In astrophysics, the von Zeipel theorem states that the radiative flux in a uniformly rotating star is proportional to the local effective gravity . The theorem is named after Swedish astronomer Edvard Hugo von Zeipel.
The theorem is:
where the luminosity and mass are evaluated on a surface of constant pressure . The effective temperature can then be found at a given colatitude from the local effective gravity:[1][2]
This relation ignores the effect of convection in the envelope, so it primarily applies to early-type stars.[3]
According to the theory of rotating stars,[4] if the rotational velocity of a star depends only on the radius, it cannot simultaneously be in thermal and hydrostatic equilibrium. This is called the von Zeipel paradox. The paradox is resolved, however, if the rotational velocity also depends on height, or there is a meridional circulation. A similar situation may arise in accretion disks.[5]
^Maeder, André (1999). "Stellar evolution with rotation IV: von Zeipel's theorem and anistropic losses of mass and angular momentum". Astronomy and Astrophysics. 347: 185–193. Bibcode:1999A&A...347..185M.
^Lucy, L. B. (1967). "Gravity-Darkening for Stars with Convective Envelopes". Zeitschrift für Astrophysik. 65: 89. Bibcode:1967ZA.....65...89L.
^Tassoul, J.-L. (1978). Theory of Rotating Stars. Princeton: Princeton Univ. Press.
^Kley, W.; Lin, D. N. C. (1998). "Two-Dimensional Viscous Accretion Disk Models. I. On Meridional Circulations In Radiative Regions". The Astrophysical Journal. 397: 600–612. Bibcode:1992ApJ...397..600K. doi:10.1086/171818.
This article about stellar astronomy is a stub. You can help Wikipedia by expanding it.
zeipel, theorem, astrophysics, zeipel, theorem, states, that, radiative, flux, displaystyle, uniformly, rotating, star, proportional, local, effective, gravity, displaystyle, text, theorem, named, after, swedish, astronomer, edvard, hugo, zeipel, theorem, disp. In astrophysics the von Zeipel theorem states that the radiative flux F displaystyle F in a uniformly rotating star is proportional to the local effective gravity g eff displaystyle g text eff The theorem is named after Swedish astronomer Edvard Hugo von Zeipel The theorem is F L P 4 p G M P g eff displaystyle F frac L P 4 pi GM P g text eff where the luminosity L displaystyle L and mass M displaystyle M are evaluated on a surface of constant pressure P displaystyle P The effective temperature T eff displaystyle T text eff can then be found at a given colatitude 8 displaystyle theta from the local effective gravity 1 2 T eff 8 g eff 1 4 8 displaystyle T text eff theta sim g text eff 1 4 theta This relation ignores the effect of convection in the envelope so it primarily applies to early type stars 3 According to the theory of rotating stars 4 if the rotational velocity of a star depends only on the radius it cannot simultaneously be in thermal and hydrostatic equilibrium This is called the von Zeipel paradox The paradox is resolved however if the rotational velocity also depends on height or there is a meridional circulation A similar situation may arise in accretion disks 5 References edit Zeipel Edvard Hugo von 1924 The radiative equilibrium of a rotating system of gaseous masses Monthly Notices of the Royal Astronomical Society 84 9 665 719 Bibcode 1924MNRAS 84 665V doi 10 1093 mnras 84 9 665 Maeder Andre 1999 Stellar evolution with rotation IV von Zeipel s theorem and anistropic losses of mass and angular momentum Astronomy and Astrophysics 347 185 193 Bibcode 1999A amp A 347 185M Lucy L B 1967 Gravity Darkening for Stars with Convective Envelopes Zeitschrift fur Astrophysik 65 89 Bibcode 1967ZA 65 89L Tassoul J L 1978 Theory of Rotating Stars Princeton Princeton Univ Press Kley W Lin D N C 1998 Two Dimensional Viscous Accretion Disk Models I On Meridional Circulations In Radiative Regions The Astrophysical Journal 397 600 612 Bibcode 1992ApJ 397 600K doi 10 1086 171818 nbsp This article about stellar astronomy is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Von Zeipel theorem amp oldid 1169992412, wikipedia, wiki, book, books, library,
