Pulsars are neutron stars, stellar corpses left over after supernova explosions of stars about ten times as massive as our Sun, with densities comparable to the atomic nucleus, spinning with periods from few milliseconds up to few seconds, and endowed with magnetic fields thousands billion times stronger than the Earths, where particles are accelerated to the relativistic regime producing electromagnetic radiation across the entire spectrum. Although there is a general consensus on the fact that pulsars radio emission is coherent in nature, whereas the emission from the optical to high-energy $gamma$-rays is due to incoherent processes, it has not been established yet at which wavelengths the transition occurs, a key information for all emission models of pulsar magnetospheres. Of course, to address this issue covering the spectral region between high-frequency radio waves and the mid-IR is crucial. We used the Atacama Large Millimetre Array (ALMA) to observe the Vela pulsar (PSR, B0833$-$45), one of the very few observed in radio and from the mid-infrared up to the very high-energy $gamma$-rays. We detected Vela at frequencies of 97.5, 145, 233, 343.5 GHz and found that its energy density spectrum follows a power-law of spectral index $alpha = -0.93 pm 0.16$. The ALMA spectrum corresponds to very high brightness temperatures - from $10^{17}$ to $10^{15}$ K - suggesting that a coherent radiative process still contributes to the mm/sub-mm emission. This is, therefore, the first indication of coherent emission other than radio originating in pulsars. At the same time, we identified an extended structure, preliminarily detected in ground-based observations. We support its interpretation as a counter-jet protruding from the pulsar.
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