The horizontal branch (HB) is a stage of stellar evolution that immediately follows the red giant branch in stars whose masses are similar to the Sun's. The helium core flash that occurs to stars at the top of the red giant branch causes substantial changes in stellar structure, resulting in an overall reduction in luminosity, some contraction of the stellar envelope, and surfaces reaching higher temperatures. Horizontal-branch stars are powered by helium fusion in the core (via the triple-alpha process) and by hydrogen fusion in a shell surrounding the core.
Horizontal branches were discovered with the first deep photographic photometric studies of globular clusters  and were notable for being absent from all open clusters that had been studied up to that time. The horizontal branch is so named because in low-metallicity samples like globular clusters, HB stars lie along a roughly horizontal line in a Hertzsprung–Russell diagram (CMD).
In main sequence stars with masses up to 2.3 times the mass of the Sun, the thermonuclear fusion of hydrogen (bearing the name of p-p chain) at the core will steadily build up a concentration of helium at a rate primarily determined by the mass of the star. In due course, the helium-enriched core becomes unable to sustain nuclear fusion of hydrogen and the fusion process migrates outward to a shell. The core becomes a region of degenerate matter that does not contribute to the generation of energy. It continues to grow and increase in temperature as the hydrogen fusion along the shell contributes more helium.
If the star has more than about 0.5 solar masses, the core eventually reaches the temperature necessary for the fusion of helium into carbon through the triple-alpha process. The initiation of helium fusion begins across the core region, which will cause an immediate temperature rise and a rapid increase in the rate of fusion. Within a few seconds the core becomes non-degenerate and quickly expands, producing an event called helium flash. The output of this event is absorbed by the layers of plasma above, so the effects are not seen from the exterior of the star. The star now changes to a new equilibrium state, and its evolutionary path switches from the red giant branch (RGB) onto the horizontal branch of the Hertzsprung–Russell diagram. This term means that the luminosity of the star will stay relatively stable while the effective temperature increases, effectively migrating horizontally across the H–R diagram.
Stars with an initial mass close to the sun dip down to the red end of the horizontal branch when core helium burning starts, but show only a small increase in temperature before core helium is exhausted. More massive stars spend an extended time on the horizontal branch and show a larger increase in temperature as they burn helium in the core. The shape of the horizontal branch is due both to the movement of individual stars bluewards as they age, and to the temperature of stars with different masses when they reach the horizontal branch. There are further variations, both in luminosity and temperature, due to metallicity and helium content.
Although the horizontal branch is named because it consists largely of stars with approximately the same luminosity across a range of temperatures, lying in a horizontal bar on color–magnitude diagrams, the branch is far from horizontal at the blue end. The horizontal branch ends in a "blue tail" with hotter stars having lower luminosity, occasionally with a "blue hook" of extremely hot stars. The hottest horizontal-branch stars, referred to as extreme horizontal branch, have temperatures of 20,000–30,000K. This is far beyond what would be expected for a normal core helium burning star. Theories to explain these stars include binary interactions, and "late thermal pulses", where a thermal pulse that Asymptotic giant branch (AGB) stars experience regularly, occurs after fusion has ceased and the stars has entered the superwind phase. These stars are "born again" with unusual properties. Despite the bizarre-sounding process, this is expected to occur for 10% or more of post-AGB stars, although it is thought that only particularly late thermal pulses create extreme horizontal-branch stars, after the planetary nebular phase and when the central star is already cooling towards a white dwarf.
The RR Lyrae "gap" and horizontal-branch morphology
Globular cluster CMDs generally show horizontal branches that have a prominent gap in the HB. This gap in the CMD incorrectly suggests that the cluster has no stars in this region of its CMD. The gap occurs at the instability strip, so many stars in this region pulsate. These pulsating horizontal-branch stars are known as RR Lyrae variable stars and they are obviously variable in brightness with periods of up to 1.2 days . It requires an extended observing program to establish the star's true (that is, averaged over a full period) apparent magnitude and color. Such a program is usually beyond the scope of an investigation of a cluster's color–magnitude diagram. Because of this, while the variable stars are noted in tables of a cluster's stellar content from such an investigation, these variable stars are not included in the graphic presentation of the cluster CMD because data adequate to plot them correctly are unavailable. This omission often results in the RR Lyrae gap seen in many published globular cluster CMDs.
Different globular clusters often display different HB morphologies, by which is meant that the relative proportions of HB stars existing blue of the RR Lyr gap, within the gap, and to the red of the gap varies sharply from cluster to cluster. The underlying cause of different HB morphologies is a long-standing problem in stellar astrophysics. Chemical composition is one factor (usually in the sense that more metal-poor clusters have bluer HBs), but other stellar properties like age, rotation and helium content have also been suggested as affecting HB morphology. This has sometimes been called the "Second Parameter Problem" for globular clusters, because there exist pairs of globular clusters which seem to have the same metallicity yet have very different HB morphologies; one such pair is NGC 288 (which has a very blue HB) and NGC 362 (which has a rather red HB). The label "second parameter" acknowledges that some unknown physical effect is responsible for HB morphology differences in clusters that seem otherwise identical.
Relationship to the red clump
A related class of stars is the clump giants, those belonging to the so-called red clump, which are the relatively younger (and hence more massive) and usually more metal-rich population I counterparts to HB stars (which belong to population II). Both HB stars and clump giants are fusing helium to carbon in their cores, but differences in the structure of their outer layers result in the different types of stars having different radii, effective temperatures, and color. Since color index is the horizontal coordinate in a Hertzsprung–Russell diagram, the different types of star appear in different parts of the CMD despite their common energy source. In effect, the red clump represents one extreme of horizontal-branch morphology: all the stars are at the red end of the horizontal branch, and may be difficult to distinguish from stars ascending the red giant branch for the first time.
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