Solar Wind: Theory
Solar Wind: Theory
The supersonic outflow of electrically charged particles,
mainly electrons and protons from the solar CORONA, is
called the SOLAR WIND. The solar wind was described
theoretically by E N PARKER, in 1958. Parker’s theory was
verified experimentally by in situ observations by Soviet
and American spaceprobes. On its way to Venus, in 1962,
the MARINER II spacecraft observed the solar wind for 104
days. The average flow speed was more than 500 km s−1 .
This observation showed that the coronal plasma expands
into a supersonic solar wind as Parker had predicted.
Parker’s solar wind theory
Parker was familiar with the work on comet tails that
had been carried out in Germany in the late 1940s and
early 1950s under the leadership of LUDWIG BIERMANN (see
COMETARY TAILS). The ‘ionic’ comet tails were observed to
be pointing radially out from the Sun. This required a
radial force much larger than the force that the photons
from the Sun can provide, and Biermann concluded that
the ‘corpuscular’ radiation from the Sun may play an
important role in forming the radially pointing comet tails.
Parker based his solar wind theory on the fact that
the solar corona has a temperature of more than a million
kelvin. He argued that the electron density and the
pressure in such a hot atmosphere decrease rather slowly,
and the pressure, far from the Sun, is orders of magnitude
larger than the pressure of the interstellar gas surrounding
the solar system. According to Parker, this imbalance
between the pressure in the outer corona and the local
interstellar medium would lead to an expansion of the
coronal gas into a supersonic solar wind.
The coronal gas, at a temperature of one million kelvin
or more, is fully ionized; the number of neutral atoms is
very small. However, the thermal energy of the plasma is
not large enough to overcome the gravitation field and
escape from the Sun. In the inner corona the pressure
decrease is determined by gravity, so the gas is in static
equilibrium. However, an ionized gas at a temperature
of more than a million kelvin is a good conductor of
heat. Hence, the coronal temperature does not decrease
significantly with increasing distance from the Sun. The
thermal energy of the plasma is almost constant whereas
the energy needed to overcome the gravitational field
decreases. In the outer corona the thermal energy is larger
than the escape energy, and the gas can escape.
In Parker’s solar wind model, the energy transport
(in the form of heat conduction) from the inner corona
plays an important role for supplying the energy needed
to bring the plasma out of the solar gravitational field.
The electrons are much better at conducting this heat than
are the ions, owing to their smaller mass, but most of
the energy flux goes into increasing the energy of the
ions. This transfer of energy from electrons to ions is
achieved through an electric field. This electric field must
be consistent with the force and energy balance in the flow.
E N C Y C LO P E D IA O F A S T R O N O M Y AN D A S T R O P H Y S I C S
Parker described the coronal gas as a fluid. This
allowed him to take into account the coupling of electrons
and ions, without calculating the electric field explicitly. In
his first study he assumed that the heat conductivity is so
high that the coronal plasma has a constant temperature.
On the basis of this assumption he could illustrate how the
coronal plasma reaches supersonic speed around 5 solar
radii from the Sun, and expands into interplanetary space
with a steadily increasing flow speed. The equations also
allow for subsonic flow, but the pressure far from the Sun
in such solutions is almost the same as the pressure in a
static, isothermal corona. Hence, the subsonic solutions
do not describe an outflow that is in force balance with the
local interstellar medium.
In the supersonic flow the flow speed is larger than
the thermal motion in the gas, and the dynamic pressure
(associated with the directed motion) is larger than the
thermal pressure (associated with the random motion).
The dynamic pressure of the spherically expanding solar
wind decreases with distance from the Sun. At a distance
where the dynamic solar wind pressure is equal to the
pressure of the interstellar gas a shock is formed: the
flow speed is reduced, the density increases and most of
the flow energy is transferred into thermal energy. The
solar wind termination shock, at 100 AU or so (1 AU =
Sun–Earth distance), has not yet been observed, but the
Voyager 1 and 2 spacecraft may cross this boundary in a
not too distant future.
Parker’s solar wind theory has formed the basis for
our understanding of the expanding solar corona as well
as the outflow of ionized gas from galaxies and stars, and
other celestial bodies, and the outflow of light ions from
the polar regions of the Earth (the polar wind).
