Multiwavelength campaign on Mrk 509 VII. Relative abundances of the warm
  absorber
  Context. The study of abundances in the nucleus of active galaxies allows us
to investigate the evolution of abundance by comparing local and higher
redshift galaxies. However, the methods used so far have substantial drawbacks
or rather large uncertainties. Some of the measurements are at odds with the
initial mass function derived from the older stellar population of local
elliptical galaxies. Aims. We determine accurate and reliable abundances of C,
N, Ne, and Fe relative to O from the narrow absorption lines observed in the
X-ray spectra of Mrk 509. Methods. We use the stacked 600 ks XMM-Newton RGS and
180 ks Chandra LETGS spectra. Thanks to simultaneous observations with INTEGRAL
and the optical monitor on-board XMM-Newton for the RGS observations and
HST-COS and Swift for the LETGS observations, we have an individual spectral
energy distribution for each dataset. Owing to the excellent quality of the RGS
spectrum, the ionisation structure of the absorbing gas is well constrained,
allowing for a reliable abundance determination using ions over the whole
observed range of ionisation parameters. Results. We find that the relative
abundances are consistent with the proto-solar abundance ratios: C/O =
1.19$\pm$0.08, N/O = 0.98$\pm$0.08, Ne/O = 1.11$\pm$0.10, Mg/O = 0.68$\pm$0.16,
Si/O = 1.3$\pm$0.6, Ca/O = 0.89$\pm$0.25, and Fe/O = 0.85$\pm$0.06, with the
exception of S, which is slightly under-abundant, S/O = 0.57$\pm$0.14. Our
results, and their implications, are discussed and compared to the results
obtained using other techniques to derive abundances in galaxies.
