Small-scale Magnetic Flux Ropes in the First two Parker Solar Probe Encounters
Yu Chen, Qiang Hu, Lingling Zhao, Justin C. Kasper, Stuart D. Bale, Kelly E. Korreck, Anthony W. Case, Michael L. Stevens, John W. Bonnell, Keith Goetz, Peter R. Harvey, Kristopher G. Klein, Davin E. Larson, Roberto Livi, Robert J. MacDowall, David M. Malaspina, Marc Pulupa, Phyllis L. Whittlesey
aa r X i v : . [ phy s i c s . s p ace - ph ] S e p Draft version September 15, 2020
Typeset using L A TEX modern style in AASTeX63
Small-scale Magnetic Flux Ropes in the First two Parker Solar ProbeEncounters
Yu Chen, Qiang Hu,
1, 2
Lingling Zhao, Justin C. Kasper,
3, 4
Stuart D. Bale,
5, 6
Kelly E. Korreck, Anthony W. Case, Michael L. Stevens, John W. Bonnell, Keith Goetz, Peter R. Harvey, Kristopher G. Klein,
8, 9
Davin E. Larson, Roberto Livi, Robert J. MacDowall, David M. Malaspina, Marc Pulupa, andPhyllis L. Whittlesey Department of Space Science, The University of Alabama in Huntsville, Huntsville, AL 35805, USA Center for Space Plasma and Aeronomic Research (CSPAR), The University of Alabama inHuntsville, Huntsville, AL 35805, USA Department of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor,MI 48109, USA Smithsonian Astrophysical Observatory, Cambridge, MA 02138, USA Physics Department, University of California, Berkeley, CA 94720-7300, USA Space Sciences Laboratory, University of California, Berkeley, CA 94720-7450, USA School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721, USA Department of Planetary Sciences, University of Arizona, Tucson, AZ 85719, USA Solar System Exploration Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771,USA Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80303, USA (Received 06/30/2020; Revised 09/08/2020; Accepted 09/10/2020)
Submitted to ApJABSTRACTSmall-scale magnetic flux ropes (SFRs) are a type of structures in the solar windthat possess helical magnetic field lines. In a recent report (Chen & Hu 2020), wepresented the radial variations of the properties of SFR from 0.29 to 8 au using in situmeasurements from the Helios, ACE/Wind, Ulysses, and Voyager spacecraft. Withthe launch of the Parker Solar Probe (PSP), we extend our previous investigationfurther into the inner heliosphere. We apply a Grad-Shafranov-based algorithm toidentify SFRs during the first two PSP encounters. We find that the number ofSFRs detected near the Sun is much less than that at larger radial distances, wheremagnetohydrodynamic (MHD) turbulence may act as the local source to producethese structures. The prevalence of Alfv´enic structures significantly suppresses the
Corresponding author: Yu [email protected]
Chen et al. detection of SFRs at closer distances. We compare the SFR event list with other eventidentification methods, yielding a dozen well-matched events. The cross-section mapsof two selected events confirm the cylindrical magnetic flux rope configuration. Thepower-law relation between the SFR magnetic field and heliocentric distances seemsto hold down to 0.16 au. INTRODUCTIONThe magnetic field exists everywhere in the solar wind. The magnetic field orfield components from time-series data sometimes can twist, rotate, and form helicallines. This type of structure is called the magnetic flux rope. Based on the scalesizes, it can be categorized into two groups: large-scale flux ropes, i.e., magneticclouds, and small-scale ones, although the size distribution of flux ropes in the solarwind is believed to be continuous. In contrast to the magnetic cloud, which hasan unambiguous solar origin corresponding to coronal mass ejection (CME), andpossesses well-defined observational signatures, the source and characteristics of small-scale flux rope (hereafter, SFR) are still under investigation.SFRs have been shown via many studies (see, e.g., Feng et al. 2007;Cartwright & Moldwin 2010; Zank et al. 2014; le Roux et al. 2015a,b; Zhao et al.2018; Hu et al. 2018) to correlate with particle energization and some other solarwind structures, such as the interplanetary shock waves, the heliospheric currentsheet (HCS), and the stream interaction regions. They are often believed to beassociated with magnetic reconnection as well. However, the main question regard-ing this structure, i.e., where it originates, is still inconclusive. Earlier statisticalanalysis via various spacecraft measurements but based on limited sample sizes sug-gested that the SFRs may be generated by small CMEs, and magnetic reconnec-tion across HCS, in both solar corona and interplanetary medium (Feng et al. 2008;Cartwright & Moldwin 2008; Yu et al. 2014). Moreover, the quantitative analysisof tens of thousands of identified flux tubes via the ACE spacecraft measurementsalso reveals the classical view that these structures form a packed “spaghetti”-likeconfiguration owing to processes on the Sun (Borovsky 2008; Bruno et al. 2001).More recently, two-dimensional (2D) magnetohydrodynamic (MHD) turbulence isalso considered as the possible source to generate these SFRs. Greco et al. (2009a,b);Pecora et al. (2019) proved that the current sheets, acting as “walls” of SFRs, natu-rally form during the dynamic evolution process of the solar wind turbulence, corre-spond well to boundaries of SFRs, by both simulation and observational studies. Fur-thermore, Zank et al. (2017) concluded that SFRs or vortex structures are a nonlin-ear component of 2D MHD fluctuations. This view is supported by the observationalanalysis of SFRs at 1 au. Using the Wind spacecraft measurements, Zheng & Hu(2018); Hu et al. (2018) provided substantial evidence in that there exists ubiquitousSFRs and they correspond to the inertial range of solar wind turbulence. agnetic flux ropes from PSP Encounters 1 & 2 ∼ ∼ ∼ > Chen et al. of SFR can be confirmed by various observational techniques, such as the waveletanalysis (Zhao et al. 2020), the minimum variance analysis of