R136a1, the most massive star confirmed in the R136 cluster of the Large Magellanic…

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Stellar structure, energy generation and evolution · Stellar structure, energy generation and evolution

Stars from the Inside, Ch Pressure against gravity: the equation of state, polytropes and the Lane-Emden equation

Problem

R136a1, the most massive star confirmed in the R136 cluster of the Large Magellanic Cloud, has a present-day mass that published estimates place near 200 M⊙200\,M_\odot, with a wide spread between studies. Take a round, conservative M=150 M⊙M = 150\,M_\odot and model it, in the Eddington standard model, as an n=3n=3 polytrope of mean molecular weight μ=0.61\mu=0.61 in which the ratio β\beta of gas pressure to total pressure is constant throughout. ((a)) Using Eddington's quartic 1−β=0.003 μ4β4(M/M⊙)21-\beta = 0.003\,\mu^4\beta^4(M/M_\odot)^2, find β\beta for M=150 M⊙M=150\,M_\odot by iterating βi+1=[1−βi0.003 μ4(M/M⊙)2]1/4\beta_{i+1} = \left[\dfrac{1-\beta_i}{0.003\,\mu^4(M/M_\odot)^2}\right]^{1/4} starting from β0=0.5\beta_0=0.5, until successive values agree to within 1%1\%. ((b)) State the fraction of the central pressure that this implies is supplied by radiation. ((c)) Given that the most luminous stars drive heavy radiatively driven winds, and that the most massive stars known cluster at a few hundred solar masses at most, comment on whether the value found in part (b) supports radiation pressure, rather than a shortage of nuclear fuel, as the effect that caps how massive a star can be.

Browse the problem library