A Combined Effect of the Earth's Magnetic Dipole Tilt and IMF By in Controlling Auroral Electron Precipitation

Auroral particle precipitation is usually assumed to be equally strong for both signs of the By component of the interplanetary magnetic field (IMF). This is also the case in most currently used precipitation models, which parameterize solar wind driving by empirical coupling functions. However, recent studies have showed that geomagnetic activity is significantly modulated by the signs and amplitudes of IMF By and the Earth's dipole tilt angle Ψ. This so called explicit By dependence is not yet included in any current precipitation models. In this paper, we quantify this By dependence for auroral electron precipitation for the first time. We use precipitation measurements of the Defense Meteorological Satellite Program (DMSP) Special Sensor J instruments from years 1995–2022. We show that the dawnside electron precipitation at energies 13.9–30 keV is greater at auroral latitudes for opposite signs of By and Ψ in both hemispheres, while the dusk sector is mostly unaffected by By and Ψ. For energies below 6.5 keV the By dependence is strong poleward of the auroral oval in the summer hemisphere, also exhibiting a strong dawn‐dusk asymmetry. We also show that By dependence of precipitation modulates ionospheric conductance.


Introduction
Space weather is mainly driven by solar wind and the interplanetary magnetic field (IMF) through reconnection between IMF and magnetospheric field lines.Most of the energy and particle transfer to the magnetosphere appears through reconnection along dayside magnetopause during southward IMF (Dungey, 1961), and to a lesser extent at high-latitude lobes during northward IMF (Dungey, 1963;Crooker & Rich, 1993).Accurate modeling of space weather has multiple benefits from both societal and scientific standpoints.One great challenge of space weather modeling is to accurately model auroral particle precipitation into the ionosphere which, together with the solar illumination, is the main driver of ionospheric conductance and thus fundamentally important for ionospheric dynamics.Hardy et al. (1985) developed the first statistical precipitation model based on Defense Meteorological Satellite Program (DMSP) Special Sensor J (SSJ) data.The Hardy model is parameterized by the geomagnetic Kp index.As the DMSP particle data set has grown over the years, new models have followed (Newell et al., 2009;Zhu et al., 2021).One example is the widely used OVATION auroral precipitation model (Newell et al., 2014), which also takes into account seasonal variation and effects of different types of aurora.Instead of the discrete Kp index, the OVATION model is parametrized by the Newell coupling function (Newell et al., 2007) dΦ/dt = v 4/3 B 2/3 T sin 8/3 (θ/2), where v is the solar wind speed, B T = The Newell coupling function has similarities to other existing coupling functions, predicting enhanced coupling with enhanced v and north-south (B z ) component.While the dawn-dusk component (B y ) is also included, its effect is symmetric with respect to its sign.That is, the OVATION model predicts equally strong precipitation for positive and negative IMF B y .However, a considerable amount of research has shown that the sign of the IMF B y component has an important effect in magnetospheric convection (Cowley, 1981;Chisham et al., 2007;Tenfjord et al., 2015) and in geomagnetic activity, which is more prominent during periods of high dipole tilt Ψ (90°minus the angle between the Earth's magnetic dipole axis and the Sun-Earth line).In geomagnetic activity, this effect can be summarized with a following rule: particle precipitation and geomagnetic activity are increased, when IMF B y and Ψ have opposite signs (Holappa et al., 2020;Reistad et al., 2020;Ohma et al., 2021).This so-called explicit B y -effect has been shown to modulate the westward electrojet (Friis-Christensen & Wilhjelm, 1975;Friis-Christensen et al., 2017;Holappa & Mursula, 2018), size of the polar cap (Reistad et al., 2020), and the substorm occurrence rate (Ohma et al., 2021).All above studies have found B y -effects following the same rule, suggesting that the above effects are connected via similar physical mechanism.Holappa et al. (2020) studied the explicit B y dependence in energetic electron precipitation in both hemispheres using the National Oceanic and Atmospheric Administration (NOAA) Polar-Orbiting Operational Environmental Satellites.They found that energetic (>30 keV) electron precipitation is modulated by the IMF B y component.In NH winter (negative Ψ) the flux of precipitating electrons is greater for positive B y than for negative B y in both hemispheres.In NH summer (positive Ψ), the B y dependence is reversed.The effect was found to be strong in the midnight and dawn sectors and weak in the dusk sector.Also, the magnitude of the B y -effect was found to be roughly equal in both hemispheres and solstices.Auroral conductance is affected mostly by electrons in the energy range 1-30 keV (Robinson et al., 1987).Thus, if the IMF B y modulation found by Holappa et al. (2020) extends to lower energies, it could have a significant impact on the auroral conductances.However, the B y dependence of auroral (1-30 keV) electron precipitation has not been yet studied directly.Nevertheless, statistical studies of field-aligned currents (FACs) have provided some indirect evidence (Anderson et al., 2008;Green et al., 2009;Laundal et al., 2018;Holappa et al., 2021;Workayehu et al., 2021), because the upward FACs are known to be related to electron precipitation (for example, Korth et al., 2014).
None of the current precipitation models are designed to take the possible seasonally dependent B y -effect in auroral particle precipitation into account.The recently developed ASHLEY precipitation model (Zhu et al., 2021) uses the sign of the IMF B y component as an input, but does not include seasonal dependence, which is crucial for B y -effects.A machine-learning precipitation model by McGranaghan et al. (2021) includes B y as an input, but its effect on precipitation patterns has not been quantified.
The goal of this paper is to quantify the possible explicit IMF B y dependence of auroral (1-30 keV) electron precipitation, especially during periods of large dipole tilt.We also quantify the B y dependence on ionospheric conductance and discuss its implications to geomagnetic activity.This is done by utilizing the database of DMSP SSJ particle data from years 1995-2022, which is also the basis for several existing precipitation models.
This paper is organized as follows.In Section 2 we present the general properties of the DMSP satellites and their instruments measuring the precipitating particles, and go through the data processing techniques forming the results.In Section 3 we show the B y -effect in the measured differential number flux and in the calculated total energy flux and average energy.Also, we show the B y -effect in the calculated Hall conductance.In Section 4 we discuss how the results affect the modern precipitation models, and how the results compare to the recent literature of the B y -effect.Finally we present our conclusions in Section 5.

