Pre-supernova feedback sets the star cluster mass function to a power law and reduces the cluster formation efficiency

Context. The star cluster initial mass function is observed to have an inverse power law exponent around 2, yet there is no consensus on what determines this distribution, and why some variation is observed in different galaxies. Furthermore, the cluster formation efficiency (CFE) covers a range of values, particularly when considering different environments. These clusters are often used to empirically constrain star formation and as fundamental units for stellar feedback models. Detailed galaxy models must therefore accurately capture the basic properties of observed clusters to be considered predictive.Aims. We study how feedback mechanisms acting on different timescales and with different energy budgets affect the star cluster mass function and CFE.Methods. We use hydrodynamical simulations of a dwarf galaxy as a laboratory to study star cluster formation. We test different combinations of stellar feedback mechanisms, including stellar winds, ionizing radiation, and supernovae (SNe).Results. Each feedback mechanism affects the CFE and cluster mass function. Increasing the feedback budget by combining the different types of feedback decreases the CFE by reducing the number of massive clusters. Ionizing radiation is found to be especially influential. This effect depends on the timing of feedback initiation, as shown by comparing early and late feedback. Early feedback occurs from ionizing radiation and stellar winds with onset immediately after a massive star is formed. Late feedback occurs when energy injection only starts after the main-sequence lifetime of the most massive SN progenitor, a timing that is further influenced by the choice of the most massive SN progenitor. Late feedback alone results in a broad, flat mass function, approaching a log-normal shape in the complete absence of feedback. Early feedback, on the other hand, produces a power-law cluster mass function with lower CFE, albeit with a steeper slope than that usually observed.