# What influence does the Interplanetary Magnetic Field have on Planetary Orbits?

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CONTEXT

The equation $$F_D=frac{GMm}{D^2}$$ is a standard equation in Newtonian gravitation. It describes the centripetal force exerted, by a source mass$$M$$, on a target particle of mass $$m$$ located at distance $$D$$. Here $$G$$ is Newton's Universal Constant of Gravitation.

The Non-Newtonian Apsidal Rotation Anomalies ( aka "Perihelion Precession", first observed by LeVerrier for Mercury) observed in planetary orbits are explained by General Relativity. For example the formula $$F_D=frac{GMm}{D^2}*left(1 + frac{3GM.P}{C^2}frac{1}{D^2} ight)$$ where $$P$$ is the semi-latus rectum of the elliptical orbit of the target and $$C$$ is the speed of light.

However it is known (e.g. Wells 2011 ) that Apsides Rotation anomalies (in the context of perihelion precession, very similar to those from GR) can also be generated from an alternative, hypothetical, model by invoking a supra-Newtonian inverse-distance-cubed force, independent of $$P$$; as per the following equation:- $$F_D=frac{GMm}{D^2} *left(1 + frac{K}{D} ight)$$ where $$K=frac{6.GM}{C^2}$$. At the distance of Earth the additional force is ~ $$6*10^{-11}$$ times the Newtonian force.

According to wikipedia:-

The Sun's Dipole Magnetic Field of 50-400 μT (at the photosphere) reduces with the inverse-cube of the distance to about 0.1 nT at the distance of Earth. However, according to spacecraft observations the Interplanetary Magnetic Field at Earth's location is around 5 nT, about a hundred times greater (see Figs 11,12 in Svalgaard & Cliver 2010 ). The difference is due to magnetic fields generated by electrical currents in the plasma surrounding the Sun.

A paper by Laine & Lin 2011 considers long-term angular orbital momentum transfer through electromagnetic interactions between Stellar Magnetic Fields and close-in Super Earths.

The source of energy is the differential motion between the (close-in Super-Earth) planet and the magnetosphere of its host star. The Lorentz force on the planet and its host star leads to an evolution toward a state of synchronous rotation. Inside the corotation radius, planets tend to lose angular momentum and migrate inward and the opposite trend occurs outside the corotation radius. Consequently, planets inside corotation migrate inward and those outside corotation migrate outward.

Their analysis is too far beyond my current knowledge of physics for me to extrapolate to the case of the modern Solar System. But it does suggest to me that electromagnetic interactions between the Sun and its rocky satellites may lead to transfer of angular momentum from the former to the latter.

QUESTION

(a) How does the Interplanetary Magnetic Field (IMF) vary with distance from the Sun (e.g. does it decay in strength with distance in proportion to $$1/D^3$$ ?, what is the orientation of $$B$$?,… )

(b) what quantitative effects does the present Solar System IMF have on the orbits of the planets and asteroids?

UPDATE

After a bit more trawling through wikipedia I guess that the problem can be modelled (initially) in terms of the force between two magnetic dipoles. The force exerted on $$m_2$$ is given by:- $$F = frac{3mu_0}{4pi |r|^4}((hat{r}*m_1)*m_2+(hat{r}*m_2)*m_1-2hat{r}(m_1. m_2)+5hat{r}((hat{r}*m_1).(hat{r}*m_2))$$ where $$r$$ is the relative position vector, $$m_1,m_2$$ are the magnetic moment vectors and $$mu_0$$ is the vacuum permeability or magnetic constant.

An alternative, equivalent formula given by Yung et al, equation 37, 1998 for the force exerted by $$m_1$$ on $$m_2$$ is:-

$$F = frac{3mu_0 |m_1| |m_2|}{4pi |r|^4}left( hat{r}(hat{m_1}.hat{m_2}) +hat{m_1}(hat{r}.hat{m_2}) +hat{m_2}(hat{r}.hat{m_1}) -5hat{r}(hat{r}.hat{m_1}).(hat{r}.hat{m_2}) ight)$$

Note that the magnitude of the dipole-to-dipole force varies in proportion to $$1/r^4$$.

The dipoles will also exert torques on each other. The torque exerted by dipole 1 on dipole 2 is given by:- $$au = m_2 * B_1$$.

Magnetic Dipole Moments for some Solar System Objects

0 3.5 * 10^29 N-m/T Sol

1 3.8 * 10^19 N-m/T Mercury

2 8.0 * 10^17 N-m/T Venus

3 7.98 * 10^22 N-m/T Earth

4 2.1 * 10^18 N-m/T Mars

5 N/A Ceres

6 1.55 * 10^27 N-m/T Jupiter

7 4.6 * 10^25 N-m/T Saturn

8 3.0 * 10^24 N-m/T Uranus

9 1.5 * 10^24 N-m/T Neptune

### Classification of the Sun's Major Planets

The major planets are classified either as inferior, with an orbit between the sun and the orbit of Earth (Mercury Mercury,
in astronomy, nearest planet to the sun, at a mean distance of 36 million mi (58 million km) its period of revolution is 88 days. Mercury passes through phases similar to those of the moon as it completes each revolution about the sun, although the visible disk varies
in astronomy, 2d planet from the sun it is often called the evening star or morning star and is brighter than any object in the sky except the sun and the moon. Because its orbit lies between the sun and the orbit of the earth, Venus passes through phases like those of
. Click the link for more information. ), or as superior, with an orbit beyond that of Earth (Mars Mars,
in astronomy, 4th planet from the sun, with an orbit next in order beyond that of the earth. Physical Characteristics

Mars has a striking red appearance, and in its most favorable position for viewing, when it is opposite the sun, it is twice as bright as
, in astronomy, 5th planet from the sun and largest planet of the solar system. Astronomical and Physical Characteristics

Jupiter's orbit lies beyond the asteroid belt at a mean distance of 483.6 million mi (778.
in astronomy, 6th planet from the sun. Astronomical and Physical Characteristics of Saturn

Saturn's orbit lies between those of Jupiter and Uranus its mean distance from the sun is c.886 million mi (1.
, in astronomy, 7th planet from the sun, at a mean distance of 1.78 billion mi (2.87 billion km), with an orbit lying between those of Saturn and Neptune its period of revolution is slightly more than 84 years.
in astronomy, 8th planet from the sun at a mean distance of about 2.8 billion mi (4.5 billion km) with an orbit lying between those of Uranus and the dwarf planet Pluto its period of revolution is about 165 years.
in astronomy, a dwarf planet and the first Kuiper belt, or transneptunian, object (see comet) to be discovered (1930) by astronomers. Pluto has an elliptical orbit usually lying beyond that of Neptune.
. Click the link for more information. , long regarded after its discovery in 1930 as the ninth planet, was gradually recognized as a Kuiper belt, or transneptunian, object (see comet comet
[Gr.,=longhaired], a small celestial body consisting mostly of dust and gases that moves in an elongated elliptical or nearly parabolic orbit around the sun or another star. Comets visible from the earth can be seen for periods ranging from a few days to several months.
. Click the link for more information. ), and in 2006 was reclassified by astronomers as a dwarf planet. Any dwarf planet beyond the orbit of Neptune is now classified as a plutoid.

