ANGEOAnnales GeophysicaeANGEOAnn. Geophys.1432-0576Copernicus PublicationsGöttingen, Germany10.5194/angeo-34-511-2016The dawn–dusk asymmetry of ion density in the dayside magnetosheath and its annual variability measured by THEMISDimmockAndrew P.andrew.dimmock@aalto.fihttps://orcid.org/0000-0003-1589-6711PulkkinenTuija I.https://orcid.org/0000-0002-6317-381XOsmaneAdnaneNykyriKatariinaDepartment of Radio Science and Engineering, School of Electrical Engineering, Aalto University, 02150, Espoo, FinlandCentre for Space and Atmospheric Research, Embry-Riddle Aeronautical University, Daytona Beach, Florida, FL 32114, USAAndrew P. Dimmock (andrew.dimmock@aalto.fi)10May201634551152825January20165April201611April2016This 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/34/511/2016/angeo-34-511-2016.htmlThe full text article is available as a PDF file from https://angeo.copernicus.org/articles/34/511/2016/angeo-34-511-2016.pdf
The local and global plasma properties in the magnetosheath play a
fundamental role in regulating solar wind–magnetosphere coupling processes.
However, the magnetosheath is a complex region to characterise as it has been
shown theoretically, observationally and through simulations that plasma
properties are inhomogeneous, non-isotropic and asymmetric about the
Sun-Earth line. To complicate matters, dawn–dusk asymmetries are sensitive to
various changes in the upstream conditions on an array of timescales. The
present paper focuses exclusively on dawn–dusk asymmetries, in particularly
that of ion density. We present a statistical study using THEMIS data of
the dawn–dusk asymmetry of ion density in the dayside magnetosheath and its
long-term variations between 2009 and 2015. Our data suggest that, in
general, the dawn-side densities are higher, and the asymmetry grows from
noon towards the terminator. This trend was only observed close to the
magnetopause and not in the central magnetosheath. In addition, between 2009
and 2015, the largest asymmetry occurred around 2009 decreasing thereafter.
We also concluded that no single parameter such as the Alfvén Mach number,
plasma velocity, or the interplanetary magnetic field strength could
exclusively account for the observed asymmetry. Interestingly, the dependence
on Alfvén Mach number differed between data sets from different time
periods. The asymmetry obtained in the THEMIS data set is consistent with
previous studies, but the solar cycle dependence was opposite to an analysis
based on IMP-8 data. We discuss the physical mechanisms for this asymmetry
and its temporal variation. We also put the current results into context with
the existing literature in order to relate THEMIS era measurements to those
made during earlier solar cycles.
Magnetospheric physics (magnetopausecuspand boundary layers; magnetosheath; solar wind-magnetosphere interactions)Introduction
The complex and nonlinear interaction between the solar wind and the
terrestrial magnetosphere presents a challenging and rich geophysical
problem. The goal is to fully understand the redistribution of the solar wind
kinetic energy as it undergoes many transitions before its impact on our
immediate geospace environment and the ionosphere. Firstly, the terrestrial
magnetic field presents an abrupt obstacle to the incoming solar wind flow
causing it to rapidly slow. This deceleration forms a fast mode shock wave
that stands upstream of the planet and effectively re-distributes the solar
wind kinetic energy into other degrees of freedom
. Immediately downstream of
the bow shock, the magnetosheath transition layer houses the “shocked” solar
wind plasma which has been significantly altered by the bow shock front. This
processing means that in general, the magnetosheath plasma is hotter, denser,
slower, more turbulent and magnetically reconfigured. Therefore it is no
surprise that the parametrisation of the upstream–downstream transition
has been the focus of investigations over the past several decades using a
combination of theoretical models, numerical simulations and in situ
observations. However, despite the many advances made during this time, and
considering the relatively close proximity between the upstream and
downstream plasma, many open questions remain.
One unresolved problem of the magnetosheath is related to the presence of
numerous dawn–dusk asymmetries. To summarise these asymmetries: magnetic
field strength, plasma velocity, temperature anisotropy and mirror mode
occurrence favour the dusk-flank and magnetic field turbulence, ion total
temperature and ion number density are stronger on the dawn-side
.
Remaining issues are the following: (1) what are their underlying physical mechanisms, and
(2) what role do they play in driving magnetospheric plasma properties such
as the formation of the cold dense plasma sheet. The latter point relates
directly to plasma transport processes other than those which are
reconnection-driven. These processes are more relevant during prolonged
periods of northward interplanetary magnetic field (IMF) when subsolar
reconnection has moved to higher latitudes
. To complicate matters, the means of transporting mass,
momentum and energy across the magnetopause involves a synthesis of
magnetohydrodynamic (MHD), kinetic, and numerous wave-particle interaction
processes. In spite of that, several candidates capable of facilitating
transport across the magnetopause have been identified: magnetic reconnection
, impulsive penetration
, Kinetic Alfvén waves
the Kelvin Helmholtz Instability (KHI)
and flux transfer events . It is noteworthy that each of
these processes do not strictly operate independently, and during certain
conditions, plasma transport may be a result of a combination of these
processes operating simultaneously. Of particular interest with regard to the
present paper is that the efficiency of plasma transport processes like the
KHI depend on the global and local magnetosheath conditions
. Therefore, it is likely that magnetosheath dawn–dusk
asymmetries play a substantial role in driving magnetospheric conditions
mainly by (1) asymmetries inherent to the natural seed population, and (2) by
regulating plasma entry processes such as KHI.
