through several distinct stages which are reflected in the outward appearance. The evolutionary stages vary depending primarily on the mass of the star, but also on its metallicity. Subgiant phase After a main-sequence star has exhausted its core hydrogen, it begins to fuse hydrogen in a thick shell around a core consisting largely of helium. The mass of the helium core is below the Schönberg–Chandrasekhar limit and is in thermal equilibrium, and the star is a subgiant. Any additional energy production from the shell fusion is consumed in inflating the envelope and the star cools but does not increase in luminosity. Shell hydrogen fusion continues in stars of roughly solar mass until the helium core increases in mass sufficiently that it becomes degenerate. The core then shrinks, heats up and develops a strong temperature gradient. The hydrogen shell, fusing via the temperature-sensitive CNO cycle, greatly increases its rate of energy production and the stars is considered to be at the foot of the red-giant branch. For a star the same mass as the sun, this takes approximately 2 billion years from the time that hydrogen was exhausted in the core. Subgiants more than about reach the Schönberg–Chandrasekhar limit relatively quickly before the core becomes degenerate. The core still supports its own weight thermodynamically with the help of energy from the hydrogen shell, but is no longer in thermal equilibrium. It shrinks and heats causing the hydrogen shell to become thinner and the stellar envelope to inflate. This combination decreases luminosity as the star cools towards the foot of the RGB. Before the core becomes degenerate, the outer hydrogen envelope becomes opaque which causes the star to stop cooling, increases the rate of fusion in the shell, and the star has entered the RGB. In these stars, the subgiant phase occurs within a few million years, causing an apparent gap in the Hertzsprung–Russell diagram between B-type main-sequence stars and the RGB seen in young open clusters such as Praesepe. This is the Hertzsprung gap and is actually sparsely populated with subgiant stars rapidly evolving towards red giants, in contrast to the short densely populated low-mass subgiant branch seen in older clusters such as ω Centauri. Ascending the red-giant branch Stars at the foot of the red-giant branch all have a similar temperature around , corresponding to an early to mid-K spectral type. Their luminosities range from a few times the luminosity