The gravitational potential of spiral perturbations I. The 2D (razor-thin) case
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911224078270464 |
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| author | Dehnen, Walter |
| author_facet | Dehnen, Walter |
| contents | I developed an efficient numerical method for obtaining the gravitational potential of razor-thin spiral perturbations and used it to assess the standard tight-winding approximation, which is found to be reasonably accurate for pitch angles $α\lesssim20^\circ$. I derived the analytic potential of razor-thin logarithmic spirals with an arbitrary power-law amplitude. Approximating a spiral locally by one of these models provides a second-order tight-winding approximation that predicts the phase offset between the spiral potential and density, the resulting radially increasing pitch of the potential, and the nonlocal outward angular-momentum transport by gravitational torques. Beyond the inner and outer edge of a spiral with $m$ arms, its potential is not winding ($α=90^\circ$), decays like $R^m$ and $R^{-1-m}$, respectively, and cannot be predicted by a local approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16615 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The gravitational potential of spiral perturbations I. The 2D (razor-thin) case Dehnen, Walter Astrophysics of Galaxies I developed an efficient numerical method for obtaining the gravitational potential of razor-thin spiral perturbations and used it to assess the standard tight-winding approximation, which is found to be reasonably accurate for pitch angles $α\lesssim20^\circ$. I derived the analytic potential of razor-thin logarithmic spirals with an arbitrary power-law amplitude. Approximating a spiral locally by one of these models provides a second-order tight-winding approximation that predicts the phase offset between the spiral potential and density, the resulting radially increasing pitch of the potential, and the nonlocal outward angular-momentum transport by gravitational torques. Beyond the inner and outer edge of a spiral with $m$ arms, its potential is not winding ($α=90^\circ$), decays like $R^m$ and $R^{-1-m}$, respectively, and cannot be predicted by a local approximation. |
| title | The gravitational potential of spiral perturbations I. The 2D (razor-thin) case |
| topic | Astrophysics of Galaxies |
| url | https://arxiv.org/abs/2507.16615 |