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We computed the contribution of the Compton and Bremsstrahlung processes witha hidden light $U(1)_D$ neutral boson $\gamma_D$ to the white dwarf G117-B15Aanomalous cooling rate, as well as the white dwarf luminosity functions (WDLF).We demonstrated that for a light mass of hidden photon ($m_{\gamma_D} \ll$ afew keV), compatible results are obtained for the recent Sloan Digital SkySurvey and the SuperCOSMOS Sky Survey observation, but the stringent limitswould be imposed on the kinetic mixing $\epsilon$. We performed $\chi^2$-teststo acquire a quantitative assessment on the WDLF data in the context of ourmodel, computed under the assumption of different kinetic mixing $\epsilon$,the age of the oldest computed stars $T_D$, and a constant star formation rate$\psi$. Then taken together, the WDLF analysis of 2$\sigma$ confidence interval$\epsilon = \left( 0.37^{+0.35}_{-0.37}\right) \times 10^{-14}$ is barelyconsistent with the cooling rate analysis at 2$\sigma$ regime $\epsilon =\left( 0.97^{+0.35}_{-0.37} \right) \times 10^{-14}$. The two approaches usedhere agree with each other in yielding an anomalous cooling rate of white dwarfin this luminosity range.

Hidden Photon Compton and Bremsstrahlung in White Dwarf Anomalous Cooling and Luminosity Functions