On the basis of their physical properties the planets are further classified as terrestrial, gas giant, or ice giant. The terrestrial planets&mdashMercury, Venus, Earth, and Mars&mdashresemble Earth in size, chemical composition, and density. Their periods of rotation range from about 24 hr for Mars to 249 days for Venus. The gas giants&mdashJupiter and Saturn&mdashare much larger in size and have thick, gaseous atmospheres consisting mostly of hydrogen and helium and low densities. The ice giants&mdashUranus and Saturn&mdashare not as large as the gas giants, have atmospheres that are not as thick, and consist mostly of elements that are heavier than helium and exist in the form of compounds such as water, ammonia, and methane that have freezing points near or above 100°K they also have lower densities than the terrestial planets. The periods of rotation for the giant planets range from about 10 hr for Jupiter to 15 hr for Neptune. This rapid rotation results in polar flattening of 2% to 10%, giving the planets an elliptical appearance.

### Recognition of the Planets

#### Identification of the Solar Planets

The ancient Greeks applied the term planet to the five major planets then known&mdashMercury, Venus, Mars, Jupiter, and Saturn&mdashas well as to the sun and moon all these bodies were observed to move back and forth against the background of the apparently fixed stars and to shine with a steady light. In the Ptolemaic system Ptolemaic system
, historically the most influential of the geocentric cosmological theories, i.e., theories that placed the earth motionless at the center of the universe with all celestial bodies revolving around it (see cosmology).
. Click the link for more information. the earth was thought to lie at rest in the center of the universe while the planets moved about it in a complicated scheme of circles. The heliocentric, or sun-centered, Copernican system Copernican system,
first modern European theory of planetary motion that was heliocentric, i.e., that placed the sun motionless at the center of the solar system with all the planets, including the earth, revolving around it.
. Click the link for more information. , introduced in the 16th cent., viewed the planets, including the earth, as revolving about the sun the moon was viewed as a natural satellite satellite, natural,
celestial body orbiting a planet, dwarf planet, asteroid, or star of a larger size. The most familiar natural satellite is the earth's moon thus, satellites of other planets are often referred to as moons.
. Click the link for more information. of the earth. At the start of the 17th cent. Johannes Kepler Kepler, Johannes
, 1571�, German astronomer. From his student days at the Univ. of Tübingen, he was influenced by the Copernican teachings. From 1593 to 1598 he was professor of mathematics at Graz and while there wrote his Mysterium cosmographicum (1596).
. Click the link for more information. refined the Copernican model by showing that the orbits of the planets around the sun were elliptical rather than circular.

With the development of the telescope other planets became visible. Uranus, detected in 1781 by Sir William Herschel, was the first planet discovered in modern times. Neptune was discovered in 1846 as the result of a mathematical analysis of the irregularities in the motion of Uranus, and the dwarf planet Pluto, whose existence was predicted from the perturbations of both Uranus and Neptune, was found in 1930. In addition to the major planets, the telescope has revealed thousands of minor planets, or asteroids, which orbit the sun in a bandlike cluster between Mars and Jupiter the largest of these, the dwarf planet Ceres Ceres
, in astronomy, a dwarf planet, the first asteroid to be discovered. It was found on Jan. 1, 1801, by G. Piazzi. He took three distinct observations on the basis of these the mathematician Gauss calculated Ceres' orbit with such accuracy that it was found one year later
. Click the link for more information. , was also the first discovered (1801), and was regarded as a planet for many years. Additional minor planets have been discovered since 1992 beyond the orbit of Neptune in the Kuiper belt at least one of these transneptunian objects, Eris, has a diameter (1,500 mi/2,400 km) slightly larger than that of Pluto. In 2016 researchers reported that peculiarities of the orbits of a number of the most distant known Kuiper belt objects would be best explained by the existence of a ninth planet with about 10 times the mass of Earth and an orbit that is 20 times farther from the sun than that of Neptune.

#### Discovery of the Extrasolar Planets

Although speculation concerning the existence of extrasolar planets (or exoplanets) and planetary systems dates back to antiquity, it was not until the last decade of the 20th cent. that astronomical tools and techniques made their detection possible. Because stars are so distant and bright and an extrasolar planet, no matter how large, is relatively small and dim, it cannot be seen or photographed directly. Its presence may be inferred from a periodic wobble in the spectrum of a target star's frequencies. This wobble, produced by gravitational influences, causes tiny shifts in the star's frequencies that are caught by telescopes and analyzed to yield information on the body affecting the star. Another technique that proved fruitful in 1999 is the use of a telescope to record the dimming of light from a star when a planet's orbit carries it between the star and the earth.

Spurred on by the discovery of three bodies orbiting a pulsar by radio astronomers in 1992, the first extrasolar planet orbiting a sunlike star was detected in 1995. Located in the constellation Pegasus Pegasus
, in astronomy, northern constellation lying SW of Andromeda and SE of Cygnus. It is named for the mythological winged horse Pegasus. The constellation is easily recognized by the Great Square formed by the bright stars Markab (Alpha Pegasi) at the southwest corner,
. Click the link for more information. , about 40 light-years from earth, the planet&mdashcalled 51 Pegasi&mdashhas about half the mass of Jupiter and is so close to the star that it has a surface temperature of about 1,000°C and completes its orbit in only four days. By the end of the decade, more than two dozen extrasolar planets were detected, including three orbiting the star Upsilon Andromedae&mdashthe first multiplanet extrasolar planetary system&mdashthat were discovered in 1999. By 2020 the number of known exoplanets exceeded 4,100, and more than 700 multiplanet systems had been identified. It is now believed that planets are more common than stars, that some 40% of sunlike stars have planetary systems planetary system,
a star and all the celestial bodies bound to it by gravity, especially planets and their natural satellites. Until the last decade of the 20th cent., the only planetary system known was the solar system, which comprises the sun and the surrounding planets,
. Click the link for more information. , and that roughly one quarter of all stars have potentially habitable planets.

