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Two new outbursts and transient hard X-rays from 1E 1048.1$-$5937

Since its discovery, 1E 1048.1$-$5937 has been one of the most active magnetars, both in terms of radiative outbursts, and changes to its spin properties. Here we report on a continuing monitoring campaign with the Neil Gehrels Swift Observatory X-ray Telescope in which we observe two new outbursts from this source. The first outburst occurred in 2016 July, and the second in 2017 December, reaching peak 0.5-10 keV absorbed fluxes of $3.2^{+0.2}_{-0.3}\times 10^{-11}$ erg s$^{-1}$ cm$^{-2}$ and $2.2^{+0.2}_{-0.2}\times10^{-11}$ erg s$^{-1}$ cm$^{-2}$, respectively, factors of $\sim$5 and $\sim 4$ above the quiescent flux. Both new outbursts were accompanied by spin-up glitches with amplitudes of $Δν= 4.47(6)\times10^{-7}$ Hz and $Δν= 4.32(5)\times10^{-7}$ Hz, respectively. Following the 2016 July outburst, we observe, as for past outbursts, a period of delayed torque fluctuations, which reach a peak spin-down of $1.73\pm0.01$ times the quiescent rate, and which dominates the spin evolution compared to the spin-up glitches. We also report an observation near the peak of the first of these outbursts with NuSTAR in which hard X-ray emission is detected from the source. This emission is well characterized by an absorbed blackbody plus a broken power law, with a power-law index above $13.4\pm0.6$ keV of $0.5_{-0.2}^{+0.3}$, similar to those observed in both persistent and transient magnetars. The hard X-ray results are broadly consistent with models of electron/positron cooling in twisted magnetic field bundles in the outer magnetosphere. However the repeated outbursts and associated torque fluctuations in this source remain puzzling.