Recently, presented compelling evidence that the dawn–dusk
asymmetry of the magnetic field strength has a direct impact on the growth of
the KHI at the night-side magnetopause. Using global and local MHD
simulations, the author showed that when the magnetic field strength
tangential to the Kelvin-Helmholtz k-vector was weaker, the Alfvén speed
was reduced, which increased the velocity shear ratio (Vshear/VA×k). As a result, during a Parker-spiral IMF, the dawn-side magnetopause
should be more favourable to the growth of the KHI since the (steady state)
tangential magnetic field strength was weaker on the quasi-parallel
magnetosheath flank. This result also took into account the faster
magnetosheath flow (and enhanced velocity shear) on the dusk-flank
during these conditions.
Interestingly, reported Cluster observations showing that
the occurrence of the KHI was larger on the dusk-flank when observations were
limited to the dayside. The results of are relevant close
to the terminator and on the nightside. Although a direct comparison between
the studies is difficult, an intriguing spatial dependence is suggested.
Recently, presented evidence that dense plasma on the
magnetospheric side originating from a plasmaspheric plume can cause the
magnetopause to be more unstable to the KHI during cases when the velocity
shear is low. The authors argued that under the plume conditions, the
instability might develop under lower velocity shears allowing the KHI to
form more sunward than usual. What is clear from these studies is that the
development of the KHI is sensitive to the local variations of plasma
properties adjacent to the magnetopause. For that reason, it is important to
quantify the dawn–dusk asymmetries, their dependence on upstream conditions,
as well as their short- or long-term temporal variability.
used IMP eight measurements to derive the dawn–dusk
asymmetry of ion density over the range -20<XGSE<-15RE. A strong
dawn-favoured asymmetry was found but appeared to obey a complicated temporal
dependency. The authors investigated two periods from 1978 to 1980 and
between 1994 to 1997 which corresponded to solar maximum and minimum,
respectively. The largest asymmetry was identified during solar maximum
whereas little to no asymmetry was recorded during solar minimum.
Interestingly, the authors found no clear evidence that the IMF orientation,
solar wind speed, or Alfvén Mach number variations could be causing the
differences between the two data sets. investigated the
dawn–dusk asymmetry of magnetosheath ion fluxes derived from Interball-1 at
more Sunward locations between -15 and +5 RE. The authors also found a
strong dawn-favoured asymmetry, and concluded that it could be related, but
not strictly driven by, the IMF orientation. using
Cluster data also ruled out the IMF as the cause for a dawn-favoured density
asymmetry. Using a combination of Time History of Events and Macroscale
Interactions during Substorms (THEMIS) dayside measurements just outside the
magnetopause, and Block-Adaptive-Tree-Solarwind-Roe-Upwind-Scheme (BATS-R-US)
MHD simulations, reported a dawn-favoured asymmetry of
approximately 20 % close to the terminator. Interestingly, since
selected data close to the solar minimum during 2008–2010, the 20 % asymmetry reported appears contradictory to the solar cycle
dependence found during the previous solar minimum by .
However, the discrepancy in the results could also suggest a difference in
the conditions on the dayside and nightside. did not
detect any strong dawn–dusk asymmetry in their analysis of the THEMIS data,
which could again indicate a temporal dependence as their study spanned the
solar minimum from October 2007 through the rising phase until December 2012.
Another explanation could be that the asymmetry was too delicate to be
identified from their processing of the data. To conclude, it is clear that
open questions remain regarding the dawn–dusk asymmetry of the ion density,
and that the effects of the temporal variations of magnetosheath ion
densities on the KHI and the associated plasma transport are not fully
understood.
The present study aims to expand upon previous work by utilising the full
THEMIS database (2008–2015) to quantitatively study the dawn–dusk asymmetry
of magnetosheath ion density. We utilised our existing data analysis tool
developed over the past 3 years (see ) to compile annual data sets of magnetosheath ion
density measurements between 2008 through 2014. We also investigate the solar
wind parameter dependence for each year separately to shed further light on
the physical driver. We discuss the findings in terms of the physical
mechanisms, and compare the results with earlier findings.
The manuscript is structured as follows. Section describes the
data sources and the methods adopted in processing these data. The final
statistical data sets are presented in Sect. in which we
describe the trends observed in each one. We discuss the physical aspects of
these results in Sect. and put them into context with the
existing literature. Finally, we draw our conclusions and provide a brief
summary in Sect. . Some additional information is provided
in Appendices and which are supplementary
to the results in Sect. .
