The detection of a short hard X-ray burst and an associated bright soft X-ray source by the Swift satellite in 2020 October heralded a new magnetar in outburst, SGR J1830-0645. Pulsations at a period of ~10.4 s were detected in prompt follow-up X-ray observations. We present here the analysis of the Swift/BAT burst, of XMM-Newton and the Nuclear Spectroscopic Telescope Array observations performed at the outburst peak, and of a Swift/XRT monitoring campaign over the subsequent month. The burst was single-peaked, lasted ~6 ms, and released a fluence of ~5e-9 erg cm^-2 (15-50 keV). The spectrum of the X-ray source at the outburst peak was well described by an absorbed double-blackbody model plus a power-law component detectable up to ~25 keV. The unabsorbed X-ray flux decreased from ~5e-11 to ~2.5e-11 erg cm^-2 s^-1 one month later (0.3-10 keV). Based on our timing analysis, we estimate a dipolar magnetic field ~5.5e14 G at pole, a spin-down luminosity ~2.4e32 erg s^-1, and a characteristic age ~24 kyr. The spin modulation pattern appears highly pulsed in the soft X-ray band, and becomes smoother at higher energies. Several short X-ray bursts were detected during our campaign. No evidence for periodic or single-pulse emission was found at radio frequencies in observations performed with the Sardinia Radio Telescope and Parkes. According to magneto-thermal evolutionary models, the real age of SGR J1830-0645 is close to the characteristic age, and the dipolar magnetic field at birth was slightly larger, ~1e15 G.
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