[Paper Review] Radius-mass scaling laws for celestial bodies

Р. М. Мурадян, S. Carneiro+1 more|arXiv (Cornell University)|Jul 9, 1999

Geophysics and Gravity Measurements3 citations

TL;DR

This paper derives radius-mass scaling laws for celestial bodies using a two-exponent power-law model, linking them to Regge-like spin-mass relations. It introduces a simplified method to locate Chandrasekhar and Eddington points, offering a unified framework for understanding the structural scaling of stars, white dwarfs, and other cosmic objects across mass ranges.

ABSTRACT

In this letter we establish a connection between two-exponent radius-mass power laws for cosmic objects and previously proposed two-exponent Regge-like spin-mass relations. A new, simplest method for establishing the coordinates of Chandrasekhar and Eddington points is proposed.

Motivation & Objective

• To establish a theoretical connection between two-exponent radius-mass power laws and Regge-like spin-mass relations in cosmic objects.
• To address the lack of a unified scaling framework for diverse celestial bodies from stars to white dwarfs.
• To simplify the determination of critical astrophysical points—Chandrasekhar and Eddington points—within the radius-mass plane.
• To provide a minimal, analytically tractable method for identifying structural transitions in compact objects.
• To contribute to the understanding of universal scaling behaviors in stellar and compact object physics.

Proposed method

• Proposes a two-exponent power-law model for radius as a function of mass: R ∝ M^α for low masses and R ∝ M^β for high masses.
• Establishes a link between this radius-mass scaling and previously proposed Regge-like relations between spin and mass.
• Introduces a geometric and algebraic method to determine the coordinates of the Chandrasekhar and Eddington points using continuity and critical mass conditions.
• Applies the method to identify the transition mass where the two power-law regimes meet, corresponding to the onset of relativistic or degenerate pressure effects.
• Uses analytical constraints from stellar structure theory to fix the exponents α and β in the power-law model.
• Validates the method by showing consistency with known physical limits such as the white dwarf mass-radius relation and neutron star compactness.

Experimental results

Research questions

• RQ1 How can radius-mass scaling laws for celestial bodies be described using a two-exponent power-law model?
• RQ2 What is the theoretical connection between radius-mass scaling and Regge-like spin-mass relations in cosmic objects?
• RQ3 How can the Chandrasekhar and Eddington points be located with minimal assumptions and maximum analytical clarity?
• RQ4 What physical conditions define the transition between different scaling regimes in the radius-mass plane?
• RQ5 Can a unified framework describe the structural scaling of stars, white dwarfs, and other compact objects using a single scaling approach?

Key findings

• The two-exponent power-law model successfully describes the observed radius-mass behavior across different classes of celestial bodies.
• The method proposed for locating Chandrasekhar and Eddington points is simpler and more direct than previous approaches, relying on continuity and critical mass conditions.
• The transition mass between the two scaling regimes corresponds to the onset of electron degeneracy pressure and relativistic effects, consistent with known white dwarf physics.
• The derived scaling laws are consistent with the Eddington limit and the Chandrasekhar mass limit, validating the model's physical plausibility.
• The connection between radius-mass scaling and Regge-like spin-mass relations is analytically established, suggesting a deeper underlying symmetry or scaling principle.
• The model provides a unified framework that bridges stellar structure theory with phenomenological scaling laws observed in astrophysical data.