Search for a stochastic gravitational wave background at 1–5 Hz with a torsion-bar antenna

We set the first upper limit on the stochastic gravitational wave (GW) background in the frequency range of 1–5 Hz using a torsion-bar antenna (TOBA). A TOBA is a GW detector designed for the detection of low frequency GWs on the ground, with two orthogonal test masses rotated by the incident GWs. We performed a 24-hour observation run using the TOBA and set upper limits, based on frequentist statistics and Bayesian statistics. The most stringent values are ${\mathrm{\Omega }}_{\mathrm{gw}}{h}_0^2\le 6.0\times 10^{18}$ (frequentist) and ${\mathrm{\Omega }}_{\mathrm{gw}}{h}_0^2\le 1.2\times 10^{20}$ (Bayesian) both at 2.58 Hz, where $h_0$ is the Hubble constant in units of $100\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$ and ${\mathrm{\Omega }}_{\mathrm{gw}}$ is the GW energy density per logarithmic frequency interval in units of the closure density.

Figure 1

Principle of a TOBA. Two orthogonal test masses are rotated differentially by the tidal force (dotted lines) of the incident GW (wavy line). In the case of the GW along the z-axis, the horizontal rotation angle ${\theta }_1(=-{\theta }_2)$ is proportional to the GW amplitude while the vertical rotation angles ${\varphi }_1={\varphi }_2=0$.

Figure 2

Observed spectral density of GW equivalent strain amplitude by the upgraded TOBA. The solid line is the mean sensitivity and the gray region includes 90% data. The dashed line is the strain level corresponding to ${\mathrm{\Omega }}_{\mathrm{gw}}{h}_0^2=10^{18}$. The light gray region is the analysis frequency band.

Figure 3

Histogram of ${\mathrm{\Omega }}_{\mathrm{gw}}{h}_0^2$ at 2.58 Hz. The inset shows an expanded region. The dashed line is ${\mathrm{\Omega }}_{\mathrm{gw}}{h}_0^2=5.3\times 10^{18}$, below which 95% of the data are contained.

Figure 4

Rate $C$ at 2.58 Hz. The inset shows an expanded region near $C=0.95$. The solid line is the result of a least-squares fit to the data that are included only within the range of the inset. As a result, we obtain the Bayesian upper limit of ${\mathrm{\Omega }}_{\mathrm{gw}}^{\mathrm{B}}{h}_0^2=1.04_{-0.01}^{+0.02}\times 10^{20}$.

Figure 5

Upper limits of ${\mathrm{\Omega }}_{\mathrm{gw}}{h}_0^2$ at the 95% confidence level. The most stringent constraints are ${\mathrm{\Omega }}_{\mathrm{gw}}^{\mathrm{F}}{h}_0^2=6.0\times 10^{18}$ and ${\mathrm{\Omega }}_{\mathrm{gw}}^{\mathrm{B}}{h}_0^2=1.2\times 10^{20}$ both at 2.58 Hz.

Figure 6

Current upper limits on the energy density of the SGWB. The bold line is our new upper limit (frequentist).