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Homework 7 Solutions

55 f 175 and hence tc 54 10 7 m m 4 3 e

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Unformatted text preview: η 2 − η − 1 = 0 This can be solved in Mathematic or numerically to yield η = 0.55, f(η) = 1.75 and hence Tc = 5.4 × 10 7 M M 4/3 (e) [5 pts] The ignition temperature for hydrogen fusion is rough 3x106 K. Using the result from part (d), estimate the minimum mass a star must have to achieve hydrogen fusion. Setting Tc = 3x106 K, we get M = 0.12 M -­‐ this is a bit higher than the 0.072 M generally accepted as the hydrogen burning limit. This offset has to do with the form of the polytrope assumed above and neglecting absorption effects. In fact, this is a good estimate for the zero metallicity (Population III) hydrogen burning limit. ques%on 1a 3(a) 1H 3He x 100 4He H abundance is generally higher than He through most of the Sun because the general elemental abundances favor H over He (e.g., from Big Bang nucleosynthesis and subsequent stellar genera%ons). H and 4He remain at constant abundance from the photosphere down to 0.72 R due to convec%ve mixing, then there is a break when we reach the radia%ve zone where 4He...
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