  We present accurate time delays for the quadruply imaged quasar HE 0435-1223.
The delays were measured from 575 independent photometric points obtained in
the R-band between January 2004 and March 2010. With seven years of data, we
clearly show that quasar image A is affected by strong microlensing variations
and that the time delays are best expressed relative to quasar image B. We
measured Delta_t(BC) = 7.8+/-0.8 days, Delta_t(BD) = -6.5+/-0.7 days and
Delta_t_CD = -14.3+/-0.8 days. We spacially deconvolved HST NICMOS2 F160W
images to derive accurate astrometry of the quasar images and to infer the
light profile of the lensing galaxy. We combined these images with a stellar
population fitting of a deep VLT spectrum of the lensing galaxy to estimate the
baryonic fraction, $f_b$, in the Einstein radius. We measured f_b =
0.65+0.13-0.10 if the lensing galaxy has a Salpeter IMF and f_b =
0.45+0.04-0.07 if it has a Kroupa IMF. The spectrum also allowed us to estimate
the velocity dispersion of the lensing galaxy, sigma_ap = 222+/-34 km/s. We
used f_b and sigma_ap to constrain an analytical model of the lensing galaxy
composed of an Hernquist plus generalized NFW profile. We solve the Jeans
equations numerically for the model and explored the parameter space under the
additional requirement that the model must predict the correct astrometry for
the quasar images. Given the current error bars on f_b and sigma_ap, we did not
constrain H0 yet with high accuracy, i.e., we found a broad range of models
with chi^2 < 1. However, narrowing this range is possible, provided a better
velocity dispersion measurement becomes available. In addition, increasing the
depth of the current HST imaging data of HE 0435-1223 will allow us to combine
our constraints with lens reconstruction techniques that make use of the full
Einstein ring that is visible in this object.
