Monthly Archives: December 2018

Planets

Thunderstorms on Saturn

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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.

Outline

Physics of a thunderstorm
The atmosphere of Saturn
The detected episodes
Radio and optical observations
The storm F
The study and its authors

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.

Satellites of Uranus

Forming the satellites of Uranus

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Merry Christmas! Today we discuss how the satellites of Uranus were formed. It is usually thought the satellites of a giant planets formed from a protoplanetary nebula. Originally there was a cloud of gas and dust, mass accumulated in the center to form the planet, and protosatellites were created from the accretion of mass as well. This was well understood for the gas giants like Jupiter, but Uranus is much smaller (23 times lighter). The Swiss study I present today, In situ formation of icy moons of Uranus and Neptune, by Judit Szulágyi, Marco Cilibrasi and Lucio Mayer, solves this problem. This study has recently been published in The Astrophysical Journal Letters.

Outline

The satellites of Uranus
From the disk to the satellites
Hydrodynamic simulations
Yes, it is possible!
What about Neptune?
The study and its authors

The satellites of Uranus

Uranus has 27 known satellites, which can be classified into 3 groups:

  • the inner moons, which are small satellites embedded in the rings,
  • the main moons, which are mid-sized icy bodies. These are the ones we are interested in today,
  • and the irregular moons, which orbit very far from the planet, and on significantly eccentric and inclined orbits. These bodies are probably former asteroids, which were trapped by the gravitational field of Uranus.

As I said, we are interested in the main 5 satellites, which are listed below. Their semimajor axes are given with respect to the mean equatorial radius of Uranus, which is 25,559 km.

U-5 Miranda U-1 Ariel U-2 Umbriel U-3 Titania U-4 Oberon
Discovery 1948 1851 1851 1787 1787
Semimajor axis 5.062 RU 7.474 RU 10.408 RU 17.055 RU 21.070 RU
Eccentricity 0.0013 0.0012 0.0039 0.0011 0.0014
Inclination 4.232° 0.260° 0.205° 0.340° 0.058°
Orbital period 1.413 d 2.520 d 4.144 d 8.706 d 13.463 d
Diameter 471.6 ± 1.4 km 1157.8 ± 1.2 km 1169.4 ± 5.6 km 1576.8 ± 1.2 km 1522.8 ± 5.2 km
Density 1.20 g/cm3 1.66 g/cm3 1.40 g/cm3 1.72 g/cm3 1.63 g/cm3

As you can see, these 5 bodies are

  • A small one (Miranda), which is pretty close to the planet,
  • two larger ones, Ariel and Umbriel, which orbit further from the planet,
  • and two even larger ones, Titania and Oberon, which orbit even further from the planet.

Discoveries

Titania and Oberon have been discovered in 1787 by the German-British astronomer William Herschel, only 6 years after the same William Herschel discovered Uranus. Actually, Uranus was (and still is) visible to the naked eye, and had been observed many times before. But how to know it was a planet, and not a star? Well, a star does not move in the sky (actually, it does a very little…), while a planet moves. But since Uranus orbits very far from the Sun, its motion is pretty slow. Herschel detected such motion, but he thought at that time that Uranus was a comet. The computation of its motion showed a pretty circular orbit, proving it was a planet.
After that, Uranus has been observed many times, and Herschel noticed two dots following Uranus. Since they followed Uranus, it meant they were gravitationally bound to it, hence satellites. These two dots were the two largest of them, i.e. Titania and Oberon.

Seventy years after the discovery of Uranus, the British merchant and astronomer William Lassell, who by the way made his fortune as a beer brewer, built his own telescope. He polished himself the mirror, and pioneered the use of the equatorial mount, which facilitated the tracking of objects with respect to the rotation of the Earth. His telescope permitted him to discover the satellite of Neptune Triton, to co-discover the satellite of Saturn Hyperion, and to discover the satellites of Uranus Ariel and Umbriel.

For Miranda, we had to wait for the Dutch-American astronomer Gerard (Gerrit) Peter (Pieter) Kuiper. He discovered Miranda in 1948 and the satellite of Neptune Nereid in 1949, at McDonald Observatory (TX, USA). Kuiper is mostly known for having proposed the existence of the so-called Kuiper Belt, i.e. a belt of asteroids orbiting beyond the orbit of Neptune. He has also been the thesis advisor of Carl Sagan.

