Editing Alpha process

{{Short description|Nuclear fusion reaction}}
[[File:Kernfusionen1_en.png|thumb|upright=1.4|Creation of elements beyond carbon through alpha process]]
The '''alpha process''', also known as '''alpha capture''' or the '''alpha ladder''', is one of two classes of [[nuclear fusion]] reactions by which stars convert [[helium]] into heavier [[chemical element|elements]]. The other class is a cycle of reactions called the [[triple-alpha process]], which consumes only helium, and produces [[carbon]].<ref name=narlikar>{{cite book |last=Narlikar |first=Jayant V. |title=From Black Clouds to Black Holes |year=1995 |publisher=[[World Scientific]] |isbn=978-9810220334 |url=https://books.google.com/books?id=0_gmjz-L70EC&pg=PA94 |page=94}}</ref> The alpha process most commonly occurs in massive stars and during [[Supernova|supernovae]].

Both processes are preceded by [[hydrogen fusion]], which produces the [[helium]] that fuels both the triple-alpha process and the alpha ladder processes. After the [[triple-alpha process]] has produced enough carbon, the alpha-ladder begins and fusion reactions of increasingly heavy elements take place, in the order listed below. Each step only consumes the product of the previous reaction and helium. The later-stage reactions which are able to begin in any particular star, do so while the prior stage reactions are still under way in outer layers of the star.

