A New Approach to Find the Böhm-Vitense gap

This paper discusses the Böhm-Vitense gap, a gap in the colours of stars that occurs when the atmosphere changes from radiative to convective in deep layers. We are using different algorithms for detecting gaps in colour-magnitude diagrams (CMDs), including the k-nearest neighbours (k-NN) and UniDip algorithms. We propose using a combination of the k-NN algorithm and the UniDip algorithm and manual verification to identify gaps unlikely to be of a statistical origin. Using the $Gaia$ photometric system, i.e. $BP-RP$, we took the data of 130 star clusters and searched for gaps in the ranges of 0.40 to 0.47 mag, and 0.56 to 0.60 mag, respectively. We analysed all data statistically and identified the gaps in the individual clusters. Finally, we applied the kernel density estimator to see how the gaps are distributed.