ANGEOAnnales GeophysicaeANGEOAnn. Geophys.1432-0576Copernicus PublicationsGöttingen, Germany10.5194/angeo-35-253-2017Average plasma sheet polytropic index as observed by THEMISFrühauffDennisd.fruehauff@tu-bs.dehttps://orcid.org/0000-0003-0092-8979MiethJohannes Z. D.GlassmeierKarl-HeinzInstitut für Geophysik und extraterrestrische Physik, Braunschweig, GermanyDennis Frühauff (d.fruehauff@tu-bs.de)24February201735225326224October201623December201610February2017This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://angeo.copernicus.org/articles/35/253/2017/angeo-35-253-2017.htmlThe full text article is available as a PDF file from https://angeo.copernicus.org/articles/35/253/2017/angeo-35-253-2017.pdf
Multi-spacecraft data from the years 2008 to 2015 of the THEMIS
mission particularly in the near-Earth plasma sheet are used in order to
empirically determine the polytropic index in the quiet and active time
magnetotail. The results of a number of previous studies in the 1990s can be
confirmed. An analysis of the total database, although showing poor
correlation, results in an average polytropic index of γ=1.72. The
active time plasma sheet is well correlated with an average γ=1.49.
However, the data scattering suggests that the analysis of the data in total
is not adequate. In order to reduce the timescales, individual spacecraft
orbits are analyzed, giving a broad distribution of polytropic indices
throughout the plasma sheet. The major part of the distribution falls in a
range between γ=0.67 and γ=2. Our results indicate a variety of
thermodynamic processes in the magnetotail and an all-time presence of heat
exchange of the plasma. A description of the plasma sheet using an equation
of state with a single γ is probably inadequate. This necessitates the
application of more sophisticated approaches, such as a parametrization of
the heat flux vector in magnetohydrodynamic equations or a superposition of
polytropic indices.
The plasma sheet is one of many important regions in the Earth's magnetotail.
A large variety of dynamic processes are located in or connected to this
region, such as magneto-hydrodynamic waves, reconnection, fast plasma flows
and convection, (e.g., ). Theoretical models and numerical
simulations, especially in terms of magneto-hydrodynamic theory, require the
closure of the system of moment equations. Usually, this is done by assuming
a relationship between plasma pressure, P, and number density, n, the
equation of state. Following the general equation for the
scalar pressure is
P=αnγ,
with α being a constant related to the specific entropy of a plasma
sheet flux tube and γ being
the polytropic index. Further assuming a
relationship between pressure, density, and temperature, T, similar to an
ideal gas, P=nkBT, the second polytropic equation gives
T=α′nγ-1.
In classical thermodynamics, the polytropic index is related to the degrees
of freedom, f, of the magnetospheric plasma:
γ=(f+2)/f.
Since the plasma can have at most f=3 degrees of freedom, it follows that
γ≤5/3. Different
thermodynamic scenarios arise from different values of γ:
γ=0, isobaric,γ=1, isothermal,γ=5/3, adiabatic,(γ=∞, isochoric), and γ<5/3, energy loss (cooling),γ>5/3, heating.
In an ideal system if (1) convection is reversible (i.e., particles are not
lost from a flux tube); (2) apart from compression, no energy is transferred;
and, (3) viscous effects are negligible, the system will behave adiabatically
, which is the usual idealization in magneto-hydrodynamic
models and simulations.
The availability of in situ satellite measurements has initiated
several studies aiming the determination of the polytropic index of the
Earth's plasma sheet over the past 30 years. Both modeling approaches but
especially observational analyses have been performed.
require a polytropic index of γ=2/3 to ensure the
stability of their magnetotail model. have used
AMPTE/IRM data of density and pressure in the plasma sheet and found that the
tail behaves adiabatic in general and especially during magnetospheric active
times. During quiet times they inferred γ<5/3, indicating cooling
mechanisms and the absence of a magnetotail ground state.
performed analyses on ISEE1/LEPEDEA data for the quiet-time plasma sheet.
