Microlensing signature of a white dwarf population in the galactic halo

Microlensing and pixel-lensing surveys play a fundamental role in the searches for galactic dark matter and in the study of the galactic structure. Recent observations suggest the presence of a population of old white dwarfs with high proper motion, probably in the galactic halo, with local mass density in the range $1.3\times 10^{-4}-4.4\times 10^{-3} M_{\odot}$ pc$^{-3}$, in addition to the standard galactic stellar disk and dark halo components. Investigation of the signatures on microlensing results towards the LMC of these different lens populations, with particular emphasis to white dwarfs, is the main purpose of the present paper. This is done by evaluating optical depth and microlensing rate of the various lens populations and then calculating through a Montecarlo program, the probability that a lens which has caused a microlensing event of duration $t_{\rm E}$ belongs to a certain galactic population. Data obtained by the MACHO Collaboration allow us to set an upper bound of $1.6\times 10^{-3} M_{\odot}$ pc$^{-3}$ to the local mass density of white dwarfs distributed in spheroidal models, while for white dwarfs in disk models all values for the local mass density are in agreement with observational results.