Data and processingData sets and instrumentation
Our magnetosheath data set were compiled entirely from measurements conducted
between October 2007 and December 2014 using the suite of instrumentation
onboard each of the THEMIS spacecraft . For this
study, ion densities were obtained through the onboard moments provided by
the ElectroStatic Analyser (ESA) instrument . We used the
level-2 (L2) data files which provide measurements at ∼3 s intervals
corresponding to the spacecraft spin period. For the filtering of our
data set, and for the input parameters to the magnetosheath boundary models,
we extracted the solar wind parameters from NASA/GSFC's OMNI data set through
OMNIWeb (http://omniweb.gsfc.nasa.gov). We used the high-resolution (1 min
cadence) observations that have been propagated from the
measuring spacecraft locations to the bow shock nose . To
account for density changes in the magnetosheath caused by density
differences in the upstream solar wind, all density values were normalised by
their corresponding upstream value so that ni=nms/nsw. All results
shown are based on the normalised database unless otherwise stated.
Compilation of magnetosheath density measurements
For each THEMIS probe location, we apply a transformation from the Geocentric
Solar Ecliptic (GSE) frame to the Magnetosheath InterPlanetary Medium (MIPM)
reference frame . The purpose of
this transformation is to automatically arrange the data in a manner which
permits a direct comparison of observations during vastly different solar
wind conditions. The MIPM frame arranges data based on the upstream IMF
vector such that the bow shock geometry of the magnetosheath dawn and dusk
flanks remain quasi-parallel and quasi-perpendicular, respectively. The MIPM
magnetosheath closely resembles the magnetosheath configuration during a
typical Parker-spiral IMF. For example, if a magnetosheath observation during
an ortho-Parker-spiral IMF was made on the dawn-flank, this would in the MIPM
frame be located on the dusk-side. Therefore, to reflect this arrangement,
from this point we adopt the notation of ∥ and ⟂ to describe
data collected on the quasi-parallel (dawn) and quasi-perpendicular (dusk)
flanks, respectively. The IMF orientation (for each magnetosheath point) is
assessed based on a 20 min average of the OMNI time series data. The
20 min window length was selected to account first, the unknown convection
time to each probe location, second, the inaccuracies associated with the
solar wind measurements, and third, to minimise the impact from erroneously
timed transient solar wind events. To account for the motion of the
magnetosheath boundaries, the fractional distance FMIPM across the model
magnetosheath is measured for each point,
FMIPM=|R|-rmprbs-rmp,
where |R| corresponds to the radial spacecraft location, rmp
and rbs are the radial distances to the model magnetopause and bow shock
positions (along R), respectively. The values of FMIPM range
from 0 at the magnetopause, to 1 at the bow shock, such that the intermediate
values indicate the relative position between these boundaries. The
instantaneous location of the magnetosheath boundaries were calculated using
the magnetopause model, and the
bow shock model based on input
variables provided by the 20 min averaged OMNI data. Each data-point is
also corrected for planetary aberration by orienting the x axis (in each MIPM
rotation) along the solar wind flow velocity vector with the planetary
orbital motion subtracted from the y component. The magnetosheath plasma
parameters were obtained by evaluating a 3-min centre-weighted average
at each location. In this case, the mean value of the ion number density is
computed. Within a given 3 min window, if values further than the standard
deviation from the mean σ/ni>1 were
present, these windows were excluded. As a precaution, we also removed time
instances when the magnetosheath flow exceeded that of the solar wind. This
criteria is set for the sole purpose of eliminating solar wind outliers close
to the bow shock arising from erroneous bow shock location identification. In
the current context, this criterion removed less than 0.1 % of our data set;
and thus, has no bearing on the results. Regarding magnetospheric points, we
remove points which lie very far from their typical distribution and are
consistent with magnetospheric values. Since we do not have simultaneous
measurements in the magnetosphere, we employ no criterion to eliminate
magnetospheric points which could be close to those observed in the
magnetosheath. However, we take many steps to validate our results and to
ensure that they are not a manifestation of magnetospheric outliers; these
are discussed later in the manuscript. For each datapoint, the MIPM location,
simultaneous solar wind conditions, and the magnetosheath plasma parameters
were stored to create a database of magnetosheath measurements spanning
October 2007 through December 2014. Temporal or parameter-based subsets could
then be extracted from this complete database. In this case, we isolated
yearly subsets to monitor the annual variations of the ion density dawn–dusk
asymmetry.
Diagram of the MIPM dayside magnetosheath in which all significant
regions and boundaries are labelled. The filled orange sectors demonstrate
the data collection region employed in the present study. Please note the following: (1) the
figure is not to scale and (2) in physical space, the collection region scales
with the magnetosheath width and is therefore larger on the
dusk-side.
