The stellar initial mass function (IMF) is the function that describes the mass distribution of stars (i.e. the number of stars born at each stellar mass) (Dib et al. 2017).
The IMF is written in the following form, where m is the mass and α3 determines the behavior of the function for the high-mass range (Weatherford et al. 2021). A low value of α3 means that more high-mass stars will form (a “top-heavy” IMF) and a high value of α3 means that fewer high-mass stars will form (a "top light" IMF) (Weatherford et al. 2021).
\begin{equation}
\xi (m) =
\begin{cases}
m^{-1.3} & 0.08\, \leq\, m/M_\odot\, \leq\, 0.5\\
m^{-2.3} & 0.5\, \leq\, m/M_\odot\, \leq\, 1.0\\
m^{-\alpha_3} & 1.0\, \leq\, m/M_\odot\, \leq\, 150.0
\end{cases}
\end{equation}
The IMF remains poorly constrained on the high-mass end as it varies over time and space (Weatherford et al. 2021). Therefore, the value of α3 is not well constrained.
The value α3 has a clear impact on the lifetime of stellar clusters (Weatherford et al. 2021). For example, a cluster with a top-heavy IMF will dissolve faster than a cluster with a flat IMF (Chatterjee et al. 2017). Dissolution is the process where stars escape a cluster over time. The top-heavy IMF cluster will produce stars and eventually black holes (BHs) of greater number and higher mass, which will cause the cluster to expand and potentially dissolve as BHs fall toward the center of the cluster (Weatherford et al. 2021). This process is known as "black hole burning" (Kremer et al. 2020a). Therefore, constraining the value of α3 will improve our understanding of star formation and cluster evolution.
One way that α3 can be constrained is by comparing simulation data to observational data. In this project, I compared N-body simulations of stellar clusters that had different values of α3 to observational data in order to constrain the value of α3.