Tag Archives: Observations

A new contact binary

Hi there! Today I will tell you on the discovery that an already known Trans-Neptunian Object is in fact probably a contact binary. This is the opportunity for me to present you 2004 TT357: A potential contact binary in the Trans-Neptunian Belt by Audrey Thirouin, Scott S. Sheppard, and Keith S. Noll. This study has recently been published in The Astrophysical Journal.

2004 TT357‘s facts

As suggested by its name, 2004 TT357 was discovered in 2004. More precisely in August by a team led by Marc W. Buie, at Kitt Peak Observatory, Arizona, USA, on the 4-m Mayall telescope. From its magnitude, its radius is estimated to be between 87 and 218 km, depending on the albedo of the asteroid, i.e. the fraction of Solar light which is reflected by its surface. This albedo is unknown. You can find below its orbital elements.

Orbital elements of 2004 TT357
Semimajor axis 54.97 AU
Eccentricity 0.43
Inclination
Orbital period 408 y

These elements show that 2004 TT357 is in a 5:2 mean-motion resonance in Neptune, i.e. it performs 2 revolutions around the Sun while Neptune makes 5. This makes 2004 TT357 a Scaterred Disc Resonant Object. Its high eccentricity is probably at least partly due to this resonance.

Contact binaries

In astronomy, a binary object is a group of two objects, which are so linked together that they orbit around a common barycenter. Of course, their separation is pretty small. There are binary stars, here we speak about binary asteroids.
A contact binary is a kind of extreme case, in which the two components touch each other. In some sense, this is a single object, but with two different lobes. This was probably a former classical binary, which lost enough angular momentum so that the two objects eventually collided, but slowly enough to avoid any catastrophic outcome. It is thought that there is a significant fraction of contact binaries in the Solar System, i.e. between 5% and 50%, depending on the group you are considering.

Characterizing a known object as a contact binary is not an easy task, particularly for the Trans-Neptunian Objects, because of their distance to us. Among them, only (139775) 2001 QG298 is a confirmed contact binary, while 2003 SQ317 and (486958) 2014 MU69 are probable ones. This study concludes that 2004 TT357 is a probable one as well.

Observations at Lowell Observatory

Lowell Observatory is located in Flagstaff, Arizona, USA. It has been founded by Percival Lowell in 1894, and among its achievements is the discovery of the former planet Pluto in 1930, by Clyde Tombaugh. Currently, the largest of its instruments is the 4.3-m Discovery Channel Telescope (DCT), which has been partly funded by Discovery Communications. This telescope has its first light in April 2012, it is located in the Coconino National Forest near Happy Jack, Arizona, at an altitude of 2,360 meters.

The Discovery Channel Telescope. © Lowell Observatory
The Discovery Channel Telescope. © Lowell Observatory

The authors used this telescope, equipped with the Large Monolithic Imager (LMI). They acquired two sets of observation, in December 2015 and February 2017, during which they posed during 600 and 700 seconds, respectively. 2004 TT357 had then a mean visual magnitude of 22.6 and 23, respectively.

The Large Monolithic Imager. © Lowell Observatory
The Large Monolithic Imager. © Lowell Observatory

Analyzing the data

You can find below the photometric measurements of 2004 TT357.

The first set of observations. The measurements are represented with the uncertainties.
The first set of observations. The measurements are represented with the uncertainties.
The second set of observations. The measurements are represented with the uncertainties.
The second set of observations. The measurements are represented with the uncertainties.

We can see pretty significant variations of the incoming light flux, these variations being pretty periodic. This periodicity is the signature of the rotation of the asteroid, which does not always present the same face to the terrestrial observer. From these lightcurves, the authors measure a rotation period of 7.79±0.01 h. From the curves, the period seems twice smaller, but if we consider that the asteroid should be an ellipsoid, then its geometrical symmetries tell us that our line of sight should be aligned twice with the long axis and twice with the short axis during a single period. So, during a rotation period, we should see two minimums and two maximums. This assumes that we are close to the equatorial plane.