Properties

Let us go back to the table, and have a look at their properties. We can see that these bodies have small eccentricities and inclinations, i.e. they orbit in the equatorial plane of Uranus, on pretty circular orbits. There is anyway an exception to this rule, which is the significant inclination of Miranda (4.2°). This inclination has probably been excited by a past 3:1 mean motion resonance with Umbriel.

Another interesting point is the density of these bodies. 1g/cm3 means a composition close to water. Pure water ice would be a little less dense. Here we have densities between 1 and 2, which means that these bodies are mixtures of ice and silicates.

This property they share is a clue, which suggests a common formation process. Let us investigate the formation from the protoplanetary disk.

From the disk to the satellites

Let us figure out how a giant planet is formed. First you have a protoplanetary nebula, made of gas and dust. Matter accumulates and aggregates at its center, creating a star (if the nebula is massive enough). To compensate this accumulation at the center (conservation of the total angular momentum), the matter which is still outside the star accelerates, and the nebula becomes a disk, which orbits the star.
Then (may be a little meanwhile, actually), you have local accretions of matter, which create the planets. And sometimes, if you have enough matter, then you have a circumplanetary disk around some of the planets, in which matter aggregates… and creates the satellites! Well, this way, it seems to be easy.
One question is: how massive need the protoplanetary disk to be, to create the satellites. It was known that it works for Jupiter. This study wonders whether it works for Uranus.

Hydrodynamic simulations

To answer this question, the authors ran intensive numerical simulations, using the hydrocode JUPITER. By hydrocode I mean that it simulates a hydrodynamic system.

Actually, a disk is made of particles of gas and dust. It is highly challenging, even if it is sometimes tried, to consider all the particles constituting it, and model their motion and their interactions. Instead, you can consider that the whole disk acts as a gas, and model the collisions between the particles as a viscosity.

Simulating this motion requires to split the disk into cells, use the method of finite elements, i.e. the state of a given part of the disk depends on the state of its neighbors… This requires intensive computing facilities. In JUPITER, you can focus on a given region, for instance where a planet is created.

The authors ran 25,000 simulations, depending on the following parameters:

  • the disk dispersion timescale,
  • the dust-to-gas ratio,
  • the dust refilling timescale: when dust accumulates at the center to create the planet, the disk needs to reach a new equilibrium. This parameter controls the velocity of this process,
  • the distance from the planet where the first proto-satellites are created,
  • the initial temperature of the central planet.

It appeared that this temperature, set to 1000K, 500K and 100K, plays a critical role in the possibility to create the satellites. Consider this effect is possible in JUPITER since 2016 and the implementation of a module, which models the radiative transfer in the disk. As a consequence, it models the effects of the heating and cooling of the gas.

Yes, it is possible!

The simulations show that the circumplanetary gaseous disk was formed when the temperature dropped below 500K (227°C, or 441°F). In that case, icy moons were formed in most of the simulations, which strongly suggests that the present satellites of Uranus were formed that way.

What about Neptune?

Neptune is somehow like Uranus, by its size. This is why the authors ran similar simulations, which showed similar results, i.e. formation of icy, mid-sized satellites. But wait, this is not what we see.

When we observe the system of Neptune, we see a large satellite, Triton, which is highly inclined, on a retrograde orbit. As we discussed here, Triton behaved like a cuckoo.

The satellite of Neptune Triton seen by Voyager 2 in 1989. © NASA
The satellite of Neptune Triton seen by Voyager 2 in 1989. © NASA

Triton was an asteroid, which has been trapped in the gravity field of Neptune. Then it was so massive than it ejected the satellites, which were present… if they existed. What this study tells us is that they probably existed. Nereid was probably one of them. Where are the others now? In my opinion, they could be almost anywhere, since the Solar System is a mess.

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.