The CoRoT (launched 2006) and Kepler (launched 2009) space telescopes, especially the latter, significantly increased the number of known possible exoplanets. Kepler had by early 2011 identified more than 50 near-earth-sized planets that were located in the habitable zone. In 2014, Kepler scientists announced the discovery of a habitable-zone planet (Kepler 186f) with a radius estimated to be 10% larger than the earth's, that orbited a cool dwarf star with four other planets because of its size, Kepler 186f was believed to be a rocky planet with the potential to have liquid water.

Super-Earths (1.2𔂿.9 times the size of the earth's radius) or sub-Neptunes (1.9𔃁.1 times bigger than the earth's radius) make up the overwhelming majority of exoplanets discovered by Kepler planets in this range are not found in solar system. Of the discovered rocky planets that are much larger than the earth, many are up to 10 times more massive (one, Kepler 10c, is 17 times as massive). Other known extrasolar planets are giant gas planets with masses ranging from one half to five times that of Jupiter, the largest of the solar planets. Many exoplanets have orbits that are highly elliptical rather than only slightly so, are closer to their star than the earth is to the sun, and have orbital periods ranging from three days to more than four years. In addition, the ages of the extrasolar planets differ from one another and from that of the solar planets the oldest planet, discovered in the globular cluster M4 in 2003, is believed to have been formed 12.7 billion years ago, within a billion years of the origin of the universe and 8 billion years before the earth. Because these data are so different from that of the solar planets, planetary scientists are rethinking the accepted theories of planetary formation.

### Bibliography

See P. Halpern, The Quest for Alien Planets: Exploring Worlds Outside the Solar System (1997) J. R. Gribbin and S. Goodwin, Empire of the Sun: Planets and Moons of the Solar System (1998).

## Cometary Physics

### VIII.D The Ion Tail

Combining the plasma measurements at comet Giacobini–Zinner on the tailward side of the comet at a cometocentric distance of 7800 km, we might produce a schematic model for the cometary magnetic field configuration as follows (see Fig. 36 ):

FIGURE 36 . The general nature of the magnetic field configuration as observed by the ICE spacecraft at comet Giacobini–Zinner. The kinky structure of the magnetic field lines at the “magnetopause” is generated by a current layer required to couple the slow-moving cometary plasma with the external solar wind.

The field draping model is basically confirmed except for the detection of the formation of a magnetosheath at the ion tail boundary. The magnetic field strength in the lobes of the ion tail is on the order of 60 nT. This relatively high field may be explained in terms of pressure balance at the tail boundary, where the total external pressure of the cometary ions was as large as the solar-wind ram pressure.

A thin plasma sheet with a total thickness of about 2000 km and a width of about 1.6 × 10 4 km was found at the center of the ion tail. The peak electron density and an electron temperature were determined to be ne = 6.5 × 102 cm −2 and Te = 1.3 × 10 4 K by the plasma wave instrument.

The plasma flow velocity gradually decreased to zero at the ion tail center. A significant amount of electron heating was seen between the ion tail and the bow shock.

We expect similar morphologies to be found in the plasma environment of comet Halley after appropriate spatial scalings. Snapshots by spacecraft flyby observations, however, do not reflect the many time-variable features seen in the ion tails of bright comets. For instance, the structure of the ion tail is often characterized by the appearance of a system of symmetric pairs of ion rays, with diameters ranging between 10 3 and a few 10 4 km, folding toward the central axis. When the ion rays are first formed, with an inclination of about 60 ° relative to the central axis, the angular speed is high with a linear speed ≈ 50 km s −1 . But near the end of the closure, the perpendicular speed is extremely low, no more than a few kilometers per second. Time-dependent MHD simulations have been applied to these phenomena with emphasis on the effect of temporal changes of the interplanetary magnetic field. No satisfactory answers to the formation of the ion rays have yet been found. A similar situation exists for the large-scale ion-tail disconnection events that had been suggested to be result of magnetic field reconnection.

## Magnetic field lines

Magnetic Field Lines Get Tangled as Sun Rotates
The Sun is not solid. It is a huge ball of plasma, which is a lot like a gas. Some parts of the Sun spin faster than other parts. Places near the Sun's equator spin fastest. The Sun's poles spin more slowly.

When a spacecraft breaks away from the influence of the Earth's magnetic field into interplanetary space, it finds there a weak magnetic field. The field may be weak, but it extends over huge distances, and can have important effects. From the observed direction of interplanetary magnetic field lines, .

Magnetic Field Lines
A magnetic field has both a strength and a direction at each point in space. For example, at each point on Earth, the magnetic field -- and thus a compass -- points in a particular direction, roughly toward the north.

Imaginary lines that indicate the strength and direction of a magnetic field. The orientation of the line and an arrow show the direction of the field. The lines are drawn closer together where the field is stronger.

Main article: Field line
Compasses reveal the direction of the local magnetic field. As seen here, the magnetic field points towards a magnet's south pole and away from its north pole.

loop through the solar atmosphere and interior to form a complicated web of magnetic structures. Many of these structures are visible in the chromosphere and corona, the outermost layers of the Sun's atmosphere.

that twist up to form solar flares occasionally become so warped that, like rubber bands under tension, they snap and break, then reconnect at other points. The gaps that form no longer hold the sun's plasma on its surface. Freed, the plasma explodes into space as a coronal mass ejection (CME).

. [H76]
Flux Unit
(a) Unit of flux density. 1 f.u. = 10-26 watts per square meter per hertz (see Jansky). [H76]
(b) In radio astronomy energy is usually measured in units of 10-26 W m-2 Hz-1.

Wind Up. Because the Sun spins faster at the equator than near the poles, the magnetic fields in the Sun tend to wind up as shown, and after a while make loops. This is an idealized diagram the real situation is much more complex.

converge at the magnetic poles, so the charges get focussed and a narrow cone of non-thermal radiation is beamed outward. If the beam sweeps past Earth, you see a flash of light.

The cusps mark the division between geomagnetic field lines on the sunward side (which are approximately dipolar but somewhat compressed by the solar wind ) and the field lines in the polar cap that are swept back into the magnetotail by the solar wind.

in a coronal hole extend out into the solar wind rather than coming back down to the Sun's surface as they do in other parts of the Sun. Coronal interstellar gas High-temperature interstellar plasma made visible by its X-ray emission.

Fraser: And there's, you know, those

coiling out of the sun - it's a really powerful analogy in my mind, and you can see these amazing videos taken by some of the recent spacecraft - the SDO mission, right? You can see these videos, time-lapse videos of the surface of the Sun.

