Extensive and Intensive Aspects of Astrophysical Systems and Fine-Tuning

Most astrophysical systems (except for very compact objects such as, e.g., black holes and neutron stars) in our Universe are characterized by shallow gravitational potentials, with dimensionless compactness |Φ|≡rs/R≪1, where rs 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 |Φ|—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. In fact, the (generally extensive) gravitational potential becomes ‘locally’ intensive at the system boundary; the compactness parameter corresponds to the binding energy (or degeneracy energy, in the case of quantum degeneracy pressure-supported systems) per proton, representing the amount of work that needs to be done in order to allow proton extraction from the system. More generally, extensive properties of gravitating systems depend on G, whereas intensive properties do not. 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, |Φ|, is always set by microphysical scales—even for the most compact objects, such as neutron stars, where |Φ| is determined by quantities like the pion-to-proton mass ratio. This observation, largely overlooked in the literature, explains why the Universe is not dominated by relativistic, compact objects and connects the relatively low entropy of the observable Universe to underlying basic microphysics. 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, |Φ|, 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. In contrast, arbitrary subsystems (e.g., a piece cut from a planet) do not exhibit this property; well within/outside the gravitating object, the rms velocity is suppressed and G reappears. Finally, we point out that a clear distinction between intensive and extensive astrophysical/cosmological properties could potentially shed new light on the mass hierarchy and the cosmological constant problems; both may be related to the large complexity of our Universe.