Category Archives: Comets

9 interstellar asteroids?

Hi there! You may have recently heard of 1I/’Oumuamua, initially known as C/2017 U1, then A/2017 U1 (see here), where C stands for comet, A for asteroid, and I for interstellar object. This small body visited us last fall on a hyperbolic orbit, i.e. it came very fast from very far away, flew us by, and then left… and we shall never see it again. ‘Oumuamua has probably been formed in another planetary system, and its visit has motivated numerous studies. Some observed it to determine its shape, its composition, its rotation… and some conducted theoretical studies to understand its origin, its orbit… The study I present you today, Where the Solar system meets the solar neighbourhood: patterns in the distribution of radiants of observed hyperbolic minor bodies, by Carlos and Raúl de la Fuente Marcos, and Sverre J. Aarseth, is a theoretical one, but with a broader scope. This study examines the orbits of 339 objects on hyperbolic orbits, to try to determine their origin, in particular which of them might be true interstellar interlopers. This study has recently been accepted for publication in The Monthly Notices of the Royal Astronomical Society.

‘Oumuamua

I detail the discovery of ‘Oumuamua there. Since that post, we know that ‘Oumuamua is a red dark object, probably dense. It is tumbling, i.e. does not rotate around a single rotation axis, in about 8 hours. The uncertainties on the rotation period are pretty important, because of this tumbling motion. Something really unexpected is huge variations of brightness, which should reveal either a cigar-shaped object, or an object with extreme variations of albedo, i.e. bright regions alternating with dark ones… but that would be inconsistent with the spectroscopy, revealing a reddish object. This is why the dimensions of ‘Oumuamua are estimated to be 230 × 35 × 35 meters.

Artist's impression of 'Oumuamua. © ESO/M. Kornmesser
Artist’s impression of ‘Oumuamua. © ESO/M. Kornmesser

One wonders where ‘Oumuamua comes from. An extrapolation of its orbit shows that it comes from the current direction of the star Vega, in constellation Lyra… but when it was there, the star was not there, since it moved… We cannot actually determine around which star, and when, ‘Oumuamua has been formed.

Anyway, it was a breakthrough discovery, as the first certain interstellar object, with an eccentricity of 1.2. But other bodies have eccentricities larger than 1, which make them unstable in the Solar System, i.e. gravitationally unbound to the Sun… Could some of them be interstellar interlopers? This is the question addressed by the study. If you want to understand what I mean by eccentricity, hyperbolic orbit… just read the next section.

Hyperbolic orbits

The simplest orbit you can find is a circular one: the Sun is at the center, and the planetary object moves on a circle around the Sun. In such a case, the eccentricity of the orbit is 0. Now, if you get a little more eccentric, the trajectory becomes elliptical, and you will have periodic variations of the distance between the Sun and the object. And the Sun will not be at the center of the trajectory anymore, but at a focus. The eccentricity of the Earth is 0.017, which induces a closest distance of 147 millions km, and a largest one of 152 millions km… these variations are pretty limited. However, Halley’s comet has an eccentricity of 0.97. And if you exceed 1, then the trajectory will not be an ellipse anymore, but a branch of hyperbola. In such a case, the object can just make a fly-by of the Sun, before going back to the interstellar space.

Wait, it is a little more complicated than that. In the last paragraph, I assumed that the eccentricity, and more generally the orbital elements, were constant. This is true if you have only the Sun and your object (2-body, or Kepler, problem). But you have the gravitational perturbations of planets, stars,… and the consequence is that these orbital elements vary with time. You so may have a hyperbolic orbit becoming elliptical, in which case an interstellar interloper gets trapped, or conversely a Solar System object might be ejected, its eccentricity getting larger than 1.

The authors listed three known mechanisms, likely to eject a Solar System object:

  1. Close encounter with a planet,
  2. Secular interaction with the Galactic disk (in other words, long term effects due to the cumulative interactions with the stars constituting our Milky Way),
  3. Close encounter with a star.

