MOND Prediction for the Velocity Dispersion of the `Feeble Giant' Crater II

TL;DR

This paper predicts a very low velocity dispersion for Crater II under MOND due to the external field effect, providing a test for MOND's validity in dwarf galaxies with unusual properties.

Contribution

It offers a novel MOND-based prediction for Crater II's velocity dispersion considering the external field effect, which is unique to MOND theory.

Findings

Predicted velocity dispersion of 2.1 km/s for Crater II.

Crater II's large size and low luminosity make it an ideal test case for MOND.

External field effect significantly influences the dynamics of Crater II.

Abstract

Crater II is an unusual object among the dwarf satellite galaxies of the Local Group in that it has a very large size for its small luminosity. This provides a strong test of MOND, as Crater II should be in the deep MOND regime ($g_{in} \approx 34\;\mathrm{km}^2\,\mathrm{s}^{-2}\,\mathrm{kpc}^{-1} \ll a_0 = 3700\;\mathrm{km}^2\,\mathrm{s}^{-2}\,\mathrm{kpc}^{-1}$). Despite its great distance ($\approx 120$ kpc) from the Milky Way, the external field of the host ($g_{ex} \approx 282\; \mathrm{km}^2\,\mathrm{s}^{-2}\,\mathrm{kpc}^{-1}$) comfortably exceeds the internal field. Consequently, Crater II should be subject to the external field effect, a feature unique to MOND. This leads to the prediction of a very low velocity dispersion: $\sigma_{efe} = 2.1^{+0.9}_{-0.6}\;\mathrm{km}\,\mathrm{s}^{-1}$.