In the neighborhood around pulsars there are charged particles (mainly electrons) that tend to travel along the

Their helical motion around the

of the Galaxy causes their distribution to appear isotropic (they are detected equally in all directions), even though astronomers believe that they originate in the shocks of supernova remnants.

emerge from the interior through one member of a sunspot pair, loop through the solar atmosphere, then reenter the solar surface through the other spot.

Much like a rubber band snaps suddenly if twisted too much, the distorted

break and reconnect to oppositely directed lines, releasing tremendous energy.

After a rotation of about 270 the

begin to twist about themselves and can diffuse through the conductor, disconnecting from the toroidal loop (C). At this stage, the rising loop is oriented in a meridian plane with the field pointing in the same direction as the original field--i.e., poloidal.

A magnetic field tends to lock into material (think of how iron filings sprinkled onto a sheet of paper on top of a magnet line up, mapping out the pattern of

Scientists had expected to find that the sun's

, which are stretched out into space by the solar wind, would keep charged particles originating in solar flares near the equator confined to a fairly narrow band near their origination point.

, generating an electric current. Though small compared to the tidal heating, this current may carry more than 1 trillion watts. It also strips some material away from Io which forms a torus of intense radiation around Jupiter (picture 23).

The particles trapped in the belts spiral along the

and bounce backwards and forwards between reflection points encountered as they approach the magnetic poles. The electron motion produces SYNCHROTRON RADIATION, a characteristic emission from the individual planetary systems.

Coronal Mass Ejections (CME's) are giant bubbles of gas whose structures are dictated by

that are ejected from the sun over the course of a few hours. Even though the corona has been viewed for thousands of years via solar eclipses, CME's were not known about until the space age.

radiating out from the cool star companions get twisted and deformed as they spiral in towards each other, generating the extra activity through stellar wind, explosive flaring and star spots.

Scientists have previously seen the explosive snap and realignment of tangled

on the sun - a process known as magnetic reconnection - but never one that had been triggered by a nearby eruption.

It has north and south magnetic poles like the Earth, and the

(above sunspots) can break and erupt into Solar Flares. These flares are a part of Solar Storms, and can sometimes be in the X-ray and gamma ray portion of the spectrum. The chart below demonstrates X-ray classifications of these flares, to offer clarity for Radio Blackouts.

We know this because when undersea volcanoes erupt, the iron minerals in the lava crystallize along the Earth's

. As the sea floor spreads out away from the rift zones, we get an excellent history of the Earth's magnetic field.

But when the IMF field lines and the geomagnetic field lines are not parallel, they tend to interact, creating a path for the solar wind particles to leak into the upper atmosphere, the most spectacular consequence of which are the auroral displays (aurora borealis and aurora australis) over the higher latitudes.

Discrete aurorae often display

or curtain-like structures, and can change within seconds or glow unchanging for hours, most often in fluorescent green. The aurora borealis most often occurs near the equinoctes. The northern lights have had a number of names throughout history.

Io's orbit cuts across Jupiter's

, turning the moon into a powerful electric generator. The electric current of 3 million amperes takes path to Jupiter's surface, creating lightnings in its upper atmosphere.
Four largest moons of Jupiter: The Galilean moons
Callisto .

Also, because of the solar wind, sometimes the

reconnect on the side of Earth opposite the Sun. They snap back like an elastic band, sending large amounts of energy back towards Earth's poles. This phenomenon, called magnetic reconnection, creates stunning displays of aurora.

An aurorae happens when these charges particles enter the

in a planet's atmosphere.
On Earth, we have charged particles hitting our magnetic field from the solar wind. However, the Cassini spacecraft showed that, like Jupiter, some of Saturn's aurorae are unaffected by the solar wind.

Auroras are caused by high energy particles from the solar wind that are trapped in the Earth's magnetic field. As these particles spiral back and forth along the

. NASA is asking scientists and engineers for ideas for a mission to Europa, which has an ocean of liquid water beneath its icy crust. The agency is also seeking idea for other missions, including one to capture a small asteroid and bring it close to the Moon. [NASA/ESA] .

Voyager 1 saw evidence of a transition from closed

to a magnetotail on the antisolar side of Jupiter. Although such a magnetotail was never in serious doubt, its existence had not been confirmed before.

In this case, the twisting, or rotating

have twisted the material shown here in false color into something resembling a DNA molecule, hence the name, Double Helix Nebula. Only part of this structure has been imaged, with the section shown here about 80 light years in extent.

Flux: A measure of the density of

over a surface area. Flux/area is proportional to the average force on a charged particle on the surface.

Archontis and colleagues modelled this process using three dimensional computer simulations and found that as

draw closer to each other due to the motion of plasma in the Sun's lower atmosphere, they "reconnect" and build a new magnetic flux system, called a plasmoid.

Light from the jets is produced by synchrotron radiation, as energetic electrons spiral around a magnetic field. The

impose an order on the radiation (or at least a portion of it), causing the electric field vectors to be aligned.

Illustration of a pulsar showing charged particles moving along the

, which create lighthouse like beams of intense electromagnetic radiation (purple). Credit: NASA
SpaceBook home
This Chapter .

An atmospheric escape process in which ions flow along open polar

. It is analogous to the solar wind, and particles can attains final velocities slightly larger than the speed of sound.

As these bursts of solar wind rise above the Sun's corona, they move along the Sun's

and increase in temperature up to tens of millions of degrees. These bursts release up to 220 billion pounds (100 billion kg) of plasma. CME's can disrupt Earth's satellites.

The blue light comes from electrons whirling at nearly the speed of light around

from the neutron star. The neutron star, like a lighthouse, ejects twin beams of radiation that appear to pulse 30 times a second due to the neutron star's rotation.

Coronal holes are closely associated with those regions on the Sun that have an "open" magnetic geometry, that is, the

associated with them extend far outward into interplanetary space, rather than looping back to the photosphere.

The protons spiral around and down the

of the Earth and penetrate into the atmosphere near the magnetic poles increasing the ionization of the D and E layers. PCA's typically last anywhere from about an hour to several days, with an average of around 24 to 36 hours.

Ionization processes in the atmosphere of Titan - II. Electron precipitation along

p. 965
G. Gronoff, J. Lilensten and R. Modolo
DOI: .

Coronal Hole - A low density, dim region in the Sun's corona. Coronal holes occur in regions of open

where gases can flow freely away from the Sun to form the solar wind .

Magnetosphere: The region around Earth dominated by Earth's magnetic field. In this region, the Earth's

guide the motions of charged particles (ions and electrons).

Arc: a simple slightly curving arc of light.
Band: an irregular shape with kinks or folds.
Patch: region resembling a cloud.
Veil: a very large area of uniform light.
Ray: straight vertical shaft aligned with Earth's

.
Picket Fence: a row of several rays.
Curtain: resembling folds of drapery.

