Classifying Magnetosheath Jets using MMS - Statistical Properties

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magnetosheath as boundary jets. Finally, encapsulated jets are jet-like structures with 23 similar characteristics to quasi-parallel jets while the surrounding plasma is of quasi-perpendicular 24 nature. 25 We present the first statistical results of such a classification and provide compar-26 ative statistics for each class. Furthermore, we investigate correlations between jet quan-27 tities. Quasi-parallel jets have the highest dynamic pressure while occurring more often 28 than quasi-perpendicular jets. The infrequent quasi-perpendicular jets, have a much smaller 29 duration, velocity, and density and are therefore relatively weaker. We conclude that quasi-

142
Using MMS data we identify and classify the jets into 4 main categories. Jets have 143 been observed for over 20 years now downstream of the quasi-parallel bow shock (Němeček 144 et al., 1998). It is believed that the majority of jets are occurring in a quasi-parallel con-145 figuration and therefore the first category we search for are the "Quasi-parallel (Qpar) 146 jets". As a complementary category, we are investigating cases of jets that are downstream 147 of the quasi-perpendicular bow shock that we call "Quasi-perpendicular (Qperp) jets". 148 Furthermore, we classified jets that are found at the boundary between a Qpar and a 149 Qperp geometry or vice versa. Our goal is to investigate if these jets are connected to  Apart from the main categories, in the jet database, we include 2 more classes. The 157 first are the ones that were identified as jets but were not classified by the algorithm by 158 not fulfilling all necessary criteria. These jets, therefore, remain as 'Unclassified jets' un-159 til further inspection. Secondly, jets found very close to either the bow shock or the mag-

185
For parts of the analysis, we use upstream solar wind measurements, publicly avail-186 able through the 1-minute resolution OMNI database. This dataset is created using mul- results in the cases that we tested manually, and was done to compensate for several pos-195 sible errors that are explicitly analyzed in the method section below. As a result, every 196 jet that has been measured by MMS in the magnetosheath is associated to average so-197 lar wind quantities from the OMNIweb database. temperature (T i ), and differential energy flux of high-energy ions (F i ). Furthermore, we 203 require three (3) sequential data points to be classified as a different region in order to 204 change the region's characterization (e.g. transitioning from the magnetosheath to the 205 solar wind). This was done to avoid cases where due to the variance of the measurements, 206 one point might be misclassified as another region. Finally, we impose a minimum du-207 ration for each region to be 15 minutes. Smaller regions were considered to be possibly 208 influenced by bow shock or magnetopause crossings.

210
For jet determination, we rely only on local magnetosheath data. Doing so, we in- curring at the flanks of the magnetosheath, and such criteria would be met all the time. 226 We then implement an additional criterion, combining all the jets that have a shorter 227 time separation than 60 seconds from each other.
Where i = 1, 2, 3...n is the number of the jet in the database.

229
This was done based on the assumption that jets with such a small time separa-  test can be seen in Figure 1. The cone angle is defined as: which in the case of subsolar point it is identical to θ Bn since the bow shock normal vec-278 torn is pointing in the x direction.

279
As shown in Figure 1, there are distinct magnetosheath characteristics associated 280 with the quasi-parallel and quasi-perpendicular bow shock. The high energy ion flux is 281 the one that is most noticeable, while the ion temperature anisotropy, and the magnetic 282 field variance are also correlated with the change of the cone angle. The exact compu-283 tation of these quantities can be found in Appendix A. Interestingly, the region which 284 is not shaded with any color is a typical example where the high resolution measurements 285 of MMS provide evidence of a short-time scale change of IMF while the cone angle mea-286 surements of 1-min resolution fully miss the rapid change that is seen in the magnetosheath.

287
The purpose of this example is to verify that the classification of jets Typical examples of each jet class can be seen in Figure 2. In Figure 2(a), we show 294 a quasi-parallel jet whereas in Figure 2(b) a quasi-perpendicular one. A boundary jet 295 can be seen in Figure 2(c) and finally an encapsulated one in Figure 2(d).

297
The classification scheme is based on the assumption that there are three distinct 298 phases in the jet phenomenon. Since the jet crosses MMS, observations include the plasma 299 environment propagating in front of the jet, the jet flow and the plasma behind the jet.