DMSP Particle Data
In this study we use DMSP particle data from years 1995-2022, from DMSP satellites F10 through F19 (with F19 covering only years 2014-2016).DMSP satellites fly in circular, sun-synchronous polar orbits (inclination 98.8°) at an altitude of roughly 850 km.The orbits are predominantly confined to the dawn-dusk sector.However, the satellites jointly cover most magnetic local times (MLTs) at high geomagnetic latitudes (MLAT) in altitude adjusted corrected geomagnetic (AACGM) coordinates, but the MLT-MLAT coverage has hemispheric differences, due to hemispheric differences in the structure of the Earth's magnetic field.The satellites carry a Special Sensor for Precipitating Particles versions 4 (SSJ/4) and 5 (SSJ/5) that measure fluxes of downward precipitating auroral electrons and ions (Hardy et al., 2008;Redmon et al., 2017).The SSJ/4 points upwards and measures electrons and ions with energies from roughly 30 eV to 30 keV in 19 logarithmically spaced energy bins, resulting in full electron and ion spectra every second.SSJ/4 instruments are used in this study with satellites F10-F15.The SSJ/5 instrument is an updated version of SSJ/4.The difference is that it measures the incoming flux of particles from a range of angles (from 4°to 90°), divided into six 15°angular sectors.However, due to constraints in telemetry, the counts from different angular sectors are averaged, resulting one spectrum every second (similarly as in SSJ/4).Due to these instrumental differences, there may by some systematic differences between the fluxes measured by SSJ/4 and SSJ/5.For instance, the larger field of view of the SSJ/5 can result into measurement of electrons outside the loss cone, if the satellite is in the ascending phase (Redmon et al., 2017).However, the observed IMF B y dependencies studied in this paper did not show systematic differences between SSJ/4 and SSJ/ 5, thus encouraging us to combine the data from both instruments to achieve the best possible data coverage.Also, the SSJ/4 and SSJ/5 data have been combined in previous studies (Wing et al., 2013;Newell et al., 2014;McGranaghan et al., 2015).All the satellites used in this study had the ascending nodes on the dusk side.