magnetic field (MVAB;Sonnerup & Scheible (1998)) (e.g., Yu et al. (2014)). SFR boundaries, however, mayvary among different techniques. Therefore, in this study, we continue to apply theGS-based program to PSP measurements in order to guarantee self-consistent SFRdetection results and enable comparisons with existing SFR databases obtained bythe same approach. Such comparisons will also shed light on the question regardingthe origin by examining whether any trend may extend to smaller radial distances ina persistent manner.This paper is organized as follows. The GS-based automated program and the corecharacteristics for this SFR detection will be introduced briefly in Section 2. Also,the detection period, criteria, and PSP data processing will be presented. The maindetection results are presented in Section 3. In Section 3.1, an overview of the ba-sic parameters, such as the magnetic field, the Alfv´en speed, the plasma properties,etc., together with identified SFR structures are shown for the full detection peri-ods of encounter 1 and part of encounter 2. In a series of recent papers, additional(generally large-scale) structures, such as the HCS, magnetic reconnection signatures,and an ICME, etc., were reported and we discuss their associations with the occur-rence of some SFRs in Section 3.3. The result of this paper is also compared withothers which use totally different methods. In Section 4, earlier detection result inChen & Hu (2020) is cited and combined with the result via PSP dataset. The com-parison between PSP and Helios SFR lists, albeit limited, is presented, and the radialvariations are shown. Finally, the main findings and future work are summarized inthe last section. METHOD AND DATAThe method for detection of SFRs in this study is a GS-based automated computerprogram. In this program, the main feature we are seeking for an SFR in time seriesdata array, based on the GS reconstruction technique, is the double-folding patternin the relation between two physical quantities, namely, the transverse pressure P t and the magnetic flux function A (also the axial component of the magnetic vectorpotential). All are calculated from in-situ spacecraft measurements. The transversepressure P t is the sum of the thermal pressure p and the axial magnetic pressure B z / (2 µ ), and the magnetic flux function A can be acquired by integrating the 1Dmagnetic field component (Hu 2017). The standard GS equation prescribes that theflux function A acts as the single variable of P t . This one-to-one correspondenceallows the determination of a 2D flux rope configuration characterized by a set ofnested isosurfaces of A . On each isosurface, the corresponding values of P t remainsthe same. Therefore the search of such a configuration is facilitated by examiningthe P t versus A arrays for the double-folding and single-valued pattern of P t ( A ). Thegoodness of the satisfaction of the single-value function relation P t ( A ) is judged by a agnetic flux ropes from PSP Encounters 1 & 2 Table 1.
Criteria of SFR detection via PSP dataset.PSP Encounter 1 Encounter 2Time Period Oct 31 - Dec 19, 2018 March 7 - May 15, 2019Duration Range (min) 5.6 ∼ h B i (nT) > > set of quantitative criteria including a fitting residue as a result of an analytic fittingfunction P t ( A ) to the data. For examples of such relations, see Section 3.3.During the process of data scanning and calculations of relevant quantities, anyarray owns the double-folding pattern will be saved as a potential candidate. Noticethat a flux rope candidate would not only need to be double-folded in P t ( A ) arrays butalso have a good quality of folding/overlapping. This requires that the data pointssplit into two branches which appear to fold back with one branch approximatelyoverlapping on top of the other. Therefore, the two residues, which evaluate thedifference between the two folding branches as well as a fitting residue of the P t ( A )function, are adopted to ensure the quality of overlapping (Hu & Sonnerup 2002;Hu et al. 2004). Last but not least, the low Alfv´enicity, i.e., the correlation betweenfluctuations of the magnetic field and velocity (Belcher & Davis Jr 1971), is requiredto distinguish flux ropes from other highly Alfv´enic structures, such as torsionalAlfv´en waves. This is implemented through a threshold condition on the Wal´en testslope, which is derived from the linear regression between the remaining flow velocityand the local Alfv´en velocity in a component-wise way (Paschmann & Daly 1998).We examine PSP data for the first two encounters from 2018 October 31 to De-cember 19 and from March 7 to May 15, 2019, respectively. The magnetic field andplasma data are measured by two instrument suites onboard: the FIELDS Experi-ment (Bale et al. 2016) and the Solar Wind Electrons Alphas and Protons (SWEAP)(Kasper et al. 2016; Case et al. 2020; Whittlesey et al. 2020). All data used in thisstudy are those tagged by “Only Good Quality” on the NASA CDAWeb. Due todifferent cadences, the magnetic field data and plasma data are not always in ac-cordance with each other in time-series. In order to bridge this inconsistency, adown-sampling process (averaged to the lower sample rate) is applied to the mag-netic field data (sometimes also to the plasma data) to match these two datasets andkeep the original plasma data as much as possible. The combined magnetic field andplasma dataset for analysis has a uniform cadence of 28 seconds.Table 1 lists the criteria of SFR detection for the first two encounters of the PSP.The detection is carried out for about one and a half months for each round. TheSFR duration range is set from about 6 to 360 min. For a flux rope candidate, theduration is the time interval length for a spacecraft crossing the structure. From theaspect of the detection algorithm, it represents the lower limit of the data segment Chen et al.