They found density and temperature to be anti-correlated, i.e., γ<1,
therefore being in contrast to the results of . The
total dataset gives γ=0.6. provide a simple model
accounting in parts for the differences between the two abovementioned
studies by making the polytropic index a function of the midnight meridian in
a magnetotail of finite width. attempt to explain the
differences between and with the
measurement positions and selection criteria. They relate the
results to initially hot flux tubes being loaded with cool
ionospheric plasma that increases the plasma density while decreasing its
temperature. further develops this explanation by outlining
that the assumption of constant specific entropy of flux tubes for the
complete dataset is not valid, since it crucially depends on the flux tube's
past. Therefore, scattering is introduced in the variables. further
points out that the usage of n-P or n-T analysis will influence the
results as (1) the term temperature is not well defined for non-Maxwellian
distributions and (2) the scattering is enhanced in the n-T diagram
through the computation of T∝P/n. A reanalysis of ISEE1/FPE data in
the n-P domain for individual spacecraft orbits gives 1<γ<5/3
using a plasma sheet criterion of β=P/(B2/(2μ0))>0.2, first
introduced by . , using AMPTE/IRM
data as well but including the plasma sheet boundary layer, find a quiet
time γ=4/3 and active time γ=5/3. They interpret their results
as the presence of a mixture of bubbles and blobs and lead
the partial contradiction of previous studies back to the choice of data
selection criteria. compare plasma sheet data of ISEE2
in near-Earth, midtail, and downtail regions and emphasize the necessity to
analyze the radial dependence of datasets. Following suggestions of
to use only neutral sheet/midnight data they find an
average γ=1.52. use CLUSTER data of the central
plasma and find a wide variety of polytropic indices ranging from 0.1 to
1.8. Active- and quiet-time results are very similar.
In this work THEMIS and ARTEMIS data from eight intervals when
THEMIS/ARTEMIS were located in their predefined tail science phases between
2008 and 2015 are used to revisit the in situ determination of the
polytropic index in the central plasma sheet. Please refer to Table for the list of intervals. The paper is organized as follows:
Sect. 2 will introduce the data selection and orbital coverage, Sect. 3
presents key elements of the resulting database, and Sect. 4 will summarize the
results.
THEMIS tail science phases used in this work.
StageStartEnd32007/15/122007/15/1272008/15/122008/15/12112010/02/032010/02/03152011/16/032011/16/03192012/13/042012/13/04232013/11/062013/11/06272014/29/062014/29/06312015/15/082015/15/08Data selection and analysis procedure
The Time History of Events and Macroscale Interactions During Substorms
(THEMIS) mission launched five identical spacecraft in 2007 into
near-equatorial orbits around Earth . At present
almost 9 years of data are available to the scientific community. The
precessing perigee of the spacecraft constellation (in geocentric coordinate
systems) accounts for seasonal science phases located in the dayside,
duskside, dawnside, and tail regions of the magnetosphere. Here, the focus is
on the tail science stages as shown in Table . Of these stages,
03, 07, and 11 provide near-Earth and midtail measurements between
-9 RE and -30 RE downtail distance of five spacecraft.
Later, two of the probes were lifted into a lunar orbit as the ARTEMIS
mission. Consequently, these two spacecraft were then located around
geocentric distances of about 60RE.
Data from three instruments on board the spacecraft are used: the fluxgate
magnetometer (FGM) provides magnetic field data at ≈4s
resolution . Particle data are provided by combined
measurements of the electrostatic analyzer (ESA) in the ≤30 keV
range and the solid-state telescope (SST)
in the 25 keV to 6 MeV range ,
providing particle moments at spin (≈3s) resolution. Position
data are given in geocentric solar magnetic (GSM) coordinates if not
specified otherwise. Auroral electrojet (AE) indices are obtained from the
World Data Center in Kyoto, Japan. To eliminate small-scale structures, all
data are averaged and re-sampled to a common time resolution of
1 min. According to and Pe≪Pi and Pe∝Pi in the plasma sheet, only ion data are
used in this study (i.e., P=Pi, n=ni).
Selection criteria
The identification of plasma sheet samples is based solely on magnetic field
(and orbital) data. Following similar studies, e.g., ,
the selection criteria are chosen to be the following:
Use data samples where both magnetic field and particle data are available.
XGSM≤-9RE,
|Y|GSM≤15RE,
|Z|GSM≤10RE.
Bxy≤20nT,
|∠(By,Bx)|≤15∘,
∠(Bz,Bxy)≥15∘.
The first criterion is necessary to make plasma sheet identification by FGM
data and analysis reasonable. The orbital criteria define an approximate
magnetotail plasma sheet box in which data are expected. Criterion (3a) ensures that
the spacecraft is not too far away from the magnetic field reversal, (3b) limits the azimuthal distance (i.e., YGSM) from the neutral
sheet, and (3c) does so for the vertical (i.e., ZGSM) distance
from the neutral sheet. To justify the selection of the above criteria, the
plasma β (the ratio of plasma and magnetic pressure) is calculated for
each data point. A histogram of the resulting distribution is shown in Fig. . As can be seen, the vast majority of measurements feature a
β>0.5, a typical identification criterion for plasma sheet samples
(β>0.2 was used in , indicated here by the
vertical line). Therefore, the above criteria perform reasonably well. The
dataset consists of 164 262 individual measurements.