Asteroids: Main Belt

Rotational stability of Ceres and Vesta

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Hi there! The question we address today is: how stable are the rotations of Ceres and Vesta? Do you remember these two guys? These are the largest two asteroids in the Main Belt, and the spacecraft Dawn visited them recently. It gave us invaluable information, like the maps of these bodies, their shapes, their gravity fields, their rotational states…
The study I present you today, Long-term orbital and rotational motions of Ceres and Vesta, by T. Vaillant, J. Laskar, N. Rambaux, and M. Gastineau, wonders how permanent the observed rotational state is. This French study has recently been accepted for publication by Astronomy & Astrophysics.

Outline

Ceres and Vesta
Simulating their rotation
The rotational stability
A symplectic integrator for a long-term study
Diffusion of the fundamental frequencies
Obliquity variations up to 20 degrees
The study and its authors

Ceres and Vesta

I already told you about these two bodies. (1)Ceres (“(1)” because it was the first asteroid to be discovered) is known since January 1801. It has been discovered by the Italian astronomer Giuseppe Piazzi at Palermo Astronomical Observatory. The spacecraft Dawn orbits it since April 2015, but is now inoperative since November 1st, 2018. We see Ceres as a body with a rocky core and an icy mantle, possibly with an internal ocean.

Before visiting Ceres, Dawn orbited Vesta, between July 2011 and September 2012. (4)Vesta has been discovered 6 years after Ceres, in 1807, by the German astronomer Heinrich Olbers. This is a differentiated body, probably made of a metallic core, a rocky mantle, and a crust. It has been heavily bombarded, showing in particular two large craters, Rheasilvia and Veneneia. Vesta is the source of the HED (Howardite Eucrite Diogenite) meteorites, which study is an invaluable source of information on Vesta (see here).

The surface of Vesta (detail). © NASA/JPL-Caltech/UCLA/MPS/DLR/IDA
The surface of Vesta (detail). © NASA/JPL-Caltech/UCLA/MPS/DLR/IDA

You can find below some numbers regarding Ceres and Vesta.

(1) Ceres (4) Vesta
Discovery 1801 1807
Semimajor axis 2.77 AU 2.36 AU
Eccentricity 0.116 0.099
Inclination 9.65° 6.39°
Orbital period 4.604 yr 3.629 yr
Spin period 9.07 h 5.34 h
Obliquity 4.00° 27.47°
Shape (965.2 × 961.2 × 891.2) km (572.6 × 557.2 × 446.4) km
Density 2.08 g/cm3 3.47 g/cm3

As you can see, Vesta is the closest one. It is also the most elongated of these bodies, i.e. you definitely cannot consider it as spherical. Both have significant orbital eccentricities, which means significant variations of the distance to the Sun (this will be important, wait a little). You can also see that these are fast rotators, i.e. they spin in a few hours, while their revolution periods around the Sun are of the order of 4 years. By the way, Vesta rotates twice faster than Ceres. Such numbers are pretty classical for asteroids.
You can also notice that Vesta is denser than Ceres, which is consistent with a metallic core.
Finally, the obliquities. The obliquity is the angle between the angular momentum (somehow the rotation axis… this is not exactly the same, but not too far) and the normal to the Sun. In other words, a null obliquity means that the body rotates along its orbit. An obliquity of 90° means that the body rolls on its orbit. An obliquity of 180° means that the body rotates along its orbit… but its rotation is retrograde (while it is prograde with a null obliquity).
Here, you can see that the obliquity of Ceres is close to 0, while the one of Vesta is 27°, which is significant. It is actually close to the obliquity of the Earth, this induces yearly variations of the insolation, and the seasons. On bodies like Ceres and Vesta, the obliquity would affect the survival of ice in deep craters, i.e. if the obliquity and the size of the crater prevents the Sun to illuminate it, then it would survive as ice.
From these data, the authors simulated the rotational motion of Ceres and Vesta.

Simulating their rotation

Simulating the rotation consists in predicting the time variations of the angles, which represent the rotational state of the bodies. For that, you must start from the initial conditions (what is the current rotational state?), and the physical equations, which rule the rotational motion.
For rigid bodies, rotation is essentially ruled by gravity. The gravitational perturbation of the Sun (mostly) and the planets affects the rotation. You quantify this perturbation with the masses of the perturbers, and the distances between your bodies (Ceres and Vesta), and these perturbers. To make things simple, just take Ceres and the Sun. You know the Solar perturbation on Ceres from the mass of the Sun, and the orbit of Ceres around it. This is where the eccentricity intervenes. Once you have the perturbation, you also need to determine the response of Ceres, and you have it from its shape. Since Vesta is more triaxial than Ceres, then its sensitivity to a gravitational should be stronger. It mostly is, but you may have some resonances (see later), which would enhance the rotational response.

