Annual and Seasonal Occurrence Pattern of Auroral Kilometric Radiation Associated with the Interplanetary Magnetic Field

Auroral kilometric radiation (AKR) is a widely existing strong radio emission from the Earth’s magnetosphere and is generated by suprathermal (1–10 keV) electrons in the polar cavity. Previous works have demonstrated that AKR can contribute to the coupling of the magnetosphere–ionosphere–atmosphere, but its relation to the interplanetary magnetic field (IMF) has not been studied so far. Here, we examine the data of Van Allen Probes and identify a total of 5000 AKR events from 2012 October to 2019 July. Most AKR events (4282) correspond to the dominant parallel component B∥(=(Bx)2+(By)2) of IMF. There are the most (1391) events in 2018 (the solar minimum year) and the least (258) events in 2014 (the solar maximum year), corresponding to more (less) occurrences for the longer duration (> 30 minutes) of southward IMF (B z < 0) in 2018 (2014). In the Earth’s Northern Hemisphere, there are the most (865) events in the autumn (August–October), corresponding to dominant B x < 0. In the Earth’s Southern Hemisphere, there are the most (830) events in the autumn (February–April), corresponding to dominant B x > 0. The probable reason for the above results is that the longer duration of B z < 0 can yield the longer magnetic reconnection, and the dominant B x < 0 (B x > 0) is favorable for the single-lobe magnetic reconnection in the northern (southern) hemisphere, allowing more suprathermal electrons into the polar source cavity and generating more AKRs. These current results suggest that IMF is very important for the occurrence of AKR and can be widely applied to similar auroral radio emissions in other magnetized planets of the solar system.


Introduction
Auroral kilometric radiation (AKR) is a kind of terrestrial radio emission with kilometer wavelength and was first observed by the ELECTRON-2 satellite from USSR in 1965 (Gurnett 1974;Kurth et al. 1975).Similar auroral radio emissions (AREs) have been detected in other magnetized planets of the solar system: Jupiter, Saturn (Saturn kilometric radiation, SKR), Uranus (Uranus kilometric radiation, UKR), and Neptune (Neptune kilometric radiation, NKR; Zarka 1998;Schippers et al. 2011).Jupiter AREs include three main components: the broadband kilometer (bKOM), the hectometer (HOM), and the decameter (DAM) components.The frequency ranges and wavelengths of these emissions are different because different planets have different strengths of background magnetic field.Voyager 1 and 2 have detected all these AREs (Zarka 1998).Galileo and Juno have provided observations of bKOM, HOM, and DAM from 10 kHz to 40 MHz (Gurnett et al. 1996).The Cassini spacecraft has provided numerous observations of SKR from 2004 to 2017 (Menietti et al. 2010;Ye et al. 2011Ye et al. , 2016Ye et al. , 2018;;Wu et al. 2021).So far, observations of UKR and NKR still come mainly from Voyager 2 (Warwick et al. 1986(Warwick et al. , 1989)).AKR emissions have been studied extensively using the abundance of satellite observations near the Earth (Schreiber et al. 2017;Zhao et al. 2019;Zhang et al. 2021Zhang et al. , 2024)).
The electron cyclotron maser instability (ECMI) has been considered as the generation mechanism of AKR and other radio emissions (Wu & Lee 1979;Calvert 1995;Mutel et al. 2007;Burinskaya 2013).Simulations of ECMI have assumed a loss-cone electron velocity distribution (Wu & Lee 1979;Omidi & Gurnett 1984) or horseshoe electron distribution (Bingham & Cairns 2000;Pritchett et al. 2002).The distribution of these electrons is modified by parallel electric fields and magnetic field gradients at lower altitude; then, these electrons provide free energy for the generation of AKR emissions.Previous works have shown that the source region of AKR is around invariant latitude |λ| = 60°-70°from 20 to 24 magnetic local time (MLT; Hashimoto 1984), corresponding to the occurrence of discrete aurora (Gurnett 1974;Kurth et al. 1975).Kurth et al. (2015) have shown the presence of AKR in the equatorial region of radiation belts via observations from Van Allen Probes.Wave-particle interaction is an important process in the magnetosphere and has been studied widely (Jin et al. 2018;Guan et al. 2020;Guo et al. 2020;He et al. 2021He et al. , 2022;;Yang et al. 2022).Various simulations have investigated the interaction between AKR and radiation belt electrons and revealed that AKR can play an important role in the coupling of the ionosphere and the magnetosphere (Summers et al. 2001;Xiao et al. 2006Xiao et al. , 2010Xiao et al. , 2011;;Zhang et al. 2020).
Using observations from the Akebono satellite, Kumamoto & Oya (1998) have reported that the intensity and occurrence of AKR in the winter polar regions are higher than those in summer polar regions, and Kumamoto et al. (2003) have shown that the ionospheric periodic (seasonal and solar cycle) variations are responsible for the AKR variations.Green et al. (2004) have presented the seasonal and solar cycle variations of the AKR source region using the data from the IMAGE and Polar spacecraft.Their observations have suggested that the dipole tilt and solar EUV play an important role in the generation of AKR.Results of Zhao et al. (2019) have shown that AKR emissions occur most frequently in the region of L > 5 and increase with the increasing L both on the dayside and nightside.Zhang et al. (2021) have constructed a concise empirical formula for the field-aligned distribution of AKR based on Arase satellite and Van Allen Probes.Recently, statistical results have presented the asymmetric distributions of AKR based on observations of the Arase satellite (Xiao et al. 2022).Previous numerous works have emphasized the importance of the interplanetary magnetic field (IMF) to the magnetosphere (Han et al. 2017(Han et al. , 2018;;Hu et al. 2021).However, the occurrence patterns of AKR associated with IMF have not been reported so far.Here, we shall present such investigation using observations of Van Allen Probes from 2012 October 1 to 2019 July 31.

