Magnetic Local Time and Interplanetary Magnetic Field By Variation of Cusp Location Dependence on Dipole Tilt

We produced a database of over 41,000 ionospheric cusp locations using 40 years of energetic particle measurements from 14 Defense Meteorological Satellite Program (DMSP) satellites. We limited the database to periods when the Auroral Electrojet (AE) was <100 nT and the Interplanetary Magnetic Field (IMF) measurements were available, then calculated the magnetic latitude (MLAT), magnetic local time (MLT) and the dipole tilt (Λ) for each boundary, multiplying Λ by −1 in the southern hemisphere. We then binned the data in running one‐hour bins from 8.5 to 15.5 MLT. To obtain the dependence of the MLAT of the cusp boundary on Λ and IMF By, we performed linear fits on the MLAT versus Λ distributions, separated by ±IMF By. The dependence (degrees MLAT/degrees Λ) is asymmetric in both MLT and hemisphere as well as IMF By. In the northern hemisphere, the dependence for By > 0 (By < 0) is greatest in the afternoon (morning) sector for both poleward and equatorward boundaries. The opposite is true in the southern hemisphere. However, in the noon sector, the dependence is nearly the same for all boundaries and By sign. In addition, separation by Λ sign shows dramatically greater dependence variance for Λ > 0 than for Λ < 0 in the afternoon and morning sectors (but not in the noon sector). The observed asymmetries revealed in this work are thought to be due to the effect of By on reconnection and the location of the reconnection X line.


