Tag Archives: Atmosphere

Modeling the atmosphere of Jupiter

Hi there! Today we have a look at Jupiter, the largest planet of our Solar System. Several spacecrafts have visited it, from Pioneer 10 in 1972 to JUNO, which still operates. These missions have given us information on the behavior of its thick atmosphere, which raise the need for advanced modeling. This is why the authors of this study, An Equatorial Thermal Wind Equation: Applications to Jupiter, developed an equation modeling its behavior at low latitudes. This modeling appears to be successful for Jupiter when confronted to Galileo data, and for Neptune as well. The study, by Philip S. Marcus, Joshua Tollefson, Michael H. Wong, and Imke de Pater, has recently been accepted for publication in Icarus.

The atmosphere of Jupiter

The planet Jupiter has a mean radius of 69,911 km, but is flattened at its poles. Its polar radius is 66,854 km, while the equatorial one is 71,492 km. This is a consequence of the rotation of the planet, which alters the shape of the atmosphere. Because, yes, Jupiter has a thick atmosphere. This is actually a gas giant planet.

It is pretty difficult to set an inner limit to the atmosphere of Jupiter, since when deep enough, the gaseous and liquid phases cohabit. This is not as if you would have encountered a solid surface. The thickness of the atmosphere is estimated to be some 5,000 km.

As you can imagine, the deeper you go, the higher the pressure. So, it may be convenient to measure the depth as a pressure and not as a distance, i.e. you express the depth in bars / pascals, instead of km / miles.

The atmosphere of Jupiter is mostly composed of hydrogen and helium, with some methane, hydrogen sulfide, and possibly water. It is composed as, from the bottom to the top:

  • the troposphere,
  • the stratosphere,
  • the thermosphere,
  • the exosphere.

Observing the atmosphere of Jupiter shows lateral bands, with different velocities. The winds are particularly strong at low latitudes, i.e. close to the equator.

The spacecraft Galileo delivered an atmospheric probe in December 1995, which transmitted measurements up to the depth of 23 bars, i.e. 150 km, before being destroyed.

The Galileo mission

Galileo was a NASA mission, which operated around Jupiter between December 1995 and September 2003. It has been launched from Kennedy Space Center, in Florida, in October 1989, and made fly-bys of Venus, twice the Earth, and two asteroids, before orbital insertion around Jupiter in 1995. The two asteroids visited were Gaspra and Ida. Galileo gave us accurate images of these small bodies (some 15 and 40 km, respectively), and discovered the small moon of Ida, i.e. Dactyl.

Gaspra seen by Galileo. © NASA
Gaspra seen by Galileo. © NASA
Ida and Dactyl seen by Galileo. © NASA
Ida and Dactyl seen by Galileo. © NASA

Galileo journeyed around Jupiter during almost 8 years, studying the planet and its main satellites. It discovered in particular an internal ocean below the surface of Europa, and the magnetic field of Ganymede. It also gave us the variations of the temperature and pressure of the atmosphere over more than 1,000 km. And this is where you need a thermal wind equation.

The Thermal Wind Equation

You can find in the literature a Thermal Wind Equation, which relates the horizontal variations of the temperature of an atmosphere to the variations of the velocity of the winds. This equation does not usually work at low latitudes, i.e. close to the equator, because at least one of its assumptions is invalid. The Rossby number, denoted Ro, and which represents the ratio between the inertial force and the Coriolis force in the fluid, should be small. In other words, the dynamics of the fluid (the atmosphere) should be dominated by the Coriolis force. But this does not work at low latitudes, when the centrifugal force dominates.

This Thermal Wind Equation is anyway often used, even at low latitudes, because the literature did not offer you any better option. This is why the authors of the present study developed its equatorial extension.

The need for an equatorial extension

An obvious reason for developing such an equation holds even in the absence of data. You need to know the limitations of the Thermal Wind Equation, and a good way for that is to confront it with a more accurate one. In the presence of data, it is even better, because you can confront your two equations with the observations. And several phenomena remained to be explained:

  • the wind variations (wind shear) measured by Galileo. The measurements were made at a latitude of 7°, which is pretty close to the equator,
  • the velocity of a Jovian stratospheric jet,
  • ammonia plumes, which had been detected in the deep atmosphere,
  • on Saturn: an equatorial jet, at latitudes smaller than 3°,
  • on Neptune: zonal vertical wind shear appears to be inconsistent with the temperature profile, which has been measured by another spacecraft, Voyager 2, in 1989. This is actually the only spacecraft which visited Neptune.

