Arecibo, A Giant in the Field

This week, Conor Hayes pays tribute the Arecibo Radio Telescope. You may know it in connection with SETI (or perhaps from movies!) but its ability to make observations along the ecliptic made it one of Planetary Science's most effective instruments. Unfortuately, the telescope recently experienced a structural failure which will require its demolition. 

Photo above:  The Arecibo Observatory as seen in June 2019. (CC BY-SA 4.0, https://commons.wikimedia.org/wiki/File:Arecibo_Radiotelescopio_SJU_06_2019_7472.jpg)

by Conor Hayes

On November 19, 2020, the astronomical community lost a (literal) giant. Following the failure of two support cables that made repair work dangerously unsafe, the National Science Foundation announced that they would be decommissioning the Arecibo Observatory. This 305-metre radio telescope has faithfully watched the skies for nearly 60 years, during which time it became perhaps the most well-known telescope on the planet, appearing in popular media like GoldenEye, Contact, and The X-Files. Its loss will be felt by all of us, most acutely by those who have dedicated their lives to radio astronomy. Given this, I felt it was appropriate to write a little bit about radio telescopes in general, as well as some of the notable discoveries made using Arecibo.

Why was Arecibo so large? When designing a new telescope, you need to balance the quality of the data it can output with how expensive it will be to build. The resolution of images taken by a telescope is covered by the following equation: R = λ / D, where R is the resolution, λ is the wavelength of the light you are observing with, and D is the diameter of the telescope’s primary mirror or objective lens.

From this equation, you can see the two-front war that radio telescopes are fighting. As with all telescopes, the larger your light collection area is, the higher resolution your data will be. However, radio telescopes face an additional problem, in that radio waves have the longest wavelengths of all electromagnetic radiation. Because the wavelength appears in the numerator of the resolution equation, observations done on, say, a 10-metre radio telescope will be significantly lower resolution than observations done on a 10-metre optical telescope. This means that radio telescopes must be significantly larger than those used to observe at shorter wavelengths if they want to achieve a comparable resolution. Fortunately, because radio waves are less impacted by small-scale imperfections in the telescope’s surface, we can get away with constructing them out of sheets of metal (or even a fine metal mesh!) rather than carefully-polished mirrors, greatly reducing the cost.

Of course, actually building and maintaining such a large structure is still massively expensive, to the point that Arecibo spent much of the last 20 years of its life under constant threat of being shut down due to funding shortfalls. To avoid this, many radio observatories, like the Very Large Array (VLA) in New Mexico, the Atacama Large Millimeter Array (ALMA) in Chile, and the upcoming Square Kilometre Array (SKA) in Australia and South Africa, use a technique called very-long-baseline interferometry (VLBI) to combine a large number of smaller telescopes into one telescope with a much larger effective collection area. VLBI was most recently leveraged to combine many radio telescopes across the planet into the Event Horizon Telescope, which took the first direct image of a black hole.

As the largest radio telescope in the world from its completion in 1963 to the construction of the Five-hundred-metre Aperture Spherical Telescope (FAST) in 2011, the Arecibo Observatory was at the forefront of radio astronomy and contributed to a number of important scientific discoveries.

In our own Solar System, Arecibo was used to determine that Mercury has a rotational period of 59 days, rather than being tidally locked as was previously assumed. Relevant to my own research into ice in the permanently shadowed regions (PSRs) of the Moon, Arecibo made some of the first radar measurements of ice in the PSRs of Mercury, observations that were later confirmed by the MESSENGER spacecraft.

Elsewhere in the universe, Arecibo was responsible for a number of other “firsts.” In 1968, scientists using Arecibo measured the rotational period of the Crab Nebula pulsar, which provided the first direct evidence of the existence of neutron stars. Just six years later, Arecibo produced its first Nobel Prize-winning research in the form of the discovery of a binary pulsar system. This system was found to have a gradually decreasing orbital period, which is consistent with energy loss in the form of gravitational waves (though gravitational waves would not be directly measured until 2016). Though the search for exoplanets has been popularized by space telescopes like Kepler and TESS, it was actually Arecibo that first found extrasolar planets due to irregularities in the measured rotational period of a pulsar. To date, one of these still holds the record for the smallest known exoplanet, with a mass around twice that of the Moon.

Finally, Arecibo played a key role in the Search for Extra-Terrestial Intelligence (SETI) and Messaging to Extra-Terrestrial Intelligence (METI) programs. Arecibo was one of the primary telescopes used by the SETI Institute to listen for possible communications from extraterrestrial life, and in 1974 broadcast a short message containing information about humanity and our location in the galaxy to M13, a globular star cluster located 25,000 light years away. Although seen as reckless and possibly dangerous by many, it is widely accepted that nothing will come of this message due to the vast distances involved.