300
These plasma environments are called, pre-jet, jet and post-jet periods, respectively.

301
The jet period is the duration in which the criterion of Eq. (1)

316
In order to determine the settings for the classification scheme, a test data set was 317 created through visual inspection, containing jets of every class. After testing the ac-318 curacy of our classification procedure the best stage from which the output was sufficient 319 to derive statistical results was chosen (Appendix B).  The number of jets in the final classified dataset is shown in Table 3.

330
The position for all the main class jets is shown in Figure 3. There, the MMS po- in the dataset. In particular, the model used here and below uses the following quan-

341
In order to derive statistical results for each of the classes, the "final cases" listed 342 in Table 3 are used. These jets met all necessary criteria from the automatic procedure 343 and have also been manually verified. As a result, unless explicitly mentioned, we use 344 the verified ("final") cases for our analysis. Finally, when we are referring to "main" classes 345 we mean the four classes described in Table 2. More information regarding the criteria In the background value (⟨X⟩ M SH ), we remove the jet period. As a result, where start/end is the starting and ending point of the jet period, and n = 33 measure-  conditions averaged over the periods that a jet was found. Coordinate system is the Geocentric Solar Ecliptic (GSE) and both axes are normalized to Earth radius (RE = 6.371 km).
The differences between the mean and max values were, statistically speaking, in-358 significant due to the short duration of the jets. Therefore, in order to make the visu-  The reason is that the background normalization in the first two cases is being done with 363 plasma which is more or less similar throughout the 5 minute period that was taken. On  Later, the maximum velocity vector (V max ) of each jet was used to propagate it back 373 in time until a bow shock crossing was found. This procedure took ∆T BSi time for each 374 jet (i) which was calculated as the number of steps multiplied by the time resolution of 375 the FPI instrument (4.5 seconds). After approximating a point of origin for each jet, the 376 distance from the bow shock is computed as: where X can be radial distance (R), distance along the yz plane (ρ), or distance along

400
Throughout the text, when referring to subsolar jets an extra criterion is applied:  To investigate the orientation of the flow, we calculate two more quantities. First, 408 we calculate the velocity in the yz plane (V ρ ), and then the angle between that veloc-409 ity and the x axis. The velocity V ρ is defined as: while the angle is defined as: An interesting quantity we investigated is the angle between the magnetic field vec-412 tor before and after the jet. This was done in order to search for any interesting prop-413 erties that could link a jet class to the pressure pulses connected to rotational discon-414 tinuities that were first described by Archer et al. (2012). To calculate the magnetic field 415 angle we took the average of the magnetic field vector for 30 sec, 1 min and 2 min be-416 fore and after the jet and determined the angle between the "averaged" magnetic field 417 measurements. All the derived quantities provided similar average and median results, 418 although the actual values varied slightly. We have decided to use the 30 sec averaged 419 magnetic field for the computation of the presented magnetic field angle.
where ∆t 1 is a 30 sec duration before the jet and ∆t 2 a 30 sec duration after the jet.

421
Another quantity that is considered is the angle between the average velocity vec- where, ∆t jet is the jet period and ∆t 2 is an 9-minute duration, of 4.5 minutes before t 1,start − 428 30s and after t 1,end + 30s.

429
To investigate the total effect of each jet we calculated the integrated dynamic pres-430 sure over the jet's duration along the flow (total fluence) as: where, n is the number of measurements within each jet period and ∆t is the time res-432 olution of the FPI instrument (4.5 seconds). 433 We also present correlation coefficients between a number of jet properties. The

442
The first observation, as shown in of the detected jets are unclassified, see Table 3). This result is in agreement with re-  ity than its associated average solar wind velocity, while all other jets had a lower one. 483 We can conclude that the main contribution of the dynamic pressure increase compared 484 to the solar wind is due to the compression that solar wind undergoes after interacting 485 with the bow shock. This, in turn, causes a density increase that can be several times 486 higher in the jets compared to the solar wind.

