Comparison of the Characteristics of Magnetic Clouds and Magnetic Cloud-Like Structures for the Events of 1995 – 2003

Using nine years of solar wind plasma and magnetic field data from the Wind mission, we investigated the characteristics of both magnetic clouds (MCs) and magnetic cloud-like structures (MCLs) during 1995 – 2003. A MCL structure is an event that is identified by an automatic scheme (Lepping, Wu, and Berdichevsky, Ann. Geophys. 23, 2687, 2005) with the same criteria as for a MC, but it is not usually identifiable as a flux rope by using the MC (Burlaga et al., J. Geophys. Res. 86, 6673, 1981) fitting model developed by Lepping, Jones, and Burlaga (Geophys. Res. Lett. 95(11), 957, 1990). The average occurrence rate is 9.5 for MCs and 13.6 for MCLs per year for the overall period of interest, and there were 82 MCs and 122 MCLs identified during this period. The characteristics of MCs and MCL structures are as follows: (1) The average duration, Δt, of MCs is 21.1 h, which is 40% longer than that for MCLs (Δt=15 h); (2) the average (minimum B _z found in MC/MCL measured in geocentric solar ecliptic coordinates) is −10.2 nT for MCs and −6 nT for MCLs; (3) the average Dst_min (minimum Dst caused by MCs/MCLs) is −82 nT for MCs and −37 nT for MCLs; (4) the average solar wind velocity is 453 km s⁻¹ for MCs and 413 km s⁻¹ for MCLs; (5) the average thermal speed is 24.6 km s⁻¹ for MCs and 27.7 km s⁻¹ for MCLs; (6) the average magnetic field intensity is 12.7 nT for MCs and 9.8 nT for MCLs; (7) the average solar wind density is 9.4 cm⁻³ for MCs and 6.3 cm⁻³ for MCLs; and (8) a MC is one of the most important interplanetary structures capable of causing severe geomagnetic storms. The longer duration, more intense magnetic field and higher solar wind speed of MCs, compared to those properties of the MCLs, are very likely the major reasons for MCs generally causing more severe geomagnetic storms than MCLs. But the fact that a MC is an important interplanetary structure with respect to geomagnetic storms is not new (e.g., Zhang and Burlaga, J. Geophys. Res. 93, 2511, 1988; Bothmer, ESA SP-535, 419, 2003).     

Grad–Shafranov Reconstruction of Magnetic Clouds: Overview and Improvements

The Grad–Shafranov reconstruction is a method of estimating the orientation (invariant axis) and cross section of magnetic flux ropes using the data from a single spacecraft. It can be applied to various magnetic structures such as magnetic clouds (MCs) and flux ropes embedded in the magnetopause and in the solar wind. We develop a number of improvements of this technique and show some examples of the reconstruction procedure of interplanetary coronal mass ejections (ICMEs) observed at 1 AU by the STEREO, Wind, and ACE spacecraft during the minimum following Solar Cycle 23. The analysis is conducted not only for ideal localized ICME events but also for non-trivial cases of magnetic clouds in fast solar wind. The Grad–Shafranov reconstruction gives reasonable results for the sample events, although it possesses certain limitations, which need to be taken into account during the interpretation of the model results.     

A Method Solving Kepler’s Equation for Hyperbolic Case

We developed a method to solve Keplers equation for the hyperboliccase. The solution interval is separated into three regions; F 1, F 1, F 1. For the region F is large, we transformed the variablefrom F to exp F and applied the Newton method to the transformed equation.For the region F is small, we expanded the equation with respect to F andapplied the Newton method to the approximated equations. For the middleregion, we adopted a discretization of the Newton method and used the Taylorseries expansion for the evaluation of transcendental functions (Fukushima,1997). Numerical measurements showed that, in the case of Intel Pentiumprocessor, the new method is more than 3.7 times as fast as the combinationof a fourth order correction formula (Fukushima, 1997) and Roysstarting procedure (Roy, 1988) and others.     