Table 2.
Detection result of SFRs via PSP dataset.SFR Occurrence Oct 31 - Nov 15, 2018 March 8 - Apr 18, 2019Total Count 24 20Radial Distance (au) 0.1717 ∼ ∼ ∼ ∼ ∼ ∼ length of the double-folding parts within a corresponding searching window. In otherwords, we assume that the spacecraft should have spent at least 6 min to cross theshortest flux rope and about 360 min (6 hr) for the longest one. In this study, allpossible small-scale flux rope candidates are assumed to be located within this range.According to the recent reports, an abundance of Alfv´enic signatures or Alfv´en wave-like structures in the predominantly slow wind were observed within fluctuations atdistances closer to the Sun during the first two PSP encounters. The duration of thesestructures is up to several minutes (Kasper et al. 2019; Bale et al. 2019). They mayexhibit similar magnetic field components rotation as a flux rope, but often with thesignificant field-aligned flow, which can be characterized by the Wal´en test in orderto be distinguished from a flux rope in quasi-static equilibrium. The exclusion ofsimilar structures other than flux ropes is crucial. In our study, the Wal´en test slopeis employed to discern whether a structure has high Alfv´enicity. According to itsdefinition, i.e., the ratio of the remaining flow speed to the local Alfv´en speed, we set0.3 as a lower threshold based on our experiences to diminish the effect of the Alfv´enicstructures. In addition, this threshold value 0.3 was used in the prior studies toindicate the level of the significant remaining flows (Hu et al. 2018). It was also usedto establish the condition for the magnetohydrostatic equilibrium (Hasegawa et al.2014) from which the GS equation is derived.Additionally, although the SFR is small scale in nature relative to the magneticcloud, it is large enough when compared to magnetic fluctuations in the background.Consequently, the removal of these noises is also essential. Considering that the rangeof radial distances for encounter 2 in this detection is wider than encounter 1, thelower limits of the average magnetic field magnitude based on the Parker magneticfield are set, respectively, i.e., as 25 and 10 nT. SFR DETECTION RESULTS VIA PSP DATASET3.1.
Overview
Table 2 summarizes selected SFR parameters from the detection results for the twoencounters, including the total count numbers, and the ranges of radial distances, scalesizes, and duration. The total numbers of SFRs detected in the first two encountersare 24 and 20 respectively. In these records, SFRs were found to locate within a widerange of heliocentric distances from 0.16 to 0.66 au, and have a distinct scale size agnetic flux ropes from PSP Encounters 1 & 2 Figure 1.
Time-series plot from 2018 October 31 to November 15. From the top to thebottom panels are the magnetic field magnitude and components in the
RT N coordinates,the Alfv´en speed, the solar wind speed, the proton temperature, the proton number den-sity, the proton β , the Wal´en test slope for each SFR candidate, the electron pitch angledistribution (PAD) for the 315 eV energy channel, and the PSP radial distance in au. Inthe 7th panel, the Wal´en slope threshold 0.3 is denoted by the horizontal dot-dashed line.Across all panels, the identified SFR intervals are marked by gray shaded areas. range. The smallest SFR (in scale size) is 0.0003 au for both encounters, and thelongest SFR (in duration) is 276.3 min ( ∼ RT N (radial, tangential, and normal) coordinates, the plasma parameters (theproton temperature T p , the proton number density N p , and the proton β , etc.), theWal´en test slope, the electron pitch angle distribution (PAD), and the radial distanceof the spacecraft. The Wal´en test slope is given for each flux rope candidate before Chen et al. applying the threshold condition. The final identified quasi-static SFRs are markedby gray shaded areas across all panels. Most shaded areas may appear like verti-cal lines because of their relatively short duration compared with the range of thehorizontal axis over the period of fifteen days.Note that these identified SFR intervals marked in Figure 1 are obtained by applyingthe Wal´en test slope threshold 0.3. They seem to distribute unevenly across the timeperiod during encounter 1. There are clearly more SFR candidates but with higherWal´en test slope, > .
3, as indicated in the 7th panel.The magnetic field has an apparent increase in strength when the spacecraft probedgradually closer to the perihelion on 2018 November 6. Few SFRs are detected aroundthis time. When PSP traveled away from the perihelion, starting from late November11, SFRs occur more frequently while the number of SFR candidates begin to decrease(7th panel, Figure 1). In general, the plasma properties, such as T p , N p , and plasma β ,do not have consistently coincident variations with the corresponding SFR intervals.This phenomenon was also observed by Yu et al. (2014), for instance, who found thathighly suppressed T p and low plasma β do not represent the typical characteristicsfor SFRs. It is also seen, as a general trend, that the identified SFRs tend to occurin rather slow solar wind streams, with V SW ≈
300 km/s. During a brief time periodpast perihelion when the solar wind speed exceeded 400 km/s, the event candidatesare much fewer.The eighth panel in Figure 1 shows the electron pitch angle distribution. Follow-ing Nieves-Chinchilla et al. (2020), the energy channel 315 eV is selected as it mayindicate the electron streaming direction with respect to the local magnetic field con-necting back to the Sun presumably. The bidirectional enhancement of the electronPAD at both 0 ◦ and 180 ◦ is not very common for most of the SFR records in this en-counter. Such signatures of enhanced bidirectional electron PAD are most prominentfor the ICME event and the HCS crossing that occurred on 2018 November 12 and13, as discussed in Giacalone et al. (2020) and Szabo et al. (2020), respectively.The detection for the PSP encounter 2 is implemented for ∼ agnetic flux ropes from PSP Encounters 1 & 2 Figure 2.
