A new paper by Alexandre Deur further details a finding on elliptical galaxies previously published in a conclusory manner.
[Submitted on 13 Oct 2020]
A correlation between the dark content of elliptical galaxies and their ellipticity
Observations indicate that the baryonic matter of galaxies is surrounded by vast dark matter halos, which nature remains unknown. This document details the analysis of the results published in MNRAS 438, 2, 1535 (2014) reporting an empirical correlation between the ellipticity of elliptical galaxies and their dark matter content. Large and homogeneous samples of elliptical galaxies for which their dark matter content is inferred were selected using different methods. Possible methodological biases in the dark mass extraction are alleviated by the multiple methods employed. Effects from galaxy peculiarities are minimized by a homogeneity requirement and further suppressed statistically. After forming homogeneous samples (rejection of galaxies with signs of interaction or dependence on their environment, of peculiar elliptical galaxies and of S0-type galaxies) a clear correlation emerges. Such a correlation is either spurious --in which case it signals an ubiquitous systematic bias in elliptical galaxy observations or their analysis-- or genuine --in which case it implies in particular that at equal luminosity, flattened medium-size elliptical galaxies are on average five times heavier than rounder ones, and that the non-baryonic matter content of medium-size round galaxies is small. It would also provides a new testing ground for models of dark matter and galaxy formation.The conclusion is as follows:
We investigated the possibility of a correlation between the dark matter content of elliptical galaxies and their ellipticity. Elliptical galaxies can differ importantly from each other, and peculiarities might bias the estimation of the dark mass, causing systematic and random variations. Therefore, it was important to select a large and homogeneous sample of galaxies. Effects of the peculiarities are then minimized by the homogeneity and suppressed statistically.
Furthemore, since the value of M/L depends on the galactic radius r at which the ratio is extracted, as well as on the wavelength at which the galaxy luminosity L is calculated (typically the B-band, but not always), it was necessary to normalize the M/L at a given r to a unique value. We chose r = 0.7Ref f and there, used the typical value 8M/L = M/L(0.7Ref f ). With this normalization, we found a clear correlation: h d(M/L)/d(Rmin/Rmax)i = −14.53 ± 4.77M/L. The dark matter information is obtained from six different approaches (virial theorem, stellar orbit modeling, orbits of planetary nebulae and globular clusters, embedded disk dynamics, hydrostatic equilibrium, and strong lensing) to minimize methodological bias. Possible effects of measurement or observation biases were studied thoroughly. Furthermore, we repeated the same analysis on the stellar M∗/L, see appendix B, and no significant correlation with ellipticity was found, as it should be. This suggests that our procedure is free of significant biases. Possible conclusions are either that:
1. There is a surprisingly strong influence of the dark matter halo on a galaxy shape, possibly from the halo shape as suggested by the stronger correlation generally seen when investigated with mass axis ratio rather than apparent (project luminous) axis ratio. This would allow us to experimentally address the question of the shape of the dark halo and be critical to understand galaxy formation.
2. The dynamical evidences from which the dark matter content of galaxy is inferred are misinterpreted. In fact, the impulse for the present study originated from a prediction from Ref.  (see also Refs. [33, 36]). In this framework, if a homogenous system is locally dense enough so that in that location, the nonlinearity of General Relativity are non negligible, this system should display a correlation between its dynamical total mass analyzed using Newton’s law of gravity (in our case, the galaxy dark mass) and its asymmetry (in our case, the galaxy ellipticity). Beside the present correlation, this effect also explains  the correlation between dynamical and baryonic matter accelerations observed in Ref. . Finally, it provides an explanation for the origin of dark energy: it emerges from the Universe inhomogeneities and anisotropies .
3. There is a significant bias in the data and/or methods, in which case they cannot be trusted to estimate accurately the dark matter content of elliptical galaxies. However, our thorough investigation of the various inter-dependences of the variables characterizing an elliptical galaxy reasonably suggests that this correlation is physical rather than a methodological, observational or measurement bias.
Finally, a practical use of the correlation is that once the total galactic mass is known the true ellipticity of the galaxy can be directly deduced.