The stellar mass function, binary content and radial structure of the
  open cluster Praesepe derived from PPMXL and SDSS data
  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 Msun for an assumed cluster distance
modulus of (m-M)_0 = 6.30 mag (d ~ 182 pc), within a radius of 3.5{\deg} around
the cluster centre. We derive a new cluster centre for Praesepe
({\alpha}_centre = 8h 39m 37s, {\delta}_centre = 19{\deg} 35' 02"). We also
derive a total cluster mass of about 630 Msun 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 Msun.
While more massive stars can be fit by a power-law {\xi}(m) ~ m^(-{\alpha})
with slope {\alpha} = 2.88 +/- 0.22, stars less massive than m = 0.65 Msun are
best fitted with {\alpha} = 0.85 +/- 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 +/- 0.24 inside the half-mass radius to {\alpha} = 4.90 +/- 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/Msun < 2.20 is required to explain the observed
number of binaries in the colour-magnitude diagram (CMD).