Occurrence of inferred plasma β values
in the complete dataset. The black vertical line
indicates a value of β=0.2 as was used as the only plasma sheet criterion by .
To further confirm the successful detection of plasma sheet samples, Fig. displays the ZGSM position of the individual
measurements over time. Clearly, sub-annual variations can be detected in the
time series. These variations stem from the definition of the GSM coordinate
system and the precession of magnetic dipole axis during Earth's orbit around
the Sun. Additionally, a long-term variation in the neutral sheet position
can be observed. The period of this oscillation lies around
10–12 years. The resemblance with solar cycle periods will be the subject
of further study.
Variation in the inferred plasma sheet position
over time. Each data point indicates a measurement made when THEMIS
was located in the plasma sheet as identified by FGM data.
The approximate positions of cycle 24 solar minimum and maximum are indicated as well.
The complete orbital distribution of measurements in the XZ and YZ plane is
shown in Fig. . For the near-Earth region, the data are quite
evenly distributed around YGSM,ZGSM=0. Further
downtail, a strong bias towards geomagnetic south can be observed.
Consequently, caution is needed when analyzing only data in these regions.
For the total dataset, the measurements beyond -12.5 RE make up
only about 8 % of all available samples.
Orbital distribution of central plasma sheet data in
the GSM frame. Blue dots indicate each individual 1 min
measurement in the XZ plane (upper panel) and YZ plane (lower panel).
The solid black lines indicate GSM zero planes.
Data analysis procedure
Following the observations of , density and pressure relations
will be used to determine an estimate for the polytropic index. According to
Eq. (), analyzing the data in log–log space will yield a
linear relationship, with the polytropic index as the slope between the two
variables:
logP=logα+γlogn.
Since a simple linear regression is based on the assumption that only the
response variable is of nonzero error, it will not yield reasonable results.
Both P and n feature measurement uncertainties. We will therefore adopt
the method by , which is based on the minimization of the
sum, S, of squared distances of the data points to the regression line
(see, e.g., ):
minS(γ)=min1γ2+1∑klog(Pk/P‾)-γlog(nk/n‾)2,
where the overbars denote geometric means of the relevant quantities. This
procedure is also known as total least-squares (TLS) method (see also
).
Results
Following previous studies, the total database will be divided into subsets
with respect to magnetospheric activity. In a second step, the analysis
follows the ideas of – that is, a statistical analysis of
individual spacecraft orbits will be performed.
The total dataset is displayed in Fig. . As can be observed the
complete point cloud does not exhibit an obvious (only) linear relationship
in the log–log space. This is especially quantified by the low
correlation of r2≈0.31. Still, even though the data are tremendously
scattered, the huge number of samples results in a TLS fit of
γ≈1.722±0.015 (95 % confidence), which is very close to an
expected value of ≈5/3.
Earlier studies have already emphasized the necessity to group the data according
to magnetospheric activity, usually using the AE index as a proxy
. Therefore, in Fig. a
color code is incorporated indicating the related AE activity index for each
measurement. The large amount of scattering stems from at least two different
groups of samples that can be distinguished by the background magnetospheric
activity.
Scatter plot of all density and plasma pressure
measurements. The total least-squares (TLS) fit comprises 164 262 data points with
r2≈0.31. The data points are color-coded with respect
to the corresponding AE index.
Figure shows the subset of data comprising AE>200 nT.
The samples now clearly exhibit a linear relationship (in log–log) with
a correlation of r2≈0.70. Describing the n-P relation through
the power law in Eq. () is therefore reasonable. The TLS fit gives
γ≈1.493±0.014, which is very close to the results of
, , , and
.
Using results of , who compiled a database of THEMIS
fast flow events in the magnetotail, we have scanned the data for
measurements that have been made in the 1 min vicinity of an occurring fast
flow (i.e., Vi≥400 km s-1). Since the observation rate of fast
flows is very low (see, e.g., , ,
and ), the number of detected fast flow encounters is
of the order of <10 %. Hence, they do not influence the analysis of the
total dataset. However, analyzed separately, the observed n-P observations
show remarkable correlation (r2≈0.70), with a fitted polytropic
index of γ≈1.605±0.063.
