Editing Red-giant branch (section)

==Evolution==
[[File:Zams and tracks.png|thumb|right|upright=1.5|Evolutionary tracks for stars of different masses:{{unordered list| the {{solar mass|0.6|link=y}} track shows the RGB and stops at the [[helium flash]].| the {{solar mass|1}} track shows a short but long-lasting subgiant branch and the RGB to the helium flash.| the {{solar mass|2}} track shows the [[subgiant]] branch and RGB, with a barely detectable blue loop onto the [[asymptotic giant branch|AGB]].| the {{solar mass|5}} track shows a long but very brief subgiant branch, a short RGB and an extended blue loop.}}]]
When a star with a mass from about {{solar mass|0.4}} ([[solar mass]]) to {{solar mass|12}} ({{solar mass|8}} for low-metallicity stars) exhausts its core hydrogen, it enters a phase of hydrogen shell burning during which it becomes a red giant, larger and cooler than on the main sequence. During hydrogen shell burning, the interior of the star goes 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.<ref name=catelan>{{cite conference|bibcode=2007AIPC..930...39C|arxiv=astro-ph/0703724|title=Structure and Evolution of Low-Mass Stars: An Overview and Some Open Problems|conference=GRADUATE SCHOOL IN ASTRONOMY: XI Special Courses at the National Observatory of Rio de Janeiro (XI CCE). |series=AIP Conference Proceedings|volume=930|pages=39–90|last1=Catelan|first1=Márcio|last2=Roig|first2=Fernando|last3=Alcaniz|first3=Jailson|last4=de la Reza|first4=Ramiro|last5=Lopes|first5=Dalton|year=2007|doi=10.1063/1.2790333|s2cid=15599804}}</ref>

Shell hydrogen fusion continues in stars of roughly solar mass until the helium core increases in mass sufficiently that it becomes [[degenerate matter|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.<ref name=salaris2005>{{cite book|bibcode=2005essp.book.....S|title=Evolution of Stars and Stellar Populations|url=https://archive.org/details/evolutionofstars0000sala|url-access=registration|pages=400|last1=Salaris|first1=Maurizio|last2=Cassisi|first2=Santi|year=2005}}</ref>

Subgiants more than about {{solar mass|2}} 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 star]]s and the RGB seen in young [[open cluster]]s 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]].<ref name=mermilliod>{{cite journal|bibcode=1981A&A....97..235M|title=Comparative studies of young open clusters. III – Empirical isochronous curves and the zero age main sequence|journal=Astronomy and Astrophysics|volume=97|pages=235|last1=Mermilliod|first1=J. C.|year=1981}}</ref><ref name=bedin>{{cite journal|bibcode=2004ApJ...605L.125B|arxiv=astro-ph/0403112|title=Ω Centauri: The Population Puzzle Goes Deeper|journal=The Astrophysical Journal|volume=605|issue=2|pages=L125|last1=Bedin|first1=Luigi R.|last2=Piotto|first2=Giampaolo|last3=Anderson|first3=Jay|last4=Cassisi|first4=Santi|last5=King|first5=Ivan R.|last6=Momany|first6=Yazan|last7=Carraro|first7=Giovanni|year=2004|doi=10.1086/420847|s2cid=2799751|url=https://zenodo.org/record/968404}}</ref>

===Ascending the red-giant branch===
[[File:Evolutionary track 1m.svg|thumb|Sun-like stars have a degenerate core on the red-giant branch and ascend to the tip before starting core helium fusion with a flash.]]
[[File:Evolutionary track 5m.svg|thumb|Stars more massive than the Sun do not have a degenerate core and leave the red-giant branch before the tip when their core helium ignites without a flash.]]
Stars at the foot of the red-giant branch all have a similar temperature around {{Val|5000|fmt=commas|ul=K}}, corresponding to an early to mid-K spectral type. Their luminosities range from a few times the luminosity of the sun for the least massive red giants to several thousand times as luminous for stars around {{solar mass|8}}.<ref name=vandenberg>{{cite journal|bibcode=2006ApJS..162..375V|arxiv=astro-ph/0510784|title=The Victoria-Regina Stellar Models: Evolutionary Tracks and Isochrones for a Wide Range in Mass and Metallicity that Allow for Empirically Constrained Amounts of Convective Core Overshooting|journal=The Astrophysical Journal Supplement Series|volume=162|issue=2|pages=375–387|last1=Vandenberg|first1=Don A.|last2=Bergbusch|first2=Peter A.|last3=Dowler|first3=Patrick D.|year=2006|doi=10.1086/498451|s2cid=1791448}}</ref>