I do not want to detail the calculations, but the authors show that when the centrifugal force dominates (significant Rossby number), then the wind shear is related to the second derivative of the temperature with respect to the longitude, instead with the first derivative, as suggested by the classical Thermal Wind Equation. The authors show that their Equatorial Thermal Wind Equation is actually a generalization of the classical one.

Successful modeling

Yes, this is a success. For instance, the authors show that the classical equation cannot be consistent with the detection of the ammonia plumes at the measured velocities, given the temperature required. However, it can be consistent with the equatorial equation, under an assumption on the longitudinal variation of the temperature. Either you consider that the equatorial equation is not accurate enough, or you see this result as a constraint on the temperature.

It works for Neptune as well

Recently, the same authors, in another study measured the wind velocity on Neptune from the Earth, with the Keck Observatory, in Hawaii. The classical Thermal Wind Equation says that these measurements are inconsistent with the temperature profile given by Voyager 2. The Equatorial Thermal Wind Equation show that the two measurements are actually consistent. This is another success!

The study and its authors

And that’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter, Facebook, Instagram, and Pinterest.

Thunderstorms on Saturn

Hi there! You know the thunderstorms on our Earth. In fact, you can have thunderstorms once you have an atmosphere. And you have many atmospheres in our Solar System, particularly on the giant planets. Today we describe a thunderstorm on Saturn, which happened between November 2007 and July 2008, and was observed by Cassini. This thunderstorm is described in Analysis of a long-lived, two-cell lightning storm on Saturn, by G. Fischer et al. This study will be published soon in Astronomy and Astrophysics.

Physics of a thunderstorm

Basically, a thunderstorm results from the encounter between cool and hot air. For instance, after a hot summer day, you have hot air in the low atmosphere, while colder air is brought by the wind. Then the hot air, which is lighter, gains altitude. This convective motion induces displacements of electric charges, and so a difference of electrostatic potential between the ground and the top atmosphere. This difference in electrostatic potential creates electric lightning, which actually balances the charges between the sky and the ground. All this results in unstable weather conditions, in particular rain and strong wind. The rain is due to the moist contained in the hot air, which coalesced as clouds while gaining altitude. Thunderstorms are among the most dangerous natural phenomena.

As I said, you can have thunderstorms on any planet with an atmosphere. Today, we are on Saturn.

The atmosphere of Saturn

The radius of Saturn is about 60,000 km, which corresponds to the distance to the center, where the atmospheric pressure reaches 1 bar. At its center Saturn has probably a rocky core, which radius is about 25,000 km. This leaves room for a very thick atmosphere, i.e. what I would call the Saturnian air, mainly composed of molecular hydrogen and helium. Interestingly for us, there are clouds in the atmosphere of Saturn, which composition depend on the altitude, itself correlated with the pressure. The less dense clouds (up to 2 bars), in the upper atmosphere, mainly consist of ammonia ice, while denser clouds contain water ice. The densest clouds, which pressure exceeds 9.5 bars, contain water droplets with ammonia in aqueous solution.

The winds on Saturn are very strong, i.e. up to 1,800 km/h, or 1,120 mph, which of course facilitates the encounters between different air masses (with different temperatures). Moreover, the atmosphere of Saturn is organized into parallel bands, as is the atmosphere of Jupiter. These bands rotate at slightly different rates, which prompted the International Astronomical Union to define 3 reference systems for the rotation of Saturn:

  • System I: spin period of 10 h14 min for the equatorial bands,
  • System II: spin period of 10 h 39 min 24 s, at the other latitudes,
  • System III: spin period of 10 h 39 min 22.3 s, for the radio emissions.

The detected episodes

To be honest with you, I did not manage to get an exhaustive list of the detected events. By the way, if you have some information, I would be glad to get it. You can comment at the end of this article.