The initial 1-year window (1 January–31 December 2008) was then incremented
every 6 months (1 July 2008–1 July 2009) until the final window spanned
1 January–31 December 2014. As a result, each window (except the first and last)
contained a 50 % overlap between the previous and next windows. The purpose
of the overlap was to provide improved temporal resolution over the complete
THEMIS interval and to minimise edge effects from window averaging. Since the
spatial coverage of the THEMIS probes in the magnetosheath were not
consistent over the entire period (see Fig. in Appendix A), some
physical restrictions were enforced to ensure that the yearly subsets
contained comparable spatial distributions of the measurements. We restricted
our data collection to the dayside magnetosheath, discarding data around the
subsolar region (0∘) and at the terminator (90∘). The extent of
this exclusion is a 15∘ sector at both locations. As a result, our
statistical data cover angles between 15∘ and 75∘ with respect
to local noon and the terminator. In addition, we only apply data collected
close to the magnetopause defined by the following range of fractional
distances, 0≤FMIPM≤0.2. Figure shows an illustration
of the data collection area highlighted by the orange shaded regions, showing
also the angular sectors excluded from the analysis. This region was chosen,
as it has continuous coverage throughout the observing period as indicated by
the yearly distribution of THEMIS measurements (Fig. in Appendix A). Furthermore, we targeted the region close to the magnetopause as our
previous results indicated that while no clear asymmetry
was present in the central dayside magnetosheath (0.33≤FMIPM≤0.66),
the data suggested an asymmetry could be present closer to the magnetopause.
also utilised THEMIS measurements within close proximity to
the magnetopause and reported a dawn-favoured asymmetry. In addition, the
plasma properties in close proximity to the magnetopause are the ones
regulating plasma transport processes.
To measure the dawn–dusk asymmetry of each annual subset, the mean and median
of ion densities on the dawn (n∥) and dusk (n⟂) flanks were
computed within the confines of the limits defined above. Because of the
large and uneven variability of the upstream conditions, we cannot further
divide the data sets to smaller angular bins, as the bins then would not have
similar solar wind statistics. For the dawn and dusk flank data sets, we
check the solar wind statistics by plotting the probability density functions
of the corresponding solar wind parameters for each dawn and dusk flank (see
Figs. –) of each yearly subset to ensure they are
comparable between the data sets. The averaged densities are then used as
indicators of the density on each flank. The asymmetry (A) is then computed
as follows
A=100n∥n⟂-1.
Therefore, A in Eq. () represents the percentage of which the
average dawn density is larger than the dusk. The nature of the asymmetry can
be inferred from the polarity of A such that
A=dawn-favoured,if A>0,dusk-favoured,if A<0.
The asymmetry is computed for each annual data set to provide an estimate of
the asymmetry as a function of the year A(t).
(a) Solar wind magnetic field strength (i-1 to i-3), plasma velocity
(ii-1 to ii-3) and Alfvén Mach number (iii-1 to iii-3) over two solar
minimum cycles between 1995 and 2015. Each panel (i to iii) presents a
distribution i(1), running mean (2) and standard deviation σ (3). The
two curves in each distribution panel were compiled using the period of
1 January 2008–31 December 2010 and 1 January 2011–31 December 2014. The blue shaded region
indicates the range of years covered by the THEMIS mission. The black and red
lines in the time series plots show running averages of 30 days and 365 days,
respectively. (b) Solar wind ion number density (i-1 to i-3), dynamic pressure (ii-1
to ii-3) and ion temperature (iii-1 to iii-3) over two solar minimum cycles
between 1995 and 2015. The colour coding and the panel arrangement in this
figure are identical to that of (a).
Statistical data of ion number density collected in the dayside
magnetosheath. Panel (a) is a statistical map whereas presented in panels
(b) and (c) are the dawn–dusk asymmetry and cross sectional cuts, respectively.
Please note: 1. All densities are normalised by their individual upstream
counterpart. 2. The cuts and asymmetry are estimated over the fractional
distance range of 0 to 0.2, i.e. between the magnetopause and the black line.
3. Error-bars correspond to maximum variation of asymmetry and parameter
value from the standard error about the mean SEM=σ/n.
ResultsSolar wind measurements
Studies aimed at characterising the interaction between the solar wind and
planetary bodies are complicated by the dynamic nature of the processes
across a large range of temporal and spatial scales. For example, the
polarity of the IMF Bz component has a profound impact through magnetic
reconnection recorded as responses in geomagnetic indices
over time periods much less than 1 hour. On the other hand, the analysis of
long-term trends present in spacecraft observations suggest that much longer
(∼ 11 year) variations originating from changes in the solar activity
also produce a measurable effect (e.g., ).
Figure a and b
show the solar wind data between 1995 and 2015 over
two solar cycles. The probability density functions on the left panels (i1,
ii1, iii1) display the distribution of solar wind properties over two
separate intervals, first between 1 January 2008 and 31 December 2010 (black line), and
second, from 1 January 2011 to 12 December 2014 (red line). These intervals divide the
THEMIS mission covering the 2009 solar minimum and the following rising
cycle. The time series plots on the right columns of Fig. a and b are time series plots over the full 20-year interval mentioned
above. The THEMIS era is marked by the shaded blue region. The time series
plots present the mean of each parameter (i2, ii2, ii2) and its standard
deviation (i3, ii3, iii3) of each of the parameters. It is clear that the
majority of plasma parameters have some dependence on the 11-year solar
cycle. In general, B, V, ni, ρ and Ti appear to decrease
during the 2009 minimum whereas MA exhibits the opposite trend. The
standard deviation of parameters also follow similar trends. It should be
mentioned that σ was computed from the 20 min averages and
therefore excludes information about the high-frequency variations. The
following results characterise the driving of the ion density dawn
dusk-asymmetry based on the solar wind input parameters during the THEMIS
observation period shown as the shaded blue area. It is clear even from this
7-year interval that the solar wind parameters also vary over slow (yearly)
timescales; which may be reflected in the magnetosheath conditions.