As their hydrogen shells continue to produce more helium, the cores of RGB stars increase in mass and temperature. This causes the hydrogen shell to fuse more rapidly. Stars become more luminous, larger and somewhat cooler. They are described as ascending the RGB.<ref name=hekker>{{cite journal|bibcode=2011MNRAS.414.2594H|arxiv=1103.0141|title=Characterization of red giant stars in the public Kepler data|journal=Monthly Notices of the Royal Astronomical Society|volume=414|issue=3|pages=2594|last1=Hekker|first1=S.|last2=Gilliland|first2=R. L.|last3=Elsworth|first3=Y.|last4=Chaplin|first4=W. J.|last5=De Ridder|first5=J.|last6=Stello|first6=D.|last7=Kallinger|first7=T.|last8=Ibrahim|first8=K. A.|last9=Klaus|first9=T. C.|last10=Li|first10=J.|year=2011|doi=10.1111/j.1365-2966.2011.18574.x|doi-access=free |s2cid=118513871}}</ref>

On the ascent of the RGB, there are a number of internal events that produce observable external features. The outer [[Convective zone|convective envelope]] becomes deeper and deeper as the star grows and shell energy production increases. Eventually it reaches deep enough to bring fusion products to the surface from the formerly convective core, known as the first [[dredge-up]]. This changes the surface abundance of helium, carbon, nitrogen and oxygen.<ref name=stoesz>{{cite journal|bibcode=2003MNRAS.340..763S|arxiv=astro-ph/0212128|title=Oxygen isotopic ratios in first dredge-up red giant stars and nuclear reaction rate uncertainties revisited|journal=Monthly Notices of the Royal Astronomical Society|volume=340|issue=3|pages=763|last1=Stoesz|first1=Jeffrey A.|last2=Herwig|first2=Falk|year=2003|doi=10.1046/j.1365-8711.2003.06332.x|doi-access=free |s2cid=14107804}}</ref> A noticeable clustering of stars at one point on the RGB can be detected and is known as the RGB bump. It is caused by a discontinuity in hydrogen abundance left behind by the deep convection. Shell energy production temporarily decreases at this discontinuity, effective stalling the ascent of the RGB and causing an excess of stars at that point.<ref name=cassisi>{{cite journal|bibcode=2011A&A...527A..59C|arxiv=1012.0419|title=The magnitude difference between the main sequence turn off and the red giant branch bump in Galactic globular clusters|journal=Astronomy & Astrophysics|volume=527|pages=A59|last1=Cassisi|first1=S.|last2=Marín-Franch|first2=A.|last3=Salaris|first3=M.|last4=Aparicio|first4=A.|last5=Monelli|first5=M.|last6=Pietrinferni|first6=A.|year=2011|doi=10.1051/0004-6361/201016066|s2cid=56067351}}</ref>

===Tip of the red-giant branch===
{{Main | Tip of the red-giant branch}}
For stars with a degenerate helium core, there is a limit to this growth in size and luminosity, known as the [[tip of the red-giant branch]], where the core reaches sufficient temperature to begin fusion. All stars that reach this point have an identical helium core mass of almost {{solar mass|0.5}}, and very similar stellar luminosity and temperature. These luminous stars have been used as standard candle distance indicators. Visually, the tip of the red-giant branch occurs at about absolute magnitude −3 and temperatures around 3,000 K at solar metallicity, closer to 4,000 K at very low metallicity.<ref name=vandenberg/><ref name=lee>{{cite journal|bibcode=1993ApJ...417..553L|title=The Tip of the Red Giant Branch as a Distance Indicator for Resolved Galaxies|journal=Astrophysical Journal |volume=417|pages=553|last1=Lee|first1=Myung Gyoon|last2=Freedman|first2=Wendy L.|last3=Madore|first3=Barry F.|year=1993|doi=10.1086/173334|doi-access=free}}</ref> Models predict a luminosity at the tip of {{solar luminosity|2000–2500}}, depending on metallicity.<ref name=salaris11997>{{cite journal|bibcode=1997MNRAS.289..406S|arxiv=astro-ph/9703186|title=The 'tip' of the red giant branch as a distance indicator: Results from evolutionary models|journal=Monthly Notices of the Royal Astronomical Society|volume=289|issue=2|pages=406|last1=Salaris|first1=Maurizio|last2=Cassisi|first2=Santi|year=1997|doi=10.1093/mnras/289.2.406|doi-access=free |s2cid=18796954}}</ref> In modern research, infrared magnitudes are more commonly used.<ref name=conn>{{cite journal|doi=10.1088/0004-637X/758/1/11|arxiv=1209.4952|title=A Bayesian Approach to Locating the Red Giant Branch Tip Magnitude. Ii. Distances to the Satellites of M31|journal=The Astrophysical Journal|volume=758|issue=1|pages=11|year=2012|last1=Conn|first1=A. R.|last2=Ibata|first2=R. A.|last3=Lewis|first3=G. F.|last4=Parker|first4=Q. A.|last5=Zucker|first5=D. B.|last6=Martin|first6=N. F.|last7=McConnachie|first7=A. W.|last8=Irwin|first8=M. J.|last9=Tanvir|first9=N.|last10=Fardal|first10=M. A.|last11=Ferguson|first11=A. M. N.|last12=Chapman|first12=S. C.|last13=Valls-Gabaud|first13=D.|bibcode = 2012ApJ...758...11C |s2cid=53556162}}</ref>

