Solar zenith angle dependence of relationships between energy inputs to the ionosphere and ion outflow fluxes


 The ionosphere is one of the important sources for magnetospheric plasma, particularly for heavy ions with low charge states. We investigate the effect of solar illumination on the number flux of ion outflow using data obtained by the Fast Auroral SnapshoT satellite at 3000–4150 km altitude from 7 January 1998 to 5 February 1999. We derive empirical formulas between energy inputs and outflowing ion number fluxes for various solar zenith angle ranges. We found that the outflowing ion number flux under sunlit conditions increases more steeply with increasing electron density in the loss cone or with increasing precipitating electron density (> 50 eV), compared with the ion flux under dark conditions. Under ionospheric dark conditions, weak electron precipitation can drive ion outflow with small averaged fluxes (~ 107 cm− 2 s− 1). The slopes of relations between the DC and Alfvén Poynting fluxes and outflowing ion number fluxes show no clear dependence on solar zenith angle. Intense ion outflow events (> 108 cm− 2 s− 1) occur mostly under sunlit conditions (solar zenith angle < 90°). Thus, it is presumably difficult to drive intense ion outflows under dark conditions, because of a lack of the solar illumination (low ionospheric density and/or small scale height owing to low plasma temperature).

We averaged ion number fluxes from IESA, electron densities in the loss cone, and 282 Poynting fluxes of DC fields and Alfvénic waves during all candidates of the outflow 283 region together in each inbound or outbound pass using the latitudinal width in ILAT in 284 each 5 s data as the weight. By using this weight for the averaging, we can treat the data 285 as if the satellite had crossed the auroral zone in the latitudinal direction with a constant 286 velocity, regardless of its orbit, which usually crosses the auroral zone obliquely. The 287 averaged data is counted as 1 event. The averaged SZA in each of these outflow events 288 is calculated using the product of the latitudinal width in ILAT and the mapped ion  (mapped to an ionospheric reference altitude with a magnetic field intensity of 50,000 324 nT). The largest value of 2 × 10 9 cm −2 s −1 corresponds to ~1.5 × 10 9 cm −2 s −1 at 1000 km 325 altitude (a magnetic field intensity of ~37,000 nT (Engwall et al. 2009)). Even this flux 326 in an extreme case is within the range covered by the dataset used in the present study. logarithmically averaged using bins of the ion number flux (one order of magnitude was 334 divided by 10 bins). The total latitudinal widths in ILAT of the outflow events were 335 used as the weight for this averaging. The logarithmically averaged values were fitted 336 with a weighted least squares method using the following formula: 337 where Fi is the ion number flux (mapped to 1000 km altitude) in cm −2 s −1 , x is the 339 energy input, and a and b are free parameters determined by the fitting. This fitting 340 formula is the same as that used by Strangeway et al. (2005) and Brambles et al. (2011). 341 In this fitting, the sum of the total latitudinal widths in ILAT of the outflow events was 342 used as the weight. The parameters selected as the energy input are those studied by 343 correlations with outflowing ion fluxes. The use of other energy input parameters, to find which input parameter is good, and to investigate the functional shape are beyond 346 scope of the present study. 347 As described above, we used logarithmically averaged energy inputs, not the outflow 348 events themselves, for this fitting for the following reason, because the ion number 349 fluxes used here are biased by the lower flux limit (10 7 cm −2 s −1 ), which was used for

Ion Number Flux 360
The electron density in the loss cone is defined as the partial electron density at the location of the satellite using 4 pitch angle bins around the precipitating direction (the 362 center of pitch angle bins ranges from −22.5° to 22.5° (Northern hemisphere) or from 363 157.5° to 202.5° (Southern hemisphere). 364     (Figures 3 and 4), however, tend to be larger than those of electron 481 precipitation, which is usually within a factor of ~3-5 (Figures 5 and 6).

A1. Calculation and Subtraction of Background of IESA 583
Background counts of IESA were subtracted from IESA data using count rates in the 584 source cone. Although the method of background subtraction was basically similar to 585 that of Yao et al. (2008aYao et al. ( , 2008b, we only used IESA data to derive the background 586 count rate, since the background count rates of IESA were slightly different from that of 587 EESA. Another difference from the method of background subtraction by Yao et al. 588 (2008aYao et al. 588 ( , 2008b is that the background count rate was calculated by a linear least-589 squares fitting using a moving window (25 s) for better handling of the data with 590 various time resolutions, while they used boxcar averaged ones. This calculation was 591 performed after the removals of spikes, which were presumably caused by erroneous 592 data. 593 594

A2.1. Magnetic Field Data 596
In some cases, processed magnetic field data are apparently incorrect. To remove 597 such incorrect data quantitatively as much as possible, the outflow events that satisfied 598 the following two criteria at any of the 5 s averaged data points in the outflow regions 599 were excluded from the present statistical analyses. 600 that from the IGRF model by >10%. 602 2. The direction of the magnetic field differs from that calculated using the IGRF 603 model by >5°. 604 Additionally, two events were excluded by visual inspection of the magnetic field 605 data. 606

