Phase Space Analysis: The Equilibrium of the Solar Magnetic Cycle |
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| Authors: | D Passos I Lopes |
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| Institution: | (1) CENTRA, Departmento de Física, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal;(2) Departamento de Física, Universidade de évora, Colégio António Luis Verney, 7002-554 évora, Portugal |
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| Abstract: | We present the results of a statistical study of the solar cycle based on the analysis of the superficial toroidal magnetic
field component phase space. The magnetic field component used to create the embedded phase space was constructed from monthly
sunspot number observations since 1750. The phase space was split into 32 sections (or time instants) and the average values
of the orbits on this phase space were calculated (giving the most probable cycle). In this phase space it is shown that the
magnetic field on the Sun’s surface evolves through a set of orbits that go around a mean orbit (i.e., the most probable magnetic cycle that we interpret as the equilibrium solution). It follows that the most probable cycle
is well represented by a van der Pol oscillator limit curve (equilibrium solution), as can be derived from mean-field dynamo
theory. This analysis also retrieves the empirical Gnevyshev – Ohl’s rule between the first and second parts of the solar
magnetic cycle. The sunspot number evolution corresponding to the most probable cycle (in phase space) is presented. |
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| Keywords: | Solar cycle: models Sunspots: magnetic fields Sunspots: statistics |
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