Introduction
Investigations of terrestrial ion outflow and escape and its dependence on
geomagnetic activity are important in order to obtain an increased
understanding of magnetospheric dynamics, but also from an atmospheric
evolution point of view. In the young solar system, the Sun is believed to
have been more active (e.g. ) with a
higher EUV flux, higher solar wind dynamic pressure, and a more intense and
active magnetic field (solar dynamo) due to faster rotation
. This indicates that the young Earth
experienced more intense geomagnetic activity compared to the present time
and hence high escaping fluxes of ionospheric ions
.
Ionospheric outflows typically originate at high latitudes, either along the
closed field lines of the auroral region, directly feeding the plasma sheet,
or along the open magnetic field lines of the polar cap and cusp. A review of
high-latitude ionospheric outflow is given by . Outflow
along open field lines will generally be put on trajectories leading
tailward, and its fate is to a high degree determined by the energisation
along the path. Cold (< 1 eV) H+ and O+ outflows can thus dominate
in both flux and density in the distant magnetotail lobes
. The cusps are regions which enable direct
interaction between the magnetosheath and the ionosphere, leading to
increased electron temperatures and higher ion upflows as a consequence in
the cusp ionosphere .
Ionospheric upflow is still gravitationally bound and needs further
energisation in order to reach the magnetosphere. The act of the mirror force
converts perpendicular energy into parallel energy for upflowing ions moving
into regions of weaker magnetic field, and thus the perpendicular heating of
plasma indirectly leads to acceleration along the field lines. Several
studies have investigated this and shown that wave–particle interaction is
effective in ion transverse heating over the whole range of altitudes in the
cusps
,
and the fate of the cusp ion outflow depends on the energisation of the ions
along its path.
One can consider the cusp O+ outflow to take one of three different main
paths (corresponding to the yellow illustrative trajectories in
Fig. ) depending on how effectively it is accelerated:
(1) low-energised ion populations will convect anti-sunward across the polar
cap and further downtail and towards the plasma sheet, where they end up on
closed field lines ; (2) sufficiently
energised ions will reach the plasma mantle with typical velocities high
enough to pass the tail X-line and consequently escape in the distant tail
; (3) highly energised ions may escape into the
dayside magnetosheath directly from the cusps
. Heavy (e.g. O+) energetic ions can
also escape to the dayside magnetosheath through magnetopause shadowing
. Escaping ions during a strong northward interplanetary
magnetic field may be brought back into the magnetosphere if dual-lobe
reconnection takes place . The fraction that might be
brought back is, however, a low percentage and its effect on the total escape
along route 3 is negligible .
An illustration of possible magnetospheric ion outflow trajectories:
(1) low-energy ion transport to the plasma sheet; (2) high-energy ion flows
in the plasma mantle leading to escape downstream in the tail; (3) high-energy ion escape directly from the cusp into the high-latitude dayside
magnetosheath. The red dashed line illustrates the magnetopause.
It is well known that the ion outflow rates are enhanced during
geomagnetically active times. For example, parameterised the
ionospheric ion outflow and found that the O+ outflow rate increased
exponentially with Kp as exp(0.5Kp). Other studies that have
shown a
clear correlation between O+ and geomagnetic activity are
, , and .
The O+ density close to the mid-latitude magnetopause was shown by
to also increase exponentially with Kp. A
consequence of increased ion outflow is an enhancement of the plasma feed
into the plasma sheet during geomagnetic storms
. The plasma sheet in turn
feeds the ring current and its relative O+ content and energy density
increases significantly with geomagnetic activity. For example,
showed that the O+ / H+ density ratio
increases exponentially with Kp (∼exp(0.17Kp)).
We will investigate and quantify the O+ escape rate and its dependence on
geomagnetic activity in two regions associated with ion escape: the plasma
mantle and the high-latitude magnetosheath. For the strongest geomagnetic
conditions, the statistics become sparse and we need to extrapolate our
results in order to say something about atmospheric loss during such events.
Specific cases of O+ outflow and escape during major geomagnetic storms
need to be investigated in the future as a complement.
