Waiting-time distributions of magnetic discontinuities: Clustering or Poisson process?

Using solar wind data from the Advanced Composition Explorer spacecraft, with the support of Hall magnetohydrodynamic simulations, the waiting-time distributions of magnetic discontinuities have been analyzed. A possible phenomenon of clusterization of these discontinuities is studied in detail. We perform a local Poisson’s analysis in order to establish if these intermittent events are randomly distributed or not. Possible implications about the nature of solar wind discontinuities are discussed.

Figure 1

Results of the test for local Poisson distribution performed on a process where $\delta t_i=a^i\delta {\tau }_i$ [see Eq. (8)], with $a=1.03$ (left panel) and $a=0.97$ (right panel). The dash-dotted line represents the curve $P\left(H\ge h\right)=1-h$ for a Poisson process. See Ref. [1] for more details.

Figure 2

(Color online) (a) Spatial distribution of magnetic discontinuities computed from simulation vs distance $s/{\lambda }_c$ at $\Delta s=0.00625{\lambda }_c$ (solid-thin red line). (b) Time series (normalized to correlation time $t_c$) of discontinuities computed from ACE data. Events are selected according the PVI method [15, 16] and the thick dashed blue lines are the values of the thresholds. We show only a portion of the entire data set.

Figure 3

Distribution of waiting times in the Hall MHD simulation (squares), detected by a classical analysis (TS method) at $\Delta s=0.00625{\lambda }_c$. The power-law $a{x}^b$ (solid line) and the exponential $c{e}^{-dx}$ (dash-dotted line) fits are also shown. The parameters and the errors of the fits are $a=0.34\pm 0.01$ and $b=-0.92\pm 0.03$; $c=1.1\pm 0.1$ and $d=1.18\pm 0.06$. Vertical dashed line is placed at one correlation length.

Figure 4

Distributions of waiting times between discontinuities detected in solar wind (open squares) using (a) the PVI method and (b) the TS classical technique. Solid lines represent the power-law fits. The parameters and the errors of the fits are $a=0.64\pm 0.08$ and $b=-1.23\pm 0.03$; $c=1.8\pm 0.06$ and $d=-1.4\pm 0.04$. Vertical lines indicate the correlation time of 50 min.

Figure 5

(Color online) $P\left(H\right)$ for the local Poissonian test, performed on solar wind data (ACE data set). Data are selected with the PVI method with different criteria, namely, all the events are taken into account (full red line), WTs with $\delta t<{10}^3\text{s}$ (dotted blue line), and $\delta t>100\text{s}$ (dashed green line). The uniform probability in [0,1] (thin dotted black line), expected under a Poisson statistics, is also shown and the average values of the stochastic variable $⟨H⟩$ are reported as well.

Figure 6

(Color online) Cumulative PDF for solar wind data selected with the PVI method. As in Fig. 5, we filter out different waiting-time ranges: all the events (full red line and squares), WTs with $\delta t<{10}^3\text{s}$ (dotted blue line and triangles), and $\delta t>100\text{s}$ (dashed green line and circles). The thin dotted black line represents $P\left(H\ge h\right)=1-h$ that describes a Poisson process.

Figure 7

(Color online) Left: CPDFs form the test for local Poisson distribution for both PVI (solid red line and circles) and TS (dashed green line and triangles). As in Fig. 6, the dotted (black) line represents the Poisson expectation $1-h$. Right: $P\left(H\right)$ for the PVI (solid red line) and TS (dashed green line) methods, together with the uniform probability in [0,1] (dotted black line).

Figure 8

(Color online) Comparison between the Hall MHD simulation and the solar wind ACE data using the PVI method. Left: CPDFs for ACE data (solid red line and circles) and for the simulation (dashed green line and triangles). Right: $P\left(H\right)$ for the solar wind (solid red line) and the simulation (dashed green line). See captions of Figs. 5, 6, 7 for more details.

Figure 9

(Color online) The CPDFs computed for the solar wind (solid red line and squares) and for a random sample (dashed green line and circles). Dotted black line represents the Poisson expectation $1-h$.