A2.2. Electric Field Data 607
Sometimes an unusually large electric field was recorded just after a data gap. Thus, 608 if there was any gap in the electric field data, the 5 s averaged Poynting flux at the 609 period was not used. If Poynting fluxes were not available at any of data points in the 610 outflow regions, the event was excluded from the statistical analyses in Sections 4.4 and 611 4.5. 612

A2.3. Ion and Electron Data 613
Sometimes ion or electron data are apparently incorrect. The ion data were excluded 614 if counts at all pitch angle bins of IESA in one third (top, middle, or bottom) of the 615 energy bins were zero. This is the most typical type of the error. The counts do not 616 become zero at such a large number of bins in the correct data (Figures 1a and 1b). can strongly affect the identification of outflow events. The upper energy limit of 70 eV is to avoid misidentification in the cusp in cases where ion precipitation was so intense 634 that the differential energy flux exceeded 5 × 10 6 eV −1 cm −2 s −1 sr −1 eV −1 even in the 635 source cone owing to pitch angle scattering. 636 637

A4. Identification of the Polar Cap 638
The polar cap was defined with the use of 5 s averaged low-energy ion data (110 eV-639 24 keV), according to the threshold of a mean differential energy flux (<10 4.6 eV −1 cm −2 640 s −1 sr −1 eV −1 ) described by Andersson et al. (2004). The mean differential energy flux 641 was calculated by using pitch angle ranges of −30°-30°, 150°-210°, and 40°-140° or 642 220°-320°. In some orbits, contamination caused by solar radiation increases count 643 rates around 90° or 270° at high latitudes. Because this increase affects the 644 identification of the polar cap, the mean differential energy flux in the pitch angle range 645 of 40°-140° or 220°-320°, whichever smaller, is selected to avoid this contamination 646 (Kitamura et al. 2015). Continuous (≥10 s, ≥2 data points) periods in which the mean 647 differential energy flux met the criterion were selected as candidates of the polar cap. 648 Sometimes this criterion was satisfied for data obtained in the subauroral zone. To exclude such cases, the candidates that are connected to the region where energetic ions 650 (>4 keV) show double loss cones (Appendix A5) without a data gap of ≥60 s or 651 equatorward of such regions were excluded. In some cases, short candidates that were 652 appeared between the auroral zone and the region of the double loss cone could not be 653 excluded. There were some cases in which the region of double loss cone was not 654 identified and candidates in the subauroral zone could not be excluded. All these two 655 types of cases, however, had polar cap periods much longer than 200 s, and thus the 656 overlooking did not affect the exclusion of the outflow events. 657 Although contamination owing to solar radiation causes increase in count rates, the 658 increase occurs around the pitch angle of 90° at high latitudes. Thus, this does not 659 strongly affect the calculations of field-aligned ion fluxes in the outflow regions (>10 7 660 cm −2 s −1 ). This is one of the reasons why we set the lower flux limit to identify the 661 outflow regions. In some cases, the contamination causes the apparent field-aligned ion 662 fluxes of the order of 10 6 cm −2 s −1 (mapped to 1000 km altitude). To treat ion outflows 663 with fluxes smaller than ~10 7 cm −2 s −1 in the future, this apparent flux must be 664 corrected. 665

A5. Identification of Double Loss Cones and the Subauroral Zone 667
Identification of regions of double loss cones was performed if the mean differential 668 energy flux of ions above 4 keV in the pitch angle ranges of 40°-140° and 220°-320° 669 (trapped population) were larger than 10 4.6 eV −1 cm −2 s −1 sr −1 eV −1 . The periods of 670 double loss cones were defined as cases where the mean differential energy flux above 4 671 keV near the center of the loss cone (in the pitch angle range from 163.125° to 196.875° 672 (Northern Hemisphere) or from −16.875° to 16.875° (Southern Hemisphere)) was lower 673 than 50% of those in the pitch angle ranges of 40°-140° and 220°-320°. Examples are 674 shown above Figure 1 with red bars. Even if there were data gaps in the interval of 675 double loss cones, the interval was treated as one continuous interval (~1940 UT). To 676 avoid misidentifications, short intervals (1 or 2 data points with double loss cones) were 677

excluded. 678
Very energetic ion conics that extended above 4 keV could be misidentified as a 679 region of double loss cones, although such cases were very rare at this altitude. Thus, in 680 the case in which the ion number flux above 4 keV exceeded 10 6 cm −2 s −1 (mapped to 681 1000 km altitude), the region was treated as the region of double loss cones only if both 682 sides of the case satisfied the criteria of double loss cones. 683 The region of ILAT < 45° or high background count rates (>50 counts/s) that were 684 connected to ILAT < 65.9° (L < 6) were removed (marked as subauroral zone). In this 685 removal, even if there were data gaps in the interval of high background count rates, the