Introduction
The ionospheric cusp is a portion of the dayside auroral region where magnetosheath particles have direct access to the low-altitude ionosphere and thermosphere.It is typically observed in both hemispheres at latitudes between 70°and 80°MLAT, between about 1000 and 1400 hr MLT, and is on the order of 2°MLAT wide.It was originally expected from the Chapman and Ferraro (1931) dipole model of the Earth's magnetic field.At ionospheric altitudes on the dayside, Heikkila and Winningham (1971) observed a high-latitude band of low-energy particle precipitation with magnetosheath-like properties that was interpreted as the signature of direct solar wind entry via a magnetic cusp.Newell and Meng (1988) identified two regions of particle entry termed "cusp proper" and "cleft/boundary layer" with direct and indirect particle entry processes, respectively.The plasma properties of the cusp proper region show magnetosheath spectral properties with little or no acceleration of the magnetosheath population, and thus indicate more direct entry than the plasma associated with the Low Latitude Boundary Layer (LLBL).These properties were interpreted as an indicator of reconnection at the magnetopause (Onsager et al., 1993).
A dispersion of the ions in energy is often observed that occurs due to the convection electric field acting as a velocity filter from the injection point to the observation point in the ionosphere.Higher-energy, and thus faster, ions arrive at the cusp earlier than the lower-energy, slower, ions (Hill & Reiff, 1977;Reiff et al., 1977;Rosenbauer et al., 1975).During southward IMF, reconnected magnetic field lines convect tailward or toward higher-magnetic latitudes (MLAT).As the field lines move tailward, higher-energy particles precipitate along the field lines closer to the reconnection site, resulting in decreasing energy with increasing MLAT.During northward IMF, field lines mainly convect sunward and the energy increases with increasing MLAT (Onsager et al., 1995).
As the location of the cusp is dependent on the solar wind ram pressure and the IMF orientation, the angle between Earth's north dipole axis and the Geocentric Solar Magnetospheric (GSM) z-axis (Λ) is expected to have an impact on the cusp location.Choe et al. (1973) predicted the cusp would be located several degrees equatorward when the dipole axis is pointed away from the solar wind ram velocity direction than when the dipole axis is pointed toward the solar wind ram velocity direction.Burch (1972) used Orbiting Geophysical Observatory (OGO) 4 data at ∼700 km to find that the low-latitude cusp boundary varied by approximately 4°invariant latitude (ILAT) over all dipole tilt angles throughout the year.Newell and Meng (1989) used DMSP F7 data at ∼800 km and found that for every 1°of Λ, the cusp latitude shifted by 0.06°MLAT with the winter cusp being at the lowest latitudes.They suggested that this effect could be induced by the variation in the dayside current systems with changing Λ angle.Newell et al. (2006) examined the dependence of the cusp location on various solar wind coupling functions using a larger database than their 1989 study.They calculated the Λ dependence to remove its impact and found a smaller slope of 0.043°cusp latitude per 1°of Λ in the southern hemisphere and a dependence of 0.046°cusp latitude per 1°of Λ in the northern hemisphere.Their study, however, was limited to DMSP passes between 11 and 13 MLT and contained data mostly from the southern hemisphere.
There have also been a number of studies examining the effect of Λ on cusp location at altitudes above the ionosphere, where the Λ dependence was found to vary with altitude.Using the MAGION-4 satellite at altitudes ranging from 5 to 15R E , Něměcek et al. (2000) found a Λ dependence with a slope of 0.15°MLAT per 1°of Λ angle, which increased near the vicinity of the magnetopause to 0.16°MLAT per 1°of tilt during northward IMF and to 0.17°MLAT per 1°of tilt during periods of southward IMF.Zhou et al. (1999) used data from the Polar Spacecraft at 5 to 10R E in the northern hemisphere to find a dependence of ∼0.07°ILAT for every 1°of Λ angle.Finally, Shi et al. (2012) used Cluster data and found a dependence of 0.054°ILAT for every 1°of Λ angle in the northern hemisphere at the mean altitude of 5.2R E , and 0.051°ILAT for every 1°of Λ angle in the southern hemisphere at a mean altitude of 6.6R E .All these studies, however, used a limited amount of data; for instance, Shi et al. (2012) used 95 data points while Newell et al. (2006) had the most data points with 1,857 (407 in the Northern hemisphere).The cusp location in Shi et al. (2012) and Něměcek et al. (2000) were taken at the center of the cusp while Newell et al. (2006) used both the poleward and the equatorial boundaries, which could have contributed slightly to the discrepancies reported.
IMF conditions have a dramatic effect on the location of the cusp as shown by, for instance, Newell et al. (2006), who investigated the impact of various solar wind coupling functions on cusp location.These functions depend on the IMF clock angle, the IMF magnitude, and the solar wind velocity.They found the best correlation was with that proposed by Wygant et al. (1983) and is given by vB T sin 4 ( θ c 2 ) , where v is the solar wind velocity, B T is the total IMF magnitude, and θ c is the IMF clock angle.The clock angle dependence of this function is "intermediate" between the pure half wave rectifier and the Kan-Lee electric field given by Kan & Lee (1979).It could be assumed that dayside coupling is independent of the sign of B y , as the various published solar wind coupling functions are symmetric with respect to B y (e.g., Kan & Lee, 1979;Perreault & Akasofu, 1978;Vasyliunas et al., 1982;Wygant et al., 1983).However, recent results have suggested, as first pointed out by Friis-Christensen and Wilhjelm (1975), that B y could affect the solar wind/magnetosphere coupling.For instance, Holappa and Mursula (2018) examined the influence on the westward electrojet by the sign of B y .They found that the AL index was 50% larger in the northern hemisphere during winter for positive B y , with the opposite effect in the summer for negative B y .Similar results were seen in the southern hemisphere.Friis-Christensen et al. (2017) found similar seasonal effects of B y sign with the westward electrojet in the current wedge being larger in the northern hemisphere for positive B y than in the southern hemisphere for negative B y .Ohama et al. (2021) recently showed that the magnetospheric substorm frequency was impacted by the relationship between Λ and B y .They found that substorm frequency increased for periods when B y and Λ have the same sign but substorm intensity was independent of B y regardless of Λ sign.
We have extended the Newell et al. (2006) study to encompass 40 years of DMSP data from 1983 to 2022.This has produced a database of over 41,000 cusp identifications (both poleward and equatorward) allowing us, for the first time, to investigate the dependence of the effect of Λ on the cusp's poleward and equatorward boundaries with respect to MLT in both the northern and southern hemispheres.