Data Processing
The DMSP particle measurements are spatially binned into an MLT-latitude grid with a grid size of 0.5 hr MLT by 0.5°MLAT, from 60°to 90°. Figure 1 shows the data coverage of the DMSP measurements in the northern and southern hemispheres of the data used in this study.That is, after sorting the data with solar wind criteria IMF |B y | > 2 nT and the normalized Newell coupling function 1 < dΦ/dt/〈dΦ/dt〉 < 2 (see Section 3.1), and large Earth's dipole tilt angles |Ψ| > 15°.
Each MLT-MLAT bin contains the mean value of the differential number fluxes.Due to the heavy-tailed distribution of the differential particle flux, the mean is sometimes significantly affected by outliers.The effect of outliers is alleviated with the following automatic procedure.First, all the bins are checked for outliers by standardizing the differential number fluxes in the bin.The potential outliers are removed from the bin, if their standardized z-score is larger than 6σ and the value is larger than 10 4 (1/cm 2 s ⋅ eV ⋅ sr).These criteria were found to eliminate most effects of outliers.
The total energy fluxes are calculated from the DMSP data from all of the 19 channels for each MLT-latitude bin from the outlier removed (first procedure) differential number fluxes.Total energy fluxes are calculated with equation (Hardy et al., 2008) where i is the channel index (from high to low), E i is the channel central energy of channel i and j (E i , Ω) is the directional-differential number flux (for further theoretical basis see, e.g., Redmon et al. (2017)).The total number fluxes J TOT (Ω) are calculated in a similar manner, only replacing the E i j (E i , Ω) (directional-differential energy flux) term with j (E i , Ω).The average energy for each bin is calculated as Assuming isotropic pitch-angle distribution at DMSP altitude, we calculate the down-going total energy flux by multiplying JE TOT (Ω) by π (Newell et al., 2014).The calculated down-going total energy flux and the average energy are used to calculate the Hall conductance for each bin using the Robinson formulas (Robinson et al., 1987) to show the potential B y -effect of auroral precipitation on ionospheric conductivity.The Robinson formulas are defined as.
where the Σ P and Σ H Pedersen and Hall conductances.The average energy E AVE is in units of keV and the downgoing total energy flux JE TOT in ergs/cm 2 s.

Differential Number Flux
For quantifying IMF B y dependence of precipitation, we sort the DMSP data with IMF B y and the Newell coupling function, averaged over the current and three previous UT hours.The Newell function is normalized by its mean 〈dΦ/dt〉 in 1995-2022.The combined effects of the IMF B y and the Earth's dipole tilt angle Ψ on the differential number fluxes of electron precipitation are shown in Table 1 to aid the reader go through the results of Figures 2-6. Figure 2 shows a map of the differential number flux (1/cm 2 s ⋅ eV ⋅ sr) in the northern hemisphere (NH) for dipole tilt Ψ < 15°(local winter).In all panels the normalized Newell coupling function dΦ/dt/〈dΦ/dt〉 is limited between 1 and 2. Thus, all panels correspond to solar wind driving slightly stronger than the long-term mean.
Because the DMSP satellites are primarily on dawn-dusk orbits, there is no data coverage in the NH at 22-04 MLT and very limited data at 12-15 MLT between 60°and 70°MLAT (see Figure 1).Each row displays a different energy channel labeled by nominal central energies of the channels.Precipitation maps are shown for five • Stronger dawnside 1.4-6.5 keV precipitation in the southern hemisphere • Weaker dawnside 10-30 keV precipitation in both hemispheres • Weaker dawnside 1.4-6.5 keV precipitation in the northern hemisphere • Weaker duskside 1.4-6.5 keV precipitation in the southern hemisphere • Stronger duskside 1.4-6.5 keV precipitation in the northern hemisphere • Weaker dawnside 10-30 keV precipitation in both hemispheres • Weaker dawnside 1.4-6.5 keV precipitation in the southern hemisphere • Stronger dawnside 10-30 keV precipitation in both hemispheres • Stronger dawnside 1.4-6.5 keV precipitation in the northern hemisphere • Stronger duskside 1.4-6.5 keV precipitation in the southern hemisphere • Weaker duskside 1.4-6.5 keV precipitation in the northern hemisphere Note.These results are shown in Figures 2-6.channels, showing every other channel starting from the highest channel (30 keV).Thus, to shorten the text, from here on out we reference these channels as 30, 13.9, 6.5, 3, and 1.4 keV.The first two columns show the differential number fluxes during positive (>2 nT) and negative B y (< 2 nT), respectively, and the third column shows their difference.The first and second columns show that the amount of precipitation changes drastically between the energy channels.The precipitation patterns in the highest energy channels (30 and 13.9 keV) show strong dawn-dusk differences and the maximum precipitation region is located close to the auroral oval, while the lower channels show more dawn-dusk symmetric distributions, which extend poleward of the auroral oval.

