Editing Subgiant (section)

==Subgiant branch==
[[File:Zams and tracks.png|thumb|left|upright=1.4|Stellar evolutionary tracks:{{unordered list|the {{solar mass|5}} track shows a hook and a subgiant branch crossing the [[Hertzsprung gap]]|the {{solar mass|2}} track shows a hook and pronounced subgiant branch|lower-mass tracks show very short long-lasting subgiant branches}}]]
The subgiant branch is a stage in the evolution of low to intermediate mass stars. Stars with a subgiant spectral type are not always on the evolutionary subgiant branch, and vice versa. For example, the stars [[FK Comae Berenices|FK Com]] and [[31 Comae Berenices|31 Com]] both lie in the Hertzsprung Gap and are likely evolutionary subgiants, but both are often assigned giant luminosity classes. The spectral classification can be influenced by metallicity, rotation, unusual chemical peculiarities, etc. The initial stages of the subgiant branch in a star like the sun are prolonged with little external indication of the internal changes. One approach to identifying evolutionary subgiants include chemical abundances such as Lithium which is depleted in subgiants,<ref name=lebre>{{cite journal|bibcode=1999A&A...345..936L|title=Lithium and rotation on the subgiant branch. I. Observations and spectral analysis|journal=Astronomy and Astrophysics|volume=345|pages=936|last1=Lèbre|first1=A.|last2=De Laverny|first2=P.|last3=De Medeiros|first3=J. R.|last4=Charbonnel|first4=C.|last5=Da Silva|first5=L.|year=1999}}</ref> and coronal emission strength.<ref name=ayres1998>{{cite journal|bibcode=1998ApJ...496..428A|title=The Coronae of Moderate-Mass Giants in the Hertzsprung Gap and the Clump|journal=The Astrophysical Journal|volume=496|pages=428–448|last1=Ayres|first1=Thomas R.|last2=Simon|first2=Theodore|last3=Stern|first3=Robert A.|last4=Drake|first4=Stephen A.|last5=Wood|first5=Brian E.|last6=Brown|first6=Alexander|year=1998|issue=1|doi=10.1086/305347|doi-access=free}}</ref>

As the fraction of hydrogen remaining in the core of a main sequence star decreases, the core [[virial theorem|temperature increases]] and so the rate of fusion increases.  This causes stars to evolve slowly to higher luminosities as they age and broadens the main sequence band in the [[Hertzsprung–Russell diagram]].

Once a main sequence star ceases to fuse hydrogen in its core, the core begins to collapse under its own gravity. This causes it to increase in temperature and hydrogen fuses in a shell outside the core, which provides more energy than core hydrogen burning. Low- and intermediate-mass stars expand and cool until at about 5,000 K they begin to increase in luminosity in a stage known as the [[red-giant branch]]. The transition from the main sequence to the red giant branch is known as the subgiant branch.  The shape and duration of the subgiant branch varies for stars of different masses, due to differences in the internal configuration of the star.

===Very-low-mass stars===
[[Red dwarf|Stars less massive]] than about {{solar mass|0.4}} are convective throughout most of the star. These stars continue to fuse hydrogen in their cores until essentially the entire star has been converted to helium, and they do not develop into subgiants. Stars of this mass have main-sequence lifetimes many times longer than the current age of the Universe.<ref name=salaris2005/>

==={{Solar mass|0.4}} to {{solar mass|0.9}}===
[[File:M5 colour magnitude diagram.png|thumb|right|upright=1.2|H–R diagram for [[globular cluster]] [[Messier 5|M5]], showing a short but densely-populated subgiant branch of stars slightly less massive than the Sun]]
Stars with 40 percent the mass of the Sun and larger have non-convective cores with a strong temperature gradient from the centre outwards. When they exhaust hydrogen at the core of the star, the shell of hydrogen surrounding the central core continues to fuse without interruption.  The star is considered to be a subgiant at this point although there is little change visible from the exterior.<ref name=pols/>  As the fusing hydrogen shell converts its mass into helium the convective effect separates the helium towards the core where it very slowly increases the mass of the non-fusing core of nearly pure helium plasma. As this takes place the fusing hydrogen shell gradually expands outward which increases the size of the outer shell of the star up to the subgiant size from two to ten times the original radius of the star when it was on the main sequence. The expansion of the outer layers of the star into the subgiant size nearly balances the increase energy generated by the hydrogen shell fusion causing the star to nearly maintain its surface temperature. This causes the spectral class of the star to change very little in the lower end of this range of star mass. The subgiant surface area radiating the energy is so much larger the potential [[circumstellar habitable zone]] where planetary orbits will be in the range to form liquid water is shifted much further out into any planetary system. The surface area of a sphere is found as 4πr<sup>2</sup> so a sphere with a radius of {{solar radius|2}} will release 400% as much energy at the surface and a sphere with a {{solar radius|10}} will release 10000% as much energy.{{citation needed|date=January 2022}}

The helium core mass is below the [[Schönberg–Chandrasekhar limit]] and it remains in thermal equilibrium with the fusing hydrogen shell.  Its mass continues to increase and the star very slowly expands as the hydrogen shell migrates outwards.  Any increase in energy output from the shell goes into expanding the envelope of the star and the luminosity stays approximately constant.  The subgiant branch for these stars is short, horizontal, and heavily populated, as visible in very old clusters.<ref name=pols/>

After one to eight billion years, the helium core becomes too massive to support its own weight and becomes degenerate.  Its temperature increases, the rate of fusion in the hydrogen shell increases, the outer layers become strongly convective, and the luminosity increases at approximately the same effective temperature.  The star is now on the [[Red-giant branch]].<ref name=salaris2005/>

===Mass {{Solar mass|1 to 8}}===
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.<ref name=pols/>

