Radiative dynamo

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A radiative dynamo is "a dynamo taking place in the radiative layers"[1] of a star.

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It is a theoretical construction to explain the magnetohydrodynamic properties of plasma occurring in the outer atmospheric layers of astronomical objects including stars. As such it is a part of theoretical stellar science and theoretical astrophysics.

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Contents

Notation [edit]

Notation: let the symbol Def. indicate that a definition is following.

Notation: let the symbols between [ and ] be replacement for that portion of a quoted text.

Universals [edit]

To help with definitions, their meanings and intents, there is the learning resource theory of definition.

Def. evidence that demonstrates that a concept is possible is called proof of concept.

The proof-of-concept structure consists of

  1. background,
  2. procedures,
  3. findings, and
  4. interpretation.[2]

The findings demonstrate a statistically systematic change from the status quo or the control group.

Dynamo [edit]

Def. any conversion of mechanical energy into electrical energy and associated magnetic fields is called a dynamo.

Def. "a dynamo taking place in the radiative layers"[1] of a star, or other astronomical object, is called a radiative dynamo, or stellar radiative dynamo.

"[M]otions resulting from [a linear magnetohydrodynamic] instability act as a dynamo to sustain the magnetic field."[3] "Supersonic flows are initially generated by the Balbus-Hawley magnetic shear instability."[3] A plasma with local magnetohydrodynamic instabilities creates mechanical turbulence, motion, or shear (a dynamo) which in turn generates or sustains the local magnetic field.

When this magnetohydrodynamic dynamo occurs between or within radiative layers, a radiative dynamo is operating.

Radiative layers [edit]

"White dwarfs whose primary spectral classification is DA have hydrogen-dominated atmospheres. They make up the majority (approximately 80%) of all observed white dwarfs.[4]"[5]. "DA spectral type, having only hydrogen absorption lines in its spectrum ... white dwarf material is initially plasma—a fluid composed of nuclei and electrons" per the same article. "Helium is unquestionably absent from the atmospheres of ... DA stars, and [there is a] low metal abundance".[6]

In a DA star the "radiative layer ... lies above the convective zone."[6]

"Only a small number of white dwarfs have been examined for fields, and it has been estimated that at least 10% of white dwarfs have fields in excess of 1 million gauss (100 T).[7][8]"[5]

Convective dynamo [edit]

"[T]he solar cycle, generally considered as the classical case of a convective dynamo process, is probably not driven by convective turbulence at all."[9]

Differential rotation [edit]

This computer generated diagram of internal rotation in the Sun shows differential rotation in the outer convective region and almost uniform rotation in the central radiative region. Credit: Global Oscillation Network Group (GONG).

"Both the core and the radiative zone dynamo models involve a significant amount of differential rotation for the generation of a large-scale toroidal field."[1] But, "the buoyant rise time [for a magnetic field generated by a core dynamo] from the core can become much longer than the age of [OBA type stars] for weakly magnetized flux-tubes".[1]

"Magnetic fields can be created in stably stratified (non-convective) layers in a differentially rotating star. A magnetic instability in the toroidal field (wound up by differential rotation) replaces the role of convection in closing the field amplification loop."[9]

At right is a diagram of the internal rotation in the Sun, showing differential rotation in the outer convective region and almost uniform rotation in the central radiative region. The transition between these regions is called the tachocline.

"Until the advent of helioseismology, the study of wave oscillations in the Sun, very little was known about the internal rotation of the Sun. The differential profile of the surface was thought to extend into the solar interior as rotating cylinders of constant angular momentum.[10] Through helioseismology this is now known not to be the case and the rotation profile of the Sun has been found. On the surface the Sun rotates slowly at the poles and quickly at the equator. This profile extends on roughly radial lines through the solar convection zone to the interior. At the tachocline the rotation abruptly changes to solid body rotation in the solar radiation zone.[11]"[12]

Brown dwarf [edit]

"Stars with masses M > 0.3 M have an outer convective zone and an interior radiative region that need not be rotating at the same rate. A poloidal magnetic field in the convective layers will be stretched and amplified into strong toroidal fields when it is dragged by convective overshoot ... into the radial shear in rotation that resides at the boundary (in and near the so-called "tachocline" ... For less massive stars and young brown dwarfs, the energy is transported throughout the star by convection; no radiative core is present. For this reason, it has been supposed that the activity and its dependence on rotation might change near the spectral type where the radiative layer disappears (about M5.5)"[13]

Sun [edit]

"The tachocline ... is a thin layer of the solar interior, straddling the convection zone and the radiative interior. It is widely believed that a toroidal magnetic field of at least 105 G permeates this layer ... The tachocline naturally divides into two sublayers: an inner "radiative" layer and an outer "overshoot" layer. By current estimates, the radiative layer is twice as thick as the overshoot layer."[14]

Asymptotic giant branch [edit]

This image shows sample stellar evolutionary tracks for single stars, zero initial rotational velocity, and solar metallicity. Credit: Rursus.

Notation: let the symbol AGB indicate an asymptotic giant branch star with a hydrogen-exhausted core.

Notation: let the symbol E-AGB indicate an AGB star with a hydrogen-exhausted core.

