A pre-main-sequence star observed in the Orion Nebula cluster has mass

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 Stellar evolution: from the Hayashi track to the iron core, and the ages of clusters

Problem

A pre-main-sequence star observed in the Orion Nebula cluster has mass M=1.5 M⊙M = 1.5\,M_\odot, radius R=3 R⊙R = 3\,R_\odot and luminosity L=4 L⊙L = 4\,L_\odot. Treat these as roughly constant over the timescale of interest, ignore any nuclear energy generation, and use the Kelvin-Helmholtz estimate for the contraction time. ((a)) Estimate the Kelvin-Helmholtz time tKH=GM2/RLt_{\rm KH} = GM^2/RL for this star, in years. ((b)) Given that the cluster itself is about 11 to 2 Myr2\,\mathrm{Myr} old, state whether this star's contraction time is consistent with it still being on its way to the main sequence.

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