===Leaving the red-giant branch===
A degenerate core begins fusion explosively in an event known as the [[helium flash]], but externally there is little immediate sign of it. The energy is consumed in lifting the degeneracy in the core. The star overall becomes less luminous and hotter and migrates to the horizontal branch. All degenerate helium cores have approximately the same mass, regardless of the total stellar mass, so the helium fusion luminosity on the horizontal branch is the same. Hydrogen shell fusion can cause the total stellar luminosity to vary, but for most stars at near solar metallicity, the temperature and luminosity are very similar at the cool end of the horizontal branch. These stars form the [[red clump]] at about 5,000 K and {{solar luminosity|50}}. Less massive hydrogen envelopes cause the stars to take up a hotter and less luminous position on the horizontal branch, and this effect occurs more readily at low metallicity so that old metal-poor clusters show the most pronounced horizontal branches.<ref name=salaris2005/><ref name=dantona>{{cite journal|arxiv=astro-ph/0209331|bibcode=2002A&A...395...69D|doi=10.1051/0004-6361:20021220|title=Helium variation due to self-pollution among Globular Cluster stars|journal=Astronomy and Astrophysics|volume=395|pages=69–76|year=2002|last1=d'Antona|first1=F.|last2=Caloi|first2=V.|last3=Montalbán|first3=J.|last4=Ventura|first4=P.|last5=Gratton|first5=R.|s2cid=15262502}}</ref>

Stars initially more massive than {{solar mass|2}} have non-degenerate helium cores on the red-giant branch. These stars become hot enough to start triple-alpha fusion before they reach the tip of the red-giant branch and before the core becomes degenerate. They then leave the red-giant branch and perform a blue loop before returning to join the asymptotic giant branch. Stars only a little more massive than {{solar mass|2}} perform a barely noticeable blue loop at a few hundred {{solar luminosity}} before continuing on the AGB hardly distinguishable from their red-giant branch position. More massive stars perform extended blue loops which can reach 10,000 K or more at luminosities of {{solar luminosity|thousands of}}. These stars will cross the [[instability strip]] more than once and pulsate as [[Classical Cepheid variable|Type I (Classical) Cepheid variable]]s.<ref name=bono>{{cite journal|bibcode=2000ApJ...543..955B|arxiv=astro-ph/0006251|title=Intermediate-Mass Star Models with Different Helium and Metal Contents|journal=The Astrophysical Journal|volume=543|issue=2|pages=955|last1=Bono|first1=Giuseppe|last2=Caputo|first2=Filippina|last3=Cassisi|first3=Santi|last4=Marconi|first4=Marcella|last5=Piersanti|first5=Luciano|last6=Tornambè|first6=Amedeo|year=2000|doi=10.1086/317156|s2cid=18898755}}</ref>

===Properties===
The table below shows the typical lifetimes on the main sequence (MS), subgiant branch (SB) and red-giant branch (RGB), for stars with different initial masses, all at solar metallicity (Z = 0.02). Also shown are the helium core mass, surface effective temperature, radius and luminosity at the start and end of the RGB for each star. The end of the red-giant branch is defined to be when core helium ignition takes place.<ref name=pols>{{cite journal|bibcode=1998MNRAS.298..525P|title=Stellar evolution models for Z = 0.0001 to 0.03|journal=Monthly Notices of the Royal Astronomical Society|volume=298|issue=2|pages=525|last1=Pols|first1=Onno R.|last2=Schröder|first2=Klaus-Peter|last3=Hurley|first3=Jarrod R.|last4=Tout|first4=Christopher A.|last5=Eggleton|first5=Peter P.|year=1998|doi=10.1046/j.1365-8711.1998.01658.x|doi-access=free}}</ref>
{| class="wikitable"
|-
! rowspan=2 | Mass<br/>({{solar mass}}) !! rowspan=2 | MS (GYrs) 
! rowspan="2" |Hook (MYrs)!! rowspan="2" | SB (MYrs) !! rowspan=2 | RGB<br/>(MYrs) !! colspan=4 | RGB<sub>foot</sub><br/> !! colspan=4 | RGB<sub>end</sub><br/>
|-
! Core mass ({{solar mass}}) !! T<sub>eff</sub> (K) !! Radius ({{solar radius}}) !! Luminosity ({{solar luminosity}}) !! Core mass ({{solar mass}}) !! T<sub>eff</sub> (K) !! Radius ({{solar radius}}) !! Luminosity ({{solar luminosity}})
|- style="text-align:right;"
| 0.6 || 58.8 
|N/A|| 5,100 || 2,500 || 0.10 || 4,634 || 1.2 || 0.6 || 0.48 || 2,925 || 207 || 2,809
|- style="text-align:right;"
| 1.0 || 9.3 
|N/A|| 2,600 || 760 || 0.13 || 5,034 || 2.0 || 2.2 || 0.48 || 3,140 || 179 || 2,802
|- style="text-align:right;"
| 2.0 || 1.2 
|10|| 22 || 25 || 0.25 || 5,220 || 5.4 || 19.6 || 0.34 || 4,417 || 23.5 || 188
|- style="text-align:right;"
| 5.0 || 0.1 
|0.4|| 15 || 0.3 || 0.83 || 4,737 || 43.8 || 866.0 || 0.84 || 4,034 || 115 || 3,118
|}

