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We analyzed broad-band X-ray and radio data of the magnetar SGR J1935+2154taken in the aftermath of its 2014, 2015, and 2016 outbursts. The source softX-ray spectrum <10 keV is well described with a BB+PL or 2BB model during allthree outbursts. NuSTAR observations revealed a hard X-ray tail, $\Gamma=0.9$,extending up to 79 keV, with flux larger than the one detected <10 keV. Imaginganalysis of Chandra data did not reveal small-scale extended emission aroundthe source. Following the outbursts, the total 0.5-10 keV flux from SGRJ1935+2154 increased in concordance to its bursting activity, with the flux atactivation onset increasing by a factor of $\sim7$ following its strongest June2016 outburst. A Swift/XRT observation taken 1.5 days prior to the onset ofthis outburst showed a flux level consistent with quiescence. We show that theflux increase is due to the PL or hot BB component, which increased by a factorof $25$ compared to quiescence, while the cold BB component $kT=0.47$ keVremained more or less constant. The 2014 and 2015 outbursts decayedquasi-exponentially with time-scales of $\sim40$ days, while the stronger Mayand June 2016 outbursts showed a quick short-term decay with time-scales of$\sim4$ days. Our Arecibo radio observations set the deepest limits on theradio emission from a magnetar, with a maximum flux density limit of 14 $\mu$Jyfor the 4.6 GHz observations and 7 $\mu$Jy for the 1.4 GHz observations. Wediscuss these results in the framework of the current magnetar theoreticalmodels.

X-ray and radio observations of the magnetar SGR J1935+2154 during its 2014, 2015, and 2016 outbursts