Equilibrium sequences of irrotational binary polytropic stars: The case of double polytropic stars

Abstract

Solutions to equilibrium sequences of irrotational binary polytropic stars in Newtonian gravity are expanded in a power of = a0/R, where R and a0 are the orbital separation of the binary system and the radius of each star for R = ∞. For each order of , we should solve ordinary differential equations for arbitrary polytropic indices n. We show solutions for polytropic indices n = 0.5, 1, 1.5 and 2 up to 6 orders. Our semi-analytic solutions can be used to check the validity of numerical solutions. PACS number(s): 04.30. Db, 04.25.Dm, 97.80.Fk

Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity: Method and tests

“…In particular, we have shown that, in the Newtonian limit, our numerical results coincides with the semi-analytical solutions recently obtained by Taniguchi & Nakamura [63,64] for compressible polytropic stars. The only discrepancies appeared to be due to missing higher order terms in Taniguchi & Nakamura's solutions and not to some inaccuracy of the numerical code.…”

“…However the analytic solution, based on an expansion up to O((R 0 /d) 6 ), loses its accuracy for very close separations and cannot be used to test the code in this regime. [63,64] along an evolutionary sequence. Solid and dashed lines denote the results of numerical and analytic calculations, respectively.…”

“…The case of compressible fluid bodies has been investigated recently by Taniguchi & Nakamura [63,64], who have obtained semi-analytic solutions for equilibrium sequences of irrotational binary polytropic stars in Newtonian gravity. For an equal-mass star binary system with γ = 2, they have produced the following simple equations for the total energy E, the total angular momentum J, the orbital angular velocity Ω and the relative change in central baryon density:…”

“…12. Relative differences in total energy E, total angular momentum J, orbital angular velocity Ω, and relative change in central baryon density δρc when comparing the numerical solution with Taniguchi & Nakamura's analytic solution [63,64] along an equilibrium sequence. The horizontal axis denotes logarithmically d/R0, where d is the separation between the two stellar centers and R0 the stellar radius at infinite separation.…”

Equilibrium sequences of synchronized and irrotational binary systems composed of different mass stars in Newtonian gravity

“…Until now, all irrotational binaries of double fluid stars have been computed under the assumption of equal mass [16][17][18][19][20]32,29] except for the Newtonian semi-analytic solutions of the ellipsoidal approximation [33] and the perturbative approach [34,35] 2 , while binary systems of different masses have been calculated in the synchronized cases in Newtonian gravity [36][37][38] and in the first post-Newtonian [39]. In the present paper, we will show numerical results of synchronized and irrotational binary systems composed of different mass stars with the same polytropic equation of state in Newtonian gravity.…”