IceTop is an air shower array located on the Antarctic ice sheet at the geographic South Pole. IceTop can detect an astrophysical flux of neutrons from Galactic sources as an excess of cosmic ray air showers arriving from the source direction. Neutrons are undeflected by the Galactic magnetic field and can typically travel 10 ($E$ / PeV) pc before decay. Two searches are performed using 4 years of the IceTop dataset to look for a statistically significant excess of events with energies above 10 PeV ($10^{16}$ eV) arriving within a small solid angle. The all-sky search method covers from -90$^{circ}$ to approximately -50$^{circ}$ in declination. No significant excess is found. A targeted search is also performed, looking for significant correlation with candidate sources in different target sets. This search uses a higher energy cut (100 PeV) since most target objects lie beyond 1 kpc. The target sets include pulsars with confirmed TeV energy photon fluxes and high-mass X-ray binaries. No significant correlation is found for any target set. Flux upper limits are determined for both searches, which can constrain Galactic neutron sources and production scenarios.
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