History
Studies of the Sun have a long history in many cultures,
but it was the studies of aurora and geomagnetic storms
that led to the studies of the solar wind.
The AURORA was part of the mythology and the life of
peoples living in the Arctic, but when Celsius and Hiorter
in Uppsala, Sweden, started systematic observations of
the ‘the magnetic needle’, in the 1740s, the correlation
between aurora and fluctuations in the geomagnetic field
was first found. Their collaboration with Graham in
London showed that geomagnetic fluctuations occurred
both in London and in Uppsala when aurora was seen in
Sweden. These findings seem to be the first to establish
the link between aurora and GEOMAGNETIC STORMS.
It took some time to find the common cause of aurora
and geomagnetic disturbances. The 11 year SUNSPOT CYCLE
was noticed by the German amateur astronomer Schwabe
in 1843, and several investigations showed a correlation
between auroral and geomagnetic activity, and sunspot
number. In the 1850s Broun found that geomagnetic
storms had a tendency to recur after 27 days, a time close
to the rotation period of the Sun, seen from the Earth.
On 1 September 1859, a large solar flare was observed by
Carrington and by Hodgson, and approximately 18 h later
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Solar Wind: Theory
there was a large geomagnetic storm with aurora at very
low latitudes. This event served as an indication that there
is a connection between solar ‘storms’ and geomagnetic
storms (see MAGNETOSPHERE OF EARTH: GEOMAGNETIC STORMS AND
SOLAR WIND ORIGINS). Throughout the last part of the 19th
century there were several studies of the possible link
between solar activity and geomagnetic storms. ‘At the
end of the century it was established that aurora and
geomagnetic storms should be regarded as manifestations
of an unknown cosmic agent of solar origin’, Kristian
Birkeland wrote in 1908.
One hundred years ago Birkeland set up an
impressive research program in Norway to investigate the
effects of charged particles from the Sun on the near Earth
environment. Together with his assistants he carried out
laboratory experiments, observations from field stations
around the world and theoretical studies. This was the first
comprehensive research effort in solar–terrestrial physics.
(Birkeland financed the research program with money he
earned from working with industry.)
Birkeland is best known for his Terella experiments,
where cathode rays interact with a magnetized sphere,
placed in a low-density gas. The experiment showed
that the cathode rays impacted on the sphere in regions
around the two poles, much like the auroral zones at high
latitudes. However, what is less known is that Birkeland
also used his magnetized sphere as a cathode to study the
emission of ‘electric corpuscules’ from the Sun. On the
basis of observations of continuous geomagnetic activity
at stations in the Arctic, Birkeland concluded that there is a
continuous flow of charged particles from the Sun. These
particles interact with all bodies in interplanetary space,
and the interaction with comets leads to the formation of
comet tails. To study this process in the laboratory he let
cathode rays impinge upon an anode of coal. On the basis
of many years of studies of the Sun and of geomagnetic
activity he was convinced that all stars, in the course of
their evolution, emit electrons and ions into space, and he
went on to speculate that most of the mass in the universe
is not in stars and nebulae but in ‘empty’ space.
At the time when Birkeland carried out his work it was
not known that the outer solar atmosphere, the corona, is
hot. It was first in the 1930s that the picture of a corona
with a temperature of more than a million kelvin began to
emerge. This was made possible by the development of
the CORONAGRAPH by BERNARD LYOT. By shielding the solar
disk with a circular plate it was possible to carry out
observations of the corona on a regular basis. Previously,
such observations could be made only during eclipses.
Lyot measured the width of the green line (5303 Å) to
0.9 Å (1 Å = 10−10 m). He suggested that the broadening
could be due to thermal motions, but the element emitting
the line was not known, so a temperature could not be
determined.
