Modelling the SPARC galaxies using a neo-MOND formalism, and the subsequent derivations of the baryonic Tully-Fisher relation and Freeman's Law

David Roscoe

Published 2018-12-09Version 1

The SPARC sample consists of 175 nearby galaxies with modern surface photometry at $3.6\,\mu m$ and high quality rotation curves. The sample has been constructed to span very wide ranges in surface brightness, luminosity, rotation velocity and Hubble type, thereby forming a representative sample on galaxies in the nearby Universe. To date, the SPARC sample is the largest collection of galaxies with both high-quality rotation curves and NIR surface photometry. The neo-MOND model used here to analyse the SPARC sample recognizably conforms to the general pattern of the classical MOND algorithm, with the primary difference that, whereas the classical MOND model is purely phenomonological, the neo-MOND model is a special case of a general theory motivated by the ideas of Leibniz and Mach (not discussed here). The consequent results can be broadly summarized by the statement that dynamical mass (computed from neo-MOND fits to SPARC rotation curves) tracks photometric mass (estimated from SPARC surface photometry) with high fidelity in a statistically perfect way. Finally, it is shown that a generalized baryonic Tully-Fisher relation arises directly from the neo-MOND model itself, whilst the classical relation and Freeman's Law arise together in a highly related fashion via a special case of the model. We are able to show that rotation curves conforming to the requirements of this special case are plentiful in three large additional samples comprising $\approx 2400$ rotation curves in total and are proportionately present in the much smaller SPARC sample.