Astrophysics-Independent Bounds on the Annual Modulation of Dark Matter Signals

We show how constraints on the time integrated event rate from a given dark matter (DM) direct detection experiment can be used to bound the amplitude of the annual modulation signal in another experiment. The method requires only mild assumptions about the properties of the local DM distribution: that it is temporally stable on the scale of months and spatially homogeneous on the ecliptic. We apply the method to the annual modulation signal in DAMA/LIBRA, which we compare to the bounds derived from XENON10, XENON100, cryogenic DM search, and SIMPLE data. Assuming a DM mass of 10 GeV, we show that under the above assumptions about the DM halo, a DM interpretation of the DAMA/LIBRA signal is excluded for several classes of models: at $6.3\sigma$ ($4.6\sigma$) for elastic isospin conserving (violating) spin-independent interactions, and at $4.9\sigma$ for elastic spin-dependent interactions on protons.

Figure 1

$3\sigma$ upper bounds on $\tilde{\eta }$. The modulation amplitude ${\tilde{A}}_{\eta }$ is shown for DAMA (for $q_{\mathrm{Na}}=0.3$) and CoGeNT for both free phase fit (general) and fixing the phase to June 2nd (symmetric). We assume a DM mass of 10 GeV and SI interactions.

Figure 2

Integrated modulation signals, ${\int }_{v_1}^{v_2}dv{A}_{\tilde{\eta }}$, from DAMA and CoGeNT compared to the $3\sigma$ upper bounds for the general halo, Eq. (6). We assume SI interactions and a DM mass of 10 GeV. The integral runs from $v_1=v_{\min }$ to $v_2=743\mathrm{km}/\mathrm{s}$ (end of the 12th bin in DAMA).

Figure 3

Integrated modulation signal ${\int }_{v_{\min }}^{v_2}dv{A}_{\tilde{\eta }}$ from DAMA compared to the $3\sigma$ upper bounds for the general halo, Eq. (6) (solid), and symmetric halo, Eq. (7) with $\sin \alpha =0.5$ (dotted). We assume a DM mass of 10 GeV, and SD interactions on protons (upper panel) and SI interactions with $f_n/f_p=-0.7$ (lower panel).

Figure 4

The probability that the integrated modulation amplitude in DAMA (summed starting from the third bin) is compatible with the bound derived from the constraints on $\tilde{\eta }$ for various experiments as a function of the DM mass. The label SI (SD), refers to spin-independent (spin dependent) interactions with $f_n=f_p$ ($f_n=0$), and IV refers to isospin-violating SI interactions with $f_n/f_p=-0.7$. For solid and dashed curves we use the bounds from Eqs. (6, 7), respectively.