On the basis of the PPMXL catalogue we perform an all-sky census of the Hyades down to masses of about 0.2 m_sun in a region up to 30 pc from the cluster centre. We use the proper motions from PPMXL in the convergent point method to determine probable kinematic members. From 2MASS photometry and CMC14 r-band photometry, we derive empirical colour-absolute magnitude diagrams and, finally, determine photometric membership for all kinematic candidates. This is the first deep (r < 17) all-sky survey of the Hyades allowing a full three-dimensional analysis of the cluster. The survey is complete down to at least M_{K_s} = 7.3 or 0.25 m_sun. We find 724 stellar systems co-moving with the bulk Hyades space velocity, which represent a total mass of 435 m_sun. The tidal radius is about 9 pc, and 275 m_sun (364 systems) are gravitationally bound. This is the cluster proper. Its mass density profile is perfectly fitted by a Plummer model with a central density of 2.21 m_sun*pc^-3 and a core radius of r_co = 3.10 pc, while the half-mass radius is r_h = 4.1 pc. There are another 100 m_sun in a volume between one and two tidal radii (halo), and another 60 m_sun up to a distance of 30 pc from the centre. Strong mass segregation is inherent in the cluster. The present-day luminosity and mass functions are noticeably different in various parts of the cluster (core, corona, halo, and co-movers). They are strongly evolved compared to presently favoured initial mass functions. The analysis of the velocity dispersion of the cluster shows that about 20% of its members must be binaries. As a by-product, we find that presently available theoretical isochrones are not able to adequately describe the near-infrared colour-absolute magnitude relation for those cluster stars that are less massive than about 0.6 m_sun.
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