 

The Arecibo Message, which was sent from the observatory towards the globular cluster M13 in November 1974. It contains information on the genetic structure of humans, our physical characteristics, and how to find us. Many felt this was a dangerous amount of information to be sending to a hypothetical alien civilization whose motivations were unknown. (CC BY-SA 3.0, https://commons.wikimedia.org/wiki/File:Arecibo_message.svg)

The Arecibo Observatory will certainly be missed, but it leaves behind a vast and rich legacy of scientific discoveries. With FAST now operational and the 100-metre Green Bank Telescope still in good working order, along with a number of existing and new interferometric arrays around the planet, the world of radio astronomy continues to be well-served. Though the end of this particular telescope’s career was perhaps more abrupt than some might have imagined, it is leaving us having done more than its fair share of the hard work of advancing our knowledge of the universe.

Mars’ Family of Rovers

In this week's post, Grace discusses the different rovers that have been to Mars in response to a query from her sister. One of the most important things we can do as scientists is to translate the excitement and meaning of what we do for the public. (above) Image credit NASA/JPL-Caltech.

By Grace Bischof

A few days ago, I received a text message from my sister asking for a fun space fact to tell the 5-year-olds she teaches who are “super into space”. I thought about all of the interesting things I’ve learned since joining PVL, from both my own and other lab members’ work, but was pretty certain that the seasonal variation of methane on Mars might not be very interesting to young children. Having just finished shadowing my first MSL shift, I had the Curiosity rover on my mind. I realized that Curiosity has been roaming the Martian surface for longer than the kids in her class have been alive. I told my sister to explain to the students that Curiosity is older than them; they might not have found it a very fun fact, but I sure did.

 

So what other rovers are there on Mars, and how old are they? Let’s work from youngest to oldest.

 

Assuming the landing goes to plan, the Perseverance rover should touch down in Jezero Crater on February 18th of 2021 as part of the Mars 2020 mission. If the age of the rover starts at landing, Perseverance might still be considered a zygote rover. Regardless of its infant age, Perseverance is set to be the largest rover to touch down on the Martian surface. Weighing in at 2260 lbs, Perseverance is approximately the size of an SUV. Perseverance is equipped with 7 instruments and has the ultimate goal of searching for signs of past or present life on MArs.

 

Curiosity is the second youngest rover that is currently on Mars. Landing on the red planet in 2012, Curiosity is set to reach its 3000^th sol in early 2021. Curiosity resides in Gale Crater and has traveled more than 21 km in its 8 years of operation. The MSL mission had 8 main objectives, which largely centered around determining if Mars was ever hospitable to life. The rover is equipped with 10 instruments, including the Rover Environmental Monitoring System and the Sample Analysis at Mars, which help to understand the meteorology and atmospheric gases on Mars, respectively. Curiosity’s many cameras have captured interesting Martian features, such as the major dust storm in Martian Year 34. In its 8 years on the planet, Curiosity has been an indispensable asset to understanding the habitability of Mars.

 

Leaping back 17 years, the twin rovers, Spirit and Opportunity, landed at separate locations on Mars in January 2003. Smaller than Perseverance and Curiosity, the twins are about the size of a golf cart. Spirit and Opportunity are the fastest rovers to roam mars, moving at a neck-breaking speed of 0.16 km/hour. Primarily, Spirit and Opportunity were to identify rocks and soil from the Martian surface. Though originally planned as a 90-sol mission, Spirit traveled the dusty plains of Mars until May 2009, when it became stuck in soft soil. Attempts to free Spirit from the soil were carried out for 9 months, but were eventually abandoned. Spirit acted as a stationary instrument until it lost connection to Earth in March 2010. Opportunity stayed active until June 2018, losing its signal to Earth after its solar panels were covered in dust from the MY 34 dust storm. Opportunity holds the record for most distance traveled on a non-Earth world, having driven a total of 42.2 km during its 11 active years. 

 

 

Opportunity: Planetary Marathoner. The Opportunity rover has covered more ground than any other rover on an extraterrestrial surface.
Credit: NASA/JPL-Caltech - https://mars.nasa.gov/resources/6471/driving-distances-on-mars-and-the-moon/

 

The oldest rover to land on Mars is called Sojourner, and landed on the planet in July 1997 (which makes Sojourner older than me by one year). Sojourner is much smaller than its younger siblings, resembling a microwave-oven in size. Carrying only 2 instruments, Sojourner took hundreds of pictures of the Martian surface, and sampled Martian rocks and dirt. Sojourner operated for 83 sols, surpassing its original mission by 53 sols. By the end of its lifetime, Sojourner had traveled 100 m.

