We report results from deep observations (~750 ks) of Tychos supernova remnant (SNR) with NuSTAR. Using these data, we produce narrow-band images over several energy bands to identify the regions producing the hardest X-rays and to search for radioactive decay line emission from 44Ti. We find that the hardest (>10 keV) X-rays are concentrated in the southwest of Tycho, where recent Chandra observations have revealed high emissivity stripes associated with particles accelerated to the knee of the cosmic-ray spectrum. We do not find evidence of 44Ti, and we set limits on its presence and distribution within the SNR. These limits correspond to a upper-limit 44Ti mass of M44 < 2.4x10^-4 M_sun for a distance of 2.3 kpc. We perform spatially resolved spectroscopic analysis of sixty-six regions across Tycho. We map the best-fit rolloff frequency of the hard X-ray spectra, and we compare these results to measurements of the shock expansion and ambient density. We find that the highest energy electrons are accelerated at the lowest densities and in the fastest shocks, with a steep dependence of the roll-off frequency with shock velocity. Such a dependence is predicted by models where the maximum energy of accelerated electrons is limited by the age of the SNR rather than by synchrotron losses, but this scenario requires far lower magnetic field strengths than those derived from observations in Tycho. One way to reconcile these discrepant findings is through shock obliquity effects, and future observational work is necessary to explore the role of obliquity in the particle acceleration process.
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