On the magnetic characteristics of magnetic holes in the solar wind between Mercury and Earth

On the magnetic characteristics of magnetic holes in the solar wind between Mercury and Earth Martin Volwerk1, Charlotte Goetz2, Ferdinand Plaschke1, Tomas Karlsson3, and Daniel Heyner2 1Space Research Institute, Austrian Academy of Sciences, Graz, Austria 2Institute for Geophysics and Extraterrestrial Physics, Technische Universität Braunschweig, Germany 3Department of Space and Plasma Physics, School of Electrical Engineering and Computer Science, Royal Institute of Technology, Stockholm, Sweden Correspondence to: M. Volwerk, Space Research Institute, Austrian Academy of Sciences, Schmiedlstr. 6, 8042 Graz, Austria (martin.volwerk@oeaw.ac.at)

The origin of these structures has been studied and e.g. Stevens and Kasper (2007) found that they 20 occur mainly when the plasma-β of the solar wind is high. This makes MHs related to structures that look similar, namely mirror mode (MM) waves, which are also characterized by magnetic depressions, usually in a "train" of structures, for high-β plasmas with a temperature asymmetry T ⊥ > T (Gary et al., 1993). Specifically, when R SK > 1 (Southwood and Kivelson, 1993) with 25 and β p,⊥ = n p k B T p,⊥ B 2 /2µ 0 . (2) Interestingly, Stevens and Kasper (2007) found that the magnetic holes mainly occurred in MM stable environments. They argue that the non-linear development of MMs may result in MHs in MM stable regions. Indeed, Hasegawa and Tsurutani (2011) proposed a turbulent diffusion model 30 for the development of MMs (Bohm-like diffusion, Bohm et al., 1949), where the higher-frequencies of the structure diffuse out. Thereby smaller MMs will disappear, whilst larger MMs tend to grow in size as they are transported away by the plasma flow from their generation region. Using data from Venus Express at Venus and Giotto at comet 1P/Halley, Schmid et al. (2014) showed that indeed the sizes of MMs increase when the spacecraft is further away from the assumed generation region.
35 Buti et al. (2001) presented another generation mechanism based on presence of large-amplitude, right-handed Alfvén wave packages, observed in the solar wind to propagate at large angles with respect to the background magnetic field. Using hybrid simulations they show that these Alfvén wave packages develop into MHs in plasma regions where there is a high plasma-β, T e < T i and T i,⊥ = T i, , through the creation of plasma inhomogeneities.

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In order to find out a possible origin region for and the development of MHs in the solar wind and their occurrence rate, the cruise phase of the MESSENGER (MErcury Surface, Space ENvironment, GEochemistry, and Ranging, Solomon et al., 2007) spacecraft on its way from the Earth to Mercury is studied. Several studies have discussed the occurrence rate of MHs (or MMs) in the solar wind. Turner et al. (1977) found an occurrence rate of MHs of 1.5 per day near Earth using Explorer 43 45 (Imp I) data. Zhang et al. (2008)

The Data
This study is performed using the MESSENGER magnetometer data (Anderson et al., 2007) during the cruise phase of the mission from Earth to Mercury (2005Mercury ( -2011. The data have a resolution of 1 s and are in heliocentric, cartesian J2000 coordinates. 1 There is not continuous data for the cruise phase, as can be seen in Fig Sun is plotted over time.

Magnetic Hole Finding Method
The magnetic field data are investigated for the presence of magnetic holes. In this paper the same One more restriction needs to be put onto the MH events: the rotation of the magnetic field should be small over the structure. In order to check this, the average magnetic field is determined by

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The occurrence rate of the MHs as a function of radial distance from the Sun is studied first.
Therefore, the region 0.3 ≤ R ≤ 1.1 AU is binned into bins of 0.05 AU. For each bin the number of magnetic holes and the dwelling time was determined, after which the ratio of the two gives the occurrence rate per hour. The histogram is given in Fig. 6, where the data are also split up into rotational bins: On average there is a 21.9 ± 5.5 % chance to observe a structure, in one hour, which relates to ∼ 5.6 per day, although there are variations in the bins. In Fig. 6   bins. The distribution outside seems to be more erratic.

"Pseudo" MHs
"Pseudo' MHs (PMHs) in this paper are defined as the structures with a slightly larger rotation of the magnetic field, i.e. 10 • < Θ ≤ 45 • , the orange part in Fig. 6. The average occurrence rate of 140 these structures is 7.9 %/hr with a standard deviation of 2.6%/hr, which means ∼ 1.9 PMHs per day.
As in the LMHs the occurrence rate near Earth 4.7 and 4.1 %/hr the deviation from the average is almost 1.5σ. In this case, the occurrence rate is relatively constant with an increase between 0.8 and 0.9 AU and a decrease between 0.95 and 1.05 AU.
In Fig. 8  plasma data for the cruise phase and therefore, the events are only studied as a function of the background magnetic field B 300 for both the width and the depth of the structures.
The LMHs, Fig. 9, show that the width is mainly concentrated below 40 s for all field strengths.
However a trend can be observed that the wider LMHs happen for stronger background fields, see e.g. the points between 120 and 160 s around B ∼ 20 nT. Similarly, there seems to be a broadening Similarly for the PMHs, Fig. 10 shows that the spread in width is broader than for the LMHs, but again with a more larger width for stronger B, although there is also a broader distribution for 170 lower magnetic field strengths up to 5 nT. The distribution of the depth is also broader for the lower magnetic field strengths, however, the green exponential curve seems to fit the strongest occurrence rates also rather well.

Discussion
There are few papers that discuss the development of the MHs as they are transported by the solar  Fig. 7 left panel. However, a trend to longer structures does exist in the PMHs shown in Fig. 8 through a slight broadening of the counts between 0.3 and 0.7 AU.
The occurrence rate near the Earth (bins 0.95 -1.00 and 1.00 -1.05 AU) are significantly lower with 3.3 and 4.1 %/hr, respectively, than the average occurrence rate between Mercury and the Earth, which was found to be ∼ 9.0 %/hr with a standard deviation of σ ≈ 3.5 %/hr. Thereby a difference 185 of ∼ 1.5σ for these two bins. Xiao et al. (2014)  For the structures with a larger rotation, the PMHs, the minimum width increases as they move away from the Sun. Just outside of Venus's orbit the distribution of the widths is broader, and then narrows towards smaller sizes. The depth also seems to change just outside of Venus's orbit to reduce 205 similarly as the width.