Many binary companions to the central stars of planetary nebulae (PNe) are found to be inflated, perhaps indicating that accretion onto the central star might occur during the PN phase. The discovery of a handful of nova eruptions and supersoft X-ray sources inside PNe supports this hypothesis. In this paper, we investigate the impact that hosting a steadily-accreting WD would have on the properties and evolution of a PN. By pairing the published accreting nuclear-burning WD models with radiation transfer simulations, we extract the time evolution of the emission line spectra and ionization properties of a PN that surrounds a 0.6$\rm M_{\odot }$ steadily nuclear-burning WD as a function of the mass accretion rate. We find that accreting WDs are able to form very extended, high excitation, [O iii]-bright PNe, which are characterised by high nebular electron temperatures. Their properties remain almost invariant with time and their visibility time can be much longer compared to PNe powered by single WDs. We discuss the implications of our findings in explaining specific characteristics observed in PNe. Finally, we examine how accreting WDs affect the planetary nebula luminosity function (PNLF) by covering WD masses in the range of 0.5-0.8$\rm M_{\odot }$ and for various accretion rates within the steady accretion regime. We find that for all but the lowest accretion rates, the [O iii]-luminosities are almost constant and clustered very close to the PNLF cut-off value. Our results suggest that mass-accreting WDs in interacting binaries might play a role in understanding the invariant cut-off of the PNLF.

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