Phase-resolved NuSTAR and Swift-XRT Observations of Magnetar 4U 0142+61

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We present temporal and spectral analysis of simultaneous 0.5-79 keV Swift-XRT and NuSTAR observations of the magnetar 4U 0142+61. The pulse profile changes significantly with photon energy between 3 and 35 keV. The pulse fraction increases with energy, reaching a value of 20%, similar to that observed in 1E 1841-045 and much lower than the 80% pulse fraction observed in 1E 2259+586. We do not detect the 55-ks phase modulation reported in previous Suzaku-HXD observations. The phase-averaged spectrum of 4U 0142+61 above 20 keV is dominated by a hard power law with a photon index, Γ 0.65, and the spectrum below 20 keV can be described by two blackbodies, a blackbody plus a soft power law, or by a Comptonized blackbody model. We study the full phase-resolved spectra using the electron-positron outflow model of Beloborodov (2013). Our results are consistent with the parameters of the active j-bundle derived from INTEGRAL data by Hascoet et al. (2014). We find that a significant degeneracy appears in the inferred parameters if the footprint of the j-bundle is allowed to be a thin ring instead of a polar cap. The degeneracy is reduced when the footprint is required to be the hot spot inferred from the soft X-ray data.