You can find below a list of thunderstorms, which have been detected by the Cassini spacecraft between 2004 and 2010. The study we discuss today is on the Storm F.

  • Storm 0: May 26–31, 2004
  • Storm A: July 13–27, 2004
  • Storm B: August 3–15, 2004
  • Storm C: Sept. 4–28, 2004
  • Storm D: June 8–15, 2005
  • Storm E: Jan. 23 – Feb. 23, 2006
  • Storm F: Nov. 27, 2007 – July 15, 2008
  • Storm G: Nov. 19 – Dec. 11, 2008
  • Storm H: Jan. 14 – Dec. 13, 2009
  • Storm I: Feb. 7 – July 14, 2010

These events were identified in detecting radio emissions, due to Saturn electrostatic discharges (SEDs for short). Before that, the Voyager spacecrafts have detected SEDs in 1980 and 1981, but attributed their origins to impacts in the rings. Since then, other events have been detected. In particular, Great White Spot events, i.e. huge disturbance encircling the planets, can be seen from the Earth. They seem to appear roughly every 30 years, which could be correlated with the duration of Saturn’s year (29.46 years). The last Great White Spot has been observed in 2010-11.

The Great White Spot observed by Cassini in February 2011. Credit: NASA/JPL-Caltech/Space Science Institute
The Great White Spot observed by Cassini in February 2011. Credit: NASA/JPL-Caltech/Space Science Institute

Radio and optical observations

As I said, these events are usually detected thanks to their radio emissions. For that, Cassini disposed of the Radio and Plasma Wave Science (RPWS) instrument, equipped with a High Frequency Receiver.
This receiver listened to Saturn in 3 different modes alternatively, allowing to cover a pretty wide range between 325 and 16025 kHz.
These radio measurements were supplemented by optical observations by the Cassini ISS (Imaging Science Subsystem), by optical observations from Earth, and even by Earth-based radiotelescopes, for the strongest discharges.

The detection of such events strongly depends on the location of the spacecraft with respect to the storm. When the spacecraft is opposite to the storm, you detect almost nothing. Almost, because measuring radio emissions permits over-the-horizon detection, especially when the SED storm is located on the night side (opposite the Sun) and Cassini on the day side. This could be due to a temporary trapping of the radio waves below Saturn’s ionosphere before they are released.

So, Cassini’s RPWS detects the discharges, ISS and the Earth-based telescopes see the storms… Let us see the results for the Storm F (November 2007 to July 2008).

The Storm F

RPWS detected about 277,000 SEDs related to this Storm F. But the analysis of the images revealed two phases.

One or two events?

From November 2007 to March 2008, ISS saw one convection cell, at the latitude of ~35° south. And in March 2008 a second cell appeared, at roughly the same latitude, and separated from the first cell by about 25° in longitude. These two cells drifted both of about 0.35° per day. The presence of these two cells with a correlated motion makes this event a very interesting one… and the authors also detected dark ovals.

Dark ovals

A storm appears as a a bright spot, while a dark oval is a dark one. Several dark ovals were seen, the largest one, nicknamed S3 drifted by 0.92° per day, i.e. much faster than the storms. These dark ovals have probably no SED activity. Several explanations have been proposed to explain these features. They could either be clouds of carbon soot particles, produced by the dissociation of methane in the lightning channels, or remnants of convection cells, in which the ammonia particles have fallen deeper into the atmosphere, leaving darker spots.

Features related to the Storm F. The rectangle focuses on the so-called Storm Alley. This image was taken by Cassini ISS on 23 April 2008. © NASA
Features related to the Storm F. The rectangle focuses on the so-called Storm Alley. This image was taken by Cassini ISS on 23 April 2008. © NASA

So, this paper describes the event. The physics behind still needs some clarification, so you can be sure that devoted papers will follow. Stay tuned!

The study and its authors

You can find the study here. And now, the authors:

And that’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter, Facebook, Instagram, and Pinterest.

What if the Earth rotated backwards?