Instruments and data criteria
In this section, we first describe the instruments that provide us with the
necessary data for our study, followed by descriptions of and criteria for
the data sets corresponding to the plasma mantle and the high-latitude
magnetosheath respectively.
Instruments
The study presented in this paper uses data obtained by instruments on-board
two spacecraft (SC1 and SC4) of the Cluster mission
, which consists in total of four spacecraft flying
in formation with an identical set of instruments on-board. The composition
distribution function (CODIF) spectrometer, described in detail by
, has mass resolution and provides ion distributions
for different species (for particle energies up to 38 keV q-1) from which
the ion moments have been calculated. The magnetic field data are provided by
the fluxgate magnetometer (FGM) , which in normal
mode has a sample frequency of 22.4 Hz. We are interested in the background
magnetic field and therefore use field data averaged over the spacecraft spin
period of 4 s, as is the ion moment data. The data set used for the plasma
mantle statistics was obtained by SC4 and covers 2001–2005. For the
high-latitude magnetosheath we use the data set compiled by
, in which times of high-energy O+ were visually
determined for 2001–2003 for SC1.
An example of a magnetopause crossing (∼ 09:18 UT) in the
southern high-latitude dayside hemisphere with Cluster 1, travelling from the
magnetosheath into the plasma mantle and then the polar cap. The first and
second panels show the H+ and O+ energy spectrograms respectively. The
third panel shows the magnetic field strength and its components. The time
intervals of the plasma mantle and magnetosheath data included in this
study (for this particular time interval) are marked with blue and red
rectangles respectively.
Plasma mantle
In order to study O+ flows in the plasma mantle, the corresponding data
need to be separated from polar cap and magnetosheath data.
Figure shows a high-latitude dayside passage of Cluster 1 from
the magnetosheath across the magnetopause at around 09:18 UT and into the
plasma mantle followed by a gradual decrease in ion flux intensity as it
moves into the polar cap. The top and middle panel show the energy
spectrograms for H+ and O+ respectively, and the bottom panel shows the
magnetic field strength and its components. The magnetosheath is often
characterised as a more fluctuant magnetic field compared to the field inside
the magnetosphere. More importantly, it is also characterised by very strong
H+ fluxes. These intense fluxes cause contamination in the O+ mass
channel, yielding false counts; this contamination can be tracked and
removed as described by . The polar cap is a region
associated with a low-energy ion environment in comparison with the plasma
mantle, which is filled with denser energetic mirrored solar wind plasma. As
a consequence, the plasma β number, defined as the thermal plasma
pressure over magnetic pressure, is typically significantly higher in the
plasma mantle. However, there is a gradual transition between the two
regions and no distinct β value that will separate them. In
statistical studies of the polar cap, data with the constraint that β is
less than 0.01 are used e.g..
Therefore, a constraint of β>0.1 in the dayside magnetosphere will
exclude typical polar cap data. Using a somewhat lower or higher limit for
β does not affect the results of this study, and therefore a
β>0.1 constraint is adopted. A blue rectangle in Fig.
marks the interval at which the criteria for the plasma mantle data associated
with this particular magnetopause crossing are fulfilled.
Distributions of β>0.1 data in the dayside magnetosphere,
covering 2001–2005. The left and right panels represent H+ and O+
temperatures and number densities respectively. The top panels (a, d) show all data, whereas the middle panels (b, e) show the data
subset corresponding to H+ T⟂ higher than
Tcut=1750 eV, marked with a vertical line in (a).
The lower panels show the data subset corresponding to H+ T⟂
lower than Tcut.
We also put regional constraints on the data set by removing the inner
magnetosphere
(RGSM=(YGSM2+ZGSM2)1/2>6 RE).
We also consider data within a range of -5<XGSM<8 RE.
This allows for good spatial coverage in the dusk–dawn extent as well
as sufficient data during the highest geomagnetic activities (high Kp).
The results and conclusions of the study presented in this paper are not very sensitive
to these exact limits, but they can be slightly altered.