DMSP SSJ Particle Detectors
The DMSP spacecraft fly in circular, sun-synchronous orbits near 840 km altitude, with 99°inclinations and orbital periods of ∼101 min.Their ascending nodes are typically near 1800 and 2000 hr solar local time (SLT), although that varies somewhat between satellites and with time as the orbit altitude decays due to atmospheric drag.DMSP F6 was the first DMSP satellite to begin monitoring the space environment, carrying precipitating ion and electron spectrometers and a thermal plasma monitor.For our study we focus on the Special Sensor for Precipitating Particles spectrometers, Versions 4 and 5 (SSJ/4 and SSJ/5), on F6 through F19 covering the years from 1983 to 2022. Figure 1 shows the coverage of all the satellites for that period restricted to periods when the SSJ/ 4 (F6-F14) and SSJ/5 (F15-F19) data were of high quality.The low-energy head of the SSJ/4 on F13 and F15 degraded shortly after launch so the data from those spacecraft were not used.Other issues such as degraded instrument performance and tape recorder degradation/failure further limit the available data.There were at least two spacecraft, and as many as five, always in orbit collecting data throughout this period, providing a total of over 100 years of spacecraft data.
The SSJ/4 and SSJ/5 instruments provide precipitating electron and ion flux in 19 energy channels ranging from 30 eV to 30 keV, though the SSJ/4 and SSJ/5 are slightly different instruments.The SSJ/4 consists of four Channeltron detectors, one each for high energy (1-30 keV) and one each for low energy (30 eV-1 keV) electrons and ions arranged in logarithmically energy steps.Each detector has a pair of cylindrical curved plates which electrostatically deflect the particles as they pass from the aperture to the detector, with a complete energy sweep occurring every second.The measurements are centered on local vertical within a solid angle of 2°by 5°for the high energy channels and 4°by 5°for the low energy channels.For a complete description of the SSJ/4 instrument, see Hardy et al. (1984).In contrast, the SSJ/5 consists of a pair of nested triquadrispherical (270°) electrostatic analyzers with a field of view of 4°by 90°ranging from zenith to the horizon divided into six 15°z ones.Microchannel plates are then used to amplify and transform single ion and electron events into charge pulses.The electron and ion counts from all six zones are summed once per second to provide output similar to the SSJ/4, other than the differing field of view.Newell et al. (1989Newell et al. ( , 2006) ) used the properties of the "cusp proper" region, defined in Newell and Meng (1988), to develop an algorithm to identify the location of the cusp for the studies based on measurements of the precipitating ion and electrons by the DMSP SSJ/4 instruments.The cusp was identified as having the following characteristics: (a) the average ion energy ≤3,000 eV, (b) the average electron energy ≤220 eV, (c) the ion spectral flux peak ≥2.0 × 10 7 eV/cm 2 s sr, and (d) the ion spectral flux peak occurred between 100 and 7,000 eV.They applied these criteria to each 1-s SSJ/4 measurement and the cusp entry was determined if 3 out of 4 consecutive spectra met these criteria.When 3 out of 4 consecutive spectra did not meet those criteria, the satellite was deemed to have exited the cusp.In cases when multiple cusp locations were found for a single polar pass, the longest duration of positive cusp identifications was used.