The core of stars below about {{solar mass|2}} 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 [[convective overshoot|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.<ref name=salaris2005/>

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 {{solar mass|1–2}} 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.<ref name=salaris2005>{{cite journal|bibcode=2005essp.book.....S|title=Evolution of Stars and Stellar Populations|url=https://archive.org/details/evolutionofstars0000sala|url-access=registration|journal=Evolution of Stars and Stellar Populations|pages=400|last1=Salaris|first1=Maurizio|last2=Cassisi|first2=Santi|year=2005}}</ref>

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&nbsp;K to around 5,000&nbsp;K.  Relatively few stars are seen in this stage of their evolution and there is an apparent lack in the H–R diagram known as the [[Hertzsprung gap]].  It is most obvious in clusters from a few hundred million to a few billion years old.<ref name=merlilliod>{{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>

===Massive stars===
Beyond about {{solar mass|8–12}}, depending on metallicity, stars have hot massive convective cores on the main sequence due to [[CNO cycle]] fusion. Hydrogen shell fusion and subsequent core helium fusion begin soon after core hydrogen exhaustion, before the star could reach the red giant branch.  Such stars, for example early B main sequence stars, experience a brief and shortened subgiant branch before becoming [[supergiant]]s.  They may also be assigned a giant spectral luminosity class during this transition.<ref name=hurley>{{cite journal|bibcode=2000MNRAS.315..543H|title=Comprehensive analytic formulae for stellar evolution as a function of mass and metallicity|journal=Monthly Notices of the Royal Astronomical Society|volume=315|issue=3|pages=543|last1=Hurley|first1=Jarrod R.|last2=Pols|first2=Onno R.|last3=Tout|first3=Christopher A.|year=2000|doi=10.1046/j.1365-8711.2000.03426.x|doi-access=free |arxiv = astro-ph/0001295 |s2cid=18523597}}</ref>

In very massive O-class main sequence stars, the transition from main sequence to giant to supergiant occurs over a very narrow range of temperature and luminosity, sometimes even before core hydrogen fusion has ended, and the subgiant class is rarely used.  Values for the surface gravity, log(g), of O-class stars are around 3.6 cgs for giants and 3.9 for dwarfs.<ref name=martins>{{cite journal|bibcode= 2005A&A...436.1049M|doi=10.1051/0004-6361:20042386|title=A new calibration of stellar parameters of Galactic O stars|journal=Astronomy and Astrophysics|volume=436|issue=3|pages=1049–1065|year=2005|last1=Martins|first1=F.|last2=Schaerer|first2=D.|last3=Hillier|first3=D. J.|arxiv = astro-ph/0503346 |s2cid=39162419}}</ref>  For comparison, typical log(g) values for K class stars are 1.59 ([[Aldebaran]]) and 4.37 ([[α Centauri B]]), leaving plenty of scope to classify subgiants such as [[Eta Cephei|η Cephei]] with log(g) of 3.47.  Examples of massive subgiant stars include [[Theta2 Orionis|θ<sup>2</sup> Orionis A]] and the primary star of the [[Delta Circini|δ Circini system]], both class O stars with masses of over {{solar mass|20}}.

===Properties===
This table shows the typical lifetimes on the main sequence (MS) and subgiant branch (SB), as well as any hook duration between core hydrogen exhaustion and the onset of shell burning, 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 subgiant branch for each star.  The end of the subgiant branch is defined to be when the core becomes degenerate or when the luminosity starts to increase.<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<br/>(MYrs) !! colspan=4 | Start !! colspan=4 | End !! rowspan=2 | Example
|-
! He Core ({{solar mass}}) !! T<sub>eff</sub> (K) !! Radius ({{solar radius}}) !! Luminosity ({{solar luminosity}}) !! He Core ({{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 || 0.047 || style="background-color:#{{Color temperature|4763|hexval}}"|4,763 || 0.9 || 0.3 || 0.10 || 4,634 || 1.2 || 0.6 || [[Lacaille 8760|{{nowrap|Lacaille 8760}}]]
|- style="text-align:right;"
| 1.0 || 9.3 || N/A || 2,600 || 0.025 || style="background-color:#{{Color temperature|5766|hexval}}"|5,766 || 1.2 || 1.5 || 0.13 || 5,034 || 2.0 || 2.2 || The [[Sun]]
|- style="text-align:right;"
| 2.0 || 1.2 || 10 || 22 || 0.240 || style="background-color:#{{Color temperature|7490|hexval}}"|7,490 || 3.6 || 36.6 || 0.25 || 5,220 || 5.4 || 19.6 || [[Sirius]]
|- style="text-align:right;"
| 5.0 || 0.1 || 0.4 || 15 || 0.806 || style="background-color:#{{Color temperature|14544|hexval}}"|14,544 || 6.3 || 1,571.4 || 0.83 || 4,737 || 43.8 || 866.0 || [[Alkaid]]
|}

In general, stars with lower metallicity are smaller and hotter than stars with higher metallicity.  For subgiants, this is complicated by different ages and core masses at the [[main sequence turnoff]].  Low metallicity stars develop a larger helium core before leaving the main sequence, hence lower mass stars show a hook at the start of the subgiant branch.  The helium core mass of a Z=0.001 (extreme [[population II]]) {{solar mass|1}} star at the end of the main sequence is nearly double that of a Z=0.02 ([[population I]]) star.  The low metallicity star is also over 1,000 K hotter and over twice as luminous at the start of the subgiant branch.  The difference in temperature is less pronounced at the end of the subgiant branch, but the low metallicity star is larger and nearly four times as luminous.  Similar differences exist in the evolution of stars with other masses, and key values such as the mass of a star that will become a supergiant instead of reaching the red giant branch are lower at low metallicity.<ref name=pols/>