Another interesting fact is the pretty high amplitude of variation of the incident light flux. If you are interested in it, go directly to the next section. Before that, I would like to tell you how this period of 7.79±0.01 h has been determined.

The authors used 2 different algorithms:

  • the Lomb periodogram technique,
  • the phase dispersion minimization (PDM).

Usually periodic signals are described as sums of sinusoids, thanks to Fourier transforms. Unfortunately, Fourier is not suitable for unevenly-spaced data. The Lomb (or Lomb-Scargle) periodogram technique consists to fit a sinusoid to the data, thanks to the least-squares method, i.e. you minimize the squares of the departure of your signal from a sinusoid, in adjusting its amplitude, phase, and frequency. PDM is an astronomical adaptation of data folding. You guess a period, and you split your full time interval into sub-intervals, which duration is the period you have guessed. Then you superimpose them. If this the period you have guessed is truly a period of the signal, then all of your time intervals should give you pretty the same signal. If not, then the period you have guessed is not a period of the signal.

Let us go back now to the variations in the amplitude.

Physical interpretation

The authors assume that periodic magnitude variations could have 3 causes:

  • Albedo variations
  • Elongation of the asteroid
  • Two bodies, i.e. a binary.

The albedo quantify the portion of Solar flux, which is reflected by the surface. Here, the variations are too large to be due to the variations of the albedo.

The authors estimate that, if 2004 TT357 were a single, ellipsoidal body, then a/b = 2.01 and c/a = 0.38, a,b, and c being the 3 axis of the ellipsoid. This is hardly possible if the shape corresponds to an equilibrium figure (hydrostatic equilibrium, giving a Jacobi ellipsoid). Moreover, this would mean that 2004 TT357 would have been ideally oriented… very unlikely

As a consequence, 2004 TT357 is probably a binary, with a mass ratio between 0.4 and 0.8. Hubble Space Telescope observed 2004 TT357 in 2012, and detected no companion, which means it is probably a contact binary. Another way to detect a companion is the analysis of a stellar occultation (see here). Fortunately for us, one will occur in February 2018.

A star occultation in February 2018

On 5 February 2018, 2004 TT357 shall occult the 12.8-magnitude star 2UCAC 38383610, in the constellation Taurus, see here. This occultation should be visible from Brazil, and provide us new data which would help to determine the nature of 2004 TT357. Are you interested to observe?

To know more

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.

How rough is Mercury?

Hi there! Today I will tell you on the smoothness of the surface of Mercury. This is the opportunity for me to present The surface roughness of Mercury from the Mercury Laser Altimeter: Investigating the effects of volcanism, tectonism, and impact cratering by H.C.M. Susorney, O.S. Barnouin, C.M. Ernst and P.K. Byrne, which has recently been published in Journal of Geophysical Research: Planets. This paper uses laser altimeter data provided by the MESSENGER spacecraft, to measure the regularity of the surface in the northern hemisphere.

The surface of Mercury

I already had the opportunity to present Mercury on this blog. This is the innermost planet of the Solar System, about 3 times closer to the Sun than our Earth. This proximity makes space missions difficult, since they have to comply with the gravitational action of the Sun and with the heat of the environment. This is why Mercury has been visited only by 2 space missions: Mariner 10, which made 3 fly-bys in 1974-1975, and MESSENGER, which orbited Mercury during 4 years, between 2011 and 2015. The study of MESSENGER data is still on-going, the paper I present you today is part of this process.

Very few was known from Mercury before Mariner 10, in particular we just had no image of its surface. The 3 fly-bys of Mariner 10 gave us almost a full hemisphere, as you can see below. Only a small stripe was unknown.

Mercury seen by Mariner 10. © NASA.
Mercury seen by Mariner 10. © NASA.

