LISA science performance in observations of short-lived signals from massive black hole binary coalescences

The observation of massive black hole binary systems is one of the main science objectives of the Laser Interferometer Space Antenna (LISA). The instrument’s design requirements have recently been revised: they set a requirement at 0.1 mHz, with no additional explicit requirements at lower frequencies. This has implications for observations of the short-lived signals produced by the coalescence of massive and high-redshift binaries. Here we consider the most pessimistic scenario: the (unlikely) case in which LISA has no sensitivity below 0.1 mHz. We show that the presence of higher multipoles (beyond the dominant $\ell =|m|=2$ mode) in the gravitational radiation from these systems, which will be detectable with a total signal-to-noise ratio $\sim {10}^3$, allows LISA to retain the capability to accurately measure the physical parameters and the redshift and to constrain the sky location. To illustrate this point, we consider a few select binaries in a total (redshifted) mass range of $4\times {10}^6–4\times {10}^7{M}_{\odot }$ whose ($\ell =|m|=2$) gravitational-wave signals last between $\approx 12\mathrm{h}$ and $\approx 20\mathrm{days}$ in band. We model the emitted gravitational radiation using the highly accurate (spin-aligned) waveform approximant IMRPhenomXHM and carry out a fully coherent Bayesian analysis on the LISA noise-orthogonal time-delay-interferometry channels.

Figure 1

Marginalized posterior density functions for selected parameters for the four systems of Table 1, with $f_{\mathrm{low}}=0.1\mathrm{mHz}$. (a) Systems ID I, (b) II, (c), III, and (IV), see corner plots in Figs. 3, 4, 5, 6, respectively. The plots show the 50% (dashed) and 90% (solid) probability contours inferred when using higher multipoles (blue) and just the (2, 2) mode (green). The solid red lines denote the injection values.

Figure 2

Impact of lowering the cutoff frequency for the LISA sensitivity band $f_{\mathrm{low}}$ on the inferred parameters of a binary back hole with $m_1=3.2\times {10}^7{M}_{\odot }$ and $m_1=8\times {10}^6{M}_{\odot }$ (run ID: I, Ia, and Ib in Table 1). Decreasing the cutoff frequency effectively means a longer duration signal within LISA’s sensitive band, typically resulting in parameter degeneracies being broken due to the amplitude and phase modulations induced by LISA’s orbital motion. Waveform models incorporating higher multipoles can partially mitigate against such changes due to the dependence of the multipoles on the binary geometry, i.e., its sky location and orientation. The coalescence time $t_c$ is defined at the Solar System barycenter; therefore, different possible sky posteriors translate into different possible coalescence times. For $f_{\mathrm{low}}=1\times {10}^{-4}$ and $5\times {10}^{-5}\mathrm{Hz}$, we find eight modes, whereas for $f_{\mathrm{low}}=1\times {10}^{-5}\mathrm{Hz}$, these degeneracies are broken and we find only one mode.

Figure 3

Binary I. Run with higher multipoles (blue) and with the (2, 2) mode only (green). The red lines denote the injected values.

Figure 4

Binary II. Run with higher multipoles (blue) and with the (2, 2) mode only (green). The red lines denote the injected values.

Figure 5

Binary III. Run with higher multipoles (blue) and with the (2, 2) mode only (green). The red lines denote the injected values.

Figure 6

Binary IV. Run with higher multipoles (blue) and with the (2, 2) mode only (green). The red lines denote the injected values.