Case Study
Van Allen Probes, launched on 2012 August 30, consist of two spacecraft (Probe A and B) carrying identical instruments.The inclination of Van Allen Probes is about 10°, and the altitudes of the perigee and apogee are 375 and 20,000 miles, respectively (Mauk et al. 2013).The electric-field power spectral density (PSD) of high-frequency waves is measured by the High Frequency Receiver (HFR) of the Electric and Magnetic Field Instrument and Integrated Science (EMFISIS).The frequency range is 10-500 kHz (Kletzing et al. 2013).Previous theories have suggested that emissions with the PSD > 10 −16 V 2 m −2 Hz −1 and the frequency higher than the local upper hybrid frequency f uh are identified as AKR emissions (Zhao et al. 2019;Zhang et al. 2021).The value of f uh can be obtained from the EMFISIS.Similarly, we define these emissions observed by each satellite during one orbit as an AKR event.
Figure 1 presents four AKR events and variations of corresponding components Bx and By of IMF.Figures 1(a)-(c) show observations in the Earth's Southern Hemisphere from 13:00 to 20:00 UT on 2017 January 18, when Bx (or By) remains almost positive (or negative).Figure 1  10 −15 V 2 m −2 Hz −1 .Figures 1(d)-(f) exhibit observations of Van Allen Probes in the Earth's Nouthern Hemisphere from 00:30 to 06:00 UT on 2016 December 24, when Bx (or By) remains almost negative (or positive).Figure 1(e) shows Event C from Probe A in the region of L = 4.2-6.5,MLT = 20-02, and Mlat = 7°-17°.The frequency of AKR ranges from 50 to 500 kHz, and the maximum PSD reaches 2 × 10 −12 V 2 m −2 Hz −1 at 03:11 UT.At the same time, Event D was observed by Probe B (Figure 1(f)) in the close region.AKR stays mainly in the frequency range from 100 to 500 kHz, and the maximum PSD reaches 1.4 × 10 −12 V 2 m −2 Hz −1 at 01:52 UT.These observations suggest that the occurrence of AKR is closely related to the direction of IMF.In the following section, we shall study the occurrence pattern of AKR and its relation to IMF using observations of Van Allen Probes.

