COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses IX. Time delays and N-body realisations of the lens in HE 0435-1223

We present accurate time delays for the quadruply imaged quasar HE 0435-1223, from the COSMOGRAIL collaboration. A new way of turning the delays into H0 is proposed, using Nbody realisations of the lensing galaxy. The delays are measured from 575 independent photometric points obtained between January 2004 and March 2010. With 6 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 measure delta_t(BA) = 8.4+/-2.1 days, delta_t(BC) = 7.8+/-0.8 days and delta_t(BD) = -6.5+/-0.7 days. HST NICMOS2 images are deconvolved in order to derive accurate astrometry of the quasar images and to infer the light profile of the lensing galaxy. In combination with VLT spectroscopy of the lens, the HST images are used to estimate the baryonic fraction, fb, in the Einstein radius. We measure fb = 0.65+0.13-0.10 if the lensing galaxy has a Kroupa IMF and fb = 0.45+0.04-0.07 if it has a Salpeter IMF. N-body realisations of the lensing galaxy are used to infer its dark matter profile, given the measured rest-frame stellar velocity dispersion, sigma_ap = 222+/-34 km/s and the baryonic fraction. These dynamical models and baryonic fraction are also required to match the lensing observables. We find that only the lensing galaxies with Kroupa IMF match all the data simultaneously. Using the time delays to estimate the Hubble constant under this assumption leads to H0 = 62+6-4 km/s/Mpc. While the relatively small formal error bars reflect the high potential of the method to provide an accurate estimate of H0, the value itself might be revised when new observational constraints are available, in particular a high precision velocity dispersion measurement (or velocity dispersion profile) of the lens and a measurement of the external shear, from integral-field spectroscopy and/or deep X-ray images.