 

The family of Mars rovers has been growing since 1997 and is set to become a family of 5 once Perseverance arrives early next year. Through incredible science and engineering feats, we have been able to explore the surface of an entirely different planet from Earth for the past 23 years. I, for one, am excited for the next 23 years of Mars exploration – and maybe by then I can think of a cooler space fact to tell a bunch of 5-year-olds.

 

For more interesting information on the rovers, see: https://spaceplace.nasa.gov/mars-rovers

K2-141b: I can see your halo

 

This week, PhD Student Giang Nguyen talks about his recent paper discussing lava planet K2-141b. This planet's extreme atmospheric conditions set up a stable ring of clouds just beyond the edge of a large lava ocean centered on the subsolar point. Examples of other large stable annular features on planets include the auroral ovals of the Earth and Jupiter. The photo above was captured by the Imager for Magnetopause to Aurora Global Exploration or IMAGE satellite.

By Tue Giang Nguyen

A few weeks ago, my paper on modelling the atmosphere of K2-141b was published. There was a press release and quite a few news organizations picked up on the story such as CNN and CBS. The public seemed excited by the idea of a scorching planet half engulfed in lava with supersonic winds and molten rock raining from above. Many have started to call K2-141b Mustafar, a fiery world Darth Vader calls his home as envisioned by George Lucas. Others, correctly so, shared how grateful they live on this blue Earth rather than K2-141b. Although K2-141b is described as a hellish landscape, from afar, I think there’s something to be admired from our little lava planet.

 

As K2-141b is tidally locked, there is a permanent dayside and nightside on the planet. This means that certain meteorological processes exist in only specific parts of the planet, mainly clouds. Near the sub-stellar point where it is hottest, the air is not saturated with mineral vapour so nothing condenses. Far away from the sub-stellar point, it is too cold and virtually all of the atmosphere has collapsed back onto the surface and nothing condenses. This means condensation, or cloud formations, can only exist in an annulus centered around the sub-stellar point.

 

In essence, when looking at K2-141b from afar, we should see a ring of clouds around the sub-stellar point. And if you adjust your perspective such that the star is directly overhead on K2-141b, the ring faces upward which makes it a halo! K2-141b has a halo of clouds which is made up of quartz-based gems, how cool is that? This should be the case for other lava planets as well where the planet’s crust, and atmosphere, is dominated by oxidized silicon. Although with this analogy, Earth also has a cool “halo” which is the aurorae (Borealis and Australis).

 

An "eye-ball" planet in which the heat of the star creates a large ocean centered on the subsolar point. In the case above, the working fluid is water and the solid ice, but if you get close enough to the parent star, rock will also melt and form an ocean, ringed by clouds. Image Credit: NASA/JPL-Caltech https://commons.wikimedia.org/w/index.php?curid=56552366

 

For atmospheric modelling, the cloud halo acts similar to the “eye-ball” icy Earth scenario where the sub-stellar point of the icy Earth is an ocean that slowly freezes as you move further away. The middle circular ocean resembles an eyeball that is surrounded by an icy surface that has a much higher albedo. A reflective cloud halo would behave similarly to ice as it reflects more light than then bare magma ocean of K2-141b. Although this is a classically hard problem in climate modelling, we can study some limiting cases that arise from K2-141b’s halo. The albedo of the clouds can be measured which helps us determine cloud properties such as particle size and back-scattering efficiency (dependent on cloud composition and crystal geometry).

 

Now that my work on K2-141b has expanded to include radiative transfer and cloud formations, I am also collaborating with more scientists. Among them are astronomers from the Max Planck Institute, climatologists from Oxford and Chicago. Their expertise on modelling and observing exoplanets will help to make much more accurate descriptions of the K2-141b’s meteorology, surface composition and interior dynamics. While what we predicted about the weather on K2-141b is frankly mind-boggling, I believe the planet has even more interesting things to tell us.

PVL Welcomes Three new MSc Students!

This year, three new students are joining PVL at the MSc level through the Physics and Astronomy Graduate Program. Though neither of them worked with the lab in their undergraduate years (and, indeed, come from three different universities) we've already started getting to know them and they us; Grace, Justin and Conor have been able to dial in to our lab meetings over the course of the summer once they moved online due to the pandemic. I know that everyone in the lab is excited to have them join us in an official capacity. They're also keen to introduce themselves to you, dear reader, and wanted to share their experience and hopes for the next couple of years.