Statistical Results
During the period of 2012 October 1-2019 July 31, we identify a total of 5000 AKR events in radiation belts.We calculate the occurrence rate of AKR events in different ranges of B x (Figure 2 2 (c), the number of AKR events decreases obviously with increasing |B z |; more than 70% events are observed when |B z | < 2 nT.In other words, the favorable condition for exciting AKR is that |B z | is smaller than B x or B y .In order to examine the role of the parallel component of IMF, we define x y 2 2 .During this period, 4280 (2945) AKR events are observed under the condition of B ∥ > |B z | (B z < 0).The probable reason is that the dominant B ∥ (B z < 0) is conducive to the magnetic reconnection, allowing more suprathermal electrons into the polar source cavity.Kumamoto et al. (2003) have presented the solar cycle variation of AKR in the source region based on 13 yr of plasma wave data observed by the Akebono satellite.Their results have shown that in polar regions of both hemispheres, the occurrence of AKR increases in the solar minimum period and decreases in the solar maximum period.Here, we study the annual distribution properties of AKR at the low latitudes using observations from 2013 January 1 to 2018 December 31 (totally 4665 events).Figure 3(a) shows the number of events every year in the Earth's Nouthern (red) and the Earth's Southern (blue) Hemispheres.In the Earth's Nouthern (Southern) Hemisphere, 589 (802) events   b) suggest that AKR at low latitudes also shows an anticorrelation with the sunspot, which is similar with observations at high latitudes (Kumamoto et al. 2003;Green et al. 2004).The condition of B z < 0 is favorable for the magnetic reconnection and magnetosphere energy accumulation.We check the data and find that the occurrences for the longer duration(> 30 min) of B z < 0 in 2018 are higher than those in 2014.This is because the longer duration of southward IMF can cause the longer magnetic reconnection, providing more free energy for the generation of AKR.
Previous studies have confirmed that the occurrence rate of intense AKR in polar regions is increased (decreased) in the winter (summer; Kumamoto & Oya 1998;Kumamoto et al. 2003).We analyze the seasonal pattern of AKR at low latitudes using observations from 2012 November to 2018 October (total of 4,474 events).The seasonal variation of AKR events in the Earth's Northern (Southern) Hemisphere is given in Figure 4(a) -(b).There are 2109 (2365) events observed in the Earth's Northern (Southern) Hemisphere: 865 (830) in the autumn, 489 (684) in the winter, 307 (455) in the spring, and 448 (396) in the summer.In both hemispheres, AKR occurs most frequently in the autumn.To further study the occurrence pattern of AKR, we analyze the monthly distribution of events from 2012 November to 2018 October.Figure 4(c) plots the number of AKR events in different months in the Earth's Northern Hemisphere.During the period, the most (346) events are observed in October, and the least (97) events are observed in February.Results of the Earth's Southern Hemisphere are shown in Figure 4(d): the most (307) events occur in March, and the least (61) occur in November.The monthly distribution of AKR corresponds to the seasonal distribution.There are 67% (58%) events observed under the condition of B x < 0 (B x > 0) in the autumn for Earth's Northern (Southern) Hemisphere. Figure 4(e) shows the monthly percentages of B x < 0 during the period, with the maximum (70%) percentage of B x < 0 occurring in September and the minimum (35%) percentage occuring in May. Figure 4(f) displays the monthly percentages of B x > 0 during the period.The maximum (65%) percentage of B x > 0 occurs in May, and the minimum (30%) percentage occurs in September.Pi et al. (2018) have shown that there is a hemispheric asymmetry of the reconnection location in the magnetosphere.Lu et al. (2021) have indicated that the magnetic reconnection occurs in dayside magnetopause in one hemisphere and behind the cusp in another hemisphere under the dominant B x .The magnetic reconnection behind the cusp is a single-lobe reconnection.Moreover, Wang et al. (2022) have suggested that the single-lobe reconnection occurs in the Earth's Northern (Southern) Hemisphere for B x < 0 (B x > 0).Therefore, more suprathermal electrons move along magnetic lines into the polar cavity in the Earth's Northern (Southern) Hemisphere during B x < 0 (B x > 0), providing more free energy for the generation of AKR.

