Gravitational Wave Memory of Primordial Black Hole Mergers

TL;DR

The paper analyzes gravitational wave memory for mergers of light primordial black holes and compares its detectability to the inspiral signal at low frequencies. It develops memory waveform templates that include detector response effects for LIGO and LISA, and combines these with PBH merger rates from an early-universe formation scenario to predict detectable event numbers. The findings indicate that, for subsolar PBHs within current and near-future detectors, the inspiral signal typically yields higher signal-to-noise ratios, while memory provides a universal, potentially out-of-band signature that could enable matched-filter searches in multi-band setups. These results inform strategies for multi-band gravitational wave observations and offer a pathway to constrain primordial black hole populations and their role in dark matter.

Abstract

The gravitational wave signal of binary compact objects has two main contributions at frequencies below the characteristic merger frequency: the gravitational wave signal associated with the early inspiral stage of the binary and the non-linear gravitational wave memory. We compare the sensitivity of upcoming gravitational wave detectors to these two contributions, with a particular interest in events with a merger phase at frequencies higher than the detector's peak sensitivity. We demonstrate that for light primordial black holes, current and upcoming detectors are more sensitive to the inspiral signal. Our analysis incorporates the evolution history of primordial black hole binaries, key to accurately estimating the relevant event rates. We also discuss the waveform templates of the memory signal at ground- and space-based interferometers, and the implications for a matched filtering search. This allows us to compare the sensitivity of high-frequency gravitational wave detectors, sensitive to the merger phase, with the sensitivity of existing interferometers.

Figures (7)

• Figure 1: Comparison between the dominant oscillatory gravitational waveform $({\rm main} )$ associated with the (2,2) mode, and the memory waveform $({\rm mem})$ for an edge-on system. For reference, we also include the analytical approximation of the memory from Eq. \ref{['eq:memapproxTD']}, using a characteristic rise time of $\Delta\tau = 13M$.
• Figure 2: Characteristic strain in frequency domain for the system shown in Fig. \ref{['fig:IMMplot']}, comparing the main oscillatory signal, the memory, and its analytical approximation. We find that Eq. \ref{['eq:memapproxTD']} with $\Delta \tau \sim 13M$ provides a good fit to the memory signal, particularly in capturing the decay at frequencies above $f_{\rm decay} = (60M)^{-1}$. At low frequencies, the characteristic strain approaches a constant value set by the final amplitude of the memory.
• Figure 3: Time-domain memory event from a merger of an equal-mass binary with total mass $M=10^{-2} M_\odot$ at distance $d=1$ kpc in LIGO. The cyan curve shows the memory signal as given by Eq. \ref{['eq:memapproxTD']} while the black curve shows leading order result for the signal template compared to the full result for three different sky positions (in blue, pink and green). The dashed purple line indicates the exponential suppression $e^{-2 \pi f_{\rm min}^{\rm det} t}$.
• Figure 4: The differential comoving number density of binaries today as a function of frequency for representative values of $f_{\rm PBH}$ and $m_{\rm PBH}$. The sharp cut corresponds to the ISCO frequency. The large frequency power-law $\propto f^{-8/3}$ is induced by $f_{\rm coal}^\prime$, while the break at lower frequencies indicates where $\tau(f)$ becomes comparable to $t_0$ and the additional scaling in the merger rate density leads to the number density scales as $\propto f^{-8/37}$.
• Figure 5: Sensitivity to PBH abundance corresponding to $N_{\rm det} > 1$ in 1 yr observation at the GW experiments AdLIGO (blue), ET (green), Magnetic Weber Bars (red), and LISA (cyan). The solid curves refer to the primary signal (inspirals and mergers), while the dashed curves are based on the memory signal. In the physical parameter space of $f_\text{PBH} < 1$, the strongest constraints are derived from the primary signal for all detectors considered. For out-of-band mergers, this implies that the GW signal generated in the early inspiral stage leads to a stronger signal than the memory effect.