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Surface Density of Disk Galaxies in MOND

Antonino Del Popolo, Morgan Le Delliou

TL;DR

This work tests whether a quasi-universal central surface density is predicted by MOND for disk galaxies. By modeling spiral galaxies as a cylindrical double-exponential disk and computing the MOND phantom density, the authors derive the central surface density $\Sigma_c^*$ and analyze its behavior in the two asymptotic regimes $x=g/a_0$. They find a dual trend: in the Newtonian (high-acceleration) regime the central surface density tends toward the MOND scale $\Sigma_M=\frac{a_0}{2\pi G}$, while at low accelerations it falls below this quasi-universal value, indicating non-universality across low- and high-acceleration systems. These results challenge the Donato et al. universality claim and are consistent with broader evidence that surface density is not universal across all galaxy types; the study also outlines plans to test predictions against SPARC data to quantify $\Sigma_c^*$ across galaxy types.

Abstract

In this paper, we extend a paper by Milgrom (2009, MNRAS 398, 1023) dealing with the existence of a quasi-universal surface density for object of all mass and structure, if they are in the Newtonian regime, i.e., that their mean acceleration is larger than MOND typical acceleration $a_0$. This result is in agreement with Donato et al. (2009)'s results, claiming the existence of a quasi-universal surface density in all masses in galaxies. The Milgrom paper also predicts that objects with mean inner acceleration smaller than the values discussed do %es not show the quasi-universal behavior of the surface density discussed. In the present paper, we extend the result of Milgrom's paper, based on a point mass model, considering spiral galaxies, modelled with a double exponential disk. Similar to Milgrom's results, we find the existence of a universal surface density for galaxies with large surface density, and a different behavior for galaxies having small surface density.

Surface Density of Disk Galaxies in MOND

TL;DR

This work tests whether a quasi-universal central surface density is predicted by MOND for disk galaxies. By modeling spiral galaxies as a cylindrical double-exponential disk and computing the MOND phantom density, the authors derive the central surface density and analyze its behavior in the two asymptotic regimes . They find a dual trend: in the Newtonian (high-acceleration) regime the central surface density tends toward the MOND scale , while at low accelerations it falls below this quasi-universal value, indicating non-universality across low- and high-acceleration systems. These results challenge the Donato et al. universality claim and are consistent with broader evidence that surface density is not universal across all galaxy types; the study also outlines plans to test predictions against SPARC data to quantify across galaxy types.

Abstract

In this paper, we extend a paper by Milgrom (2009, MNRAS 398, 1023) dealing with the existence of a quasi-universal surface density for object of all mass and structure, if they are in the Newtonian regime, i.e., that their mean acceleration is larger than MOND typical acceleration . This result is in agreement with Donato et al. (2009)'s results, claiming the existence of a quasi-universal surface density in all masses in galaxies. The Milgrom paper also predicts that objects with mean inner acceleration smaller than the values discussed do %es not show the quasi-universal behavior of the surface density discussed. In the present paper, we extend the result of Milgrom's paper, based on a point mass model, considering spiral galaxies, modelled with a double exponential disk. Similar to Milgrom's results, we find the existence of a universal surface density for galaxies with large surface density, and a different behavior for galaxies having small surface density.
Paper Structure (3 sections, 34 equations, 1 figure)

This paper contains 3 sections, 34 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Surface Density
  3. Discussion

Figures (1)

  • Figure 1: Left panel: the MOND column density in terms of the ratio $\Sigma_b/\Sigma_M$. Right panel: The MOND column density in terms of the ratio of the acceleration, $a_N$, and $\mu$. In both panels, the shaded regions bounded by dashed curves represent the $1\sigma$ evaluation induced by the approximations described in the text.