Conclusion
As a widely existing radio emission, AKR has an important role in the coupling of the magnetosphere-ionosphere-atmosphere.The periodic characteristic of AKR related to the IMF has not been examined so far.In this study, we study the occurrence pattern of AKR associated with IMF.In total, we identify 5000 events using observations of Van Allen Probes from 2012 October to 2019 July.Main conclusions are summarized as below.
1. Most AKR events (4282) correspond to the dominant perpendicular component of IMF.This is because the dominant B ∥ is favorable for the magnetic reconnection, yielding injection of more suprathermal electrons into the polar source cavity.
2. In the Earth's Northern Hemisphere, there are the least (168) AKR events in 2014 (the solar maximum year) and the most (589) AKR events in 2018 (the solar minimum year).In the Earth's Southern Hemisphere, there are the least (90) AKR events in 2014 and the most (802) AKR events in 2018.The annual distribution of AKR has an anticorrelation with the sunspot number.The annual occurrence pattern of AKR corresponds to the occurrence of a longer duration of southward IMF (B z < 0).The probable reason is that the longer duration of B z < 0 can lead to the longer magnetic reconnection.
3. In the Earth's Northern Hemisphere, there are the most events (865) in the autumn (August-October), corresponding to those events of dominant B x < 0. In the Earth's Southern Hemisphere, there are the most events (830) in the autumn (February-April), corresponding to those events of dominant B x > 0. When B x < 0 (B x > 0), the single-lobe magnetic reconnection tends to occur in the Earth's Northern (Southern) Hemisphere, pushing more suprathermal electrons into the Earth's Northern (Southern) polar source cavity, producing more AKRs.This study first confirms that the direction of IMF plays an important role in the generation of AKR in the magnetosphere.

Figure 1 .
Figure 1.AKR events (A-D) observed by Van Allen Probes.(a) The Bx and By of IMF from 13:00 to 20:00 UT on 2017 January 18.(b) AKR Event A observed by Probe A in the Earth's Southern Hemisphere during the period.The electric-field spectra measured by EMFISIS/HFR.(c) AKR Event B observed by Probe B in the Earth's Southern Hemisphere.(d) The Bx and By of IMF from 00:30 to 06:00 UT on 2016 December 24.(e) AKR Event C observed by Probe A in the Earth's Northern Hemisphere.(f) AKR Event D observed by Probe B in the Earth's Northern Hemisphere.

Figure 2 .
Figure 2. The statistical results of IMF from 2012 October 1 to 2019 July 31.(a) The percentage of AKR events in different ranges of IMF B x .(b) The percentage of AKR events in different ranges of IMF B y .(c) The percentage of AKR events in different ranges of IMF B z .

Figure 3 .
Figure 3.The annual occurrence pattern of AKR.(a) The number of AKR events in the Earth's Northern (red) and Earth's Southern (blue) Hemisphere per year from 2013 to 2018.(b) The number of sunspots per year during the period.

Figure 4 .
Figure 4.The seasonal and monthly occurrence pattern of AKR from 2012 November to 2018 October.(a) The seasonal distribution of AKR events in the Earth's Northern Hemisphere.(b) The seasonal distribution of events in the Earth's Southern Hemisphere.(c) The monthly distribution of AKR events in the Earth's Northern Hemisphere.(d) The monthly distribution of AKR events in the Earth's Southern Hemisphere.(e) The monthly percentages of B x < 0. (f) The monthly percentages of B x > 0.