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I was reading the following from the textbook An Introduction to Modern Astrophysics by Bradley W. Carroll Dale A. Ostlie,

"Due to the onset of the highly temperature-dependent CNO reactions, a steep temperature gradient is established in the core, and some convection again develops in that region. At the local maximum in the luminosity on the H–R diagram near the short dashed line, the rate of nuclear energy production has become so great that the central core is forced to expand somewhat, causing the gravitational energy term to become negative [recall that ϵ = $ϵ_(nuclear)$ + $ϵ_(gravity)$] This effect is apparent at the surface as the total luminosity decreases toward its main-sequence value, accompanied by a decrease in the effective temperature."

I cant make sense of the sentence 'gravitational energy term to become negative'. Isn't gravitational energy always negative? Also how the expansion of central core cause this change in graviataional energy?

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  • $\begingroup$ In principle it depends only on your choice of the origin if energy is positive or negative. But to get your question right: You are talking about a young star getting on the main sequence, and it seems to be a heavy star since the CNO cycle is important? $\endgroup$ Commented Jun 27, 2022 at 20:22
  • $\begingroup$ At early stages CNO reactions are significant irrespective of their mass, no? $\endgroup$ Commented Jun 28, 2022 at 9:14

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The gravitational energy term is the rate at which energy is released by changes of gravitational potential energy. i.e. the $\epsilon$ terms are rates of change of energy. For instance, if a star contracts, this releases gravitational potential energy that adds to the power generated by nuclear fusion.

In a main sequence star, the "gravitational energy" term is close to zero because the star changes in size very slowly and basically all the luminosity is provided by nuclear fusion.

In the phase of evolution discussed in your quote, the core expands and the gravitational potential energy becomes less negative. This requires energy and so in the terminology of Carroll & Ostlie, the "gravitational energy term" becomes negative and the luminosity, which must be equal to the sum of the nuclear energy and gravitational energy terms, will fall.

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