We have determined possible cluster members of the nearby open cluster Praesepe ( M44 ) based on J and K photometry and proper motions from the PPMXL catalogue and z photometry from the Sloan Digital Sky Survey ( SDSS ) .
In total we identified 893 possible cluster members down to a magnitude of J = 15.5 mag , corresponding to a mass of about 0.15 M _ { \odot } for an assumed cluster distance modulus of ( m - M ) _ { 0 } = 6.30 mag ( d \approx 182 pc ) , within a radius of 3.5 ^ { \circ } around the cluster centre .
We derive a new cluster centre for Praesepe ( \alpha _ { centre } = 8 ^ { h } 39 ^ { m } 37 ^ { s } , \delta _ { centre } = 19 ^ { \circ } 35 ^ { \prime% } 02 ^ { \prime \prime } ) .
We also derive a total cluster mass of about 630 M _ { \odot } and a 2D half-number and half-mass radius of 4.25 pc and 3.90 pc respectively .
The global mass function ( MF ) of the cluster members shows evidence for a turnover around m = 0.65 M _ { \odot } .
While more massive stars can be fit by a power-law \xi ( m ) \sim m ^ { - \alpha } with slope \alpha = 2.88 \pm 0.22 , stars less massive than m = 0.65 M _ { \odot } are best fitted with \alpha = 0.85 \pm 0.10 .
In agreement with its large dynamical age , we find that Praesepe is strongly mass segregated and that the mass function slope for high mass stars steepens from a value of \alpha = 2.32 \pm 0.24 inside the half-mass radius to \alpha = 4.90 \pm 0.51 outside the half-mass radius .
We finally identify a significant population of binaries and triples in the colour-magnitude diagram of Praesepe .
Assuming non-random pairing of the binary components , a binary fraction of about 35 % for primaries in the mass range 0.6 < m / M _ { \odot } < 2.20 is required to explain the observed number of binaries in the colour-magnitude diagram ( CMD ) .