Written by Grace Bischof, Conor Hayes and Justin Kerr
Organized by Conor Hayes

Grace Bischof (center in image above) Hi! My name is Grace Bischof and I’m extremely excited to be joining the PVL group as a first year Master’s student this fall. I started my academic career at Western University in London, Ontario and earned my B.S. in physics. I had the privilege of being taught by amazing, passionate physics and astronomy professors who inspired a love for physics (even when it was challenging).  I’m very grateful for the experience I had as an undergraduate student in Physics at Western.

During my undergrad, I participated in research in the area of microfluidics. We designed and tested a T-junction microfluidic device to produce micron-sized beads of human decellularized adipose tissue to be used as a 3-dimensional cell culture method. While I enjoyed the research I participated in, medical physics was not the area of physics that truly interested me.

Like many who do space research, I’ve been captivated with space since I was a kid. When I applied for Master’s programs, I knew that I wanted to do research beyond Earth and was so thrilled to be accepted into this group. In the PVL group, I am going to be involved with the Martian Atmospheric Gas Evolution (MAGE) project. In the lab, we will test an enhanced spectrometer that will (hopefully!) eventually be deployed to Mars to gain a better understanding of the planet’s methane cycle.

I’m looking forward to the next couple of years at York with the PVL group!

Conor Hayes (left in image above) My name is Conor Hayes and I am joining PVL this year as a new Physics and Astronomy M.Sc. student. I received my B.S. in Astronomy and Astrophysics from The Ohio State University in Columbus, Ohio. My research there, through the Center for Cosmology and Astroparticle Physics, was focused primarily on conducting a spectroscopic analysis of five ultra-diffuse galaxy candidates in low-density environments.

My work at PVL will be much closer to home, looking at ices in the permanently shadowed regions (PSRs) of the Moon. PSRs are notable because, as their name implies, they receive very little light from the Sun or other sources, which allows them to protect volatiles like water ice against sublimation on geological timescales. Consequently, PSRs can act as a record of the history of volatiles in the solar system in addition to serving as a potential source of important resources for long-term human inhabitation of other celestial bodies.

When I applied for York’s Physics and Astronomy graduate program, my intent had been to complete the M.Sc. by Coursework degree. However, when I was contacted about the possibility of joining PVL, that plan changed quickly. Although I’ve not yet had substantial experience in planetary science (as it was not an area of much focus in the Department of Astronomy at Ohio State), the study of planets, particularly those closest to home, has held my fascination for quite some time. Consequently, I had to jump on this opportunity when it arose.

Justin Kerr (right in image above) Hi everyone, my name is Justin Kerr and I am a new M.Sc. student with the PVL through York’s Physics and Astronomy program. I am no stranger to York University, as I did my undergrad in Physics and Astronomy here as well. My previous research during that degree primarily consisted of particle physics, with my main project involving searching for magnetic monopoles using the Large Hadron Collider with the ATLAS collaboration. I also hold a BA in History which I completed before returning to university to study physics; my primary areas of interest at the time were Viking Age Scandinavia and medieval Europe. I am now looking forward to bringing my varied experience to the PVL for work in planetary physics.

My work at the PVL will consist of two projects. The first will involve joining the team in the development and testing of the Mars Atmospheric Panoramic camera and Laser Experiment (MAPLE). This project aims to use low-power lasers and a small panoramic camera system to detect small dust and ice particles near the Martian surface. I will also be working on modelling exoplanet atmospheres to determine the size of their “geocorona” (a term normally used to refer to the bubble of hydrogen in the outermost part of Earth’s atmosphere, extending past the orbit of the moon). It is expected that exoplanets possessing water would have an exosphere equivalent to Earth’s geocorona, but we do not yet know whether the size of it is affected by the presence of life. The goal of the project will be to determine what features of these exoplanet “geocoronas” future telescopes should look for as a biosignature when hunting for life-bearing exoplanets. I can’t wait to get started on these two exciting projects with the PVL, and look forward to telling you more about them over my time here.

High-Energy Particle Physics in Thunderstorms

 (the image above depicts a blue jet, a form of upper atmospheric electrical discharge: By Gemini Observatory / AURA - Gemini Observatory / Association of Universities for Research in Astronomy (AURA)., Public Domain, https://commons.wikimedia.org/w/index.php?curid=61319099 )
It's September, a time when new students join our research group. This year we have three and, for the first time, all those students hail from a Physics & Astronomy background. Therefore it is appropriate that one of our new MScs, Justin Kerr, gets first crack at talking about an interesting intersection between high-energy particle physics and planetary science. By way of introduction, I'd love tell you more about the article, but I wouldn't want to steal his thunder! You'll just have to read on...