However, the β and regional constraints are not sufficient. In
Fig. , the H+ (blue bars) and O+ (red) perpendicular
temperatures and number densities for β>0.1 are presented. Panels (a)
and (d) (top panels) show the distribution for all β>0.1 data.
In the H+ data there are two clearly distinct peaks: around a few hundred eV
and a few thousand eV for the temperature, and around 0.3 and 10 cm-3
for the density, suggesting two distinct plasma populations within our
data set. We investigate this by separating the data into two subsets of
T⟂(H+)<Tcut and
T⟂(H+)>Tcut with Tcut=1750 eV,
marked in panel (a) as a vertical black dot-dashed line. The data
corresponding to H+ perpendicular temperatures larger than
Tcut are shown in panels (b) and (e) (middle panels), and the data
corresponding to the lower H+ perpendicular temperatures are shown in
panels (c) and (f) (bottom panels). It becomes clear that the data separation
with respect to temperature also separates the density data, such that the lower
density population relates to the high temperature population and the higher
densities to the lower temperature population. This indeed confirms that
there are two distinct populations with clear differences in the H+
characteristics represented in the data set.
The H+ population with high temperatures and low densities is consistent
with the average characteristics of the plasma sheet presented by e.g.
and , whereas the population
of lower temperatures but higher densities is what we expect to observe in the
plasma mantle (e.g. ). The corresponding O+
data also reveal differences in the characteristics between the two regions.
For the plasma-sheet-like population, the O+ temperatures are about the
same as the H+ temperatures, and the O+ density is typically 1 order
of magnitude lower than the H+ density; this is consistent with plasma sheet
measurements presented by . In the plasma mantle,
however, the O+ temperature spans a large range, from a few tens of
eV up to 10 keV, but is in general considerably lower than for the
plasma-sheet-like population. The O+ density in the plasma mantle is
higher than the plasma sheet O+ densities, but still 1 to 2 orders of
magnitude smaller than the corresponding H+ densities, which is consistent with
plasma mantle observations .
For the purpose of investigating O+ fluxes in the plasma mantle, we
constrict the data with the condition T⟂(H+)<1750 eV in
order to exclude the plasma-sheet-like population. The number of data points
corresponding to the plasma mantle is just over 382 000, and the
distribution as a function of Kp is shown as blue bars in Fig. .
Moderate geomagnetic activity is most common, but some data for the highest
values of Kp are also available. The number of data points for periods of
Kp = 9 is below 100; this is too low to be visible in the chart due to the linear
scale, and we leave it out of the statistical analysis.
The high-latitude magnetosheath
O+ data in the high-latitude dayside magnetosheath covering 2001 to 2003
were identified by through the visual inspection of O+
energy spectrograms for ion energies larger than 3 keV in order to avoid
false counts due to the intense H+ fluxes in the magnetosheath
. The middle panel of Fig. shows such
typical magnetosheath high-energy O+ populations (marked with red
rectangles) in the interval up to the magnetopause crossing at ∼ 09:18.
Studies of such populations were presented by , who
reported that the populations had D-shaped velocity distributions, indicating
that they had passed through a rotational discontinuity at the magnetopause,
which is consistent with escape along open field lines. Only the months January to
June were considered when picking out these types of magnetosheath O+
populations as this period corresponds to a Cluster apogee in the dayside,
allowing for regular passages through the high-latitude dayside
magnetosheath. This data set allowed to estimate an
average total anti-sunward O+ flux of 0.7×1025 s-1,
corresponding to direct escape from the cusps. In this study, we will use the
same data set to study how the total escape from the cusps depends on the
geomagnetic activity. The distribution of the O+ observations in response
to geomagnetic activity is shown in Fig. , where the magnetosheath
data (roughly 92 000 data points) are binned (red bars) according to the
simultaneously measured Kp values. Unfortunately, no magnetosheath data for
conditions of Kp≥7 are present in the data set. For Kp = 6
we have very few data points, such that the O+ data are not visible in the
figure due to the choice of a linear scale.
