Gravitational acceleration and tidal effects in spherical-symmetric density profiles

TL;DR

This paper analyzes various spherical density profiles and their gravitational and tidal effects, comparing theoretical predictions with observations, and applies the findings to globular clusters to understand their stability and dark matter influence.

Contribution

It provides a detailed classification of power-law and related density profiles, examines extremum points in gravitational acceleration, and assesses tidal effects on globular clusters with respect to dark matter.

Findings

Maximum gravitational acceleration points identified in density profiles

Predicted velocity curves compared with observational data

Tidal radius analysis applied to 17 globular clusters

Abstract

Pure power-law density profiles, $\rho(r)\propto r^{b-3}$, are classified in connection with the following reference cases: (i) isodensity, $b=3$, $\rho=$ const; (ii) isogravity, $b=2$, $g=$ const; (iii) isothermal, $b=1$, $v=[GM(r)/r]^{1/2}=$ const; (iv) isomass, $b=0$, $M=$ const. A restricted number of different families of density profiles including, in addition, cored power-law, generalized power-law, polytropes, are studied in detail with regard to both one-component and two-component systems. Considerable effort is devoted to the existence of an extremum point (maximum absolute value) in the gravitational acceleration within the matter distribution. Predicted velocity curves are compared to the data inferred from observations. Tidal effects on an inner subsystem are investigated and an application is made to globular clusters within the Galaxy. To this aim, the tidal radius is defined by balancing the opposite gravitational forces from the Galaxy and the selected cluster on a special point of the cluster boundary, lying between related centres of mass. The position of 17 globular clusters with respect to the stability region, where the tidal radius exceeds the observed radius, is shown for assigned dark-to-visible mass ratios and density profiles, among those considered, which are currently used for the description of galaxies and/or dark matter haloes.