The rotational stability

The question of the rotational stability is: you know, the numbers I gave you on the rotation… how much would they vary over the ages? This is an interesting question, if you want to know the variations of temperature on the surface. Would the ice survive? Would the surface melt? Would that create an atmosphere? For how long? Etc.
For instance, the same team showed that the obliquity of the Earth is very stable, and we owe it to our Moon, which stabilized the rotation axis of the Earth. This is probably a condition for the habitability of a telluric planet.

Let us go back to Ceres and Vesta. The authors focused on the obliquity, not on the spin period. In fact, they considered that the body rotated so fast, that the spin period would not have any significant effect. This permitted them to average the equations over the spin period, and resulted in a rotational dynamics, which moves much slower. And this allows to simulate it over a much longer time span.

A symplectic integrator for a long-term study

A numerical integration of the equations of the rotational motion, even averaged over the fast angle (I mean, the rotation period), may suffer from numerical problems over time. If you propagate the dynamics over millions of years, then the resulting dynamics may diverge significantly from the real one, because of an accumulation of numerical errors all along the process of propagation.

For that, use symplectic integrators. These are numerical schemes, which preserve the global energy of the dynamics, if you have no dissipation of course. But there are many problems of planetary dynamics, which permit you to neglect the dissipation.

When you can neglect the dissipation, your system is conservative. In that case, you can use the mathematical properties of the Hamiltonian systems, which preserve the total energy. That way, your solution does not diverge.

But how to determine whether your dynamics is stable or not? There are many tools for that (Lyapunov exponents, alignment indexes…) Here, the authors determined the diffusion of the fundamental frequencies of the system.

Diffusion of the fundamental frequencies

Imagine you orbit around the Sun, at a given period… actually the period depends on your semimajor axis, so, if it remains constant, then the orbital period remains constant. If your orbit is also disturbed by another perturber, you will see periodic variations in your orbital elements, which correspond to the period of the perturber. Very well. So, analyzing the frequencies which are present in your motion should give you constant numbers…

But what happens if your bodies drift? Then your frequencies will drift as well. In detecting these variations, which result from the so-called diffusion of the fundamental frequencies of the system, you detect some chaos in the system. I took the example of the orbital dynamics, but the same works for the rotation. For instance, the orbital frequencies appear in the time evolution of the rotational variables, since the orbit affects the rotation. But you also have proper frequencies of the rotational motion, for instance the period at which the angular momentum precesses around the normale to the orbit, and this period may drift as well…

The diffusion of the fundamental frequencies is one indicator of the stability. The authors also checked the variations of the obliquity of Ceres and Vesta, along their trajectories. They simulated the motion over 40 Myr (million years), in considering different possible numbers for the interior, and different initial obliquities.

Let us see now the results.

Obliquity variations up to 20 degrees

If you consider different possibilities, i.e. we do not know how these bodies were 40 Myr ago, then we see that it is theoretically possible for them to have been highly influenced by a resonance. This means that one fundamental frequency of the rotation would have been commensurable with periodic contributions of the orbital motion, and this would have resulted in a high response of the obliquity. For the present trajectories, the author estimate that the obliquity of Ceres could have varied between 2 and 20° these last 20 Myr, and the obliquity of Vesta between 21 and 45°.

To be honest, this is only a part of a huge study, which also investigates the stability of the orbital motions of Ceres and Vesta. Actually, these bodies are on chaotic orbits. This does not mean that they will be ejected one day, but that their orbits becomes uncertain, or inaccurate, after some tens of Myr.

The study and its authors

  • You can find the study here. The authors made it also freely available on arXiv, many thanks to them for sharing! And now the authors
  • Unfortunately I did not find any webpage for the first author Timothée Vaillant. You can find here the one of Jacques Laskar, second author of the study,
  • and the IAU page of Mickaël Gastineau.

