Publikace ÚTF

Static Thin Disks with Power-law Density Profiles

Kotlařík P., Kofroň D., Semerák O.

The task of finding the potential of a thin circular disk with power-law radial density profile is revisited. The result, given in terms of infinite Legendre-type series in the above reference, has now been obtained in closed form thanks to the method of Conway employing Bessel functions. Starting from a closed-form expression for the potential generated by the elementary density term ρ 2l , we cover more generic-finite solid or infinite annular-thin disks using superposition and/or inversion with respect to the rim. We check several specific cases against the series-expansion form by numerical evaluation at particular locations. Finally, we add a method to obtain a closed-form solution for finite annular disks whose density is of "bump" radial shape, as modeled by a suitable combination of several powers of radius. Density and azimuthal pressure of the disks are illustrated on several plots, together with radial profiles of free circular velocity.
journal:The Astrophysical Journal
pages:id.161 (16 pages)
grants:Mass and charge currents in general relativity and astrophysics, GAČR 21-11268S; 2021-2023; hlavní řešitel: Oldřich Semerák
apj_931_161.pdf (1402.94 kB)

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