Cusp Identification
One of the issues with using the DMSP data for this study is the orbital dynamics of the spacecraft.As the DMSP satellites are in sun-synchronous orbits, geographic longitude (GLON) and UT are locked so the orbit tracks in magnetic coordinates vary dramatically with GLON as well as UT.This is illustrated in Figure 2 which shows the orbit tracks in a single day for several satellites over the period of the study.Note that the tracks vary noticeably throughout the day and show large differences in MLT between hemispheres.F6-F9 had local times of ascending node (LTANs) in the morning and thus passed on the midnight side of the terminator in the southern hemisphere while they passed on the dayside of the terminator in the northern hemisphere.For F6, with LTAN near 0600, the orbits never passed through the cusp in the northern hemisphere.F7 had an LTAN of about 0930 and thus the orbit tracks cut through the cusp nominally in the pre-noon sector in the southern hemisphere and the post-noon sector in the northern hemisphere.This configuration was reversed for F10-F19 with LTAN in the evening.While several passes cut predominantly perpendicularly through the cusp, many passes, especially in the afternoon, cut though the cusp at a low angles and skim along the cusp boundary.In some cases, these passes may enter the cusp at the equatorward side and never reach the poleward boundary, leading to possible misidentification of the exit as a poleward boundary.To avoid these issues, we limited the boundary identifications to those in which the satellite included data up to at least 78°MLAT, the MLT differences in the identified poleward and equatorward boundaries were less than two hours, and the MLAT differences were between 0.4°and 4°.
The MLAT and MLT used in this study were calculated using the Altitude Adjusted Corrected Geomagnetic (AACGM) system that was originally defined by Baker and Wing (1989).In AACGM coordinates, points along a given magnetic field line are given the same coordinates and thus reflect magnetic conjugacy better than other coordinate systems.The software used to calculate the AACGM coordinates was downloaded from the Super-DARN website at the Thayer School of Engineering at Dartmouth and uses up to date IGRF coefficients (Shepherd, 2014).
By visually inspecting many cusp crossings throughout the entirety of DMSP observations, we determined that a better criterion for identifying the cusp boundaries from the ion energy flux (criterion #3 in the Newell et al., 2006 algorithm) is the total integrated ion flux rather than the peak in a single energy channel.We then identified cusp entry and exit points for all passes throughout the 40-year period using the following criteria modified from Newell et al. (2006) (we will explain the reasoning behind these modifications later): (a) the average ion energy was ≤8,000 eV, (b) the average electron energy ≤220 eV, (c) the total integrated ion flux ≥0.1 erg/cm 2 s, and (d) the ion spectral flux peak occurred between 100 and 7,000 eV.Applying these criteria to DMSP measurements from the DMSP F6-F19 satellites found over 241,000 cusp entry and exit points.We then calculated the AACGM MLAT and MLT of each of the boundaries and applied the orbital restrictions mentioned previously to avoid issues with skimming passes.We limited the MLT to 0830-1530 hr, and to avoid the effects of solar/geomagnetic activity on the cusp boundary locations, we constrained the database to periods when AE < 100 nT.After applying these restrictions, we were left with ∼35,000 equatorward and poleward boundaries in the northern hemisphere and ∼16,000 in the southern hemisphere.Other authors have chosen to restrict their investigation to periods with positive IMF B z (Guo et al., 2013) when investigating the Λ dependence since the cusp location is known to have a stronger dependence on negative B z than positive B z (Newell et al., 2006).However, restricting AE to values less than 100 nT removed events associated with substorms and tended to remove events with large negative B z , achieving the same effect.We identified the IMF and solar wind parameters associated with each boundary using high resolution data from NASA's OMNI website (Papitashvili & King, 2020) and were able to acquire IMF data for over 40,000 of our remaining boundaries (29,150 in the northern hemisphere and 11,617 in the southern hemisphere).Of those, less than 1% had B z < 5 nT and 7% had B z < 2 nT.In contrast, of the ∼216,000 boundaries of our ∼241,000 identified boundaries for which IMF data was available, ∼5% had B z < 5 nT and 19% had B z < 2 nT.The occurrence of negative and positive B y (for AE < 100 nT) was almost exactly even.