339 hyperbolic objects

The authors identified 339 objects, which had an eccentricity larger than 1 on 2018 January 18. The objects were identified thanks to the Jet Propulsion Laboratory’s Small-Body Database, and the Minor Planet Center database. The former is due to NASA, and the latter to the International Astronomical Union.

Once the authors got their inputs, they numerically integrated their orbits backward, over 100 kyr. These integrations were made thanks to a dedicated N-body code, powerful and optimized for long-term integration. Such algorithm is far from trivial. It consists in numerically integrating the equations of the motion of all of these 339 objects, perturbed by the Sun, the eight planets, the system Pluto-Charon, and the largest asteroids, in paying attention to the numerical errors at each iteration. This step is critical, to guarantee the validity of the results.

Some perturbed by another star

And here is the result: the authors have found that some of these objects had an elliptical orbit 100 kyr ago, meaning that they probably formed around the Sun, and are on the way to be expelled. The authors also computed the radiants of the hyperbolic objects, i.e. the direction from where they came, and they found an anisotropic distribution, i.e. there are preferred directions. Such a result has been obtained in comparing the resulting radiants from the ones given by a random process, and the distance between these 2 results is estimated to be statistically significant enough to conclude an anisotropic distribution. So, this result in not based on a pattern detected by the human eye, but on statistical calculations.

In particular, the authors noted an excess of radiants in the direction of the binary star WISE J072003.20-084651.2, also known as Scholz’s star, which is currently considered as the star having had the last closest approach to our Solar System, some 70 kilo years ago. In other words, the objects having a radiant in that direction are probably Solar System objects, and more precisely Oort cloud objects, which are being expelled because of the gravitational kick given by that star.

8 candidate interlopers

So, there is a preferred direction for the radiants, but ‘Oumuamua, which is so eccentric that it is the certain interstellar object, is an outlier in this radiant distribution, i.e. its radiant is not in the direction of Scholz’s star, and so cannot be associated with this process. Moreover, its asymptotical velocity, i.e. when far enough from the Sun, is too large to be bound to the Sun. And this happens for 8 other objects, which the authors identify as candidate interstellar interlopers. These 8 objects are

  • C/1853 RA (Brunhs),
  • C/1997 P2 (Spacewatch),
  • C/1999 U2 (SOHO),
  • C/2002 A3 (LINEAR),
  • C/2008 J4 (McNaught),
  • C/2012 C2 (Bruenjes),
  • C/2012 S1 (ISON),
  • C/2017 D3 (ATLAS).

Do we know just one, or 9 interstellar objects? Or between 1 and 9? Or more than 9? This is actually an important question, because that would constrain the number of detections to be expected in the future, and have implications for planetary formation in our Galaxy. And if these objects are interstellar ones, then we should try to investigate their physical properties (pretty difficult since they are very small and escaping, but we did it for ‘Oumuamua… maybe too late for the 8 other guys).

Anyway, more will be known in the years to come. More visitors from other systems will probably be discovered, and we will also know more on the motion of the stars passing by, thanks to the astrometric satellite Gaia. Stay tuned!

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 Brazil Nut Effect on asteroids

Hi there! You know these large nuts called Brazil nuts? Don’t worry, I will not make you think that they grow on asteroids. No they don’t. But when you put nuts in a pot, or in a glass, have you ever noticed that the biggest nuts remain at the top? That seems obvious, since we are used to that. But let us think about it… these are the heaviest nuts, and they don’t sink! WTF!!! And you have the same kind of effect on small bodies, asteroids, planetesimals, comets… I present you today a Japanese study about that, entitled Categorization of Brazil nut effect and its reverse under less-convective conditions for microgravity geology by Toshihiro Chujo, Osamu Mori, Jun’ichiro Kawaguchi, and Hajime Yano. This study has recently been published in The Monthly Notices of the Royal Astronomical Society.

Brazil Nut and Reverse Brazil Nut effects

The idea is easy to figure out. If you have a pot full of different nuts, then the smallest ones will be naturally closer to the bottom, since they are small enough to fill the voids between the largest ones. For the same reason, if you fill a bucket first with stones and then with sand, the sand will naturally reach the bottom, flowing around the stones. Flowing is important here, since the sand pretty much behaves as a fluid. And of course, if you put the sand in the bucket first, and then the stones, the stones will naturally be closer to the top. Well, this is the Brazil Nut Effect.

