Long-term outburst activity of comet 17P/Holmes and constraints on ejecta size distributions

A quantitative understanding of cometary outbursts requires robust constraints on the size distribution of ejected particles, which governs outburst dynamics and underpins estimates of released gas and dust. In the absence of direct measurements of particle sizes, assumptions about the size distribution play a central role in modelling dust-trail formation, their dynamical evolution and observability, and the potential production of meteor showers following encounters with Earth. We analyse brightness amplitude variations associated with outbursts of comet 17P/Holmes from 1892 to 2021, with particular emphasis on the exceptional 2007 mega-outburst. During this event the comet underwent a rapid and substantial brightening: at its peak, the expanding coma reached a diameter exceeding that of the Sun and briefly became the largest object in the Solar System visible to the naked eye. We constrain the size distribution and total mass of porous agglomerates composed of ice, organics, and dust ejected during the outburst. The inferred particle size distribution is consistent with a power law of index q, yielding effective particle sizes between 10^-6 m for q = 4 and 5 x 10^-3 m for q = 2. Accounting for effective particle size, sublimation flux, and bulk density, we find that the total number of ejected particles increases with both q and sublimation flux. These results place constraints on the physical properties of outburst ejecta and provide physically motivated initial conditions for long-term dust-trail evolution modelling. They further indicate that cometary outburst brightness is determined primarily by the number of particles and their size distribution, rather than by the total ejected mass alone, with direct implications for the origin and evolution of meteoroid streams and the interplanetary dust population.