Figures 3a-3d show examples of four of the identified boundaries from multiple satellites and time periods.They all show the typical energy dispersion in the ion precipitation (bottom panel in the figures) caused by the aforementioned ion velocity filter effect.The figures illustrate some of the different configurations of the orbits.For instance, the cusp identified in Figure 3a is in the afternoon and MLAT is increasing within the cusp while the ion energy is decreasing with time (MLAT), while the cusp identified in Figure 3b is in the morning and MLAT is decreasing within the cusp while the ion energy is increasing with time (decreasing with MLAT).
Figure 4a shows a plot of all identified equatorward boundaries in both the northern and southern hemispheres that met the AE < 100 nT criteria for the entire period of the study, 1982-2020.For a clearer look at the results, we plotted the data for an expanded four-year period, 1996-2000, in Figure 4b.The effect of Λ is apparent in these plots, where the seasonal variations of Λ are opposite between the northern and southern hemispheres.At northern summer solstice (the red vertical line in Figure 4a) the boundaries are most poleward in the northern hemisphere (positive Λ) and equatorward in the southern hemisphere (negative Λ).The opposite effect is seen during southern summer solstice (the vertical blue line in Figure 4a).
Figures 5a-f show the resulting linear fits of the MLAT versus both the equatorward and poleward boundaries in both hemispheres in one-hour MLT bins centered at 1000, 1200, and 1400 MLT.Note that as Λ is defined by the angle between the north dipole axis and GSM z-axis, it was multiplied by 1 for the southern hemisphere.Dipole tilt naturally varies diurnally (with UT) by the offset between the Earth's spin axis and the dipole axis,±11.2°,and annually by the Earth's axial tilt, 23.5°, such that the total variation is ±∼34°.For instance, on northern summer solstice, Λ varies between 34.4°and 12.2°; on northern spring equinox, Λ varies between 10.9°and 11.4°.Thus, in general, positive dipole tilt values correspond to summer conditions in both hemispheres, so in all figures, positive (negative) dipole tilt corresponds generally to summer (winter).The data show that the effect of dipole tilt on cusp MLAT is very linear.The observed variance from the linear fits is expected due to the impacts of various solar wind/geomagnetic phenomena on cusp location not being completely removed using the AE < 100 nT criteria.There is a clear paucity of data in the afternoon sectors (especially in the southern hemisphere) compared to the morning sectors due to the orbital DMSP configurations discussed previously and illustrated in Figure 2. In addition, the reduced chi-square (Χ 2 ) and standard deviation (σ) of the fits increase in the afternoon as many of the passes in the afternoon sector are oriented at less acute angles with respect to the cusp boundary (skimming) which leads to more deviation in the identified boundaries.However, there are still sufficient data to show a linear relationship between Λ and cusp MLAT.
We used a number of different criteria, modified from the Newell et al. (2006) study, for cusp identification, performed linear fits as in Figures 5a-5f to the data, and used Χ 2 and σ for goodness of fit to determine the most efficacious criteria.The data were binned in running one-hour MLT bins every 0.25 hr; standard deviation results for nine series of criteria are shown in Figures 6a-6d for the poleward and equatorward boundaries in both hemispheres from 0900 to 1500 MLT.In all nine series, the criteria for the cusp identification on the average electron energy was ≤220 eV and on the ion spectral flux was that the peak occurred between 100 and 7,000 eV.The criteria on the ion flux and energy were: (1) The spectral peak in a single energy channel was ≥2.0 × 10 7 eV/cm 2 s sr and the average ion energy was ≤3,000 eV (the Newell et al. ( 2006) criteria).
(2) The spectral peak in a single energy channel was ≥1.0 × 10 7 eV/cm 2 s sr and the average ion energy was ≤3,000 eV.(3) The spectral peak in a single energy channel was ≥5.0 × 10 6 eV/cm 2 s sr and the average ion energy was ≤3,000 eV.(4) The total integrated ion energy flux was ≥0.1 erg/cm 2 s and the average ion energy was ≤8,000 eV.
(5) The total integrated ion energy flux was ≥0.2 erg/cm 2 s and the average ion energy was ≤8,000 eV. ( 6) The total integrated ion energy flux was ≥0.1 erg/cm 2 s and the average ion energy was ≤6,000 eV. ( 7) The total integrated ion energy flux was ≥0.2 erg/cm 2 s and the average ion energy was ≤6,000 eV. ( 8) The total integrated ion energy flux was ≥0.1 erg/cm 2 s and the average ion energy was ≤4,000 eV. ( 9) The total integrated ion energy flux was ≥0.2 erg/cm 2 s and the average ion energy was ≤4,000 eV.Criteria (4) consistently provided the lowest σ.This was also consistent for Χ 2 (not shown).Thus, these criteria are valid for identifying the location of the cusp boundaries and were shown in Figures 3-5 and subsequent analysis.

