A new approach to template banks of gravitational waves with higher
  harmonics: reducing matched-filtering cost by over an order of magnitude
Digvijay Wadekar Tejaswi Venumadhav Ajit Kumar Mehta Javier Roulet Seth Olsen Jonathan Mushkin Barak Zackay Matias Zaldarriaga
Searches for gravitational wave events use models, or templates, for the
signals of interest. The templates used in current searches in the
LIGO-Virgo-Kagra (LVK) data model the dominant quadrupole mode $(\ell,m)=(2,2)$
of the signals, and omit sub-dominant higher-order modes (HM) such as
$(\ell,m)=(3,3)$, $(4,4)$, which are predicted by general relativity. Hence,
these searches could lose sensitivity to black hole mergers in interesting
parts of parameter space, such as systems with high-masses and asymmetric mass
ratios. We develop a new strategy to include HM in template banks that exploits
the natural connection between the modes. We use a combination of
post-Newtonian formulae and machine learning tools to model aligned-spin
$(3,3)$, $(4,4)$ waveforms corresponding to a given $(2,2)$ waveform. Each of
these modes can be individually filtered against the data to yield separate
timeseries of signal-to-noise ratios (SNR), which can be combined in a
relatively inexpensive way to marginalize over extrinsic parameters of the
signals. This leads to a HM search pipeline whose matched-filtering cost is
just $\approx 3\times$ that of a quadrupole-only search (in contrast to being
$\approx\! 100 \times$, as in previously proposed HM search methods). Our
method is effectual and is generally applicable for template banks constructed
with either stochastic or geometric placement techniques. Additionally, we
discuss compression of $(2,2)$-only geometric-placement template banks using
machine learning algorithms.