Editing Dynamo theory (section)

==Formal definition==
Dynamo theory describes the process through which a rotating, convecting, and electrically conducting fluid acts to maintain a magnetic field.  This theory is used to explain the presence of anomalously long-lived magnetic fields in astrophysical bodies. The conductive fluid in the geodynamo is liquid iron in the outer core, and in the [[solar dynamo]] is ionized gas at the [[tachocline]]. Dynamo theory of astrophysical bodies uses [[Magnetohydrodynamics|magnetohydrodynamic]] equations to investigate how the fluid can continuously regenerate the magnetic field.<ref name="hydromagnetic dynamo">{{cite journal|doi=10.4249/scholarpedia.2309|doi-access=free |title=Hydromagnetic dynamo theory |year=2007 |last1=Brandenburg |first1=Axel |journal=Scholarpedia |volume=2 |issue=3 |page=2309 |bibcode=2007SchpJ...2.2309B }}</ref>

It was once believed that the [[dipole]], which comprises much of the [[Earth's magnetic field]] and is misaligned along the rotation axis by 11.3 degrees, was caused by permanent magnetization of the materials in the earth. This means that dynamo theory was originally used to explain the Sun's magnetic field in its relationship with that of the Earth. However, this hypothesis, which was initially proposed by [[Joseph Larmor]] in 1919, has been modified due to extensive studies of magnetic [[secular variation]], [[paleomagnetism]] (including [[geomagnetic reversal|polarity reversal]]s), seismology, and the solar system's abundance of elements. Also, the application of the theories of [[Carl Friedrich Gauss]] to magnetic observations showed that Earth's magnetic field had an internal, rather than external, origin.

There are three requisites for a dynamo to operate:

*An electrically conductive fluid medium
*Kinetic energy provided by planetary rotation
*An internal energy source to drive convective motions within the fluid.<ref>{{cite book |author=E. Pallé |title=The Earth as a Distant Planet: A Rosetta Stone for the Search of Earth-Like Worlds (Astronomy and Astrophysics Library) |publisher=Springer |location=Berlin |year=2010 |pages=316–317 |url=https://books.google.com/books?id=qLuVCJtRTV0C&pg=PA316 |isbn=978-1-4419-1683-9 |access-date=17 July 2010}}</ref>

In the case of the Earth, the magnetic field is induced and constantly maintained by the convection of liquid iron in the outer core.  A requirement for the induction of field is a rotating fluid.  Rotation in the outer core is supplied by the [[Coriolis effect]] caused by the rotation of the Earth.  The Coriolis force tends to organize fluid motions and electric currents into columns (also see [[Taylor column]]s) aligned with the rotation axis.  Induction or generation of magnetic field is described by the [[induction equation]]:
<math display="block">\frac{\partial \mathbf{B}}{\partial t} = \eta \nabla^2 \mathbf{B} + \nabla \times (\mathbf{u} \times \mathbf{B}) </math>
where {{math|'''u'''}} is velocity, {{math|'''B'''}} is magnetic field, {{mvar|t}} is time, and <math>\eta = 1 / (\sigma\mu)</math> is the [[magnetic diffusivity]] with <math>\sigma</math> electrical conductivity and <math>\mu</math> [[Permeability (electromagnetism)|permeability]].  The ratio of the second term on the right hand side to the first term gives the [[magnetic Reynolds number]], a dimensionless ratio of advection of magnetic field to diffusion.

===Tidal heating supporting a dynamo===
Tidal forces between celestial orbiting bodies cause friction that heats up their interiors. This is known as tidal heating, and it helps keep the interior in a liquid state. A liquid interior that can conduct electricity is required to produce a dynamo. Saturn's Enceladus and Jupiter's Io have enough tidal heating to liquify their inner cores, but they may not create a dynamo because they cannot conduct electricity.<ref name="Enceladus">{{cite web | url=http://www.nasa.gov/mission_pages/cassini/whycassini/cassini20100708-b.html | title=Saturn's Icy Moon May Keep Oceans Liquid with Wobble | publisher=NASA | date=October 6, 2010 | access-date=August 14, 2012 | author=Steigerwald, Bill | archive-date=March 24, 2015 | archive-url=https://web.archive.org/web/20150324222212/http://www.nasa.gov/mission_pages/cassini/whycassini/cassini20100708-b.html | url-status=dead }}</ref><ref name="Io geologic">{{cite web | url=https://clas.asu.edu/node/12161 | title=Geologic map of Jupiter's moon Io details an otherworldly volcanic surface | publisher=Astrogeology Science Center | date=March 19, 2012 | access-date=August 14, 2012 | author=Cassis, Nikki }}{{dead link|date=September 2017 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> Mercury, despite its small size, has a magnetic field, because it has a conductive liquid core created by its iron composition and friction resulting from its highly elliptical orbit.<ref name="mercury core">{{cite web | url=http://carnegiescience.edu/news/mercury%E2%80%99s_surprising_core_and_landscape_curiosities | title=Mercury's Surprising Core and Landscape Curiosities | publisher=Carnegie Institution for Science | website=MESSENGER | date=March 21, 2012 | access-date=August 14, 2012 | archive-date=January 18, 2015 | archive-url=https://web.archive.org/web/20150118213837/http://carnegiescience.edu/news/mercury%E2%80%99s_surprising_core_and_landscape_curiosities | url-status=dead }}</ref> It is theorized that the Moon once had a magnetic field, based on evidence from magnetized lunar rocks, due to its short-lived closer distance to Earth creating tidal heating.<ref name="lunar dynamo">{{cite web | url=http://news.ucsc.edu/2011/11/lunar-dynamo.html | title=Ancient lunar dynamo may explain magnetized moon rocks | publisher=University of California | date=November 9, 2011 | access-date=August 14, 2012 | author=Stevens, Tim}}</ref> An orbit and rotation of a planet helps provide a liquid core, and supplements kinetic energy that supports a dynamo action.