Supernova constraint on self-interacting dark sector particles

We examine the constraints on sub-GeV dark sector particles set by the proto-neutron star cooling associated with the core-collapse supernova event SN1987a. Considering explicitly a dark photon portal dark sector model, we compute the relevant interaction rates of dark photon ($A^{\prime }$) and dark fermion ($\chi$) with the Standard Model particles as well as their self-interaction inside the dark sector. We find that even with a small dark sector fine structure constant ${\alpha }_D\ll 1$, dark sector self-interactions can easily lead to their own self-trapping. This effect strongly limits the energy luminosity carried away by dark sector particles from the supernova core and thus drastically affects the parameter space that can be constrained by SN1987a. We consider specifically two mass ratios $m_{A^{\prime }}=3m_{\chi }$ and $3m_{A^{\prime }}=m_{\chi }$ which represent scenarios where the decay of $A^{\prime }$ to $\chi \overline{\chi }$ is allowed or not. For $m_{A^{\prime }}=3m_{\chi }$, we show that this effect can completely evade the supernova bounds on widely examined dark photon parameter space for a dark sector with ${\alpha }_D\gtrsim {10}^{-7}$. In particular, for the mass range $m_{\chi }\lesssim 20\mathrm{MeV}$, supernova bounds can only be applied to weakly self-interacting dark sector with ${\alpha }_D\lesssim {10}^{-15}$. For $3m_{A^{\prime }}=m_{\chi }$, bounds in regions where ${\alpha }_D\gtrsim {10}^{-7}$ for $m_{\chi }\lesssim 20\mathrm{MeV}$ can be evaded similarly. Our findings thus imply that the existing supernova bounds on light dark particles can be generally eluded by a similar self-trapping mechanism. This also implies that nonstandard strongly self-interacting neutrino is not consistent with the SN1987a observation. Same effects can also take place for other known stellar bounds on dark sector particles.

Figure 1

Supernova profiles (density, temperature, electron chemical potential, and plasma frequency) used in this work from the $18M_{\odot }$ progenitor model in Ref. [79], extracted at the time 1 s post the core bounce. The vertical dash line indicates where the neutrinosphere is located.

Figure 2

Luminosity of different dark sector particles as a function of ${\alpha }_D$ for a fixed value of $\epsilon ={10}^{-8}$. In the left (right) panel, $m_{A^{\prime }}=9\mathrm{MeV}$ and $m_{\chi }=3\mathrm{MeV}$ ($m_{A^{\prime }}=3\mathrm{MeV}$ and $m_{\chi }=9\mathrm{MeV}$). The horizontal dotted lines label the neutrino luminosity $L_{\nu }=3\times {10}^{52}\mathrm{erg}/\mathrm{s}$ used to set the supernova bound [Eq. (2)]. The vertical dashed lines indicate the transition from the nondiffuse (smaller ${\alpha }_D)$ to the diffuse (larger ${\alpha }_D)$ regime (see text for details). Note that $\chi$ is in the nondiffuse limit for the range of ${\alpha }_D$ shown in the right panel.

Figure 3

Luminosity of different dark sector particles as a function of $\epsilon$ for fixed values of ${\alpha }_D={10}^{-17}$ (left), ${10}^{-9}$ (right). In the left (right) panel, $m_{A^{\prime }}=9\mathrm{MeV}$ and $m_{\chi }=3\mathrm{MeV}$ ($m_{A^{\prime }}=3\mathrm{MeV}$ and $m_{\chi }=9\mathrm{MeV}$). The horizontal dotted lines label the neutrino luminosity $L_{\nu }=3\times {10}^{52}\mathrm{erg}/\mathrm{s}$ used to set the supernova bound [Eq. (2)]. The vertical dashed lines indicate the transition from the nondiffuse (smaller $\epsilon$) to the diffuse (larger $\epsilon$) regime (see text for details). Note that $\chi$ is in the nondiffuse limit for the range of $\epsilon$ shown in the left panel.

Figure 4

Dark sector luminosity $L_D$ contours in the ${\alpha }_D-\epsilon$ plane for $m_{A^{\prime }}=9\mathrm{MeV}$, $m_{\chi }=3\mathrm{MeV}$ (left) and $m_{A^{\prime }}=3\mathrm{MeV}$, $m_{\chi }=9\mathrm{MeV}$ (right). Solid black (brown) curves indicate where $L_D=L_{\nu }$ ($L_D=0.1L_{\nu }$). Regions inside the $L_D=L_{\nu }$ are excluded by the supernova bound. Thin dash lines show where the transition from the nondiffuse to diffuse regime occur. See text for discussions on regions labeled (I), (II), and (A), (B).

Figure 5

The $L_D=L_{\nu }$ contour on the ${\alpha }_D-m_{\chi }$ plane for a fixed value of $\epsilon ={10}^{-8}$ and mass ratios $m_{A^{\prime }}/m_{\chi }=3$ (left), $1/3$ (right). Regions below the contours are excluded by the SN bound. Above the contours, the self-trapping of dark sector particles limit their luminosities and cannot be excluded by the supernova bound.

Figure 6

The excluded regions (enclosed by the solid curves) on the $\epsilon \text{−}{m}_{A^{\prime }}$ plane for different ${\alpha }_D$ values, with fixed mass ratios $m_{A^{\prime }}/m_{\chi }=3$ (left), $1/3$ (right). Note that we include bounds from considering the degree of freedom of dark photon only (dotted black curves) for comparison. The thin gray curve in the right panel shows regions excluded by the terrestrial experiments extracted from [83]. These curves show that even with tiny values of ${\alpha }_D$, supernova bounds on dark photon parameter space can be largely affected.