New search pipeline for gravitational waves with higher-order modes using mode-by-mode filtering

Nearly all template-based gravitational wave (GW) searches only include the quasi-circular quadrupolar modes of the signals in their templates. Including additional degrees of freedom in the GW templates corresponding to higher-order harmonics, orbital precession, or eccentricity is challenging because: ($i$) the size of template banks and the matched-filtering cost increases significantly with the number of degrees of freedom, $(ii)$ if these additional degrees are not included properly, the search can lose sensitivity overall (due to an increase in the rate of background triggers). Here, we focus on including aligned-spin higher harmonics in GW search templates. We use a new mode-by-mode filtering approach, where we separately filter GW strain data with three harmonics [namely $(\ell, |m|)=(2,2)$, $(3,3)$ and $(4,4)$]. This results in an increase in the matched-filtering cost by only a factor of $3$ compared to that of a $(2,2)$-only search. We develop computationally cheap trigger-ranking statistics to optimally combine the different signal-to-noise ratios (SNR) timeseries from different harmonics, which ensure only physically-allowed combinations of the different harmonics are triggered on. We use an empirical template-dependent background model in our ranking statistic to account for non-Gaussian transients. In addition, we develop a tool called band eraser which specifically excises narrow time-varying noisy bands in time-frequency space (without having to excise entire time chunks in the data). New GW candidate events that we detect using our $\texttt{IAS-HM}$ search pipeline and the details of our template banks are discussed in accompanying papers: Wadekar et al. [1] and [2] respectively. Apart from higher harmonics, we expect our methodology to also be useful for cheap and optimal searches including orbital precession and eccentricity in GW waveforms.