Hi there! I recently realized that over more than 100 articles, I never spoke about our Earth. Of course, you can say that, when I mean planets, I implicitly mean planets other than our Earth… There was probably something like that…
Anyway, our Earth is our home, and as such, it is of the uttermost importance. In particular, the global warming threatens it, and threatens the mankind itself. This is why we must study the Earth, but don’t worry, the Earth is studied.
Today I present simulations of the climate that the Earth would have, if it rotated backwards, at the same rate.
Of course, this is a theoretical study, which does not reproduce a real situation. But this is anyway interesting, because it permits us to understand the role of the different factors, which affect the climate. What is the role of the spin direction?
This is the question this study answers. The study is The climate of a retrograde rotating Earth, by Uwe Mikolajewicz et al., and it has recently been published in Earth System Dynamics.

The climate of our Earth

The climate of our Earth is influences by 4 factors:

  1. the astronomical factors
  2. the atmospheric circulation
  3. the oceanic circulation
  4. the ones I forget

The astronomical factors (axial tilt)

The obliquity of the Earth, or axial tilt, is responsible for the seasons. The rotation axis of our Earth is not orthogonal to its orbital plane around the Sun (the ecliptic), but is tilted by some 23° (somehow the angle between your index and your middle fingers, when you open your hand). The consequence is that the two poles do not see the sunlight six months a year, alternatively. And the other regions of the Earth have varying day durations, which affect the temperature. You have the seasons.

The team of Jacques Laskar (IMCCE, Paris Observatory) has shown that the Moon stabilizes the axial tilt of the Earth (see here). In other words, a moonless Earth would have experienced large variations of the axial tilt, hence large variations of the climate. So large that they may have threatened the development of life on Earth, since we need to adapt to the climate. We can do it when the changes are slow enough… and our fear with global warming is not (only) the warming itself, but its acceleration… Anyway, we are alive thanks to our Moon.

In fact, the astronomic forcing affects the climate on a wider range. The Serbian geophysicist and astronomer Milutin Milanković has hypothesized (and this has been confirmed by several teams since then) that the variations of the orbit and the rotation of the Earth were responsible for the paleoclimates. This theory is now known as the Milanković cycles.

But astronomic forcing is not everything. This affects the insolation of a given place, providing some energy to heat the Earth (not the whole energy actually, but let us neglect this point). Once a planet is illuminated, it responds… and the response depends on its constituents, the atmosphere playing a critical role.

The atmospheric circulation

As you know, our Earth is surrounded by an atmosphere, which is a layer of air, mostly composed of nitrogen and oxygen. Its pressure decreases with the altitude, 3 quarters of it being in the 11 lowest kilometers, while the boundary at the atmosphere is considered to be at about 100 km. This atmosphere is responsible for greenhouse effect, which heats the surface. It also increases the pressure, this permits the existence of liquid water. Moreover, it protects us from ultraviolet radiation, meteorites (many of them being fragmented when encountering the atmosphere), and allows us to breath. You can forget life on an atmosphereless Earth.

Beside this, the atmospheric circulation redistributes the thermal energy on Earth. You know the winds.
More precisely, this circulation is structured as cells, which take hot air at given locations of the surface, before releasing it back somewhere else. The main effect is due to latitudinal cells (Hadley, Ferrel, and polar cells), which permit heat transfers between different latitudes, but there is also a longitudinal motion, known as zonal overturning circulation.

Oceans play a key role in the regulation of our climate, since they have a kind of thermal inertia, which affects the temperature of the coastal areas.

The oceanic circulation

I mean the oceanic currents, which are water displacements. This may transfer hot water to colder regions, and conversely. An example is the North Atlantic Drift, aka Gulf Stream, which is responsible for the pretty moderate winters in Europe, while Canada freezes. There are also currents designated as gyres, since they have a pretty circular motion on a very large scale.
Moreover, you also have formation of water masses in the Atlantic, i.e. masses of water, which properties (temperature, salinity,…) are pretty homogeneous, and different from the surrounding waters.

Atmospheric and oceanic circulations are influence by the Coriolis effect, which is the consequence of the Earth rotation… and this study is on the influence of the Earth rotation.

The ones I forget

Sorry, I don’t remember 🙂

Let me mention anyway the influence of the land, which of course blocks the oceanic currents, and also may affect the atmospheric ones, in particular if you have mountains.