Grotrian argued, from the early 1930s, that the corona
is hot, but it was the identification of coronal lines,
as emission lines from highly ionized elements, that
established that the corona is hot. Edlén identified the
E N C Y C LO P E D IA O F A S T R O N O M Y AN D A S T R O P H Y S I C S
green line (5303 Å) as an emission line from iron atoms that
have lost 13 electrons, Fe XIV, and he showed that many
of the other coronal lines were emitted by highly ionized
elements. These elements cannot exist in the corona unless
the temperature is a million kelvin or more. With such a
high temperature one could describe the relatively slow
electron density fall-off and the widths of the coronal
spectral lines. However, it was not easy to understand
how it is possible to maintain a hot corona overlaying
a ‘cold’ CHROMOSPHERE. The rapid increase in temperature
from the chromosphere to the corona is consistent with a
heat conductive energy loss from the corona. This energy
loss must be balanced by coronal heating. Biermann
and Schwarzschild claimed that acoustic waves could
transport energy into the corona from the lower layers
in the solar atmosphere, whereas ALFVÉN suggested that
MAGNETOHYDRODYNAMIC WAVES (later called Alfvén waves)
may carry the energy necessary to heat the corona.
Already in 1941, Alfvén had published a model of a
hot static corona, extending out to 10 solar radii, and in the
early 1950s there were indications that the solar corona
extends even further into interplanetary space. Hewish
and Vitkevich observed fluctuations in radio signals that
pass through interplanetary space relatively close to the
Sun. They found electron density irregularities extending
out to at least 20 solar radii and that the ‘super corona’
changed over the sunspot cycle. Latitude variations
were also observed. These observations, together with
Biermann’s observations of ionic comet tails and Forbush’s
observations of the variations of the low energy cosmic ray
intensity over the sunspot cycle, were known when Parker
formulated his solar wind theory.
The solar wind
In 1958 Parker published a paper on the ‘dynamics of the
interplanetary gas and magnetic field’ in the Astrophysical
Journal. In this paper he presents a model of an expanding
solar corona; the coronal gas is allowed to flow out from
the Sun in the form of a solar wind. With this model
Parker could describe the transition from a quasi-static
inner corona to a supersonic solar wind with speeds of
several hundred kilometers per second at the orbit of
Earth. Parker used hydrodynamic equations, and he
considered an isothermal, spherically symmetric, radial
flow. This model suffers from several shortcomings, where
the most severe may be that the energy balance in the
flow is not addressed. However, with this very simple
model, Parker could illustrate how the hot coronal gas
expands and expels the interstellar gas from interplanetary
space. Parker’s solar wind model bears some similarities
to Bondi’s and McCrea’s models of accretion of interstellar
gas onto a central object. Formally, the two problems are
identical, but the physics of Parker’s solar wind model
is more difficult to understand than the physics of the
accretion flow.
The simplicity of the model invited criticism.
Chamberlain pointed out that the temperature in the flow
is determined by degradation of the heat conductive flux
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Solar Wind: Theory
and adiabatic cooling, whereas in the Parker model it was
taken to be constant. This also implied that the energy
per unit mass in Parker’s model is infinite. Chamberlain
argued that the energy per unit mass should be set to zero.
This assumption led to a low-speed ‘breeze’ solution of
the fluid equations. Parker included the energy balance in
the flow in his model and showed how heat is conducted
outward from the inner corona and converted into flow
energy by the pressure gradient force. This model could
also describe the supersonic solar wind.
Opponents argued that a fluid treatment of the
coronal gas is not valid, and that a kinetic approach should
be used. During the 1960s there were several attempts
to construct exospheric solar wind models. Many of
these studies gave results in better agreement with the
breeze solution than with the supersonic wind solution.
One reason some of the exospheric models gave low flow
speeds is that the electric field in the models was too small.
This electric field is set up by the plasma to balance the
pressure gradient force in the electron gas. In the fluid
model the electric field does not appear explicitly. In the
kinetic models this is not the case. Many of the exospheric
models used the electric field of a static corona. This is
smaller than the field in a subsonic–supersonic solar wind
and gives rise to a smaller acceleration of the protons than
is found in the hydrodynamic model.
In Parker’s model the solar magnetic field is ‘dragged
out’ by the solar wind. Because of the high electric
conductivity the electric field in the expanding gas is
small. As a consequence, the magnetic field is connected
to the source region at the Sun. When the Sun rotates,
the gas emitted from one region in the corona is situated
on a spiralling field line, and the direction of the field
depends on the polarity in the corona. In the ECLIPTIC,
the average magnetic field is in the ecliptic plane, and the
angle between the average field and the radial direction is
around 45◦ at the orbit of Earth.
