1.4 Sunspots and the butterfly diagram

Historically, next to cyclic polarity reversal the sunspot butterfly diagram has provided the most stringent observational constraints on solar dynamo models (see Figure 3

). In addition to the obvious cyclic pattern, two features of the diagram are particularly noteworthy:

Sunspots are restricted to latitudinal bands some $o -~ 30$ wide, symmetric about the equator.
Sunspots emerge closer and closer to the equator in the course of a cycle, peaking in coverage at about $± 15o$ of latitude.

Sunspots appear when deep-seated toroidal flux ropes rise through the convective envelope and emerge at the photosphere. Assuming that they rise radially and are formed where the magnetic field is the strongest, the sunspot butterfly diagram can be interpreted as a spatio-temporal “map” of the Sun’s internal, large-scale toroidal magnetic field component. This interpretation is not unique, however, since the aforementioned assumptions are questionable. In particular, we still lack even rudimentary understanding of the process through which the diffuse, large-scale solar magnetic field produces the concentrated toroidal flux ropes that will later give rise to sunspots upon buoyant destabilisation. This remains perhaps the most severe missing link between dynamo models and solar magnetic field observations. On the other hand, the stability and rise of toroidal flux ropes is now fairly well-understood (see, e.g., Fan, 2004 , and references therein). In fact, from the point of view of solar cycle modelling this represents perhaps the most significant advance of the past two decades.

Figure 3:

The sunspot “butterfly diagram”, showing the fractional coverage of sunspots as a function of solar latitude and time (courtesy of D. Hathaway).

Magnetographic mapping of the Sun’s surface magnetic field (see Figure 4

) have also revealed that the Sun’s poloidal magnetic component undergoes cyclic variations, changing polarities at times of sunspot maximum. Note on Figure 4

the poleward drift of the surface fields, away from sunspot latitudes. This pattern can be given two interpretations:

It reflects the existence of a mid-to-high-latitude dynamo “branch” that, somehow, fails to produce full-blown sunspots.
The surface fields originates from the transport of magnetic flux released by the decay of sunspots at low latitudes.

Observational evidence currently favors the second of these possibilities (but do see Petrovay and Szakály, 1999 ).

Figure 4:

Synoptic magnetogram of the radial component of the solar surface magnetic field. The low-latitude component is associated with sunspots. Note the polarity reversal of the weaker, high-latitude magnetic field, occurring approximately at time of sunspot maximum (courtesy of D. Hathaway).