4 spin-dependent couplings to protons, and not neutrons, can give a good fit to the DAMA data whilst remain- ing consistent with other experiments. This scenario is subject to limits from scattering in the Sun [10] however limits from capture in WDs should be weak as WDs are mostly composed of $^{12}$C and $^{16}$O which have no nuclear spin. It is tempting to consider limits from scattering on $^{13}$C which makes up ∼ 1% of all carbon and has nuclear spin I = 1 / 2, however this spin is carried by an unpaired neutron and thus the scenario described in [45] will lead to negligible capture rates in WDs. Therefore we only consider spin-independent scattering iDM in this work. To calculate the capture rate in a WD we use the equa- tions contained in Section II. of [10]. To take account of the incoherent scattering of DM in the nucleus we also use the Helm form factor [56] and follow [2] in making the conservative assumption that the WDs are entirely composed of carbon. We also assume the DM couplings to neutrons and protons are the same. This can be cor- rected for specific models by re-scaling the cross-section accordingly. To find the DM velocity dispersion we make the as- sumption of hydrostatic equilibrium and integrate the hydrostatic equation for spherical geometry using the baryon and DM distributions shown in Fig. 1. We find that the DM velocity dispersion doesn’t exceed 8 km s − 1 and, as the capture rate decreases with increasing disper- sion, we set v$_{0}$ to this value. Similarly the WD velocity through the DM is likely to be of the order of the veloc- ity dispersion and we find this doesn’t exceed 6 km s − $^{1}$, however to set conservative limits we set v$_{⋆}$ = 20 km s − 1 which is the escape velocity at the inner radius at which the WDs are observed. We calculate the escape velocity and density of nuclei within a given WD using the Salpeter equation of state [17]. Due to the large escape velocity of a WD the typ- ical kinetic energy of an in-falling DM particle is of the order ∼ 1 MeV. Therefore all of the in-falling particles easily have enough kinetic energy to overcome the inelas- tic splitting and scatter. This makes the inelastic split- ting relatively unimportant up to splittings δ ∼ 1 MeV, where the capture rate starts to decrease. This is shown in Fig. 2. Although the splittings associated with iDM are much too small to decrease the capture rate signifi- cantly we include them in our calculations for the sake of thoroughness. The capture rate typically falls as the inverse of the DM mass, therefore the luminosity should be largely in- dependent of the DM mass. However there is a subtle in- terplay between two factors which leads to a dependence not only on the DM mass but also on the WD mass. The first factor is due to the conversion between a DM- nucleon and DM-nucleus cross-section at zero momentum transfer, which results in a factor of σ$_{χN}$ ∝ ( µ$_{χN}$ /µ$_{χn}$ ) 2 where µ is the reduced mass and N ( n ) subscripts denote the nucleus (nucleon). This factor has a preference for heavy DM particles. However there is also suppression due to the nuclear form factor [57]. Therefore, although We will now discuss some of the assumptions that have gone into this calculation. The greatest source of uncer- tainty is the estimation of the DM density. It should be noted that there are some models where globular clusters are not formed due to the collapse of a DM dominated halo, in particular the observations made by Gilmore and As described in [2] the time-scale for equilibrium be- tween the capture and annihilation of DM in WDs is roughly of the order of one year, and therefore we can safely assume that the capture rate is one-half of the anni- hilation rate. We also assume that all of the energy of the annihilating particles contributes to the black-body lumi- nosity of the WDs, however specific DM models could be investigated by calculating the fraction of energy lost as neutrinos per annihilation and weakening the limits ac- cordingly. Which of these two factors wins out depends on the WD mass. As heavy WDs have greater escape veloci- ties ( ∼ (7 − 12) × 10 3 km s − $^{1}$), heavy DM particles feel the form factor suppression more and light DM particles lead to greater luminosities. For light WDs the escape velocities are lower ( ∼ (2 − 3) × 10 3 km s − $^{1}$) the form factor suppression is subdominant and heavier DM par- ticles lead to a greater luminosity. The mass dependence for two different WDs is illustrated in Fig. 3. heavier DM particles have a larger range of scattering energies, the higher energy events are suppressed. This effect therefore discriminates against heavy DM particles. FIG. 2: The DM capture rate for a solar mass WD as a function of inelastic splitting δ . The DM parameters are m$_{χ}$ = 50 GeV and σ$_{n}$ = 10 − 41 cm $^{2}$. The capture rate is largely independent of the inelastic splitting up to δ ∼ 1 MeV, when it starts to fall off rapidly. 1 10 100 1000 10 4 0.2 0.5 1.0 2.0 5.0 10.0 d @ keV D Capture Rate @ 10 30$^{s}$ - 1 D V. UNCERTAINTIES