OK, now let us make the story go one step further… You have an empty bucket, and you put sand inside… a third of it, or a half… this results as a flat structure. You put stones, which then cover the sand, lying on its surface… and you shake. You shake the bucket, many times… what happen? the sand is moving, and makes some room for the stones, or just some of them, which migrate deeper… if you shake enough, then some of them can even reach the bottom. This is the Reverse Brazil Nut Effect.

And the funny thing is that you can find this effect on planetary bodies! Wait, we may have a problem… when the body is large enough, then the material tends to melt, the heaviest one migrating to the core. So, the body has to be small enough for its interior being ruled by the Brazil Nut Effect, or its reversed version. If the body is small enough, then we are in conditions of microgravity. The authors give the examples of the Near-Earth Asteroid (433)Eros, its largest diameter being 34.4 km, the comet 67P/Churyumov-Gerasimenko, which is ten times smaller in length, and the asteroid (25143)Itokawa, its largest length being 535 meters. All of these bodies are in conditions of microgravity, and were visited by spacecraft, i.e. NEAR Shoemaker for Eros in 2001, Rosetta for Churyumov-Gerasimenko in 2014, and Hayabusa for Itokawa in 2003. And all of these space missions have revealed pebbles and boulders at the surface, which motivated the study of planetary terrains in conditions of microgravity.

Eros seen by NEAR Shoemaker. © NASA/JPL-Caltech/JHUAPL
Eros seen by NEAR Shoemaker. © NASA/JPL-Caltech/JHUAPL

I mentioned the necessity to shake the bucket to give a chance to Reverse Brazil Nut Effect. How to shake these small bodies? With impact, of course. You have impactors everywhere in the Solar System, and small bodies do not need impactors to be large to be shaken enough. Moreover, this shaking could come from cometary activity, in case of a comet, which is true for Churyumov-Gerasimenko.

The authors studied this process both with numerical simulations, and lab experiments.

Numerical simulations

The numerical simulations were conducted with a DEM code, for Discrete Element Modeling. It consisted to simulate the motion of particle which touch each others, or touch the wall of the container. These particles are spheres, and you have interactions when contact. These interactions are modeled with a mixture of spring (elastic interaction, i.e. without dissipation of energy) and dashpot (or damper, which induces a loss of energy at each contact). These two effects are mixed together in using the so-called Voigt rheology.

In every simulation, the authors had 10,224 small particles (the sand), and a large one, named intruder, which is the stone trying to make its way through the sand.

The simulations differed by

  • the density of the intruder (light as acryl, moderately dense as glass, or heavy as high-carbon chromium steel),
  • the frequency of the shaking, modeled as a sinusoidal oscillation over 50 cycles,
  • the restitution coefficient between the sand of the intruder. If it is null, then you dissipate all the energy when contact between the intruder and the sand, and when it is equal to unity then the interaction is purely elastic, i.e. you have no energy loss.

Allowing those parameters to vary will result in different outcomes of the simulations. This way, the influence of each of those parameters is being studied.

A drawback of some simulations is the computation time, since you need to simulate the behavior of each of the particles simultaneously. This is why the authors also explored another way: lab experiments.

Lab experiments

You just put sand in a container, you put an intruder, you shake, and you observe what is going on. Well, said that way, it seems to be easy. It is actually more complicated than that if you want to make proper job.

The recipient was an acryl cylinder, put on a vibration test machine. This machine was controlled by a device, which guaranteed the accuracy of the sinusoidal shaking, i.e. its amplitude, its frequency, and the total duration of the experiment. The intruder was initially put in the middle of the sand, i.e. half way between the bottom of the recipient and the surface of the sand. If it reached the bottom before 30,000 oscillation cycles, then the conclusion was RBNE, and if it raised from the surface the conclusion was BNE. Otherwise, these two effects were considered to be somehow roughly balanced.