:<math chem>\begin{array}{ll}
\ce{ ~{}_6^{12}C\ ~~+ {}_2^4He\ -> ~{}_{8}^{16}O\ \ ~+ \gamma~,}& E=\mathsf{7.16\ MeV}
\\
\ce{ ~{}_8^{16}O\ ~~+ {}_2^4He\ -> {}_{10}^{20}Ne\ \ + \gamma~,}& E=\mathsf{4.73\ MeV}
\\
\ce{ {}_{10}^{20}Ne\ ~+ {}_2^4He\ -> {}_{12}^{24}Mg\ + \gamma~,}& E=\mathsf{9.32\ MeV}
\\
\ce{ {}_{12}^{24}Mg\ + {}_2^4He\ -> {}_{14}^{28}Si\  ~~+ \gamma~,}& E=\mathsf{9.98\ MeV}
\\
\ce{ {}_{14}^{28}Si\ ~~+ {}_2^4He\ -> {}_{16}^{32}S\ \ ~~~+ \gamma~,}& E=\mathsf{6.95\ MeV}
\\
\ce{ {}_{16}^{32}S\ ~~~+ {}_2^4He\ -> {}_{18}^{36}Ar\ ~\ + \gamma~,}& E=\mathsf{6.64\ MeV}
\\
\ce{ {}_{18}^{36}Ar\ ~+ {}_2^4He\ -> {}_{20}^{40}Ca\ \ + \gamma~,}& E=\mathsf{7.04\ MeV}
\\
\ce{ {}_{20}^{40}Ca\ + {}_2^4He\ -> {}_{22}^{44}Ti\ ~~+ \gamma~,}& E=\mathsf{5.13\ MeV}
\\
\ce{ {}_{22}^{44}Ti\ ~+ {}_2^4He\ -> {}_{24}^{48}Cr\ ~+ \gamma~,}& E=\mathsf{7.70\ MeV}
\\
\ce{ {}_{24}^{48}Cr\ + {}_2^4He\ -> {}_{26}^{52}Fe\ ~\ + \gamma~,}& E=\mathsf{7.94\ MeV}
\\
\ce{ {}_{26}^{52}Fe\ + {}_2^4He\ -> {}_{28}^{56}Ni\ ~\ + \gamma~,}& E=\mathsf{8.00\ MeV}
\end{array}</math>
The energy produced by each reaction, {{mvar|E}}, is mainly in the form of [[gamma ray]]s ({{mvar|&gamma;}}), with a small amount taken by the [[By-product|byproduct]] element, as added [[momentum]].
[[File:Binding energy curve - common isotopes.svg|thumb|371x371px|Binding energy per nucleon for a selection of nuclides. Not listed is {{sup|62}}Ni, with the highest binding energy at 8.7945&nbsp;MeV.]]
It is a common misconception that the above sequence ends at <math>\, {}_{28}^{56}\mathrm{Ni} \,</math> (or <math>\, {}_{26}^{56}\mathrm{Fe} \,</math>, which is a decay product of <math>\, {}_{28}^{56}\mathrm{Ni} \,</math><ref name=":0">{{cite journal |last=Fewell |first=M.P. |date=1995-07-01 |title=The atomic nuclide with the highest mean binding energy |journal=American Journal of Physics |volume=63 |issue=7 |pages=653–658 |doi=10.1119/1.17828 |bibcode=1995AmJPh..63..653F |issn=0002-9505}}</ref>) because it is the most tightly bound [[nuclide]] – i.e., the nuclide with the highest [[nuclear binding energy]] per [[nucleon]] – and production of heavier nuclei would consume energy (be [[endothermic]]) instead of release it ([[exothermic]]). <math>\, {}_{28}^{62}\mathrm{Ni} \,</math> ([[Nickel-62]]) is actually the most tightly bound nuclide in terms of binding energy<ref>{{cite web |author=Nave, Carl R. |orig-date=c. 2001 |date=c. 2017 |title=The most tightly bound nuclei |website=hyperphysics.phy-astr.gsu.edu |series=HyperPhysics pages |department=Physics and Astronomy |publisher=[[Georgia State University]] |url=http://hyperphysics.phy-astr.gsu.edu/hbase/NucEne/nucbin2.html#c1 |access-date=2019-02-21}}</ref> (though <math>{}^{56}\textrm{Fe}</math> has a lower energy or mass per nucleon). The reaction <math>{}^{56}\textrm{Fe}+{}^{4}\textrm{He}\rightarrow {}^{60}\textrm{Ni}</math> is actually exothermic, and indeed adding alphas continues to be exothermic all the way to <math>\ {}_{50}^{100}\mathrm{Sn}\ </math>,{{AME2020 II|ref}} but nonetheless the sequence does effectively end at iron. The sequence stops before producing elements heavier than nickel because conditions in stellar interiors cause the competition between [[photodisintegration]] and the alpha process to favor photodisintegration around [[iron]].<ref name=":0" /><ref>{{cite journal |last1=Burbidge |first1=E. Margaret |author-link1=Margaret Burbidge |last2=Burbidge |first2=G.R. |author-link2=Geoffrey Burbidge |last3=Fowler |first3=William A. |author-link3=William Alfred Fowler |last4=Hoyle |first4=F. |author-link4=Fred Hoyle |date=1957-10-01 |title=Synthesis of the elements in stars |journal=Reviews of Modern Physics |volume=29 |issue=4 |pages=547–650 |bibcode=1957RvMP...29..547B |doi=10.1103/RevModPhys.29.547 |doi-access=free}}</ref> This leads to more <math>\, {}_{28}^{56}\mathrm{Ni} \,</math> being produced than <math>\, {}_{28}^{62}\mathrm{Ni} ~.</math>

All these reactions have a very low rate at the temperatures and densities in stars and therefore do not contribute significant energy to a star's total output. They occur even less easily with elements heavier than [[neon]] ({{nobr|{{mvar|Z}} > 10}}) due to the increasing [[Coulomb barrier]].

== <span class="anchor" id="Alpha elements">Alpha process elements</span> ==
'''Alpha process elements''' (or '''alpha elements''') are so-called since their most abundant isotopes are integer multiples of four – the mass of the helium nucleus (the [[alpha particle]]). These isotopes are called ''[[alpha nuclide]]s''.
[[File:Nuclear energy generation.svg|right|upright=1.5|thumb|250px|[[Logarithm]] of the relative energy output ({{mvar|ε}}) of [[Proton–proton chain reaction|proton–proton]] ({{math|p-p}}), [[CNO cycle|CNO]], and [[Triple-alpha process|triple-{{mvar|α}}]] fusion processes at different temperatures ({{mvar|T}}). The dashed line shows the combined energy generation of the {{math|p-p}} and CNO processes within a star.]]

