White dwarfs as dark matter detectors

Dark matter that is capable of sufficiently heating a local region in a white dwarf will trigger runaway fusion and ignite a type Ia supernova. This was originally proposed by Graham et al. and used to constrain primordial black holes which transit and heat a white dwarf via dynamical friction. In this paper, we consider dark matter (DM) candidates that heat through the production of high-energy standard model (SM) particles, and show that such particles will efficiently thermalize the white dwarf medium and ignite supernovae. Based on the existence of long-lived white dwarfs and the observed supernovae rate, we derive new constraints on ultraheavy DM with masses greater than $10^{16}\mathrm{GeV}$ which produce SM particles through DM-DM annihilations, DM decays, and DM-SM scattering interactions in the stellar medium. As a concrete example, we place bounds on supersymmetric Q-ball DM in parameter space complementary to terrestrial bounds. We put further constraints on DM that is captured by white dwarfs, considering the formation and self-gravitational collapse of a DM core which heats the star via decays and annihilations within the core. It is also intriguing that the DM-induced ignition discussed in this work provide an alternative mechanism of triggering supernovae from sub-Chandrasekhar, nonbinary progenitors.

Figure 1

The minimum energy deposit (2) necessary to trigger runaway fusion, based on numerical results for ${\lambda }_T$ [15] and the WD mass-density relation [21].

Figure 2

Dominant energy loss and thermalization processes in the WD as a function of energy, with energy decreasing toward the right. Hadronic processes are shown in the upper panel and EM processes in the lower panel. High energy particles will induce showers that terminate into elastic thermalization of the WD ions, moving from left to right in the diagram. The quoted energies are for a $\sim 1.37M_{\odot }$ WD, although the cartoon is qualitatively the same for all densities.

Figure 3

Stopping lengths for incident hadrons as a function of kinetic energy in a WD of density $n_{\mathrm{ion}}\sim {10}^{31}{\mathrm{cm}}^{-3}$ ($\approx 1.25M_{\odot }$), including the hadronic shower length (magenta). Any discontinuities in the stopping lengths are due to approximate analytic results in the different energy regimes. See Appendix pp1 for calculation details.

Figure 4

Stopping lengths of incident photons (orange) and electrons (purple) as a function of kinetic energy in a WD of density $n_{\mathrm{ion}}\sim {10}^{31}{\mathrm{cm}}^{-3}$ ($\approx 1.25M_{\odot }$), including the EM shower length (dashed). Any discontinuities in the stopping lengths are due to approximate analytic results in the different energy regimes. See Appendix pp1 for calculation details.

Figure 5

Photonuclear (left) and electronuclear (right) interactions. The shaded region contains, at high energies, the familiar pointlike processes of deep inelastic scattering and for energies below ${\mathrm{\Lambda }}_{\mathrm{QCD}}$ is best described by exchange of virtual mesons.

Figure 6

Constraints on DM-carbon elastic scattering cross section. Bounds come from demanding that the DM transit triggers runaway fusion (15) and occurs at a rate (17) large enough to either ignite a $1.25M_{\odot }$ WD in its lifetime or exceed the measured SN rate in our galaxy (blue shaded). We also demand that the DM penetrates the nondegenerate stellar envelope, taken at the highest densities, without losing appreciable kinetic energy. Constraints from the CMB/large-scale structure [34] are depicted as well.

Figure 7

Constraints on DM-DM collision cross section to SM products of energy $\epsilon \gg \mathrm{MeV}$. Bounds come from demanding that the DM transit interaction triggers runaway fusion (18) and occurs at a rate (19) large enough to either ignite an observed $1.25M_{\odot }$ WD in its lifetime or exceed the measured SN rate in our galaxy (blue shaded). Also shown are the CMB [35] (red) and CR flux (black) constraints on DM annihilations.

Figure 8

Constraints on DM decay to SM products of energy $\epsilon \gg \mathrm{MeV}$. Bounds come from demanding that the DM transit interaction triggers runaway fusion (18) and occurs at a rate (20) large enough to either ignite an observed $1.25M_{\odot }$ WD in its lifetime or exceed the measured SN rate in our galaxy (blue shaded). Also shown are the CMB [36] (red) and CR flux (black) constraints on DM lifetime.

Figure 9

Constraints on DM-DM collision cross section to SM products of energy $\epsilon \gg \mathrm{MeV}$, assuming DM is captured with an elastic scattering cross section ${\sigma }_{\chi n}={10}^{-32}{\mathrm{cm}}^2$. Bounds come from the observation of $1.25M_{\odot }$ WDs in local DM density. We consider the annihilation rate during the in-falling thermalization stage (27) (blue shaded) and during self-gravitational collapse (28) to a stable radius $r={10}^{-10}\mathrm{cm}$ (green shaded). See text for details.

Figure 10

Constraints on DM decay to SM products of energy $\epsilon \gg \mathrm{MeV}$, assuming DM is captured with an elastic scattering cross section ${\sigma }_{\chi n}={10}^{-32}{\mathrm{cm}}^2$. Bounds come from the observation of $1.25M_{\odot }$ WDs in local DM density. We consider the rate of decays during the in-falling thermalization stage (blue shaded) and for a decaying DM core (green shaded). See text for details.

Figure 11

Viable parameter space (above the black line) in which DM-nucleon elastic scattering leads to DM capture in a $1.25M_{\odot }$ WD. All of this space is subject to constraints on DM decay and DM-DM annihilation analogous to those given in Figs. 10 and 9. Note the blue region, reproducing Fig. 6, indicates DM which causes SN via elastic heating. We also indicate here estimates of the scattering constraints from cosmology, direct detection, MACRO, and ancient mica [42].

Figure 12

Interaction of a baryonic Q-ball with a nucleus $A$. The Q-ball destroys the nucleus and absorbs its baryonic charge, while the excess energy is radiated into roughly $A$ outgoing pions of energy ${\mathrm{\Lambda }}_{\mathrm{QCD}}$.

Figure 13

Constraints on Q-ball DM. Bounds come from demanding that the Q-ball interaction during a DM transit is capable of igniting WDs, occurring at a rate large enough to either ignite a single observed $1.25M_{\odot }$ WD in its lifetime (WD in local DM density is blue shaded) or exceed the measured SN rate in our galaxy. Also shown is the corresponding constraint from gravitational heating of WDs (orange shaded), and existing limits from terrestrial detectors (red) [46].