Time-series plot from 2019 March 29 to April 11. The format follows that ofFigure 1. field also has increased strength when the PSP was closer to the perihelion, but withrelatively less rapid fluctuations in the B t and B n components. The plasma β is alsomuch depressed around the perihelion. The other different aspect from encounter 1result is the occurrence of SFR candidates around the perihelion. Albeit the numberof structures with high Alfv´enicity is still far more than that of SFRs, the Wal´en testslope values are generally smaller. There are three SFR events identified around theperihelion. Moreover, the variability in the electron PAD also appears to be greaterthan in encounter 1. There are markedly some SFRs in encounter 2 associated withthe electron PAD enhancement nearby. The topic of the correspondence betweenSFRs and the associated electron PAD signatures remains an important one and hasyet to be further studied in the era of the PSP and the Solar Orbiter missions. Thegeneration of the list of SFR events as we strive to do here will assist in this specificstudy and other relevant studies.0 Chen et al.
Occurrence Rate
By adopting the GS-based technique, a total number of 44 SFRs were identifiedduring the first two PSP encounters. Although the implemented detection is aimedfor 1.5 months at least per orbit, the distributions of SFRs cluster within a half to onemonth due to incomplete data coverage. In Zheng & Hu (2018), the SFR databasevia the Wind spacecraft measurements from 1996 to 2016 (covering two solar cycles)yields an average monthly count of SFRs about 294 at 1 au. By combining the resultsof two encounters and considering the total time periods, the equivalent monthly countvia PSP is still notably fewer, i.e., about 27 per month. As shown in the previoussubsection, this is a result of the strict Wal´en test slope threshold we implemented.This discrepancy in counts due to enhanced Alfv´enicity closer to the Sun may beascribed to the possible solar source of SFRs. One traditional view suggests thatSFRs originate as streamer blobs of variable sizes that can be traced back to the Sun.This type of structures is usually observed by white-light coronagraphic imaging,and has been reported by such remote-sensing observations via PSP and STEREO(Korreck et al. 2020; Nieves-Chinchilla et al. 2020).An alternative view infers that these small structures could be generated locally,which is correlated to a cascade of 2D MHD turbulence (Zheng & Hu 2018; Hu et al.2018; Pecora et al. 2019). To some extent, this view can reconcile the contradictionof the number of SFRs at different locations in the heliosphere. A group of SFRsoriginating from the Sun can be recognized more easily at places closer to the Sun,while the turbulence source for generating a part of SFRs may be dominating atfarther distances as it was suggested that turbulence may become more importantat farther radial distances (Matthaeus et al. 1990). Although the Sun may still havenoticeable consequences on the SFR occurrence and properties at these distances,this impact may not be as powerful as the effect due to the solar wind turbulenceand local dynamic processes (e.g., Zank et al. 2014). For example, the solar cycledependency of SFR occurrence is obvious at 1 au (see, e.g, Zheng & Hu 2018), butsuch dependency is modulated by variations with both the radial distances and theheliographic latitudes at farther distances (Chen et al. 2019).In Chen & Hu (2020), the radial variation of SFRs was investigated by examiningone-year detection results via Helios, ACE, Ulysses, and Voyager datasets from 0.29to about 7-8 au at low latitude regions. Those authors reported that SFR countdecays with increasing radial distance r due to the possible merging process, whichfollows a power-law with an index -0.77 (or a deduced index around -1.5 for a 2Dregion). In the situation of solar origin, one would speculate the occurrence rate ofSFRs to reduce with increasing r in a consistent way. Such a trend if any has yet tobe further quantified with more SFR events from PSP, especially for r < .
