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We report on a 350-ks NuSTAR observation of the magnetar 1E 1841-045 taken in2013 September. During the observation, NuSTAR detected six bursts of shortduration, with $T_{90}<1$ s. An elevated level of emission tail is detectedafter the brightest burst, persisting for $\sim$1 ks. The emission showed apower-law decay with a temporal index of 0.5 before returning to the persistentemission level. The long observation also provided detailed phase-resolvedspectra of the persistent X-ray emission of the source. By comparing thepersistent spectrum with that previously reported, we find that the sourcehard-band emission has been stable over approximately 10 years. The persistenthard X-ray emission is well fitted by a coronal outflow model, where $e^{+/-}$pairs in the magnetosphere upscatter thermal X-rays. Our fit of phase-resolvedspectra allowed us to estimate the angle between the rotational and magneticdipole axes of the magnetar, $\alpha_{mag}=0.25$, the twisted magnetic flux,$2.5\times10^{26}\rm \ G\ cm^2$, and the power released in the twistedmagnetosphere, $L_j=6\times10^{36}\rm \ erg\ s^{-1}$. Assuming this model forthe hard X-ray spectrum, the soft X-ray component is well fit by atwo-blackbody model, with the hotter blackbody consistent with the footprint ofthe twisted magnetic field lines on the star. We also report on the 3-yearSwift monitoring observations obtained since 2011 July. The soft X-ray spectrumremained stable during this period, and the timing behavior was noisy, withlarge timing residuals.

Deep NuSTAR and Swift Monitoring Observations of the Magnetar 1E 1841-045