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A crucial component to maximizing the science gain from the multi-messengerfollow-up of gravitational-wave (GW) signals from compact binary mergers is theprompt discovery of the electromagnetic counterpart. Ideally, the GW detectionand localization must be reported early enough to allow for telescopes to slewto the location of the GW-event before the onset of the counterpart. However,the time available for early warning is limited by the short duration spent bythe dominant ($\ell = m = 2$) mode within the detector's frequency band.Nevertheless, we show that, including higher modes - which enter the detector'ssensitivity band well before the dominant mode - in GW searches, can enable usto significantly improve the early warning ability for compact binaries withasymmetric masses (such as neutron-star-black-hole binaries). We investigatethe reduction in the localization sky-area when the $\ell = m = 3$ and $\ell =m = 4$ modes are included in addition to the dominant mode, considering typicalslew-times of electromagnetic telescopes ($30-60$ sec). We find that, in LIGO'sprojected "O5" ("Voyager") network with five GW detectors, some of theneutron-star-black-hole mergers, located at a distance of $40$ Mpc, can belocalized to a few hundred sq. deg. $\sim 45$ sec prior to the merger,corresponding to a reduction-factor of $3-4$ ($5-6$) in sky-area. For athird-generation network, we get gains of up to 1.5 minutes in early warningtimes for a localization area of $100$ sq. deg., even when the source is placedat $100$ Mpc.

Of Harbingers and Higher Modes: Improved gravitational-wave early-warning of compact binary mergers