Proposal by an SOI Associated Investigator in response to the SOI Announcement of Opportunity
Abstract
The present proposal concerns analysis of the archived
(level-1, calibrated) set of
full-disk magnetograms recorded by the SOI, with the aim of
exploring the evolution of the global magnetic field pattern on
the various time scales covered by the data set. Both the rotational
properties of the pattern and the evolution in terms of the harmonic
modal components will be analysed, to shed light on the interior
sources of the field pattern and the nature of the solar dynamo.
The program will be combined with a corresponding investigation with
the GOLF circular polarization data set, which should allow the
sources of the mean-field signal to be identified.
1. Scientific Objectives
1.1. Evolution on Different Time Scales
SOI will provide us with a long time series of frequently recorded
full-disk magnetograms, which will be of unprecedented quality,
in particular in terms of homogeneity of the full-disk data set,
allowing us to explore the evolution of the field pattern over a
large range of spatial and temporal frequencies.
As in the case of the pattern of Doppler velocities, the pattern of solar magnetic fields can be decomposed in its spherical harmonics components, and a time series analysis can be applied to the harmonic coefficients, e.g. to search for resonant modal behavior. This has been done with the Mt Wilson and Kitt Peak data sets for long time scales ( >1yr). The SOI data will allow this work to be extended to much shorter time scales while overlapping at intermediate time scales with what could be covered by previous work.
The following subsection, while summarizing some previous results concerning longer time scales, provides an indication of the kind of approach we have in mind to explore with the SOI data set the evolution of the magnetic-field pattern on the time scales accessible with this new data set.
1.1.1. Previous Modal Analysis for Long Time Scales
The first application of this approach (Stenflo and Vogel, 1986)
showed that the axisymmetric modes (with m=0) strictly obey a parity
selection rule. Thus modes of odd parity (odd values of ) are
dominated by the 22yr Hale resonance, with less than 10% of the
power at the second harmonic at frequency (11yr)-1. In contrast
the modes of even parity show no trace of the 22yr cycle. Later
papers on the axisymmetric modes (e.g.Stenflo, 1988, 1994) have
led to determinations of interesting properties for
the modal amplitudes and phases as functions of l and the
identification of a band of higher-frequency power, for which the
frequency increases with the spherical harmonic degree l.
Interpretations of these results in terms of stochastic dynamo theory have been given by Hoyng (1990) and Hoyng et al.(1994). The determined modal amplitudes and phases will be used as boundary conditions for future dynamo modelling by Dikpati and Petrovay (private communication). The harmonic coefficients are the natural and optimum constraints to use with practically any dynamo theory, since it is natural to expand the solutions of the dynamo equations in a set of orthogonal mathematical functions, and the spherical harmonics represent the most natural orthogonal set when working in spherical geometry, which we do for stellar and planetary dynamos.
The evolution of the non-axisymmetric modal structure has been more difficult to determine and interpret, since the longitude reference system on the sun is not well defined due to differential rotation. The evolutionary frequencies get mixed with the rotational frequencies since the evolutionary time scale is not well separated from the time scale of winding by differential rotation, in contrast to the p mode oscillations, which have an entirely different time scale. Nevertheless, the first attempt at analysing the non-axisymmetric modes and, with special ``tricks'', isolate the evolutionary from the rotational effects, has revealed besides the 22yr resonance a number of low-amplitude, discrete modes of higher frequencies (Stenflo and Güdel, 1988). A new attack on the non-axisymmetric problem is presently being undertaken (Stenflo, in progress), using the entire data set of Mt Wilson full-disk magnetic maps (in the form of matrices).
1.1.2. Rotational Properties
The phase velocity of the magnetic pattern
has been found to obey two distinctly
different rotation laws. While cross-correlation with small time
lags (1-4days) to determine the longitude displacement of the
pattern in full-disk magnetograms gives a steep differential
rotation law (Snodgrass, 1983) that is very similar to the Doppler
rotation law, autocorrelation analysis of the synoptic magnetic field
sampled around the central meridian gives maximum correlation for
lags when the pattern recurs after an integer number of rotation
periods and results in a rotation law that is quasi-rigid (Stenflo,
1989, 1990). The coexistence of these two rotation laws appear to
demand that the high-latitude large-scale surface pattern has to be
replenished in a time scale of less then a month, in contradiction with
the surface redistribution models for the solar cycle by
Babcock (1961), Leighton (1964), and Sheeley et al., (1987). For
detailed arguments, see Stenflo (1992). An alternative view is advocated
by Wang and Sheeley (1994), who claim that flux that has emerged at
low latitudes as active regions and is diffused by discrete
random walk across the solar surface will produce a flux pattern with
the observed properties. It has not yet been possible with available
observational data to rule out one or the other of these two
opposing viewpoints.
