Revisiting Supernova 1987A Constraints on Dark Photons

TL;DR

Revisiting SN1987A constraints, the paper studies dark photons with masses below about 100 MeV, incorporating finite-temperature and density effects on the in-medium kinetic mixing. The authors compute production and absorption rates from bremsstrahlung, semi-Compton scattering, and e+e- decays, and apply Raffelt's luminosity bound with both resonant (low mixing) and nonresonant (high mixing) regimes. They quantify systematic uncertainties by using multiple proto-neutron-star profiles and different choices of the far radius, yielding a robust excluded region in the m'-epsilon plane, and highlighting the impact of non-thermal spectra on the bounds. Overall, the work tightens and clarifies the SN1987A bounds on dark photons, revealing a constant-epsilon^2 m'^2 scaling at low m' and stronger high-epsilon limits due to high-energy emission, with implications for future astrophysical probes of dark-sector physics.

Abstract

We revisit constraints on dark photons with masses below ~ 100 MeV from the observations of Supernova 1987A. If dark photons are produced in sufficient quantity, they reduce the amount of energy emitted in the form of neutrinos, in conflict with observations. For the first time, we include the effects of finite temperature and density on the kinetic-mixing parameter, epsilon, in this environment. This causes the constraints on epsilon to weaken with the dark-photon mass below ~ 15 MeV. For large-enough values of epsilon, it is well known that dark photons can be reabsorbed within the supernova. Since the rates of reabsorption processes decrease as the dark-photon energy increases, we point out that dark photons with energies above the Wien peak can escape without scattering, contributing more to energy loss than is possible assuming a blackbody spectrum. Furthermore, we estimate the systematic uncertainties on the cooling bounds by deriving constraints assuming one analytic and four different simulated temperature and density profiles of the proto-neutron star. Finally, we estimate also the systematic uncertainty on the bound by varying the distance across which dark photons must propagate from their point of production to be able to affect the star. This work clarifies the bounds from SN1987A on the dark-photon parameter space.

Figures (8)

• Figure 1: Scattering and decay processes involving $A'$ particles: (left) bremsstrahlung in neutron-proton ($n-p$) scattering, (center) "semi-Compton" scattering, and (right) decay. The bremsstrahlung diagram is accompanied by two more diagrams at the same order (the $A'$ attached to the incoming $p$ and a charge-exchange interaction). The grey blob in the bremsstrahlung diagram represents non-perturbative $n-p$ scattering. The $A'$ can be produced inside the star by bremsstrahlung and semi-Compton scattering, but inverse versions of bremsstrahlung and semi-Compton contribute to absorption of $A'$ particles on their way out of the star. Decay to $e^+e^-$, possible only for $m'>2m_e$, where $m_e$ is the electron mass, is not in equilibrium due to the low density of positrons in the proto-neutron star.
• Figure 2: Luminosity as a function of mixing angle $\epsilon$ for a fixed $m'$. Above $\epsilon_{\rm pr}(m')$, enough dark photons are produced that their luminosity may exceed $L_\nu$. For $\epsilon>\epsilon_{\rm tr}(m')$, dark photons produced far in the interior of the proto-neutron star are trapped. This means that enough of their energy will be reprocessed into neutrino energy, preventing serious energy depletion. The range $\epsilon_{\rm pr}(m') \leq \epsilon \leq \epsilon_{\rm tr}(m')$ is ruled out. If $L(m',\epsilon)$ exceeds $L_\nu$ for no value of $\epsilon$ at a given mass $m'$, there is no constraint. If we neglected the optical depth entirely, we would find that the luminosity scales like $\sim \epsilon^2$, shown as a dashed line labelled "No Trapping". Similarly, if we took the standard assumption that the emission is a blackbody spectrum from a surface at which the average dark photon has unit optical depth, we would find that the luminosity scales like $\sim e^{-\epsilon^2}$. This underestimates the contribution of very high-energy dark photons and leads to the bound shown with the dotted line labelled "Thermal Emission". The thermal emission bound is weaker than the real bound.
• Figure 3: Profiles of temperature and density for the different profiles described in Sec. \ref{['stellar-unc']}: the "fiducial model" described in Eq. (\ref{['fiducial']}), two obtained from the reference runs of Fischer:2016cyd, and one profile from NakazatoNakazato:2012qf. We cut off each plot at $R_\nu$, which we define as the radius at which the temperature is $T=3\mathop{\mathrm{MeV}}\nolimits$ for the profiles of Eq. (\ref{['fiducial']}) and Fischer:2016cyd and the radius which equals the thermal neutrino mean free path for the profile of Nakazato:2012qf. Note that the value of $R_\nu$ differs across the simulations, and in the figures each profile is scaled by its corresponding value for $R_\nu$.
• Figure 4: Frequency $\omega_*$ (solid) and velocity $v_*$ (dotted) at which the dark photon hits a resonance; we show the longitudinal (transverse) mode in blue (orange). For the longitudinal (transverse) mode, the resonant modes are on shell only if $\omega_p\geq m'$$\left(\sqrt{\frac{2}{3}}m'\leq \omega_p \leq m'\right)$.
• Figure 5: The differential power $dP/dV d\omega$ and luminosity $dL/dV d\omega$ for (left)$m'=1\mathop{\mathrm{MeV}}\nolimits$ and (right)$m'=1.1\mathop{\mathrm{MeV}}\nolimits$. The power is shown as the thick solid line. The luminosity is shown with a small (large) value of the mixing angle in dashed (dotted) lines: for $m'=1\mathop{\mathrm{MeV}}\nolimits$, small and large mixing corresponds to $\epsilon=10^{-9}$ and $10^{-5}$, respectively, while at $m'=1.1\mathop{\mathrm{MeV}}\nolimits$, small and large correspond to $\epsilon=10^{-8}$ and $10^{-6}$, respectively. The units are such that the integral of the curves together over $r$ and $\omega$ gives the luminosity of dark photons in units of $L_\nu$, so if this integral exceeds 1 the Raffelt bound is violated. The relative normalizations between curves demonstrate the effect of the overall $\epsilon$ scaling in $dP/dV d\omega$. We also compare to a Planck spectrum in the dot-dashed red line, shown at the radius $R_s$ for which the thermal luminosity $L_{\rm th}(m')= \pi^3 g_*(m') R_s^2 T(R_s)^4/30 = L_\nu$, following Rrapaj:2015wgs. At large mixing and low mass, the energy spectrum is neither resonant nor thermal: the peak of luminosity is above the Planck spectrum and above the resonance peak for large $\epsilon$ when $e^+e^-$ is not on shell. This implies stronger limits than when simply assuming a thermal spectrum --- see Sec. \ref{['DFA-breakdown']} for details.