Mercury’s crust revisited

Airy vs. Pratt isostasy

Figure 1: Pratt (left) vs. Airy (right) isostasy. There are two main ideas how mountain masses are supported. In Pratt’s theory (left), the density changes and less dense crustal blocks “float” higher, whereas the more dense blocks form basins. In Airy’s theory (right) the density is constant, but the crustal blocks have different thicknesses. Higher mountains have deeper “roots” into the denser material below. Image credit: Shih-Arng Pan

In today’s volume of the “Earth and Planetary Science Letters”, Michael M. Sori from the “Lunar and Planetary Laboratory” of the University of Arizona (US) writes about how he used data obtained with the MESSENGER (Mercury Surface, Space Environment, Geochemistry and Ranging) orbiter to re-measure the crust thickness of Mercury. Crust thickness is an important geophysical parameter, which allows to further constrain terrestrial planet formation scenarios. And since Mercury is always good for a surprise, the new calculations show that Mercury’s crust is only 26±11 km thick, i.e. much thinner (and also denser) than previously thought.

First estimates of the Mercury crust thickness were published by Anderson et al. (1996). Their estimates were based on data obtained with the Mariner 10 spacecraft. They concluded that the crust is 100–300 km thick. Almost ten years later, with a wealth of new instruments on-board MESSENGER to create gravity and topography maps, Padovan et al. (2015) concluded that Mercury’s crustal thickness is on average 35±18 km. The authors assumed topography was predominantly compensated by Airy isostasy, where columns contain equal masses. The equal mass approach was now shown to overestimate the thickness of Mercury’s crust, and instead an equal pressure approach (first described by Hemingway and Matsuyama 2017) should be used. In the next paragraphs, further explanations follow, describing the meaning of isostasy and the equal-mass vs. equal-pressure approaches.

Airy vs. Pratt isostasy and the “equal mass” vs. “equal pressure” assumptions

Mercury grain density

Figure 2: Grain density measurements on top of a MESSENGER image of Mercury. Image Credit: Michael M. Sori (2018)

Mercury grain density vs. elevation

Figure 3: The data shows that Mercury is inconsistent with Pratt isostasy (red dashed line), because no correlation between density and elevation is observed. Image Credit: Michael M. Sori (2018).

Isostasy is a fundamental concept in Geology, meaning that lighter crust floats on the denser underlying mantle. It thus explains why mountains and valleys are stable over large timescales. This is called isostatic equilibrium (this equilibrium can be disturbed by erosion or volcanic activity). There are two main ideas how mountain masses are supported (see Figure 1). In Pratt’s theory, the density changes across the surface and less dense crustal blocks “float” higher, whereas the more dense blocks form basins. On the other side, in Airy’s theory the density is constant, but the crustal blocks have different thicknesses. Higher mountains have deeper “roots” into the denser material below. Thus, in case of Pratt isostasy, one would expect a correlation between density and elevation across the surface of a planet, with mountains having lower densities.

In the study, Sori (2018) shows grain density measurements across several regions of Mercury (see Figure 2). Using MESSENGER’s topography maps, the author could then look for a correlation between density and elevation. As shown in Figure 3, such a correlation does not exist. Thus, it can be assumed that Airy isostasy is a better description for the topography of Mercury.

Now we come back to the meaning of “equal mass” and “equal pressure” approach. The latter one was used by the author of the study. This is the crucial difference that finally led to the new lower value for the crustal thickness. First, it is important to know that the gravitational potential is typically not constant across topographic lines (=lines of constant altitude) of a planet. This is due to variations in density. However, lines of constant gravitational potential (equipotential lines) can still be calculated. One such line of constant gravitational potential is the zero-level (on Earth roughly the sea level) and is called geoid. The quantity called geoid-topography ratio (GTR) thus reflects variations in density. And finally, the GTR is used to calculate the thickness of the crust. The main question is how equipotential surfaces are calculated. As shown by Douglas J. Hemingway and Isamu Matsuyama (2017), the spherical geometry of the problem must be taken into account when calculating equipotential surfaces (which will affect the crust thickness calculation). And here is the problem. Previous publications have assumed a constant width of the crustal blocks (in cartesian coordinates). This is what is called the “equal mass” approach, but in fact one would need to take into account the spherical symmetry (polar coordinates) and thus cone-shaped blocks that put different “pressure” on the surface (compare Figure 1 and Figure 5). This is why the newly calculated thickness is roughly 25% lower than previous results. Note that, the same issue will also affect previous calculations of other objects in the solar system. However, since the difference is larger for smaller objects, Mercury is affected most of all planets, since it is the smallest planet in the solar system.