The auroral emission is caused by electrically charged particles striking atoms in the upper atmosphere from above. The particles travel along Jupiter's

. This is the same mechanism that causes auroras on Earth.

Aurora emissions, similar to Earth's Northern Lights, have been observed at Jupiter's poles and appear to be related to material from Io that spirals along

eventually falling into Jupiter's atmosphere.

It spewed a coronal mass ejection (CME) whose leading edge swept past Earth around noon Thursday Eastern Standard Time (17:00 UT), buffeting the Earth's magnetic field and filling it with energetic charged particles. When such particles come streaming down the Earth's

The quakes are so strong that they can break

, releasing a burst of gamma-ray energy. Originally confused with gamma-ray bursts, which only occur once at any given location (because afterwards, there is nothing left to continue to make more bursts).

causing the aurora penetrated into the Martian atmosphere, creating auroras below 100 km above the surface, Earth's auroras range from 100 km to 500 km above the surface. Magnetic fields in the solar wind drape over Mars, into the atmosphere, and the charged particles follow the solar wind

Now a rapidly spinning strong magnetic field can produce radiation as particles are accelerated along the

. Thus the magnetic fields produce beams of radiation along the magnetic pole directions. As the poles sweep by our line of sight we see the beam momentarily leading to a pulse of radiation.

The charged particles in the gaseous coma get pushed away by the Solar wind along the

that point outward away from the Sun, and they form a separate "ion tail," or gas tail.

by a perfectly conducting fluid. If a magnetic field is somehow established in a fluid with infinite conductivity, a motion of the fluid will carry the field lines and hence the field energy with it.

## 3 Effects From Upstream Drivers and Crustal Fields

In this section, we examine five separate drivers: solar wind dynamic pressure (pdyn), Martian crustal field orientation with respect to the direction to the Sun, and IMF strength (Bimf), cone angle (θimf), and clock angle (Φimf). The IMF clock angle is defined in section 2.1. The cone angle is defined as the angle between IMF and MSO/MSE +x directions. It has been shown that the global crustal field distribution and the rotation of the planet have collective effects on the Martian plasma and magnetic environment (Fang et al., 2015 , 2017 ). For simplicity, here we only consider the SZA of the strongest crustal field location (178°E, 53°S Langlais et al., 2004 ). In this study, one orbital-averaged IMF is used to organize the data from each spacecraft orbit into MSE, which brings in an uncertainty related to the time variability of IMF. In order to take the IMF variability into consideration, we define a relative standard deviation (RSD) for the IMF data from one spacecraft orbit as , where SBx, SBy, and SBz are the standard deviations for the three components of the upstream magnetic field measurements during one spacecraft orbit and Bimf is the magnitude of the orbital averaged IMF. We define an additional parameter Δαimf as the direction change in degrees between two subsequent orbital-averaged IMF (the angle between two IMF vectors). RSDimf represent IMF variability during the upstream measurements from one spacecraft orbit, while Δαimf represents IMF variability between two subsequent spacecraft orbits.

We will compare the spatial distributions of sheath magnetic field strengths and clock angle departures in the cylindrical (x, ρ) coordinate system with different upstream conditions and different crustal field locations. The |ΔΦ| and B distributions are compared using the same method as described in section 2.2. To examine the effects from each driver separately, we will carefully constrain other drivers as well as the IMF variabilities RSDimf and Δαimf. For all the comparisons discussed in the subsections, we have checked the data coverage in the MSE (y, z) plane to make sure the spatial asymmetries as discussed in section 2.2 do not affect the results.

### 3.1 Effects From Solar Wind Dynamic Pressure

We find from MAVEN upstream data that the solar wind dynamic pressure is not only positively correlated with IMF magnitude (see also Dong et al., 2017 ) but also has a slight positive correlation with IMF variabilities RSDimf and Δαimf. In order to examine the effects from solar wind dynamic pressure, it is important to exclude the influence from different IMF conditions. Thus, we constrain Bimf using its 25th and 75th percentiles as 1.74 nT < Bimf < 3.47 nT and constrain the IMF variabilities as RSDimf < 0.5 and Δαimf < 90°. With these constraints, we have examined that all other parameters have generally consistent distributions between the high and low solar wind dynamic pressure conditions sorted by the median value 0.596 nPa(see Figure S2 in the supporting information).

Figure 4 shows that higher solar wind dynamic pressures lead to both larger clock angle departures and larger magnetic field strengths in the sheath. According to previous studies (e.g., Brain et al., 2005 Edberg et al., 2009 Ramstad et al., 2017 ), higher dynamic pressures tend to push plasma boundaries closer to the planet. Thus, the stronger compression of the draped field inside the BS will result in higher sheath field strengths. Besides, within a compressed smaller region inside the BS, the distortion of the draping field lines will be greater, resulting in larger clock angle departures. In addition, higher solar wind dynamic pressure also leads to stronger interactions with the Martian atmosphere. The processes like ion pickup and acceleration can drive perturbations in the sheath magnetic field, which can also increase the clock angle departures.

From Figure 4f, we can see that near the empirical BS the magnetic field strengths under the high dynamic pressure condition are actually smaller. It is likely an effect from the BS variation, with the BS being pushed closer to the planet under the high dynamic pressure condition. The data selection method partially based on the empirical boundaries as described in section 2 will result in some upstream data misidentified as in the magnetosheath. Under the high dynamic pressure condition, when the real BS tends to be inside the empirical BS, some data near the empirical BS in Figure 4d are actually upstream IMF data and are weaker than the real sheath magnetic field in Figure 4e, which leads to the blue pixels near the BS in Figure 4f.

### 3.2 Effects From IMF

#### 3.2.1 IMF Magnitude

As mentioned section 3.1, the IMF strength is positively correlated with solar wind dynamic pressure. The upstream data also indicate that weaker IMF is usually associated with higher variabilities (RSDimf and Δαimf). This is reasonable: a perturbation with the same magnitude would cause a greater change in the field direction for weaker IMF. Therefore, to investigate the effects from IMF magnitudes, we apply constraints on both solar wind dynamic pressure: 0.427 nPa < pdyn < 0.979 nPa based on the 25th and 75th percentiles, and IMF variabilities: RSDimf < 0.5 and Δαimf < 90°. Then we separate the data by the median value (2.45 nT) of Bimf into weak and strong IMF conditions. With these constraints, the other parameters have similar distributions between the strong and weak IMF conditions (see Figure S3 in the supporting information).

