  In the present work we study the branon dark matter particles impact on
compact objects, and we provide the first constraints of the parameter space
using white dwarf stars. The branon dark matter model is characterized by two
free parameters, namely the branon mass particle M and the brane tension factor
$f$. The latter determines the strength of the interaction of branon dark
matter particles with baryons. By considering a typical white dwarf star we
were able to obtain constraints on branon dark matter and compare with current
limits obtained by direct detection searches and dark matter abundance. In
particular our results show that i) for heavy branons with a mass $M > 10 GeV$
white dwarfs fail to provide us with bounds better than current limits from DM
direct detection searches, and ii) for light branons in the mass range $2 keV <
M < 1 GeV$, which cannot be probed neither with current dark matter experiments
nor with the next generation of detectors, the dark matter abundance constrain
determines $f$ as a function of $M$ in the range $0.1 GeV < M < 1 GeV$ for the
branon mass and $1 GeV < f < 5 GeV$ for the brane tension factor. Furthermore,
our findings indicate that the limits from white dwarfs are not stronger than
the dark matter abundance constrain.
