Introduction
The position of the trapping boundary for energetic electrons in the outer
radiation belt (ORB) contains information about the topology of the magnetic
field lines of the Earth. For a long time this has been analyzed using data
from both low-orbiting and high-apogee satellites
.
Using the data of high-apogee satellites, showed that the
polar boundary of the ORB, also known as the trapping boundary, is located
near to ∼9 RE in the dayside sector and near to ∼7–8 RE
close to midnight. These results were further supported by
using data from the CRRES and SCATHA satellites, and covering distances from
∼6 to ∼8.3 RE (CRRES) and from ∼7 to ∼8.5 RE
(SCATHA). Results obtained by ,
and show that the isotropic boundary of energetic
particles (i.e., the boundary where pitch angles of particles become
isotropic) is located equatorward of the trapping boundary. It means that the
ORB trapping boundary can be clearly identified using low-orbiting satellite
measurements.
A good understanding of the relative positions of the trapping boundary and
the equatorial edge of the auroral oval is important for the analysis of the
structure of magnetospheric plasma domains and the topology of the
geomagnetic field. Comparison of the relative position of the trapping
boundary and the auroral oval was statistically done using ground-based
auroral observations and satellite observations of the trapping boundary.
compared the position of Feldstein's auroral oval with
the trapping boundary of the 40 keV electrons obtained by
and statistically showed that the trapping boundary is located inside the
auroral oval. However, later compared the
position of the auroral oval with the results of Alouette-2 observations and
concluded that the auroral oval is situated just on the polar border of the
trapped radiation region of electrons with energy >35 keV.
analyzed particle fluxes with energies 0.27, 11, 28 and
63 keV, from the COSMOS-424 satellite, and showed that the trapping boundary
is located poleward of the region of low-energy electron precipitation.
However, this study was done using the data obtained for only 21 orbits, and
was not widely known. stressed (p. 120 in their paper)
that a poleward (high-latitude) boundary of the diffuse auroral belt without
any discrete auroral forms “constitutes the equatorward boundary of the
auroral oval and at the same time it is the high-latitude boundary of the
radiation belt (RB) of electrons with energies from a few tens to hundreds of
kiloelectronvolts (STB – stable trapping boundary for radiation belt
electrons)”.
According to the traditional point of view see, for
example,, the auroral oval is mapped to the plasma sheet.
In this case the trapping boundary should be located equatorward or at the
equatorial boundary of the auroral oval. However,
and
showed that most of the auroral oval does not map to
the plasma sheet. It is mapped to the plasma ring surrounding the Earth at
geocentric distances from ∼7 RE to the magnetopause, near noon, and
to ∼10–13 RE near midnight. They suggested that the plasma in the
magnetosphere is in magnetostatic equilibrium, and used the value of plasma
pressure as a natural tracer of magnetic field lines, comparing the pressure
at low latitudes and at the equatorial plane. showed
that the outer boundary of this ring in the night sector coincides with the
external boundary of the ring current. Results obtained by
and
showed that the auroral oval is mapped to the region of
quasitrapping, where drift trajectories of energetic electrons with pitch
angles smaller than near to 90∘ surround the Earth
due to the drift shell splitting effect (which is ordinarily named the
Shabansky effect). Such mapping suggests that the trapping boundary should be
located poleward of the equatorial boundary of the auroral oval.
Therefore, it is very important to establish the true location of the
trapping boundary with respect to the equatorial auroral oval boundary. This
can be done using simultaneous observations of both auroral electron
precipitation and fluxes of energetic electrons. It is well known that the
location of the auroral oval and the location of the trapping boundary are
strongly affected by geomagnetic activity. Therefore, it is necessary to
compare these relative locations using simultaneous measurements of the
auroral oval and trapping boundary on the same satellite. However, there are
some difficulties related to the detection of the trapping boundaries during
the periods of low geomagnetic activity (for example during the solar
minimum). In these cases, the level of electron fluxes inside the ORB can be
rather low, close to the limit of sensitivity of the instrument. Thus, the
detected trapping boundary can be located closer equatorward with respect to
the true trapping boundary.