The Formation of Large-Scale Current Sheets within Magnetic Clouds

Magnetic clouds are a class of interplanetary coronal mass ejections (CME) predominantly characterised by a smooth rotation in the magnetic field direction, indicative of a magnetic flux rope structure. Many magnetic clouds, however, also contain sharp discontinuities within the smoothly varying magnetic field, suggestive of narrow current sheets. In this study we present observations and modelling of magnetic clouds with strong current sheet signatures close to the centre of the apparent flux rope structure. Using an analytical magnetic flux rope model, we demonstrate how such current sheets can form as a result of a cloud’s kinematic propagation from the Sun to the Earth, without any external forces or influences. This model is shown to match observations of four particular magnetic clouds remarkably well. The model predicts that current sheet intensity increases for increasing CME angular extent and decreasing CME radial expansion speed. Assuming such current sheets facilitate magnetic reconnection, the process of current sheet formation could ultimately lead a single flux rope becoming fragmented into multiple flux ropes. This change in topology has consequences for magnetic clouds as barriers to energetic particle propagation.     

Statistical Comparison of Magnetic Clouds with Interplanetary Coronal Mass Ejections for Solar Cycle 23

We compare the number and characteristics of interplanetary coronal mass ejections (ICMEs) to those of magnetic clouds (MCs) by using in-situ solar wind plasma and magnetic field observations made at 1 AU during solar cycle 23. We found that ≈ 28% of ICMEs appear to contain MCs, since 103 magnetic clouds (MCs) occurred during 1995  – 2006, and 307 ICMEs occurred during 1996 – 2006. For the period between 1996 and 2006, 85 MCs are identified as part of ICMEs, and six MCs are not associated with ICMEs, which conflicts with the idea that MCs are usually a subset of ICMEs. It was also found that solar wind conditions inside MCs and ICMEs are usually similar, but the linear correlation between geomagnetic storm intensity (Dst _min) and relevant solar wind parameters is better for MCs than for ICMEs. The differences between average event duration (Δt) and average proton plasma β (〈β〉) are two of the major differences between MCs and ICMEs: i) the average duration of ICMEs (29.6 h) is 44% longer than for MCs (20.6 hours), and ii) the average of 〈β〉 is 0.01 for MCs and 0.24 for ICMEs. The difference between the definition of a MC and that for an ICME is one of the major reasons for these average characteristics being different (i.e., listed above as items i) and ii)), and it is the reason for the frequency of their occurrences being different.     

On Multi-Line Spectro-Polarimetric Diagnostics of the Quiet Sun’s Magnetic Fields

On the long way to establish reliable physical properties of the solar atmosphere from different kinds of magnetic field measurement, significant progress has been achieved, but many important issues are still waiting for solution. This is essential for the investigation of weak magnetic fields of the quiet Sun, which usually cover most of the solar surface. Weak magnetic fields significantly contribute to the formation of the interplanetary magnetic field. The problem of reliable diagnostics of such fields hardly ever has a simple solution using only single spectral line observations. A better chance is given by multi-spectral line spectro-polarimetric observations, especially with lines having very different properties. In the present study, we use simultaneous high-precision Stokes-meter measurements of the quiet solar magnetic fields in 15 lines in the vicinity of Fe?i?525.0?nm. These measurements cover the whole range of heliocentric distances. Magnetic field strength ratios of different spectral lines with respect to Fe?i 525.0?nm vary between 1.07 and 2.12. This ratio depends also on the heliocentric position, moving closer to the limb it decreases and approaches values of about unity in most cases. To interpret the observations, different model approaches are compared. SIR-inversions (Stokes Inversion based on Response functions) with a two-component atmospheric model approach reproduce the basic observables much better than with one-component atmospheres. Our best fits are connected with field strengths of 1?–?2?kG and filling factors of less than five percent. To check the justification for the recent re-calibration of the data from the Michelson Doppler Imager (MDI) onboard SOHO, we carried out a numerical experiment, and we confirm our former conclusion that there is no need for such a re-calibration.     