Mercury Crust Thickness

Figure 4: Geoid-topography ratios (GTRs) as a function of crustal thickness (for an Airy isostasy). The “equal mass” (red) and “equal pressure” (blue) approach are compared to each other, showing that equal pressure reduces the derived crust thickness to the published value of 26km. Image credit: Michael M. Sori (2018)

Airy vs Pratt in polar coordinates

Figure 5: Airy vs Pratt in polar coordinates. This is the same as Figure 1, but showing the crustal blocks in polar coordinates. It can be seen that the crustal blocks are not constant in width, but cone-shaped. The bottom of the cone is the area where pressure is put on the underlying surface. An equipotential surface is then found along lines of “equal pressure” rather than “equal mass”. Image credit: Johannes Puschnig

As explained, the equal pressure approach is a better representation of a state of equilibrium. This is also supported by the fact that the new average crustal thickness value of 26±11 km agrees well with other MESSENGER based models and observations, e.g. with Mercury’s crust being of magmatic origin or excavation of mantle material onto the surface, which was proposed by Padovan et al. (2015).

With this publication another issue of Mercury could be resolved, but many things are left unknown and Mercury still keeps scientist busy. The next large step forward is likely to come when BepiColombo finally orbits Mercury in 2025.

Spotting the zodiacal light in spring

The zodiacal light is a nocturnal phenomena that is revealed only to those who dare to escape the city lights. In spring, after sunset and once twilight fades away into a dark and moonless night, a gentle luminous band opens up when looking towards west. Its majestic cone then seems to stand high above the horizon, as if it was trying to guide the observer. In fact, the zodiacal light directs us to the very beginning of the solar system, roughly 4.5 billion years ago, when our Earth and the other planets were formed from and within a circumsolar dust disk. Although the solar wind steadily sweeps away dust, new dust grains are formed through outgassing comets and minor planet collisions. Most of these objects orbit the sun in a relatively well defined and narrow plane, which is called the ecliptic, i.e. the plane of the Earth’s orbit. As a result, the ecliptic is continuously fed with fresh dust and gas, which causes the redirection of sun rays through reflection and scattering, which are then captured as zodiacal light by some enthusiasts on Earth. Although zodiacal light can be seen all year round, spring and autumn are best suited for observations from mid latitudes, because then the path of the sun crosses the horizon at a steep angle, making the twilight zone short.

zodiacal light

Zodiacal light observed from Roque de los Muchachos Observatory, La Palma, Canary islands, Spain in April 2016.

Observing Comet C/2013 US10 (Catalina)

Comet C/2013 US10 (Catalina) was first discovered by the Catalina Sky Survey on October 31, 2013. It originates from the Oort cloud, a vast spherical reservoir of comets far beyond Neptun. By chance, gravitational perturbations can push Oort objects into the inner solar system, where they are eventually discovered. In some cases, comets get bright enough to be observed by naked eye or with small amateur telescopes or binoculars. The latter one is true for Comet C/2013 US10 (Catalina).

On Jan. 17, 2016 the comet passed its closest point to Earth at a distance of 110 million km. Using my 10-inch Newtonian telescope, I have imaged the comet that day from a suburban location. The result shown below is a stack of 17 frames of 120 sec. exposure time each. The inverted version on the bottom clearly shows the two tails of the comet.

Comet C/2013 US10 (Catalina)

Comet C/2013 US 10 (Catalina) imaged in L with a GSO 254mm f/5 Newtonian telescope and an ATIK 383L+ mono CCD camera

Comet C/2013 US10 (Catalina)

Comet C/2013 US 10 (Catalina) imaged in L with a GSO 254mm f/5 Newtonian telescope and an ATIK 383L+ mono CCD camera

 

Aurora Borealis – observed from Vallentuna

It is an amazing spectacle when a solar storm of charged particles hits the Earth’s magnetosphere. The particles following the magnetic field finally collide with particles of the Earth’s atmosphere – mostly oxygen and nitrogen. These collisions lead to either an ionization or excitation of atoms/molecules at an altitude of around 100 km. Subsequently, the recombination is responsible for the emission of a photon. The typically green colour arises from oxygen. On March 17, 2015 a strong solar storm hit the Earth and even at the relatively low latitude of Stockholm one could follow this energetic event.