And we see on this image many craters! The details have different resolutions, since this depends on the distance between Mercury and the spacecraft when a given image was taken. This map is actually a mosaic.
MESSENGER gave us full maps of Mercury (see below).

Mercury seen by MESSENGER. © USGS
Mercury seen by MESSENGER. © USGS

Something that may be not obvious on the image is a non-uniform distribution of the craters. So, Mercury is composed of cratered terrains and smooth plains, which have different roughnesses (you will understand before the end of this article).
Craters permit to date a terrain (see here), i.e. when you see an impact basin, this means that the surface has not been renewed since the impact. You can even be more accurate in dating the impact from the relaxation of the crater. However, volcanism brings new material at the surface, which covers and hides the craters.

This study focuses on the North Pole, i.e. latitudes between 45 and 90°N. This is enough to have the two kinds of terrains.

Three major geological processes

Three processes affect the surface of Mercury:

  1. Impact cratering: The early Solar System was very dangerous from this point of view, having several episodes of intense bombardments in its history. Mercury was particularly impacted because the Sun, as a big mass, tends to focus the impactors in its vicinity. It tends to rough the surface.
  2. Volcanism: In bringing new and hot material, it smoothes the surface,
  3. Tectonism: Deformation of the crust.

If Mercury had an atmosphere, then erosion would have tended to smooth the surface, as on Earth. Irrelevant here.

To measure the roughness, the authors used data from the Mercury Laser Altimeter (MLA), one of the instruments of MESSENGER.

The Mercury Laser Altimeter (MLA) instrument

This instrument measured the distance between the spacecraft and the surface of Mercury from the travel time of light emitted by MLA and reflected by the surface. Data acquired on the whole surface permitted to provide a complete topographic map of Mercury, i.e. to know the variations of its radius, detect basins and mountains,… The accuracy and the resolution of the measurements depend on the distance between the spacecraft and the surface, which had large variations, i.e. between 200 and 10,300 km. The most accurate altimeter data were for the North Pole, this is why the authors focused on it.

Roughness indicators

You need at least an indicator to quantify the roughness, i.e. a number. For that, the authors work on a given baseline on which they had data, removed a slope, and calculated the RMS (root mean square) deviation, i.e. the average squared deviation to a constant altitude, after removal of a slope. When you are on an inclined plane, then your altitude is not constant, but the plane is smooth anyway. This is why you remove the slope.

But wait a minute: if you are climbing a hill, and you calculate the slope over 10 meters, you have the slope you are climbing… But if you calculate it over 10 km, then you will go past the summit, and the slope will not be the same, while the summit will affect the RMS deviation, i.e. the roughness. This means that the roughness depends on the length of your baseline.

This is something interesting, which should be quantified as well. For this, the authors used the Hurst exponent H, such that ν(L) = ν0LH, where L is the length of the baseline, and ν the standard deviation. Of course, the data show that this relation is not exact, but we can say it works pretty well. H is determined in fitting the relation to the data.

Results

To summarize the results:

  • Smooth plains: H = 0.88±0.01,
  • Cratered terrains: H = 0.95±0.01.

The authors allowed the baseline to vary between 500 m and 250 km. The definition of the Hurst exponent works well for baselines up to 1.5 km. But for any baseline, the results show a bimodal distribution, i.e. two kinds of terrains, which are smooth plains and cratered terrains.

It is tempting to compare Mercury to the Moon, and actually the results are consistent for cratered terrains. However, the lunar Maria seem to have a slightly smaller Hurst exponent.

To know more

That’s it for today! The next mission to Mercury will be Bepi-Colombo, scheduled for launch in 2018 and for orbital insertion in 2025. Meanwhile, please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter and Facebook.

