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We present the results of targeted searches for gravitational-wave transientsassociated with gamma-ray bursts during the second observing run of AdvancedLIGO and Advanced Virgo, which took place from 2016 November to 2017 August. Wehave analyzed 98 gamma-ray bursts using an unmodeled search method thatsearches for generic transient gravitational waves and 42 with a modeled searchmethod that targets compact-binary mergers as progenitors of short gamma-raybursts. Both methods clearly detect the previously reported binary mergersignal GW170817, with p-values of $<9.38 \times 10^{-6}$ (modeled) and $3.1\times 10^{-4}$ (unmodeled). We do not find any significant evidence forgravitational-wave signals associated with the other gamma-ray bursts analyzed,and therefore we report lower bounds on the distance to each of these, assumingvarious source types and signal morphologies. Using our final modeled searchresults, short gamma-ray burst observations, and assuming binary neutron starprogenitors, we place bounds on the rate of short gamma-ray bursts as afunction of redshift for $z \leq 1$. We estimate 0.07-1.80 joint detectionswith Fermi-GBM per year for the 2019-20 LIGO-Virgo observing run and 0.15-3.90per year when current gravitational-wave detectors are operating at theirdesign sensitivities.

Search for gravitational-wave signals associated with gamma-ray bursts during the second observing run of Advanced LIGO and Advanced Virgo