For a 7 Mʘ AGB model sequence, "[o]n the E-AGB, the convective envelope appears clearly separated from the stellar core by a radiative layer ... Density and temperature drop significantly within this layer".[15] "As evolution proceeds luminosity and radiation pressure increase ... The base of the convective envelope moves inwards into deeper and hotter parts of the interior until nuclear reactions become important ... just before the first thermal pulse ..., the radiative "buffer" layer disappears, and the convection cuts into the hydrogen-burning shell. ... high lithium abundances ... in ... oxygen rich, luminous (Mbol = -6.2... -6.8) AGB stars [are produced at the base of the convective envelope which] has a base temperature of 75 ˑ 106K, sufficient to reduce the duration of the Li-rich phase well below 104yrs".[15]

See also [edit]

References [edit]

  1. 1.0 1.1 1.2 1.3 P. Petit, F. Lignières, G.A. Wade, M. Aurière, T. Böhm, S. Bagnulo, B. Dintrans, A. Fumel, J. Grunhut, J. Lanoux, A. Morgenthaler, and V. Van Grootel (November-December 2010). "The rapid rotation and complex magnetic field geometry of Vega". Astronomy and Astrophysics 523 (11): A41-9. doi:10.1051/0004-6361/201015307. Bibcode2010A&A...523A..41P. Retrieved on 2011-12-19. 
  2. Ginger Lehrman and Ian B Hogue, Sarah Palmer, Cheryl Jennings, Celsa A Spina, Ann Wiegand, Alan L Landay, Robert W Coombs, Douglas D Richman, John W Mellors, John M Coffin, Ronald J Bosch, David M Margolis (August 13, 2005). "Depletion of latent HIV-1 infection in vivo: a proof-of-concept study". Lancet 366 (9485): 549-55. doi:10.1016/S0140-6736(05)67098-5. Retrieved on 2012-05-09. 
  3. 3.0 3.1 Axel Brandenburg, Åke Nordlund, Robert F. Stein, and Ulf Torkelsson (June 1995). "Dynamo-generated Turbulence and Large-Scale Magnetic Fields in a Keplerian Shear Flow". The Astrophysical Journal 446 (6): 741-54. doi:10.1086/175831. Bibcode1995ApJ...446..741B. Retrieved on 2012-01-18. 
  4. G. Fontaine, F. Wesemael (2001). "White dwarfs". In P. Murdin. Encyclopedia of Astronomy and Astrophysics. IOP Publishing/Nature Publishing Group. ISBN 0-333-75088-8. 
  5. 5.0 5.1 (June 15, 2012) "White dwarf". Wikipedia. San Francisco, California: Wikimedia Foundation, Inc. Retrieved on 2012-07-08. 
  6. 6.0 6.1 H. L. Shipman (April 1977). "Masses, radii, and model atmospheres for cool white-dwarf stars". The Astrophysical Journal 213 (4): 138-44. doi:10.1086/155138. Bibcode1977ApJ...213..138S. Retrieved on 2012-03-11. 
  7. S. Jordan, R. Aznar Cuadrado, R. Napiwotzki, H. M. Schmid, S. K. Solanki (2007). "The fraction of DA white dwarfs with kilo-Gauss magnetic fields". Astronomy and Astrophysics 462 (3): 1097. doi:10.1051/0004-6361:20066163. Bibcode2007A&A...462.1097J. 
  8. James Liebert, P. Bergeron, J. B. Holberg (2003). "The True Incidence of Magnetism Among Field White Dwarfs". The Astronomical Journal 125: 348. doi:10.1086/345573. Bibcode2003AJ....125..348L. 
  9. 9.0 9.1 H. C. Spruit (January 2002). "Dynamo action by differential rotation in a stably stratified stellar interior". Astronomy and Astrophysics 381 (3): 923-32. doi:10.1051/0004-6361:20011465. Retrieved on 2012-01-18. 
  10. Glatzmaler, G. A (1985). "Numerical simulations of stellar convective dynamos III. At the base of the convection zone". Solar Physics 125: 1–12. 
  11. Jørgen Christensen-Dalsgaard and M. J. Thompson (2007). The Solar Tachocline:Observational results and issues concerning the tachocline. Cambridge University Press. pp. 53–86. 
  12. (November 10, 2012) "Solar rotation". Wikipedia. San Francisco, California: Wikimedia Foundation, Inc. Retrieved on 2012-11-16. 
  13. Robert E. Rutledge, Gibor Basri, and Lars Bildsten (August 1, 2000). "Chandra detection of an X-ray flare from the brown dwarf LP 944-20". The Astrophysical Journal 538 (2). doi:10.1086/312817. Retrieved on 2012-03-11. 
  14. D. A. Schecter, J. F. Boyd, and P. A. Gilman (April 20, 2001). ""Shallow-Water" Magnetohydrodynamic Waves in the Solar Tachocline". The Astrophysical Journal 551 (2): L185-8. doi:10.1086/320027. Retrieved on 2012-03-11. 
  15. 15.0 15.1 T. Blöcker and D. Schönberner (April 1991). "A 7 Mʘ AGB model sequence not complying with the core mass-luminosity relation". Astronomy and Astrophysics 244 (2): L43-6. Bibcode1991A&A...244L..43B. Retrieved on 2012-03-11. 

Further reading [edit]

  • P. Petit, F. Lignières, G.A. Wade, M. Aurière, T. Böhm, S. Bagnulo, B. Dintrans, A. Fumel, J. Grunhut, J. Lanoux, A. Morgenthaler, and V. Van Grootel (November-December 2010). "The rapid rotation and complex magnetic field geometry of Vega". Astronomy and Astrophysics 523 (11): A41-9. doi:10.1051/0004-6361/201015307. Bibcode2010A&A...523A..41P. Retrieved on 2011-12-19. 

External links [edit]