But wait: the goal is to model the surface of small bodies, i.e. in conditions of microgravity. The authors did the experiment on Earth, so…? There are ways to reproduce microgravity conditions, like in a parabolic flight, or on board the International Space Station, but this was not the case here. The authors worked in a lab, submitted to our terrestrial gravity. The difficulty is to draw conclusions for the asteroids from Earth-based lab experiments.

At this point, the theory assists the experimentation. If you write down the equations ensuing from the physics (I don’t do it… feel free to do so if you want), these equations ruling the DEM code for instance, you will be able to manipulate them (yes you will) so as to make them depend on dimensionless parameters. For instance: your size is in meters (or in feet). It has the physical dimension of a length. But if you divide your size with the one of your neighbor, you should get something close to unity, but this will be a dimensionless quantity, as the ratio between your size and your neighbor’s. The size of your neighbor is now your reference (let him know, I am sure he would be delighted), and if your size if larger than 1, it means that you are taller than your neighbor (are you?). In the case of our Brazil Nut experiment, the equations give you a gravity, which you can divide by the local one, i.e. either the gravity of your lab, or the microgravity of an asteroid. The result of your simulation will be expressed with respect to this ratio, which you can then re-express with respect to the microgravity of your asteroid. So, all this is a matter of scale. These scaling laws are ubiquitous in lab experiments, and they permit to work in many other contexts.

Triggering the Reverse Brazil Nut effect

And here are the results:

  • The outcomes of the experiments match the ones of the numerical simulations.
  • The authors saw practically no granular convection, i.e. the sand initially at the bottom does not migrate to the top. This is here an analogy with fluid mechanics, in which water at the bottom can raise to the top, especially when it warms (warm water is less dense than cold one).
  • Densest intruders are the likeliest to migrate to the bottom.
  • The authors identified 3 distinct behaviors for the particles, depending on a dimensionless acceleration Γ.

These behaviors are:

  1. Slow Brazil Nut Effect,
  2. Fast BNE, for which the intruder requires less oscillation cycles to raise,
  3. Fluid motion, which may induce RBNE. This is favored by rapid oscillations of the shaking.

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, and (NEW) Instagram.

Breaking an asteroid

Hi there! Asteroids, these small bodies in the Solar System, are fascinating by the diversity of their shapes. This is a consequence of their small sizes. Another consequence is their weakness, which itself helps to split some of them into different parts, sometimes creating binary objects, asteroids families… The study I present you today, Internal gravity, self-energy, and disruption of comets and asteroids, by Anthony R. Dobrovolskis and Donald G. Korycansky, proposes an accurate computation of the required energy to provoke this break-up, at any place of the asteroid, i.e. you are more efficient when you hit at a given location. This study has recently been accepted for publication in Icarus.

Shapes of asteroids

Please allow me, in this context, to call asteroid a comet, a comet being a small body, i.e. like an asteroid, but with a cometary activity. The important thing is that the involved bodies are small enough.

Beyond a given size, i.e. a diameter of ~400 km, a planetary body is roughly spheroidal, i.e. it is an ellipsoid with it two equatorial axes almost equal and the polar one smaller, because of its rotation. For a tidally despun body, like the Moon, or a satellite of a giant planet, the shape is more triaxial, since the tidal (gravitational) action of the parent planet tends to elongate the equatorial plane. The same phenomenon affects Mercury.

However, for smaller bodies, the self-gravitation is not strong enough to make the body look more or less like a sphere. As a consequence, you can have almost any shape, some bodies are bilobate, some are contact binaries, i.e. two bodies which permanently touch together, some others are rubble piles, i.e. are weak aggregates of rocks, with many voids.

These configurations make these bodies likely to undergo or have undergone break-up. This can be quantified by the required energy to extract some material from the asteroid.