Results
Figure 2 (especially the third column) shows a clear B y dependence for the highest energy channels (30 and 13.9 keV).The number fluxes are generally higher for B y > 2 nT for the entire auroral oval covered by the DMSP measurements, especially on the dawnside region at 60°-70°MLAT.However, the number fluxes are higher for B y < 2 nT for the pre-noon region, which is most clearly seen in the 6.5 keV energy channel.The 3 keV channel shows only weak B y dependence and the 1.4 keV channel shows no systematic B y -effect.
Figure 3 shows the precipitation map in NH for Ψ > 15°(NH summer) in a similar format as Figure 2. The B y dependence during positive tilt (quantified in the third column) is clearly opposite to that during negative tilt (Figure 2), in agreement with the earlier results on the B y dependence of high energy precipitation (Holappa et al., 2020).The number fluxes are greater for B y < 2 nT than for B y > 2 nT on the dawn side in all channels.There are, however, also other differences between summer and in winter precipitation patterns: a strong dawndusk difference is seen in channels 6.5 keV, 3 and 1.3 keV, so that the number fluxes increase on the dawnside during B y < 2 nT and on the duskside during B y > 2 nT.The B y -effect is seen to extend to higher latitudes with decreasing energies.
Figure 4 shows the precipitation map in NH for |Ψ| < 10°(neutral tilt).The B y dependence varies between the higher and lower channels.The 30 keV channel shows greater number fluxes for B y > 2 nT at dawnside auroral latitudes similar to Figure 2, but weaker.However, channel 13.9 keV shows unclear B y dependence on the dawnside, but greater number fluxes on the duskside for B y > 2 nT.Channels 3 and 1.4 keV display similar, but much weaker B y dependence seen for NH summer in Figure 3. On average (all channels together), precipitation is greater for B y > 2 nT on the duskside and correspondingly for B y < 2 nT on the dawnside.
Figure 5 shows the precipitation map of the differential number flux in the southern hemisphere (SH) with dipole tilt Ψ < 15°(SH summer).The notable difference to the northern hemisphere (Figure 3) is the better MLT-MLAT coverage.However, the data coverage is poor at the dayside between 10 and 15 MLT (Figure 1), which produces clear anomalies in all panels.In the first two columns, channels from 6.5 to 30 keV show similar precipitation patterns maximizing at the auroral latitudes between 21 and 09 MLT.In the lower energy channels precipitation extends roughly from 17 MLT to 09 MLT.The third column shows a clear B y dependence for energies between 6.5 and 30 keV.The number fluxes are clearly greater for B y > 2 nT at 22-09 MLT.The effect is in the same direction as in the NH local summer, implying it is from the same, global physical mechanism.Channels between 1.4 and 6.5 keV show increased number fluxes in the duskside, and the channel 3 keV does not show as clear increase of dawnside number fluxes during B y > 2 nT.The channel 1.4 keV shows a high latitude dawn-dusk difference, which is opposite and weaker to that in NH summer (Figure 3).
Figure 6 shows the precipitation map in SH during Ψ > 15°(SH winter).The number fluxes are generally slightly larger overall than in SH summer (Figure 5).A B y dependence is also seen in the highest energy channels (30 and 13.9 keV) at dawn and pre-midnight sectors, but it is weaker than in SH summer.Channels from 6.5 to 1.4 keV do not show a clear B y -effect.
Comparing the above results from the two hemispheres we can summarize that at the dawn sector auroral latitudes precipitation increases for opposite signs of IMF B y and Ψ in both hemispheres.However, the B y dependence is stronger in the summer hemisphere.In the summer hemisphere IMF B y drives a clear dawn-dusk asymmetry in high-latitude (>70°) precipitation.This effect is most clear for the lowest energy (1.4 keV) for which the precipitation patterns during positive and negative B y are almost mirror images of each other.This "mirroring" is seen best in the SH (Figure 5), where the MLT coverage is better than in the NH.
To further quantify the B y dependence in the NH at dawn, Figure 7 shows a meridional cut at 05-07 MLT of the differential number fluxes from Figures 2 and 3 together with their standard errors.The dawside precipitation shows larger number fluxes for B y > 2 nT than for B y < 2 nT for 30 keV during Ψ < 15°.However, 3 keV shows slightly larger number fluxes for B y < 2 nT than for B y > 2 nT.Other energies show only small or no clear B y -effect.During Ψ > 15°the number fluxes are larger and peak roughly 0.5°MLAT poleward for B y < 2 nT than for B y > 2 nT for energies between 6.5 and 30 keV.Energy channels 1.4 and 3 keV show number fluxes extending to higher latitudes with decreasing energy for both Ψ < 15°(winter) and Ψ > 15°(summer) regardless of the sign of IMF B y .However, for Ψ > 15°there is a clear B y dependence at high latitudes so that the number fluxes reach higher latitudes for B y < 2 nT.The number fluxes at dusk (17-19 MLT, Figure 8) show only slightly larger number fluxes for B y > 2 nT than for B y < 2 nT during Ψ < 15°for energies between 3 and 13.9 keV.However, during Ψ > 15°energies from 1.4 to 6.5 keV show larger number fluxes that extend to higher latitudes for B y > 2 nT than for B y < 2.
In the calculation of the standard errors σ/ ̅̅̅ ̅ N √ we used the number of orbits as the factor N. This ensures that we treat only measurements made during different orbits as statistically independent from each other.As seen in Figure 7, errorbars at the dawnside stay relatively small, indicating that the results are statistically reliable.However, Figure 8 shows much larger errorbars for 30 and 13.9 keV channels for both tilt angles at dusk, while 6.5, 3, and 1.4 keV channels show relatively small errorbars for both tilt angles, comparable to ones in the dawn side in Figure 7. Therefore, the relatively high uncertainties should be kept in mind when interpreting the highenergy part of dusk precipitation (30 and 13.9 keV) in Figures 2 and 3.

