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

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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.
Keywords
galaxies: evolution, galaxies: kinematics and dynamics, galaxies: spiral, N-BODY SIMULATIONS, NUMERICAL EXPERIMENTS, FLAT GALAXIES, SPIRAL MODES, DYNAMICS, BAR

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MLA
De Rijcke, Sven, Jean-Baptiste Fouvry, and Walter Dehnen. “How Gravitational Softening Affects Galaxy Stability - I. Linear Mode Analysis of Disc Galaxies.” MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 485.1 (2019): 150–162. Print.
APA
De Rijcke, S., Fouvry, J.-B., & Dehnen, W. (2019). How gravitational softening affects galaxy stability - I. Linear mode analysis of disc galaxies. MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 485(1), 150–162.
Chicago author-date
De Rijcke, Sven, Jean-Baptiste Fouvry, and Walter Dehnen. 2019. “How Gravitational Softening Affects Galaxy Stability - I. Linear Mode Analysis of Disc Galaxies.” Monthly Notices of the Royal Astronomical Society 485 (1): 150–162.
Chicago author-date (all authors)
De Rijcke, Sven, Jean-Baptiste Fouvry, and Walter Dehnen. 2019. “How Gravitational Softening Affects Galaxy Stability - I. Linear Mode Analysis of Disc Galaxies.” Monthly Notices of the Royal Astronomical Society 485 (1): 150–162.
Vancouver
1.
De Rijcke S, Fouvry J-B, Dehnen W. How gravitational softening affects galaxy stability - I. Linear mode analysis of disc galaxies. MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY. 2019;485(1):150–62.
IEEE
[1]
S. De Rijcke, J.-B. Fouvry, and W. Dehnen, “How gravitational softening affects galaxy stability - I. Linear mode analysis of disc galaxies,” MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, vol. 485, no. 1, pp. 150–162, 2019.
@article{8605616,
  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.},
  author       = {De Rijcke, Sven and Fouvry, Jean-Baptiste and Dehnen, Walter},
  issn         = {0035-8711},
  journal      = {MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY},
  keywords     = {galaxies: evolution,galaxies: kinematics and dynamics,galaxies: spiral,N-BODY SIMULATIONS,NUMERICAL EXPERIMENTS,FLAT GALAXIES,SPIRAL MODES,DYNAMICS,BAR},
  language     = {eng},
  number       = {1},
  pages        = {150--162},
  title        = {How gravitational softening affects galaxy stability - I. Linear mode analysis of disc galaxies},
  url          = {http://dx.doi.org/10.1093/mnras/stz309},
  volume       = {485},
  year         = {2019},
}

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