* The stable alpha elements are: [[carbon|C]], [[oxygen|O]], [[neon|Ne]], [[magnesium|Mg]], [[silicon|Si]], and [[sulfur|S]].
* The elements [[argon|Ar]] and [[calcium|Ca]] are ''"[[observationally stable]]"''. They are synthesized by alpha capture prior to the [[Silicon burning process|silicon fusing]] stage, that leads to {{nobr|[[Type II supernova]]e.}}
* [[silicon|Si]] and [[calcium|Ca]] are purely alpha process elements.
* [[magnesium|Mg]] can be separately consumed by [[proton capture]] reactions.

The status of oxygen ([[oxygen|O]]) is contested – some authors<ref name=":1">{{Cite book |last=Mo |first=Houjun |url=https://www.worldcat.org/oclc/460059772 |title=Galaxy formation and evolution |date=2010 |publisher=Cambridge University Press |others=Frank Van den Bosch, S. White |isbn=978-0-521-85793-2 |location=Cambridge |pages=460 |oclc=460059772}}</ref> consider it an alpha element, while others do not. [[oxygen|O]] is surely an alpha element in low-[[metallicity]] [[Stellar population#Population II stars|Population II star]]s: It is produced in [[Type II supernova|Type II supernovae]], and its enhancement is well correlated with an enhancement of other alpha process elements.

Sometimes [[carbon|C]] and [[nitrogen|N]] are considered alpha process elements since, like [[oxygen|O]], they are synthesized in nuclear alpha-capture reactions, but their status is ambiguous: Each of the three elements is produced (and consumed) by the [[CNO cycle]], which can proceed at temperatures far lower than those where the alpha-ladder processes start producing significant amounts of alpha elements (including [[carbon|C]], [[nitrogen|N]], & [[oxygen|O]]). So just the presence of [[carbon|C]], [[nitrogen|N]], or [[oxygen|O]] in a star does not a clearly indicate that the alpha process is actually underway – hence reluctance of some astronomers to (unconditionally) call these three "alpha elements".

== Production in stars ==
The alpha process generally occurs in large quantities only if the star is sufficiently massive – more massive than about 10 [[solar mass]]es.<ref name=":2" /> These stars contract as they age, increasing core temperature and density to high enough levels to enable the alpha process. Requirements increase with atomic mass, especially in later stages – sometimes referred to as [[Silicon-burning process|silicon burning]] – and thus most commonly occur in [[Supernova nucleosynthesis|supernovae]].<ref>{{Cite journal |last1=Truran |first1=J. W. |last2=Cowan |first2=J. J. |last3=Cameron |first3=A. G. W. |date=1978-06-01 |title=The helium-driven r-process in supernovae. |journal=The Astrophysical Journal |volume=222 |pages=L63–L67 |doi=10.1086/182693 |bibcode=1978ApJ...222L..63T |issn=0004-637X|doi-access=free }}</ref> Type II supernovae mainly synthesize oxygen and the alpha-elements ([[neon|Ne]], [[magnesium|Mg]], [[silicon|Si]], [[sulfur|S]], [[argon|Ar]], [[calcium|Ca]], and [[titanium|Ti]]) while [[Type Ia supernova]]e mainly produce elements of the [[iron peak]] ([[titanium|Ti]], [[vanadium|V]], [[chromium|Cr]], [[manganese|Mn]], [[iron|Fe]], [[cobalt|Co]], and [[nickel|Ni]]).<ref name=":2">{{Citation |last1=Truran |first1=J.W. |title=Origin of the Elements |date=2003 |url=https://linkinghub.elsevier.com/retrieve/pii/B0080437516010598 |journal=Treatise on Geochemistry |publisher=Elsevier |language=en |doi=10.1016/b0-08-043751-6/01059-8 |isbn=978-0-08-043751-4 |access-date=2023-02-17 |last2=Heger |first2=A.|volume=1 |page=711 |bibcode=2003TrGeo...1....1T |url-access=subscription }}</ref> Sufficiently massive stars can synthesize elements up to and including the iron peak solely from the hydrogen and helium that initially comprises the star.<ref name=":1" />

