  We report constraints on the nucleon-dark matter particle cross section using
the internal luminosity of observed white dwarf stars in the globular cluster
Messier 4. Our results cover the parameter space corresponding to relatively
light dark matter particles, in the mass range $0.1~GeV-5~GeV$, which is known
to be very difficult to be probed by direct dark matter searches. The
additional luminosity coming from self-annihilations of dark matter particles
captured inside the stars must not exceed the observed luminosity. Imposing
that condition, we obtain for the spin independent cross section of light dark
matter particles on baryons $\sigma_{N\chi}$ the upper bound: $\sigma_{N\chi} <
4 \times 10^{-41}{\rm cm^2}$.