by Justin Kerr

    Here in Toronto, its currently thunderstorm season. To go along with the high humidity, we’ve had severe storms nearly every week recently reignited my long-held interest. So, when I saw a new paper posted on arXiv last week that covered a new sensor network observing thunderstorms using methods related to my previous research area of particle physics, I simply couldn’t resist digging in to the topic for this week’s post. While it might be surprising to many that high-energy particle physicists would have work to do with thunderstorms, the link between the two fields was experimentally confirmed in the 1980s. Even so, most of the knowledge about exactly how thunderstorms produce high energy particles is still hypothetical due to the difficulty of observing large thunderstorms. This is something the new paper sought to address.
    But first, let’s take a look what high-energy particles are produced by thunderstorms and how that might be happening. The first type of high-energy event being produced by thunderstorms is the terrestrial gamma-ray flash (TGF), which are rapid bursts lasting less than a millisecond. TGFs are expected to occur when an already energetic electron (likely produced by a cosmic ray entering the thunderstorm) is accelerated to near the speed of light by the intense electric field created by a lightning strike. This relativistic electron then begins a process known as a relativistic runaway electron avalanche (RREA). The RREA process consists of the initial electron colliding with the electrons surrounding atoms in the atmosphere with enough energy to knock them off. These electrons are then accelerated themselves and go on to knock off even more electrons in a chain reaction, creating a massive “avalanche” of high-energy electrons. As the electrons produced by RREA are slowed down by collisions with atomic nuclei in the atmosphere, they produce gamma rays via the Bremsstrahlung process. The gamma rays then escape upwards, where they can be detected by aircraft or satellites. 

Figure 1: Expected method of TGF formation at the top of a thundercloud. Source: https://en.wikipedia.org/wiki/Terrestrial_gamma-ray_flash#/media/File:TGF_production_by_quasi-static_fields.svg

    Several satellites have now recorded measurements of TGFs. They were first discovered by the Compton Gamma-Ray Observatory in 1994. In the 2000s, the RHESSI experiment showed the electrons could reach energies exceeding 20 MeV – which is in the range of the highest energies produced in linear accelerators for medical radiotherapy. Even more recently, the Fermi Gamma-ray Space Telescope discovered evidence of antimatter production from TGFs in 2009. When a positron meets an electron, the two annihilate and produce two photons each with an energy of 0.511 MeV (the energy equivalent of the rest mass of an electron/positron). The positrons have been experimentally shown to be produced when photons of energies exceeding 10 MeV trigger photonuclear reactions in atmospheric nuclei, creating radioactive nuclei and free neutrons. When positrons created in the TGF process either traveled directly upwards or rode along Earth’s magnetic field to the spacecraft they annihilated with electrons in the spacecraft, allowing it to see the telltale 0.511 MeV photons in its gamma ray detector. The Fermi team was able to trace these incoming positrons back along Earth’s magnetic field lines to specific thunderstorms producing them. With Fermi’s detection of numerous TGFs, it is now estimated that about 500 TGFs occur every day worldwide. Recently some rare TGFs have even been detected going downwards towards the ground, potentially opening up new opportunities to better study their formation.
    The second type of high-energy event known to be occurring in thunderstorms is gamma-ray glow. Gamma-ray glow was discovered by x-ray observations from aircraft above thunderstorms in the 1980s. This glow is much longer lasting than a TGF, with events potentially lasting tens of minutes. Energetic particles in a glow can reach similar energies to that of TGFs and are expected to be produced by the same RREA process. Unfortunately, the production of gamma-ray glow is somewhat less understood than that of TGFs. The glow seems to be produced by long-lasting stable electric fields in thunderclouds, and it is usually terminated when a lightning strike dissipates the stable field.
    The good news is that the ground-directed nature of gamma-ray glow is now providing new opportunities to study high-energy processes in thunderstorms without the need for difficult and expensive observations from above. While gamma ray photons are normally absorbed by the atmosphere in about 1km and thus long before they reach the ground from a typical thunderstorm, the Thundercloud Project in Japan has a way around this. In the winter, Japan has thunderstorms with cloud bases at heights of less than 1km and so ground based observations of their high-energy particles can be made. By assembling a network of sensors around Ishikawa Prefecture and Niigata Prefecture in Japan, they were able to record 51 gamma-ray events in the last four years. From this data, they have been able to show distinctive evidence of gamma-glow termination by lightning strikes. They were also able to detect a few downward TGFs, which show time-resolved proof of photonuclear reactions producing free neutrons and positrons. Their full results are currently in pre-print and set to be published in Progress of Theoretical and Experimental Physics.
    With the new results from the Thundercloud Project and hopefully more studies to come, we will be able to significantly advance our understanding of the processes involved in the high-energy phenomena of thunderstorms. It is certainly amazing how much there still is to learn about thunderstorms occurring right here on Earth, and how something so standard in our daily lives can be utilizing processes which we previously thought were restricted to particle accelerators or high-energy astrophysical phenomena. So the next time you hear an approaching thunderstorm, remember that you don’t need to travel to CERN or Fermilab to witness high-energy physics in action!

