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

We computed the contribution of the Compton and Bremsstrahlung processes with a hidden light $U(1)_D$ neutral boson $γ_D$ to the white dwarf G117-B15A anomalous cooling rate, as well as the white dwarf luminosity functions (WDLF). We demonstrated that for a light mass of hidden photon ($m_{γ_D} \ll$ a few keV), compatible results are obtained for the recent Sloan Digital Sky Survey and the SuperCOSMOS Sky Survey observation, but the stringent limits would be imposed on the kinetic mixing $ε$. We performed $χ^2$-tests to acquire a quantitative assessment on the WDLF data in the context of our model, computed under the assumption of different kinetic mixing $ε$, the age of the oldest computed stars $T_D$, and a constant star formation rate $ψ$. Then taken together, the WDLF analysis of 2$σ$ confidence interval $ε= \left( 0.37^{+0.35}_{-0.37}\right) \times 10^{-14}$ is barely consistent with the cooling rate analysis at 2$σ$ regime $ε= \left( 0.97^{+0.35}_{-0.37} \right) \times 10^{-14}$. The two approaches used here agree with each other in yielding an anomalous cooling rate of white dwarf in this luminosity range.