2.3 Geomagnetic and interplanetary precursors

Relations between the cycle related variations of geomagnetic indices and solar activity were noted long ago. It is, however, important to realize that the overall correlation between geomagnetic indices and solar activity, even after 13-month smoothing, is generally far from perfect. This is due to the fact that the Sun can generate geomagnetic disturbances in two ways:

(a) By material ejections (such as CMEs or flare particles) hitting the terrestrial magnetosphere. This effect is obviously well correlated with solar activity, with no time delay, so this contribution to geomagnetic disturbances peaks near, or a few years after, sunspot maximum. (Note that the occurrence of the largest flares and CMEs is known to peak some years after the sunspot maximum – see Figure 16 in Hathaway, 2010bJump To The Next Citation Point.)
(b) By a variation of the strength of the general interplanetary magnetic field and of solar wind speed. Geomagnetic disturbances may be triggered by the alternation of the Earth’s crossing of interplanetary sector boundaries (slow solar wind regime) and its crossing of high speed solar wind streams while well within a sector. The amplitude of such disturbances will clearly be higher for stronger magnetic fields. The overall strength of the interplanetary magnetic field, in turn, depends mainly on the total flux present in coronal holes, as calculated from potential field source surface models of the coronal magnetic field. At times of low solar activity the dominant contribution to this flux comes from the two extended polar coronal holes, hence, in a simplistic formulation this interplanetary contribution may be considered linked to the polar magnetic fields of the Sun, which in turn is a plausible precursor candidate as we have seen in the previous subsection. As the polar field reverses shortly after sunspot maximum, this second contribution often introduces a characteristic secondary minimum in the cycle variation of geomagnetic indices, somewhere around the maximum of the curve.

The component (a) of the geomagnetic variations actually follows sunspot activity with a variable time delay. Thus a geomagnetic precursor based on features of the cycle dominated by this component has relatively little practical utility. This would seem to be the case, e.g., with the forecast method first proposed by Ohl (1966), who noticed that the minimum amplitudes of the smoothed geomagnetic aa index are correlated to the amplitude of the next sunspot cycle (see also Du et al., 2009).

An indication that the total geomagnetic activity, resulting from both mechanisms does contain useful information on the expected amplitude of the next solar cycle was given by Thompson (1993), who found that the total number of disturbed days in the geomagnetic field in cycle n is related to the sum of the amplitudes of cycles n and n+1 (see also Dabas et al., 2008).

A method for separating component (b) was proposed by Feynman (1982) who correlated the annual aa index with the annual mean sunspot number and found a linear relationship between R and the minimal value of aa for years with such R values. She interpreted this linear relationship as representing the component (a) discussed above, while the amount by which aa in a given year actually exceeds the value predicted by the linear relation would be the contribution of type (b) (the “interplanetary component”). The interplanetary component usually peaks well ahead of the sunspot minimum and the amplitude of the peak seemed to be a good predictor of the next sunspot maximum. However, it is to be noted that the assumption that the “surplus” contribution to aa originates from the interplanetary component only is likely to be erroneous, especially for stronger cycles. It is known that the number of large solar eruptions shows no unique relation to R: in particular, for R > 100 their frequency may vary by a factor of 3 (see Figure 15 in Hathaway, 2010b), so in some years they may well yield a contribution to aa that greatly exceeds the minimum contribution. A case in point was the “Halloween events” of 2003, that very likely resulted in a large false contribution to the derived “interplanetary” aa index (Hathaway, 2010a). As a result, the geomagnetic precursor method based on the separation of the interplanetary component predicts an unusually strong cycle 24 (Rm ∼ 150), in contrast to most other methods, including Ohl’s method and the polar field precursor, which suggest a weaker than average cycle (Rm ∼ 80 – 90).

In addition to the problem of neatly separating the interplanetary contribution to geomagnetic disturbances, it is also wrong to assume that this interplanetary contribution is dominated by the effect of polar magnetic fields at all times during the cycle. Indeed, Wang and Sheeley Jr (2009Jump To The Next Citation Point) point out that the interplanetary magnetic field amplitude at the Ecliptic is related to the equatorial dipole moment of the Sun that does not survive into the next cycle, so despite its more limited practical use, Ohl’s original method, based on the minima of the aa index is physically better founded, as the polar dipole dominates around the minimum. The total amount of open interplanetary flux, more closely linked to polar fields, could still be determined from geomagnetic activity if the interplanetary contribution to it is further split into:

(b1) A contribution due to the varying solar wind speed (or to the interplanetary magnetic field strength anticorrelated with it), which in turn reflects the strength of the equatorial dipole.
(b2) Another contribution due to the overall interplanetary field strength or open magnetic flux, which ultimately reflects the axial dipole.

Clearly, if the solar wind speed contribution (b1) could also subtracted, a physically better founded prediction method should result. While in situ spacecraft measurements for the solar wind speed and the interplanetary magnetic field strength do not have the necessary time coverage, Svalgaard and Cliver (20052007) and Rouillard et al. (2007) devised a method to reconstruct the variations of both variables from geomagnetic measurements alone. Building on their results, Wang and Sheeley Jr (2009Jump To The Next Citation Point) arrive at a prediction of Rm = 97 ± 25 for the maximum amplitude of solar cycle 24. To what extent the effect of the Halloween 2003 events has been removed from this analysis is unclear. In any case, the prediction agrees fairly well with that of Bhatt et al. (2009Jump To The Next Citation Point) who, assuming a preliminary minimum time of August 2008 and applying a modified form of Ohl’s method, predict a cycle maximum in late 2012, with an amplitude of 93 ± 20.

The actual run of cycle 24 will be certainly most revealing from the point of view of these complex interrelationships.

The open magnetic flux can also be derived from the extrapolation of solar magnetograms using a potential field source surface model. The magnetograms applied for this purpose may be actual observations or the output from surface flux transport models, using the sunspot distribution (butterfly diagram) and the meridional flow as input. Such models indicate that the observed latitude independence of the interplanetary field strength (“split monopole” structure) is only reproduced if the source surface is far enough (> 10 R⊙) and the potential field model is modified to take into account the heliospheric current sheet (current sheet source surface model, Schüssler and Baumann, 2006Jiang et al., 2010a). The extrapolations are generally found to agree well with in situ measurements where these are available.

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