Sources: https://www.nasa.gov/mission_pages/GLAST/news/fermi-thunderstorms.html,
https://arxiv.org/pdf/2007.13618.pdf,
https://www.nature.com/articles/s42005-019-0168-y,
https://en.wikipedia.org/wiki/Terrestrial_gamma-ray_flash

Orbital Resonances and Musical Harmonies

This week, our summer undergraduate researcher, Simon Friesen, takes a step back from pondering the dusty skies of Mars to consider the Music of the Spheres. Music has long been associated with mathematics and the physical sciences. I know more than a few researchers who started out studying music only to later find themselves drawn to the harmonies of nature. This includes past PVL researchers as well as a few people with whom I went to graduate school. No talent or study ever goes to waste and there are surprising patterns that arise again and again in different fields. One such variation on a theme in planetary science takes place when considering orbital resonances and how this data can be represented musically.

by Simon Friesen

Orbital resonances are found throughout the solar system (and there are even some examples found between exo-planets and their stars). There are two main types of orbital resonances: unstable resonances, which clear objects at specific radii from the parent body (think gaps between the rings of Saturn caused by its inner moons); and mean-motion resonances which maintain and self-correct the orbits of the bodies involved.

For the purposes of this exploration, I want to focus on the stable orbits between planets or moons in the solar system. Three of the moons of Jupiter – Ganymede, Europa, and Io – are in a stable ratio of orbits of 1:2:4 (specifically, for every single orbit that Ganymede completes, Europa will complete two orbits and Io; four). These types of orbital resonances are somewhat rare in our solar system, but do include the following notable examples: Pluto – Neptune, 2:3; Tethys – Mimas (moons of Saturn), 2:4; Dione – Enceladus (other moons of Saturn), 1:2; Hyperion – Titan (further moons of Saturn), 3:4; Haumea – Neptune (suspected), 7:12; 225088 Gonggong – Neptune, 3:10; and Pluto’s moons, Styx – Nix – Hydra, have a ratio of 11:9:6. We will also take a look at orbital resonances found in distant exo-planet systems later.

The term resonance is also a common feature of another interest of mine: music. The exploration of some of the mathematical formalism behind harmonious sounds was done by Pythagoras, who found that sounds based frequencies that were small number ratios of each other sounded consonant. This work laid the foundation for myriad western tuning systems and western harmonies. Pythagoras found that frequencies of ratios 1:2, 2:3, and 4:3 sounded best together. To try this out for yourself, find an online tone generator and open up two copies in different tabs. For a 2:1 ratio, try 440 Hz (A4 on the piano; I’ll use this as a reference tone for all the other harmonies we’ll explore later) and 880 Hz. This is known in western music as the octave. For 2:3, use 440 Hz and 660 Hz. This is called an interval of a fifth. For 4:3, use 440 Hz and 586.67 Hz. This interval is known as a fourth. These Pythagorean intervals can be used to construct the twelve notes in the Pythagorean scale. This scale, and many other scales that came after it, suffers from the circle of fifths not being closed and from certain terrible-sounding intervals called wolf intervals.

Multiple variations on western tuning systems have been developed since Pythagoras’ day including, but not limited to: Just Intonation tuning, which created better sounding thirds at a ratio of 4:5 (try 440 Hz and 550 Hz); Meantone scales, which preserved nice thirds but had slightly worse fifths (compare 440 Hz and 657.95 Hz to the previous 660 Hz); Well Temperament, favoured by Bach and granting each key signature its own distinct character; and 12-Tone Equal Temperament (12-TET), which spreads all 12 notes in an octave logarithmic-evenly across the octave. I encourage you to look these scales up in more detail; each one has strengths and weaknesses. I’ll reference these scales later when looking for the closest match to intervals created from orbital resonances.

We’ve established that scales and tuning systems can be created using ratios of frequencies, and that orbital resonances occur within our solar system that are based on ratios of orbits. I want to explore what some of these ratios sound like. From previous; Ganymede, Europa, and Io are in stable orbit ratios of 1:2:4 respectively. This is exactly the same as Pythagoras’ octave; try it out using 440 Hz, 880 Hz and 1760 Hz. Similar to this, Tethys and Mimas have a ratio of orbits of 2:4 (880 Hz and 1760 Hz); and Dione and Enceladus have a ratio of 1:2 (back to 440 Hz and 880 Hz). Pluto and Neptune have a stable ratio of orbits of 2:3, the same as Pythagoras’ interval of a fifth (440 Hz and 660 Hz). Hyperion and Titan have a ratio of orbits of 3:4, giving us the same interval as a Pythagorean fourth (440 Hz 586.67 Hz).