Discovery of 6 new Extreme Trans-Neptunian Objects

Hi there! You know the Trans-Neptunian Objects, these bodies which orbit beyond the orbit of Neptune… There are the furthest known objects in the Solar System. Today I will particularly tell you on the most distant of them, which have a semimajor axis larger than 150 AU, while Neptune is at 30 AU… Yes, we can observe some of them. 6 have been recently discovered by the OSSOS survey, in OSSOS. VI. Striking biases in the detection of large semimajor axis Trans-Neptunian Objects, by Cory Shankman and 11 collaborators (full list at the end). This paper has recently been published in The Astronomical Journal. In this study, the authors particularly focus on the possible observational biases, and discuss the Planet Nine hypothesis.

The OSSOS survey

I should probably write OSSOSurvey instead, since it stands for Outer Solar System Origins Survey. It is a systematic observation program that ran on the Canada-France-Hawaii Telescope (CFHT) between 2013 and 2017, devoted to the discovery and orbit determination of Trans-Neptunian Objects. For that, the program used an imager with a field of 1×1 degree, to image 21 square degree fields, in different parts of the sky. During the 4 years, these fields were regularly re-observed to follow the motion of the discovered objects. 16 months of astrometric observations are required to obtain an accurate orbit.
The authors announce that OSSOS permitted the detection of more than 830 TNOs, with a “40% detection efficiency at r(ed)-band magnitude 24.4-24.5”. OSSOS followed another survey, CFEPS, for Canada-France-Hawaii Ecliptic Plane Survey, which discovered some 200 Kuiper Belt Objects, i.e. Trans-Neptunian Objects, which are not as far as the objects we discuss today. This makes more than 1,000 small objects discovered by the CFHT.

Some TNOs detected by CFEPD and OSSOS. Replotted from the public data. Copyright: The Planetary Mechanics Blog.
Some TNOs detected by CFEPD and OSSOS. Replotted from the public data. Copyright: The Planetary Mechanics Blog.

The Canada-France-Hawaii Telescope

The Canada-France-Hawaii Telescope is a joint facility of the University of Hawaii, the French Centre National de la Recherche Scientifique, and the Canadian National Research Council. It has also partnerships with institutions based in the two Chinas, South Korea, and Brazil. It has a 3.58-m telescope, which is functional since 1979.
It is ideally situated, close to the summit of the Mauna Kea mountain, Hawaii (altitude: 4,204 m). It is equipped of different instruments, to observe in the visible to infrared bands. One of them, the wide field imager MegaCam, was used for OSSOSurvey.

Observational biases

If you are looking for stars to the West, you will find some. But only on the West, and brighter than a given magnitude. Does that mean that there are no fainter stars, and no stars in the opposite direction? Of course not. You have found only those stars because your observation means and protocol precluded from discovering other stars. This is an observational bias.

This is a very important issue for understanding surveys, i.e. how to extrapolate the catalog of discovered objects to the existing but unknown ones? Observational biases can be due to:

  • The direction in which you observe. Since our sky is moving, this is strongly correlated to the observation date.
  • The weather. Hard to see something behind a cloud.
  • Your field of view. Is there something behind this tree?
  • The limitations of your instrument.
  • The albedo of your object. How efficiently does it reflect the incident Solar light?

There is something very significant in the name of CFEPS… E stands for ecliptic, which is the orbital plane of the Earth. The Solar System is roughly planar (with many exceptions of course), and it made sense to look for objects with a small orbital inclination. Consequence: most of the objects discovered by CFEPS have a low inclination… observational bias, which was in fact a way to optimize the chances to discover objects. But it would be wrong to conclude from these discoveries a lack of objects with a small inclination.

OSSOS had observational biases as well, mostly due to the absence of observations in the direction of the Galactic Plane, and to the allocated observation time. The Galactic Plane is full of stars, which complicates the observations of faint objects. This is why the authors maximized their chances in avoiding that part of the sky. As a consequence, OSSOS could not detect objects with an ascending node (the point where the orbit of the object crosses the ecliptic) between -120° and -20°, and had a poor sensitivity between 115° and 165°.

