Constraints on Axionlike Dark Matter with Masses Down to ${10}^{-23}\mathrm{eV}/c^2$

We analyzed a 6.7-yr span of data from a rotating torsion-pendulum containing $\approx {10}^{23}$ polarized electrons to search for the “wind” arising from ultralight, axionlike dark matter with masses between ${10}^{-23}$ and ${10}^{-18}\mathrm{eV}/c^2$. Over much of this range we set a 95% confidence limit $F_a/C_{\mathrm{e}}>2\times {10}^{15}\mathrm{eV}$ on the axionlike decay constant.

Figure 1

Spin pendulum. The light green and darker blue volumes are Alnico and Sm ${\mathrm{Co}}_5$, respectively. Upper left: Top view of a single magnetized “puck”; its spin moment points to the right. Lower right: The assembled pendulum with its magnetic shield shown cut-away to reveal the four pucks inside. Two of the four mirrors (light gold) used to monitor the pendulum twist are prominent. Arrows with filled heads show the relative densities and directions of the electron spins, open-headed arrows show the directions of $\mathit{B}$. The pucks are arranged so that the spin dipole is centered on the pendulum, and the different materials have a vanishing composition-dipole moment. The eight tabs on the shield held small screws that were used to tune out the pendulum’s residual $q_{21}$ gravitational moment. The 103 g pendulum had a rotational inertia of $169\mathrm{g}{\mathrm{cm}}^2$.

Figure 2

${\beta }_N$ and ${\beta }_W$ values from all 241 subsets. The different subsets have varying noise levels which are reflected in the assigned uncertainties (not shown).

Figure 3

Upper two panels: Histograms of $a_{\mathrm{X}\cos }$ and $a_{\mathrm{X}\sin }$ coefficients for ${10}^{-8}\le f_a\le {10}^{-4}\mathrm{Hz}$. Results for $a_{Y\cos }$ and $a_{Y\sin }$ are very similar. All four quadrature amplitudes are characterized by zero-mean Gaussians with $\sigma =0.154\mathrm{z}\mathrm{eV}$. Lower panel: Histogram of corresponding $a_X$ amplitudes. The results follow the expected Rayleigh distribution, the 95%-confidence upper limit on $a_X$ (as well as on $a_Y$) is 0.38 zeV.

Figure 4

Spectral distribution of $a_X$. The lighter (orange) jagged line shows the fit amplitudes. The two smooth lines show the sensitivities of the analysis. The lower (blue) smooth curve shows the 95% C.L. Rayleigh uncertainties in the individual fit amplitudes while the upper red curve contains a trials penalty. Absent a signal, the Rayleigh distribution predicts that 5% of the amplitudes will lie above the lower curve and that there is a 5% probability that a single amplitude anywhere in our frequency range will lie above the upper curve; as expected no amplitude exceeds the upper curve. The darker (blue) jagged line shows the result of adding to our ${\beta }_N$ and ${\beta }_W$ data a synthetic $1\mu \mathrm{Hz}$ $X_{\cos }$ signal with an amplitude of 2.5 zeV. The extracted amplitude, $2.498\pm 0.144\mathrm{z}\mathrm{eV}$, is resolved at $17\sigma$. Small satellite peaks in the synthetic signal arise from gaps in our time-series data.

Figure 5

95%-confidence constraints on $C_e/F_a$. The color coding of the lines is identical to that in Fig. 4. The structure near $m_a=47\mathrm{z}\mathrm{eV}$ is the sidereal bump and the smooth increase at the highest masses reflects the signal attenuation due to finite measurement durations. The jagged black line shows the 95% C.L. upper limit as a function of $m_a$ computed from the Rice distribution [25] (the generalization of the conventional $\text{mean}+2\sigma$ appropriate for quadrature amplitudes). For clarity, starting at $m_a>2\mathrm{z}\mathrm{eV}$ we averaged adjacent points. See Supplemental Material [26] for the unaveraged values. Absent a signal, the Rayleigh distribution predicts that 5% of the unaveraged amplitudes (orange) should lie above the $2.45\sigma$ line (in fact for the top, middle, and bottom panels 4.8%, 5.2%, and 5.2% do); and that there is only a 5% chance that a single unaveraged amplitude anywhere in the distribution should lie above the $5.32\sigma$ line (in fact none do). The dashed line shows $C_n/F_a$ constraints from an axion-wind analysis [12] of neutron electric-dipole data. The black horizontal line shows the constraint from a spin-spin force experiment [27]. The shaded green region is disfavored by stellar cooling [28].