The Binary Fraction and Mass Segregation in Alpha Persei Open Cluster
  We have obtained membership probabilities of stars within a field of radius
$\sim3^\circ$ around the centre of the open cluster Alpha Persei using proper
motions and photometry from the PPMXL and WISE catalogues. We have identified
810 possible stellar members of Alpha Persei. We derived the global and radial
present-day mass function (MF) of the cluster and found that they are well
matched by two-stage power-law relations with different slopes at different
radii. The global MF of Alpha Persei shows a turnover at
$m=0.62\,\mathrm{M}_{\odot}$ with low and high-mass slopes of
$\alpha_\mathrm{low}=0.50\pm0.09$ ($0.1<m/\mathrm{M}_{\odot}<0.62$) and
$\alpha_\mathrm{high}=2.32\pm0.14$ ($0.62\leq m/\mathrm{M}_{\odot}<4.68$)
respectively. The high-mass slope of the cluster increases from $2.01$ inside
$1\hbox{$.\!\!^\circ$}10$ to $2.63$ outside $2\hbox{$.\!\!^\circ$}2$, whereas
the mean stellar mass decreases from $0.95$ to $0.57\,\mathrm{M}_{\odot}$ in
the same regions, signifying clear evidence of mass segregation in the cluster.
From an examination of the high-quality colour-magnitude data of the cluster
and performing a series of Monte Carlo simulations we obtained a binary
fraction of $f_{\rm bin}=34\pm12$ percent for stars with
$0.70<m/\mathrm{M}_{\odot}<4.68$. This is significantly larger than the
observed binary fraction, indicating that this open cluster contains a large
population of unresolved binaries. Finally, we corrected the mass-function
slopes for the effect of unresolved binaries and found low- and high-mass
slopes of $\alpha_\mathrm{low}=0.89\pm0.11$ and
$\alpha_\mathrm{high}=2.37\pm0.09$ and a total cluster mass of
$352\,\mathrm{M}_{\odot}$.