Dawn–dusk asymmetry of ion density in the dayside magnetosheath as a
function of year from 2008 to 2014 (a). The grey and orange bars in panel
(a) represent the dawn–dusk asymmetry calculated using mean and median averages,
respectively. The blue solid and dashed horizontal lines in the same panel
show the mean and median dawn–dusk asymmetry for the entire interval between
2008 through 2014, respectively. The error bar limits are determined based on
the maximum variation of the asymmetry based on the standard error about the
mean SEM=σ/n. Panel (b) shows monthly mean averages of solar wind
conditions over the same time period as in panel (a).
The dayside magnetosheath ion density during typical conditions
Fig. shows the ion density measurements collected by THEMIS
between October 2007 and December 2014 in the dayside magnetosheath. Panel
(a) shows a statistical map which was compiled using bin sizes of 0.5 × 0.5 RE.
The dawn and dusk flanks correspond to the regions of YMIPM<0 and
YMIPM>0, respectively. The bar graph in panel (b) presents the dawn–dusk
asymmetry computed as described in Eqs. () and (). Since
the data coverage is sufficient, we computed the asymmetry as a function of
the angle from local noon A(θ) and no angular bins were excluded.
Please note that angles of 0 and 90∘ correspond to local noon
and the terminator, respectively. The grey bars show the mean estimates
whereas the orange bars are calculated from the median. The angular
resolution of each bar is 15∘ which is then incremented by a 50 %
overlap to form the next bin. As mentioned previously, the data in panels (b and c) include data only within 0.2FMIPM of the magnetopause. The blue
error-bars were calculated from the maximum possible variation of the
asymmetry resulting from the standard error of the mean. Panel (c) shows the
mean and median cross-sectional cuts of the data used to estimate the
asymmetry presented in panel (b). The error-bars here also originate from the
standard error within each bin. In general, the mean and median averages
yielded the same result, and the asymmetries provided are comfortably within
the calculated bounds of error. There is a dawn-favoured asymmetry which
ranges from around 1 % at local noon to approximately 19 % at the terminator.
In general, the asymmetry grows with increasing angular distance from the
subsolar region. The average asymmetry measured between local noon and the
terminator is approximately 8 and 10 % for mean and median averages,
respectively. Based on data collected in the central magnetosheath (not
shown), the asymmetry alternated between the dawn and dusk flanks, and so
these data proved inconclusive. Our data are therefore suggestive that the
dawn–dusk asymmetry is dependent upon the spatial location in which it is
measured throughout the magnetosheath. This spatial dependence is both a
function of the radial distance across the magnetosheath and the distance
from the subsolar region, i.e. A(FMIPM,θ).
Probability density functions of the magnetosheath ion number
densities normalised by their corresponding solar wind values. In all panels
the solid black line corresponds to the dawn flank whereas the dashed red
line indicates the dusk-side. Panels (a) and (b) correspond to longer
intervals surrounding and following the 2009 solar minimum. The remaining
panels (c–n) correspond to the distributions of 1-year intervals from January
2008 incremented by 6 months until July 2014. The intervals for each
distribution in panels (c–n) are labelled in the top right of each panel.
Panels (c–n) are plotted on identical x and y scales.
Dawn–dusk asymmetry of normalised ion number density in the dayside
magnetosheath as a function of Alfvén Mach number. Panels (a) and
(b) show the asymmetry calculated using mean and median averages,
respectively. Grey and orange bars represent the asymmetry calculated for two
separate time intervals of 2008 through 2010 and 2011 through 2014. In each
panel, the vertical orange lines indicate the mean and median values of
Alfvén Mach number whereas the horizontal solid and dashed green lines show
the mean and median asymmetries for each of the two time intervals,
respectively. Each error bar corresponds to the maximum variation of the
dawn/dusk asymmetry based on the standard error about the mean.
Annual variability of dawn–dusk asymmetry
Figure shows the dawn–dusk asymmetry of ion density between
2008 though 2014, A(t2008→2014). The grey and orange bars in
Fig. a indicate the annual asymmetry based on mean and median
averages, respectively. For comparative purposes, the solid and dashed blue
lines show the asymmetry calculated over the entire database. Each error-bar
is calculated in the same manner as that in Fig. b. A time
series plot of solar wind parameters for MA, |V|,
|B| and ni are shown underneath in panel (b) as indicated by
the grey, red, green and blue solid lines, respectively. These solar wind
parameters are 30-day averages of the entire OMNI data set and not limited to
the subset corresponding to the magnetosheath datapoints. We also checked
the corresponding upstream conditions for this subset, and they were very
similar to the full data set. What is striking in Fig. a is
the large asymmetry recorded from 2008 throughout mid-2010. These years
encompass the 2009 solar minimum, evidenced by the values of the solar wind
properties plotted in Fig. b below. The corresponding solar
wind parameters during 2008–2010 are the following: MA∼11, |V|∼400 km s-1, |B|∼3 nT and ni∼5 cm-3. During the
period 2011–2014, the asymmetry reduced to less than 5 %. An increase
during the period 2012–2013 does not reach the values recorded by THEMIS
during the solar minimum interval. Because the data presented here are
collected through an automated process in close proximity to the
magnetopause, it is important to ensure that the asymmetry is not
artificially created by outliers introduced by the inaccuracy of the
magnetopause model. Since the magnetopause is not an infinitesimally thin
boundary and its position is a complex function of the solar wind and
magnetospheric dynamics, outliers of magnetospheric origin close to the
magnetopause can be expected. For this reason, we plot the probability
density function of each yearly data set in Fig. which clearly
demonstrates that the core of each dawn-flank distribution is shifted to
higher density values than its dusk-side counterpart. In addition, this also
demonstrates that the asymmetry values (based on lower order moments) do not
result from comparing ill-matched distribution functions between each flank.
