Search for an Ultralight Scalar Dark Matter Candidate with the AURIGA Detector

A search for a new scalar field, called moduli, has been performed using the cryogenic resonant-mass AURIGA detector. Predicted by string theory, moduli may provide a significant contribution to the dark matter (DM) component of our Universe. If this is the case, the interaction of ordinary matter with the local DM moduli, forming the Galaxy halo, will cause an oscillation of solid bodies with a frequency corresponding to the mass of moduli. In the sensitive band of AURIGA, some 100 Hz at around 1 kHz, the expected signal, with $Q=△f/f\sim 10^6$, is a narrow peak, $△f\sim 1\mathrm{mHz}$. Here the detector strain sensitivity is $h_s\sim 2\times {10}^{-21}{\mathrm{Hz}}^{-1/2}$, within a factor of 2. These numbers translate to upper limits at 95% C.L. on the moduli coupling to ordinary matter $(d_e+d_{m_e})\lesssim {10}^{-5}$ around masses $m_{\varphi }=3.6\times {10}^{-12}\mathrm{eV}$, for the standard DM halo model with ${\rho }_{\mathrm{DM}}=0.3\mathrm{GeV}/{\mathrm{cm}}^3$.

Figure 1

Scheme of the gravitational wave detector AURIGA. The system comprises three coupled resonators with nearly equal resonant frequency of about 900 Hz: the first longitudinal mode of the cylindrical bar, the first flexural mode of the mushroom-shaped resonator, which is also one of the plates of the electrostatic capacitive transducer, and the low-loss electrical $LC$ circuit. The electrical current of the $LC$ resonator is detected by a low noise dc SQUID amplifier.

Figure 2

Frequency spectrum of the bar relative deformation computed on August 2015 AURIGA data (blue curve), obtained by averaging $N=400$ power spectrums from one-hour-long data streams. The experimental result is compared to the predicted noise power spectrum density by Fluctuation-Dissipation theorem (red line), showing a good matching. The thickness of the data curve is due to the noise variance, reduced by averaging the power spectrums. Holes in data correspond to excluded spurious peaks associated with the known external background. Moreover, these spurious peaks have shape and width not matching the expectation from the moduli signal [see Fig. 3].

Figure 3

(blue triangle) Simulation of a moduli signal with moduli couplings $(d_e+d_{m_e})=5\times {10}^{-4}$ and frequency $f_{\varphi }\backsimeq 867\mathrm{Hz}$ plus white noise with standard deviation $\sigma =2\times {10}^{-21}{\mathrm{Hz}}^{-1/2}$, equal to the detector noise level at $f_{\varphi }$. (red circle) Same simulated signal injected into the real data. The signal is a narrow peak with a $△f\backsimeq 1\mathrm{mHz}$ bandwidth and spread around about 10 bins. (green line) Plot of the power density spectrum in Eq. (5) plus a constant accounting for the white noise with the same parameters of the simulation.

Figure 4

Distributions of the possible values of three generic bins in the relative bar deformation spectrum shown in Fig. 2. The distributions are well fitted by a Gaussian (red lines) with a mean equal to the noise level at the considered bin frequency and a standard deviation the standard deviation of the noise: (left) $f=857\mathrm{Hz}$, $⟨h^2⟩=2.1\times {10}^{-41}{\mathrm{Hz}}^{-1}$, ${\sigma }_{h^2}=1.0\times {10}^{-42}{\mathrm{Hz}}^{-1}$, ${\chi }^2/ndf=12.2/8$; (center) $f=890\mathrm{Hz}$, $⟨h^2⟩=2.1\times {10}^{-41}{\mathrm{Hz}}^{-1}$, ${\sigma }_{h^2}=1.1\times {10}^{-42}{\mathrm{Hz}}^{-1}$, ${\chi }^2/ndf=4.8/5$; (right) $f=940\mathrm{Hz}⟨h^2⟩=8.1\times {10}^{-42}{\mathrm{Hz}}^{-1}$, ${\sigma }_{h^2}=3.8\times {10}^{-43}{\mathrm{Hz}}^{-1}$, ${\chi }^2/ndf=8.3/7$.

Figure 5

Upper limits on the sum of the moduli couplings ($d_e+d_{m_e}$) to ordinary matter (red curve) obtained from AURIGA data and reported in the moduli parameter space: bottom and top horizontal axes represent the moduli mass $m_{\varphi }$ and corresponding frequency $f_{\varphi }=m_{\varphi }/2\pi$, vertical axis represents the sum of moduli coupling $(d_e+d_{m_e})$ values. Depicted green area shows the natural parameter space preferred by theory. Other regions represent 95% C. L. limits on fifth-force tests (5F, gray) and equivalence-principle tests (EP, orange): continuous curves ($5\mathrm{F}\text{−}{d}_{m_e}$ and $\mathrm{EP}\text{−}{d}_{m_e}$) refer to upper limits on $d_{m_e}$, whereas dashed curves ($5\mathrm{F}\text{−}{d}_e$ and $\mathrm{EP}\text{−}{d}_e$) refer to upper limits on $d_e$.