A QUMOND galactic N-body code - I. Poisson solver and rotation curve fitting

Abstract

Here we present a new particle‐mesh galactic N‐body code that uses the full multigrid algorithm for solving the modified Poisson equation of the quasi‐linear formulation of modified Newtonian dynamics (QUMOND). A novel approach for handling the boundary conditions using a refinement strategy is implemented and the accuracy of the code is compared with analytical solutions of Kuzmin discs. We then employ the code to compute the predicted rotation curves for a sample of five spiral galaxies from the THINGS sample. We generated static N‐body realizations of the galaxies according to their stellar and gaseous surface densities and allowed their distances, mass‐to‐light ratios (M/L values) and both the stellar and gas scale‐heights to vary in order to estimate the best‐fitting parameters. We found that NGC 3621, NGC 3521 and DDO 154 are well fitted by MOND using expected values of the distance and M/L. NGC 2403 required a moderately larger M/L than expected and NGC 2903 required a substantially larger value. The surprising result was that the scale‐height of the dominant baryonic component was well constrained by the rotation curves: the gas scale‐height for DDO 154 and the stellar scale‐height for the others. In fact, if the suggested stellar scale‐height (one‐fifth the stellar scale‐length) was used in the case of NGC 3621 and NGC 3521 it would not be possible to produce a good fit to the inner rotation curve. For each of the four stellar dominated galaxies, we calculated the vertical velocity dispersions which we found to be, on the whole, quite typical compared with observed stellar vertical velocity dispersions of face‐on spirals. We conclude that modelling the gas scale‐heights of the gas‐rich dwarf spiral galaxies will be vital in order to make precise conclusions about MOND.

Isolated and non-isolated dwarfs in terms of modified Newtonian dynamics

“…Alternatively, considerations similar to Angus et al (2012) could be made: they varied the gaseous scale-height while fitting the rotation curve of DDO 154, and found that increasing the scale-height from 0.3 kpc to 0.7 kpc reduced the χ 2 by 30%. The effect of increasing the scale-height of KK 246 would mainly be to reduce the velocity of the MOND prediction at the innermost point.…”

Star formation triggered by galaxy interactions in modified gravity

“…After the pioneering work of Brada & Milgrom (1999), only a handful of codes have been designed (Nipoti et al 2007;Llinares et al 2008;Angus et al 2012), but all with their own caveats, notably regarding the treatment of hydrodynamics. The first treatment of gas in MOND simulations was proposed by Tiret & Combes (2008a), who used sticky particles, but a full hydrodynamical treatment of gas has become possible only recently thanks to the patches of the RAMSES code developed by Lüghausen et al (2015) and Candlish et al (2015).…”

Practically linear analogs of the Born-Infeld and other nonlinear theories

“…Thus, U ′ → 1/2 in this limit and so it is seen that the total phantom charge vanishes: q p (x)d 3 x = 0. This is clearly true also for the PL theory (10), where, again, applying a Gauss integration over the whole volume gives…”

“…This PL version of MOND has since been put to good use for predicting and calculating MOND effects in the solar system [8] [9], for calculating MOND fields of galaxies (e.g. [10]), and structure formation in MOND [11]. Here, I essentially extend the concept to more general NL problems.…”