Issue 
A&A
Volume 526, February 2011



Article Number  A20  
Number of page(s)  13  
Section  The Sun  
DOI  https://doi.org/10.1051/00046361/201014617  
Published online  15 December 2010 
Online material
Appendix A: Cross–correlation functions
In Figs. 9 − 13, we present the crosscorrelation functions between different parameters, which we used to perform the correlation scatter plots presented in the paper. All crosscorrelation functions are derived up to a time lag of ±10 days, with a step of 6 h (data resolution) in all investigated cases. The time lags are always expressed in days. Negative lag between two quantities, e.g., V and Ap, hereinafter denoted as the V − Ap correlation, means that V is delayed with respect to Ap.
Appendix B: Correlation between solarwind parameters
We calculated the crosscorrelation functions for all combinations of V, T, n, and B. In Figs. 9 and 14, the crosscorrelation functions and the scatter plots for the highestcorrelationcoefficient timelag are presented for the most tightly correlated combinations. All considered correlations are listed in Table 4 where the time lags Δt, the corresponding linear least squares fit parameters a and b, and the correlation coefficient R are presented. A given “X − Y” correlation corresponds to the linear form Y(t) = aX(t^{∗}) + b, where X(t^{∗}) represents the value of X that occurred Δt days before the actual value of Y(t), i.e., t^{∗} is the “retarded time”, t^{∗} = t − Δt.
Table 4 shows that the most tightly correlated parameters are V and T, having the correlation coefficient R = 0.8, when V is delayed after T for Δt = 0.25 days. Furthermore, Fig. 9 shows that in the V − n and V − B case, the correlation coefficients are higher when the parameters are anticorrelated (the negative correlation coefficient in Table 4). This reflects the main physical property of HSSs, which is a depleted density and magnetic field in the stream itself. The anticorrelations are most significant for the time lags Δt = 0.75 d and Δt = 2.25 d, respectively, meaning that the dips of B and n are delayed with respect to the peak of V. The positive correlations of both the V − B and V − n relationships and their negative time lags (peaks of n and B preceding the peak of V by 2.5 d and 1.75 d), are related to the magnetic field and density compression in the “interacting region” at the frontal edge of HSSs. We note that the time lag in the n − B correlation is Δt = + 0.5 d, meaning that the peak of B is delayed with respect to the peak in n.
The distribution of data points in V–n and V–B graphs in Figs. 14b and c shows two “branches”, one almost horizontal and another almost vertical. The vertical one corresponds to the slow solar wind (V ≈ 300−400 km s^{1}), and the horizontal one to the fast solar wind (V > 400 km s^{1} and low values of n and B). If fitted by the powerlaw, the relationships are given by n = 1.4 × 10^{6} × V^{−2.0 ± 0.1}, and B = 4710 × V^{−1.1 ± 0.1}, with the correlation coefficients R = 0.69 and R = 0.58, respectively. Although the applied powerlaw fit is obviously more appropriate than the linear fit, it still shows a large deviation from the data in the slowwind velocity range (v < 400 km s^{1}). Thus, the obtained powerlaw relationships can be applied only to the fast solar wind.
Relationships T(V), n(V), B(V), T(B), B(n), and T(n).
Fig. 9
Crosscorrelation functions describing relationships between solar wind parameters (V − T, V − n, and V − B). 

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Fig. 10
Crosscorrelation functions describing the relationship between the solar wind parameters and Dst index (V − Dst, B − Dst, BV–Dst, and BV^{2} − Dst). 

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Fig. 11
Crosscorrelation functions describing relationships between the solar wind parameters and Ap index (V–Ap, B–Ap, BV–Ap, and BV^{2} − Ap). 

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Fig. 12
Crosscorrelation functions describing relationships between the coronal hole fractional areas CH and the solar wind parameters. 

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Fig. 13
Crosscorrelation functions for CH–Dst and CH–Ap relationships. 

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Fig. 14
Correlations V–T, V–n, and V–B. The linear least squares fits are shown by full lines and the powerlaw fits by dashed lines. The fit parameters, the correlation coefficient R, and the applied time lag Δt are shown in the insets. 

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We note that the first relationship, which can be expressed as nV^{2} = const., resembles that of kinetic energy conservation. Similarly, the latter correlation (approximately BV = const.) resembles to the magnetic flux conservation. However, we emphasize that these relationships cannot be interpreted in this way, since there is time lag between the adopted values of V and n, as well as V and B. These empirical forms reflect a complex/dynamical timespace relationship in the solar wind, that nevertheless produce a quite simple quantitative relationship. Although their meaning is not clear, they are certainly interesting, and deserve further analysis/interpretation from the theoretical point of view.
© ESO, 2010
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