It took only a few years before the solar wind
‘controversy’ could be settled. In situ observations of
the interplanetary plasma were carried out by the Soviet
spacecraft Lunik 2 and the American spaceprobe Explorer
10. However, it was not until the fall of 1962, after the
Mariner II observations of the solar wind, that Parker’s
solar wind model was accepted. On route to Venus,
Mariner II obtained 104 days of observations. It measured
an average solar wind flow speed of 504 km s−1 . The
proton density was around 5 cm−3 , much lower than the
density in a static corona. The average interplanetary
magnetic field showed a spiral structure very similar to
the model proposed by Parker.
The Mariner II flight took place during the declining
phase of the sunspot cycle. There were several high-speed
solar wind streams, with a recurrence period of 27 days
(seen from the Earth), during the mission, that gave rise
to recurrent geomagnetic storms with the same period.
Thus, the source of recurrent geomagnetic storms could be
identified as high-speed solar wind streams, but the solar
source regions of these streams, often called M-regions,
E N C Y C LO P E D IA O F A S T R O N O M Y AN D A S T R O P H Y S I C S
were not identified. It was 10 years later that ‘coronal
holes’, were first identified as the source regions of quasisteady high-speed solar wind; coronal holes are regions in
the corona, with unipolar magnetic field and low electron
density. During the declining part of the sunspot cycle
the polar regions develop into large coronal holes, and the
high-speed solar wind from these regions fills up a large
fraction of interplanetary space.
Solar wind from a given corona
When Parker formulated his solar wind theory he took the
inner solar corona to be a reservoir of particles and energy
for the outflowing solar wind. Therefore it can be argued
that he made the assumption that the energy balance in
the corona is between coronal heating and inward heat
conductive energy loss and that the energy loss in the
solar wind is not large enough to significantly change the
structure of the inner corona.
This model can describe the basic dynamics of the
corona–solar wind system quite well, i.e. the expansion of
the coronal gas into a supersonic solar wind. However,
Parker realized that the model could not describe the
quasi-steady high-speed solar wind streams that were
observed, mainly during the declining phase of the
sunspot cycle. He found that energy has to be added
beyond the inner boundary to speed up the flow. Many
years later Leer and Holzer showed that this energy has to
be deposited in the supersonic region of the flow; energy
deposition close to the Sun increases the solar wind particle
flux whereas energy deposition in the supersonic flow
increases the energy per unit mass in the flow and therefore
the flow speed.
There are several problems with a model where the
electron density and temperature in the inner corona are
taken to be independent of the solar wind outflow. If
we assume that the electron (proton) density at the inner
boundary is fixed, and let the temperature increase, the
solar wind proton flux increases rapidly. By varying the
temperature from one to two million kelvin the solar wind
proton flux changes by a factor of 100 or so. However, the
solar wind proton flux is observed to be fairly constant
whereas the coronal temperature shows considerable
variation. This inconsistency cannot be resolved in a
reasonable manner within the framework of a traditional
solar wind model. In order to obtain a more complete
description of the solar wind we must include the coronal
energy balance in the model.
Formation of the corona and acceleration of the
solar wind
In Parker’s theory the solar wind is a consequence of the
coronal heating process, so the inclusion of the coronal
energy balance would be a natural extension of his model.
This can be done by moving the inner boundary from
the corona into the upper chromosphere. A significant
energy flux is needed to balance the radiative losses from
the chromosphere, but the energy flux deposited in the
outermost part of the solar atmosphere, where the electron
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Solar Wind: Theory
density is very small, is not radiated away locally. The
temperature increases until some other loss mechanism
balances the heat input. In magnetically closed regions,
where the coronal plasma is trapped by the magnetic field,
inward heat conduction is the most significant energy loss,
whereas in regions where the magnetic field extends into
interplanetary space, and the coronal plasma is free to
escape, energy may also be lost in the solar wind. How
much of the energy that is lost as inward heat flux and
as solar wind energy flux may depend on the amplitude
of the energy flux and how and where this energy flux is
deposited in the corona.