Dawn–dusk asymmetry Alfvén Mach number dependence
The data presented in Fig. describe the dawn–dusk asymmetry
as a function of the upstream Alfvén Mach number, A(MA). Since MA
changes from ∼ 11 during 2009 to ∼ 8.5 in 2013 (see Figs. and ), then it is logical to examine its role in
regulating the asymmetry. The grey bars in Fig. correspond to
measurements during 2008–2009 whereas the orange bars represent data during
2010–2014. These intervals differ slightly from the ones before, however
these provided adequate data for each interval while still splitting them
between solar minimum and the rising phase. The error-bars are calculated in
the same manner as explained previously. For reference, the average dawn–dusk
asymmetry for both intervals are indicated by the solid and dashed green
horizontal lines. The vertical orange lines mark the average MA for both
intervals. Both panels show the same data but the asymmetries were calculated
using mean (Fig. a) and median (Fig. b) averages,
respectively. Each bar corresponds to an average MA using a window length
3. This window is then incremented by 1.5 from 5 to 15. As before,
overlapping windows allow better resolution over the parameter range. The
total (dawn + dusk) amount of data present in the 2008–2009 and 2010–2014
data sets for each MA window were [11029, 17955, 23023, 21802, 16631,
11 467, 6705] and [24 501, 31 991, 30 122, 22 786, 16 308, 9929, 6383] points,
respectively for MA= [6.5, 8.0, 9.5, 11.0, 12.5, 14.0, 15.5]. The data
were relatively evenly distributed between the dawn and dusk flanks. What is
immediately obvious from Fig. is that around solar minimum, the
asymmetry appears to be inversely correlated with MA. What is puzzling is
that for the rising solar maximum period (2011–2015) there appears to be no
clear Mach number dependence, and the asymmetry is relatively unchanged over
the entire MA regime. These dependencies are true of both the mean and
median processed data. We varied the widths of the MA bins and obtained
the same result. A similar observation was also reported by
in which the MA dependence differed between their
temporal data sets; we will return to this point in the discussion.
Discussion
The aim of this investigation was to accurately quantify the dawn–dusk
asymmetry of ion density in the dayside magnetosheath and determine its time
dependence using THEMIS measurements. To compile our data sets, we extracted
magnetosheath observations from the complete THEMIS catalogue using our
magnetospheric data analysis tool (see ). We quantitatively
showed the asymmetry during typical solar wind conditions (Fig. ), which was shown to be more pronounced and clearer closer to
the magnetopause compared to the central magnetosheath. To study the annual
dependence of the asymmetry, we segmented the complete data set into 12-month
subsets for which we computed the asymmetry. To compensate for the varying
data coverage of the THEMIS probes over the time period, we confined our
statistical data collection to a fixed region such that comparable data
coverage was reached between the data sets. All data were collected on the
dayside magnetosheath for angles of 15∘≤θ≤75∘, with
respect to local noon (0∘) and the terminator (90∘). In
addition, we only included data collected close to the magnetopause within
20 % of the magnetosheath thickness (fractional distance range of 0≤FMIPM≤0.2, with respect to the magnetopause (0) and the bow shock
(1); see Fig. and Fig. in Appendix A). The
dawn–dusk asymmetry was then evaluated (see Eqs. and )
for each subset to determine the temporal variability (Fig. ).
As the earlier results on the asymmetry have been partially conflicting, it
is worth mentioning that the results are statistically significant and that
the distribution functions on each flank have statistically similar
properties (Fig. ). We also confirmed that the asymmetries do
not arise from different solar wind conditions during measurements made in
the dawn and dusk flanks (see Figs. and ) or from
inaccuracies in the magnetopause determination. If a mismatch of outliers
were present in the data sets, the mean and median would be skewed by longer
tails generated by the very low densities even if the distribution cores
would overlap; this was shown not to be the case. In addition, we also
ensured that the results were not driven by the size of the data sets. To
investigate this, we randomly sampled each subset so they were of equal size.
These data yielded remarkably similar results, indicating that the orbital
changes over the mission duration did not affect our results. As a final
check, we systematically varied the limits of FMIPM (from 0.1 to 0.3)
and θ, effectively changing the data selection region shown by the
orange region in Fig. by moving away from the magnetopause.
We found that even though we eliminated data very close to the magnetopause
(0<FMIPM<0.1) our conclusions were unchanged; suggesting magnetospheric
data were not responsible for driving the asymmetry. It is also noteworthy
that our estimates for 2008–2010 are remarkably similar to that of
using the same data set but different methodology;
suggestive of a robust result.