Aurora Borealis observed from Vallentuna (Stockholm, Sweden)

Aurora Borealis observed from Vallentuna (Stockholm, Sweden)

Aurora Borealis observed from Vallentuna (Stockholm, Sweden)

Aurora Borealis observed from Vallentuna (Stockholm, Sweden)

 

Comet C/2014 Q2 (Lovejoy)

Comet C/2014 Q2 (Lovejoy) is bright (around 5mag) enough to be easily seen with binoculars or small telescopes in constellation Eridanus. On really good sites one should be able to spot it even with naked eye. However, currently the observing conditions are hard, because of today’s full moon. Additionally in the northern hemisphere the comet’s elevation is very low. I have spotted it two days ago from Vallentuna (near Stockholm, Sweden) when it was only 18 degrees above the horizon at maximum. I have taken some pictures with my CCD camera and was really impressed how fast the comet moves on the sky (see video).

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The really good news is that the observing conditions are going to be better during the next days and weeks. C/2014 Q2 (Lovejoy) will climb further up, reaching constellation Taurus around 9th of January, just two days after it reaches the closest position to Earth at a distance of around 70 million kilometers.

Ringsystem um Asteroid “Chariklo” im äußeren Sonnensystem entdeckt

Die Europäische Südsternwarte (ESO) berichtet in Ihrer heutigen Pressemitteilung von der überraschenden und erstmaligen Entdeckung eines Ringsystems um einen Asteroiden. Der Planetoid Chariklo wurde von mehreren Observatorien aus – darunter auch La Silla in Chile – beobachtet. Grund der Beobachtung war eine bevorstehende Sternbedeckung durch den Asteroiden. Solche Ereignisse werden genutzt, um die Größe von Kleinplaneten abzuleiten. Dabei wurde überraschenderweise kurze Zeit vor sowie kurze Zeit nach der eigentlichen Bedeckung, ein Helligkeitsabfall des Sterns registriert. Daraus kann zweifelsfrei geschlossen werden, dass sich um Chariklo ein Ringsystem aus Staub und Eis gebildet haben muss ähnlich wie man es von Saturn, Uranus oder Neptun kennt. Letztere wurden ebenfalls durch Sternbedeckungen entdeckt.

Die Scheibe aus Eis und Staub könnte dabei das Resultat aus einem Impaktereignis sein. Weiters ist nun anzunehmen, dass Chariklo noch kleinere Begleiter hat, welche das Ringsystem aufrechterhalten.

Ring um Planetoid entdeckt

Image Credit: ESO

Planeten mit der Webcam

Jupiter

Jupiter

  • Datum: 21.04.2006
  • Zeit: 00h 00m
  • Ort: Sophienalpe
  • Aufnahmetechnik: Webcam: Philips ToUCam Pro (640×480 Pixel); fokal mit 2xBarlow am VC200L
  • verwendeter Filter: IR Sperrfilter
  • Brennweite: 3600mm
  • Blende: f/18
  • Belichtungszeit: je 1/250
  • verwendeter Film: CCD Chip
  • digitale Bildverarbeitung: Addition von ca. 500 Einzelbildern mit Registax, dann 2fache Vergrösserung

Saturn

Saturn

  • Datum: 20.04.2006
  • Zeit: ca. 23h 45m
  • Ort: Sophienalpe
  • Aufnahmetechnik: Webcam: Philips ToUCam Pro (640×480 Pixel); fokal mit 2xBarlow am VC200L
  • verwendeter Filter: IR Sperrfilter
  • Brennweite: 3600mm
  • Blende: f/18
  • Belichtungszeit: je 1/250
  • verwendeter Film: CCD Chip
  • digitale Bildverarbeitung: Addition von ca. 500 Einzelbildern mit Registax, dann 2fache Vergrösserung