Different climates

All of these effects make meteorology a very complicated science. And you also have different climates on Earth, such as (following Köppen climate classification):

  • tropical climates (constant high temperatures),
  • dry climates (deserts),
  • temperate climates,
  • continental climates, where you have large variations of temperature between summer and winter,
  • and polar climates (the coldest ones).

You cannot pretend simulating the climate of the Earth if you don’t get these 5 climates.

The Max Planck Institute Earth System Model

The authors are experts in climate simulation. This is a very difficult task, since you have to implement the interactions between all the physical parameters (insolation, oceanic currents, atmospheric circulation,…), in a code which is non-linear and depends on multiple variables. Basically, when an equation is non-linear, you cannot simply derive its solution. Instead, you need to integrate the equation numerically, and the solution may be very sensitive to your parameters, your initial conditions (how is the climate when you start the simulations?), and your numerical scheme.

In particular, you split the atmosphere and the oceans on a grid of finite elements, and your numerical code simulates the solution element by element, time after time. This requires high performance computing tools.

The authors dispose of a dedicated numerical model, the Max Planck Institute Earth System Model (MPI-ESM), which couples the atmosphere, ocean and land surface through the exchange of energy, momentum, water and carbon dioxide. This homemade tool has been developed after years of study. It interfaces the simulations of different physical processes, all of them having been developed and improved since many years.
The authors have used the MPI-ESM many times in the past, which makes it reliable.

Intensive numerical simulations

In present study, the authors ran two sets of simulations:

  • CNTRL, which are consistent with our knowledge of the Earth,
  • and RETRO. To each CNTRL simulation corresponds a RETRO one, in which the Earth rotates backwards.

Each set is composed of 1,850 climate conditions (i.e. 1,850 different simulations), over 6,990 years. The authors point out that the simulations should be over a long enough duration, to permit the climate to reach an equilibrium state. The simulations show that in practice, the equilibrium is reached in some 2,000 years.

CNTRL simulations are necessary since, if you just compare a RETRO simulation with our observed climate, you cannot be sure whether the difference comes from the retrograde rotation, or from an effect which would have been inaccurately modeled. Moreover, running so many simulations permits to distinguish robust solutions, which give in some sense the same climate for many simulations, from anecdotic ones, i.e. due to particular initial conditions. Such a non-linear system of equations (Navier-Stokes, etc.) may be chaotic, which implies to be possibly very sensitive to the initial conditions, in a given range which we do not really know…

In the RETRO simulations, the backward rotation is modeled as:

  • the inversion of the Coriolis parameter in the oceanic and atmospheric circulations,
  • the inversion of the Sun’s diurnal march in the calculations of radiative transfer.

And one the simulations have run, they get the results. The question you may ask is: would that affect the global temperature of the Earth? It appears that no. You have no change on average, I mean the mean temperature remains pretty the same, but you have dramatic local changes. Let me emphasize two of them.

The Atlantic and the Pacific exchange their roles

As you can imagine, the inversion of the rotation results in inversion of the oceanic currents and the zonal winds. No need to run the simulations to predict this. But the simulations show unexpected things.

The Atlantic ocean is known for its water masses, and the CNTRL simulations get them. However, the RETRO simulations do not have them in the Atlantic, but in the Pacific Ocean.

A green Sahara

Another change is that the monsoons occur in the Sahara and Arabian Peninsula. This dry area, made of desert, would be a forest if the Earth rotated backwards! However, the world’s biggest desert would have been in the Southern Brazil and Argentina.

You can finally ask: why the authors did this study, since a backward rotating Earth is not realistic? Just because we need to fully understand the climate, and the rotation direction is one of the effects affecting it. We do not know whether this could apply to an extrasolar planet, or whether the results would help us to understand something else… That’s research, but trust me, it is useful one! Climate science has become a critical topic.

The study and its authors

And now, the authors:

And that’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter, Facebook, Instagram, and Pinterest.

