NuSTAR Observations of Magnetar 1E 1048.1-5937

We report on simultaneous NuSTAR and XMM-Newton observations of the magnetar 1E 1048.1$-$5937 obtained in July 2013, along with Rossi X-ray Timing Explorer (RXTE) data for the same source obtained from December 2002 through March 2012. The NuSTAR data provide a clear detection of this magnetar's persistent emission up to 20 keV. We detect a previously unreported small secondary peak in the average pulse profile in the 7-10 keV band, which grows to an amplitude comparable to that of the main peak in the 10--20 keV band. We show using RXTE data that this secondary peak is likely transient. We find that the pulsed fraction increases with energy from a value of $\sim$0.55 at $\sim$2 keV to a value of $\sim$0.75 near 8 keV but shows evidence for decreasing at higher energies. After filtering out multiple bright X-ray bursts during the observation, we find that the phase-averaged spectrum from combined NuSTAR and XMM data is well described by an absorbed double blackbody plus power-law model, with no evidence for the spectral turn-up near $\sim$10 keV as has been seen in some other magnetars. Our data allow us to rule out a spectral turn-up similar to those seen in magnetars 4U 0142+61 and 1E 2259+586 of $\Delta\Gamma >= 2$, where $\Delta\Gamma$ is the difference between the soft-band and hard-band photon indexes. The absence of a significant spectral turn-up is consistent with what has been observed from a particularly active subset of magnetars having high spin-inferred magnetic fields, and with previously reported trends suggesting the degree of spectral turn-up is correlated with spin-down rate and/or spin-inferred magnetic field strength.