Despite the significant number of particle measurements carried out by
low-orbiting satellites, the relative location of the trapping boundary and
the equatorial boundary of the auroral oval, and how they could be affected
by geomagnetic activity, still require careful studies. In this work, we use
data of the METEOR-M1 satellite to establish the location of the trapping
boundary and of the auroral oval for different levels of geomagnetic
activity, which were quantified using the AE and PC geomagnetic indices. The
paper is organized as follows. First, we describe the METEOR-M1 satellite
instrumentation and the data analysis, including important caveats. Then we
obtain the position of the trapping boundary of electrons with energies
>100 keV relative to the equatorial boundary of the auroral oval, and how
it varies for small and large values of the AE and PC indices of geomagnetic
activity. At the end, we shall discuss the role that our results might play
in the determination of features of the high-latitude magnetospheric
topology.
Instrumentation and data analysis
We used the data from the METEOR-M1 satellite launched on 17 September 2009
into a polar solar-synchronous circular orbit with an altitude of ≈830 km, a period of ∼100 min, and an inclination of 98∘. We
used the data of the GGAK-M set of instruments, composed of semiconductor and
scintillator detectors, and electrostatic analyzers. In particular, it
measured energetic electrons with energies from 0.1 to 13 MeV, and
low-energy electrons with energies from 0.032 to 16.64 keV (see more details
and available data in http://smdc.sinp.msu.ru/index.py?nav=meteor_m1;
last access: October 2017).
For automatic detection of the polar boundary of the ORB and the equatorial
boundary of the auroral oval we compared the corresponding fluxes with a
background reference flux, calculated for each orbit. For energetic particles
we calculated the average flux of electrons with energies >100 keV in the
polar cap and its standard deviation. We assumed that the measured flux can
be classified as ORB electron flux if the difference between this flux and
the background flux was greater than 5 standard deviations during the
continuous time interval of at least 1 min duration (the separate
single-point spikes are not taken into account). The nearest poleward point
that satisfies the described criterion is selected as the polar boundary of
the ORB. These selection criteria show stable results of the ORB detection,
but as a rule they define the boundary at the end of the decline of electron
intensity from ORB maximum to the background level. This means that electron
fluxes lower than the established criteria, and belonging to the ORB, could
be missed. This is why it might shift slightly the obtained boundary
equatorward with respect to the true boundary, especially in the case of
low-intensity ORB crossing (see the introduction). This means that we could
underestimate the number of events for which the polar boundary of the ORB is
observed inside the auroral oval. Such underestimation changes slightly the
results of the statistical analysis. However, it cannot change the answer to
the main question: whether the trapping boundary is located inside the oval
or coincides with its equatorial boundary.
The automatic detection of the polar boundary of ORB, identified as the
trapping boundary, might be affected by the sharp local increases in the
energetic electron fluxes sometimes observed at the trapping boundary
see or just poleward of
it. Such fluxes are usually much smaller than the maximum fluxes of the ORB
precipitating electrons. Nevertheless, they can be observed during a few
hours at the same location in a few consecutive polar satellite orbits
, and
alter the automatic detection of the boundary. It was one of the reasons to
do a visual inspection of all events.
To calculate the position of the auroral oval boundary, we use the value of
the total energy flux. We produce the spectra approximation from 0.032 till
16.64 keV with energy step dε=0.01 keV. Energy flux was
calculated as the integral characteristic of low-energy electron spectrum
Fluxε=2π∫j(ε)⋅εd(ε) (where j(ε) is the flux for the current
value of energy ε). We first calculated the average value and
standard deviation of the electron energy flux measured at L<3 RE,
where L is the McIlwain parameter. In the next step we considered the
fluxes that exceed the background flux by 7 standard deviations. If the
obtained boundary was located at L>3 RE, we repeated this procedure but
calculated the average flux and its standard deviation up to the boundary,
determined in the first step. Based on the definition of
the auroral oval, we also imposed an additional criterion on the value of the
total energy electron flux: it should be greater than
0.2 erg cm-2 s-1. The results obtained were also confirmed by a
visual inspection.
An example of the location of the polar boundary of ORB inside the
auroral oval at AE >150 nT. (a) Spectrogram of low-energy
electrons; (b) red solid line – total energy flux, calculated from
the electron spectra presented on the top; green solid line – counts of
electrons with energy ≥100 KeV; dashed red lines mark the position of
the equatorial boundaries of the auroral oval; dashed green lines – the
position of the polar boundaries of ORB.