From Figures 5a and 5b, it seems that under strong IMF condition |ΔΦ| is larger on the dayside and nightside, but weaker near terminator. However, the differences are small in most regions. A Kolmogorov-Smirnov test (0.56) did not show statistically significant difference between the two data sets from Figures 5a and 5b. Thus, we do not consider it as a clear dependence of the clock angle departures on IMF magnitudes.

As expected, stronger upstream IMF results in significantly stronger draped field in the sheath as shown in Figures 5d–5f. However, if we normalize the sheath magnetic field by the upstream IMF magnitudes as shown in Figures 5g–5i, the trend is reversed. From Figure 5i we can tell that in the sheath region the normalized field strength is slightly smaller under strong IMF conditions except for the region near the empirical BS. This means that the sheath field strengths do not vary proportionally with the upstream IMF. As discussed in Halekas, Brain, et al. ( 2017 ), stronger IMF implies a lower Alfven Mach number, which leads to a smaller compression factor in the sheath.

The deep red pixels near the empirical BS in Figure 5i are likely an effect from the BS location variation similar to that discussed in section 3.1. Edberg et al. ( 2010 ) have shown that the Martian BS varies with upstream magnetosonic Mach number (Mms). With other upstream parameters constrained, weaker IMF means larger Mms, which will cause the BS to move inward. As a result, some data near the empirical BS in Figure 5h are actually upstream IMF data, which are significantly weaker than the sheath field near the BS in panel (g).

#### 3.2.2 IMF Cone Angle

For IMF cone angles, we consider two conditions: IMF is more perpendicular or more parallel to the solar wind direction (MSO/MSE −x axis). We separate the data into the cases of |90° − θimf| < 45° (perpendicular IMF) and |90° − θimf| > 45° (parallel IMF). We have examined the distributions of other parameters between the two data sets, which are similar to each other, except for the clock angle (see Figure S4 in the supporting information). For the parallel IMF condition, MSO north/southward IMF (45° < Φimf < 135° or 225° < Φimf < 315°) tends to occur more frequently. In the next section, we will discuss the effects from IMF clock angle, which is unlikely to make a significant difference by itself with other parameters constrained.

The effects from perpendicular and parallel IMF are clear and straightforward as shown in Figure 6. The sheath magnetic field is stronger under the perpendicular IMF condition, while the clock angle departures are smaller. This is the same mechanism as the difference between the quasi-perpendicular and quasi-parallel BS as discussed in section 2.2. For the perpendicular IMF condition, the whole dayside BS is a quasi-perpendicular shock, where the field lines are smoothly draped and compressed in the sheath. For the parallel IMF condition, the whole dayside BS is a quasi-parallel shock, where the draped field lines are more drastically distorted, noisier, and without a steep increase of the field strength at the BS.

#### 3.2.3 IMF Clock Angle

A previous study by Brain et al. ( 2006 ) based on the MGS data at

400 km indicates that the westward IMF (with a negative y component in MSO) tends to drive more perturbations in the draped field than the eastward IMF (with a positive y component in MSO). With proper constraints on other drivers, we also compared the eastward and westward IMF cases and did not find a significant difference between them. It is possible that the effects discussed in Brain et al. ( 2006 ) are not significant in the magnetosheath. According to our analysis of the sheath magnetic field data, the biggest difference is found between the east/westward (E/W) IMF (Φimf > 315°, 0° < Φimf < 45°, or 135° < Φimf < 225°) and the north/southward (N/S) IMF (45° < Φimf < 135° or 225° < Φimf < 315°) cases. Meanwhile, we also find that the N/S IMF cases are usually associated with parallel IMF conditions |90° − θimf| > 45° and higher IMF variability between two subsequent orbits (Δαimf). The former correlation is due to the natural IMF directions. The latter correlation is also understandable: since N/S IMF cases are significantly rarer than E/W IMF, it is more likely for the N/S IMF to change directions between the measurements from two spacecraft orbits. To exclude the effects from IMF cone angle and variability, we have applied the constraints: |90° − θimf| < 45° and Δαimf < 60°. Although there is still a significant difference in the Δαimf distributions as shown in Figure 7 (see Figure S5 in the supporting information for the distributions of other parameters), these constraints are almost the strictest ones that can be applied without losing decent data coverage since the N/S IMF cases are relatively rare.

From Figure 8, we can tell that the clock angle departures are clearly smaller under E/W IMF conditions but there is no significant difference in the magnetic field strengths. One possible reason for the different effects from E/W and the N/S IMF can be that the N/S IMF is more likely to interact with the crustal fields through reconnections (Harada et al., 2018 ), since the strongest crustal fields tend to have more north/southward components (Acuna et al., 1999 ). However, in section 3.3 we will see that the crustal fields actually do not make a significant difference in the sheath field clock angle departures, consistent with the model results by Fang et al. ( 2018 ), which shows that the interaction with crustal fields are not the reason for the difference between N/S and E/W IMF. The difference in the IMF variability as shown in Figure 7 is another possible reason. The higher IMF variability between two subsequent orbits associated with N/S IMF cases means larger uncertainties in the orbital averaged upstream IMF data when applying it to the sheath region, which will lead to larger difference between the clock angles of the sheath field and IMF as in shown Figures 8a–8c. We have also noticed that the difference as shown in Figure 8c becomes smaller as we tighten the constraints on Δαimf from no constraints to <90° and then to <60° (not shown here). Therefore, it seems that the most likely reason for the difference between the E/W and N/S IMF effects is the higher variability (Δαimf) associated with N/S IMF.

### 3.3 Effects From Crustal Fields

Previous studies have shown that the crustal fields can affect plasma boundary locations (e.g., Brain et al., 2005 Crider et al., 2002 Edberg et al., 2008 Fang et al., 2015 , 2017 ) and ion escape (e.g., Fang et al., 2017 Ramstad et al., 2016 ) at Mars and can also interact with IMF (Harada et al., 2018 ). In this section, we investigate whether the crustal fields make any observable difference in the sheath magnetic field distributions. The data are divided into three subsets with the strongest crustal field on the dayside (SZA < 75°), near terminator (75° < SZA < 105°), or on the nightside (SZA > 105°). Since the draped field dominates the sheath region, we constrain the upstream IMF magnitudes the same way as in section 2.1. We have examined that all other drivers have generally consistent distributions between the dayside, terminator, and nightside crustal field conditions (see Figure S6 in the supporting information).