In the specific case of extreme TNOs, there is another bias due to their dynamics: a small object orbiting at a distance of 150 AU has no chance to be detected from the Earth. So, the only detected objects came close enough, which means that their orbits is highly elongated, i.e. highly eccentric. The 8 objects considered in this study, i.e. 6 newly discovered and 2 already known, have a pericentric distance between 31 and 50 AU, which involves an eccentricity between 0.727 and 0.932 (the eccentricity of the Earth is some 0.016). Among the extreme TNOs, only the highly eccentric ones can be detected. This does not mean that they are all highly eccentric.

The reason why the scientific community became excited about the Planet Nine is that a clustering of the orbits of the extreme TNOs was identified in other data, in particular a clustering of the pericentres of the objects. It was then concluded that this clustering was the dynamical signature of the Planet Nine, proving its existence. OSSOS gives independent data, are they clustered?

Answering such a question is not straightforward when the data are scattered. Looking at them with the naked eye is not enough, there are mathematical tools which can measure the statistical relevance of an hypothesis. In particular, the Planet Nine hypothesis should be compared with the null hypothesis, i.e. an equal distribution of the pericentres of the extreme TNOs.

Statistical tests

A common tool is the Kolmogorov-Smirnov test, or KS-test. The idea is to determine a distance between your sample and the one that a given law would give you. If the distance is small enough, then it makes sense to conclude that your sample obeys the law you tested.
This test has been refined as Kuiper’s test, which is insensitive to cyclic transformations of the variables. Cyclic phenomena are everywhere in orbital dynamics.

This study

The following table presents you the 8 eTNOs presented in this study.

Name Semimajor axis Eccentricity Inclination Magnitude
2013 GP136 150.2 AU 0.727 33.5° 23.1
2013 SY99 735 AU 0.932 4.2° 24.8
2013 UT15 200 AU 0.780 10.7° 24.1
2015 KH163 153 AU 0.739 27.1° 24.7
2015 RY245 226 AU 0.861 24.6
2015 GT50 312 AU 0.877 8.8° 24.5
2015 RX245 430 AU 0.894 12.1° 24.1
2015 KG163 680 AU 0.940 14° 24.3

All of them have been discovered by OSSOS, the first two ones being known before that study. The 6 other ones are the 6 newly discovered. We can see that all have huge semimajor axes and eccentricities. You can see the high relative magnitudes in the red band during their discoveries. Their discoveries were made possible by their high eccentricities, which reduce significantly the minimal distances to the Sun and to the Earth.

And now their orbits are drawn!

Projection of the orbits of the 8 eTNOs on the ecliptic. The orbit of Neptune is embedded into the small circle delimited by the orbits. Copyright: The Planetary Mechanics Blog, after inspiration from OSSOS.
Projection of the orbits of the 8 eTNOs on the ecliptic. The orbit of Neptune is embedded into the small circle delimited by the orbits. Copyright: The Planetary Mechanics Blog, after inspiration from OSSOS.

Do they look clustered?

What about the Planet Nine?

The Kuiper’s test used by the authors say that the orbital elements of the detected eTNOS are statistically consistent with a uniform repartition. We must be careful with words. This means that there is no evidence of clustering in this sample. That does not mean that there is no Planet Nine. We should keep in mind that 8 objects do not constitute a statistically relevant sample.

My feeling is that if you were skeptical about the existence of the Planet Nine, you remain skeptical. However, if you believed in it, there is still room for belief. The fact is that this study does not comfort the existence of the Planet Nine.

To know more…

  • The study, made freely available by the authors on arXiv. You can also find a presentation of the study by the authors themselves here.
  • A presentation by Nature.
  • The website of the OSSOS survey, and its Twitter.
  • The quest for the Planet Nine.

And the authors of the study:

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 rotation of Fagus

Hi there! Today I will tell you on the rotation of the asteroid (9021) Fagus. The first determination of its spin period is given in Rotation period determination for asteroid 9021 Fagus, by G. Apostolovska, A. Kostov, Z. Donchev, and E. Vchkova Bebekovska. This study has recently been published in the Bulgarian Astronomical Journal.

