Bright siren without electromagnetic counterpart by LISA-Taiji-TianQin network

TL;DR

This work investigates whether a space-based GW detector network (LISA-Taiji-TianQin) can uniquely identify MBHB host galaxies using GW signals alone, enabling bright sirens for $H_0$ without EM counterparts. By combining five MBHB population models with two galaxy-number-density scenarios and employing IMRPhenomD waveforms with Fisher-matrix parameter estimation, the study quantifies identification horizons, detection rates, and resulting $H_0$ constraints. The results show that the network dramatically improves sky localization (by ~$10^2$) and modestly improves distance accuracy, enabling an identification horizon up to $z\sim 1.2$ in favorable cases; detection rates and $H_0$ precision depend strongly on MBHB population and GND assumptions, with some models achieving sub-percent $H_0$ errors. This approach offers a promising path to precision cosmology via GW-only host identification, highlighting the critical role of networked space-based GW detectors for future ABG cosmology.

Abstract

Gravitational waves (GWs) with electromagnetic counterparts (EMc) offer a novel approach to measure the Hubble constant ($H_0$), known as bright sirens, enabling $H_0$ measurements by combining GW-derived distances with EM-derived redshifts. Host galaxy identification is essential for redshift determination but remains challenging due to poor GW sky localization and uncertainties in EMc models. To overcome these limitations, we exploit the ultra-high-precision localization ($ΔΩ_s \sim 10^{-4} \, \text{deg}^2$) with a space-based GW detector network (LISA-Taiji-TianQin), which permits unique host identification solely from GW signals. We integrate five massive black hole binary (MBHB) population models and two galaxy number density models to compute the redshift horizon for host galaxy identification and evaluate $H_0$ constraints. We find that (1) The network enhances localization by several orders of magnitude compared to single detectors; (2) The identification horizon reaches $z\sim 1.2$ for specific MBHBs in the most accurate localization case; (3) The population model choice critically impacts the outcomes: the most refined population models yield to independent EMc identification rate of 0.6-1 $\text{yr}^{-1}$ with $H_0$ constraints $< 1\%$ fractional uncertainty, the less refined models lead to the rate $<0.1\text{yr}^{-1}$ and $1-2\%$ uncertainty on $H_0$.

Figures (9)

• Figure 1: The merger rate of all population models across varying redshift (left) and binary mass (right). The MBHB population at high redshift ($z>4$) is predominated in the LightSeed-Nodelay and HeavySeed-Nodelay models, whereas the IV24 and QY25 models predict a significant MBHB population at low redshifts ($z < 4$). In the HeavySeed-Delay model, the population is largely uniformly distributed in a redshift range of 1 to 6. Regarding binary mass, the LightSeed-Nodelay model predicts a prevalence of low-mass MBHBs with total masses below $10^5 M_\odot$, while the HeavySeed-Delay and HeavySeed-Nodelay models show a dominance of MBHBs with masses in the range $10^6-10^7M_\odot$. The mass distribution of IV24 is largely uniform in the range of $10^4-10^8 M_\odot$. The QY25 model favors high-mass MBHBs with mass over $10^6M_\odot$.
• Figure 2: The GND in different models as the redshift changes. The blue line represents the filter in the mass range of $10^8-10^{9} M_\odot$, defined by Eq. (\ref{['eq:galaxy-number-density']}), while the orange line represents the filter in the mass range of $10^9-10^{14} M_\odot$.
• Figure 3: The sky map of fractional distance uncertainty (left column) and sky location uncertainty from equal-mass MBHBs of $10^6M_\odot$ at a distance of $10^4 \text{Mpc}$, comparing single detectors and their network. The top three panels in each column represent the single detectors, and the bottom panel represents their network. The sky maps in each column share the same color bar. While the distance uncertainty exhibits only weak sky angular sensitivity, varying by less than an order of magnitude across the sky, the sky location uncertainty is highly sensitive to sky location, varying by factors of $10^2-10^4$. Taiji provides the best constraint on both distances and sky locations, due to its longest arm length. LISA ranks second, while Tianqin has the worst constraint. The network enhances the accuracy of the distance uncertainty by a factor of $2-3$ for a single detector. Additionally, the network highly improves the sky location accuracy by a factor of $\sim 10^2$.
• Figure 4: The sky map of the volume uncertainty with an equal mass of $10^6M_\odot$ at a distance of $10^4 \text{Mpc}$, comparing individual detectors and their network. The top panels represent the individual detectors, and the bottom panel represents their network. All the sky maps share the same color bar. The sky location uncertainty reaches its minimum at the celestial equator and its maximum at the celestial pole. We choose the equatorial point $(\theta_s=10^\circ,\phi_s=90^\circ)$ for subsequent calculation, representing the most accurate case. We set the declination $\theta_s=10^\circ$ to prevent the extinction effects from the Galactic plane. Conversely, to represent the most uncertain case, we choose the polar point $(90^\circ,89^\circ)$.
• Figure 5: The identification horizon for the detector network with the uniform GND ($0.02\text{ Mpc}^{-3}$) at the polar point (left figure) and equatorial point (right figure) for MBHBs with different masses. The maximum identification horizon for both points is reached at the equal-mass system with masses of $\sim 10^6M_\odot$. The identification horizons get closer with a lower or higher mass and a lower mass ratio.