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5. Brown Dwarf Luminosity Lifetimes. Zero-age main sequence stars much less than $0.5M_{\odot}$ are the subject of much discussion because they straddle the planet-star regime (e.g., Jupiter) and represent an alternate form of \"dark matter\". Assume a brown dwarf's luminosity derives from gravitational contraction alone. Its mass is $0.05M_{\odot}$, and its luminosity is $3 \times 10^{-5}L_{\odot}$. Such stars maintain a tight correlation between radius and mass given by $R \approx 9 \times 10^8 (M/M_{\odot})^{-1/3}cm$. If we assume that its luminosity has been constant (even when the star had a much larger radius), (a) calculate a radiation temperature and wavelength to demonstrate these stellar objects as \"dark\". (b) how long can a star of this type radiate before the contraction is halted by electron degeneracy pressure?

          5. Brown Dwarf Luminosity Lifetimes. Zero-age main sequence stars much less than $0.5M_{\odot}$ are the
subject of much discussion because they straddle the planet-star regime (e.g., Jupiter) and represent an
alternate form of \"dark matter\". Assume a brown dwarf's luminosity derives from gravitational contraction
alone. Its mass is $0.05M_{\odot}$, and its luminosity is $3 \times 10^{-5}L_{\odot}$. Such stars maintain a tight correlation between
radius and mass given by $R \approx 9 \times 10^8 (M/M_{\odot})^{-1/3}cm$. If we assume that its luminosity has been constant
(even when the star had a much larger radius),
(a) calculate a radiation temperature and wavelength to demonstrate these stellar objects as \"dark\".
(b) how long can a star of this type radiate before the contraction is halted by electron degeneracy
pressure?

5. Brown Dwarf Luminosity Lifetimes. Zero-age main sequence stars much less than 0.5M⊙ are the
subject of much discussion because they straddle the planet-star regime (e.g., Jupiter) and represent an
alternate form of d̈ark matter.̈ Assume a brown dwarf's luminosity derives from gravitational contraction
alone. Its mass is 0.05M⊙, and its luminosity is 3 × 10^-5L⊙. Such stars maintain a tight correlation between
radius and mass given by R ≈ 9 × 10^8 (M/M⊙)^-1/3cm. If we assume that its luminosity has been constant
(even when the star had a much larger radius),
(a) calculate a radiation temperature and wavelength to demonstrate these stellar objects as d̈ark.̈
(b) how long can a star of this type radiate before the contraction is halted by electron degeneracy
pressure?

Added by Steven M.

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