Average Magnetic Field Magnitude Profiles of <Emphasis Type="Italic">Wind</Emphasis> Magnetic Clouds as a Function of Closest Approach to the Clouds’ Axes and Comparison to Model

We examine the average magnetic field magnitude (\(| \boldsymbol{B} | \equiv B\)) within magnetic clouds (MCs) observed by the Wind spacecraft from 1995 to July 2015 to understand the difference between this \(B\) and the ideal \(B\)-profiles expected from using the static, constant-\(\alpha\), force-free, cylindrically symmetric model for MCs of Lepping, Jones, and Burlaga (J. Geophys. Res. 95, 11957, 1990, denoted here as the LJB model). We classify all MCs according to an assigned quality, \(Q_{0}\) (\(= 1, 2, 3\), for excellent, good, and poor). There are a total of 209 MCs and 124 when only \(Q_{0} = 1\), 2 cases are considered. The average normalized field with respect to the closest approach (\(\mathit{CA}\)) is stressed, where we separate cases into four \(\mathit{CA}\) sets centered at 12.5 %, 37.5 %, 62.5 %, and 87.5 % of the average radius; the averaging is done on a percentage-duration basis to treat all cases the same. Normalized \(B\) means that before averaging, the \(B\) for each MC at each point is divided by the LJB model-estimated \(B\) for the MC axis, \(B_{0}\). The actual averages for the 209 and 124 MC sets are compared to the LJB model, after an adjustment for MC expansion (e.g. Lepping et al. in Ann. Geophys. 26, 1919, 2008). This provides four separate difference-relationships, each fitted with a quadratic (Quad) curve of very small \(\sigma\). Interpreting these Quad formulae should provide a comprehensive view of the variation in normalized \(B\) throughout the average MC, where we expect external front and rear compression to be part of its explanation. These formulae are also being considered for modifying the LJB model. This modification will be used in a scheme for forecasting the timing and magnitude of magnetic storms caused by MCs. Extensive testing of the Quad formulae shows that the formulae are quite useful in correcting individual MC \(B\)-profiles, especially for the first \({\approx\,}1/3\) of these MCs. However, the use of this type of \(B\) correction constitutes a (slight) violation of the force-free assumption used in the original LJB MC model.     

Evolution of the Sun’s Polar Fields and the Poleward Transport of Remnant Magnetic Flux

Observations of the solar photosphere show spatially compact large-amplitude Doppler velocity events with short lifetimes. In data from the Imaging Magnetograph eXperiment (IMaX) on the first flight of the Sunrise balloon in 2009, events with velocities in excess of 4\(\sigma \) from the mean can be identified in both intergranular downflow lanes and granular upflows. We show that the statistics of such events are consistent with the random superposition of strong convective flows and p-mode coherence patches. Such coincident superposition complicates the identification of acoustic wave sources in the solar photosphere, and may be important in the interpretation of spectral line profiles formed in solar photosphere.

     

Solar-Terrestrial Relations: Magnetic Turbulence in the Earth’s Magnetosphere and Geomagnetic Activity

Recent spacecraft observations of magnetic turbulence in the ion foreshock, in the magnetosheath, in the polar cusp regions, and in the magnetotail will be reviewed. Turbulence features like the fluctuation level, the spectral power law index, the turbulence anisotropy and intermittency, and the turbulence driver will be addressed.     

Multispacecraft Observations of Magnetic Clouds and Their Solar Origins between 19 and 23 May 2007

We analyze a series of complex interplanetary events and their solar origins that occurred between 19 and 23 May 2007 using observations by the STEREO and Wind satellites. The analyses demonstrate the new opportunities offered by the STEREO multispacecraft configuration for diagnosing the structure of in situ events and relating them to their solar sources. The investigated period was characterized by two high-speed solar wind streams and magnetic clouds observed in the vicinity of the sector boundary. The observing satellites were separated by a longitudinal distance comparable to the typical radial extent of magnetic clouds at 1 AU (fraction of an AU), and, indeed, clear differences were evident in the records from these spacecraft. Two partial-halo coronal mass ejections (CMEs) were launched from the same active region less than a day apart, the first on 19 May and the second on 20 May 2007. The clear signatures of the magnetic cloud associated with the first CME were observed by STEREO B and Wind while only STEREO A recorded clear signatures of the magnetic cloud associated with the latter CME. Both magnetic clouds appeared to have interacted strongly with the ambient solar wind and the data showed evidence that they were a part of the coronal streamer belt. Wind and STEREO B also recorded a shocklike disturbance propagating inside a magnetic cloud that compressed the field and plasma at the cloud’s trailing portion. The results illustrate how distant multisatellite observations can reveal the complex structure of the extension of the coronal streamer into interplanetary space even during the solar activity minimum. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

<Emphasis Type="Italic">In Situ</Emphasis> Signatures of Interchange Reconnection between Magnetic Clouds and Open Magnetic Fields: A Mechanism for the Erosion of Polar Coronal Holes?

