Prospects for Detecting Gravitational Waves at 5 Hz with Ground-Based Detectors

We propose an upgrade to Advanced LIGO (aLIGO), named LIGO-LF, that focuses on improving the sensitivity in the 5–30 Hz low-frequency band, and we explore the upgrade’s astrophysical applications. We present a comprehensive study of the detector’s technical noises and show that with technologies currently under development, such as interferometrically sensed seismometers and balanced-homodyne readout, LIGO-LF can reach the fundamental limits set by quantum and thermal noises down to 5 Hz. These technologies are also directly applicable to the future generation of detectors. We go on to consider this upgrade’s implications for the astrophysical output of an aLIGO-like detector. A single LIGO-LF can detect mergers of stellar-mass black holes (BHs) out to a redshift of $z\simeq 6$ and would be sensitive to intermediate-mass black holes up to $2000M_{\odot }$. The detection rate of merging BHs will increase by a factor of 18 compared to aLIGO. Additionally, for a given source the chirp mass and total mass can be constrained 2 times better than aLIGO and the effective spin 3–5 times better than aLIGO. Furthermore, LIGO-LF enables the localization of coalescing binary neutron stars with an uncertainty solid angle 10 times smaller than that of aLIGO at 30 Hz and 4 times smaller when the entire signal is used. LIGO-LF also significantly enhances the probability of detecting other astrophysical phenomena including the tidal excitation of neutron star $r$ modes and the gravitational memory effects.

Figure 1

Proposed sensitivity for LIGO-LF (solid black line) and its noise budget (dashed lines). Also shown in the dotted red curve is the spectrum of a $200M_{\odot }–200M_{\odot }$ binary BH merger (in the detector frame) at 10 Gpc. LIGO-LF’s sensitivity to such systems is greatly enhanced relative to aLIGO (solid blue line) and $\mathrm{A}+$ (solid magenta line). Throughout this Letter, we will adopt the same coloring convention when we compare different sensitivities (i.e., we use black, magenta, and blue for LIGO-LF, $\mathrm{A}+$, and aLIGO, respectively).

Figure 2

Inertial sensor noise for aLIGO (blue line) and the requirement for LIGO-LF (black line). Custom tiltmeters can be used to improve aLIGO sensor noise below 0.5 Hz (blue dashed line). A novel 6D seismometer (red line) can surpass the requirement in the entire band.

Figure 3

Left: The horizon (solid line) and range (dashed line) for binaries with different (source-frame) total masses. A single LIGO-LF may reach a cosmological redshift of $z\simeq 6$. Right: Expected detection rate of coalescing stellar-mass BH binaries as a function of the total mass. We divide $M_1$ and $M_2$ each into eight logarithmic bins from $10M_{\odot }$ to $100M_{\odot }$ and marginalize over the mass ratio to derive the event rate per total mass bin. LIGO-LF can detect $\sim 4000$ events per year, 18 times more than the expected number for aLIGO. All the numbers are calculated assuming a single detector.

Figure 4

The 90% credible intervals of the detector-frame chirp mass ${\mathcal{M}}_c^{(d)}$ (top left), total mass $M_{\mathrm{tot}}^{(d)}$ (top right), and effective spin ${\chi }_{\mathrm{eff}}$ (bottom) are all significantly smaller for LIGO-LF than for aLIGO. LIGO-LF also reduces biases, especially for ${\mathcal{M}}_c^{(d)}$ and ${\chi }_{\mathrm{eff}}$ when the spin is antialigned (bottom left).

Figure 5

Left: The cumulative uncertainty in localization, $\mathrm{\Delta }{\mathrm{\Omega }}_s$, for the HLIV network. We consider NS binaries at the Coma cluster with two inclinations, 30° (solid line) and 75° (dashed line), and marginalize over the polarization and time of arrival. LIGO-LF improves the localization by a factor of 3.5 over aLIGO using the entire signal and by a factor of 5 over $\mathrm{A}+$ using only the sub-30 Hz data. Right: The uncertainty (solid line) in measuring the phase shift due to the resonant excitation of the NS $r$ mode $\delta {\mathrm{\Phi }}_r$ as a function of the NS spin frequency $f_{\mathrm{spin}}$. We consider the single detector case and fix the sources at 50 Mpc with optimal orientation. Also shown in the red dashed line is the expected physical $r$-mode phase shift. The effect is detectable when the real phase shift is greater than the statistical error.

Figure 6

SNR from the GW memory effect as a function of the source-frame total mass. The sources are fixed at $z=0.1$ and an inclination of 30°. The peak SNR seen in LIGO-LF is 4 (2) times greater than that seen in aLIGO ($\mathrm{A}+$).