# 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.

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.

# The fate of Jupiter’s Trojans

Hi there! Today we discuss about the Trojans of Jupiter. These are bodies which orbit on pretty the same orbit as Jupiter, i.e. at the same distance of the Sun, but 60° before or behind. These asteroids are located at the so-called Lagrange points L4 and L5, where the gravitational actions of the Sun and of Jupiter balance. As a consequence, these locations are pretty stable. I say “pretty” because, on the long term, i.e. millions of years, the bodies eventually leave this place. The study I present today, The dynamical evolution of escaped Jupiter Trojan asteroids, link to other minor body populations, by Romina P. Di Sisto, Ximena S. Ramos and Tabaré Gallardo, addresses the fate of these bodies once they have left the Lagrange points. This study made in Argentina and Uruguay has recently been published in Icarus.

## The Trojan asteroids

Jupiter orbits the Sun at a distance of 5.2 AU (astronomical units), in 11.86 years. As the largest (and heaviest) planet in the Solar System, it is usually the main perturber. I mean, planetary objects orbit the Sun, they may be disturbed by other objects, and Jupiter is usually the first candidate for that.

As a result, it creates favored zones for the location of small bodies, in the sense that they are pretty stable. The Lagrange points L4 and L5 are among these zones, and they are indeed reservoirs of populations. At this time, the Minor Planet Center lists 7,039 Trojan asteroids, 4,600 of them at the L4 point (leading), and 2,439 at the L5 trailing point. These objects are named after characters of the Trojan War in the Iliad. L4 is populated by the Greeks, and L5 by the Trojans. There are actually two exceptions: (624) Hektor is in the Greek camp, and (617) Patroclus in the Trojan camp.

## These are dark bodies

The best way to know the composition of a planetary body is to get there… which is very expensive and inconvenient for a wide survey. Actually a NASA space mission, Lucy, is scheduled to be launched in 2021 and will fly by the Greek asteroids (3548) Eurybates, (15094) Polymele, (11351) Leucus, and (21900) Orus in 2027 and 2028. So, at the leading Lagrange point L4. After that, it will reach the L5 point to explore the binary (617) Patroclus-Menetius in 2033. Very interesting, but not the most efficient strategy to have a global picture of the Trojan asteroids.

Fortunately, we can analyze the light reflected by these bodies. It consists in observing them from the Earth, and decompose the light following its different wavelengths. And it appears that they are pretty dark bodies, probably carbon-rich. Such compositions suggest that they have been formed in the outer Solar System.

## Asymmetric populations

We currently know 4,600 Trojan asteroids at the L4 point, and 2,439 of them at the L5 one. This suggests a significant asymmetry between these two reservoirs. We must anyway be careful, since it could be an observational bias: if it is easier to observe something at the L4 point, then you discover more objects.

The current ratio between these two populations is 4,600/2,439 = 1.89, but correction from observational bias suggests a ratio of 1.4. Still an asymmetry.

## Numerical simulations with EVORB

The authors investigated the fate of 2,972 of these Trojan asteroids, 1,975 L4 and 997 L5, in simulating their trajectories over 4.5 Gyr. I already told you about numerical integrations. They consist in constructing the trajectory of a planetary body from its initial conditions, i.e. where it is now, and the equations ruling its motion (here, the gravitational action of the surrounding body). The trajectory is then given at different times, which are separated by a time-step. If you want to know the location at a given time which is not one considered by the numerical integration, then you have to interpolate the trajectory, in using the closest times where your numerical scheme has computed it.

When you make such ambitious numerical integrations, you have to be very careful of the accuracy of your numerical scheme. Otherwise, you propagate and accumulate errors, which result in wrong predictions. For that, they used a dedicated integrator, named EVORB (I guess for something like ORBital EVolution), which switches between two schemes whether you have a close encounter or not.