The red spot of Jupiter

Hi there! Today: the red spot of Jupiter. When you observe Jupiter with a common telescope, you just cannot miss it (if it is on the visible side, of course, since Jupiter rotates in about 9.5 hours). It is a red oval, located in the southern equator of Jupiter, as large as 3 Earth. It is actually an anticyclonic storm, which persists since at least 1830. The different space missions have permitted to observe its evolution and measure the winds composing it. Today I present the result of observations by the spacecraft Juno. The study, The rich dynamics of Jupiter’s Great Red Spot from JunoCam: Juno images, has recently been published in The Astronomical Journal.

The Red Spot

This Red Spot has been continuously observed since 1830. To be honest, I don’t know who observed it at that time, but the fact is that it is stable since at least 188 years. Before that, several astronomers, including Giovanni Cassini, claimed to have observed it between 1665 and 1713. It is even depicted by Donato Creti in 1711. But, because of the absence of observations between 1713 and 1830,

  1. we do not know whether it is the same spot or not,
  2. it could have disappeared and reappeared during the 18th century.
Astronomical Observations: Jupiter, by Donato Creti (1711).
Astronomical Observations: Jupiter, by Donato Creti (1711).

And this is possible, since the red spot is currently shrinking. We know it thanks to the different spacecraft having met Jupiter (Pioneer, Voyager, Galileo, Cassini, and now Juno) and the Hubble Space Telescope. It attained its maximal known width by the end of the 19th century, some 25,000 miles (40,000 km), while it is a little more than 10,000 miles (16,000 km) by now. At this rate, it should become a circle by 2040.

Global view of Jupiter, with the Red Spot at 22° South. © Space Telescope Science Institute/NASA
Global view of Jupiter, with the Red Spot at 22° South. © Space Telescope Science Institute/NASA

It rotates counter-clockwise with a period of 6 days, while the atmosphere of Jupiter rotates clockwise. The top of the spot is higher of 8 kilometers than the surrounding clouds, which makes it colder.

The spacecraft JUNO orbits Jupiter since July 2016, and permits a new analysis of the Red Spot.

The spacecraft JUNO

The NASA spacecraft JUNO, for JUpiter Near-polar Orbiter, has been launched to Jupiter from Cape Canaveral in August 2011. It orbits Jupiter since July 2016, on a polar orbit. This means that it flies over the poles of Jupiter. Its orbit is very eccentric, with a period of 53 days.

Contrary to Galileo, it is interested only in the planet itself, not in its satellites. Its payload is composed of 9 instruments, and among its objectives are the map of the magnetic field of Jupiter, the map of its gravitational field, which contains information on the solid core which is beneath the atmosphere, and a better knowledge of the chemical composition of the atmosphere.

Among the nine instruments is the camera JunoCam, which provided the data permitting this study.

The data: JunoCam images

JunoCam has not been conceived as a science, but as an outreach instrument, i.e. designed to give beautiful images. And it does.
But in this case, it appears that its data can be used for science. You can find below some images of the Red Spot by Juno, this video having been made by Gerald Eichstädt, one of the authors of the study. You can find more of them on its Youtube channel.

JunoCam has a field of 58°, and 4 filters:

  • Blue at 480.1 nanometers (nm),
  • Green at 553.5 nm,
  • Red at 698.9 nm. These three filters are in the visible spectrum,
  • while the fourth one is centered in the methane absorption band at 893.3 nm. This last one belongs to the near infrared spectral domain.

The authors used the images taken in visible light, i.e. with the first three filters, during a close fly-by of the Red Spot on 2017 July, 11.

From raw data to measurements

To make good science from raw data, you have to treat them. In particular, the authors needed to

  • consider the exact location and orientation of the spacecraft,
  • correct the images from distortion. For that, they assumed that the camera had Brown-Conrady radial distortion, or decentering distortion, which would be due to physical elements in a lens not being perfectly aligned.

Once they made these corrections, they got 4 images, distributed over 581 seconds. In comparing the location of the cloud features on these four images, they got the wind velocities in the upper level of the spot.

5 features in the spot

And from these velocities, they identified 5 structures, which are listed in the Table below.

