On the Origin of Scales and Scaling Laws in Star Formation

Abstract

Stars are the fundamental objects of astrophysics and their formation is a key process that influences the evolution of galaxies and planets, and the development of life. Understanding how stars form is crucial even for seemingly unconnected fields of astronomy, as the interpretation of observed starlight from galaxies (even as a background) and other unresolved sources relies on our understanding of star formation. There is no comprehensive theory of star formation, despite intense effort on both the theoretical and observational sides, due to the complicated, non-linear physics involved (e.g., magnetohydrodynamics, gravity, radiation) and the enormous dynamic range of the problem. My goal has been to identify the role different physical processes (e.g., turbulence, feedback) play in star formation. Using the semi-analytical framework that I developed, I found that a large number of star formation models are inherently sensitive to the initial conditions of the progenitor clouds (e.g., temperature). This led to another study where I predicted the expected variation of the initial mass function (IMF) of stars in a Milky-Way-like galaxy for different star formation models. I showed that IMF models where the peak is either set by turbulent properties or cooling physics (using an effective equation of state) are unable to reproduce the universal IMF of the Milky Way. I also utilized my semi-analytical tools to predict higher-order statistics of star formation: stellar correlation, multiplicity and the companion mass distribution for binaries. I showed that due to observational biases all explored models could roughly reproduce the observed multiplicity and companion mass distributions. This means that observations are currently unable to differentiate between most models. While working on these projects I found that several scaling relations (e.g., the slopes of IMF, stellar correlation function and gas column density distribution) are insensitive to our choice of physical model; they are universal. Inspired by this I developed an analytic model that I used to show that scale-free structure formation inherently leads to these scaling relations. This provides a deep physical reason why the mass functions and correlation functions of very different systems (e.g., stars, protostellar cores, star clusters, Dark matter halos) follow roughly the same power-law relations. My previous findings with my semi-analytical models indicated that isothermal collapse would lead to an infinite fragmentation cascade, i.e. there is no inherent low-mass cut-off. Part of the literature supports these findings and claims that additional physics is needed to imprint a mass scale into the problem, but there are theoretical models and simulations that claim that such a cut-off exists. Using GIZMO, a fully adaptive, meshless MHD code, I have carried out a convergence study and have shown that the isothermal fragmentation cascade continues to ever smaller scales without limit.