Astrophysical uncertainties of dark matter direct detection experiments

The effects of astrophysical uncertainties on the exclusion limits at dark matter direct detection experiments are investigated for three scenarios: elastic, momentum dependent, and inelastically scattering dark matter. We find that varying the dark matter galactic escape velocity and the Sun’s circular velocity can lead to significant variations in the exclusion limits for light ($\lesssim 10\mathrm{GeV}$) elastic and inelastic scattering dark matter. We also calculate the limits using 100 velocity distributions extracted from the Via Lactea II and GHALO N-body simulations and find that a Maxwell-Boltzmann distribution with the same astrophysical parameters generally sets less constraining limits. The elastic and momentum dependent limits remain robust for masses $\gtrsim 50\mathrm{GeV}$ under variations of the astrophysical parameters and the form of the velocity distribution.

Figure 1

The differential scattering rate at a germanium detector for $M_{\chi }=100\mathrm{GeV}$ for elastic, inelastic, and momentum dependent (MD) spin-independent scattering. The normalization of each curve is different.

Figure 2

Varying $v_{\mathrm{esc}}$ within the 90% confidence limit found by the RAVE survey: $v_{\mathrm{esc}}=498\mathrm{km}/\mathrm{s}$ (dotted), $544\mathrm{km}/\mathrm{s}$ (solid), and $608\mathrm{km}/\mathrm{s}$ (dashed). Varying $v_{\mathrm{esc}}$ has a negligible effect on the limits for momentum dependent and elastically scattering dark matter except at low masses, where the limits are shifted horizontally by $\sim 0.5\mathrm{GeV}$. For inelastically scattering dark matter, the effect is much larger, especially for CDMS-II-Ge. The two principal features to note are a shift left (right) and down (up) when $v_{\mathrm{esc}}$ is increased (decreased).

Figure 3

The fractional change in ${\sigma }_n$ relative to value at $v_{\mathrm{esc}}=544\mathrm{km}/\mathrm{s}$ for $v_{\mathrm{esc}}=498\mathrm{km}/\mathrm{s}$ (dotted) and $v_{\mathrm{esc}}=608\mathrm{km}/\mathrm{s}$ (dashed) for inelastically scattering dark matter with $\delta =130\mathrm{keV}$. The blue, red, and green lines show the change for CDMS-II-Ge, XENON10, and CRESST-II, respectively.

Figure 4

The exclusion limits for $v_0=195\mathrm{km}/\mathrm{s}$ (dotted), $v_0=220\mathrm{km}/\mathrm{s}$ (solid), and $v_0=255\mathrm{km}/\mathrm{s}$ (dashed). Varying $v_0$ leads to a larger vertical shift in the exclusion limits compared to varying $v_{\mathrm{esc}}$ for all panels (cf. Figure 2). The horizontal shift for all experiments at masses $\sim 10\mathrm{GeV}$ for elastic and momentum dependent scattering is $\sim 1–2\mathrm{GeV}$, larger than when $v_{\mathrm{esc}}$ is varied (cf. Figure 2). In contrast, when varying $v_0$ in the inelastic case, the horizontal shift is smaller compared to varying $v_{\mathrm{esc}}$.

Figure 5

The fractional change in ${\sigma }_n$ relative to value at $v_0=220\mathrm{km}/\mathrm{s}$ for $v_0=195\mathrm{km}/\mathrm{s}$ (dotted) and $v_0=255\mathrm{km}/\mathrm{s}$ (dashed) for elastically (top panel), momentum dependent (middle panel), and inelastically scattering dark matter with $\delta =130\mathrm{keV}$ (bottom panel). The blue, brown, red, and green lines show the change for CDMS-II-Ge, CDMS-II-Si, XENON10, and CRESST-II, respectively. For clarity we only show the change for CDMS-II-Ge and XENON10 in the top panel and CDMS-II-Ge and CDMS-II-Si in the middle panel.

Figure 6

The exclusion limits from the Via Lactea II (upper panels) and ${\mathrm{GHALO}}_{\mathrm{s}}$ (lower panels) simulations. The legend is the same as Fig. 4. The solid bands shows the range of limits from the velocity distribution of 100 random spheres centered at 8.5 kpc. For comparison, the dashed line shows the limits from a Maxwell-Boltzmann velocity distribution with the same astrophysical parameters as found in the simulation halos. The Maxwell-Boltzmann distribution generally sets less constraining limits on ${\sigma }_n$.

Figure 7

The exclusion limits for CRESST-II, assuming inelastic scattering from 100 random spheres from the Via Lactea II (left panel) and $\mathrm{GHAL}{\mathrm{O}}_{\mathrm{s}}$ (right panel) simulations. The dotted red and dashed blue lines indicate the range of limits when we exclude five and 16 of the highest and lowest cross sections at each mass. For comparison, the long-dashed black line shows the limits from a Maxwell-Boltzmann distribution with the same astrophysical parameters and dispersion. At $M_{\chi }\sim 60\mathrm{GeV}$, we find that some of the spheres are not able to set any limits. As in Fig. 6, we find that the Maxwell-Boltzmann distribution generally sets less constraining limits on ${\sigma }_n$.