Planck 2015 results. III. LFI systematic uncertainties
  We present the current accounting of systematic effect uncertainties for the
Low Frequency Instrument (LFI) that are relevant to the 2015 release of the
Planck cosmological results, showing the robustness and consistency of our data
set, especially for polarization analysis. We use two complementary approaches:
(i) simulations based on measured data and physical models of the known
systematic effects; and (ii) analysis of difference maps containing the same
sky signal ("null-maps"). The LFI temperature data are limited by instrumental
noise. At large angular scales the systematic effects are below the cosmic
microwave background (CMB) temperature power spectrum by several orders of
magnitude. In polarization the systematic uncertainties are dominated by
calibration uncertainties and compete with the CMB $E$-modes in the multipole
range 10--20. Based on our model of all known systematic effects, we show that
these effects introduce a slight bias of around $0.2\,\sigma$ on the
reionization optical depth derived from the 70\,GHz $EE$ spectrum using the 30
and 353\,GHz channels as foreground templates. At 30\,GHz the systematic
effects are smaller than the Galactic foreground at all scales in temperature
and polarization, which allows us to consider this channel as a reliable
template of synchrotron emission. We assess the residual uncertainties due to
LFI effects on CMB maps and power spectra after component separation and show
that these effects are smaller than the CMB amplitude at all scales. We also
assess the impact on non-Gaussianity studies and find it to be negligible. Some
residuals still appear in null maps from particular sky survey pairs,
particularly at 30 GHz, suggesting possible straylight contamination due to an
imperfect knowledge of the beam far sidelobes.