Observations
Based on the data of the plasma mantle and magnetosheath described in
Sect. , average fluxes scaled to ionospheric altitudes in order
to cancel any altitude dependencies are calculated as a function of Kp. If
the total particle flux is assumed to be conserved along a magnetic flux
tube,
the local particle flux F can be scaled to an ionospheric altitude as
FI=FBI/B, where BI is the ionospheric
magnetic field strength set to 50 000 nT and B is the locally measured
field strength. The result is shown in Fig. and reveals a clear
increase in flux with increased geomagnetic activity for both the plasma
mantle (blue) and the high-latitude dayside magnetosheath (red). The error
bars represent the standard deviations and are slightly shifted in the
figure for visibility. Note that results are obtained only for Kp ≤ 8
and ≤6 for the plasma mantle regime and the magnetosheath respectively.
The fluxes in the plasma mantle typically increase by 1.5 orders of magnitude
between quiet times and times of the most extreme geomagnetic conditions. The
scaled O+ flux in the magnetosheath is in principle the same as in the
plasma mantle, at least up to Kp = 6.
We will estimate the total O+ flux in the plasma mantle and magnetosheath
separately as functions of Kp using the method implemented by
when calculating the average O+ escape flux from
the cusp into the high-latitude magnetosheath. They divided the data into
spatial segments aligned with the magnetosheath high-latitude flow, yielding
an escape cross section when also considering an effective outflow region
with a dusk–dawn extent of 106∘ at the highest latitudes. The flow is
typically tangential to the magnetopause, and therefore a magnetopause shape
model, introduced by , was used to define the
stream-aligned segments in which O+ occurrence rates and average fluxes
were used to calculate the total O+ escape rate. A much more detailed
description of the method is given by . We note that
the most significant plasma mantle outflows are at high latitudes as one
would expect, and it turns out that the same dusk–dawn extent as observed for
the magnetosheath is suitable for the plasma mantle calculations.
The plasma mantle bulk flow is similar to the magnetosheath flow in terms of
the
magnetopause-aligned flux. The method requires, however, good spatial
coverage with significant data points. The most common are times with Kp = 3,
followed by Kp = 2 and 4 and then Kp = 1 and 5 (Fig. ), and
the method works fine for data corresponding to these Kp indices
individually. However, the amounts of data for Kp = 0, 6, 7, and 8 are too
small. We therefore combine the data for Kp = 0 and 1 and let the corresponding
escape rate correspond to the average Kp value for this subset. For the
highest geomagnetic activity conditions (Kp = (6, 7, 8)), the combined
number of data points is even lower. This can be seen in
Fig. , where the spatial coverage of the plasma mantle
O+ data is shown for different Kp values. However, the spatial coverage
for this high geomagnetic activity subset is still decent and the same method
can be applied. In the figure, the data are divided into bins of 1RE×1RE for which average O+ fluxes (defined by
the colour bar) and bulk velocities (arrows) are determined in order to
visualise the spatial coverage and bulk flow. An arrow for reference is in
the upper right corner in the first plot (Kp = (0, 1)) and has a length
corresponding to 100 km s-1. For clarity, we note that for the
estimate of the total escape, we consider the average within each
magnetopause tangential segment rather than the averages of the bins.
For the magnetosheath we use the same data set as .
The data cover, as already mentioned, a smaller range of geomagnetic
activity and we calculate the O+ escape rate for Kp = (0, 1),
Kp = 2, Kp = 3, and Kp = (4, 5, 6).
Distribution of O+ observations over Kp for the plasma mantle
(blue) and dayside magnetosheath (red) respectively.
The average O+ escape rates are shown in Fig. as blue
(plasma mantle) and red (magnetosheath) solid lines with circles and squares
respectively. As expected, the O+ escape flux increases with higher
geomagnetic activity for both escape paths, but with plasma mantle total
O+ flux typically a factor of 3 higher than in the magnetosheath. The black
dashed line is the least-squares fit to the plasma mantle data, and its
formula will be presented and discussed in Sect. . For quiet
times (Kp ≈ 1), the total O+ escape rate (considering the
plasma mantle route) is ∼6×1025 s-1, whereas for the
highest geomagnetic activity conditions (average Kp ≈ 7) the rate
is ∼1026 s-1.
