How gravitational softening affects galaxy stability I. Linear mode analysis of disc galaxies

Abstract

Linear perturbation is used to investigate the effect of gravitational softening on the retrieved two-armed spiral eigenmodes of razor-thin stellar discs. We explore four softening kernels with different degrees of gravity bias, and with/without compact support (compact in the sense that they yield exactly Newtonian forces outside the softening kernel). These kernels are applied to two disc galaxy models with well-known unsoftened unstable modes. We illustrate quantitatively the importance of a vanishing linear gravity bias to yield accurate frequency estimates of the unstable modes. As such, Plummer softening, while very popular amongst simulators, performs poorly in our tests. The best results, with excellent agreement between the softened and unsoftened mode properties, are obtained with softening kernels that have a reduced gravity bias, obtained by compensating for the sub-Newtonian forces at small interparticle distances with slightly super-Newtonian forces at radii near the softening length. We present examples of such kernels that, moreover, are analytically simple and computationally cheap. Finally, these results light the way to the construction of softening methods with even smaller gravity bias, although at the price of increasingly complex kernels.

arXiv comment14 pages, 7 figures, submitted to MNRAS

References in corpus (20)

• E pur si muove: Galiliean-invariant cosmological hydrodynamical simulations on a moving mesh
• Self-Perpetuating Spiral Arms in Disk Galaxies
• Towards optimal softening in 3D N-body codes: I. Minimizing the force error
• Transient spirals as superposed instabilities
• Spiral Instabilities in N-body Simulations I: Emergence from Noise
• Optimal Smoothing for N-Body Codes
• The Stability of Disks in Cusped Potentials
• Secular diffusion in discrete self-gravitating tepid discs II: accounting for swing amplification via the matrix method
• Stochasticity in N-body Simulations of Disc Galaxies
• Direct Integration of the Collisionless Boltzmann Equation in Six-dimensional Phase Space: Self-gravitating Systems
• THE OPTIMAL N-BODY METHOD FOR STABILITY STUDIES OF GALAXIES
• Gravitational softening as a smoothing operation
• Unstable Bar and Spiral Modes of Disk Galaxies
• Unstable Disk Galaxies. I. Modal Properties
• Vlasov versus N-body: the Hénon sphere
• Global m=1 instabilities and lopsidedness in disc galaxies
• Galactic bar: normal mode of the stellar disk or superposition of transient spirals?
• Spiral eigenmodes triggered by grooves in the phase space of disc galaxies
• A new framework for numerical simulations of structure formation
• Bisymmetric normal modes in soft-centred and realistic galactic discs

Cited by in corpus (4)

• Inferring galaxy dark halo properties from visible matter with Machine Learning
• On the long-term evolution of razor-thin galactic discs: Balescu-Lenard prediction and perspectives
• Linear response of rotating and flattened stellar clusters: the oblate Kuzmin-Kutuzov Stäckel family
• Numerical Study of Bar Suppression in Galaxy Models Due to Disc Heating