The unique quality and homogeneity of the SOI data set will allow detailed cross-correlation analysis over a wide range of spatial and temporal scales to an extent not possible with previous data sets. The dependence of the rotational phase velocity on the spatial and temporal scales involved will be the type of information needed to allow us to distinguish between the different interpretative models. The resolution of this controversy will significantly advance our understanding of the mechanisms behind the solar activity cycle.
As an important byproduct of this analysis we will obtain information on the rate of flux emergence as a function of latitude and longitude. It is crucial for our understanding of the solar cycle to know whether significant amounts of flux emerge from the solar interior at high latitudes (in contrast to the tenets of the Babcock-Leighton model), and whether this emergence has ``active longitudes''.
1.2. Sources of the Mean Magnetic Field
The SOI analysis will also support a project that I am proposing for
the analysis of the circular polarization data from GOLF, with the
aim of identifying the sources of the mean-field signal seen in
integrated sunlight.
Previous ground-based observations of the mean magnetic field, carried out at the Crimean and Stanford observatories, have shown that the polarity of the mean field is closely correlated with the polarity of the interplanetary magnetic field (after accounting for the 4 day transit time of the solar wind to earth), and it also displays a sector structure. This demonstrates that the interplanetary field is rooted in the large-scale pattern of the photospheric magnetic fields. However, the actual photospheric sources of the mean field have not been identified, although it is known that coronal holes as regions of large-scale, diverging fields are sources of high-speed solar wind streams.
GOLF and SOI in combination offer us the possibility of making a fresh approach to this problem and will help us to quantitatively better understand the relation between the mean field and the global, spatial pattern of evolving solar magnetic fields, including the magnetic ``roots'' in the solar interior and the dynamo that is the source of the observed fields. The new situation from the observational side is that GOLF and SOI will provide us with a time series of the mean magnetic field that will be of unprecedented quality, extremely homogenous, with high polarimetric accuracy, and of great length. One new situation from the interpretational side is that the techniques of harmonic decomposition and time series analysis of the magnetic field pattern have been developed in recent years, together with an advanced understanding of the meaning of the evolving modal components and pattern phase velocities in the context of understanding the solar dynamo and the interior magnetic structure (see Sect. 1.1.1 above). These techniques however have never yet been applied to the context of understanding the mean-field signal.
When integrating the line-of-sight component of the magnetic field (the degree of circular polarization) over the solar disk we effectively filter out the modes of high degree and order, and get contributions dominated by the modes of the lowest values, weighted by the spatial filter function. These large-scale, low-order modes are the ones that are expected to have the deepest reaching links to the solar interior, and are the ones that are best connected to the solar wind (which explains the good correlation between the mean photospheric magnetic field and the interplanetary magnetic field).
On the solar rotation time scale the field pattern, and thus also the mean magnetic field, varies due to solar rotation, flux emergence and disappearance (submerging, uprooting, annihilation), and field-line redistribution (due to velocity fields, like meridional circulation and turbulent diffusion). Describing the observed pattern in SOI full-disk magnetograms in terms of a harmonic expansion and performing the type of disk integration that is done by GOLF, we can expand the GOLF signal in terms of the SOI harmonic coefficients, with a relative weight attached to each coefficient. We will examine the time series of these weights to search for any possible pattern in the behavior, e.g.if there are periodicities in the waxing and waning of a given modal contribution, or if there are correlations between different modal contributions. The first stage of the analysis will be exploratory in nature. To understand and properly interpret the new patterns and relations that may be uncovered in the GOLF data the analysis will be accompanied by examinations of the corresponding SOI full-disk magnetograms.
2. Resource Requirements
The present proposal concerns only the use of archived SOI data,
processed according to Level-1 (calibrated).
No resources from the SOI project or Science Support Center at
Stanford are requested, other than to be provided convenient access
to the archived set of SOI full-disk magnetograms as soon as these
magnetograms become available in archive form (Level-1).
The data analysis will be carried out at my home institute.
References
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