Exocomets size distribution in the $\beta$ Pictoris planetary system
The star $\beta$ Pictoris harbors a young planetary system, which is characterized by the presence of a gaseous and dusty debris disk, at least two massive planets and many minor bodies. For more than thirty years, exocomets transiting the star have been detected using spectroscopy, probing the gaseous part of the cometary comas and tails. The detection of the dusty component of the tails can be performed through photometric observations of the transits. Since 2018, the Transiting Exoplanet Survey Satellite has observed $\beta$ Pic for a total of 156 days. Here we report an analysis of the TESS photometric data set with the identification of a total of 30 transits of exocomets. Our statistical analysis shows that the number of transiting exocomet events ($N$) as a function of the absorption depth ($AD$) in the light curve follows a power law in the form $dN(AD) \propto AD^{-\alpha}$, where $\alpha=2.3\pm 0.4$. This distribution of absorption depth leads to a differential comet size distribution proportional to $R^{-\gamma}$, where $\gamma =3.6 \pm 0.8$, showing a striking similarity to the size distribution of comets in the Solar system and the distribution of a collisionally relaxed population ($\gamma_{\rm D}= 3.5$).