In Figure 9, the three data sets with different crustal field SZA are compared with each other. From Figures 9a–9f, we do not see any significant difference in clock angle departures. However, Figures 9g and 9l exhibit that when crustal fields are on the dayside, the dayside sheath magnetic field also becomes stronger comparing to the cases when crustal fields are near terminator and on the nightside. Although Figure 9k does not show a strong difference between the terminator and nightside crustal field conditions, we can still see slightly stronger sheath magnetic field near the terminator, which could be the contribution from the terminator crustal fields. There is a strong difference of the magnetic field strengths near the empirical BS as shown in Figures 9j and 9l. Again, this is likely the effects from BS variations as discussed in sections 3.1 and 3.2.1. It implies that the dayside crustal fields can push the BS outward (Edberg et al., 2008 Fang et al., 2017 ), and the real BS tends to be inside the empirical BS when the crustal fields are on the nightside or near terminator. Thus, some data near the empirical BS in Figures 9h and 9i are actually upstream IMF, which are significantly weaker than sheath magnetic fields.

From the Martian crustal field models (e.g., Cain et al., 2003 Morschhauser et al., 2014 ), the crustal field strengths at the altitudes of

1,500–3,000 km (approximate altitudes of the dayside sheath region) are only a few nanoteslas. The difference in the sheath magnetic field strengths as shown in Figures 9j and 9l is well within a factor of 2 and is estimated to be a few nanoteslas, consistent with the crustal field strengths in the dayside sheath region. The interactions between the crustal fields and draped IMF, such as reconnection (Harada et al., 2018 ), are likely to change the direction of the draped field. However, the magnetosheath is a very noisy environment with many different wave activities and perturbations (Fowler et al., 2017 Ruhunusiri et al., 2015 ). Therefore, if these interactions do not occur frequently enough or have no strong effects, they may not be observable in the statistical maps. Overall, the crustal field effects on the sheath magnetic field we have observed are most likely due to a superposition of the crustal field and the draped field (see also Brain et al., 2003 ).

It is worth noticing that when the crustal fields are at a certain SZA, the data at the same SZA in the 2-D cylindrical coordinate system are not necessarily from the same region in the (y, z) plane as the crustal fields. Although it is unlikely to significantly affect the discussion of the dayside and nightside crustal field conditions, when the crustal fields are near the terminator, some data near the terminator in Figures 9b and 9h are not really close to the crustal fields. Thus, the effects from the crustal fields near the terminator may not be well represented in such a coordinate system. However, it can still be clearly seen how the crustal fields on the dayside modified the sheath magnetic field strengths.

## Influence of the solar wind magnetic field on the Earth and Mercury magnetospheres in the paraboloidal model

We study the dependence of Mercury's magnetospheric magnetic field structure on the interplanetary magnetic field (IMF). Special attention is paid to the case of radial IMF. Mercury is the smallest planet in the solar system and it does not have a substantial atmosphere or ionosphere. Mercury is the closest planet to the Sun, and it possesses a week intrinsic magnetic field. Due to these circumstances, IMF plays a major role in the hermean magnetospheric dynamics. Using a paraboloidal model of Mercury's magnetosphere, we study the magnetospheric magnetic field topology for different orientations of IMF including examples representative of the first MESSENGER's flyby. Variations in IMF lead to variations in the Mercury's magnetospheric magnetic field structure, which in turn, lead to changes in the distribution of open and closed magnetic field lines. Comparison with the much better investigated Earth's magnetosphere is fulfilled for clarifying the physical processes (mainly reconnection) existent in the hermean magnetosphere. We also consider the cases when MESENGER, being the Mercury's orbiter, observed flux transfer events (FTEs) in the hermean magnetosphere. When the radial IMF component (BIMFx) is significant, which is character to the Mercury, the quasi-neutral line is placed in one of the cusps (depending on the sign of BIMFx). The FTE generation at Mercury can be connected with this line, similarly to the case of southward IMF at Earth, when FTEs arise at the dayside magnetopause at the quasi-neutral line. We show examples of observations supporting this result for Mercury.

### An optional activity, to draw the expected shapes of interplanetary magnetic field lines.

The Law of Field Line Preservation

Here this "dragging" process will be explained, and it will be used to obtain the expected shape of those field lines.

When some process moves plasma inside a magnetic field, what happens depends of the relative strength of the two. If the magnetic field is strong --as happens in the corona, close to the Sun--then it dominates, and determines where the plasma can or cannot go. That is why magnetic field-line loops tend to keep back the solar wind, unlike the outward-bound lines in the "coronal holes" between them.

If two or more ions start out located on the same field line, they will always share the same field line.

If they then manage to move, the field line gets deformed: it is as if the magnetic field is "frozen" into the plasma.

Using this "law of field line preservation", we will now derive the shape of interplanetary magnetic field lines.

In the middle of the bottom (short side) of a sheet of paper, draw a small circle, about one inch across: that will represent the Sun, viewed from far above its north pole. If the Sun rotates once in 27 days, then each day it rotates by

( Alternative method: Let center of the Sun be the origin of a system of cartesian coordinates, with the x-axis parallel to the bottom of the page. Draw the two axes, with the y-axis extending to near the top of the page. With a pencil, draw faintly the line y=4, parallel to the x axis but 4" (4 inches) above it.
On that line mark points at distances 15/16", 2" and 3 3/8" on both sides of the y-axis, then draw radial lines from the center of the Sun through those points, extending them until they are 1/2" from the sides of the sheet or 1" from the top.
For those used to metric units, let the radius of the Sun be 1 cm (diameter=2cm), the pencil line follows y=10 cm and the marks on it are at distances of approximately 23.7, 50.2 and 83.9 millimeters from the y-axis. Extend the lines until they reach within 1 cm of the sides or 3 cm of the top.)

On each of the spokes, mark the point where it emerges from the Sun, and mark from there, along each spoke, additional points at intervals of 1.5 inches. Each interval marks the distance the solar wind covers in one day.

( Yes, the Sun is drawn much too big on this scale, but we will ignore the difference this makes. Besides, the solar wind does not start moving from the Sun's surface, but from some greater distance.)

The magnetic field at all these points is already so weak that the solar wind overpowers it and shifts its field lines, while its own motion--radially outward--remains unchanged. We will now derive the shape of those lines.

(As a shortcut, you can download the drawing here. A version with higher resolution is linked here you will not see any difference on your screen, whose resolution is limited to 72 dpi, but you can copy the file and use it with some graphic program that has higher resolution.)

Mark with the number 1 the point where the line furthest to your right emerges from the Sun. You are told that 7 ions are located at that point, close to each other and on the same magnetic field line. You are also told that in the coming week, all 7 are destined to join the solar wind, one day apart. On day one , however, they are all still at the starting point, although one ion has just started moving outwards

On day 3, the ion which started out first is at "second base," and the one which started on day 2 is at the first point out on its spoke. All others are at the base of the 3rd spoke, to which the Sun has now rotated, and one more ion has just begun to move. Mark all three point with the number 3.

