Science with the space-based interferometer eLISA. I: Supermassive black hole binaries

TL;DR

This paper assesses how different eLISA design choices—arm length, number of links, low-frequency noise, and mission duration—affect the science return for detecting and characterizing supermassive black-hole binaries. Using a Fisher-matrix framework with spin-precessing inspiral waveforms and an IMR-based rescaling, it compares 12 baseline configurations across three MBH population scenarios to quantify detection rates and parameter-estimation capabilities. The findings show that six-link configurations with good low-frequency sensitivity deliver substantially more high-redshift detections and enable electromagnetic counterpart identification, while shorter arms can be cost-effective if the low-frequency goal is preserved; merger-ringdown modeling significantly enhances parameter constraints for six-link designs. The study emphasizes the need for improved IMR waveform models for precessing binaries to fully exploit eLISA's MBHB science potential and highlights the trade-offs between mission cost and science reach.

Abstract

We compare the science capabilities of different eLISA mission designs, including four-link (two-arm) and six-link (three-arm) configurations with different arm lengths, low-frequency noise sensitivities and mission durations. For each of these configurations we consider a few representative massive black hole formation scenarios. These scenarios are chosen to explore two physical mechanisms that greatly affect eLISA rates, namely (i) black hole seeding, and (ii) the delays between the merger of two galaxies and the merger of the black holes hosted by those galaxies. We assess the eLISA parameter estimation accuracy using a Fisher matrix analysis with spin-precessing, inspiral-only waveforms. We quantify the information present in the merger and ringdown by rescaling the inspiral-only Fisher matrix estimates using the signal-to-noise ratio from non-precessing inspiral-merger-ringdown phenomenological waveforms, and from a reduced set of precessing numerical relativity/post-Newtonian hybrid waveforms. We find that all of the eLISA configurations considered in our study should detect some massive black hole binaries. However, configurations with six links and better low-frequency noise will provide much more information on the origin of black holes at high redshifts and on their accretion history, and they may allow the identification of electromagnetic counterparts to massive black hole mergers.

Figures (13)

• Figure 1: Analytic fits to the sensitivity curves for different configurations investigated in this paper. In both panels the curves running from the top down are for A1 (blue), A2 (green) and A5 (red) configurations, and all curves have the same high-frequency noise by design. The (black) curve with wiggles at high frequency is the numerical sensitivity for eLISA/NGO, which is shown in both panels for reference. Dashed curves include only instrumental noise, while solid lines represent the total noise (including the contribution from CWD confusion noise). The left panel shows all configurations with pessimistic (N1) acceleration noise levels; the right panel assumes optimistic (N2) acceleration noise levels.
• Figure 2: Schematic summary of the model of mymodel, with the improvements of spin_modelletternewpaper. Red boxes on the left highlight the elements that heavily affect rates (black hole seeding and delays), for which we consider multiple options in this paper.
• Figure 3: Predicted merger rates per unit redshift (left panel) and per unit total redshifted mass $M_z=(m_1+m_2)(1+z)$ (right panel) for the three models described in the text.
• Figure 4: Contribution of each halo mass to the total merger rate for models popIII (long-dashed brown lines), Q3-nod (short-dashed green lines) and Q3-d (solid orange lines). Lines in the top panel are proportional to the number of mergers per halo (i.e., removing the Press & Schechter weights), whereas lines in the bottom panel represent the halo contribution to the cosmic merger rate $dN/d{\rm log}M_H$. In both panels, thin lines are the results of our MBH population models; thick lines are extrapolations assuming a linear relation between the number of mergers and the halo mass.
• Figure 5: SNR gain ${\cal R}(\rho)$ as a function of redshifted total mass $M_z$. PhenomC waveforms applied to one realization of the Q3-nod population model are represented by black ($0.5<m_{2z}/m_{1z}<1$) and blue ($0<m_{2z}/m_{1z}<0.5$) dots. The red and green dots are computed using non-spinning PhenomC waveforms at a fixed $M_z$ for decreasing values of $m_{2z}/m_{1z}$ (from top to bottom); red dots are for $m_{2z}/m_{1z}>0.5$ and green dots are for $m_{2z}/m_{1z}<0.5$. This calculation refers to the detector configuration that we labeled N2A1M2L6.