29 au.Despite the uncertainty regarding the source of SFRs, strict criteria of detection canresult in the suppression of the identification of SFRs. At the present time, one ofthese important limits is to remove the flux-rope-like structure, i.e., highly Alfv´enic agnetic flux ropes from PSP Encounters 1 & 2 P t ( A ), no matter how high the Alfv´enicity of the structure is. It could be expectedto have such a small reduction (3%) in the total count at 1 au since the Alfv´enicitymay reduce outward to farther distances and could only survive in the fast wind(e.g., Panasenco et al. 2020). However, the threshold value 0.3 becomes critical forthe PSP detection when identifying SFRs with the same procedures but under thecircumstances with lots of highly Alfv´enic structures. The total number of SFRswould be 175 and 209, respectively, during these two encounters when loosening thislimit to 1.0. Now, the equivalent monthly count becomes 230, which is comparableto 1 au detection result. In other words, 88% of possible SFR candidates are elimi-nated due to high Alfv´enicity during the first two encounters. This raises a questionregarding the essence of these Alfv´enic structures. For instance, the torsional Alfv´enwave embedded within a small flux rope was reported by Gosling et al. (2010) at 1au, but it is extremely rare. The ongoing PSP observations offer the opportunity tolook for and further characterize these structures.3.3. SFR Occurrence in Conjunction with Other Structures
With the release of PSP data in the first encounter, a variety of solar wind structures,such as the HCS, magnetic reconnection regions, and an ICME, etc., were reportedin a number of recent papers. The correlation and validation, therefore, can beexamined by comparing the event list in this paper with other studies. Table 3 listsall identified SFR events with the time interval, duration, scale size, the averagemagnitude of the SFR magnetic field, the sign of the magnetic helicity ( σ m ), andthe axis orientation. Here, the magnetic helicity of each flux rope is consistent withone particular parameter which is derived within each interval, i.e., the product ofthe magnetic flux function A and the axial field component B z , as a proxy to themagnetic helicity density. The sign of the extremum is either positive or negative inthe array of A · B z , which yields the sign of magnetic helicity of the correspondingSFR. The axis orientation is given by two directional angles (in degrees), the polarangle θ and the azimuthal angle φ . They describe the angle between the flux rope2 Chen et al.
Figure 3.
Distributions of SFR duration for all events (except for the single ICME fluxrope event with the longest duration) in the same detection period from Table 3 and thosereported in Zhao et al. (2020). cylindrical axis ˆ z and the local N -direction, and the angle between the R -directionand the projection of z -axis onto the RT -plane, respectively.In this list, some SFRs occur in association with other specific solar wind struc-tures. For example, events No.7 and No.14 are correlated with magnetic reconnectionregions, which were reported in Phan et al. (2020). Also, 3 SFRs on 2018 November12 and 13 are probably HCS related events, as demonstrated in Szabo et al. (2020)who discussed the occurrence of HCS traversal by PSP and listed a few possible SFRswith slow rotating magnetic field components. This type of correlation was also foundby Hu et al. (2018) via the Wind spacecraft dataset, which showed that the SFRs aremore inclined to accumulate near HCS in the slow wind.Alternatively, Zhao et al. (2020) identified 40 SFRs from 2018 October 22 to Novem-ber 15 by using a wavelet-based analysis. The spectrograms of reduced magnetichelicity, cross-helicity, and residue energy were calculated from the time-series datato support the identification of quasi-static SFR structures. These SFRs are char-acterized as possessing (all normalized) relatively enhanced magnetic helicity, smallcross-helicity, and residue energy close to -1. The latter two conditions correspondto low Alfv´enicity. Therefore their results comply with our identification of the sametype of quasi-static SFRs, governed by the GS equation in our approach. In the samedetection period, there are 12 SFRs (event numbers with asterisks in Table 3) in thisstudy coinciding with the list in Zhao et al. (2020). The signs of magnetic helicity ofthese overlapping events are the same as those derived by the wavelet analysis. Figure3 shows the distributions of SFR duration, which includes all events from these twosets of results in the same detection period. Although the SFR duration is in generala little longer in Zhao et al. (2020) than in this study, smaller duration dominates forboth sets, and the temporal scales via the two methods are quite comparable. Amongthese overlapping events, we select two SFRs as examples and present the time-seriesdata with cross-section maps via the GS reconstruction in what follows. agnetic flux ropes from PSP Encounters 1 & 2
10 nT nT B z x (10 -3 AU) -6-4-20246810 y ( - A U ) -40 -30 -20 -10 0 10 20 A (T m) P t ( n P a ) A b R f =0.12 Figure 4.
Time-series plot and GS reconstruction result of SFR No. 15, 2018 November13, 9:49:43 - 12:09:43 UT. The flux rope interval is enclosed by the gray block. From thetop to the sixth panels: Time-series data; the format follows that of Figure 1. The seventhand eighth panels show the electron PAD and the product of the magnetic flux function A and the axial magnetic field B z , respectively. The bottom left panel is the standardcross-section map from the GS reconstruction with ˆ z = [0 . , . , . B z as indicated by the color bar, while the black contoursrepresent the transverse field lines. The spacecraft path is along the line y =0, with themeasured transverse field vectors marked by the white arrows. The bottom right panel isthe P t ( A ) plot: the blue circles, red dots, and the black line represent the measured datapoints along the spacecraft path from the observations, as well as the fitting curve withthe fitting residue R f as denoted, respectively. The vertical line denoted by A b marks themagnetic flux function value corresponding to the white contour line in the bottom leftpanel. Chen et al.
10 nT nT B z x (10 -3 AU) -1.5-1-0.500.51 y ( - A U ) -3 -2 -1 0 1 2 3 4 A (T m) P t ( n P a ) A b R f =0.11 Figure 5.
Time-series plot and GS reconstruction result of SFR No.16: 2018 November13, 23:12:51 - 23:41:47 UT, with ˆ z = [0 . , − . , . Figure 4 presents the event No.15, which occurred on 2018 November 13. Theduration of this SFR is about 140 min, and the scale size is 0.0194 au. The magneticfield components have strong bipolar rotation, while other parameters have merelyslight variation except that plasma β has significant variation near the end. On theseventh panel, the electron pitch angle distribution (PAD) is plotted. Although theresolution (15 min) is not ideal during this time interval, the electron PAD at 315eV has relatively strong and intermittent enhancement at both 0 ◦ and 180 ◦ , some agnetic flux ropes from PSP Encounters 1 & 2 Table 3.