Results and Discussion
As discussed in the introduction, the IMF B y can dramatically impact solar wind/magnetosphere coupling and dayside reconnection.Thus, we chose to examine the effect of the B y sign on the dependence of cusp location on Λ. Figure 7 shows the results of the examination of the B y impact in the same format as that shown in Figures 5a-5f.The fit results are summarized in Table 1.This separation by B y sign demonstrates a B y dependence and provides an explanation of the increase in the variance in the data for positive Λ.There is an asymmetry in both MLT and hemisphere, with the slope of the fits being greater in the northern hemisphere at 1000 MLT for B y > 0 Journal of Geophysical Research: Space Physics 10.1029/2023JA031886 and smaller at 1400 MLT for B y < 0. The opposite is true in the southern hemisphere where the magnitude of the slope is greater at 1400 MLT for B y < 0 and smaller for B y > 0 at 1000 MLT.This is seen for both the equatorward and poleward boundaries.However, at 1200 MLT, there is essentially no dependence on B y , with the slope being nearly the same for both B y positive and negative, in both the northern and southern hemispheres for the poleward and equatorward boundaries.To illustrate this B y dependence more clearly, we binned the data in running one-hour bins separated by 0.25 hr from 0900 to 1500 MLT, fit the data as in Figures 5 and 7, and plotted the results in Figure 8.In the northern hemisphere, the slope for B y > 0 peaks in the morning sector near 1000 MLT and for B y < 0 in the afternoon sector near 1400 MLT.In contrast, in the southern hemisphere, the slope for B y > 0 peaks in the afternoon sector between 1300 and 1400 MLT and for B y < 0 in the morning sector between 1000 and 1100 MLT.The trend is similar for both the equatorward and poleward boundaries.
The slope near noon is essentially the same for both signs of B y and for both the equatorward and poleward boundaries.The fit errors in the southern hemisphere are greater due to the lack of data, but the trend of the results in the southern and northern hemispheres being asymmetric is consistent with all other presented results.
For completeness, we examined the dependence on B z (as mentioned previously, after selection for AE < 100 nT, only a small number of boundaries were acquired for larger negative values of B z ; less than 1% had B z < 5 nT and 7% had B z < 2 nT) in a similar fashion.There was a minor dependence on B z with the slopes being slightly larger for B z > 0 but with no asymmetry in the slopes with either MLT or hemisphere.Given the lack of significant impact, we chose not to show these results.
These MLT and hemispherical asymmetries are likely the result of the impact of B y on the reconnection X line (Moore et al., 2002).It is well known that dayside reconnection and plasma flows are dramatically impacted by the IMF B y sign (e.g., Cowley, 1981;Khurana et al., 1996;Trattner et al., 2012;Tenfjord et al., 2015;Holappa and Mursulka, 2018).The direction/magnitude of B y determines how the newly opened flux tubes on the dayside are asymmetrically transported to the nightside; a nonzero B y results in a skewed convection pattern in the high latitude ionosphere.Crooker et al. (1987) showed that the location of the cusp changes in the azimuthal direction with IMF B y .Using measurements from the ISEE and HEOS spacecraft, they showed an approximately 1 R E shift of the cusp location toward dawn (dusk) in the northern hemisphere and dusk (dawn) in the southern hemisphere for positive (negative) B y .Park et al. (2006) used MHD modeling to investigate the impact of B y and Λ on reconnection.A nonzero B y caused the reconnection site to move away from the subsolar point; a positive Λ caused the reconnection site in the summer hemisphere to be shifted sunward and equatorward, while the reconnection point in the winter hemisphere moved tailward and poleward.While it seems logical to believe that the observed asymmetries are due to the effect of B y on reconnection, further investigation and modeling is necessary to fully understand these results.
Figure 7 also shows that there does not seem to be a significant difference in the B y dependence for negative Λ, yet there appears to be a significant difference for positive Λ.To examine this dependence, we separated the data by positive and negative Λ and performed linear fits on the cusp MLAT versus Λ for ±B y as before.We first performed fits on the data for negative Λ and ±B y and then locked the linear intercept at Λ = 0 and performed the fits for positive Λ.The results are shown in Figure 9 and summarized in Table 2.In every case, the fits are nearly independent of the sign of B y for negative Λ.However, the dependence on B y sign in the morning and afternoon sectors is dramatic for positive Λ with strong hemispherical asymmetries as bolded and italicized in Table 2.For instance, in the northern hemisphere at 1000 MLT, for Λ < 0, the slope is nearly the same for negative and positive B y , while for Λ > 0, the slope is much smaller for B y < 0 than for B y > 0. However, in the southern hemisphere, the B y dependence is reversed; there, for Λ < 0 the slope is again similar for positive and negative B y , but for Λ > 0, the slope is much larger for B y < 0 than for By > 0. In contrast, in the 1400 MLT sector, the dependencies are reversed from the 1000 MLT sector; For instance, in the northern hemisphere, for Λ < 0 the slope is again nearly the same but for Λ > 0, the slope is much larger for B y < 0 than B y > 0, and, as in the 1000 MLT sector, the results are reversed for the southern hemisphere.In the 1200 MLT sector, unlike for the results at 1000 and 1400 MLT, the slope is essentially independent of the B y sign for all dipole tilts, but in the morning and afternoon sectors is highly dependent on B y for Λ > 0. The greatest slopes occur in the morning sector in the northern (southern) hemisphere B y > 0 (B y < 0) and in the afternoon sector in the northern (southern) hemisphere for B y < 0 (B y > 0).Several factors could be driving this B y and Λ polarity and MLT relationship.For instance, positive dipole tilt is associated with stronger solar illumination, and as mentioned previously, Newell and Meng (1989) suggested that the impact of variations in solar illumination on the dayside current system could be responsible for variations in cusp location associated with changing Λ.In addition, several studies have shown that the relative polarities of B y and Λ have varying impacts on ionospheric currents, particle precipitation, ionospheric convection, and the average size of the auroral oval.This is the result of the combination of B y and Λ polarity dramatically affecting the global dayside reconnection rate (Reistad et al., 2022).For instance, for positive Λ, Reistad et al. (2020) found larger polar caps in both hemispheres when B y was negative compared to positive.They suggested that this could be the result of the fact that when Λ is nonzero, B y has an influence on the amount of magnetic flux the magnetotail lobes typically can support, for a given dayside reconnection rate.Also, contributions from the global dayside reconnection rate depend on B y polarity when Λ is nonzero, allowing for a stronger Dungey cycle and more energy input to the system when B y and Λ have opposite signs.These effects would undoubtedly be expected to impact the location of the cusp.Clearly further study and modeling efforts are necessary to understand these results.