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.

Satellites of Jupiter

Astrometry from close approaches

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Hi there! Today, we discuss of astrometry of the satellites of Jupiter. It consists in answering the question : where are they? Basically, you look at them, and you see where they are… well, it is more complicated than that, actually.
This is the opportunity to present APPROX – mutual approximations between the Galilean moons: the 2016-2018 observational campaign, by Bruno Morgado and several collaborators. Since this paper presents an observation campaign, involving Brazil and France, there are many observers, hence many co-authors. This study has recently been published in The Monthly Notices of the Royal Astronomical Society.

Outline

Astrometry of the natural satellites
Detecting physical phenomena
Absolute and relative astrometry
Many observational difficulties
The mutual approximation technique
The observation campaign
Very accurate results
The study and its authors

Astrometry of the natural satellites

In fact, you can make astrometry of any celestial object. Star, satellite, galaxy, whatever… It is of course easier when the body looks like a dot.

When we look at the celestial sphere, you look in 2D. The space is in 3D, but technically we see a projection of this volume on a sphere, which is called the celestial sphere. Since it is a 2D space, you can also consider two coordinates. Let us call them right ascension and declination. So, you want to know the motion of these bodies, you observe them, and measure their positions.

The astronomers of the past, I mean in the pre-photographic era, used a filar micrometer. This consisted of a screw and a reticle, made of two threads. When observing two celestial bodies, the observer saw two lines in the field, that (s)he could move thanks to the micrometric screw, one on one body, the other line on the other body, and from the motion of the screw he knew the projected (apparent) distance between the two bodies. So, only one dimension at that time.

And then came the photography: you take a picture of the field (small part of the sky), and you measure the coordinates of the bodies. This way you can get two coordinates. The techniques improved since then, with automatic surveys, taking automatic images of the sky, measuring automatically the coordinates,etc.

But why doing that?

Detecting physical phenomena

It is for understanding the motion of an object. For instance, if you take a natural satellite, you know that it orbits its parent planet, following the classical gravitation law of Newton (improved since Einstein and the discovery of general relativity, but you do not need that refinement to understand the dynamics of the natural satellites). But first you have to make sure it is a satellite of that planet. If it follows it on the sky, then it is fine. And to simulate its motion, you must know some parameters, especially the mass of the planet, of the satellite, the flattening of the planet, the masses of the other satellites (yes, they disturb each other). Well, that becomes tricky. And this is why you need those astrometric observations. Your dynamical model depends on some parameters, you fit them to the observations, and then you have the masses.

This way, you can say: OK, we have everything we need. Why still doing that once we have the masses? You can say that we need more accuracy, but once a spacecraft tours around the planet, it gives you all the data you need, doesn’t it? Including astrometric positions, and direct measurements of the masses.

My answer to that is:

  1. A spacecraft covers a pretty limited time span. You would need observations outside of that range, even less accurate, to detect a drift between the dynamical model and the real motion. And that drift would mean that something significant is not in the model, or maybe it is, but not accurately enough.
  2. And this comes to my second argument: the dissipative processes, especially the tides. During centuries we could consider that celestial mechanics was a conservative discipline, in the sense that there was no dissipation to consider. Of course, we knew there was some dissipation, otherwise it is physically irrelevant, but that dissipation was so small that at that time you could safely neglect it. Not any more.

Let us be more specific about tides. The parent body (Jupiter for the Galilean satellites, Saturn for its satellites, the Sun for the planet) exerted a differential torque on the volume of the small one, which generates stress and strain. In an extreme case, i.e. close enough to the planet (inside what we call the Roche limit), bodies can be destroyed (and this gives you the rings of Saturn).
For the classical satellites of the giant planets, the dissipation appears as volcanoes on Io, fractures on Europa, geysers on Enceladus. And in ephemerides (i.e. orbital motion) the induced energy losses result in secular (i.e. a very slow drift) migration over the ages. And we are now accurate enough to detect this tidal effect on the Moon, and in the systems of Jupiter and Saturn.

Numbers regarding this effect tell us how the planetary material reacts to solicitations, and permits us to extrapolate the migration, i.e. know the past and future of these systems.

Now let us go back to techniques of astrometry.

