The quantitative spectral analysis of medium resolution optical spectra of A and B supergiants obtained with DEIMOS and ESI at the Keck Telescopes is used to determine a distance modulus of 24.93 \pm 0.11 mag for the Triangulum Galaxy M33 .
The analysis yields stellar effective temperatures , gravities , interstellar reddening , and extinction , the combination of which provides a distance estimate via the Flux-weighted Gravity–Luminosity Relationship ( FGLR ) .
This result is based on an FGLR calibration that is continually being polished .
An average reddening of < E ( B - V ) > \sim 0.08 mag is found , with a large variation ranging from 0.01 to 0.16 mag however , demonstrating the importance of accurate individual reddening measurements for stellar distance indicators in galaxies with evident signatures of interstellar absorption .
The large distance modulus found is in good agreement with recent work on eclipsing binaries , planetary nebulae , long period variables , RR Lyrae stars , and also with HST observations of Cepheids , if reasonable reddening assumptions are made for the Cepheids .
Since distances based on the tip of the red giant branch ( TRGB ) method found in the literature give conflicting results , we have used HST ACS V - and I -band images of outer regions of M 33 to determine a TRGB distance of 24.84 \pm 0.10 mag , in basic agreement with the FGLR result .
We have also determined stellar metallicities and discussed the metallicity gradient in the disk of M33 .
We find metallicity of Z _ { \odot } at the center and 0.3 Z _ { \odot } in the outskirts at a distance of one isophotal radius .
The average logarithmic metallicity gradient is -0.07 \pm 0.01 dex kpc ^ { -1 } .
However , there is a large scatter around this average value , very similar to what has been found for the H ii regions in M 33 .