Haumea and Neptune have a supposed ratio of orbits of 7:12. To hear this, use 440 Hz, and 440 * (12/7) = 754.28 Hz. This harmonic interval is closest a 12-TET 6^th interval (use n = 9 in the formula 440 * 2^n/9 = 739.99 Hz; to hear it, use 440 Hz and 739.99 Hz). Does one interval sound better to you?

Hydra, Nix, and Styx have a ratio of orbits of 6:9:11. 6:9 is the same as 2:3, so the interval is a Pythagorean fifth. To find the frequency of the highest pitch, we use: 440 * 11/6 = 806.67 Hz. This is closest to a Just major seventh interval, but is close to a quarter tone flatter. Putting all three tones together (440 Hz, 660 Hz, and 806.67 Hz) creates something that you might describe as an A major 7^th suspension chord, but is really outside of western tonality.

Orbital resonances have also been found in exo-planets and extra-solar systems. Though it is still a rare phenomenon, some of these extra-solar systems also exhibit longer chains of orbital resonances than are found in our solar system.

On the simple end of things, Kepler-29 has an observed 7:9 resonance between a pair of planets. Translating this to our 440 Hz reference pitch gives us 440 * (9/7) = 565.71 Hz. This pitch is close to both a Pythagorean and a 12-TET major third. Kepler-37 has three planets in ratios of 8:15:24. Referencing 440 Hz we find the upper two pitches to be 440 * (15/8) = 825 Hz, and 440 * (24/8) = 1320 Hz (I will omit calculations from here on; all further frequencies will be created from ratios in a similar manner). The middle tone is a Just major seventh, and the high pitch is an octave plus a fifth, giving us another A major 7^th suspended chord. Kepler-233 has a series of planets in a 3:4:6:8 ratio of orbits (frequencies 440 Hz, 586.67 Hz, 880 Hz, and 1173.33 Hz). This chord is only made of octaves and fourths, so we might consider it an A-suspended 4^th chord.

Kepler-80 has six planets in a 4:6:9:12:18 ratio (440 Hz, 660 Hz, 990 Hz, 1320 Hz, and 1980 Hz). This chord is made of a fifth, a second (up an octave, in tune with the Pythagorean and Just scales), and two further fifths in upper octaves. This chord would then be a stellar example of an A major suspended second. Kepler-90 has six planets in a ratio close to (but not exactly) 2:3:4:7:11 (440 Hz, 660 Hz, 880 Hz, 1540 Hz, and 2420 Hz). This chord consists of a fifth, an octave, a high sharp major second, and a high sharp minor seventh, making this some strange variation on an A 9^th suspended 2^nd, but is not really part of any scale system. Finally, TRAPPIST-1 has an astounding 7 planets in a ratio close to 2:3:4:6:9:15:24 (440 Hz, 660 Hz, 880 Hz, 1320 Hz, 1980 Hz, 3300 Hz, and 5280 Hz (feel free to skip this one)). This chord consists of a fifth, an octave, a high fifth, a high Pythagorean second, and an extremely high fifth, giving us an A major suspended 2^nd chord.

And so, we now have a wider understanding of both western harmonies and resonances between orbiting objects in and beyond our solar system. I had expected to find many more notes that did not fit neatly into scales, but surprisingly only Kepler-90; pluto’s moons Hydra, Nix, and Styx; Haumea and Neptune; and Kepler 29 produced notes not included from our reference scales. The universe seems to doubling or 1.5-factor periods in orbits. Some of the intervals outlined here could inform new tuning systems or harmonies to explore musically.

Via Wikipedia: "Sequence of conjunctions of Hydra (blue), Nix (red) and Styx (black) over one third of their resonance cycle. Movements are counterclockwise and orbits completed are tallied at upper right of diagrams (click on image to see the whole cycle)." Photo: By WolfmanSF - Own work, CC0, https://commons.wikimedia.org/w/index.php?curid=4175932

Let It Snow (on K2-141b)

When we Canadians think of snow, it's of the water-ice variety. And though every snowflake is unique, they're all made of the same stuff and share a similar geometry. But depending on the temperature-pressure regime and the composition, many different other types of snow are possible on other planets. On Mars, it can be both water ice or carbon dioxide ice snows. For Saturn, ammonia ice snow is common. But on exoplanets, still stranger snows can fall to a planet's surface. Yet, as Giang describes below, there might be some surprising parallels.