Scatter plot of density and plasma pressure measurements
for data with AE>200 nT. The TLS fit comprises 26 576
data points with r2≈0.7.
Fitted polytropic index as a function of AE index subsets.
The upper panel shows the resulting polytropic index as its 95 %
confidence interval (blue) and the squared correlation coefficient
(black). The lower panel displays the available number of observations for each subset.
Figure indicates the existence of at least two, but potentially
more subsets of data with respect to the AE index. Therefore, the database is
divided into a range of AE intervals with a spacing of 50 nT. For the
following analysis, only data with XGSM>-12.5RE to
account for any possible bias introduced by the orbital coverage. For each
subset the TLS procedure is applied. The results are shown in Fig. .
As displayed by the bottom panel, each subset contains at least
100 individual samples. For all data with AE>250 nT the
correlation is around r2≈0.7 or higher. For those intervals, the
resulting mean polytropic index fit is around γ≈(1.56±0.08). No statistical significant deviations or trends can be
observed. Below AE<200 nT the correlation is very low, which can be
attributed to data scattering as already observed in Fig. .
In contrast to the above procedure, several arguments indicate that the
analysis needs to be performed on shorter timescales, i.e., to distinguish
between individual spacecraft orbits, since the usual approach is to assume
constant specific entropy for all observed flux tubes. Possible reasons for
the violation of this assumption, and therefore data scattering, have been
summarized by , , and :
The specific entropy of a flux tube crucially depends on its past.
Flux tubes may thus contain different ratios of plasmas from different energetic
regions, and may have been energized non-adiabatically by substorm activity or other mechanisms.
Flux tubes may have lost particles through various processes during their evolution.
For near-Earth plasma especially, initially hot flux tubes may have been loaded with
cold ionospheric plasma, consequently changing their specific entropy.
If any spacecraft were to only observe similar types of flux tubes during its orbits,
scattering should be weak. Yet, the relative motion of a spacecraft across different flux
tubes already causes scattering in the data.
Distribution of polytropic indices for as fitted for each individual
spacecraft orbit. The data are divided into low (blue) and high (orange) AE
index subsets. For the chosen bin width (Δγ=0.2)
the peaks of the distributions are located at γ=1.1 and γ=1.5
(AE<100 nT) and γ=1.1 (AE>200 nT).
Following the last argument, data scattering should be reduced by analyzing
individual spacecraft orbits. For each of those time series, the spacecraft
can still be expected to cross different flux tubes, but the deviations
should be smaller. We have therefore first divided the initial database into
the two obvious groups that can be seen in Fig. , namely
AE<100 nT and AE<200 nT. For each subset, TLS fitting is
applied for the individual spacecraft orbits. The results are only considered
if r2≥0.7. The resulting histograms are shown in Fig. . The
two distributions are very similar, both featuring mean values around
γ≈1.35 with a standard deviation of σγ≈0.68.
Consequently, no shift of the distribution towards lower polytropic indices
as reported by previous works can be observed
. Instead, if analyzed individually, both
active- and quiet-time distributions are similar and cover a wide range of
polytropic indices (e.g., ). It should be noted that there
is a small portion of events (<1 %) in the ranges γ→0 and γ→4.
Since these events, by definition of the procedure, feature well-correlated
data, this indicates that they might be of special physical nature. The
reason for their fitted polytropic index being so different from the greater
part of the distribution needs to be the subject of further study.
From Figs. and it can be inferred that, during both
quiet and active times, the spacecraft observe flux tubes following a similar
distribution of polytropic indices. Only during active times, though, do
these flux tubes contain plasma of similar specific entropy as well
(indicated by the smaller degree of deviation from a linear relationship in
Fig. . The quiet-time data feature a zoo of different (background)
plasma portions with a large variety of specific entropies, leading to a high
degree of scatter in the n-P space.
Radial and hemispheric dependence
Although the radial range of THEMIS tail data is limited to
either near-Earth space (i.e., -10RE) or lunar orbit
(-60RE), we follow the suggestions of to
analyze the radial distribution of polytropic indices.
Figure shows the fitted polytropic index for a range of bins in
XGSM direction along the magnetotail. For the correlation of the
subsets of data to be meaningful, we include only the magnetospheric active
data according to AE>200 nT. Still, as can be observed in the
plot, the correlation for data beyond -20RE is very weak,
making the fitting process insignificant. Even for the near-Earth data, the
squared correlation coefficient rarely reaches 0.7, making the
interpretation of the parameters difficult. For the bins in the regions -20
to -16RE and -11RE a polytropic index close to
adiabaticity is derived. However, around -13RE a clear
depression can be observed. The fit results in a polytropic index close to
the isothermal regime, indicating energy loss of the plasma in this region.