List of Small-scale Flux Ropes identified during
PSP
Encounter 1 & 2.
No. Time Interval Duration Scale Size h B i Sign of σ m ( θ, φ )UT (sec) (au) (nT)1 ∗ − (60, 140)3 ∗ − (120, 120)4 ∗ − (80, 240)6 2018 Nov 2 12:23-12:29 365 0.0008 43.28 + (20, 200)7 2018 Nov 2 12:29-13:21 3109 0.0064 64.86 − (30, 140)8 2018 Nov 4 19:50-19:57 365 0.0004 86.02 + (100, 160)9 ∗ − (130, 260)10 2018 Nov 11 22:08-22:19 701 0.0018 51.68 − (130, 80)11 ∗ ∗ ∗ − (40, 100)15 ∗ ∗ − (50, 320)17 ∗ − (20, 40)18 ∗ − (60, 60)19 2018 Nov 14 06:37-06:48 701 0.0005 30.81 + (100, 20)20 2018 Nov 14 08:51-09:04 757 0.0016 41.13 − (110, 300)21 2018 Nov 14 13:18-13:27 533 0.0013 36.57 − (120, 280)22 ∗ − (110, 320)23 2018 Nov 14 19:06-19:15 561 0.001 26.22 − (110, 320)24 2018 Nov 14 21:23-21:28 337 0.0006 30.35 + (70, 320)25 2019 Mar 7 15:01-15:10 533 0.0015 13.32 − (70, 300)26 2019 Mar 7 21:59-Mar 8 0:01 7365 0.0181 15.73 + (40, 300)27 2019 Mar 8 01:16-01:51 2101 0.0037 14.48 − (50, 340)28 2019 Mar 13 01:19-05:56 16577 0.0316 12.76 + (80, 80)29 2019 Mar 14 06:00-06:07 421 0.0008 13.95 − (30, 220)30 2019 Mar 14 17:24-17:30 365 0.0007 12.73 + (120, 260)31 2019 Mar 15 12:47-13:17 1821 0.005 30.00 + (120, 100)32 2019 Mar 20 04:12-04:19 449 0.0006 12.72 + (130, 220)33 2019 Mar 20 15:44-15:50 337 0.0008 13.44 + (10, 20)34 2019 Mar 27 10:35-10:42 421 0.0008 23.64 − (40, 220)35 2019 Mar 27 19:21-19:27 393 0.0008 13.71 + (20, 220)36 2019 Apr 1 14:15-14:39 1401 0.0026 45.24 + (80, 120)37 2019 Apr 2 15:47-15:56 505 0.0003 68.49 − (110, 180)38 2019 Apr 4 00:24-00:29 337 0.0008 98.99 − (10, 160)39 2019 Apr 4 5:55-06:05 617 0.0012 101.98 − (130, 140)40 2019 Apr 4 16:11-16:25 841 0.0012 107.17 + (80, 160)41 2019 Apr 6 13:08-13:13 337 0.0006 94.31 + (110, 120)42 2019 Apr 7 22:29-22:39 561 0.0009 57.89 − (110, 320)43 2019 Apr 18 13:50-13:56 337 0.0012 14.78 + (160, 140)44 2019 Apr 18 15:07-15:16 533 0.0019 13.32 + (130, 80) ∗ Indication of the overlapping event with the result in Zhao et al. (2020). Chen et al. within the identified SFR intervals. The parameter, A · B z , has one positive peakwhich signifies the time when spacecraft passes the center point of this flux rope.The positive maximum value indicates that the sign of helicity is +1, correspondingto right-handed chirality as seen on the cross-section map. Figure 5 displays anothercase. In this case, the electron PAD appears to have slight variation only which lackspronounced features. So do other plasma parameters. The parameter A · B z hasa negative peak and the SFR is with left-handed chirality. These two cases havesimilar properties as reported in Zhao et al. (2020). Notice that the magnetic fieldcomponents in the second case have comparatively weak rotations. This type of SFRcan be definitely identified by the GS-based program which is based on more insightfulphysical considerations than approaches based on visual inspection.On the other hand, visual inspection is more straightforward in identifying ICMEsand the relatively large-scale flux ropes embedded. A 6-hour ICME (or magneticcloud) interval at the beginning of 2018 November 12 can be identified from thePSP in-situ measurements (e.g., Giacalone et al. 2020). Zhao et al. (2020) pre-sented a time-series plot of this structure with the parameters including the mag-netic field, the solar wind velocity, the proton number density, and temperature,etc. An ICME flux rope with 264 minutes duration is recognized. On the contrary,Nieves-Chinchilla et al. (2020) suggested another scenario that this ICME flux ropeprobably consists of two flux ropes or a combination of a real and a “fake” flux rope,instead of being regarded as one large ICME flux rope. Here, by “fake” they meanthat this structure has similar in-situ signatures to a flux rope but has open fieldlines.Due to the difference in techniques and criteria, the automatic identification inthis study divides the presumably large ICME flux rope interval into three SFRs.Because the detection is carried out by the automated program, which is tailoredtoward relatively small duration events (usually less than 6 hours; Hu et al. (2018)),the flux rope candidates with the best double-folding patterns are selected, insteadof the longest ones which may have relatively poor quality as judged by the set ofcriteria in Table 1. Furthermore, flux rope boundaries also depend on the data andthe method of how to process the data. It is known that different methods often yielddifferent boundaries defining a flux rope interval. RADIAL VARIATION OF SFRS FROM 0.16 AU TO 1 AUIn Chen & Hu (2020), we reported the SFR database via the Helios spacecraftmeasurements and the associated statistical analysis of SFR properties. The detectionwas implemented to cover almost the full Helios mission, which lasted from 1975 to1984 for Helios 1 and 1976 to 1980 for Helios 2. The detection criteria are similar tothose listed in Table 1 except for the duration range. The Helios time-series data arebased on 1 min cadence. Therefore, the duration range starts at 9 min instead of 6min. The upper limit is also modified to be 2255 min. Although multiple searching agnetic flux ropes from PSP Encounters 1 & 2 -0.8 -0.6 -0.4 -0.2 Distance (au) D u r a t i on ( m i n ) =0.425 0.372 -0.8 -0.6 -0.4 -0.2 Distance (au) -4 -3 -2 -1 S c a l e S i z e ( au ) =0.66 0.393 Figure 6.