We showed that the magnetosheath ion density is higher on the dawn flank near
the magnetopause (Fig. b). We also examined the central
magnetosheath, but in this region no clear trends were identified. These
results are qualitatively and quantitatively similar to those by
who also examined the asymmetry using THEMIS data close to
the magnetopause. Both studies also suggest that the asymmetry grows as a
function of distance from local noon, in concert (but not necessarily driven)
with the increase in asymmetrical magnetosheath thickness. Our results are in
agreement with and , who also
reported higher densities on the dawn-side magnetosheath. The repeatability
of the asymmetry using several spacecraft (THEMIS, Cluster, and IMP 8) and
different processing methodologies strongly suggests that the asymmetry is of
physical origin as opposed to a manifestation from statistical or technical
means. It is also worth reiterating that the MIPM magnetosheath is similar to
the GSE magnetosheath during a Parker-spiral IMF; therefore these results
should be statistically relevant as this is the most common IMF orientation.
Over the THEMIS era, the maximum asymmetry was observed during and around the
solar minimum year 2009. From 2011 onwards, the asymmetry reduced and became
more ambiguous. To further examine the solar cycle dependence, we
investigated the role played by the solar wind Alfvén Mach number (see
Figs. and ), but these data did not suggest a clear
link between the two. Around solar minimum, the maximum asymmetry (22.5 %)
occurred during lower Alfvén Mach number (MA= 6–7) while a much lower
asymmetry (2.5 %) was observed for higher Alfvén Mach numbers (MA= 13–14). After 2010, there were no clear trends, and the asymmetry varied less
than 5 percentage points over the entire regime of Alfvén Mach numbers.
While the Alfvén Mach number likely plays a role in regulating the
asymmetry to some extent, there also seems to be other factors contributing
to its long-term variability. The Alfvén Mach number dependence can either
arise from the modification of the downstream plasma properties as indicated
by the Rankine-Hugoniot jump conditions , or by the
asymmetrical changes in the magnetosheath thickness . The
asymmetrical magnetosheath thickness alone has been shown to produce
dawn–dusk asymmetries in MHD simulations using the BATS-R-US code
. One further thing to note is that around
solar minimum, the standard deviation of the Alfvén Mach number was
enhanced (see Fig. iii-3), but the possible impact of this effect
on the asymmetry is unclear.
It is well established that solar wind–magnetosphere coupling undergoes
seasonal (semiannual) variations and therefore, by means
of feedback to the magnetosheath, could have an impact on magnetosheath
conditions close to the magnetopause. This is particularly important since
the THEMIS probes sampling of the dawn and dusk flanks (in the GSE & GSM
frames) are seasonally dependent. If these feedback processes were strong,
then even though solar wind data were comparable over 12-months intervals, an
asymmetry could manifest in the data set. However, we do not believe these are
responsible for the trends we observed. We computed the dawn–dusk asymmetry
of the dawn–dusk sampling, and by comparing this with the ion density
asymmetry variations, this did not offer any conclusive or clear relation. In
addition, this is a good time to re-iterate the arrangement of data in the
MIPM frame. Even during periods when THEMIS occupied only a single flank,
data would still be placed on the appropriate flank based on the IMF
orientation. Therefore, in general, both flanks are sampled over the entire
year (albeit not equally) which should reduce such seasonal effects. Finally,
since the magnetosphere is best described in a GSM frame, and we adopt the
MIPM frame in the magnetosheath, matching or quantifying such feedback
processes is not straightforward, and in the scope of the current
investigation, would be speculative at best. However, it is possible they may
play a role, and further work is needed to identify and quantify their
statistical impact on magnetosheath properties.
Temporal variation of the ion density dawn–dusk asymmetry was previously
reported by using magnetosheath observations from IMP
8, together with solar wind observations from ISEE 1, ISEE 3, and WIND. It
should be noted that the data analysed by were
collected between -20≤XGSE≤-15RE while our study focused
entirely on the dayside. In addition, the orbit of IMP 8 covered much higher
latitudes in which ZGSE varied between ±20REwhereas THEMIS is
closer to the equatorial plane. In spite of these differences, both studies
present strong evidence of a dawn-favoured asymmetry, which exhibit
significant variations as a function of the solar cycle phase. However, the
nature of the temporal dependence is not consistent between the two
investigations; covered the solar maximum during August
1978–February 1980 and the solar minimum during November 1994 to October
1997. In contrast to our results indicating the strongest asymmetry during
solar minimum, obtained a maximum asymmetry during the
solar maximum time period. In agreement with our results,
report a clearer dependence on Mach number during solar
minimum, and no discernible relationship to upstream parameters during solar
maximum. The authors also conclude that the Alfvén Mach number was not
responsible for driving the asymmetry differences between the solar cycle
maximum and minimum. While the final reason for the contradicting results of
the asymmetry remains unclear, a partial explanation could be that the plasma
conditions during the two minima and maxima periods were markedly different.