Total Energy Flux, Average Energy and Ionospheric Conductivity
Figure 9 shows the total energy fluxes for the NH calculated with Equation 2 for Ψ < 15°in the first row and Ψ > 15°in the second in a similar format as Figures 1-4. Figure 9 shows similar B y dependencies as Figures 2 and  3.During Ψ < 15°the total energy fluxes are generally larger for IMF B y > 2 at both dawn and dusk.However, for Ψ > 15°IMF B y drives a clear dawn-dusk asymmetry in energy fluxes with higher dawn (dusk) energy flux for B y < 2 (B y > 2) nT.The B y -effect during Ψ > 15°is seen at higher latitudes than for Ψ < 15°.This is due to the effect of Ψ onto the particle precipitation measured by the lower energy channels, as seen in Figure 3. Figure S1 in Supporting Information S1 shows the total energy fluxes for the SH in a similar format.
Figure 10 shows the average energy (eV) for the NH in a format similar to Figure 9.When the tilt angle Ψ and IMF B y have opposite signs, the average energy increases on the dawnside.During Ψ > 15°, the average energies also only show weak dawn-dusk difference compared to Figure 9. Also, the average energy increases in only slightly higher latitudes in the duskside during B y > 2 nT, than in the dawnside during B y < 2 nT. Figure S2 in Supporting Information S1 shows the average energy for the SH.The total energy flux and average energy are known to directly affect the ionospheric Hall and Pedersen conductances.This relation is described by the Robinson formulas given in Equations 4 and 5. Figure 11 shows the Hall conductances (in Siemens) calculated from the total energy flux and average energy, in a similar format as Figures 9 and 10.During Ψ < 15°the Hall conductance is increased with B y > 2 nT, similarly as the total energy flux and average energy in Figures 9 and 10.Duskside Hall conductance is increased for positive B y for both Ψ < 15°and Ψ > 15°.However, the dawnside Hall conductance shows a different B y dependence, so that negative (positive) B y increases the Hall conductance during Ψ < 15°(Ψ > 15°).An additional effect is seen in the dayside in Ψ < 15°, where B y < 2 nT seems to increase the Hall conductance at latitudes above 70°.Many studies have shown that the variability of the westward electrojet is mainly controlled by variations of the Hall conductance (rather than the electric field) [for example, Sugino et al., 2002;Sergeev et al., 2018].Therefore, the result here implies that the conductance would enhance the westward electrojet more during Ψ > 15°and B y < 2 nT, and during Ψ < 15°and B y > 2 nT.