Absolute and relative astrometry

When you measure the coordinates of a celestial body, you need an origin, i.e. a zero, which is a reference. But the reference is usually not present in your field of view, which is limited (one degree is a huge field).
Fortunately, we can use the background stars as references. The stars are catalogued with their coordinates, and so if you have e.g. 20 catalogued stars in your field, then you have 20 points, which you know the coordinates. And this gives you the coordinates of the other points, i.e. the Solar System bodies.
Making catalogues of stars is not an easy task. ESA’s space observatory Gaia is on it!

Artist's impression of Gaia. © ESA
Artist’s impression of Gaia. © ESA

Differential astrometry is an alternative: for instance if you work on the natural satellites of a given system (let us say the Galilean satellites of Jupiter), it could be enough to know where the satellites are with respect to the other ones and to the parent planet. So, you make differential astrometry: you measure the difference between the coordinates of two given bodies.

As I told you, it is a little more complicated than just taking a picture. You must do it properly. Let us see that now.

Many observational difficulties

Of course, your sky should be clear. But this is not enough. When you take two pictures of an object, which does not move, will they put you the object at the same location? Not necessarily! Because of the seeing, which is due to the wind (the atmosphere), and which kind of noises your images. But this is not enough: you are not sure that all of the pixels of your camera have the same response. Of course they should… if only they could… You always have instrumental problems. You can partially compensate that by making a flat fielding, i.e. you take an image of a starless field (for instance before opening the dome) and this gives you the response of the sensors.
Another problem comes from the fact, that these bodies are not dots. You need to know where the center of mass is… which is not the center of figure, because of a phase effect. When you look at the Moon, it is usually not the full Moon, since part of it is in the umbra… the same happens for the other bodies. Beside this, there are problems due to the anisotropy of the reflection of the light on the surfaces of the satellites.

And let me finally mention timing problems: you do measure a position at a given time. But you need to be exact on that time! If not, then your measurement is inaccurate. In other words, you need to care for errors in positions and in time. If you record your images with a laptop, the internal clock may drift by several seconds. I can tell you that from my experience. So, you have to check it constantly. You can have an accurate clock with GPS systems.

I hope you are now convinced that astrometry is truly a science.

The mutual approximation technique

Other astrometry techniques than taking pictures exist. For instance, you can look for occultations: when an asteroid occultates a star, you do not see the star anymore. Since you know where the star is, you know where the asteroid was during the occultation. This technique also permits to get clues on the shape of the asteroid, with multiple observations, and sometimes even detect asteroids and rings. See here.

In the specific case of this study, the authors developed a technique, which is based on the timing of a minimum of the apparent distance between the two satellites. When two satellites are close to each other in the sky (I mean, in projection onto the celestial sphere), you reach a so-called precision premium, i.e. you optimize the accuracy of the measurements. The reason is that your measurement does not suffer from the field distortion. The two dots are so close that you have the same problems for both. So, the differential measurement is not affected.

Here, the authors measure the timing of the minimum of distance, from which they can determine a position, knowing the relative motion of the satellites from the available orbital theories (the ephemerides). Measuring this instant is not trivial, since actually it has no reason to correspond exactly to a recorded data. So, you take a series of images, on all of them you measure the distance, you plot it with respect to the date. And then you fit a polynomial function to the obtained data; the instant you measure corresponds to the minimum of your polynomial.

The authors published this technique two years ago, and this paper present a campaign of observations.

The observation campaign

The authors observed 66 different mutual approximations, from 6 different sites, which are

    • Itajubá (Minas Gerais, Brazil), equipped with a 60-cm telescope,
    • Foz do Iguaçu (Paraná, Brazil), equipped with a 28-cm telescope,
    • Guaratinguetá (São Paulo, Brazil), equipped with a 40-cm telescope,
    • Vitória (Espiríto Santo, Brazil), equipped with a 35-cm telescope,
    • Curitiba (Paraná, Brazil), equipped with a 25-cm telescope,
    • and the Observatoire de Haute-Provence (France), equipped with a 120-cm telescope.