The energies involved

For that, an energy budget must be performed. The relevant energies to consider are:

  • The impact disruption energy: the minimum kinetic energy of an impactor, to shatter the asteroid and remove at least half of its mass,
  • The shattering energy: the minimum energy needed to shatter the asteroid into many small pieces. It is part of the impact disruption energy. This energy is roughly proportional to the mass of the asteroid. It represents the cohesion between the adjacent pieces.
  • The binding energy: this energy binds the pieces constituting the asteroid. In other words, once you have broken an asteroid (don’t try this at home!), you have to make sure the pieces will not re-aggregate… because of the binding energy. For that, you have to bring enough energy to disperse the fragments.
  • The self-gravitational energy: due to the mutual gravitational interaction between the blocks constituting the asteroids. Bodies smaller than 1 km are strength-dominated, i.e. they exist thanks to the cohesion between the blocks, which is the shatter energy. However, larger bodies are gravity-dominated.
  • The kinetic energy of rotation: the spin of these bodies tends to enlarge the equatorial section. In that sense, it assists the break-up process.

This study addresses bodies, which are far enough from the Sun. This is the reason why I do not mention its influences, i.e. the tides and the thermic effects, which could be relevant for Near-Earth Objects. In particular, the YORP effect is responsible for the fission of some of them. I do not mention the orbital kinetic energy of the asteroid either. Actually the orbital motion is part of the input energy brought by an impact, since the relative velocity of the impactor with respect to the target is relevant in this calculation.

I now focus on the two cases studied by the authors to illustrate their theory: the asteroid Kleopatra and the comet 67P/Churyumov-Gerasimenko.

2 peculiar cases: Kleopatra and Churyumov-Gerasimenko

216 Kleopatra is a Main-Belt asteroid. Adaptive optics observations have shown that is is constituted of two masses bound by material, giving a ham-bone shaped. As such, it can be considered as a contact binary. It is probably a rubble pile. Interestingly, observations have also shown that Kleopatra has 2 small satellites, Alexhelios and Cleoselene, which were discovered in 2008.

Reconstruction of the shape of Kleopatra. © NASA
Reconstruction of the shape of Kleopatra. © NASA

However, 67P Churyumov-Gerasimenko is a Jupiter-family comet, i.e. its aphelion is close to the orbit of Jupiter, while its perihelion is close to the one of the Earth. It has an orbital period of 6.45 years, and was the target of the Rosetta mission, which consisted of an orbiter and a lander, Philae. Rosetta orbited Churyumov-Gerasimenko between 2014 and 2016. The shape of this comet is sometimes described as rubber ducky, with two dominant masses, a torso and a head, bound together by some material, i.e. a neck.

Churyumov-Gerasimenko seen by Rosetta. © ESA
Churyumov-Gerasimenko seen by Rosetta. © ESA
216 Kleopatra 67P/Churyumov-Gerasimenko
Semimajor axis 2.794 AU 3.465 AU
Eccentricity 0.251 0.641
Inclination 13.11° 7.04°
Spin period 5.385 h 12.761 h
Mean radius 62 km 2.2 km
Magnitude 7.30 11.30
Discovery 1880 1969

The irregular shapes of these two bodies make them interesting targets for a study addressing the gravitation of any object. Let us see now how the authors addressed the problem.

Numerical modeling

Several models exist in the literature to address the gravity field of planetary bodies. The first approximation is to consider them as spheres, then you can refine in seeing them as triaxial ellipsoids. For highly irregular bodies you can try to model them as cuboids, and then as polyhedrons. Another way is to see them as duplexes, this allows to consider the inhomogeneities dues to the two masses constituting bilobate objects. The existence of previous studies allow a validation of the model proposed by the authors.

And their model is a finite-element numerical modeling. The idea is to split the surface of the asteroid into small triangular planar facets, which should be very close to the actual surface. The model is all the more accurate with many small facets, but this has the drawback of a longer computation time. The facets delimit the volume over which the equations are integrated, these equations giving the local self-gravitational and the impact disruption energies. The authors also introduce the energy rebate, which is a residual energy, due to the fact that you can remove material without removing half of it. This means that the impact disruption energy, as it is defined in the literature, is probably a too strong condition to have extrusion of material.
The useful physical quantities, which are the gravitational potential, the attraction, and the surface slope, are propagated all along the body thanks to a numerical scheme, which accuracy is characterized by an order. This order quantifies the numerical approximation which is made at each integration step. A higher order is more accurate, but is computationally more expensive.

