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

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posted on 22.05.2019, 14:57 by Sven De Rijcke, Jean-Baptiste Fouvry, Walter Dehnen
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.


JBF acknowledges support from Program number HST-HF2-51374 that was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555. SDR acknowledges financial support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 721463 to the SUNDIAL ITN network. WD acknowledges support by STFC grant ST/N000757/1.



Monthly Notices of the Royal Astronomical Society, 2019, 485(1), pp. 150–162

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/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Physics and Astronomy


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Monthly Notices of the Royal Astronomical Society


Oxford University Press (OUP), Royal Astronomical Society



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