These facilities permitted the determination of 104 central instants, which obviously means that some events, in fact 28 of them, were observed at least twice, i.e. from different sites. All of these telescopes were equipped with a narrow-band filter centered at 889 nanometers. This eliminates the light pollution by Jupiter.

Very accurate results

The authors get a mean accuracy of 11.3 mas (milli-arcseconds), which is ten times more accurate than classical observations. A good way to determine this accuracy is by a statistical comparison between the measurements, and the numbers predicted by the theory.
At this distance, i.e. the distance to Jupiter, 11.3 mas means 40 km, which is much smaller than the radii of these satellites (Io, Europa, Ganymede, and Callisto).

So, you see, this is a very promising technique, and supplementing the database of astrometric observations with such high-quality data can only lead to new discoveries.

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.

Comets

The Oort remembers

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Hi there! You may know that in the Solar System, we have long period comets. These are comets which visit us, i.e. visit the vicinity of the Sun and the Earth, but on orbits which suggest that they will not come back before some centuries, maybe more. The Dutch astronomer Jan Oort hypothesized in 1950 that these comets originate from a hypothetical, I mean unobserved, cloud, which is now known as the Oort cloud. It is supposed to lie between 2,000 and 200,000 astronomical units (AU).
In the study we discuss today, The “memory” of the Oort cloud, by Marc Fouchard, Arika Higuchi, Takashi Ito and Lucie Maquet, the authors wonder how the original Oort cloud was like. For that, they investigate whether the present observations of the comets originating from it contain any information on its original shape. This study has recently been published in Astronomy and Astrophysics.

Outline

The Oort cloud
The observable comets
Numerical simulations
Four classes of observable comets
Two models of cloud
The disk remembers
The study and its authors

The Oort cloud

As I said, the Oort cloud as a reservoir for long-period comets had been suggested by Jan Oort in 1950. Actually, its existence had been hinted 18 years before, in 1932 by the Estonian astronomer Ernst Öpik, but he did not think that the small bodies constituting this cloud could eventually become observable comets, in the sense that they would have anyway orbited too far from the Sun, even at perihelion.

We now think that the Oort cloud consists of two parts: an inner and an outer cloud. The inner cloud would have the shape of a torus, limiting the inclination of its constituents. It would lie between 2,000 and 20,000 AU (remember: Neptune orbits at only 30 AU). However, the outer cloud, or isotropic cloud, would have a spherical distribution. It would lie between 20,000 and 50,000 AU, and be much less dense than the inner one.

The observable comets

The information we dispose of come from the orbits of observable comets. A comet is a small icy body, which presents a cometary activity, i.e. outgassing. This comes from the sublimation of the ice.
This activity is favored by the temperature, which is directly linked to the distance to the Sun. This is particularly striking for comets, which have significantly elongated (eccentric) orbits around the Sun. When an orbit is eccentric, you have significant variations of the distance between the Sun and the body, in other words, significant variations of the temperature, and consequently of the cometary activity.
Dynamically, a comet can be characterized by its orbital elements. The most interesting one is, in my opinion, the semimajor axis, which gives you the period (the time interval between two approaches of the comet to the Sun).
Some comets have periods smaller than 20 years, and are called Jupiter-family comets. From 20 to 200 years, you have the Halley-type comets (after the well-known comet 1P/Halley), and beyond that limit you have the long-period comets. These are the comets, which are of interest for us, i.e. they are supposed to originate from the Oort cloud.
In fact, there are comets which orbits are even longer than that… in the sense that these comets may never return. These are comets with very high orbital eccentricities (>0.99), they are almost parabolic… and some of them are even hyperbolic, i.e. they are not dynamically bound to the Sun. Those ones may come from an extrasolar system, but this is another story…

Anyway, we speak about the long-period comets. And the question is: what information do their orbits contain on the primordial Oort cloud?

Numerical simulations

To understand how this information is preserved, the authors ran simulations of the orbits of more than 200 million comets. These are fictitious comets, evolving under the influence of

  • planetary perturbations,
  • stellar passages,
  • the Galactic tide.

Planetary perturbations

Planetary perturbations are the gravitational actions of the four giant planets (Jupiter, Saturn, Uranus, and Neptune). They may have dramatic consequences in case of close encounter: the comet is such a small body with respect to a giant planet that it could have almost every orbit after the encounter. Some comets might even be destroyed (remember Shoemaker-Levy 9).