Energy balance in a static corona
Let us first consider the energy balance in magnetically
closed regions, where the energy deposited as heat is lost as
inward heat conduction. To make the problem as simple as
possible we can consider a spherically symmetric corona,
with a ‘lid’ on it. This outer boundary does not allow
transport of either plasma or energy.
If this static corona is heated by an energy flux from
the Sun, say 100 W m−2 at the solar surface, and this
energy flux is deposited in the corona over a length
scale comparable with a solar radius, we find a coronal
temperature in the range 1.5–2.0 million K; a corona at this
temperature will lose 100 W m−2 into the TRANSITION REGION
in the form of an electron heat flux. However, the heat
conductive loss from the corona depends sensitively on
the coronal temperature; a corona at 0.5 million K loses
only 1 W m−2 as inward heat flux. Because of the very
strong temperature dependence of the heat conduction in
an ionized gas we find that a small heat input is sufficient
to maintain a rather hot corona.
In a corona where the electron (proton) density is
so low that the electrons and protons are not thermally
coupled, the proton heating must be balanced by heat
conduction in the proton gas. As there is no reason to
expect that the protons are heated less than the electrons,
the lower heat conductivity in the protons leads to a proton
temperature that is higher than the electron temperature.
The electron density in the inner corona is determined
by the pressure in the chromosphere–corona transition
region, and this pressure is determined by the heat
conductive flux from the corona. If we assume that the
radiative losses from the transition region are balanced
by the heat flux from the corona, we find that an inward
heat flux of 100 W m−2 corresponds to a transition region
pressure of pT R = 7 × 10−3 N m−2 . The pressure is
proportional to the heat flux, so a heat flux of 10 W m−2
corresponds to 7 × 10−4 N m−2 . A large inward heat flux
leads to a high transition region pressure, a large electron
density in the inner corona and strong collisional coupling
between electrons and protons. A small inward heat flux
is consistent with a low pressure in the transition region
and a low electron density in the corona.
E N C Y C LO P E D IA O F A S T R O N O M Y AN D A S T R O P H Y S I C S
Energy balance in coronal holes
In magnetically open regions the energy that is deposited
in the corona can be lost as inward heat flux and as solar
wind energy flux. Which of these two loss mechanisms is
the most important one may depend on how and where
energy is transferred to the coronal plasma. If most of the
energy is added to the electrons, as heat, a large fraction
may be lost as inward heat flux. However, if most of the
energy is added to the ions the inward heat flux may be
reduced significantly.
In order to investigate the energy balance of coronal
hole regions we can construct mathematical models
extending from the upper chromosphere, through the
transition region and corona, and far into interplanetary
space. The heating of the corona is specified through the
amplitude of the energy flux and how and where this
energy flux is deposited. These types of studies show that
heating of the very inner corona leads to a large inward
heat flux, whereas only a small fraction of the energy flux
is lost in the solar wind. Heating further out from the
Sun leads to a larger solar wind energy loss, but there is
a significant difference between models with electron and
proton heating.
In models with extended electron heating the inward
heat flux is a significant fraction of the energy flux, and
because of the high heat conductivity in the electrons the
temperature in the corona does not exceed 1.5 million K
for a reasonable heat input. The large inward heat flux
is consistent with a large transition region pressure and
a quite large electron density in the inner corona. The
solar wind emanating from such a corona does not reach
a high flow speed far from the Sun. A typical value is
300 km s−1 . In these models, where the electrons are
heated, a large fraction of the outward energy flux from
the corona is carried as electron heat conduction. This
energy is transferred to the ions via the polarization electric
field. This model has many similarities to the ‘classical’
solar wind model, where electron heat conduction from
the inner corona supplies the energy flux that is needed to
drive the solar wind.
If most of the energy is added to the protons, the
inward heat flux is much smaller, the transition region
pressure is low, the electron density in the inner corona
is low, the thermal coupling may be weak and the coronal
proton temperature may be quite high. In models with
extended proton heating most of the energy deposited in
the corona is lost in the solar wind. The density in the
corona and the solar wind proton flux are small, so the
energy per unit mass in the flow, and the flow speed far
from the Sun, can be quite large. In order to obtain flow
speeds of 800 km s−1 , measured in the high-speed wind by
the Ulysses spacecraft, a large fraction of the energy must
be deposited in the outer corona where the proton density
is so low that the heat cannot be conducted away. Then,
the heating leads to a high proton temperature and rapid
acceleration of the flow.
