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 $352\,\mathrm{M}_{\odot}$.