Location Size Winds’ velocity
Compact cloud clusters Northern part 500 x 250 km 30-50 m/s
Mesoscale waves Northern boundary 2,000 x 500 km 50 m/s
Internal spiraling vortices South-West 1,000 x 1,000 km 75 m/s
Central nucleus Center 5,200 x 3,150 km 10-20 m/s
Large dark thin filaments Border 2,000-7,000 x 150 km 2-4 m/s

In particular,

  • the compact cloud clusters are composed of between 50 and 60 single wind cells, each with a size between 50 and 70 kilometers. This size suggests ammonia condensation.
  • The mesoscale waves could either be atmospheric gravity waves, i.e. when buoyancy tries to restore equilibrium between two media (see picture below, of atmospheric gravity waves observed on Earth), or shear instability waves, due to high wind.
  • Satellite image of atmospheric gravity waves over the Arabian Sea. Their visibility is due to sunlight, caused by the "impression" of the atmospheric waves on the sea surface. ©Jeff Schmaltz MODIS Rapid Response Team, NASA-GSFC
    Satellite image of atmospheric gravity waves over the Arabian Sea. Their visibility is due to sunlight, caused by the "impression" of the atmospheric waves on the sea surface. ©Jeff Schmaltz MODIS Rapid Response Team, NASA-GSFC
  • The cause of the internal spiraling vortices still needs to be understood.
  • The central nucleus is probably a cyclonic region, with turbulent winds.
  • It is not clear whether the large dark thin filaments are traced by darker aerosols, or represent areas with differetn altitudes and particles densities. They could be Vortex Rossby Waves, which accelerate the tangential winds, and play an important role in hurricanes. You can find more details here.

The study and its authors

And that’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter, Facebook, Instagram, and Pinterest.

When a comet meets the Solar wind

Hi there! Today, let us talk about the environment of a comet. As you know, a comet is an active body, which emits ionized particles and dust. The Sun itself emits charged particles, which constitute the Solar wind. We discuss today of the interaction between these two emissions. The environment of charged particles around a comet has been measured by the spacecraft Rosetta, and this has motivated modeling these interactions. I present you Solar wind dynamics around a comet: The paradigmatic inverse-square-law model, by M. Saillenfest, B. Tabone, and E. Behar. This study has recently been accepted for publication in Astronomy and Astrophysics.

The spacecraft Rosetta

Let us first speak about the mission Rosetta. Rosetta was a European mission, which orbited the comet 67P/Churyumov–Gerasimenko between 2014 and 2016. It was named after the Rosetta Stone, which permitted the decipherment of Egyptian hieroglyphs. The mission Rosetta was supposed to give us clues on the primordial Solar System, i.e. on our origins, from the study of a comet.

It was launched in March 2004 from Kourou (French Guiana), and then started a 10-years journey, during which it made 3 fly-bys of the Earth and one of Mars. You can say: “why going back to Earth?” The reason is that Rosetta was supposed to orbit 67P/Churyumov–Gerasimenko (spoiler alert: it did it). For this orbital insertion to be possible, it had to arrive slowly enough… but also had to leave Earth fast enough, to get rid off its attraction, and also to shorten the journey. Fly-bys permitted to slow the spacecraft in exchanging energy with the Earth (or Mars).

Rosetta also visited two asteroids: (2867) Šteins, and (21) Lutetia, in September 2008 and July 2010, respectively. It was inserted into orbit around 67P in August 2014, released the lander Philae in November, and the mission ended in September 2016. In particular, Rosetta was present when 67P reached its perihelion in August 2015. At this point, the comet was at its closest distance to the Sun (1.25 astronomical unit, while its mean distance is almost thrice this number), where the cometary activity is maximal.

The asteroids (2867) Šteins (left) and (21) Lutetia (right), seen by Rosetta. © ESA
The asteroids (2867) Šteins (left) and (21) Lutetia (right), seen by Rosetta. © ESA

So, Rosetta consisted of two modules: the orbiter itself, and the lander Philae. The orbiter had 11 instruments on board, and the lander 10. These instruments permitted, inter alia, to map the comet and measure its geometry, to constrain its internal structure and its chemistry, and to characterize its environment.

This environment is strongly affected by the Solar wind, especially in the vicinity of the perihelion, but not only.

