Euclid: Asteroid rotation periods from the Euclid Ecliptic Survey
The Euclid Ecliptic Survey was conducted during the calibration phase of the mission, 23-31 December 2023, as a campaign to study Solar System objects. We used data from this survey to analyse more than 23 000 appeareances of 2321 known asteroids. Due to their high apparent angular motion relative to the background stars (5-$60^{\prime\prime}\,\mathrm{h}^{-1}$), these objects appear as streaks in VIS long-exposure images. We set out to estimate their spin periods, since only $7\%$ of them have periods published in the literature. We used multiple apertures along each streak to increase the time resolution of our light curves. Our method combines a Lomb-Scargle approach with a Markov chain Monte Carlo (MCMC) algorithm to characterise the posterior distributions. Some asteroids show multimodality in the MCMC search, indicating period aliases; in these cases, we report all aliases and their likelihoods. We validate our pipeline by comparing our fitted periods with 48 published periods, including period harmonics. We find that $44\%$ of our periods are within $1\%$ of those published and $98\%$ are within $15\%$, and we establish that with $98\%$ confidence the best solution can be found among the first three aliases. All reliable periods reported agree with our current understanding of the spin-period distribution for asteroids. We find 16 periods below the spin barrier of 2.2 h with absolute magnitudes below 19, and thus 16 candidate super-fast rotators. We provide light curves for all 2321 objects observed and 889 high-quality periods in an open-access catalogue. The asteroids with reported periods include five Mars crossers, four Cybeles, four Hildas, three Hungarias, and 877 asteroids in other regions of the main belt. Our results represent the first batch of spin periods extracted from Euclid light curves and include the first-ever period measurements for $93\%$ of the objects.