Solar Dynamo Theory

TheSun’smagnetic field is the engine and energy source driving all phenomena collectively defining solar activity, which in turn structures the whole heliosphere and significantly impacts Earth’s atmosphere down at least to the stratosphere. The solar magnetic field is believed to originate through the action of a hydromagnetic dynamo process operating in the Sun’s interior, where the strongly turbulent environment of the convection zone leads to flow-field interactions taking place on an extremely wide range of spatial and temporal scales. Following a necessarily brief observational overview of the solar magnetic field and its cycle, this review on solar dynamo theory is structured around three areas in which significant advances have been made in recent years: (a) globalmagnetohydrodynamical simulations of convection and magnetic cycles, (b) the turbulent electromotive force and the dynamo saturation problem, and (c) flux transport dynamos, and their application to model cycle fluctuations and grandminima and to carry out cycle prediction. 251 A nn u. R ev . A st ro . A st ro ph ys . 2 01 4. 52 :2 51 -2 90 . D ow nl oa de d fr om w w w .a nn ua lr ev ie w s. or g A cc es s pr ov id ed b y St an fo rd U ni ve rs ity M ai n C am pu s L an e M ed ic al L ib ra ry o n 11 /2 3/ 14 . F or p er so na l u se o nl y. AA52CH06-Charbonneau ARI 30 July 2014 7:18 1. SOLAR MAGNETISM Forget your old astronomy textbook; the Sun is a variable star, its variability is strongly imprinted across interplanetary space, there is no such thing as the solar constant, and the Sun’s magnetic field is behind it all. It structures the solar atmosphere from the photosphere across the corona and into the solar wind and heliosphere, modulates the Sun’s corpuscular and radiative output, and drives all geoeffective solar eruptive phenomena collectively defining solar activity. Nor is the Sun anomalous in this respect; every solar-type star observed with sufficient sensitivity shows similar signs of magnetically driven activity. Numerous good reviews are available on the observational side of solarmagnetism (e.g., Solanki et al. 2006, de Wijn et al. 2009); consequently, the following overview focuses on aspects most pertinent to solar dynamo theory. The solar magnetic field is structured and evolves over an astoundingly wide range of spatial and temporal scales (see Figure 1). Sunspots (Figure 1a) are now understood to be the surfacemanifestations of emergingmagnetic fields produced in the solar interior. Restricted to low heliocentric latitudes but seldom seen very near the equator, sunspots are the seats of strong magnetic fields (∼0.1–0.5 T), and the larger sunspots usually appear in pairs of opposite magnetic polarities (black versus white on Figure 1b). The favored physical picture is that of magnetic flux ropes rising from below and piercing the photosphere in the form of so-called -loops (Parker 1955a, Caligari et al. 1995, Fan 2009 and references therein). The leading spots (with respect to the direction of solar rotation, from left to right in Figure 1a,b) show the same magnetic polarity in each hemisphere, with this leading polarity reversing across hemispheres. These striking hemispheric regularities, known as Hale’s Polarity law (Hale et al. 1919), reflect the presence of an internal magnetic field that is spatially well organized on the scale of the Sun as a whole and is antisymmetric about the solar equator. Temporally extended observations (Figure 1c,d) also reveal some remarkable large-scale order. The number of sunspots on the solar disk waxes and wanes on a timescale of about 11 years, with sunspot emergences occurring at midlatitudes in the beginning of this cycle and progressively closer to the equator as the cycle proceeds. The reversal of the relative magnetic polarities of sunspot pairs from one cycle to the next indicates that the underlying magnetic cycle has a period of twice that of the sunspot cycle. A well-defined dipole moment is also present, with the average polar cap magnetic field reaching a few 10−3 T at times of sunspot minimum and reversing its polarity at times of maximum sunspot counts, i.e., it lags the deep-seated sunspot-producing magnetic field by about half a sunspot cycle. The sunspot record extends back to the beginning of the telescopic era in the early seventeenth century and, taken as a proxy of solarmagnetism,makes it possible to trace the solarmagnetic cycle over that time span (red curve on Figure 1d; see also Hathaway 2010). The sunspot cycle shows significant variability in both its amplitude and duration, including an extended “quiet” epoch spanning the years 1645 to 1715, now known as the Maunder Minimum, during which very few sunspots were observed (Eddy 1976). Other indirect proxies, notably cosmogenic radioisotopes (e.g., Beer 2000, Usoskin 2013), make it possible to go much further back in time, although with some loss of temporal resolution. These data nonetheless show that episodes similar to the MaunderMinimumhave occurred intermittently in themore distant past ( gray bands inFigure 1d; see also Usoskin et al. 2007, McCracken et al. 2013). Although the strongest magnetic fields observed at the solar surface are found in sunspots, magnetographic observations also reveal their presence away from sunspots and active regions, in the form of small magnetic elements of sizes going down to the smallest spatial scale currently resolved by solar observing instruments (de Wijn et al. 2009). These small magnetic elements collectively define the magnetic network, and have sizes distributed as a power-law (Parnell et al. 252 Charbonneau A nn u. R ev . A st ro . A st ro ph ys . 2 01 4. 52 :2 51 -2 90 . D ow nl oa de d fr om w w w .a nn ua lr ev ie w s. or g A cc es s pr ov id ed b y St an fo rd U ni ve rs ity M ai n C am pu s L an e M ed ic al L ib ra ry o n 11 /2 3/ 14 . F or p er so na l u se o nl y. AA52CH06-Charbonneau ARI 30 July 2014 7:18