We outline a method to determine the direction of solar open flux transport that results from the opening of magnetic clouds (MCs) by interchange reconnection at the Sun based solely on in-situ observations. This method uses established findings about i) the locations and magnetic polarities of emerging MC footpoints, ii) the hemispheric dependence of the helicity of MCs, and iii) the occurrence of interchange reconnection at the Sun being signaled by uni-directional suprathermal electrons inside MCs. Combining those observational facts in a statistical analysis of MCs during solar cycle 23 (period 1995 – 2007), we show that the time of disappearance of the northern polar coronal hole (1998 – 1999), permeated by an outward-pointing magnetic field, is associated with a peak in the number of MCs originating from the northern hemisphere and connected to the Sun by outward-pointing magnetic field lines. A similar peak is observed in the number of MCs originating from the southern hemisphere and connected to the Sun by inward-pointing magnetic field lines. This pattern is interpreted as the result of interchange reconnection occurring between MCs and the open field lines of nearby polar coronal holes. This reconnection process closes down polar coronal hole open field lines and transports these open field lines equatorward, thus contributing to the global coronal magnetic field reversal process. These results will be further constrainable with the rising phase of solar cycle 24.     

<Emphasis Type="Italic">Wind</Emphasis> Magnetic Clouds for the Period 2013 – 2015: Model Fitting,Types, Associated Shock Waves,and Comparisons to Other Periods

We give the results of parameter fitting of the magnetic clouds (MCs) observed by the Wind spacecraft for the three-year period 2013 to the end of 2015 (called the “Present” period) using the MC model of Lepping, Jones, and Burlaga (J. Geophys. Res.95, 11957, 1990). The Present period is almost coincident with the solar maximum of the sunspot number, which has a broad peak starting in about 2012 and extending to almost 2015. There were 49 MCs identified in the Present period. The modeling gives MC quantities such as size, axial attitude, field handedness, axial magnetic-field strength, center time, and closest-approach vector. Derived quantities are also estimated, such as axial magnetic flux, axial current density, and total axial current. Quality estimates are assigned representing excellent, fair/good, and poor. We provide error estimates on the specific fit parameters for the individual MCs, where the poor cases are excluded. Model-fitting results that are based on the Present period are compared to the results of the full Wind mission from 1995 to the end of 2015 (Long-term period), and compared to the results of two other recent studies that encompassed the periods 2007?–?2009 and 2010?–?2012, inclusive. We see that during the Present period, the MCs are, on average, slightly slower, slightly weaker in axial magnetic field (by 8.7%), and larger in diameter (by 6.5%) than those in the Long-term period. However, in most respects, the MCs in the Present period are significantly closer in characteristics to those of the Long-term period than to those of the two recent three-year periods. However, the rate of occurrence of MCs for the Long-term period is \(10.3~\mbox{year}^{-1}\), whereas this rate for the Present period is \(16.3~\mbox{year}^{-1}\), similar to that of the period 2010?–?2012. Hence, the MC occurrence rate has increased appreciably in the last six years. MC Type (N–S, S–N, All N, All S, etc.) is assigned to each MC; there is an inordinately large percentage of All S, by about a factor of two compared to that of the Long-term period, indicating many strongly tipped MCs. In 2005, there was a distinct change in variability and average value (viewed at \(1/2\) year averages) of the duration, MC speed, axial magnetic field strength, axial magnetic flux, and total current to lower values. In the Present period, upstream shocks occur for 43% of the 49 cases; for comparison, the Long-term rate is 56%.     