Once the code has been run on test cases, the authors applied it on Kleopatra and Churyumov-Gerasimenko, for which the shape is pretty well known. They used meshes of 4,094 and 5,786 faces, respectively.

Results

The validation phase is successful. The authors show that with a 3rd order numerical scheme, they recover the results present in the literature for the test cases with an accuracy of ~0.1%, which is much better than the accuracy of the shape models for the real asteroids. Regarding Kleopatra and Churyumov-Gerasimenko, they get the gravity field at any location, showing in particular excesses of gravity at the two lobes.

Such a study is particularly interesting for further missions, which would determine the gravity field of asteroids, which would then be compared with the theoretical determination by this code. Other applications are envisaged, the authors mentioning asteroid mining.

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 and Facebook.

And Merry Christmas!

Rotation and activity of a comet

Hi there! We, Earthians, are regularly visited by periodic comets, the most famous one being probably 1P/Halley, which will visit us in 2061. Since we cannot wait, we study others of that kind. Today I tell you about 49P / Arend-Rigaux. This is the opportunity for me to present you The rotation and other properties of Comet 49P/Arend-Rigaux, 1984 – 2012, by Nora Eisner, Matthew M. Knight and David G. Schleicher. This study has recently been published in The Astronomical Journal.

The comet 49P / Arend-Rigaux

The comet 49P / Arend-Rigaux has been discovered in February 1951 at the Royal Observatory of Belgium, by Sylvain Arend and Fernand Rigaux. It is a periodic comet of the Jupiter family, i.e. with a period smaller than 20 years. Its period is actually 6.71 years, its semimajor axis 3.55 AU (astronomical units, 1 AU being 150 millions km, i.e. the Sun-Earth distance), its eccentricity 0.6, and its orbital inclination 19°, with respect to the ecliptic. These numbers are extracted from the JPL Small-Body Database Browser, and are calculated at the date Apr 6, 2010. I have plotted below the distances Sun-comet and Earth-comet.

Distance to the Sun.
Distance to the Sun.
Distance to the Earth.
Distance to the Earth.

The distance to the Sun clearly shows the periodic variations. The orbit of the Earth is at 1 AU, the one of Mars at 1.5 AU, and the one of Jupiter at 5.2 AU. Every 6.71 years, the comet reaches its perihelion, i.e. minimizes its distance to the Sun. This proximity warms the comet and provokes an excess of cometary activity, i.e. sublimation of dirty ice. At these occasions, the distance with the Earth is minimized, but with variations due to the orbital motion of the Earth. We can see for instance that the comet gets pretty close to the Earth in 1951 (when it was discovered), in 1984, and in early 2032. These are favorable moments to observe it. The paper I present you today is mainly (but not only) based on photometric observations made between January and May 2012, at Lowell Observatory.

Observations at Lowell Observatory

Lowell Observatory is located close to Flagstaff, AZ (USA). It was founded by the famous Percival Lowell in 1894, and is the place where Clyde Tombaugh discovered Pluto, in 1930. Among its facilities is the 4.28 m Discovery Channel Telescope, but most of the data used in this study were acquired with the 1.1 m Hall telescope, which is devoted to the study of comets, asteroids, and Sun-like stars. The authors also used a 79 cm telescope. The observations were made in the R(ed) band.

The data

Besides these 33 observation nights during the first half of 2012, the authors used data acquired close to the 1984 and 2005 perihelion passages, even if the 2005 ones revealed unusable. The observations consists to measure the magnitude (somehow, the luminosity) of the comet, in correcting for atmospheric problems, so as to be able to detect the variations of this magnitude. You can find below an example of data:

Magnitude of 49P / Arend-Rigaux measured in April 2012.
Magnitude of 49P / Arend-Rigaux measured in April 2012.

Of course, the data have holes, since you cannot observe during the day. Moreover, the comet needs to be visible from Arizona, otherwise it was just impossible to observe it and make any measurements.

