Multiwavelength Campaign on Mrk 509 X. Lower limit on the distance of
  the absorber from HST COS and STIS spectroscopy
  Active Galactic Nuclei often show evidence of photoionized outflows. A major
uncertainty in models for these outflows is the distance ($R$) to the gas from
the central black hole. In this paper we use the HST/COS data from a massive
multi-wavelength monitoring campaign on the bright Seyfert I galaxy Mrk 509, in
combination with archival HST/STIS data, to constrain the location of the
various kinematic components of the outflow. We compare the expected response
of the photoionized gas to changes in ionizing flux with the changes measured
in the data using the following steps: 1) We compare the column densities of
each kinematic component measured in the 2001 STIS data with those measured in
the 2009 COS data; 2) We use time-dependent photionization calculations with a
set of simulated lightcurves to put statistical upper limits on the hydrogen
number density that are consistent with the observed small changes in the ionic
column densities; 3) From the upper limit on the number density, we calculate a
lower limit on the distance to the absorber from the central source via the
prior determination of the ionization parameter. Our method offers two
improvements on traditional timescale analysis. First, we account for the
physical behavior of AGN lightcurves. Second, our analysis accounts for the
quality of measurement in cases where no changes are observed in the absorption
troughs. The very small variations in trough ionic column densities (mostly
consistent with no change) between the 2001 and 2009 epochs allow us to put
statistical lower limits on the distance between 100--200 pc for all the major
UV absorption components at a confidence level of 99%. These results are mainly
consistent with the independent distance estimates derived for the warm
absorbers from the simultaneous X-ray spectra.