By Giang Nguyen

K2-141b is a recently discovered lava planet where almost half the planet is a giant magma ocean that we’ve estimated to be 140 km deep. Since the planet orbits so close to its star, temperatures are hot enough to vapourize magma which forms a thin mineral vapour atmosphere. My work on the planet involves simulating atmospheric and oceanic flow given likely compositions of K2-141b. As this work on the initial characterization of K2-141b’s atmosphere is coming to an end, I’ll be expanding on my work with more complexities for my next project.

One of the complexities that I’ve been very interested in is the condensation process on K2-141b as well as incorporating more constituents into our previously idealized pure atmosphere. This would help me understand and envision what the weather on K2-141b would be like. On Earth, when I think of weather, I think of things like wind, clouds, and precipitation. Clouds are particularly noteworthy here as they precede rain and snow. On Earth, clouds and precipitation usually involve water but on Mars, carbon dioxide plays a large role as well. On K2-141b, the hydrological cycle likely depends on silicates.

Silica (silicon dioxide) is the dominant composition of a rocky planet’s crust where up to half of the crust is expected to be silica. The crust is also likely made up with magnesium oxide and titanium oxide. However, since the atmosphere is likely to be made up of very volatile compounds, we expect sodium, silicon monoxide and oxygen along with trace amounts of iron and magnesium. As these molecules are evaporated from the hot dayside where the pressure is high, they are pushed by winds to the cold nightside where the pressure is low. When the atmosphere cools, the mineral vapour condenses into liquid droplets, likely forming clouds, and rains out onto the magma ocean. However, when the atmosphere is cool enough where silica condenses as a solid, interesting things happen.

On Earth, snow forms when water vapour directly turns into ice; liquid droplets that freezes do not become snow but instead become sleet. During the snow making process, water will freeze onto existing ice crystals in a pattern specific to the water ice’s hexagonal crystal structure. Although we tend not to think of solid material as ice, it is useful to think so on lava planets where rocks are simply frozen magma. Therefore, when the mineral vapour condenses, the result would be clouds of mineral. As silicon monoxide and oxygen freezes out and combine, you essentially get quartz.

Quartz is a common mineral on Earth and is useful in keeping time (although modern timekeeping standards now rely on quantum time constants and radioactive decay). One can easily imagine seeing quartz on beaches and in the wild, but it is much harder to imagine the quartz falling out of the sky as snow on K2-141b. How different would snowflakes be on this lava planet than on Earth?

Well, as mentioned before, the typical photogenic Earth snowflake has 6 arms due to the hexagonal structure of water ice. Quartz also has a hexagonal crystal structure, so a quartz snowflake should also follow suit with 6 arms where each arm should have fractal hexagonal pattern. Significant impurities in K2-141b’s atmosphere such as iron or magnesium that binds with the quartz would give the snow a much more diverse colour palette.

The most abundant impure molecule expected to bind with the quartz should be iron (as FeO or just Fe). Note that sodium is actually the most volatile molecule, but it is fairly scarce on the crust which invites skepticism on how much sodium can be evaporated into the atmosphere. Impurities in crystal composition gives colour to an otherwise clear gemstone and iron can transform the colourless quartz into an array of beautiful gems. On Earth, quartz have different varieties when iron impurity is present: rose quartz, purple amethyst, yellow citrine, and green prasiolite.

Of the quartz variety mentioned above, their prevalence on Earth can be directly influenced by humans as most of the citrine and prasiolite are created from heat treatments of the natural occurring amethyst. However, it can be pretty hot on a planet that’s half molten magma so these minerals may form naturally on K2-141b. Traces of magnesium can also find themselves bound to silicates and iron and form other gems such as peridot or chrysolite (gem-quality olivine).

Ultimately, weather systems are largely unknown for exoplanets and our proposed atmospheric and surface compositions are educated guesses at best. However, it is exciting to envision a planet with pink, purple, green, and yellow Earth-like snowflakes made of quartz flying through the sky. Imagine what twilight would look like when even the crystal clouds have a slight purple or pink hue. In conclusion, if this isn’t one of the most cinematic sci-fi setting ever, I don’t know what is.

Here's what hexagonal symmetry can do, working with water ice on Earth. Just imagine what might be possible on K2-141b! (photo by Lt. Cindy McFee - Edited version of Image:410px-Sun halo optical phenomenon.jpg., Public Domain, https://commons.wikimedia.org/w/index.php?curid=5267988 ).