Extensive and Intensive Aspects of Astrophysical Systems and Fine-Tuning

Abstract

Most astrophysical systems in our Universe are characterized by shallow gravitational potentials, with dimensionless compactness $|\Phi| \equiv r_s / R \ll 1$, where $r_{s}$ and $R$ are their Schwarzschild radius and typical size, respectively. While the existence and characteristic scales of such virialized systems depend on gravity, we demonstrate that the value of $|\Phi|$ -- and thus the non-relativistic nature of most astrophysical objects -- arises from microphysical parameters, specifically the fine structure constant and the electron-to-proton mass ratio, and is fundamentally independent of the gravitational constant $G$. It then follows that peak rms values of large-scale astrophysical velocities and escape velocities associated with naturally formed astrophysical systems are determined by electromagnetic and atomic physics, not by gravitation, and that the compactness $|\Phi|$ is always set by microphysical scales -- even for the most compact objects, such as neutron stars, where $|\Phi|$ is determined by quantities like the pion-to-proton mass ratio. Our results emphasize the central but underappreciated role played by dimensionless microphysical constants in shaping the macroscopic gravitational landscape of the Universe. In particular, we clarify that this independence of the compactness $|\Phi|$ from $G$ applies specifically to entire, virialized or degeneracy pressure-supported systems, naturally formed astrophysical systems -- such as stars, galaxies, and planets -- that have reached equilibrium between self-gravity and microphysical processes. Finally, we point out that a clear distinction between intensive and extensive astrophysical/cosmological properties could potentially shed a new light on the mass hierarchy and the cosmological constant problems; both may be related to the large complexity of our Universe. (abbridged)