As I say in previous articles like this one, a close encounter with a planet may dramatically alter the trajectory of a small body. And this is why it should be handled with care. Out of any close encounter, EVORB integrates the trajectory with a second-order leapfrog scheme. This is a symplectic one, i.e. optimized for preserving the whole energy of the system. This is critical in such a case, where no dissipative effect is considered. However, when a planet is encountered, the scheme uses a Bulirsch-Stoer one, which is much more accurate… but slower. Because you also have to combine efficiency with accuracy.

In all of these simulations, the authors considered the gravitational actions of the Sun and the planets from Venus to Neptune. Venus being the body with the smallest orbital period in this system, it rules the integration step. They authors fixed it to 7.3 days, which is 1/30 of the orbital period of Venus.

And these numerical simulations tell you the dynamical fate of these Trojans. Let us see the results!

## The Greek are more stable than the Trojans

It appears that, when you are in the Greek camp (L4), you are less likely to escape than if you are in the Trojan one (L5). The rate of escape is 1.1 times greater at L5 than at L4. But, remember the asymmetry in the populations: L4 is much more populated than L5. The rates of escape combined with the overall populations make than there are more escapes from the Greek camp (18 per Myr) than from the Trojan one (14 per Myr).

## Where are they now?

What do they become when they escape? They usually (90% of them) go in the outer Solar System, first they become Centaurs (asteroids inner to Neptune), and only fugitives from L4 may become Trans-Neptunian Objects. And then they become a small part of these populations, i.e. you cannot consider the Lagrange points of Jupiter to be reservoirs for the Centaurs and the TNOs. However, there are a little more important among the Jupiter-Family Comets and the Encke-type comets (in the inner Solar System). But once more, they cannot be considered as reservoirs for these populations. They just join them. And as pointed out a recent study, small bodies usually jumped from a dynamical family to another.

## The study and its authors

You can find the study here. The authors made it freely available on arXiv, many thanks to them for sharing!

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.

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.

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.
• 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.

# On the early evolution of Jupiter

Hi there! Today we will discuss on how Jupiter formed. I guess you know Jupiter, i.e. the largest planet of our Solar System. It is a gaseous planet, which means that it is composed of a large and thick atmosphere, which surrounds a solid core. Jupiter is currently studied by the NASA spacecraft Juno. The study I present you, The primordial entropy of Jupiter, by Andrew Cumming, Ravi Helled, and Julia Venturini, simulates different possible paths for the accretion of the atmosphere of Jupiter. The goal is to compare the outcomes with the current atmosphere, to eventually discard some scenarios and constrain the primordial Jupiter. This study has recently been published in The Monthly Notices of the Royal Astronomical Society.

## The planet Jupiter

Jupiter is the largest planet of our Solar System, and the most massive one. It is about 1,000 more massive than our Earth, and 1,000 less massive than the Sun. As such, it has a tremendous influence on the architecture of our System, particularly the small bodies. The Main Asteroid Belt presents gaps, which are due to mean-motion resonances with Jupiter. Jupiter is also responsible for the destabilization of the orbits of objects which pass close to it. A famous example is the comet Shoemaker-Levy 9 which Jupiter tidally destroyed before its impact. You can find below a comparison between Jupiter, Saturn, and our Earth.

Jupiter Saturn Earth
Equatorial radius 71,492 km 60,268 km 6,378 km
Polar radius 66,854 km 54,364 km 6,357 km
Distance to the Sun 5.20 AU 9.58 AU 1 AU
Orbital period 11.86 yr 29.46 yr 1 yr
Spin period 9 h 55 m 10 h 33 m 23 h 56 m
Density 1.326 g/cm3 0.687 g/cm3 5.514 g/cm3

I compare with our Earth given our special connection with that planet, but the comparison with Saturn is much more relevant from a physical point of view. For gaseous planets, the radius correspond to an atmospheric pressure of 1 bar. I here provide a unique spin period, but the gaseous planets experience differential rotation, i.e. the equator may spin slightly faster than the poles.

You can see that our Earth is much denser than the giant guys. The reason is the thick atmosphere, which is less dense than a rocky body. Actually Jupiter is assumed to have a rocky core as well, which would be surrounded by hydrogen, which pressure increases with the depth.

