Gamma rays from dark mediators in white dwarfs

We consider self-annihilation of dark matter, $\chi$, into metastable mediators, $Y$, and their subsequent decay into photons inside white dwarfs. We focus on reactions of the type $\chi \overline{\chi }\to YY$, where mediators, besides having a finite decay lifetime at rest ${\tau }_{\mathrm{rest}}\lesssim 1\mathrm{s}$, may suffer energy loss in the medium before they decay into photons, $Y\to \gamma \gamma$. We obtain attenuated gamma-ray luminosities arising from the combination of both effects. Using complementary sets of astrophysical measurements from cold white dwarfs in the M4 globular cluster as well as direct and indirect dark matter searches, we discuss further constraints on dark mediator lifetimes.

Figure 1

In-medium dark mediator velocity as a function of the radial distance inside the WD for $m_{\chi }=500\mathrm{MeV}$ and $m_Y=10\mathrm{MeV}$. We fixed ${\sigma }_{Y,N}={\sigma }_{\chi ,N}={10}^{-38}$, ${10}^{-39}$, ${10}^{-40}{\mathrm{cm}}^2$ with dot-dashed, dotted and dashed lines, respectively. See text for details.

Figure 2

Energy flux at distance $d=2R$ due to DM annihilation as a function of the photon energy for different values of ${\tau }_{\mathrm{rest}}=0.8\mathrm{s}$ (solid lines) and ${\tau }_{\mathrm{rest}}=0.1\mathrm{s}$ (dashed lines). It is normalized to the product $2{\mathrm{\Gamma }}_{\mathrm{ann}}{m}_{\chi }$. We consider two values for the ${\sigma }_{\chi ,N}={10}^{-39}{\mathrm{cm}}^2$ (green) and ${\sigma }_{\chi ,N}=5\times {10}^{-39}{\mathrm{cm}}^2$ (magenta). We assume ${\sigma }_{\chi ,N}={\sigma }_{Y,N}$ and fix $m_{\chi }=800\mathrm{MeV}$ and $m_Y=100\mathrm{MeV}$. See text for details.

Figure 3

WD internal luminosity due to DM annihilation as a function of the WD mass for different values of ${\tau }_{\mathrm{rest}}=0.001$, 0.01, 0.1, 1 s using $m_{\chi }=500\mathrm{MeV}$ and mediator masses, $m_Y=375\mathrm{MeV}$ (solid lines) and $m_Y=10\mathrm{MeV}$ (dash-dotted lines). We fixed ${\sigma }_{\chi ,N}={\sigma }_{Y,N}={10}^{-39}{\mathrm{cm}}^2$. Red points are experimental data for M4 GC from [6].

Figure 4

Constraints for the mediator lifetime as a function of DM-nucleon cross section for the case $m_Y/m_{\chi }\to 1$. We fixed ${\sigma }_{\chi ,N}={\sigma }_{Y,N}$. Colored region depicts the excluded parameter space, see the text for more details. Green line is a lower limit signaling where the mediator scatters at least once in the WD.

Figure 5

${\tau }_{\text{limit}}$ (boundary of excluded ${\tau }_{\mathrm{rest}}$ region) as a function of the ratio $m_Y/m_{\chi }$ for different values of ${\sigma }_{\chi ,N}$,${\sigma }_{Y,N}$. See text for details.