This type of model study of the corona–solar wind
system is limited by the assumptions made, but some
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Solar Wind: Theory
general results seem to emerge. High-speed solar wind
streams cannot be found in models where most of the
energy is deposited in the very inner corona. In models
with significant electron heating the inward heat flux is
too large, the coronal electron density is too high and
the coronal temperature is too low to generate high-speed
wind. The high-speed streams can be obtained in models
where most of the energy is deposited in the protons. The
energy may be deposited as heat or it may go into direct
acceleration of the flow, but none of these processes will
lead to a large flow speed unless the energy is deposited
sufficiently far out in the corona. Most of the energy flux
deposited in the corona, in these models, is lost in the solar
wind. As the asymptotic flow speed is comparable with
the escape speed of the Sun, the solar wind mass flux is
proportional to the the energy flux deposited in the corona.
Ulysses and SOHO
In the 1990s there have been two successful space missions
that have contributed significantly to our understanding
of the solar wind. The Ulysses spacecraft has observed the
solar wind at all solar latitudes (see SOLAR WIND: ULYSSES).
The first orbital period was during the declining phase of
the sunspot cycle. The observations showed a fast and
steady solar wind at latitudes larger than 20◦ . Close to the
ecliptic the flow speed was lower and more variable. The
solar wind mass flux showed little variation with latitude.
The fast solar wind streams originate in large coronal
holes. Observations of spectral lines from large polar
coronal holes, with instruments on board the Solar and
Heliospheric Observatory (SOHO), show that heavy ions
are warmer than protons which themselves are warmer
than the electrons. These observations support a model
of high-speed wind, with significant energy deposition in
the protons and not in electrons. The fact that we observe
heavy ions in the corona may be taken as an indication
that their temperature is high. If the temperature of heavy
ions were equal to the proton temperature, the density
of heavy ions would fall off so rapidly with heliocentric
distance that it would be difficult to see them in the corona.
However, does a high temperature tell us that a heavy ion
is preferentially heated?
Particle escape seems to be the most important energy
loss process for protons and heavy ions in coronal holes.
As the flux of escaping particles is an exponential function
of the thermal energy over the escape energy a modest
heating of heavy ions leads to a high temperature. If
the energy input per unit mass is the same for protons
and heavy ions the temperature should be proportional
to mass. However, if the ion temperature increases with
mass, more rapidly than proportional to mass, we can
conclude that the heavy ions are preferentially heated. So
far, only a few ion temperatures have been measured in
large coronal holes with the Ultraviolet Coronagraph and
Spectrograph (UVCS) on board SOHO, but observations of
spectral lines from oxygen atoms that have lost 5 electrons,
O VI, seem to indicate that there are heavy ions in the
corona that are preferentially heated.
E N C Y C LO P E D IA O F A S T R O N O M Y AN D A S T R O P H Y S I C S
Summary
Parker’s solar wind theory forms the basis for our
understanding of the interplanetary plasma.
The
dynamics of the solar wind is described by models
developed more than 40 years ago. The extension of these
models, which includes the coronal energy balance, has
led to a fairly good understanding of the acceleration of
the solar wind.
The solar wind is driven by the energy deposited in
the corona. This process is not understood. In the future
the emphasis will therefore be on trying to understand
coronal heating. A better understanding of how energy is
transported into the corona and transferred to the gas will
also give us a deeper understanding of how the solar wind
is accelerated.
Bibliography
Eather R H 1980 Majestic Lights (American Geophysical
Union)
Golub L and Pasachoff J M 1997 The Solar Corona
(Cambridge: Cambridge University Press)
Jokipii J R, Sonett C P and Giampapa M S (eds) 1997 Cosmic
Winds and the Heliosphere (Tucson, AZ: University of
Arizona Press)
Parker E N 1958 Dynamics of the interplanetary gas and
magnetic fields Astrophys. J. 128 664–76
Copyright © Nature Publishing Group 2001
Brunel Road, Houndmills, Basingstoke, Hampshire, RG21 6XS, UK Registered No. 785998
and Institute of Physics Publishing 2001
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Egil Leer
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