As seen in Fig. , there are large variations in the
measured scaled fluxes for a given Kp value. Therefore, the estimated values
given above, for which the whole range of flux values were considered, can be
seen as average O+ escape rates. To get an estimate of how high (and low)
the escape rate may be for a given geomagnetic condition, we instead only
consider the flux data over the 80th (below the 20th) percentile within each
segment. The results give an upper and lower estimate of the range of escape
rates for a given geomagnetic condition, also shown in Fig. as
coloured areas; light blue is the plasma mantle route and light red is the
dayside magnetosheath route. The upper and lower estimates typically have the
same dependence on Kp as the average escape rates, but are significantly
higher or lower, which is consistent with the large standard deviations observed in
the scaled fluxes (Fig. )
Discussion
Kp dependence
The total O+ escape from the terrestrial magnetosphere as a function of
geomagnetic activity for two different escape routes (via the plasma mantle
and subsequent escape in the far tail and via open magnetic field lines
directly from the cusp into the high-latitude magnetosheath) has been
statistically investigated and quantified. As expected, there is a clear
increase in the O+ escape with increased Kp index for both escape routes,
as shown in Fig. . In the same figure, the least-squares fit of
O+ escape via the plasma mantle (superscript pm) as a function of Kp is an
exponential function given by
ΦO+pm(Kp)=3.9×1024exp(0.45Kp),[s-1].
The average O+ flux measured for the plasma mantle (blue circles)
and in the magnetosheath (red squares), scaled to an ionospheric reference
altitude as a function of Kp with error bars representing the standard
deviations.
The spatial distribution of plasma mantle O+ flux in cylindrical
coordinates, (Xgse,
Rgse=(Ygse2+Zgse2)1/2), for periods of
different geomagnetic conditions: Kp = (0, 1), Kp = 2, Kp = 3,
Kp = 4, Kp = 5, and Kp = (6, 7, 8). The colour bar defines the
average flux intensity, and the arrows represent the average O+ bulk
velocity.
The O+ escape directly from the cusp into the high-latitude magnetosheath
(superscript ms) is typically a factor of 3 smaller than the escape via the
plasma mantle for a given geomagnetic activity condition, such that
ΦO+ms≈ΦO+pm/3.
These expressions can be extrapolated to predict average escape fluxes for
the very strongest geomagnetic storms: ΦO+pm(Kp=9)=2.25×1026 s-1 and a total escape of 3×1026 s-1, if also considering the escape directly from the cusp
into the dayside magnetosheath. Note that this value is an average including
both hemispheres, i.e. the summer and winter hemispheres, because the Cluster
trajectory with a 90∘ inclination was nearly north–south symmetric
during 2001–2005.
The exponential dependence of O+ escape on Kp (Φ∝exp(0.45Kp)) is similar and consistent with an O+ outflow study by
, who mapped and integrated high-invariant latitude
(> 56∘) O+ outflows using data obtained by Dynamics Explorer 1
(DE1) for an O+ energy range of 0.01–17 keV. They found an ∝exp(0.50Kp) relation for a Kp range from 0 to 6. The total
O+ flux in their study was about a factor of 2.3 larger than the results
presented in our study, given a certain condition on the geomagnetic
activity. It makes no real sense to further compare our results with those of
, since the lower limit of the invariant latitude of
56∘ includes the whole polar cap, cusp, and auroral region.
calculated the total O+ outflow for the cusp region
specifically, also using data provided by instruments on-board DE1, and
obtained a flux rate of 2×1025 s-1 without investigating
any dependence on geomagnetic activity. This outflow is similar to the escape
rates that we present in this study for average geomagnetic conditions,
suggesting that a significant part of the O+ cusp outflow will eventually
escape, in principle via route 2 or 3 (Fig. ).
