Dark Matter Clumps as Sources of Gravitational-Wave Glitches in LIGO/Virgo/KAGRA data

Abstract

We consider the hypothetical possibility that non-stationary glitch features in the noise of ground-based gravitational-wave detectors could be produced by small dark matter clumps that pass through the earth in the vicinity of gravitational-wave detectors. We first derive the gravitational-wave strain that would be generated by the passage of such a dark matter clump. We find that the strain is primarily sourced by the Newtonian gravitational acceleration of the mirrors toward the clump and by the Shapiro time delay of the photons in the laser beams as they pass through the gravitational potential created by the dark matter clump. We also find that the Newtonian acceleration effect dominates the gravitational-wave strain for both ground and space-based interferometers. We then compare our dark matter clump, gravitational-wave strain model to 84 Koi-Fish glitches detected during the second observing run of the LIGO/Virgo/KAGRA collaboration through a Markov Chain Monte Carlo Bayesian analysis. We find that all glitches but 9 can be confidently rejected as having originated from dark matter clumps. For the remaining glitches, the dark matter hypothesis cannot be excluded, and the maximum \textit{a posteriori} parameters yield minimum densities of about $10^{-7} {\rm{g}}/{\rm{cm}}^3$, within the model. These results allow us to place the first direct upper limits with gravitational-wave detectors on the local over-density of dark matter in the form of clumps in the local neighborhood of Earth, namely $ρ_{{\rm DM} \, {\rm clumps}} \lesssim 10^{-15} {\rm{g}}/{\rm{cm}}^{-3}$.

Figures (26)

• Figure 1: Time-frequency spectrogram examples for Scattered Light (left) and Koi-Fish (right) glitches. Observe how the Scattered Light event is spread over long times, while the Koi-Fish event is of much shorter duration.
• Figure 2: Left: Illustration of the Newtonian effect, wherein each mirror experiences a gravitational force toward the DM clump. Right: Illustration of the Shapiro effect, wherein a DM clump time-delays the photons in the arms. Additionally, this figure shows the system of unit vectors along the $x$, $y$, and $z$ axes that we use throughout this work.
• Figure 3: Illustration of the crossing of the DM clump through the $x$-arm, showing the three regions relevant to computing the integral of Eq. \ref{['eq:Delta_l']}. Each region is labeled with its corresponding integral term.
• Figure 4: Comparison of the Fourier transform of the strain due to the Newtonian and the Shapiro effects. The solid lines represent the Newtonian effect, while the dashed lines represent the Shapiro effect. In the left panel, we consider a DM clump with different values of its mass. This DM clump has a size of $R_{DM} < 0.5 \ \text{km}$ and passes through the detector at $x_0 = 2.0 \ \text{km}$ and $y_0 = 0.5 \ \text{km}$, with a velocity of $v_{DM} = 200 \; \text{km/s}$ perpendicular to the detector's plane. In the right panel, we consider a DM clump with different values of its radius. This DM clump has a mass of $M_{DM} = 10^8 \ \text{kg}$ and passes through the $x$ arm at $x_0 = 2.0 \ \text{km}$ and $y_0 = 0$, with a velocity of $v_{DM} = 200 \ \text{km/s}$ perpendicular to the detector's plane. Observe in the right panel that a characteristic frequency related to the radius of the DM clump, given by $v_{DM}/R_{DM}$, enters the Fourier transform of the strain in the Shapiro effect case. Observe also that, in both panels, the Newtonian effect is more significant than the Shapiro effect in the relevant frequency range, which is determined by the characteristic spectral noise density shown in black. Both the Fourier transform of the strain and the square root of the characteristic spectral noise density have units of $\text{Hz}^{-1}$.
• Figure 5: Approximate and exact Fourier transforms of the strain for the Newtonian and Shapiro effects for a DM clump with mass $M_{DM} = 10^8 \ \text{kg}$, velocity $v_{DM} = 200 \ \text{km/s}$, and location $x_0 = 2.0 \ \text{km}$ and $y_0 = 0.5 \ \text{km}$. Observe that there is good agreement between the approximate and the exact models for frequencies below $f_c = v_{DM}/L$.