Discussion
Figures 2-6 show that auroral electron precipitation at 1-30 keV energies clearly depends on the combination of IMF B y direction and dipole tilt angle Ψ.We found that the energetic part (13.9-30 keV) of the auroral precipitation at the dawn sector is greater for opposite signs of IMF B y and Ψ in both hemispheres, in a similar way as found in >30 keV electrons in Holappa et al. (2020).However, the B y dependence of auroral electrons is more prominent in the summer hemisphere.For less energetic part of auroral precipitation (below 6.5 keV) IMF B y dependence is somewhat different.Figures 3 and 5 show a strong dawn-dusk asymmetry between positive and negative B y poleward of the auroral oval in the summer hemisphere.
The dawnside (diffuse electron) precipitation is known to be mostly due to wave-particle interactions between electrons and whistler-mode waves resulting into pitch angle scattering of bouncing electrons (Li et al., 2009;Thorne et al., 2010).However, also broadband accelerated electron precipitation is found to peak at prenoon (Newell et al., 2009).Whistler-mode waves are known to originate from non-isotropic 10-30 keV electrons 10.Average energies (eV) for the northern hemisphere, in a similar format as in Figure 9.
injected into the inner magnetosphere during substorms (Tsurutani & Smith, 1974;Li et al., 2010).Also, substorms are known to increase the diffuse electron precipitation on the dawnside (Wing et al., 2013).Thus, it is probable that the IMF B y modulates the energetic (13.9-30 keV) dawnside precipitation via occurrence rate of substorms, because substorm occurrence rate is found to show similar B y dependence (Ohma et al., 2021).This is supported by Figure 10, which shows that the average energy of precipitating electrons increases on dawnside, probably due to injected energetic electrons by increased frequency of substorms.
The duskside precipitation is known to consist mostly of monoenergetic electrons, accelerated due to fieldaligned potential differences (Newell et al., 2009).These accelerated electrons are known to be often confined within the upward (R1) FAC in the dusk-to-midnight sector (Ohtani et al., 2010;Korth et al., 2014).The B y dependence of these FACs has been studied in the past (Weimer & Edwards, 2021;Anderson et al., 2008;Tenfjord et al., 2015;Laundal et al., 2018;Workayehu et al., 2021).The duskside R1 FAC is known to shift and expand into higher latitudes for positive B y in the NH summer and for negative B y in the SH summer (Green et al., 2009;Holappa et al., 2021).This is similar to the B y -effect in the low-energy part (<6.5 keV) of duskside precipitation in Figures 3 and 5.A similar B y dependence has also been found in the duskside auroral brightness in NH summer (Shue et al., 2001).
The precipitation patterns of 1.4 keV electrons in the summer hemisphere for positive and negative IMF B y are almost mirror images of each other, which could be explained by the dawn-dusk asymmetry of FACs due to asymmetric magnetospheric convection driven by IMF B y (Cowley, 1981;Tenfjord et al., 2015;Reistad et al., 2021).The B y -effect in 1.4 keV electron precipitation seen in the summer hemisphere would then be explained by dawn or dusk magnetic field lines convecting at higher latitudes depending on the sign of B y (Tenfjord et al., 2015).Enhanced conductivity due to increased solar illumination on these field lines in turn allow stronger FACs (Green et al., 2009) (and thus particle precipitation).
The statistical patterns of the low energy precipitation at high latitudes during summer could be affected by different auroral structures that follow the same rule of IMF B y as the precipitation patterns, for example, transpolar arcs that form polewards of the auroral oval during quiet times.In the NH they form on the dawnside during a negative IMF B y and in the duskside during a positive IMF B y , while the IMF B y dependence is opposite in the SH (Kullen et al., 2002;Fear & Milan, 2012).The TPAs are known to be brighter in summer (Kullen et al., 2008), which may contribute to stronger B y dependence of low energy precipitation in the summer hemisphere.We note that for high energies (6.5-30 keV), the IMF B y -effect is seen on to the whole auroral oval from 60°to 70°MLAT, while TPAs usually form poleward of the expanded auroral oval, associated with electron precipitation with maximum energies of 2-3 keV (Zhu et al., 1997).It should be kept in mind that all different precipitation mechanisms are mixed in the statistical patterns derived in this paper.Therefore, without further studies we cannot make strong conclusions on how IMF B y modulates different precipitation mechanisms, especially at low (<6 keV) energies.
We calculated the total energy flux and average energy of precipitating electrons and derived ionospheric conductances from these parameters using the Robinson formulas.Our results show that IMF B y indeed affects the ionospheric conductance, especially in the dawn sector where the Hall conductance is greater for opposite signs of B y and Ψ (the difference being about 5 S during moderate solar wind driving dΦ/dt/〈dΦ/dt〉).Similar results were found by Weimer and Edwards (2021) using an ionospheric data assimilation method, and by Carter et al. (2020) for the dayside NH summer Hall conductances using DMSP SSUSI measurements.Shue et al. (2001) found greater auroral brightness in the dawnside for negative B y during NH summer, which is consistent with our results.
Our results contribute also toward understanding the physics behind IMF B y dependence of the westward electrojet, which was found already by Friis-Christensen and Wilhjelm (1975) using ground magnetometers in Greenland.Later studies based on polar-orbiting satellites (Friis-Christensen et al., 2017;Smith et al., 2017;Workayehu et al., 2021) and the AL index (Holappa & Mursula, 2018) have quantified this B y dependence in more detail and found that the NH westward electrojet is about 40%-50% stronger for negative tilt and positive IMF B y .However, the NH westward electrojet shows a much weaker B y dependence during positive tilt (NH summer).This summer-winter difference may be related to seasonal variation of ionospheric conductivity.The IMF B y dependence of conductance (through particle precipitation) quantified above is relatively more significant in the dark winter hemisphere while in the summer hemisphere conductance is also affected by sunlight.The B y dependence of conductance could explain why the westward electrojet is modulated strongly by IMF B y in the winter hemisphere, but only weakly in the summer hemisphere (Holappa & Mursula, 2018).This effect is possibly more significant at dawn than close to midnight, where the auroral oval is less sensitive to seasonal changes in solar irradiation (Laundal et al., 2018).
Considering the modern auroral precipitation models, our results show the importance of the combined effects of IMF B y and Ψ into future precipitation models.That is, dependence on B y polarity and Ψ should be added and the two hemispheres should be treated separately.Understandably, current precipitation models combine both hemispheres for the best data coverage (Newell et al., 2014;Zhu et al., 2021).However, this artificially reduces the B y dependence and dawn-dusk asymmetries found in this paper.For doing this, it will be important to include all possible particle measurements from different satellites for accurate quantification of B y dependence in the future models.

