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We present accurate time delays for the quadruply imaged quasar HE 0435-1223.The delays were measured from 575 independent photometric points obtained inthe R-band between January 2004 and March 2010. With seven years of data, weclearly show that quasar image A is affected by strong microlensing variationsand that the time delays are best expressed relative to quasar image B. Wemeasured Delta_t(BC) = 7.8+/-0.8 days, Delta_t(BD) = -6.5+/-0.7 days andDelta_t_CD = -14.3+/-0.8 days. We spacially deconvolved HST NICMOS2 F160Wimages to derive accurate astrometry of the quasar images and to infer thelight profile of the lensing galaxy. We combined these images with a stellarpopulation fitting of a deep VLT spectrum of the lensing galaxy to estimate thebaryonic 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 estimatethe velocity dispersion of the lensing galaxy, sigma_ap = 222+/-34 km/s. Weused f_b and sigma_ap to constrain an analytical model of the lensing galaxycomposed of an Hernquist plus generalized NFW profile. We solve the Jeansequations numerically for the model and explored the parameter space under theadditional requirement that the model must predict the correct astrometry forthe quasar images. Given the current error bars on f_b and sigma_ap, we did notconstrain H0 yet with high accuracy, i.e., we found a broad range of modelswith chi^2 < 1. However, narrowing this range is possible, provided a bettervelocity dispersion measurement becomes available. In addition, increasing thedepth of the current HST imaging data of HE 0435-1223 will allow us to combineour constraints with lens reconstruction techniques that make use of the fullEinstein ring that is visible in this object.

COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses IX. Time delays, lens dynamics and baryonic fraction in HE 0435-1223