# Higher harmonics increase LISA's mass reach for supermassive black holes

## TL;DR

Including higher harmonics in LISA data analysis significantly enhances its ability to detect more massive supermassive black hole binaries, expanding the observable mass range and improving signal-to-noise ratios.

## Contribution

This paper demonstrates that incorporating all known harmonics into matched filtering greatly increases LISA's mass reach for supermassive black hole observations.

## Key findings

- LISA can observe supermassive black hole mergers with masses up to 10^8-10^9 solar masses.
- Including higher harmonics boosts SNRs, enabling detection at greater distances.
- The mass range accessible to LISA is significantly expanded by considering all harmonics.

## Abstract

Current expectations on the signal to noise ratios and masses of supermassive black holes which the Laser Interferometer Space Antenna (LISA) can observe are based on using in matched filtering only the dominant harmonic of the inspiral waveform at twice the orbital frequency. Other harmonics will affect the signal-to-noise ratio of systems currently believed to be observable by LISA. More significantly, inclusion of other harmonics in our matched filters would mean that more massive systems that were previously thought to be {\it not} visible in LISA should be detectable with reasonable SNRs. Our estimates show that we should be able to significantly increase the mass reach of LISA and observe the more commonly occurring supermassive black holes of masses $\sim 10^8M_\odot.$ More specifically, with the inclusion of all known harmonics LISA will be able to observe even supermassive black hole coalescences with total mass $\sim 10^8 M_\odot (10^9M_\odot)$ (and mass-ratio 0.1) for a low frequency cut-off of $10^{-4}{\rm Hz}$ $(10^{-5}{\rm Hz})$ with an SNR up to $\sim 60$ $(\sim 30)$ at a distance of 3 Gpc. This is important from the astrophysical viewpoint since observational evidence for the existence of black holes in this mass range is quite strong and binaries containing such supermassive black holes will be inaccessible to LISA if one uses as detection templates only the dominant harmonic.