We can see a kind of periodicity in the magnitude, this is a signature of the rotation of the comet.

Measuring the rotation

Most of the planetary bodies are kinds of triaxial ellipsoids. Imagine we are in the equatorial plane of one of them. We see an alternation of the long and short axes of its equatorial section. If the albedo of the surface element we face depends mainly on its curvature (it depends on it, but mainly may be an overstatement), then we should see two peaks during a period. As a consequence, the period of the lightcurve we observe should be half the rotation period of the comet.

In combining all the measurements, the authors managed to derive a rotation period of 13.45 ± 0.01 hour. For that, they used two different algorithms, which gave very close results, giving the authors confidence in their conclusions. The first one, Phase Dispersion Minimization (PDM), consists to assume a given period, split the measurements into time intervals of this period, and overlap them. The resulting period gives to the best overlap. The other algorithm is named Lomb-Scargle, following its authors. It is a kind of Discrete Fourier Transform, but with the advantage of not requiring uniformly sampled data.

In addition to this rotation period, the authors detected an increasing trend in the 2012 data, as if the spin of the comet accelerated. This is in agreement with an alteration of the measured rotation from the Earth, which moves, and reveals a retrograde rotation, i.e. an obliquity close to 180°. In other words, this is an illusion due to the motion of the observer, but this illusion reveals the obliquity.

Moreover, in comparing the 2012 data with the ones of 1984, the authors managed to detect a variation in the rotation period, not larger than 54 seconds. This is possible regarding the fact that the comet is altered by each perihelion passage, since it outgasses. In this case, that would imply a change of at the most 14 seconds of the rotation period between two passages. Such variations have also been detected for at least 4 other comets (2P/Encke, 9P/Tempel 1, 10P/Tempel 2, and 103P/Hartley 2, see Samarinha and Mueller (2013)).

Comet Period (h) Variation (s)
2P/Encke 11 240
9P/Tempel 1 41 -840
10P/Tempel 2 9 16.2
103P/Hartley 2 18 7200
49P/Arend-Rigaux 13.45 -(>14)

Finally, since the lightcurve is a signature of the shape as well, the authors deduced from the amplitude of variation that the axial ratio of the nucleus, i.e. long axis / short axis, should be between 1.38 and 1.63, while an independent, previous study found 1.6.

Cometary activity

49P / Arend-Rigaux has a low activity. Anyway, the authors detected an event of impulse-type outburst, which lasted less than 2 hours. The analysis of the coma revealed an excess of cyanides with respect to the 1984 passage. Moreover, 49P / Arend-Rigaux is the first comet to show hydroxyde.

The study and its authors

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

The activity of the comet C/2015 ER61

Hi there! Today’s post is on the comet C/2015 ER61. Behind this weird name is a small object orbiting the Sun on a highly elongated orbit, which currently shows us a tail. The associated study is Beginning of activity in long-period comet C/2015 ER61 (PANSTARRS), by Karen J. Meech, Charles A. Schambeau, Kya Sorli, Jan T. Kleyna, Marco Micheli, James Bauer, Larry Denneau, Jacqueline V. Keane, Elizabeth Toller, Richard Wainscoat, Olivier Hainaut, Bhuwan Bhatt, Devendra Sahu, Bin Yang, Emily Kramer and Gene Magnier. It has recently been published in The Astronomical Journal.

C/2015 ER61‘s facts

This comet was discovered two years ago, in March 2015, by the telescope Pan-STARRS 1, located on the Haleakalā, Hawai’i. Its distance to the Sun was then 8.44 Astronomical Units, its absolute magnitude about 12, and no tail was visible. As such, it was supposed to be a Manx object, a Manx being a tailless cat. A Manx object would be a comet, which had no activity anymore, as if the lighter elements had already gone.

