Quantifying star formation

Observations of star-forming regions only allow us to view a single snapshot in time of their evolution. By combining observations of different star-formation regions we can build up a statistical picture of how stars form in groups, how these groups dynamically evolve and eventually disperse into the field. But to fully understand how these regions formed in the first place we need to make use of numerical simulations which allow us to follow the evolution of a single star-forming region. Then we can make quantitative comparisons using a suite of methods that can be used to characterise star-forming regions (i.e. the spatial distribution of stars, or if a region is mass segregated and to what degree). By using these methods we can make inferences on not only the initial conditions of the observed star-forming regions (degree of substructure, local surface density and virial state), but also the initial conditions of planet formation. As these methods are used to infer the physics of star and planet formation they must be extensively tested on synthetic data to ensure that the methods are robust. The work herein is my investigations into the robustness of these methods on simulated data, and if these new methods can be used to reliably make inferences on the properties and physics of star-forming regions. I compare two new methods to more established and widely used methods to test their reliability. I show that INDICATE, a new clustering metric which has been used to investigate the star formation history of regions, can accurately identify areas of clustering in synthetic regions and gives results in agreement with other methods. However, INDICATE cannot be used to distinguish between star-forming regions with different morphologies, but it can be used to identify the presence of mass segregation. I investigate the evolution of phase space densities (quantified using the Mahalanobis density) of simulated star-forming regions using N -body simulations. This work was performed to better understand how the 6D phase space density evolves with time, and if its evolution depends on the initial conditions of the simulations. The method has been used to infer the likely star-formation conditions of exoplanet host stars with hot Jupiters being very dense. I find that using the 6D (position-velocity) phase space density of star-forming regions does not allow their initial conditions to be reliably discerned. I finish by investigating this possible link between the 6D phase space density of exoplanet host stars, quantified using the Mahalanobis density, and their initial formation conditions. I find that the phase space density of host stars and non-host stars does not evolve significantly differently for simulations with different initial conditions. I compare my results to previous works and find results in agreement with other works, that the Mahalanobis density is not detecting traces of the initial conditions but is instead measuring the kinematics of the host stars.