On day 4, the Sun has rotated to the 4th spoke and 4 ions remain at the base point of that spoke, including one which is just starting to move. The other three, in the order they were released, are at 3rd, 2nd and 1st "base." Mark all four points with the number 4.

And so on, day after day. The points marked 5, for instance, are where the particles are on the 5th day. Obviously, you must give up on marking any ions which have gone past the limits of the paper.

Now connect--preferably with a red pen, or in some color different from that of the rest of the drawing--all points with the number 2, also the ones with 3, 4, 5, 6 or 7, and perhaps also those with 8, 9 and 10. Take those marked 6 : they show where the ions are after 5 days have passed--about the time the first of them reaches Earth's orbit. Since at the beginning they were all on the same magnetic field line, after 5 days they still are. The line you have drawn therefore gives the expected shape of an interplanetary magnetic field line, a shape also known as the Parker Spiral after the Chicago physicist who predicted both the solar wind and its effect on the magnetic field.

You may use a straight ruler for the connection: the actual lines curve smoothly, but even with lines composed of straight sections it becomes clear that the shape is a spiral. This agrees with observations at the Earth's orbit, where the average interplanetary magnetic field is found to make an an angle of 45° with the flow of the solar wind, similar to what the drawing shows. In other words--after being 5 days on their way, and reaching 150,000,000 km from the Sun, the magnetic field lines still "remember" the Sun's rotation.

## Postscript, 17 November 1999

It was also noted that with increasing distance from the Sun, the spiral shape of interplanetary magnetic field lines becomes more and more tightly wound, until their shape differs little from circles.

Both points were well illustrated by the phenomena that followed intense solar activity in April-May 1998, reported by Robert Decker of the Applied Physics Lab of the Johns Hopkins University in Maryland. That activity created a disturbance in the solar wind, as well as a flow of protons with energies about 1000 times that of the solar wind, and these were observed by a number of spacecraft--ACE at the L1 Lagrangian point (near Earth, distance from the Sun about 1 AU), by Ulysses (5 AU), and by Voyagers 1-2--Voyager 2 at 56 AU and Voyager 1 at 72 AU.

The solar wind disturbance arrived at Voyager 1 about 7.5 months later, propagating radially at the velocity of the solar wind flow in which it was embedded. The protons, on the other hand, although they moved much faster, were relatively few in number, which forced them to spiral along field lines. They were observed by Voyager 1 after 6 months--1.5 months before the disturbance in the solar wind reached that distance--and Dr. Decker calculated that their spiral path took them 10 times around the Sun, a total distance of about 2000 AU.

How the interplanetary medium interacts with planets depends on whether they have magnetic fields or not. Bodies such as the Moon have no magnetic field and the solar wind can impact directly on their surface. Over billions of years, the lunar regolith has acted as a collector for solar wind particles, and so studies of rocks from the Moon's surface can be valuable in studies of the solar wind.

High energy particles from the solar wind impacting on the Moon's surface also cause it to emit faintly at X-ray wavelengths.

Planets with their own magnetic field, such as the Earth and Jupiter, are surrounded by a magnetosphere within which their magnetic field is dominant over the Sun's. This disrupts the flow of the solar wind, which is channelled around the magnetosphere. Material from the solar wind can 'leak' into the magnetosphere, causing aurorae and also populating the Van Allen Belts with ionised material.

## 2. Overview of the Event

[3] Figure 1 shows plasma parameters during the IFE, recorded at 3.08 AU from the Sun, at −57.0° solar ecliptic (SE) latitude (heliographic latitude −64.2°). The event occurred during a gradual decrease in solar wind velocity on the trailing edge of a stream interaction region. The most striking feature is the thorn- or cusp-shaped B field magnitude (|B|) profile. |B| reached ∼2.6 times background levels, starting to rise at ∼1600 UT, and returning to ambient levels by ∼2010 UT. The double-peaked maximum of 0.78 nT was reached during 1859–1904 UT, with a dip to ∼0.6 nT between the peaks. Coincident with the dip was a field rotation of ∼99°. Immediately surrounding the double peak, the |B| profile was nearly symmetrical.

[4] Electron number density (ne) variations, derived from Unified Radio and Plasma Wave (URAP) radio receiver background levels, were small, apart from a brief peak at the |B| maximum coincident with the brief dip between the |B| maxima, immediately followed by a ∼25% decrease compared to ambient values, which lasted until |B| also returned to ambient levels. The near-symmetrical |B| profile around 1900 UT contrasts with the distinctly asymmetrical ne profile. Other plasma parameter changes were not as marked. There was a possible subtle proton number density (np) dip, again after the |B| peak, and a possible slight α particle number density dip before the peak. The flow deflection was comparable to other deviations on the same day. The proton temperature was slightly decreased compared to ambient values, with brief peaks before and after the |B| peak. There were no unusual energetic particle fluxes in anisotropy telescopes' data (S. Dalla, personal communication, 2000).

## Do Intrinsic Magnetic Fields Protect Planetary Atmospheres from Stellar Winds?

The accumulation of detailed ion flux measurements from long-lived spacecraft orbiting the solar system’s terrestrial planets have enabled recent studies to estimate the rate of solar wind driven atmospheric ion escape from Venus, Earth, and Mars, as well as the influence of solar wind and solar extreme ultraviolet (EUV) ionizing radiation on the atmospheric ion escape rates. Here, we introduce the basic forces and processes of ion escape, review the recent studies of ion escape rates, and provide a general framework for understanding ion escape as a process that can be limited by potential bottlenecks, such as ion supply, solar wind energy transfer, and transport efficiency, effectively determining the state of the ion escape process at each planet. We find that ion escape from Venus and Earth is energy-limited, though exhibit different dependencies on solar wind and EUV, revealing the influence of Earth’s intrinsic magnetic field. In contrast, ion escape from Mars is in a supply-limited state, mainly due to its low gravity, and has likely contributed relatively little to the total loss of the early Martian atmosphere, in comparison to neutral escape processes. Contrary to the current paradigm, the comparisons between the solar system planets show that an intrinsic magnetic dipole field is not required to prevent stellar wind-driven escape of planetary atmospheres, and the presence of one may instead increase the rate of ion escape. Anticipating the atmospheres of the exoplanets that will begin to be characterized over the coming decade, and the need to explain their evolution, we argue that a modern, nuanced, and evidence-based view of the magnetic field’s role in atmospheric escape is required.

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