Distribution of SFR properties with the radial distances r: (a) duration, and(b) scale size, derived for each SFR. Results via the Helios dataset are presented by the 2Dhistograms. The bin grids are 60 x 60 in size. All individual records via PSP are directlyplotted by red circles. The white curve represents the average value of each bin in r , andevent count is indicated by the color bar. The green line is a power-law fitting curve for therespective PSP points with the corresponding power-law exponent α denoted on top. windows are applied, most records have duration less than 6 hours, and the meanvalue is about 25 min. The study of the radial evolution of SFR properties between0.29 au and > r from the Helios SFR database (Chen & Hu 2020)together with the limited set of PSP results. The bin size in r is set as 0.01 au toaccount for discontinuous data gaps from 0.29 to 1 au, and the PSP detection resultis over-plotted directly, extending down to 0.16 au. As aforesaid, the SFR durationindicates the temporal presence of a structure, whereas the scale size is a measureof the spatial size of the SFR cross-section along the projection of the spacecraftpath. In Chen & Hu (2020), we found that both the SFR duration and scale sizepossess power-law distributions for r ∈ [0.29, 7-8] au, but with different indices. InFigure 6(a) and (b), this conclusion is affirmed by the average value of each bin in r (white curve), showing overall linear variation with increasing r on the log-log scale.Moreover, event counts peak around 0.001 ∼ r , it is far less clear in indicating any discernible trend based on thescattered points in Figure 6. The event count is not sufficient. To guide the eyes, afitting curve ∝ r α is drawn with the caveat that the standard errors are quite largefor α . A clear trend of the increase or decrease with the radial distance r for the inner8 Chen et al. -0.8 -0.6 -0.4 -0.2 Distance (au) B ( n T ) =-1.515 0.13 -0.8 -0.6 -0.4 -0.2 Distance (au) -0.5 B t ( n T ) =-1.474 0.2 -0.8 -0.6 -0.4 -0.2 Distance (au) -1.0 -0.5 B z ( n T ) =-1.815 0.247 Figure 7.
Distributions of SFR magnetic field averaged over each SFR interval with theradial distances r : (a) the total magnetic field, (b) the transverse field B t , and (c) the axialfield B z . The format follows that of Figure 6. range ( r < .
29 au) is inconclusive, and has yet to be established by providing moreevents from upcoming encounters.Figure 7 shows the distributions of the various averages of the SFR magnetic fieldwith respect to r . The relation between the scattered points and the nominal power-law fitting function (green line) is tighter, as indicated by the fitting results of α withuncertainties. The green line seems to largely follow the decaying trend of the whitecurve in each panel. The various averages of the SFR magnetic field have evidentdecaying relations with respect to r , and this trend remains valid down to smaller r closer to the Sun. The power-law indices are also approximately the same as thevalues reported in Chen & Hu (2020), i.e., α ≈ -1.4, for r ≥ .
29 au. Although it wasspeculated that such a consistent and perhaps unified variation seems to comply withthe basic background Parker spiral magnetic field (Chen & Hu 2020), such a trendmay break for the inner range of radial distances, i.e., r < .