(9021) Fagus’s facts

(9021) Fagus is a small, Main Belt asteroid. You can find below some of its characteristics:

Semimajor axis 2.58 AU, i.e. 386 millions km
Eccentricity 0.173
Inclination 13.3°
Orbital period 4.14 y
Diameter 13.1 km
Absolute magnitude 12.4
Discovery February 14, 1988

Its small magnitude explains that its discovery was acknowledged only in 1988. Once identified, it was found on older photographic plates, providing observations from 1973 (yes, you can observe an object before it was discovered… you just do not know that you observed it). This body is so small, that the authors of this study observed it by accident: in 2013, they observed in fact (901) Brunsia during two nights, which is brighter (absolute magnitude: 11.35), but Fagus was in the field. The collected photometric data were supplemented in March 2017 by two other nights of observations, which permitted the authors to determine the spin (rotation) period with enough confidence.

Measuring the rotation

I address the measurement of the rotation of an asteroid here. Such a small body may have an irregular shape, and tumble. But since it is very difficult to get accurate data for such a small body, it is commonly assumed that the body rotates around one principal axis, this hypothesis being confronted with the observations. In other words, if you can explain the observations with a rotation around one axis, then you have won.

The irregularity of the shape makes that the light flux you record presents temporal variations, i.e. the surface elements you face is changing, so the reflection of the incident Solar light is changing, which means that these variations are correlated with the rotational dynamics. If these variations are dominated by a constant period of oscillation, then you have the rotation period of the asteroid. Typically, the rotation period of the Main-Belt asteroids are a few hours. These numbers are strongly affected by the original dynamics of the planetary nebula, the despinning of the asteroids being very slow. This is a major difference with the planetary satellites, which rotates in a few days since they are locked by the tides raised by their parent planet. For comparison, the spin period of the Moon is 28 days.

Photometric observations

Detecting the photometric variations of the incident light of such a small body requires to be very accurate. The overall signal is very faint, its variations are even fainter. To avoid errors, the observer should consider:

  • The weather. A bright sky is always better, preferably with no wind, which induces some seeing, i.e. apparent scintillation of the observed object.
  • The anthropogenic light pollution.
  • The variations of the thickness of the atmosphere during the observation. If your object is at the zenith, then it is pretty good. If it is low in the sky, then its course during the night will involve variations of the thickness of the atmosphere during the observations.
  • Instrumental problems. Usually you use a chip of CCD sensors, these sensors do not have exactly the same response. A way to compensate this is to measure a flat, i.e. the response of the chip to a homogeneous incident light flux.

The observation conditions can be optimized, for instance in observing from a mountain area. The observer should also be disciplined, for instance many professional observatories forbid to smoke under the domes. In the past, this caused wrong detections. A good way to secure the photometric results is to have several objects in the fields, and to detect the correlations between their variations of flux. Intrinsic properties of an object would emerge from light variations, which would be detected for this object only.

The observation facilities

The observations were made at Rozhen Observatory, also known as Bulgarian National Astronomical Observatory. It is located close to Chepelare, Bulgaria, at an altitude of 1,759 m. It consists of 4 telescopes.

The 2013 observations were made with a 50/70 cm Schmidt telescope, and the 2017 ones with a 2m-Ritchey-Chrétien-Coude telescope. In both cases, the observations were made through a red filter. The faintness of the asteroid required exposure times between 5 and 6 minutes.

