Open AccessA small contribution to the giant problem
Author(s) -
Eggleton Peter P.,
Faulkner John,
Can Robert C.
Publication year - 1998
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.1998.01655.x
Subject(s) - physics , polytropic process , chandrasekhar limit , envelope (radar) , radiative transfer , astrophysics , jump , limit (mathematics) , core (optical fiber) , plane (geometry) , white dwarf , geometry , quantum mechanics , optics , mathematical analysis , telecommunications , radar , stars , mathematics , computer science
We present a simple analytic model of a composite polytropic star, which exhibits a limiting Scho¨nberg–Chandrasekhar core mass fraction strongly analogous to the classic numerical result for an isothermal core, a radiative envelope and a μ‐jump (i.e. a molecular weight jump) at the interface. Our model consists of an n c = 5 core, an n e = 1 envelope and a μ‐jump by a factor ≥ 3; the core mass fraction cannot exceed 2/π. We use the classic U V plane to show that composite models will exhibit a Scho¨nberg–Chandrasekhar limit only if the core is ‘soft’, i.e. has n c ≥ 5, and the envelope is ‘hard’, i.e. has n e < 5; in the critical case ( n c = 5), the limit only exists if the μ‐jump is sufficiently large, ≥ 6/( n e + 1).