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Miyamoto-Nagai discs embedded in the Binney logarithmic potential: analytical solution of the two-integrals Jeans equations
Astrophysics of Galaxies · Submitted 15 Dec 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We present the analytical solution of the two-integrals Jeans equations for Miyamoto-Nagai discs embedded in Binney logarithmic dark matter haloes.
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We present the analytical solution of the two-integrals Jeans equations for Miyamoto-Nagai discs embedded in Binney logarithmic dark matter haloes. The equations can be solved (both with standard methods and with the Residue Theorem) for arbitrary choices of the parameters, thus providing a very flexible two-component galaxy model, ranging from flattened discs to spherical systems. A particularly interesting case is obtained when the dark matter halo reduces to the Singular Isothermal Sphere. Azimuthal motions are separated in the ordered and velocity dispersion components by using the Satoh decomposition. The obtained formulae can be used in numerical simulations of galactic gas flows, for testing codes of stellar dynamics, and to study the dependence of the stellar velocity dispersion and of the asymmetric drift in the equatorial plane as a function of disc and halo flattenings. Here, we estimate the inflow radial velocities of the interstellar medium, expected by the mixing of the stellar mass losses of the lagging stars in the disc with a pre-existing gas in circular orbit.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present the analytical solution of the two-integrals Jeans equations for Miyamoto-Nagai discs embedded in Binney logarithmic dark matter haloes. | contribution 1.00 | 0.96 | 0.70 | asserted 1.00 |
| s1 | The equations can be solved (both with standard methods and with the Residue Theorem) for arbitrary choices of the parameters, thus providing a very flexible two-component galaxy model, ranging from flattened discs to spherical systems. | contribution 0.34 | 0.80 | 0.32 | asserted 0.87 |
| s2 | A particularly interesting case is obtained when the dark matter halo reduces to the Singular Isothermal Sphere. | result 0.39 | 0.50 | 0.07 | asserted 0.97 |
| s3 | Azimuthal motions are separated in the ordered and velocity dispersion components by using the Satoh decomposition. | method 1.00 | 0.83 | 0.05 | asserted 1.00 |
| s4 | The obtained formulae can be used in numerical simulations of galactic gas flows, for testing codes of stellar dynamics, and to study the dependence of the stellar velocity dispersion and of the asymmetric drift in the equatorial plane as a function of disc and halo flattenings. | future work 0.62 | 0.40 | 0.12 | asserted 0.54 |
| s5 | Here, we estimate the inflow radial velocities of the interstellar medium, expected by the mixing of the stellar mass losses of the lagging stars in the disc with a pre-existing gas in circular orbit. | result 0.49 | 0.86 | 0.09 | asserted 0.79 |
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Original abstract
We present the analytical solution of the two-integrals Jeans equations for Miyamoto-Nagai discs embedded in Binney logarithmic dark matter haloes. The equations can be solved (both with standard methods and with the Residue Theorem) for arbitrary choices of the parameters, thus providing a very flexible two-component galaxy model, ranging from flattened discs to spherical systems. A particularly interesting case is obtained when the dark matter halo reduces to the Singular Isothermal Sphere. Azimuthal motions are separated in the ordered and velocity dispersion components by using the Satoh decomposition. The obtained formulae can be used in numerical simulations of galactic gas flows, for testing codes of stellar dynamics, and to study the dependence of the stellar velocity dispersion and of the asymmetric drift in the equatorial plane as a function of disc and halo flattenings. Here, we estimate the inflow radial velocities of the interstellar medium, expected by the mixing of the stellar mass losses of the lagging stars in the disc with a pre-existing gas in circular orbit.
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In general it is expected (e.g., by chemical evolution studies) that disc galaxies host radial flows in their equatorial regions [ref] .
The effect of stellar migration on Galactic chemical evolution: a heuristic approach · General properties of the solution · 0.89
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