Conclusions
We used electron precipitation measurements of the DMSP SSJ instruments from years 1995-2022.The data was spatially binned into precipitation maps, and sorted for steady solar wind flow (normalized Newell coupling function 1 < dΦ/dt/〈dΦ/dt〉 < 2), positive (>2 nT) and negative (< 2 nT) IMF B y polarity, and for times of large Earth's dipole tilt angle (Ψ > 15°and Ψ < 15°).We showed that for fixed solar wind driving, the IMF B y and the Earth's dipole tilt angle Ψ together modulate the auroral electron precipitation (1-30 keV) as summarized in Table 1.The main conclusions are.
1.The dawn sector precipitation increases for opposite signs of IMF B y and Ψ at auroral latitudes for energies between 13.9 and 30 keV in both hemispheres.This leads to higher average energy of precipitating electrons for opposite signs of B y and Ψ in both hemispheres.However, the B y dependence is more pronounced in the summer hemisphere.The IMF B y dependence is different on the duskside, where precipitation increases for positive B y during all seasons in the NH.
Our results emphasize the need to include the effect of B y and Ψ in future auroral precipitation models.Thus, more data of auroral precipitation are needed to maintain large enough data coverage after sorting the data by B y polarity, season, and for separate hemispheres to include the explicit B y dependence.