For example, dynamic pressure, density, velocity and magnetic field strength
are visibly lower during 2009 as opposed to 1996 (see Figs. and ), and the values during the 2011–2014 maximum period are at the
same level as during the minimum of 1996. Thus, although the ion density
dawn–dusk asymmetry does vary with the 11-year solar cycle, the behaviour of
the plasma properties during each solar cycle have to be taken into account.
With the increased sophistication and resolution of numerical models and
simulations , in conjunction
with the long-term monitoring of solar wind conditions, we should be well
equipped to resolve the drivers of this asymmetry.
To summarise: this paper shows strong evidence of a dawn-favoured asymmetry
of ion density throughout the dayside magnetosheath and that its magnitude
varies as a function of time. The physical processes leading to magnetosheath
dawn–dusk asymmetries
,
are fundamental in solar wind–magnetosphere coupling as they can directly
impact plasma transport processes at the magnetopause. Our results imply that
the role they play is time dependent and this needs to be taken into
consideration in the analysis of long duration data sets of both magnetosheath
and magnetospheric measurements. Furthermore, the present results are of
importance to numerical simulations attempting to accurately reproduce the
magnetosheath behaviour in response to upstream conditions. Open questions
remain on the detailed solar wind driver of the ion density asymmetry, and
further work is required to use the state-of-the-art numerical models to
resolve the causal relationships.
Conclusions
We have studied the dawn–dusk asymmetry of ion density in the dayside
magnetosheath and quantified its annual variability using THEMIS data. Our
conclusions can be summarised as follows:
Ion densities were higher on the dawn-side magnetosheath close to the
magnetopause (average ∼ 8 %) but this trend was unclear in the central
magnetosheath.
The asymmetry increased with angular distance from the subsolar point and peaked at the terminator (∼ 20 %).
Our results are consistent with previous studies reporting a dawn-favoured
asymmetry , but the solar cycle dependence in
our data is different from that reported by .
In our data set, the peak asymmetry (∼20%) was observed during
2009 coinciding with the solar minimum.
The asymmetry notably decreased and became inconclusive in the years
2011–2014 which took place after the 2009 minima.
We examined the role of the Alfvén Mach number and found a larger
asymmetry during low values at solar minimum, but for the years 2011–2014
we identified no clear trend.
We conclude that additional work is required to explain the solar cycle
relationship measured by different data sets. In addition, these results
should be of consequence to the regulation of viscous plasma transport
processes (such as KHI), since they are sensitive to the local plasma
properties in close vicinity to the magnetopause. Finally, magnetosheath
dawn–dusk asymmetries and their temporal dependencies should be kept in mind
for future investigations which include such processes, and in particular
when they utilise observations over a long period of time.
Data availability
The OMNI data were accessed by NASA/GSFC's Space Physics Data Facility's OMNIWeb. These data can be accessed at http://omniweb.gsfc.nasa.gov. THEMIS
data were accessed via http://themis.ssl.berkeley.edu/index.shtml. All data are available free of charge.
The annual data coverage of the THEMIS probes in the MIPM frame
between 2008 and 2014. The colour in each statistical map corresponds to the
number of points within each 0.5 RE square bin. Please note, these data are
plotted in a base 10 logarithmic scale. As discussed in the main body of the
manuscript, the 60∘ angular sector in which the data were used are
indicated in each panel.
Figure shows the yearly coverage of THEMIS magnetosheath
measurements in the MIPM frame. The colour scale represents the number of
points per 0.5 × 0.5 bin.
Figures , and show probability density
functions of the solar wind Alfvén Mach number, ion number density and
magnetic field strength, respectively. Each of the PDFs show the matching
solar wind conditions for each yearly dawn and dusk magnetosheath subset. The
purpose of these figures are to demonstrate that the dawn–dusk asymmetries
reported in the main manuscript are unlikely to originate from statistical
bias in the solar wind measurements between dawn and dusk. The important
comparison to make in each figure is not the variations as a function of
year, but the differences between the dawn and dusk PDFs for each year.
Yearly probability density functions of solar wind Alfvén Mach
number which correspond to magnetosheath data points on the dawn and dusk
flanks. The “2” in each yearly label indicates that the data set spans the
middle of that year to the middle of the next. e.g. 2012 2 = July 2012–July
2013.
Yearly probability density functions of solar wind ion number
density which correspond to magnetosheath data points on the dawn and dusk
flanks. The “2” in each yearly label indicates that the data set spans the
middle of that year to the middle of the next. e.g. 2012 2 = July 2012–July
2013.
Yearly probability density functions of solar magnetic field
strength (|B|) which correspond to magnetosheath data points on the dawn
and dusk flanks. The “2” in each yearly label indicates that the data set spans
the middle of that year to the middle of the next. e.g. 2012 2 = July 2012–July 2013.
Acknowledgements
The authors would like to acknowledge the support of the Academy of Finland
grants #288472 and #267073/2013. We acknowledge use of NASA/GSFC's Space
Physics Data Facility's OMNIWeb (http://omniweb.gsfc.nasa.gov) service, and
OMNI data. Authors would also like to thank the THEMIS instrument teams for
the use of their data.
The topical editor, E. Roussos, thanks two anonymous referees for help in evaluating this paper.
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