This result indicates a possible connection to the flow-braking region which
is usually found at similar downtail distances (see, e.g. ,
, , and for
observations and possible mechanisms).
To study possible hemispheric differences in the Y and Z directions of
the tail, the orbit-wise analysis is carried out in the relevant hemispheres.
Each orbit for which the squared correlation exceeds 0.7 is assigned to
the corresponding region if all of its data points fulfills one of the
following criteria:
BX,GSM>5nT→ northern magnetospheric hemisphere;BX,GSM<5nT→ southern magnetospheric hemisphere;YGSM>1RE→ duskside hemisphere;YGSM<-1RE→ dawnside hemisphere.
Please note that magnetic field data are used to distinguish between northern
and southern hemispheres, since the GSM coordinates may not always be a
sufficient measure of neutral sheet distance. In case of dawn–dusk
hemispheres, no similar condition can be derived from magnetic field data.
Furthermore, YGSM is expected to work reasonably well. The
resulting distributions are shown in Figs. and .
Similar to Fig. the spread of the fitted polytropic indices is
large. At the same time, the mean values of the different regions are not
significantly different. We conclude that no obvious north–south or dawn–dusk
symmetries can be observed in the data.
Radial dependence of the complete dataset for which AE>200 nT.
The upper panel shows the 95 % confidence interval of
the fitted polytropic index (blue) and the squared correlation
coefficient (black). The lower panel displays the available number of observation for each bin.
Dawn–dusk hemispheric dependence of near-Earth data
(i.e., XGSM>-12.5RE). The hemispheres
are defined through |Y|GSM>1RE.
North–south hemispheric dependence of near-Earth data
(i.e. XGSM>-12.5RE). The hemispheres are
defined through |Bx|GSM>5 nT.
Comparison with ARTEMIS data
As a matter of completeness, the data from the ARTEMIS part of the mission
are analyzed as well. The data selection criteria are equal to those
described in Sect. 2.1 with the addition of the following orbit
requirement:
IF XSSE<0 THEN YZSSE≥1RM,
where the orbital information is based on selenocentric solar ecliptic (SSE)
coordinates, similar to the geocentric solar ecliptic (GSE) definition with
the exception of having the Moon's center at the origin, and the Moon's
radius, RM. This additional requirement ensures that eclipse
data, i.e., spacecraft shadow passes, are not included in the dataset. The
resulting orbital distribution covers ranges of XGSM between
-66 and -52 RE.
The total linear regression of the data is shown in Fig. . Similar
to the THEMIS data, a slight grouping of subsets can be observed considering
the AE index. However, a very clear linear relationship of data during strong
magnetospheric activity is not evident. Again, fitting the whole dataset
results in a very poor correlation of r2≈0.34 with an estimated
polytropic index of γ≈1.566±0.029.
The analysis of individual spacecraft orbits is displayed in Fig. . The histogram is qualitatively very similar to Fig. ,
again featuring a maximum between γ=1 and 2. However, since the
number of detected orbits is much lower in case of ARTEMIS, the statistics
are very poor. From this analysis no obvious difference between near-Earth
and downtail regions can be inferred.
Scatter plot of all density and plasma pressure
measurements with the ARTEMIS probes. The TLS fit comprises
21 054 data points with r2≈0.34. The data points
are color-coded with respect to the corresponding AE index.
Distribution of polytropic indices for as fitted for
each individual spacecraft orbit. The fit is considered
successful if r2≥0.7.
Summary
This study revisits the observational determination of the polytropic index
in the Earth's magnetotail using data from the THEMIS and ARTEMIS missions.
Taking the usual approach
, i.e., fitting a power law
equation of state to the total point cloud of density and pressure
observations, the results indicate a polytropic index very close to an
expected adiabatic index of γ=5/3. Yet, the amount of scattering and
the poor linear correlation of the data indicate that this simple approach
does not yield useful results.
The addition of AE index data as a proxy for magnetospheric activity shows
that the near-Earth point cloud in the n-P space is actually made from
two separate distributions, one for the quiet-time magnetotail and one for an
active magnetotail with AE>200 nT. While the former point cloud
still displays a large amount of data scattering with a polytropic index
clearly below adiabatic behavior, the active magnetotail data are well
correlated with a fitted polytropic index of γ≈1.5. A similar
result is obtained when analyzing the polytropic indices for smaller subsets
of data with respect to their activity index (see Fig. ). These
results compare well to previous studies such as ,
, . The analysis of data during fast flow
events only results in a small dataset with highly correlated density and
pressure variations. The fitted polytropic index is very close to the
adiabatic value.
