If the supermassive black hole (SMBH) at the center of our Galaxy grew adiabatically, then a dense spike of dark matter is expected to have formed around it. Assuming that dark matter is composed primarily of weakly interacting massive particles (WIMPs), a star orbiting close enough to the SMBH can capture WIMPs at an extremely high rate. The stellar luminosity due to annihilation of captured WIMPs in the stellar core may be comparable to or even exceed the luminosity of the star due to thermonuclear burning. The model thus predicts the existence of unusual stars, i.e. WIMP burners, in the vicinity of an adiabatically grown SMBH. We find that the most efficient WIMP burners are stars with degenerate electron cores, e.g. white dwarfs (WD) or degenerate cores with envelopes. If found, such stars would provide evidence for the existence of particle dark matter and could possibly be used to establish its density profile. In our previous paper we computed the luminosity from WIMP burning for a range of dark matter spike density profiles, degenerate core masses, and distances from the SMBH. Here we compare our results with the observed stars closest to the Galactic center and find that they could be consistent with WIMP burners in the form of degenerate cores with envelopes. We also cross-check the WIMP burner hypothesis with the EGRET observed flux of gamma-rays from the Galactic center, which imposes a constraint on the dark matter spike density profile and annihilation cross-section. We find that the EGRET data is consistent with the WIMP burner hypothesis. New high precision measurements by GLAST will confirm or set stringent limits on a dark matter spike at the Galactic center, which will in turn support or set stringent limits on the existence of WIMP burners at the Galactic center.