Binary Stars Beyond the Main Sequence and the Enigma of UV-Dim Stars

Binary stars play a crucial role in the dynamics and evolution of star clusters. However, our understanding of their frequency and distribution beyond the Main Sequence (MS) remains limited. Another intriguing yet enigmatic phenomenon involves UV-dim stars, whose presence in very young clusters has not been fully explored, leaving open the question of whether this trait emerges at cluster formation or develops over time. In this thesis, I derived high-precision multi-band photometry obtained from Hubble Space Telescope images of the young, star-forming cluster NGC 346 and the intermediate-age cluster BS 90, both located in the Small Magellanic Cloud and within the same field of view. Using this photometry, I investigate two distinct, unrelated topics: the occurrence of binary systems in evolved stellar stages, and the presence of UV-dim stars in young environments. To constrain the binary fraction in the Horizontal Branch (HB) and Red Giant Branch (RGB), I have combined the derived photometry with synthetic binary modeling, enabling the first direct identification and quantification of binary systems beyond the MS. I applied this method to three clusters of different ages: the old Galactic globular cluster 47 Tucanae, the intermediate-age cluster BS 90, and the young Large Magellanic Cloud cluster NGC 1783, developing a new approach for estimating binary fractions in evolved stellar stages, and extending the investigation to environments where the MS is not easily accessible. The method accounts for contamination by field stars and asymptotic giant branch (AGB) stars, refining the results based on the quality of the data for each cluster. The findings reveal significant differences in binary fraction between the MS, HB, and RGB. For instance, in 47 Tucanae, I derived a binary fraction of f_{bin}^{q>0.9} = 0.040 ± 0.012 in the HB and f_{bin}^{q>0.9} = 0.020 ± 0.004 in the RGB, compared to a literature value of f_{bin}^{q>0.5} = 0.009 ± 0.003 for the MS. Assuming a flat mass-ratio distribution, the inferred total binary fraction from HB and RGB stars appears inconsistent with the one derived from the MS. This paradox suggests two possible explanations: either the mass-ratio distribution is peaked around unity, making the binary fractions compatible, or the observed discrepancy arises from the presence of Blue Straggler Stars (BSSs), which could influence the binary fraction estimates in evolved populations. Following this second scenario, I derived the BSS fraction in the RGB for 47 Tucanae of f_{BSS} = 0.018 ± 0.004. Finally, I investigate the presence of UV-dim stars in the very young cluster NGC 346. The detection of UV-dim candidates in this ~3 Myr-old cluster, for the first time, provides evidence that this phenomenon may be an intrinsic feature of early cluster evolution. The presence of UV-dim stars in such a young system challenges existing theories about their origin, suggesting that they may form much earlier than previously thought. This discovery opens new paths for understanding their formation mechanisms and the role of circumstellar dust in shaping their observed properties.