We present synthetic single-line and continuum linear-polarisation signatures due to electron scattering in axially-symmetric Type II supernovae (SNe) which we calculate using a Monte Carlo and a long-characteristic radiative-transfer code. Aspherical ejecta are produced by prescribing a latitudinal scaling or stretching of SN ejecta inputs obtained from 1-D non-LTE time-dependent calculations. We study polarisation signatures as a function of inclination, shape factor, wavelength, line identity, post-explosion time. At early times, cancellation and optical-depth effects make the polarisation intrinsically low, causing complicated sign reversals with inclination or continuum wavelength, and across line profiles. While the line polarisation is positive (negative) for an oblate (prolate) morphology at the peak and in the red wing, the continuum polarisation may be of any sign. These complex polarisation variations are produced not just by the asymmetric distribution of scatterers but also of the flux. Our early-time signatures are in contradiction with predictions for a centrally illuminated aspherical nebula, although this becomes a better approximation at nebular times. For a fixed asymmetry, our synthetic continuum polarisation is generally low, may evolve non-monotonically during the plateau phase, but it systematically rises as the ejecta become optically thin. Changes in polarization over time do not necessarily imply a change in the asymmetry of the ejecta. The SN structure (e.g., density/ionization) critically influences the level of polarisation. Importantly, a low polarisation (<0.5%) at early times does not necessarily imply a low degree of asymmetry as usually assumed. Asphericity influences line-profile morphology and the luminosity, which may compromise the accuracy of SN characteristics inferred from these.Comment: 25 pages, 23 figures, accepted to MNRA
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