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Light weakly interacting particles could be copiously produced in the Sunwhich, as a well-understood star, could provide severe constraints on such newphysics. In this work, we calculate the solar production rates of light gaugebosons (e.g. dark photon) arising from various $U(1)$ extensions of thestandard model. It is known that the dark photon production rate is suppressedby the dark photon mass if it is well below the plasmon mass of the medium. Weshow that for more general $U(1)$ gauge bosons, this suppression is absent ifthe couplings are not in alignment with those of the photon. We investigate afew frequently discussed $U(1)$ models including $B-L$, $L_{\mu}-L_{\tau}$, and$L_{e}-L_{\mu(\tau)}$, and derive the stellar cooling bounds for these models.

Production rates of dark photons and $Z'$ in the Sun and stellar cooling bounds