect extraplanar LINER-like emission in two highly inclined galaxies, and identify it with diffuse ionised gas. We investigate spatially resolved metallicities and find a positive correlation between metallicity and star formation rate (SFR) surface density. We further study the relation between N/O vs O/H on resolved scales. We find that, at given N/O, regions within individual galaxies are spread towards lower metallicities, deviating from the sequence defined by galactic central regions as traced by Sloan 3 fibre spectra. We suggest that the observed dispersion can be a tracer for gas flows in galaxies: infalls of pristine gas and/or the effect of a galactic fountain.

A fully three-dimensional, nonlinear, time-dependent spherical interface dynamo is investigated using a finite-element method based on the three-dimensional tetrahedralization of the spherical system. The spherical interface dynamo model consists of four zones: an electrically conducting and uniformly rotating core, a thin differentially rotating tachocline, a uniformly rotating turbulent convection envelope, and a nearly insulating exterior. The four regions are coupled magnetically through matching conditions at the interfaces. Without the effect of a tachocline, the conventional nonlinear 2 dynamo is always stationary, axisymmetric, and equatorially antisymmetric even though numerical simulations are always fully threedimensional and time dependent. When there is no tachocline, the azimuthal field is confined to the convection zone while the poloidal magnetic field penetrates into the radiative core. The effects of an interface dynamo with a tachocline having a purely axisymmetric toroidal velocity field are as follows: (1) the action of the steady tachocline always gives rise to an oscillatory dynamo with a period of about 2 magnetic diffusion units, or about 20 yr if the magnetic diffusivity in the convection zone is 10 8 m 2 s À1 ; (2) the interface dynamo solution is always axisymmetric, selects dipolar symmetry, and propagates equatorward (for the assumed form of) although the simulation is fully three-dimensional; (3) the generated magnetic field mainly concentrates in the vicinity of the interface between the tachocline and the convection zone; and (4) the strength of the toroidal magnetic field is dramatically amplified by the effect of the tachocline. Extensions of Cowling's theorem and the toroidal flow theorem to multilayer spherical shell regions with radially discontinuous magnetic diffusivities are presented.

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