EUV and seasonal effects
According to , , and
, EUV flux is another leading factor that controls the
escape flux, with much higher EUV flux associated with the summer hemisphere
than the winter hemisphere. Figure shows a wide range of
escaping flux for a given Kp value, with 1 to 2 orders of magnitude
difference between the lower (below the 20th percentile) and the upper (over
the 80th percentile) values. This is largely influenced by the influx of the
solar EUV to the ionosphere
.
The average O+ escape rates for the plasma mantle (solid blue
line and circles) and the dayside magnetosheath (solid red line and squares)
as a function of Kp. The dashed black line is a least-squares fit to the average escape rates for the plasma mantle.
The thin dot-dashed lines correspond to estimated upper and lower O+ escape rates in the plasma
mantle (blue area) and the magnetosheath (red) based on the highest and lowest flux values
observed under the different geomagnetic conditions.
A solid estimate including the EUV dependence must include an estimation of
the EUV influx to the ionosphere and the solar zenith angle, but such a
formulation is model-dependent since we need to assume an effective latitude.
Instead, we use the upper value in Fig. as an estimate of the
escape rate from the summer hemisphere.
Escape rate in the past
By considering the highest 20 % of the values instead of all data points, the
O+ loss rate from the cusp and plasma mantle becomes as high as
1027 s-1 for Kp = 9. This O+ escape rate is 2 orders of
magnitude larger than observed for typical average conditions
(). Considering the evolution
of G-type stars (or all main sequence stars), the young Sun was much more
active than it is today in terms of higher emission of EUV radiation, faster
solar wind, and a faster rotation, with more active sunspots and stronger IMF
as a consequence due to a more effective solar dynamo
e.g.. Conditions during major
geomagnetic storms are currently sometimes considered as a proxy for
normal conditions in the ancient solar system , and
therefore Eq. () and the corresponding expression for the
high-latitude magnetosheath can be used to estimate atmospheric loss during
ancient epochs. However, a possible issue is that the relative abundance of
oxygen in the atmosphere has changed considerably over time
e.g., and consequently the
question arises of how this change affects the O+ outflow and escape over time. Measurements at Mars and Venus, which have CO2-dominant atmospheres,
show
oxygen-dominated upper ionospheres and outflows and references
therein. This indicates that the relative abundance of oxygen
and even the composition of the atmosphere as a whole will not significantly
affect the upper ionosphere. Therefore the upper ionosphere of the ancient
Earth was most probably O+-dominated independent of the oxygen abundance
in the atmosphere, allowing us to extrapolate our result for present Earth to
ancient times.
If Kp(t) is the average geomagnetic activity as a function of
time, then the total loss L of O+ from a time t0 until the present day
tn can be expressed as
L=∫t0tnΦ(Kp(t))dt,
with Φ given by Eq. (). We do not know how the average Kp has
changed explicitly over time, but we can make rough estimates of the total
O+ escape. Assuming that Kp=10 four billion years ago and
decreasing linearly with time (exponential decay in terms of geomagnetic
deviation in nT), the total O+ loss becomes ∼4.8×1017 kg,
corresponding to 40 % of today's total oxygen mass in the atmosphere.
investigated an X17.2 flare on 28 October 2003
during the “Halloween period” and concluded that
the conditions served as a proxy for the Sun at the age of 2.3 billion years.
Using this as a reference time and Kp = 9 as associated with the
Halloween events and integrating over four billion years, we get a total
O+ loss that is 1.3 times the total oxygen mass in the atmosphere today.
Both estimates give a total O+ loss of the same order as atmospheric
oxygen content at the present time. These estimates assume that all ions detected
in the O+ mass channel of the CODIF spectrometer are indeed O+.
However, given the finite mass resolution of the instrument (m/Δm∼5-7), N+ ions could also be part of the population. N+ ions have
been observed to take substantial proportions in the outflow during very
active periods . A better
understanding of and insight into the solar and geomagnetic conditions on
geological timescales is needed in order to further investigate this
matter and is left for future consideration. A systematic survey of the
outflows using high mass-resolution instrumentation, as with the recently
proposed ESA ESCAPE mission, would allow a detailed investigation, a
separation of the O+ and N+ escape rates, and a study of their links to the solar
and magnetospheric activity.