Information on the star at the centre of the Helix "Eye Of God" Nebula
The central star is a hot DAO white dwarf. As far as I can tell, the numbers that are the most reliable are those from Napiwotzki et al. (1999). They use a direct spectral fitting technique to estimate the surface gravity and effective temperature of the central white dwarf star. These are $g = 10^{(7.00 \pm 0.22)}$ cm/s$^2$ and $T_{\rm eff} = 103600 \pm 5500$ K.

They use these numbers and theoretical white dwarf evolutionary models (there is little alternative for a star that isn't part of a binary system) to estimate a mass of $0.57 \pm 0.02 M_{\odot}$.

At a distance now known to be around  $219 \pm 24$ pc (Harris et al. 2007), this makes the luminosity of the white dwarf around 100 times that of the Sun. A bit of calculation shows that for this gravity and mass, then although the star is small (about $0.04 R_{\odot}$), it is much bigger than most white dwarfs. That is because it is recently formed (planetary nebulae are recently formed objects) and hot; the white dwarf is still contracting towards its final equilibrium size of around $0.015 R_{\odot}$.

The CDS SIMBAD entry for the star is http://simbad.u-strasbg.fr/simbad/sim-id?Ident=WD+2226-210&amp;NbIdent=1&amp;Radius=2&amp;Radius.unit=arcmin&amp;submit=submit+id

It is listed in several catalogues, so goes by various names e.g. 2MASS J22293854-2050136, WD 2226-210.

The most recent (and probably most accurate) distance measurement is from the Gaia DR2 parallax survey, giving $201 \pm 4$ pc ($655 \pm 13$ light years).