Prospects for joint multiband detection of intermediate-mass black holes by LGWA and the Einstein Telescope

TL;DR

This work addresses detecting intermediate-mass black holes (IMBHs) via gravitational waves, emphasizing the decihertz window accessible to LGWA and the higher-frequency sensitivity of the Einstein Telescope (ET). It builds three IMBH population models, simulates GW signals with IMR waveforms, and uses a Fisher-information approach to forecast parameter precision and detection prospects for ET, LGWA, and their joint network. The key finding is that LGWA excels for high-mass IMBH mergers while ET is more sensitive to lower-mass systems; together, they provide broader detection horizons and enable more accurate reconstruction of intrinsic distributions in $M_1$, $q$, and $z$. This multi-band strategy promises a more complete census of IMBHs and tighter constraints on their formation and evolution.

Abstract

Gravitational-wave (GW) detection offers a novel approach to exploring intermediate-mass black holes (IMBHs). The GW signals from IMBH mergers mainly fall in the decihertz frequency band. The lunar-based GW detector, the Lunar Gravitational-Wave Antenna (LGWA), exhibits high sensitivity in this band, making it particularly well-suited for detecting IMBHs. However, for lower-mass IMBHs, the late inspiral and merger signals enter the sensitive frequency range of ground-based GW detectors. In this work, we aim to explore how multi-band observations with LGWA and the third-generation ground-based GW detector, the Einstein Telescope (ET), can contribute to detecting the population of IMBHs. We consider three population distribution cases of IMBHs, including two population models based on astrophysical motivations and a uniform distribution, and compute the signal-to-noise ratios for LGWA, ET, and their combination to directly compare their capabilities in detecting IMBH mergers. Our results suggest that LGWA possesses strong detection capability for high-mass IMBH mergers. At redshift $z = 1$, LGWA's detection rate for IMBH binaries with primary masses above $5 \times 10^4~M_\odot$ is largely insensitive to orbital inclination and mass ratio. In contrast, ET is more suited for detecting IMBH binaries with primary masses below $10^3~M_\odot$. The multi-band observation of LGWA and ET possesses strong detection capabilities across the full IMBH mass spectrum. Furthermore, we find that the multi-band detection can significantly and effectively recover the IMBH population distributions. In summary, we conclude that the multi-band observations of LGWA and ET will provide powerful detection capabilities for IMBHs and are expected to significantly enhance our understanding of this important yet still poorly observed class of black holes.

Figures (8)

• Figure 1: Characteristic strains of ET, LISA, and LGWA (two configurations), along with that of a merging IMBH binary with component masses of $1000$--$1000\,M_\odot$ at redshift $z=1$. The soft cyan triangle marks the frequency one day before coalescence. Characteristic strains are defined as $\sqrt{fS_{\rm n}}$ for the sensitive curves of detectors and $2f|h(f)|$ for the GW signal.
• Figure 2: Detection horizons for equal-mass, non-spinning binary black holes as a function of total source-frame mass for ET, LGWA, and LISA detectors.
• Figure 3: Detection rate of binary black hole mergers as a function of the primary mass $M_1$ and redshift $z$, for different GW detector configurations. The color scale indicates the relative detection rate. Top: ET only. Middle: LGWA only. Bottom: Multi-band detection with both ET and LGWA.
• Figure 4: Similar to Figure \ref{['fig:z_m']}, showing the detection rate of binary black hole mergers at redshift $z=1$, but in the parameter space of primary mass $M_1$ and mass ratio $q$.
• Figure 5: Similar to Figures \ref{['fig:z_m']} and \ref{['fig:q_m']}, showing the detection rate in the parameter space of primary mass $M_1$ and inclination angle $\iota$ at redshift $z = 1$.