The Schmidt telescope used for the 2013 observations. Copyright: P. Markishky
The Schmidt telescope used for the 2013 observations. Copyright: P. Markishky
The 2m telescope, used for the 2017 observations. Copyright: P. Markishky
The 2m telescope, used for the 2017 observations. Copyright: P. Markishky

The softwares

The authors used two softwares in their study: CCDPHOT, and MPO Canopus. CCDPHOT is a software running under IDL, which is another software, commonly used to treat astrophysical data, and not only. With CCDPHOT, the authors get the photometric measurements. MPO Canopus could give these measurements as well, but the authors used it for another functionality: it fits a period to the lightcurve, in proving an uncertainty. This is based on a Fourier transform, i.e. a spectral decomposition of the signal. In other words, the lightcurves, with are recorded as a set of pairs (time, lightflux), are transformed into a triplet of (amplitude, frequency, phase), i.e. it is written as a sum of sinusoidal oscillations. If one of these oscillations clearly dominates the signal, then its period is the rotation period of the asteroid.

Result

And the result is this: the rotation period of (9021)Fagus is 5.065±0.002 hours. In practice, being accurate on such a number requires to collect data over several times this interval. An ideal night of observation would permit to measure during about 2 periods. Here, data have been collected over 4 nights.
Up to now, we had no measurement of the spin period of Fagus, which makes this result original. It not only helps to understand the specific Fagus, but it is also a new data in the catalog of the rotational periods of Main-Belt asteroids.

To know more…

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.

An asteroid pair

Hi there! Today I present you the study of an asteroid pair. Not a binary, a pair. A binary asteroid is a couple of asteroids which are gravitationally bound, while in pair, the asteroids are just neighbors, they do not live together… but have. The study is entitled Detailed analysis of the asteroid pair (6070) Rheinland and (54287) 2001 NQ8, by Vokrouhlický et al., and it has recently been published in The Astronomical Journal.

Asteroid pairs

I have presented asteroid families in a previous post. These are groups of asteroids which present common dynamical and physical properties. They can be in particular identified from the clustering of their proper elements, i.e. you express their orbital elements (semimajor axis, eccentricity, inclination, pericentre, …), you treat them properly so as to get rid off the gravitational disturbance of the planets, and you see that some of these bodies tend to group. This suggests that they constitute a collisional family, i.e. they were a unique body in the past, which has been destroyed by collisions.
An asteroid pair is something slightly different, since these are two bodies which present dynamical similarities in their osculating elements, i.e. before denoising them from the gravitational attraction of the planets. Of course, they would present similarities in their proper elements as well, but the fact that similarities can be detected in the osculating elements means that they are even closer than a family, i.e. the separation occurred later. Families younger than 1 Myr (1 million of years) are considered to be very young; the pair I present you today is much younger than that. How much? You have to read me before.
A pair suggests that only two bodies are involved. This suggests a non-collisional origin, more particularly an asteroid fission.

Asteroid fission

Imagine an asteroid with a very fast rotation. A rotation so fast that it would split the asteroid. We would then have two components, which would be gravitationally bound, and evolving… Depending on the energy involved, it could remain a stable binary asteroid, a secondary fission might occur, the two or three components may migrate away from each other… and in that case we would pair asteroid with very close elements of their heliocentric orbits.
It is thought that the YORP (Yarkovsky – O’Keefe – Radzievskii – Paddack) could trigger this rotational fission. This is a thermic effect which alter the rotation, and in some cases, in particular when the satellite has an irregular shape, it could accelerate it. Until fission.
Thermic effects are particularly efficient when the Sun is close, which means that NEA (Near Earth Asteroids) are more likely to be destroyed by this process than Main Belt asteroids. Here, we deal with Main Belt asteroids.

The pair 6070-54827 (Rheinland – 2001 NQ8)

The following table present properties of Rheinland and 2001 NQ8. The orbital elements are at Epoch 2458000.5, i.e. September 4th 2017. They come from the JPL Small-Body Database Browser.

