A very intense, long-lasting radio flare on HD 32918

We report the brightest microwave flare yet detected from an active chromosphere star. The K2III star HD 32918 emitted $$6\times {10}^{12}\,\text{W}\,\text{Hz}^{-1}$$ at 8.4 GHz near the flare peak, and flare emission was still detectable three weeks later. The episode consisted of at least three separate flares with successively decreasing amplitudes. The 8.4-GHz emission was essentially unpolarized while the radio spectrum varied as v^1.2 near the flare peak and as v^0.6 about three weeks later. High time-resolution measurements at 8.4 GHz showed no second-to-second variation, with the shortest time-scale for significant variation being about 15 min. At the flare peak the estimated brightness temperature for the 8.4-GHZ source, assuming a size of one stellar diameter, was $$\sim3\times {10}^{10}\text {K}$.$ The observed flare parameters can be explained by gyrosynchrotron emission from an optically thick source. A spherically symmetrical source model in which both the magnetic field strength and the density of mildly relativistic electrons decrease outwards can explain the measured radio spectra, brightness temperatures and circular polarization. If we assume minimum magnetic field values to contain the radiating electrons, a dipole field $${B(R)}\propto{R}^{-3}$$ and power-law electron energy spectrum ${N(E)}\propto{E}^{-2}$ for $$E\leqq10\,\text{MeV}$$, we find that we have B≈44 G at 1 R_* from the source centre, decreasing to B≈0.5 G at 4.4 R_*, where R_* and 4.4 R_* are the radii of the 8.4 and 0.843-GHz sources, respectively. Near the flare peak the density of electrons with energies $$\geqq100\,\text{KeV}\, \text{is}\,\sim1.1\times {10}^{5}\,\text{cm}^{-3}\,\text{at}\, {R}_{\ast}$$ from the source centre, falling as R⁻² to $$5.7\times {10}^{3}\,\text{cm}^{-3}\,\text{at}\,4.4\, {R}_{\ast}\,\text{at}\,4.4\,{R}_{\ast}$$. To explain the variation of spectral index of the radio flare during its decay phase, we assume that the radiating electron distribution decays more rapidly towards the centre of the source than nearer its edge. This requires an electron density $$\sim2\times {10}^{3}\,\text{cm}^{-3}\,\text{at}\,{R}_{\ast}\,\text{and}\,\sim8.9\times {10}^{3}\,\text{cm}^{-3}\,\text{at}\,4.4\,{R}_{\ast}$$ to explain the 8.4- and 0.843-GHz observations, respectively.