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We show the peak magnitude for orphan afterglows from the jets ofgravitational wave (GW) detected black-hole/neutron star - neutron star(BH/NS-NS) mergers highly depends on the jet half-opening angle $\theta_j$.Short $\gamma$-ray bursts (GRB) with a homogeneous jet structure and$\theta_j>10^\circ$, the orphan afterglow viewed at the typical inclination fora GW detected event, 38$^\circ$, is brighter at optical frequencies than thecomparable macronova emission. Structured jets, where the energetics andLorentz factor $\Gamma$ vary with angle from the central axis, may havelow-$\Gamma$ components where the prompt emission is suppressed; GWelectromagnetic (EM) counterparts may reveal a population of failed-GRB orphanafterglows. Using a Monte Carlo method assuming a NS-NS detection limit we showthe fraction of GW-EM counterparts from homogeneous, two-component, power-lawstructured, and Gaussian jets where the variable structure models include awide low energy and $\Gamma$ component: for homogeneous jets, with a{$\theta_j=6^\circ$ and typical short GRB parameters, we find {\it r}-bandmagnitude $m_r\leq21$ counterparts for $\sim 13.6\%$ of GW detected mergers;where jet structure extends to a half-opening angle of $25^\circ$,two-component jets produce $m_r\leq21$ counterparts in $\sim30\%$ of GWdetected mergers; power-law structured jets result in $\sim37\%$; and Gaussianjets with our parameters $\sim13\%$.} We show the features in the lightcurvesfrom orphan afterglows can be used to indicate the presence of extendedstructure.

Electromagnetic Counterparts to Structured Jets from Gravitational Wave Detected Mergers