Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5487750 | New Astronomy | 2018 | 14 Pages |
Abstract
In view of astrophysical applications, we obtain very large scale numerical solutions to the Lane-Emden equations for spherical polytropes of index mâ¯>â¯5 and for the isothermal sphere (m=â), by considering Ïâ1, the inverse function of the gravitational potential. Since the domain of Ïâ1 is bounded, and the asymptotic behavior of its end-point singularities is known, highly accurate solutions can be obtained by spectral collocation methods. This leads to solutions for Ï that extend accurately to extremely large radii, well beyond those achieved by traditional numerical schemes on [0, â). As a reference, we include a table of values for the isothermal sphere (Lane-Emden function of the 2nd kind) spanning r=10â4 through r=10150 with at least nine significant figures. The corresponding semi-analytical asymptotic solution as râ¯ââ¯â is
Ïa(r)=lnr22+1.1779636±1Ã10â7r1/2cos(72lnr+1.0623271±1Ã10â7).
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Astronomy and Astrophysics
Authors
Yuta Ito, Andrew Poje, Carlo Lancellotti,