Typically, the first stage of the alpha process (or alpha-capture) follows from the [[Triple-alpha process|helium-burning]] stage of the star once helium becomes depleted; at this point, free <math>{}_6^{12}\textrm{C}</math> capture helium to produce <math>{}_{8}^{16}\textrm{O}</math>.<ref name=":3">{{Cite book |last=Clayton |first=Donald D. |url=https://www.worldcat.org/oclc/9646641 |title=Principles of stellar evolution and nucleosynthesis : with a new preface |date=1983 |publisher=University of Chicago Press |isbn=0-226-10953-4 |edition= |location=Chicago |pages=430–435 |oclc=9646641}}</ref> This process continues after the core finishes the helium burning phase as a shell around the core will continue burning helium and [[Convection|convecting]] into the core.<ref name=":2" /> The second stage ([[Neon-burning process|neon burning]]) starts as helium is freed by the photodisintegration of one <math>{}_{10}^{20}\textrm{Ne}</math> atom, allowing another to continue up the alpha ladder. Silicon burning is then later initiated through the photodisintegration of <math>{}_{14}^{28}\textrm{Si}</math> in a similar fashion; after this point, the <math>\, {}_{28}^{56}\mathrm{Ni} \,</math>peak discussed previously is reached. The [[Supernova remnant|supernova shock wave]] produced by stellar collapse provides ideal conditions for these processes to briefly occur. 

During this terminal heating involving photodisintegration and rearrangement, nuclear particles are converted to their most stable forms during the supernova and subsequent ejection through, in part, alpha processes. Starting at <math>{}_{22}^{44}\textrm{Ti}</math> and above, all the product elements are radioactive and will therefore decay into a more stable isotope; for instance, <math>\, {}_{28}^{56}\mathrm{Ni} \,</math> is formed and decays into <math>{}_{26}^{56}\textrm{Fe}</math>.<ref name=":3" />

== Special notation for relative abundance ==
The abundance of total alpha elements in stars is usually expressed in terms of [[logarithm]]s, with astronomers customarily using a square bracket notation:
:<math chem> \left[ \frac{ \alpha }{\, \ce{Fe} \,} \right] ~\equiv~ \log_{10}{\left(\, \frac{ N_{\mathrm{E}\alpha} }{\, N_\ce{Fe} \,} \,\right)_\mathsf{Star}} - \log_{10}{\left(\frac{ N_{\mathrm{E}\alpha} }{\, N_\ce{Fe} \,}\,\right)_\mathsf{Sun} } ~,</math> 
where <math>\, N_{\mathrm{E}\alpha} \,</math> is the number of alpha elements per unit volume, and <math chem>\, N_\ce{Fe} \,</math> is the number of iron nuclei per unit volume. It is for the purpose of calculating the number <math>\, N_{\mathrm{E}\alpha} \,</math> that which elements are to be considered "alpha elements" becomes contentious. Theoretical [[galaxy formation and evolution|galactic evolution]] models predict that early in the universe there were more alpha elements relative to iron.

==References==
{{reflist|25em}}

== Further reading ==
* {{cite journal
 |first1=J. Trevor |last1=Mendel
 |first2=Robert N. |last2=Proctor
 |first3=Duncan A. |last3=Forbes
 |date=21 August 2007 |orig-date=31 May 2007 |publication-date=26 July 2007 
 |title=The age, metallicity and {{mvar|&alpha;}}-element abundance of galactic globular clusters, from single stellar population models
 |journal=Monthly Notices of the Royal Astronomical Society
 |volume=379 |issue=4 |pages=1618–1636
 |arxiv=0705.4511v2
 |doi=10.1111/j.1365-2966.2007.12041.x |doi-access=free
 }}

{{Nuclear processes}}
{{Star}}

[[Category:Nuclear fusion]]
[[Category:Nucleosynthesis]]