487
The average and median jet duration of the main class jets is found to be 39 and  ible when looking at the distance on the yz plane from the bow shock. Encapsulated jets 505 are also found at a much higher radial distance (R) from the bow shock, again with the 506 ρ component having much higher values than the rest of the classes. It should be noted 507 that Qperp jets are found to occur primarily under low-velocity solar wind conditions. 508 As a result, the bow shock model used for those cases generates a bow shock further away 509 from the Earth than for the cases of Qpar and Boundary jets. Finally, the time that it 510 took each jet to reach the MMS is much different. Qpar and boundary jets need on av-511 erage ∼ 3 minutes while the much slower Qperp jets require much more at around ∼ 512 8 minutes. Encapsulated jets also take a long time to reach MMS from their origin point 513 (∼ 7 min) but in contrast to Qperp jets, this is due to the large distance that they have 514 to cover rather than their velocity.

515
To analyze the different geometric properties of each class, we also include Figure.  Avg: 11.6 Med: 11.7 Avg: 11.5 Med: 11.7 Avg: 11.6 Med: 11.6 Avg: 10.8 Med: 10.9    Specifically, average beta values appear to be closer to unity for the Qperp and en-566 capsulated cases, while they are on average higher (⟨β qpar ⟩ ∼ 10 , (⟨β boundary ⟩ ∼ 6) 567 for the other classes. When looking at the difference to the background, it appears that 568 Qpar and boundary jets have a negative beta difference (∆β < 0). This could indicate 569 that magnetic pressure has a larger effect in the jet than in the surrounding magnetosheath 570 plasma.

571
The velocity components of each class are shown in Figure 9. Here, we present the cially encapsulated jets had a distribution that produced an average velocity close to zero, 574 in both components, due to equally frequent jets exhibiting a high negative and posi-575 tive V y,z . As a result, providing a histogram without the absolute values would limit the 576 information of each class, and would not contribute to a meaningful comparison.

606
In this subsection, we will report on some observations on correlations between dif-607 ferent jet properties. It should be noted that all correlations mentioned were found to 608 have a p-value of less than 0.01, unless stated otherwise. The computation of the p-value 609 was done through the exact permutation distributions of each subset (Edgington, 2011).

610
There is a moderate correlation between the magnetic field rotation angle (θ B ) and   Table 4 correspond to the same time (P max ) and are there-648 fore a better metric for quantifying the cases that exhibit a density decrease. However, 649 the calculation that includes the maximum density and velocity points are also impor- Relative difference in density and velocity for the maximum value of each quantity, measured within the jet period.
the lowest limit case metric, showing how many jets exhibit an increase or decrease in 652 velocity and density.

653
When comparing our results to earlier studies, we find that they are quite similar.   ure 8 also support SLAMS since Qpar and boundary jets have not only a higher mag-700 netic pressure than Qperp jets, but also a higher value than their surrounding plasma.

701
It should be noted, however, that the anti-correlation observed for Qperp jets can not 702 be directly explained through any known mechanism. The observed anti-correlation should 703 be treated with caution since it was only found for the "final cases" of Qperp jets ( Ta-704 ble 3). When we look at the whole body of Qperp jets the observed correlation disap-705 pears.

706
In Figure 12 All main class jets have a small to medium anti-correlation relation between the 713 ion temperature and the velocity difference within the jet period (Figure 12(b,d)). As  Finally, based on the differences between thermal and magnetic pressure shown in  (Table 3). On the other hand, the observed anti-correlation is con-

797
The results of this study show that quasi-parallel jets are considerably more fre-  Quasi-perpendicular jets have a much smaller dynamic pressure than the rest of 812 the classes and their dynamic pressure is mainly due to a velocity increase rather than 813 a density enhancement. Their duration is significantly smaller (median: 4.5 seconds per 814 jet) and their total integrated dynamic pressure is more than an order of magnitude lower 815 than the corresponding values of the other jet types. While their existence is clear ac-816 cording to the criterion used, their importance regarding magnetospheric influence is to 817 be questioned.

818
Their properties, when compared to Qpar jets, suggest that either a different mech-819 anism or a smaller scale version of Qpar generation mechanism causes their generation.

820
The density differences can be in principle, attributed to the absence of SLAMS that are 821 believed to occur only in the ion foreshock generated under quasi-parallel bow shock. On 822 the other hand, we hypothesize that their low velocities compared to the other classes 823 could be the result of one or more of the following effects. The jet criterion used (Eq.

824
(1)) is fulfilled more easily during low dynamic pressure conditions compared to high dy- and Qperp solar wind is smaller than one standard deviation. Therefore it is statistically 856 unlikely that it is the effect contributing the most.