We used the AE index that represents the dynamics
of the auroral electrojet to identify the intervals of substorm activity. We
also used the Polar Cap (PC) index
, which was created as
a proxy of the dawn–dusk electric field in the polar cap and Region 1
currents of intensity. We took for the analysis
the 1 min values of the AE and PC indices when the spacecraft was at the
equatorial boundary of the auroral oval. Taking into account that there are
two PC indices, obtained for the Northern Hemisphere (PCN) and Southern
Hemisphere (PCS), we used the corresponding PCN (PCS) indices for northern
(southern) crossings of the auroral oval.
Figure shows an example of two crossings of the auroral oval in
the morning and evening MLT sectors on 1 February 2010, when the trapping
boundary was located inside the auroral oval. The top panel shows the
spectrogram of low-energy electrons, and the bottom panel shows total energy
flux, calculated from the electron spectra presented on the top (red solid
line) and counts of electrons with energy ≥100 keV (green solid line).
Dashed red lines in both panels indicate the position of the equatorial
boundaries of the auroral oval and dashed green lines show the position of
the polar boundaries of ORB. It is clearly seen that the curves of total
energy flux and counts of electrons with energy ≥100 keV show the
position of the trapping boundary poleward of the equatorial boundary of the
auroral oval.
An example of observation of the polar boundary of ORB outside the
auroral oval at AE <150 nT. The notations are the same as in
Fig. .
According to the omniweb database (http://omniweb.gsfc.nasa.gov; last
access: November 2017), the solar wind number
density (NSW) and velocity (VSW), and three
components of the interplanetary magnetic field (IMF) for both equatorial
borders, were very common: Bx≈2 nT, By≈-4 nT,
Bz≈-1 nT, NSW≈6 cm-3, and
VSW≈450 km s-1. This event took place in the
absence of geomagnetic storms (Dst ≈-7 nT), and during moderate
auroral activity (AE ≈300 nT and AL ≈-260 nT). The values of the PC index were also moderate
(PCS ≈3) (see http://pcindex.org; last access: November 2017). As can be seen, for this event the trapping
boundary of energetic electrons, shown by green dashed lines, is located
inside the auroral oval. The differences between the latitudes of the
equatorial boundary of the oval and the trapping boundary, ΔLat, are
equal to -5.8∘ for the dawn and -1.7∘ for the dusk
boundaries.
An example of observation of the polar boundary of ORB inside the
auroral oval at AE <150 nT. The notations are the same as in
Fig. .
Figure shows an event of the trapping boundary located outside
the auroral oval observed on 17 January 2010. The satellite crossed twice the
auroral oval during very quiet geomagnetic conditions (Bx≈2 nT,
By≈-1 nT, Bz≈2 nT, NSW≈6 cm-3, and VSW≈350 km s-1, Dst ≈-2 nT, AE ≈15 nT, AL ≈-15 nT, PCN <1). The observed
difference was comparatively small: ΔLat =1∘ for the dawn
and 3.3∘ for the dusk boundaries.
Comparison of events shown in Figs. and could
bring a conclusion that the relative location of the trapping boundary and
the equatorial boundary of the auroral oval might be affected by the shift of
the oval to higher latitudes with the decrease in the geomagnetic activity.
However, there are many other events observed for low activity for which the
trapping boundary was observed inside the oval. One example of such kinds of
events is shown in Fig. .
It took place on 26 January 2010 during quiet geomagnetic conditions (IMF
Bx≈-2 nT, By≈4 nT, Bz≈-1.5 nT,
NSW≈3.5 cm-3, and
VSW≈370 km s-1, Dst ≈-17 nT, AE ≈50 nT, AL ≈-30 nT, PCS ≈2). For this event,
ΔLat =-5.1∘ for the dawn and -2.2∘ for the dusk sectors.
The existence of different types of events requires making a statistical
analysis to clarify how the geomagnetic conditions could affect the relative
location of both boundaries.
The distribution of ΔLat for AE > 150 nT (red bins) and
< 150 nT (blue bins) for the Northern Hemisphere (a) and
Southern Hemisphere (b). N shows the number of events under the
described criteria.
