%A B Ercolano %A R Wesson %A Y Zhang %A MJ Barlow %A O De Marco %A T Rauch %A XW Liu %T Observations and three-dimensional photoionization modelling of the Wolf-Rayet planetary nebula NGC 1501 %J Monthly Notices of the Royal Astronomical Society %K atomic data, stars : Wolf-Rayet, ISM : abundances, planetary nebulae : individual : NGC 1501 %X Deep optical spectra of the highâ€excitation planetary nebula NGC 1501 and its W04 central star are presented. A recombination line abundance analysis of the emissionâ€line spectrum of the central star yields He : C : O mass fractions of 0.36 : 0.48 : 0.16, similar to those of PG 1159 stars. A detailed empirical analysis of the nebular collisionally excited line (CEL) and optical recombination line (ORL) spectrums are presented, together with fully threeâ€dimensional photoionization modelling of the nebula. We found very large ORL–CEL abundance discrepancy factors (ADFs) for O^{2+} (32) and Ne^{2+} (33). The mean value of ∼5100 K for the T_{e} derived from He I recombination lines ratios is 6000 K, lower than the value of 11 100 K implied by the [O III] line ratio. This result indicates the existence of a second, low-temperature nebular component, which could account for the observed ORL emission. Electron temperature fluctuations (t^{2}) cannot account for the high ADFs found from our optical spectra of this nebula. A threeâ€dimensional photoionization model of NGC 1501 was constructed using the photoionization code_{mocassin}, based on our new spectroscopic data and using the threeâ€dimensional electron density distribution determined from longâ€slit echellograms of the nebula by Ragazzoni et al. The central star ionizing radiation field is approximated by a model atmosphere, calculated using the Tübingen nonâ€local thermodynamic equilibrium model atmosphere package, for abundances typical of the W04 nucleus of NGC 1501 and PG 1159 stars. The nebular emissionâ€line spectrum was best reproduced using a central star model with an effective temperature of Teff= 110 kK and a luminosity of L_{*}= 5000 L_{⊙}. The initial models showed higher degrees of ionization of heavy elements than indicated by observations. We investigated the importance of the missing lowâ€temperature dielectronic recombination rates for thirdâ€row elements and have estimated upper limits to their rate coefficients. Our singleâ€phase, threeâ€dimensional photoionization model heavily underpredicts the optical recombination line emission. We conclude that the presence of a hydrogenâ€deficient, metalâ€rich component is necessary to explain the observed ORL spectrum of this object. The existence of such knots could also provide a softening of the radiation field, via the removal of ionizing photons by absorption in the knots, thereby helping to alleviate the overionization of the heavy elements in our models. %I OXFORD UNIV PRESS %L discovery10095990 %N 2 %V 354 %O This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions. %D 2004 %P 558-574