Evolution into a main sequence star - the gravitational energy term

Question

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 can't make sense of the phrase 'gravitational energy term to become negative'. Isn't gravitational energy always negative?

Also, how does the expansion of the central core cause this change in gravitational energy?

Answer 1

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.