From its magnitude, it was guessed that its radius was about 10 km. Its apparent lack of activity triggered enough interest for the object to be followed, this in particularly permitted to determine its orbit, and showed that it had a huge eccentricity, i.e. some 0.998. When the eccentricity reaches 1, then the orbit is parabolic, so the orbit of C/2015 ER61 is almost parabolic. Further observations showed the beginning of a period of activity, proving that C/2015 ER61 (I would appreciate a funnier nickname…) is actually not a Manx. This period is not done yet, and the activity is actually increasing, as the comet is approaching the Sun. At its smallest distance, i.e. the perihelion, its distance to the Sun is 1.04 AU, i.e. it almost crosses the orbit of the Earth (don’t worry, I said “almost”). So, observing this comet today reveals a tail.

We are actually pretty lucky to be able to observe it, since its orbital period is some 10,000 years. This comet is considered to belong to the Oort cloud, which is a reservoir of comets at the edge of our Solar System.

Cometary outgassing

Since the comet model by Fred L. Whipple, published between 1950 and 1955, a comet is seen as a kind of dirty snowball, with a nucleus, and icy elements, which tend to sublimate when approaching the Sun, because of the elevation of the temperature. This hypothesis was confirmed in 1986 when we were visited by the well-known comet 1P/Halley (you know, Halley’s comet).
The idea is this: you have some water ice, some CO, some CO2, trapped on the comet. When it is warm enough, it sublimates.

But the intensity of the sublimation depends on several parameters:

  • the thermal inertia of the comet: how does the temperature elevate?
  • its albedo: which fraction of the incident Solar light flux is reflected?
  • its density
  • the quantity of elements, which are likely to be sublimated
  • their depth: if they are not at the surface, the heat needs to be conducted deep enough for them to sublimate
  • the distance to the Sun (of course)
  • etc.

This means that observing and measuring this outgassing gives some physical properties of the comet.

The observation facilities

To conduct this study, several observation facilities were used:

  • Pan-STARRS1 (PS1): This stands for Panoramic Survey Telescope and Rapid Response System. This is a 1.8m wide-field telescope,
  • Gemini North: this is a 8.19 m telescope, which is based in Hawai’i. It has a twin brother, Gemini South, which is based in Chile,
  • Canada-France-Hawai’i Telescope (CFHT): this 3.58m telescope is part of the Mauna Kea Observatory. For this study, the MegaPrime/Megacam wide-field imager was used, which gives of fied of view of 1°,
  • ATLAS: (for Asteroid Terrestrial-impact Last Alert System). This will be a network of two 0.5m-telescopes, both based in Hawai’i. At this time, only the ATLAS-Haleakalā has begun full operation,
  • Himalayan Chandra Telescope (HCT): this is a 2.01 m optical-infrared telescope, which is part of the Indian Astronomical Observatory, which stands on Mount Saraswati, Digpa-ratsa Ri, Hanle, India,
  • Wide-field Infrared Survey Explorer (WISE): this is an infrared space telescope, on a Sun-synchronous polar orbit. It is used in the program NEOWISE, NEO standing for Near-Earth Objects.

The diversity of observation facilities explains the numbers of authors signing this study. The observations span from February 2014 to February 2017, which means that there are pre-discovery observations. It is always easier to find an object when you know where it is, which permitted to find C/2015 ER61 on images, which were taken before its discovery.

Results

These observations (see the Figure) has shown a variation of the magnitude, which could be expected since the comet approached the Earth, but too large to be explained by its trajectory. Actually, it is enhanced by the activity of the comet, more precisely by the sublimation of CO and CO2, starting in early 2015.

The measured apparent magnitude of the comet, with respect to the date and the distance to the Sun. We can see that the comet is brighter when closer to the Sun, because of the outgassing. The measurements have some uncertainties, which are not represented here. This figure is drawn for the Tab.1 Observation Log of the paper.

The authors modeled the warming of the comet and the sublimation of the elements, in using the well-known heat equation. The observed tail suggests a radius of the nucleus of about 9 km, which is consistent with previous guesses. Moreover, they suggest that the CO2 is present at a depth of about 0.4 m. If it were present at the surface, then sublimation would have been observed even when the comet was 20 AU away from the Sun.

The closest approach of the comet with the Earth was on April 4, and with the Sun on May 10, which would result in a peak of activity… probably with some delay, please give the comet a chance to warm!

To know more

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