Investigating the accuracy achievable in reconstructing the angular sizes of stars through stellar intensity interferometry observations

Context: In recent years, stellar intensity interferometry has seen renewed interest from the astronomical community because it can be efficiently applied to Cherenkov telescope arrays. Aims: We have investigated the accuracy that can be achieved in reconstructing stellar sizes by fitting the visibility curve measured on the ground. The large number of expected available astronomical targets, the limited number of nights in a year, and the likely presence of multiple baselines will require careful planning of the observational strategy to maximise the scientific output. Methods: We studied the trend of the error on the estimated angular size, considering the uniform disk model, by varying several parameters related to the observations, such as the total number of measurements, the integration time, the signal-to-noise ratio, and different positions along the baseline. Results: We found that measuring the value of the zero-baseline correlation is essential to obtain the best possible results. Systems that can measure this value directly or for which it is known in advance will have better sensitivity. We also found that to minimise the integration time, it is sufficient to obtain a second measurement at a baseline half-way between 0 and that corresponding to the first zero of the visibility function. This function does not have to be measured at multiple positions. Finally, we obtained some analytical expressions that can be used under specific conditions to determine the accuracy that can be achieved in reconstructing the angular size of a star in advance. This is useful to optimise the observation schedule.