Stellar passages

These comets, initially in the proto-Oort cloud, orbit very far from the Sun. This means that they are only weakly dynamically bound to it, and potentially sensitive to perturbations from other stellar systems. In particular if one of them passes by. The authors considered this effect in adding random passing stars. The velocities of the stars measured by the astrometric satellite Gaia permit to constrain the most recent stellar passages, but far from all of them.

The Galactic tide

The Galactic tide is the deformation of our Milky Way under the gravitational influence of the other galaxies. Previous studies have shown that it has a significant influence on the Oort cloud. The gravitational force exerted by the Sun is there weak enough for the Galactic tide to be significant.

Galactic tide can actually be seen on images of galaxies, which are close enough. This results in galaxies with irregular shape.

Tidal interaction between two galaxies, seen by the Hubble Space Telescope.
Tidal interaction between two galaxies, seen by the Hubble Space Telescope.

Four classes of observable comets

Before presenting the way the authors addressed that question, I would like to mention that they considered 4 different sub-classes of these long-period, observable comets.

First, let us define an observable comet: an observable comet has a perihelion at less than 5 AU of the Sun. The perihelion is the point of the orbit, which is the closest to the Sun, and 5 AU roughly corresponds to the orbit of Jupiter. Among these observable comets, the authors called

  • jumpers the comets which perihelion was larger than 10 AU during the previous passage,
  • and creepers the other ones.

And among these jumpers and creepers, the authors identified the comets, prefixed KQ, which required the assistance of a close encounter with a giant planet (a planetary kick) to push them outward, making them then sensitive enough to the stellar passages and the galactic tide to be injected into the observable zone.
The letters K and Q come from the two guys who identified this phenomenon, i.e. Nathan Kaib and Thomas Quinn, in 2009.

So, the four classes of observable long-period comets that the authors distinguished are

  • the jumpers,
  • the KQ-jumpers,
  • the creepers,
  • the KQ-creepers.

The reason why they distinguished these four classes is that they have different behaviors. So, different outcomes regarding the dynamics may be expected.

Two models of cloud

So, the question is: when you start from a given proto-Oort cloud, how will the observable comets look like? I mean, how many of them will be observable? How will their perihelions be distributed? How inclined will they be?

And this depends (I should rather say: is assumed to depend) on the structure of your initial proto-Oort cloud. For that, the authors considered two models:

  • A disk-like distribution, in which the inclinations are limited to 20°,
  • an isotropic cloud, in which the comets may have any inclination. As such, it looks like the shell of an empty sphere.

And among these two models, the authors used several sets of initial conditions or their comets, in changing the distribution of orbital energy from one set to another.

Now, let us discuss the results.

The disk remembers

Unsurprisingly, the disc model results in 4 to 8 times more observable comets than the isotropic one. This should have been expected, since the giant planets have limited inclinations. So, you should have a limited inclination yourself to receive the assistance of a planet to become observable. Since it is not a sine qua non condition, you can have observable comets with high inclinations anyway, thanks to the Galactic tide and stellar passages.

Another outcome of the paper is that the KQ objects are preferably retrograde. This maximizes their odds to survive, i.e. not to be ejected from the Solar System, in being less sensitive to planetary perturbations. This is not an original result, since Kaib and Quinn already met this conclusion, but it always gives confidence to find a result, which was already known. It suggests that your study is right.

The new result is in the memory. The present study shows that, if you started from an isotropic disk, then stellar passages have wiped out its structure. However, the observable comets would keep from an initial disk (and here I quote the paper):

  • a concentration of comets along the ecliptic plane for semimajor axes smaller than 7,000 AU,
  • the typical wave structure of the Galactic tide.

Now, we should determine whether the initial Oort cloud was more like a disk, a more like a shell. This actually depends on the whole process of formation of the Solar System. Several scenarios compete, which means that we currently do not know. Anyway, this study suggests that counting the observable comets could give a clue on the nature of the original distribution (disk-like or shell-like), and if it is a disk, then we could be able to guess part of its structure.

The future can only bring us more information, thanks to the observational data of comets to be discovered.

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.