Gravimeter Search for Compact Dark Matter Objects Moving in the Earth

Dark matter could be composed of compact dark objects (CDOs). These objects may interact very weakly with normal matter and could move freely inside the Earth. A CDO moving in the inner core of the Earth will have an orbital period near 55 min and produce a time-dependent signal in a gravimeter. Data from superconducting gravimeters rule out such objects moving inside the Earth unless their mass $m_D$ and or orbital radius $a$ are very small so that $m_{D}a<1.2\times {10}^{-13}{M}_{\oplus }{R}_{\oplus }$. Here, $M_{\oplus }$ and $R_{\oplus }$ are the mass and radius of the Earth, respectively.

Figure 1

Density of the Earth $\rho (r)$ versus radius $r$ (solid black line) [31]. The dotted blue line shows the average density (of matter interior to $r$) $\overline{\rho }(r)$. Finally, the orbital frequency $\nu$ for a circular orbit inside the Earth of radius $r$ is shown as the dashed red line using the right-hand scale.

Figure 2

Fourier amplitude spectrum of gravity residuals at station BFO versus frequency, solid black. The time series starts on July 20, 2011 and is 6.7 years long. The gravity data have been corrected for the atmospheric pressure with an admittance of $-3.0\mathrm{nm}{\mathrm{s}}^{-2}/\mathrm{hPa}$. The red line with a cross shows calibration injections at a frequency of 0.303 mHz with an amplitude of $3\mathrm{pm}/{\mathrm{s}}^2$ and different phases shown by the blue band.

Figure 3

Fourier amplitude spectrum of pressure-corrected gravity residuals at station CB similar to Fig 2. The dataset starts on January 1, 2010 and is nine years long. The spectrum of one sinusoid at 0.3 mHz with the same data gaps and the same tapering as the gravity residuals is shown in red. Its amplitude is $7\mathrm{pm}/{\mathrm{s}}^2$.

Figure 4

Power spectral density of pressure-corrected gravity residuals at BFO for the CDO target frequency band. The longer dataset includes the magnitude Mw9.1 Tohoku event (March 11, 2011) and shows four out of the five singlets of the rotationally split fundamental spheroidal mode ${}_0{S}_2$. The longer dataset starts on October 1, 2010 and the shorter on July 20, 2011. They are 7.5 and 6.7 years long, respectively.