Conclusions
Using 40 years of energetic particle measurements from 14 DMSP satellites, corresponding to over 100 years of satellite measurements, we produced a database of over 240,000 ionospheric cusp boundaries using a modified version of the Newell et al. (1989) ionospheric cusp identification algorithm.We applied criteria to avoid misidentification of the boundaries due to skimming satellite passes and limited our analysis to periods when AE was less than 100 nT to avoid periods of geomagnetic activity.After applying these criteria, and requiring the availability of IMF measurements, we ended up with ∼41,000 cusp boundary identifications (both poleward and equatorward).This is the largest database of cusp measurements to date and has allowed us to investigate the impact of the Earth's dipole tilt on cusp location as a function of MLT.The AE limitation also limited periods when the IMF B z was significantly negative; of the cusp identifications for which these criteria were met, 1% had B z < 5 nT and 7% had B z < 2 nT.
As a result of the DMSP orbits (sun synchronous and LTAN for most of the satellites in the afternoon to evening sectors) and the offset between magnetic and geographic axes, there is a preponderance of observations in the northern hemisphere (∼72%) and in the morning sector; thus the standard deviations of the fits is largest in the southern hemisphere where the number of valid cusp crossings is lower.However, the vast number of cusp identifications still allowed unambiguous analysis of the dipole tilt in all sectors.
While the initial plots of MLAT versus Λ shown in Figure 5 are very linear, there is a substantial variance in the data, particularly in the morning and afternoon sectors for Λ > 0. We found a clear B y sign dependence, explaining much of the variance in the data.There is a consistent asymmetry in both MLT and hemisphere with the cusp location's dependence on dipole tilt angle being greater in the northern hemisphere in the morning sector for B y > 0 and smaller in the afternoon for B y < 0. The opposite is true in the southern hemisphere where the dependence on dipole tilt angle is greater (more negative) for B y < 0 and smaller (less negative) for B y > 0. This is seen for both the equatorward and poleward boundaries.However, in the noon sector, the dipole tilt angle has little effect on the location of the cusp for both B y positive and negative in both the northern and southern hemispheres.In addition, the variance does not increase with positive Λ.
The plots of MLAT versus Λ appeared to show a significant difference in the B y dependence for Λ > 0 with minimal difference for Λ < 0. In the noon sector, the slope is independent of the sign of B y for all dipole tilts, but in the morning and afternoon sectors is highly dependent on B y for Λ > 0. This dependence is asymmetric for the afternoon and morning sectors and for the northern and southern hemispheres.The greatest slopes occur in the morning (afternoon) sector in the northern (southern) hemisphere.
Numerous studies have been performed on the impact of IMF B y on reconnection and the location of the reconnection X line which in turn would be expected to impact the cusp location and distribution in MLT and hemisphere.A few studies have examined the relationship of B y and dipole tilt on reconnection; but none have examined the cusp MLAT dependence on B y and dipole tilt, largely due to a lack of sufficient data illustrating this relationship.The observed asymmetries revealed in this work are assumed to be due to the effect of B y on reconnection; further investigation and modeling are necessary to fully understand these results.