Statistical analysis
We analyzed the data from METEOR-M1, obtained for more than 6200 auroral
ovals and the outer boundary of the ORB crossings. For each crossing, we
determined the difference between the geomagnetic latitudes of the equatorial
boundary of the auroral oval and of the trapping boundary, ΔLat. The
negative difference ΔLat <0 means that the trapping boundary is
located inside the auroral oval, while the positive difference ΔLat >0 indicates that the trapping boundary is located equatorward of
the auroral oval. The METEOR-M1 satellite has a Sun-synchronous orbit. That
is why we obtained ΔLat only for a limited range of MLTs.
The distribution of ΔLat for PC > 1 (red bins) and
< 1 (blue bins) for the Northern Hemisphere (a) and Southern
Hemisphere (b). N shows the number of events under described
criteria.
To analyze how these differences could be affected by geomagnetic activity,
we divided all data into two data sets according to the AE or PC indices.
Figure shows the distribution of the latitude differences
ΔLat for AE >150 nT and AE <150 nT for the Northern
Hemisphere (a) and Southern Hemisphere (b). As can be seen, the number of
events for which the trapping boundary is observed inside the auroral oval
increases significantly with the increase in geomagnetic activity, quantified
through the AE index. For AE >150 nT the trapping boundary is located
inside the auroral oval for the majority of events for both hemispheres,
while for AE <150 the trend is not so clear – the number of events
where the trapping boundary is located inside and outside of the auroral oval
is nearly the same. However, for both sets there are a comparatively large
number of events, for which this difference is comparatively small.
Figure shows the distribution of the latitude differences
ΔLat for PC >1 and <1 and for the Northern Hemisphere
(a) and Southern Hemisphere(b), respectively. Comparing Figs.
and , we can see that both distributions are very similar, which
can be explained by the high correlation between the AE and PC indices
obtained by . This correlation is related to the
formation of ionospheric current systems as a result of the
magnetosphere–ionosphere interactions, and the dominant role of the Region 1
currents of in the formation of the PC index
. However, the obtained similarity in the
behavior of the boundaries, using the AE and PC indices as separate measures
of geomagnetic activity, was not evident at the beginning of this study. This
supports the picture obtained by in which the trapping
boundary is located inside the auroral oval. We underline that the described
effect can be clearly seen only in the case of simultaneous measurements of
plasma and energetic electrons onboard the same satellite, which allow us to
observe the trapping boundary inside the auroral oval directly during the
local measurements. The statistical comparison of boundaries masks this
effect, because the scattering of the position of the discussed boundaries in
different crossings can be rather large (the standard deviation in the
statistical position of the boundaries ≈±2∘ for the
trapping boundaries and ≈±3∘ for the equatorial
boundaries of the auroral oval), whereas the main parts of ΔLat
distributions in Figs. and show the difference
between boundaries within the limits ±2∘ in the case of low
geomagnetic activity. The observed scatterings in positions of the boundaries
are in agreement with early established scattering of the auroral oval
boundaries seeand references therein and the outer
ORB boundary .
The distributions of the position of the equatorial boundary of the
auroral oval (green bins) and the polar ORB boundary (red bins) from L
(where L is the McIlwain parameter) for the Northern Hemisphere (a, b) and Southern Hemisphere (c, d) for AE <150 nT (a, c) and AE >150 nT (b, d).
The analysis of the shifts of the studied boundaries with the increase in
geomagnetic activity requires special attention and is far from the main
subject of our research. Figure shows the L (McIlwain
parameter) distribution of both boundaries for AE <150 and
AE >150 nT in both hemispheres. It is possible to see the real shift of
the equatorial boundary of the auroral oval equatorward with the increase in
AE, which is well known due to multiple auroral oval observations. At the
same time the position of the trapping boundary practically does not change
with the increase in AE. This result is in agreement with
, in that, in comparison with plasma boundaries, the
energetic particle boundaries show a lower degree of correlation with solar
wind Bz, VBz, and the Kp index of geomagnetic activity.