Magnetic Clouds at/near the 2007?�C?2009 Solar Minimum: Frequency of Occurrence and Some Unusual Properties

Magnetic clouds (MCs) have been identified for the period 2007??C?2009 (at/near the recent solar minimum) from Wind data, then confirmed through MC parameter fitting using a force-free model. A dramatic increase in the frequency of occurrence of these events took place from the two early years of 2007 (with five MCs) and 2008 (one MC) compared to 2009 (12 MCs). This pattern approximately mirrors the occurrence-frequency profile that was observed over a three-year interval 12 years earlier, with eight events in 1995, four in 1996, and 17 in 1997, but decreased overall by a factor of 0.62 in number. However, the average estimated axial field strength [??|B _O|??] taken over all of the 18 events of 2007??C?2009 (called the ??recent period?? here) was only 11.0 nT, whereas ??|B _O|?? for the 29 events of 1995??C?1997 (called the ??earlier period??) was 16.5 nT. This 33% average drop in ??|B _O|?? is more or less consistent with the decreased three-year average interplanetary magnetic field intensity between these two periods, which shows a 23% drop. In the earlier period, the MCs were clearly of mixed types but predominantly of the South-to-North type, whereas those in the recent period are almost exclusively the North-to-South type; this change is consistent with global solar field changes predicted by Bothmer and Rust (Geophys. Monogr. Ser. 99, 139, 1997). As we have argued in earlier work (Lepping and Wu, J. Geophys. Res. 112, A10103, 2007), this change should make it possible to carry out (accurate short-term) magnetic storm forecasting by predicting the latter part of an MC from the earlier part, using a good MC parameter-fitting model with real-time data from a spacecraft at L₁, for example. The recent set??s average duration is 15.2 hours, which is a 27% decrease compared to that of the earlier set, which had an average duration of 20.9 hours. In fact, all physical aspects of the recent MC set are shown to drop with respect to the earlier set; e.g., as well as the average internal magnetic field drop, the recent set had a somewhat low average speed of 379 km?s^?1 (5% drop), and the average diameter had a 24% drop. Hence, compared to the earlier set, the recent set consists of events that are smaller, slightly slower, and weaker in every respect (and fewer in number), but in a relative sense the two three-year sets have similar frequency-of-occurrence profiles. It is also interesting that the two sets have almost the same average axial inclinations, i.e., axial latitude ??31° (in GSE). These MC characteristics are compared to relevant solar features and their changes. A preliminary assessment of the statistics on possible shocks and pressure pulses upstream of these recent MCs yields the following: About 28% of the MCs, at most, had shocks, and 33% had shocks and/or pressure pulses. These are low values, since typically the percentage of cases with shocks is about 50%, and the percentage with shocks and/or pressure pulses is usually about 75%.     

Methane emissions from Earth’s degassing: Implications for Mars

The presence of methane on Mars is of great interest, since one possibility for its origin is that it derives from living microbes. However, CH₄ in the martian atmosphere also could be attributable to geologic emissions released through pathways similar to those occurring on Earth. Using recent data on methane degassing of the Earth, we have estimated the relative terrestrial contributions of fossil geologic methane vs. modern methane from living methanogens, and have examined the significance that various geologic sources might have for Mars.Geologic degassing includes microbial methane (produced by ancient methanogens), thermogenic methane (from maturation of sedimentary organic matter), and subordinately geothermal and volcanic methane (mainly produced abiogenically). Our analysis suggests that ～80% of the “natural” emission to the terrestrial atmosphere originates from modern microbial activity and ～20% originates from geologic degassing, for a total CH₄ emission of ～28.0×10⁷ tonnes year^?1.Estimates of methane emission on Mars range from 12.6×10¹ to 57.0×10⁴ tonnes year^?1 and are 3–6 orders of magnitude lower than that estimated for Earth. Nevertheless, the recently detected martian, Northern-Summer-2003 CH₄ plume could be compared with methane expulsion from large mud volcanoes or from the integrated emission of a few hundred gas seeps, such as many of those located in Europe, USA, Mid-East or Asia. Methane could also be released by diffuse microseepage from martian soil, even if macro-seeps or mud volcanoes were lacking or inactive. We calculated that a weak microseepage spread over a few tens of km², as frequently occurs on Earth, may be sufficient to generate the lower estimate of methane emission in the martian atmosphere.At least 65% of Earth’s degassing is provided by kerogen thermogenesis. A similar process may exist on Mars, where kerogen might include abiogenic organics (delivered by meteorites and comets) and remnants of possible, past martian life. The remainder of terrestrial degassed methane is attributed to fossil microbial gas (～25%) and geothermal-volcanic emissions (～10%). Global abiogenic emissions from serpentinization are negligible on Earth, but, on Mars, individual seeps from serpentinization could be significant. Gas discharge from clathrate-permafrost destabilization should also be considered.Finally, we have shown examples of potential degassing pathways on Mars, including mud volcano-like structures, fault and fracture systems, and major volcanic edifices. All these types of structures could provide avenues for extensive gas expulsion, as on Earth. Future investigations of martian methane should be focused on such potential pathways.     

