  The understanding of (sub-)millimetre polarisation has made a leap forward
since high-resolution imaging with ALMA came available. Amongst other effects,
self-scattering (i.e., scattering of thermal dust emission on other grains) is
thought to be the origin of millimetre polarisation. This opens the first
window to a direct measurement of dust grain sizes in regions of optically
thick continuum emission as it can be found in protoplanetary disks and
star-forming regions. However, the newly derived values of grain sizes are
usually around ${\sim}100\,\mu$m and thus one order of magnitude smaller than
those obtained from more indirect measurements as well as those expected from
theory (${\sim}1\,$mm). We see the origin of this contradiction in the applied
dust model of today's self-scattering simulations: a perfect compact sphere.
The aim of this study is to test our hypothesis by investigating the impact of
non-spherical grain shapes on the self-scattering signal. We apply discrete
dipole approximation simulations to investigate the influence of the grain
shape on self-scattering polarisation in three scenarios: an unpolarised and
polarised incoming wave under a fixed as well as a varying incident
polarisation angle. We find significant deviations of the resulting
self-scattering polarisation when comparing non-spherical to spherical grains,
in particular outside the Rayleigh regime, i.e. for >100$\,\mu$m size grains
observed at $870\,\mu$m wavelength. Self-scattering by oblate grains produces
higher polarisation degrees compared to spheres which challenges the
interpretation of the origin of observed millimetre polarisation. A (nearly)
perfect alignment of the non-spherical grains is required to account for the
observed millimetre polarisation in protoplanetary disks. Our findings point
towards a necessary re-evaluation of the dust grain sizes derived from (sub-)mm
polarisation.