857
From the discussion above, we can conclude that all four effects (absence of SLAMS, 858 observational bias, differences in SW, smaller scale ripples) could in principle take place 859 and contribute to the differences that were observed between the jet properties of Qpar 860 and Qperp jets.

861
The distance from the bow shock appears to be different for quasi-parallel and quasi-862 perpendicular jets, with Qpar jets occurring on average closer to the bow shock than Qperp 863 jets. It should be noted, that this result might be artificial since (as discussed above) Qperp 864 jets are found more frequently during low solar wind dynamic pressure conditions, which 865 affects the positions of the bow shock and the magnetopause. As a result, when MMS 866 measures a Qperp jet it will be further away from the bow shock and closer to the mag-867 netopause than a Qpar jet found in the same position.To quantify this effect, we used 868 the average conditions found in the solar wind when Qpar and Qperp jets were observed 869 and derived a model for the magnetopause and the bow shock. It was found that the av-   are also alike (see Figures 5 & 7). Moreover, the correlations between the different quan-946 tities were very similar to the ones found in Qpar jets. 947 We, therefore, suggest that Qpar and boundary jets form a superset of jets with 948 very similar properties and possibly the same origin. It is unlikely that different phys-949 ical mechanisms may generate two subsets of jets with so similar statistical properties.

950
One of the things that was not tested however, is how frequent these jets occur compared

963
The first ones are those that exhibit a positive V x or that have an extremely small 964 velocity, |V x | < 20 km/s (Figure 9, top left). These rare cases (7/57) could be the re-965 sult of a plasma reflection from the magnetopause (e.g. (Shue et al., 2009)). This pic-966 ture is also consistent with the general trend that encapsulated jets are found closer to 967 the magnetopause than the rest of the jets, and could also explain why some of the jets  netosheath region, although for drawing any stronger conclusions more in-depth anal-1032 ysis is required.

1033
Another possibility could be that a diffusion process due to magnetic reconnection 1034 or Kelvin-Helmholtz instabilities at the boundary between the jet and the background 1035 flow occurs, reducing the density of the jet as it travels in the magnetosheath.

1036
To summarize, the encapsulated jets are found on average further away from the 1037 bow shock, they have on average a very large velocity in the yz plane while they usu-1038 ally exhibit a density drop. Their exact nature still needs to be determined. If their ori-1039 gin is associated to the bow shock and not other magnetospheric related events, they can 1040 provide vital information regarding the evolution of the jet since we hypothesize that they 1041 are flows that while having a high velocity they have undergone an expansion that low-1042 ers their density compared to Qpar jets. As a result, such a jet, if created at the flanks of the bow shock, it could create a very interesting case study to investigate the dynamic Averaged "very high" ion differential energy flux Averaged "high" ion differential energy flux Averaged "medium" ion differential energy flux F M = 1 5 Summed magnetic field standard deviation Ion temperature anisotropy Total high / medium energy flux ratio where, i is the energy channel of the ion energy spectrum and j is the component of the the period of time that is initialized as described in Eq. 5.The next stages take the re-1127 maining unclassified jets and change the time average window along with the thresholds 1128 (Table A1) Table 3.
izes the Qpar and Qperp classes that are shown in Table 3. Moving on to stage 4, the 1130 algorithm identifies potential boundary and encapsulated jets by normalizing the data 1131 and using relative thresholds for the classification. The last stage removes one criterion 1132 (F H ) in order to allow more jets to be classified to increase the sample size. This stages 1133 finalizes the non-emphasized list shown in Table 3. The last step is to manually verify 1134 the cases and determine if certain misclassifications occurred, this results in the empha-1135 sized (bold) cases shown in Table 3, that are called "final cases". More information re-1136 garding the exact procedure can be found in the supplementary material.  Table 2, or that has been categorized as "unclassified". This set has been thoroughly 1141 checked by visual inspection in order to represent a characteristic sample of the desired 1142 classes that we are looking to classify.