Figure 1 .
Figure 1.The temporal coverage of all the satellites used in this study, restricted to periods when the data are of high quality.

Figure 2 .
Figure 2. Polar dials in MLAT and MLT showing the orbit tracks over a single day for several satellites used in the study.Red (blue) tracks are for the northern (southern) hemisphere.The nominal location of the cusp is indicated by the black contour on the dayside.

Figure 3 .
Figure 3. (a-d) Examples of the identified boundaries from multiple satellites and time periods.From top to bottom the panels show the total integrated ion and electron flux, the average ion and electron energies, and the electron and ion spectrograms.Note the ion spectrogram has the energy decreasing vertically.A polar dial showing the orbit tracks in MLT and MLAT is in the upper right-hand corner of the plots.The vertical lines indicate the identified cusp boundaries.

Figure 4 .
Figure 4.All identified cusp equatorward boundaries in the northern and southern hemispheres for the periods of 1982-2020 (a) and 1996-2000 (b).The red (blue) vertical line in (a) shows the time of a northern hemisphere summer (winter) solstice.

Figure 5 .
Figure 5. MLAT versus Λ for three selected one-hour MLT bins for the poleward and equatorward cusp boundaries in the Northern and Southern hemispheres.Red solid lines are linear fits to the data; the goodness of fit coefficients σ and Χ 2 are included in the figures.The northern hemisphere dipole tilt was multiplied by 1 for the southern hemisphere.Positive (negative) dipole tilt generally corresponds to summer (winter).

Figure 6 .
Figure 6.(a-f) Standard deviation results of the fits illustrated in Figure 5 for the nine series of criteria listed for the poleward and equatorward boundaries in both hemispheres.

Figure 7 .
Figure 7. (a-f) Fitting results in the same format as Figures 5a-5f but separated by B y sign; red for B y > 0 and black for B y < 0.

Figure 8 .
Figure 8.(a) and (b) Slopes of the fits for 0900-1500 < MLT.Red lines indicate the B y > 0 results and blue lines the B y < 0 results and solid and dashed lines indicate the results for the (a) equatorward and (b) poleward boundaries, respectively.The slopes in the southern hemisphere are multiplied by negative one.The error bars indicate the standard deviations of the fits.

Figure 9 .
Figure 9. (a-c) MLAT versus Λ in the same format as Figures 5a-5f and 7a-f with the linear fits separated by positive and negative Λ. Red is for B y > 0 and black is for B y < 0.

Table 1
Fit Slopes From Figure7at Selected MLTs by B y Sign, and Hemisphere

Table 2
Fit Slopes From Figure9at Selected MLTs by B y Sign, Dipole Tilt Sign, and Hemisphere