(6070) Rheinland (54827) 2001 NQ8
Semimajor axis (AU) 2.3874015732216 2.387149297807496
Eccentricity 0.2114524962733347 0.211262507795103
Inclination 3.129675305535938° 3.128927421642917°
Node 83.94746016534368° 83.97704257098502°
Pericentre 292.7043398319871° 292.4915004062336°
Orbital period 1347.369277588708 d (3.69 y) 1347.155719572348 d (3.69 y)
Magnitude 13.8 15.5
Discovery 1991 2001

Beside their magnitudes, i.e. Rheinland is much brighter than 2001 NQ8, this is why it was discovered 10 years earlier, we can see that all the slow orbital elements (i.e. all of them, except the longitude) are very close, which strongly suggests they shared the same orbit. Not only their orbits have the same shape, but they also have the same orientation.

Shapes and rotations from lightcurves

A useful tool for determining the rotation and shape of an asteroid is the lightcurve. The object reflects the incident Solar light, and the way it reflects it will tell us something on its location, its shape, and its orientation. You can imagine that the surfaces of these bodies are not exclusively composed of smooth terrain, and irregularities (impact basins, mountains,…) will result in a different Solar flux, which also depends on the phase, i.e. the angle between the normale of the surface and the asteroid – Sun direction… i.e. depends whether you see the Sun at the zenith or close to the horizon. This is why recording the light from the asteroid at different dates tell us something. You can see below an example of lightcurve for 2001 NQ8.

Example of lightcurve for 2001 NQ8, observed by Vokrouhlický et al.

Recording such a lightcurve is not an easy task, since the photometric measurements should be denoised, otherwise you cannot compare them and interpret the lightcurve. You have to compensate for the variations of the luminosity of the sky during the observation (how far is the Moon?), of the thickness of the atmosphere (are we close to the horizon?), of the heterogeneity of the CCD sensors (you can compensate that in measuring the response of a uniform surface). And the weather should be good enough.

Once you have done that, you get a lightcurve alike the one above. We can see 3 maxima and 2 minima. Then the whole set of lightcurves is put into a computational machinery which will give you the parameters that best match the observations, i.e. periods of rotation, orientation of the spin pole at a given date, and shape… or at least a diameter. In this study, the authors already had the informations for Rheinland but confirmed them with new observations, and produced the diameter and rotation parameters for 2001 NQ8. And here are the results:

(6070) Rheinland (54827) 2001 NQ8
Diameter (km) 4.4 ± 0.6 2.2 ± 0.3
Spin period (h) 4.2737137 ± 0.0000005 5.877186 ± 0.000002
Spin pole (124°,-87°) (72°,-49°) or (242°,-46°)

We can see rapid rotation periods, as it is often the case for asteroids. The locations of the poles mean that their rotations
are retrograde, with respect to their orbital motions. Moreover, two solutions best match the pole of 2001 NQ8.

Dating the fission

The other aspect of this study is a numerical simulation of the orbital motion of these two objects, backward in time, to date their separation. Actually, the authors considered 5,000 clones of each of the two objects, to make their results statistically relevant.
They not only considered the gravitational interactions with other objects of the Solar System, but also the Yarkovsky effect, i.e. a thermal pull due to the Sun, which depends on the reflectivity of the asteroids, and favors their separation. For that, they propose new equations implementing this effect. They also simulated the variations of the spin pole orientation, since it affects the thermal acceleration.

And here is the result: the fission probably occurred 16,340 ± 40 years ago.

Perspectives

Why doing that? Because what we see is the outcome of an asteroid fission, which occurred recently. The authors honestly admit that this result could be refined in the future, depending on

  • Possible future measurements of the Yarkovsky acceleration of one or two of these bodies,
  • The consideration of the mutual interactions between Rheinland and 2001 NQ8,
  • Refinements of the presented measurements,
  • Discovery of a third member?

To date the fission, they dated a close approach between these two bodies. They also investigated the possibility that that
close approach, some 16,000 years from now, could have not been the right one, and that the fission could have been much older. For that, they ran long-term simulations, which suggest that older close approaches should have been less close: if the pair were older, Yarkovsky would have separated it more.

To know more

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