1143
To create an initial classification scheme, some coarse threshold values and tech-1144 niques are implemented which we evaluated using the manually derived test set in or-1145 der to quantify the accuracy and the misclassification ratio of the code. The first accu-1146 racy results can be seen in Table B1. final result of the classification scheme regarding its accuracy can be seen in Table B2.
1157 Table A1. Quantities and thresholds used for each stage of the classification procedure. Number in the subscript indicates the average time window in seconds used for each quantity. Prime quantities (X ′ ) indicate a re-scaling of the quantity (min-max normalization: (X ∈ [0, 1]). Average quantities (⟨X⟩), are computed starting from 1 minute before the jet up to 1 minute after.
Finally, Γ = 0.05 representing a threshold barrier for the normalized quantities. The differential ion energy flux is given in (keV/cm 3 · s · sr · keV) and the standard deviation of the magnetic field vector in (nT).

Introduction
The supporting information consists of:  (Text S1): A detailed description of the algorithm used for the classification of the jets used in the analysis of the main paper. The purpose of this text is to inform the reader of the details of the procedure not given in the appendix.  ( Figure S2): A detailed flowchart to be read along with text S1 for a detailed step-bystep guide through the algorithm used for the classification of jets.  (Dataset S3): A full table of the dataset that was primarily used for the analysis (See Table 3 on the main paper) is included.
As described in the main article in subsection 3.2, we first identified 8499 jets from MMS1 measurements between May 2015 and May 2019 according to the criteria shown in Equations (1) and (3) in the main article.
These are then filtered to remove 'bad events' and sorted into the different classes (Qpar, Qperp, Boundary, and Encapsulated jets) according to the algorithm, described here and in the flow chart ( Figure S2).
Data Pre-process: This initial stage consists of finding cases of "Missing data" (Class 8) and "Border" (Class 7) jets from the 8499 unclassified cases. Class 7 jets are those found close to a magnetopause or a bow shock crossing.
As shown in Eq. 3 of the main article, the initial necessary information for the classification of a jet contains the pre-jet, jet and post-jet periods. Therefore, the first step is to find jets containing unreliable measurements within these periods, to remove them from the classification process. These jets correspond to the Class 8.
The second class removed in the initial pre-process is class 7 ("Border jets") which corresponds to jets found very close to a magnetopause or a bow shock crossing. These jets are found by checking whether a crossing was observed up to 5 minutes before or after the jet. If so, these jets are removed from the dataset. All the crossings were found from an automatic procedure that is also used to find where MMS resides in magnetosheath measurements (See subsection 3.1 on the main article).
These procedures remove 45 (Class 8) and 1346 (Class 7) jets. The rest of the database is filtered with the help of the following stages to determine the different jet classes and provide a sufficiently large sample to conduct statistical analysis.
Each of the remaining jets is moved to the next stages of the algorithm until is classified into one of the main classes. The main classes are the Qpar, Qperp, boundary and encapsulated jets (Table 3). If a jet is not classified in these 5 stages it is automatically considered "Unclassified" (Class 0) Stage 1 -Initial Classification: The first stage corresponds to a non-iterative algorithm that tries to directly classify jets to one of the main classes. This is done by applying the thresholds described in Table 3 while using the pre/post jet time shown in Eq.6 of the main article. In particular, the code assigns a characterization for the three periods (Pre, jet, post) and then depending on these three values determines the class of the jet.
Firstly, the rules N.1 are applied. If the jet is not classified then, by using N.2, the algorithm determines whether there is a good indication that the jet can be classified in a future stage. These rules are used to determine if at least 1 period for possible boundary jets or 2 periods for possible encapsulated jets are not characterized as unknown (class 0). If so, these jets are moved to the next stages for further process.
If a jet is found to have all its corresponding periods (pre, jet, post) classified as "unknown" (class 0) then the whole is moved to the unclassified category and is not analyzed furtherly. This stage is the most robust and works very well for Quasi-parallel (Class 1) and Quasiperpendicular (Class 2) jets. However, while allowing some cases of boundary and encapsulated jets to be classified, the majority of these jets were moved temporarily to classes 4 and 6 to be further processed in later stages and get possibly classified.
Stage 2 -Adjusting pre/post time: In the second stage, the pre/post time of each jet that was not classified previously is changed.
The adjustment that takes place is of two different variations. The first one that is applied is to move the pre and post time period by 1/2 of its value backward and forward in time respectively. After doing that, we try to classify the jets once more.