Figure 2 .
Figure 2. Precipitation map of the differential number fluxes (1/cm 2 s ⋅ eV ⋅ sr) in the northern hemisphere with dipole tilt Ψ < 15°(local winter) for five channels.The channel central energies are shown on the left for each row.The first two columns show the differential number fluxes, when the IMF B y > 2 nT and B y < 2 nT, and the third column shows the difference of these two precipitation maps.The maps cover MLATs from 60°to 90°.A large gap in data exists from 22 to 04 MLT.

Figure 3 .
Figure 3. Precipitation map of the differential number fluxes (1/cm 2 s ⋅ eV ⋅ sr) in the northern hemisphere with dipole tilt Ψ > 15°(local summer) in similar format as in Figure 2.

Figure 4 .
Figure 4. Precipitation map of the differential number fluxes (1/cm 2 s ⋅ eV ⋅ sr) in the northern hemisphere with dipole tilt |Ψ| < 10°(neutral tilt) in similar format as in Figure 2.

Figure 5 .
Figure 5. Precipitation map of the differential number fluxes (1/cm 2 s ⋅ eV ⋅ sr) in the southern hemisphere with dipole tilt Ψ < 15°(local summer) in similar format as in Figures 2-4.

Figure 6 .
Figure 6.Precipitation map of the differential number fluxes (1/cm 2 s ⋅ eV ⋅ sr) in the southern hemisphere with dipole tilt Ψ > 15°(local winter) in similar format as in Figures 2-6.

Figure 9 .
Figure 9.Total energy fluxes (eV/cm 2 s ⋅ sr) for the northern hemisphere.The first row are the total energies for tilt angle Ψ < 15°and the second row for tilt angle Ψ > 15°.First column shows the total energies for IMF B y > 2 nT, second row for B y < 2 nT, and the third row the difference of the two total energy flux maps.

Figure 11 .
Figure 11.Calculated Hall conductances (S) for the northern hemisphere, in a similar format as in Figures 9 and 10.The conductances were calculated using the Robinson formulas.

Table 1
Summary of the IMF B y and the Earth's Dipole Tilt Angle Ψ Effects on the Number Fluxes of Electron Precipitation