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vogt russell theorem wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 history 2 formulation 3 modern interpretation 4 limitations 5 see also 6 references toggle the table of contents vogt russell theorem 10 languages català deutsch suomi français italiano 한국어 português русский українська 中文 edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikimedia commons wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia wiki illustration to vogt s theorem vogt russell theorem is a hypothesis in stellar astrophysics stating that the structure of a star in hydrostatic and thermal equilibrium is determined solely by its total mass and chemical composition 1 the idea dates back to 1926 when heinrich vogt astronomer formulated the theorem with internal communications and seminars its first publication only appeared in 1931 2 independently henry norris russell developed the same theorem in the early 1930s 3 as numerical modelling techniques improved researchers discovered that the relationship is not universal and that the equations of stellar structure can yield multiple solutions for the same set of global parameters 4 thus the theorem is treated today as a local approximation valid mainly for main sequence stars and under physical conditions without extreme effects 5 history edit the original formulation of the principle attributed to heinrich vogt astronomer dates from 1926 but there is no publication from that year the first formal exposition appears in his 1931 article in astronomische nachrichten in which he discusses how the constitution of a star in hydrostatic and thermal equilibrium depends essentially on total mass and chemical composition 2 independently henry norris russell published in 1931 two technical articles in the monthly notices of the royal astronomical society analyzing how the internal stellar structure and global parameters such as radius and luminosity are determined by these same two fundamental parameters total mass and chemical composition 3 6 russell presented more detailed versions of these ideas in review articles on the journal of the royal astronomical society of canada in 1933 7 these works consolidated the notion later called the vogt russell theorem despite not providing a mathematical proof of uniqueness formulation edit the theorem states the internal structure of a star in hydrostatic and thermal equilibrium including profiles of pressure temperature density and luminosity as well as its observable global parameters radius and luminosity would be uniquely determined by the total mass m displaystyle m and the initial chemical composition x i displaystyle x_ i this formulation use the four fundamental equations of stellar structure hydrostatic equilibrium mass conservation energy transport and energy conservation to construct the main proposition 1 if one assumes sphericity absence of significant rotation absence of strong magnetic fields and thermal equilibrium the system is mathematically well conditioned and in principle admits a single continuous solution that satisfies the boundary conditions at the center and at the surface 4 modern interpretation edit numerical studies developed from the second half of the twentieth century onward showed that under some conditions like near structural limits such as the schönberg chandrasekhar limit or in cases involving instabilities multiple mathematical solutions may exist for the same values of m displaystyle m and x i displaystyle x_ i 4 these solutions may include stable and unstable states indicating that the originally postulated uniqueness is not universal 4 8 for most stars under normal conditions like nondegenerate main sequence stars numerical solutions do indeed converge to a single stable solution this explains the narrow band occupied by stars with the same mass and composition in the hertzsprung russell diagram 1 the good agreement with the mass luminosity relation 9 the good agreement of stellar evolution models that use only m displaystyle m and x i displaystyle x_ i as initial parameters 1 thus although the theorem is not strictly valid as a general law it remains fundamental as a practical first approximation in stellar astrophysics 4 8 limitations edit the theorem fails when 4 the star is near structural limits e g the schönberg chandrasekhar limit there is significant rapid rotation strong magnetic fields influence energy transport strong electron degeneracy is present the star is not in thermal equilibrium in these regimes multiple solutions arise invalidating uniqueness 5 see also edit stellar evolution main sequence hertzsprung russell diagram mass luminosity relation references edit 1 2 3 4 carroll b w ostlie d a 2017 an introduction to modern astrophysics 2nd ed cambridge university press isbn 978 1 108 42216 1 1 2 vogt h 1931 zur theorie des sternaufbaues astronomische nachrichten 244 49 56 ads 1 2 russell h n 1931 notes on the constitution of the stars monthly notices of the royal astronomical society 91 951 958 ads 1 2 3 4 5 6 kippenhahn r weigert a weiss a 2012 stellar structure and evolution 2nd ed springer isbn 978 3642303040 isbn check isbn value checksum help 1 2 gautschy alfred 2018 the theorem that was none ii the profound 70s arxiv 1812 11864 astro ph sr russell h n 1931 notes on the constitution of the stars addendum monthly notices of the royal astronomical society 92 147 150 ads russell h n 1933 the constitution of the stars journal of the royal astronomical society of canada 27 375 394 ads 1 2 kähler helmuth 1978 the vogt russell theorem and new results on an old problem the hr diagram dordrecht springer netherlands pp 303 311 doi 10 1007 978 94 009 9851 3_56 inactive 22 december 2025 isbn 978 90 277 0906 6 retrieved 2025 11 17 citation cs1 maint doi inactive as of december 2025 link fernandes joão gafeira ricardo andersen johannes 2021 revisiting the mass and radius luminosity relations for fgk main sequence stars astronomy astrophysics 647 a90 arxiv 2103 11044 bibcode 2021a a 647a 90f doi 10 1051 0004 6361 202040035 issn 0004 6361 retrieved from https en wikipedia org w index php title vogt russell_theorem oldid 1370395433 category stellar astronomy hidden categories pages with isbn errors cs1 maint doi inactive as of december 2025 this page was last edited on 20 august 2026 at 22 00 utc page was rendered with 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