Observers especially know Jupiter for its Great Red Spot, i.e. a giant storm, which is observed since the 17th century.

Jupiter is currently the target of the NASA mission Juno.

## The mission Juno

The NASA mission Juno has been sent from Cape Canaveral in August 2011, and orbits Jupiter since July 2016, on a polar orbit. The nominal mission will be completed in July 2018, but I hope it will be extended (I do not have information on this point, sorry). Its goals are to understand origin and evolution of Jupiter, look for solid planetary core, map magnetic field, measure water and ammonia in deep atmosphere, observe auroras.

It is composed of 9 instruments. Beside impressive images of cyclones in the atmosphere of Jupiter, it for instance gave us its gravity field of Jupiter with an unprecedented accuracy. Such a result permits to constrain the interior, see for instance this study, in which the authors modeled different interiors for Jupiter. They then compared the resulting, theoretical gravity field, which the one actually measured by Juno. They deduced that the core contains between 7 and 25 Earth masses of heavy elements.

The study I present today does not model the present Jupiter, but instead simulates the evolution of Jupiter from its early life to present. Once more, the goal is to compare with current and future observations. Let us see how a giant planet evolves.

## The formation of a giant planet

There are two identified scenarios for the triggering of the formation of a planet:

• Disk instability: a massive disk fragments into planet-sized self-gravitating clumps
• Core accretion: solid particles collide and coagulate into larger and larger bodies until a body large enough to accrete a gaseous envelope.

The core accretion model consists of 3 phases:

1. Primary core/heavy-element accretion: here you create the solid core,
2. Slow envelope/gas accretion: in this phase, the solid core continues growing, while gas accretes as well,
3. Rapid gas accretion: this is the final stage, where the core has already been formed.

Here the authors simulate the Phase 3. They are particularly interested in the heat transfer inside the atmosphere. There are two ways to transport heat in such an environment: by radiation, or by convection, i.e. transport of gas, which is a much more effective process. Moreover, convection permits the transport of heavy elements, and so a gradient of density in the atmosphere. This gradient of density would eventually stop the convection, the atmosphere reaching a kind of equilibrium.

Let us see how the authors simulated that process.

## Simulations of different scenarios

The authors simulated the gas accretion of Jupiter using the numerical MESA code, for Modules for Experiments in Stellar Astrophysics. Yes, stellar, not planetary. But this is very relevant here, since a gaseous planet and a star are both made of a thick gaseous envelope.

These simulations differ by

• The initial mass of the core,
• its initial luminosity, which affects the heat transfers during the accretion process. This could be expressed in terms of entropy, which is a thermodynamical quantity expressing the overall activity of a fluid. It will then express the quantity of conductive transfers,
• the initial mass of the envelope,
• the temperature of the accreted material,
• the time-dependent accretion rate. In some simulations it is an ad-hoc model, fitted from previous studies, and in other ones it is directly derived from formation models. The accretion rate is obviously time-dependent, since it slows down at the end of the accretion,
• the opacity of the material, which is defined as the ratio of the gravitational acceleration over the pressure, multiplied by the optical depth. This affects the heat transfers.

And from all of these simulations, the authors deduce some properties of the final Jupiter, to be compared with future observations to constrain the evolution models.

## The initial state constrains the final one

And here are some of the results:

• Lower opacity and lower solid accretion rate lead to a low mass core,
• if the gas accretion rate is high then the proto-Jupiter is likely to be fully radiative, i.e. no convection,
• the rate at which the accretion slows down at the end determines the depth of the convection zone,

etc.

At this time, we do not dispose of enough data to constrain the initial parameters and the accretion rates, but why not in the future? Juno is still on-going, and we hope other missions will follow. For instance, stable regions in Jupiter’s interior can be probed with seismology. Seismology of giant planets would be pretty similar to helioseismology, i.e. this would consist in the detection of acoustic waves, which would be generated by convection in the interior.

## The study and its authors

• You can find the study here. The authors made it freely available on arXiv, thanks to them for sharing! And now the authors:
• The website of Andrew Cumming, first author of the study,
• and the one of Ravit Helled.

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.