While it is tempting to conclude that the active magnetotail is
quasi-adiabatic and the quiet-time tail is not, one has to be careful about
the actual cause of data scattering in the point cloud. Since the analysis
incorporates data of a variety of locations within the plasma sheet and might
contain a zoo of dynamic structures intrinsic to the tail, it seems natural
to assume that the contributions to the point cloud feature different
specific entropies, leading to a vertical offset in the n-P space, while
at the same time indeed showing adiabatic behavior when considered
separately. To summarize the arguments in Sect. 3, the spacecraft will have
crossed a variety of different flux tubes, each with different specific
entropy, which mainly depends on the flux tube's past. Each of these may have
undergone heating, energy loss, or even particle loss during its passage
through the tail. Therefore, the assumption of the total linear regression,
namely that the observed specific entropy of the flux tubes is approximately
constant, can not be justified.
Consequently, and as already suggested by others, such as ,
, and , an analysis on smaller timescales
can be performed by fitting individual polytropic indices for each spacecraft
orbit (see Fig. ). For a large number of orbits, the data
correlation is high enough to be incorporated into a histogram. The
distribution of polytropic indices is very similar for both quiet and active
magnetotail. This result is in contrast to the interpretation of the total
least-squares fit only.
The main findings of this work can be summarized as follows:
Both quiet and active time plasma sheets show a population
of flux tubes with similar polytropic indices. This means that, here,
the quiet tail is not different from the active tail. However, since
data scattering in the quiet-time tail is higher, the distributions of
specific entropies must be different from one another.
Data during fast flows show remarkable correlation with a polytropic
index very close to 5/3.
The total distribution of polytropic indices is broad, with approximately
68 % of all indices between γ=0.67 and γ=2. Clearly, the
magnetotail features processes that show all different kinds of thermodynamic
scenarios leading to an average polytropic index between isothermal and adiabatic.
Some of the events found in the THEMIS data seem to be of very different
physical nature. Their properties need to be evaluated in detail in future studies.
The spatial distribution of polytropic indices through the magnetotail reveals
a depression region around -13RE where close-to-isothermal behavior is
observed in the plasma data. This observation is possibly related to flow-braking
mechanisms in the dipole region of the magnetotail.
No asymmetries between north–south or dawn–dusk regions can be reported.
The addition of data from the ARTEMIS mission and, therefore, downtail region
of the plasma sheet indicates a very similar behavior. However, due to the limited
number of available orbits that satisfy the criteria, a quantitative
analysis based on THEMIS data alone remains difficult.
A thermodynamic closure equation like Eq. () together with the assumption
of adiabatic behavior is input to many magnetospheric and magnetotail models and
magnetohydrodynamic simulations. The analysis of THEMIS data on individual orbits
indicates that many different values of the polytropic index are determined when
traversing different flux tubes in the plasma sheet. Therefore, the validity of
a single polytropic index as input to models and simulations seems questionable.
Since heat flux or exchange appears to be common even in quiet times, application of
this simplification might change the outcome to certain extent. Whether or not
the relative change of the results is substantial is certainly a question best
to be answered by theoretical considerations. A first step into this direction
has been done by , who aims at a description of a superposition
of polytropic indices in the heliosheath. Our results indicate that a similar
treatment should be considered when modeling magnetospheric regions, such as
the magnetotail.
Data availability
THEMIS data and the latest calibration files are publicly available at
http://themis.ssl.berkeley.edu/ or via the SPEDAS software. Auroral
electrojet data can be found at http://wdc.kugi.kyoto-u.ac.jp/.
The authors declare that they have no conflict of
interest.
Acknowledgements
Auroral electrojet indices for all necessary events were obtained from the
World Data Center in Kyoto, Japan. We acknowledge NASA contract NAS5-02099 and V. Angelopoulos for use of data from the THEMIS Mission. Specifically: C. W. Carlson and J. P. McFadden for use of ESA data and D. Larson for use of
SST data. This project is financially supported by the German Ministerium
für Wirtschaft und Energie and the Deutsches Zentrum für Luft- und
Raumfahrt under contract 50 OC 1403. The
topical editor, C. Owen, thanks the two anonymous referees for help in
evaluating this paper.
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