effective temperature. The star is now on the Red-giant branch. Mass Stars as massive and larger than the Sun have a convective core on the main sequence. They develop a more massive helium core, taking up a larger fraction of the star, before they exhaust the hydrogen in the entire convective region. Fusion in the star ceases entirely and the core begins to contract and increase in temperature. The entire star contracts and increases in temperature, with the radiated luminosity actually increasing despite the lack of fusion. This continues for several million years before the core becomes hot enough to ignite hydrogen in a shell, which reverses the temperature and luminosity increase and the star starts to expand and cool. This hook is generally defined as the end of the main sequence and the start of the subgiant branch in these stars. The core of stars below about is still below the Schönberg–Chandrasekhar limit, but hydrogen shell fusion quickly increases the mass of the core beyond that limit. More-massive stars already have cores above the Schönberg–Chandrasekhar mass when they leave the main sequence. The exact initial mass at which stars will show a hook and at which they will leave the main sequence with cores above the Schönberg–Chandrasekhar limit depend on the metallicity and the degree of overshooting in the convective core. Low metallicity causes the central part of even low mass cores to be convectively unstable, and overshooting causes the core to be larger when hydrogen becomes exhausted. Once the core exceeds the C–R limit, it can no longer remain in thermal equilibrium with the hydrogen shell. It contracts and the outer layers of the star expand and cool. The energy to expand the outer envelope causes the radiated luminosity to decrease. When the outer layers cool sufficiently, they become opaque and force convection to begin outside the fusing shell. The expansion stops and the radiated luminosity begins to increase, which is defined as the start of the red giant branch for these stars. Stars with an initial mass approximately can develop a degenerate helium core before this point and that will cause the star to enter the red giant branch as for lower mass stars. The core contraction and envelope expansion is very rapid, taking only a few million years. In this time the temperature of the star will cool from its main sequence value of 6,000–30,000 K