Discussion and conclusions
We analyzed the relative position of the trapping boundary and the equatorial
boundary of the auroral oval using simultaneous measurements of the energetic
electrons with energy >100 keV and the auroral electrons made at the same
METEOR-M1 satellite. Previous comparisons of the relative position of these
boundaries were made mostly statistically using data from different
satellites. Our analysis shows that the differences in the positions of both
boundaries are typically smaller than the statistical scattering in the
position of each boundary. This fact explains why previous statistical
studies led to different conclusions, and why the use of statistical results
about the location of each boundary cannot answer the question about the
relative position of the trapping boundary and the equatorial boundary of the
auroral oval.
Our study shows the trapping boundary is often located inside the auroral
oval. The number of such events would be enhanced if instruments of better
sensitivity were used. This is because the trapping boundary is defined as
the boundary where particle fluxes become lower than a threshold determined
by the sensitivity of a detector in the case of a low level of electron flux
inside the ORB, so an increase in the sensitivity would move the detected
trapping boundary poleward, i.e., deeper inside the auroral oval. The
analysis of the latitudinal difference in the position of both boundaries for
AE more or less than 150 nT, and for PC more or less than 1, shows that the
number of events when the trapping boundary is observed inside the auroral
oval significantly increases with both AE and PC indices.
The location of the trapping boundary inside the auroral oval agrees with the
latest results on the auroral oval mapping discussed by .
They argue that the auroral oval has the form of a comparatively thick ring
for all MLTs. Mapping of the plasma sheet to the ionospheric altitudes cannot
produce the structure with non-zero thickness near noon. Therefore, it seems
natural to map the auroral oval into the plasma ring that surrounds the
Earth, as selected by ,
and filled with plasma similar to the plasma in the plasma sheet. Results of
and
also support such a conclusion and locate the quiet
time equatorial boundary of the auroral oval at ∼7 RE near midnight
and the polar boundary at ∼10–13 RE. It is also important to
remember that starting from this magnetospheric region is
classified as the region of quasitrapping for energetic particles. It
contains enclosed drift trajectories inside the magnetosphere, and only particles with near to
90∘ pitch angles have drift trajectories crossing the magnetopause.
The drift trajectories of particles with other pitch angles are locked inside
the magnetosphere. Therefore, the registration of the trapping boundary of
energetic electrons with nearly zero pitch angles inside the auroral oval
seems quite natural.
The observation of the trapping boundary of energetic electrons inside the
oval can also be important for the solution of the problem of acceleration of
electrons in the ORB, taking into account that the injection of a seed
population of relativistic electrons during magnetic storms takes place at
the equatorial boundary of the auroral oval see the results and
discussion in. Electrons of such a seed population
must be trapped inside the magnetosphere and further accelerated to
relativistic energies during the recovery phase of a storm, forming a new
ORB. Our current studies were done for comparatively quiet geomagnetic
conditions. They also point out the necessity to keep studying the position
of the ORB boundaries, taking into account an overlapping of the part of the
auroral oval and the ORB, using a more sophisticated instrument for the
measurement of energetic electrons, and to extend this study to the
geomagnetic storm time intervals. For our study we used integrated fluxes of
the precipitating electrons with the energy >100 keV. Hence, our results
provide the information about an averaged value of polar boundaries, which
might vary significantly from the dynamic low-energy seed population
(∼100 keV) up to the high (ultra-relativistic energies >1 MeV),
taking into account that the seed electron acceleration to higher energies
and the radial diffusion contribute to the redistribution of the electron
population see. It is necessary to add that the recent results
including the observations of the Van Allen probes has led to significant
advances in the study of the dynamics of the ORB. For example,
showed the existence of a rather stable core of the ORB.
The energy dependence of the inner boundary of the ORB was carefully analyzed
by , and injection of the seed population at low
latitudes was studied by . Recent studies
are of special interest,
showing a strong increase in transverse electric fields in subauroral
polarization streams (SAPS), which according to can
modify the picture of particle injection in the slot region. However, it will
be interesting to continue research of the outer radiation belt considering
the results obtained in our paper.
In summary, we can conclude that the trapping boundary of electrons with
energy >100 KeV, which coincides with the polar boundary of the ORB, is
often located inside the auroral oval. This applies almost always to high
geomagnetic activity times and also, though less often, to low geomagnetic
activity times. All this might help to re-analyze the relation between the
dynamics of radiation belts and auroral phenomena.