The Solar wind

The Solar corona emits a stream of charges particles, which is mainly composed of electrons, protons, and alpha particles (kind of charged helium). This emission is called Solar wind. It is so energetic, that the emitted particles go far beyond the orbit of Pluto, constituting the heliosphere. The heliosphere has the shape of a bubble, and its boundary is called the heliopause. Voyager 1 crossed it in August 2012, at a distance of 121 AU of the Sun. At the heliopause, the pressure of the Solar wind is weak enough, to be balanced by the one of the interstellar medium, i.e. the winds from the surrounding stars. Hence, Voyager 1 is in this interstellar space, but technically still in the Solar System, as under the gravitational attraction of the Sun.

Anyway, our comet 67P/Churyumov-Gerasimenko is much closer than that, and has to deal with the Solar wind. Let us see how.

The physics of the interaction

Imagine you are on the comet, and you look at the Sun… which should make you blind. From that direction comes a stream of these charged particles (the Solar wind), and you can consider that their trajectories are parallel if far enough from the comet. Of course, the Sun does not emit on parallel trajectories, i.e. the trajectories of all these particles converge to the Sun. But from the comet, the incident particles appear to arrive on parallel trajectories.

While a charged particle approaches the comet, it tends to be deflected. Here, the dominating effect is not the gravitation, but the Lorentz force, i.e. the electromagnetic force. This force is proportional to the electric charge of the particle, and also involves its velocity, and the electric and magnetic fields of the comet.

The authors showed in a previous paper that the trajectories of the charged particles could be conveniently described in assuming that the magnetic field obeys an inverse-square law, i.e. its amplitude decreases with the square of the distance to the comet. If you are twice further from the comet, then the magnetic field is four times weaker.

I do not mean that the magnetic field indeed obeys this law. It is in fact more complex. I just mean that if you model it with such an ideal law, you are accurate enough to study the trajectories of the Solar wind particles. And this is what the authors did.

By the way, the authors suggest that any magnetic field following an inverse-power law could work. Of course, the numbers would have been different, but the global picture of the trajectories would be pretty much the same. It seems, at this time, too challenging to determine which of these models is the most accurate one.

Reducing the problem

The authors used analytical calculations, i.e. maths, which are in fact close to the classical ones, you make to show that the gravitation results in elliptic, parabolic, or hyperbolic, trajectories.

A wonderful tool assisting such studies is the First Integrals. A First Integral is a quantity, which remains constant all along a trajectory. For instance, in a gravitational problem where no energy is dissipated, then the total energy (kinetic + potential energies) is conserved. This is a First Integral. Another First Integral in that problem is the norm of the total angular momentum. And the existence of these two quantities helps to understand the shape of the possible orbits.

The authors showed that this is quite similar here. Even if the equations are slightly different (anyway the inverse-square law is a similarity), they showed that the problems has 2 First Integrals. And from these 2 First Integrals, they showed that knowing only 2 parameters is in fact enough to characterize the trajectories of the Solar wind particles. These two parameters are called rC and rE, they have the physical dimension of a distance, and are functions of all the parameters of the problems. rE characterizes the stream, it is related to its velocity, while rC characterizes a given particle. If you know just these 2 parameters, then you can determine the trajectory.

An empty cavity around the comet

The authors give a detailed description of the trajectories. To make things simple: either the particles orbit the comet, or they just pass by. But anyway, there is an empty space around the comet, i.e. a spherical cavity in which no Solar wind particle enters.

To come: comparison with in situ measurements

The journey of Rosetta around 67P crossed the boundary of this empty cavity. In other words, we have measurements of the density of charged particles at different distances from the comet, and also for different distances from the Sun, since the orbital phase of the mission lasted 2 years, during which 67P orbited the Sun. The authors promise us that a study of the comparison between the model and the in situ measurements, i.e. the observations, is to come. We stay tuned!

Rosetta does not operate anymore, and has landed (or crashed…) on 67P in September 2016. It is still there, and has on-board a kind of modern Rosetta stone. This is a micro-etched pure nickel prototype of the Rosetta disc donated by the Long Now Foundation, as part of its Rosetta Project. The disc was inscribed with 6,500 pages of language translations. This is a kind of time capsule, aiming at preserving part of our culture. Maybe someone will one day find it…

The study and its authors

And that’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter, Facebook, Instagram, and Pinterest.