Application of Chebyshev collocation method for relocating of spacecrafts in Hill’s frame

In this study, the Chebyshev collocation method is used for solving the spacecraft relative motion of equations in Hill’s frame. Three different models of governing equations of relative motion (M1, M2, and M3) are considered and the maneuver cost required moving the spacecraft from one state to another is computed in the form of delta velocity at the first terminal point as a function of time of flight (TOF) and inter-satellite distance (ISD). A quantitative as well as qualitative difference is observed in the maneuver cost with the inclusion of radial and/or out of plane separation in along track separation of chaser. Also, a relative comparison of path profiles is made by considering M1, M2 and M3 models. Path profiles for M3 model are found close to M2 model for short intervals for a fixed ISD, whereas path profiles for M2 and M3 do not match even for small values of ISD for a fixed but long TOF. Path profiles for M1 models match to M2 model for very low values of target orbit eccentricities.     

Hubble’s Law Implies Benford’s Law for Distances to Galaxies

A recent article by Alexopoulos and Leontsinis presented empirical evidence that the first digits of the distances from the Earth to galaxies are a reasonably good fit to the probabilities predicted by Benford’s law, the well known logarithmic statistical distribution of significant digits. The purpose of the present article is to give a theoretical explanation, based on Hubble’s law and mathematical properties of Benford’s law, why galaxy distances might be expected to follow Benford’s law. The new galaxy-distance law derived here, which is robust with respect to change of scale and base, to additive and multiplicative computational or observational errors, and to variability of the Hubble constant in both time and space, predicts that conformity to Benford’s law will improve as more data on distances to galaxies becomes available. Conversely, with the logical derivation of this law presented here, the recent empirical observations may be viewed as independent evidence of the validity of Hubble’s law.     

Lagrange’s planetary equations for the motion of electrostatically charged spacecraft

A spacecraft that generates an electrostatic charge on its surface in a planetary magnetic field will be subject to a perturbative Lorentz force. Active modulation of the surface charge can take advantage of this electromagnetic perturbation to modify or to do work on the spacecraft’s orbit. Lagrange’s planetary equations are derived using the Lorentz force as the perturbation on a Keplerian orbit, incorporating orbital inclination and true anomaly for the first time for an electrostatically charged vehicle. The planetary equations reveal that orbital inclination is a second-order effect on the perturbation, explaining results found in earlier studies through numerical integration. All of the orbital elements are coupled, but the coupling notably does not depend on the magnitude of the electrostatic charge or on the strength of the magnetic field. Analytical expressions that characterize this coupling are tested with a propellantless escape example at Jupiter. A closed-form solution exists that constrains the set of equatorial orbits for which planetary escape is possible, and a sufficient condition is identified for escape from inclined orbits. The analytical solutions agree with results from the numerically integrated equations of motion to within a fraction of a percent.     

Reversals of the Sun’s Polar Magnetic Fields in Relation to Activity Complexes and Coronal Holes

A spatiotemporal analysis of long-term measurements of the Sun’s magnetic field was carried out to study changes in its zonal structure and reversals of the polar fields in Cycles 21?–?24. A causal relationship between activity complexes, their remnant magnetic fields, and high-latitude magnetic fields has been demonstrated in the current cycle. The appearance of unipolar magnetic regions near the poles is largely determined by the decay of long-lived activity complexes. The nonuniform distribution of sunspot activity and its north–south asymmetry result in the asymmetry of remnant fields that are transported poleward due to meridional circulation. The asymmetry of high-latitude magnetic fields leads to an asynchrony of polar-field reversals in both hemispheres. The interaction of high-latitude unipolar magnetic regions with the polar fields affects the embedded coronal holes. The evolution of large-scale magnetic fields was also studied in a time–latitude aspect. It is shown that regular reversals of the Sun’s polar fields resulted from cyclic changes in high-latitude magnetic fields. A triple polarity reversal of the polar fields in Cycle 21 and short-term polarity alternations at the poles were interpreted taking into account the interaction of the remnant fields with the Sun’s polar fields.