29 au. SUMMARY AND DISCUSSIONIn summary, we have applied the GS-based automated detection program to thePSP spacecraft measurements and provided the resulting list of SFR records duringthe first two encounters over the time periods, 2018 October 31 to December 19, and2019 March 7 to May 15. The new results contain 44 SFRs with duration rangingfrom 5.6 to 276.3 min. The occurrence rate is compared with 1 au result. An overviewof the detection result in the full encounter 1 and part of encounter 2 is presented viatime-series plots of measured and derived parameters. With the new event list, somerecords are discussed further in the context of previous reports on the connectionwith other structures and cross-check with similar analysis results. Moreover, theSFR database obtained earlier by using the
Helios spacecraft measurements is citedto investigate the radial variation of SFRs from 0.16 to 1 au combined with thelimited number of PSP events from the first two encounters. The main findings aresummarized as follows.1. Overview of SFRs in the first two encounters reveals that the SFR occurrencerate is far less than that in deep space, owing largely to the prevalence of agnetic flux ropes from PSP Encounters 1 & 2 P t ( A ) plots. The final GS reconstruction resultslend confidence in their 2D cylindrical flux rope configurations.4. In an early report (Chen & Hu 2020), the SFR properties, such as the duration,scale size, and the average magnitude of the magnetic field, have distributionsfollowing power laws with different indices. In addition, these properties haveclear decaying relations with respect to the increasing radial distance r from0.29 to 7-8 au. For the limited number of events via the PSP detection, themagnetic field seems to retain these decaying relations. However, the other SFRproperties appear to distribute over wider ranges.As mentioned earlier, the discrepancy in occurrence rate is owing to the detectioncriterion of the Wal´en test slope threshold. Nearly 88% of candidates are ruled outunder a strict limit on the existence of Alfv´enic structures. Considering that theAlfv´enicity can change along with the evolution of structure in the solar wind, it ispossible for a scenario that Alfv´enicity reduces when solar wind plasma moves fartheraway from the Sun (Panasenco et al. 2020). In other words, the event candidatesthat are recognized with high Alfv´enicity, i.e., large Wal´en test slope, close to the Sunmay evolve to become quasi-static SFRs at farther distances as Alfv´enicity decreases.This scenario also raises uncertainty on the decaying relation between the scale sizeparameter of quasi-2D non-propagating structures including SFRs with respect toheliocentric distances. The existence of the power-law tendency of the scale size wasconfirmed mainly for SFRs produced in MHD turbulence in the solar wind over arange of farther distances beyond about 0.3 au. Whether this tendency holds forcloser radial distances is still unknown.The detection of SFRs in this paper is based on the first two PSP encounters only.The total count of SFRs inevitably affects the current results and is not sufficient to0 Chen et al. yield statistically significant analysis result, especially for the inner radial distancerange ( r < .
29 au). The future work will be extended to include additional encoun-ters when the PSP mission continues to venture even closer to the Sun.ACKNOWLEDGMENTSWe would like to thank Drs. Anthony Case, Kelly Korreck, and Michael Stevens atCfA for their help with acquiring and processing the PSP data. The PSP dataare provided by the NASA CDAWeb. YC and QH acknowledge NASA grants80NSSC19K0276, 80NSSC18K0622, and NSF grant AGS-1650854 for support. Spe-cial thanks also go to the SCOSTEP/VarSITI program for support of the develop-ment and maintenance of the online small-scale magnetic flux-rope database website,http://fluxrope.info. REFERENCES
Bale, S., Goetz, K., Harvey, P., et al.2016, Space science reviews, 204, 49Bale, S., Badman, S., Bonnell, J., et al.2019, Nature, 576, 237Belcher, J. W., & Davis Jr, L. 1971,Journal of Geophysical Research, 76,3534Borovsky, J. E. 2008, Journal ofGeophysical Research (Space Physics),113, A08110Bruno, R., Carbone, V., Veltri, P.,Pietropaolo, E., & Bavassano, B. 2001,Planetary Space Science, 49, 1201Cartwright, M. L., & Moldwin, M. B.2008, Journal of Geophysical Research:Space Physics, 113,doi:10.1029/2008JA013389, a09105Cartwright, M. L., & Moldwin, M. B.2010, Journal of Geophysical Research(Space Physics), 115, A08102, a08102Case, A. W., Kasper, J. C., Stevens,M. L., et al. 2020, The AstrophysicalJournal Supplement Series, 246, 43Chen, Y., & Hu, Q. 2020, TheAstrophysical Journal, 894, 25Chen, Y., Hu, Q., & le Roux, J. A. 2019,ApJ, 881, 58Feng, H. Q., Wu, D. J., & Chao, J. K.2007, Journal of Geophysical Research:Space Physics, 112, a02102 Feng, H. Q., Wu, D. J., Lin, C. C., et al.2008, Journal of Geophysical Research:Space Physics, 113, A12105, a12105Fox, N., Velli, M., Bale, S., et al. 2016,Space Science Reviews, 204, 7Giacalone, J., Mitchell, D. G., Allen,R. C., et al. 2020, The AstrophysicalJournal Supplement Series, 246, 29Gosling, J. T., Teh, W.-L., & Eriksson, S.2010, The Astrophysical JournalLetters, 719, L36Greco, A., Matthaeus, W. H., Servidio, S.,Chuychai, P., & Dmitruk, P. 2009a,The Astrophysical Journal Letters, 691,L111Greco, A., Matthaeus, W. H., Servidio, S.,& Dmitruk, P. 2009b, Phys. Rev. E, 80,046401Hasegawa, H., Sonnerup, B. U., Hu, Q., &Nakamura, T. 2014, Journal ofGeophysical Research: Space Physics,119, 97Hu, Q. 2017, Sci. China Earth Sciences,60, 1466Hu, Q., Smith, C. W., Ness, N. F., &Skoug, R. M. 2004, Journal ofGeophysical Research: Space Physics,109, doi:10.1029/2003JA010101, a03102Hu, Q., & Sonnerup, B. U. ¨O. 2001,Geophysical Research Letters, 28, 467 agnetic flux ropes from PSP Encounters 1 & 221