Intermediate-mass stars only lose a small fraction of their mass as main-sequence and subgiant stars, but lose a significant amount of mass as red giants.<ref name=meynet>{{cite journal|bibcode=1993A&AS...98..477M|title=New dating of galactic open clusters|journal=Astronomy and Astrophysics Supplement Series|volume=98|pages=477|last1=Meynet|first1=G.|last2=Mermilliod|first2=J.-C.|last3=Maeder|first3=A.|year=1993}}</ref>

The mass lost by a star similar to the Sun affects the temperature and luminosity of the star when it reaches the horizontal branch, so the properties of red-clump stars can be used to determine the mass difference before and after the helium flash. Mass lost from red giants also determines the mass and properties of the [[white dwarf]]s that form subsequently. Estimates of total mass loss for stars that reach the tip of the red-giant branch are around {{solar mass|0.2–0.25}}. Most of this is lost within the final million years before the helium flash.<ref name=origlia>{{cite journal|bibcode=2002ApJ...571..458O|title=ISOCAM Observations of Galactic Globular Clusters: Mass Loss along the Red Giant Branch|journal=The Astrophysical Journal|volume=571|issue=1|pages=458–468|last1=Origlia|first1=Livia|last2=Ferraro|first2=Francesco R.|last3=Fusi Pecci|first3=Flavio|last4=Rood|first4=Robert T.|year=2002|doi=10.1086/339857|arxiv = astro-ph/0201445 |s2cid=18299018}}</ref><ref name=mcdonald>{{cite journal|bibcode=2011ApJS..193...23M|arxiv=1101.1095|title=Fundamental Parameters, Integrated Red Giant Branch Mass Loss, and Dust Production in the Galactic Globular Cluster 47 Tucanae|journal=The Astrophysical Journal Supplement|volume=193|issue=2|pages=23|last1=McDonald|first1=I.|last2=Boyer|first2=M. L.|last3=Van Loon|first3=J. Th.|last4=Zijlstra|first4=A. A.|last5=Hora|first5=J. L.|last6=Babler|first6=B.|last7=Block|first7=M.|last8=Gordon|first8=K.|last9=Meade|first9=M.|last10=Meixner|first10=M.|last11=Misselt|first11=K.|last12=Robitaille|first12=T.|last13=Sewiło|first13=M.|last14=Shiao|first14=B.|last15=Whitney|first15=B.|year=2011|doi=10.1088/0067-0049/193/2/23|s2cid=119266025}}</ref>

Mass lost by more massive stars that leave the red-giant branch before the helium flash is more difficult to measure directly. The current mass of Cepheid variables such as [[δ Cephei]] can be measured accurately because there are either binaries or pulsating stars. When compared with evolutionary models, such stars appear to have lost around 20% of their mass, much of it during the blue loop and especially during pulsations on the instability strip.<ref name=xu>{{cite journal|bibcode=2004A&A...418..213X|title=Blue loops of intermediate mass stars . I. CNO cycles and blue loops|journal=Astronomy and Astrophysics|volume=418|pages=213–224|last1=Xu|first1=H. Y.|last2=Li|first2=Y.|year=2004|doi=10.1051/0004-6361:20040024|doi-access=free}}</ref><ref name=neilson>{{cite journal|bibcode=2011A&A...529L...9N|arxiv=1104.1638|title=The Cepheid mass discrepancy and pulsation-driven mass loss|journal=Astronomy & Astrophysics|volume=529|pages=L9|last1=Neilson|first1=H. R.|last2=Cantiello|first2=M.|last3=Langer|first3=N.|year=2011|doi=10.1051/0004-6361/201116920|s2cid=119180438}}</ref>