At first, the algorithm determines if 4/5 of the total measurements of the whole period (Including pre-time, jet time and post time) correspond to either quasi-parallel or quasiperpendicular plasma (Rules N.3). If so, we classify the jet to its corresponding class of Qpar or Qperp jet. This addition compared to the previous stage was done to avoid misclassification cases that could result from the variance of the pre-jet and post-jet periods.
The same rules as stage are then applied to determine if a jet belongs to one of the main classes. The only difference originates from the adjustment of the pre and post jet time periods.
The above variation is repeated 6 times, with each iteration adjusting the pre-jet and post-jet time further away from the jet by 1 measurement (4.5 seconds).
If a jet fails to be classified with the above variation, another one is used. Specifically, the algorithm takes up to a 30% increase of the initial time and up to 30% decrease to account for individual variations per jet that were possibly not accurately captured in Eq. 6.
Once more, the procedure follows the method described in Stage 1. Therefore, in total 6 tries for variation A of time adjustment and 6 more tries of Variation B are applied. If a jet remains in classes 4 and 6 it is moved to the next stage.
Stage 3 -Changing average time window: In the third stage, the same adjustments of the pre and post jet time periods are used, while changing the thresholds that are required to be satisfied.
In all previous stages, we have used a 60-second average window for the magnetic field and a 30 second one for the rest of the quantities. However, doing so, we filtered out small time scale changed that are useful to determine boundary and encapsulates cases. As a result, as shown in Table A1 of the main article (second row), a new set of thresholds is used corresponding to different smoothing of the quantities. In particular, a 30-second window is now used for the magnetic field while the rest of the quantities remain as originally obtained from the MMS.
This stage was effective in finding a few more cases of Boundary (Class 3) and Encapsulated (Class 5) jets. Most importantly, it finalizes the dataset for the Qpar and the Qperp jets.
At this point, it was found that both Qpar and Qperp jets that fit the necessary and the extra criteria (Table A1 and discussion in appendix) have a large enough sample to treat them statistically. As a result, to avoid any false-positive cases, we stop searching for classes 1 and 2 and we keep the jets that reached stage 3 as our final sample for these two classes.
It is important to mention that at this point only a very few cases of boundary and encapsulated jets (Tables B1, B2) are found. This shows that the complexity of these jets is difficult to be captured by the techniques used so far.
To increase the sampling of the underrepresented classes (boundary/encapsulated), the algorithm uses only possibly candidates (Classes 4 and 6) to pass through the next stages.
Stage 4 -Normalizing each quantity: In this stage, a normalization technique is applied to the measurements creating relative thresholds for each case (Table A1).
This procedure increases the number of cases that were initially not classified due to the strict thresholds imposed in the previous stages. On the other hand, it could also increase the number of false positives, making manual verification in a later stage necessary.
At this point, the code introduces a normalization to the quantities (Table A1, last row) and utilizes only one variation of pre/post jet time adjustment (variation B).
Jets that still did not get classified to either category are moved to the final stage.
Stage 5 -Removing a necessary criterion: In stage five, the exact same procedure as in stage 4 is applied but with removing one necessary criterion. The criterion removed from necessary criteria is the one corresponding to high energy flux (Table A1) By doing so, more samples were allowed to be classified, enlarging significantly the database. Every jet that fails to be classified at this stage is automatically named "Unclassified" (class 0). Manual Verification: As described above, while Qpar and Qperp jets contained a few to no false positives, this is not the case for the boundary and encapsulated ones. Stages 4 and 5 allowed us to significantly increase the size of the database but at the cost of allowing several false-positive cases.
As a result, the first and the second author of the article did the following procedure to ensure that the database accurately reflects the intended classes: At first, we removed the very few cases of Qpar and Qperp jets that appeared to be close to partial crossing of bow shock or magnetopause. From that procedure, we also found very few cases that contained rapid changes of the magnetosheath (from Qpar to Qperp or vice versa). It was decided that these jets should be moved to "Unclassified" as part of the manual verification procedure.
Finally, plenty of boundary cases were removed since they were considered false positives. These cases originated from stages 4 and 5 which due to the relative thresholds applied (Table  A1) classified many jets but were prone to false positives. The same procedure was done for the encapsulated jets, which reduced slightly their final number (Table 3).
This final process provides the "final" cases that are highlighted in Table 3 of the main articles. These cases are also given in the accompanying supplementary material (Data set S3).  Table. 3).