Understanding Exoplanets with Data Science
Exoplanets I: Methods and Discoveries
Discovering the Universe
7 years ago, the 17 year old me had chosen to explore the field of Exoplanets for my final year of my high school called ‘Travail de Maturité’. I had reached out to Prof. Didier Queloz, co-discoverer of the first exoplanet, who used to teach at Geneva University to discuss the analytical components of my paper and solicit his views on the prospects of habitability and therefore the significance of exoplanets. He generously took out the time to meet with me for an interview, and later also gave me a guided tour of the Geneva Observatory and his lab.
My project work was awarded a perfect grade, and I was also subsequently invited to CERN to publicly present my insights at a prestigious Switzerland France « Science Sharing » event for students.
My presentation was well received, particularly for bringing a focus relevant to human existence in a theoretical and research driven field such as astrophysics. Indeed, the prospect of finding life elsewhere, which could help us better understand ourselves as human beings, was appreciated by the audience, and was rooted in parallels in my own experience.
In October 2019, the same Prof. Didier Queloz, along with Michel Mayor and James Peebles were jointly awarded the Nobel Prize in Physics.
This article is part of the very report I had then written with his inputs asan introduction to Exoplanets. In light of the recent news, I am making it available to view now, as it is very relevant and gives an insight on the discoveries of exoplanets, in the context of data science, i.e. how the data is collected, analysed, and interpreted. We can also co-relate the discoveries with many laws of Physics, such as Kepler’s Third Law, and observe how all planets in the Universe end up following the very same pattern.
I have split the content into multiple parts as given below:
- Part I: Methods and Discoveries
- Part II: Interpretation of Data
- Part III: Habitability and Conclusion
A Short History of Exoplanetology
Mankind has long since speculated about planetary systems other than our own. Philosophers hypothesized centuries ago that our solar system was not unique; that there were in fact countless more that existed in the seemingly limitless ocean of stars. The possibility of life existing on a planet orbiting another star was not just a plausible theory but it also had the advantage of the odds on its side. The fact that there are hundreds of billions of galaxies in the observable universe, with each galaxy containing some hundred billion stars; it seems almost ridiculous to suggest that Earth might be the only planet in the whole universe capable of supporting life.
However, the lack of scientific evidence to back this visionary viewpoint meant that the thinking over the past two thousand years ranged over all extremes. On the one hand, some — like Epicurus — believed in the existence of worlds in the universe other than ours and in their capacity to harbour life. On the other hand, many — such as Aristotle — faithfully held the view that the Earth was unique in the universe and that other similar worlds could not exist. Christianity and other faiths would also claim the hand of God in the creation of Earth and all living beings.
Hence, the search for extrasolar planets became a subject of intense scientific investigation. Due to the lack of evidence, it was unknown how common they were, how similar they were to the planets of the Solar System, or how typical was the makeup of our own Solar System in comparison with planetary systems around other stars. The question of habitability was also an important one. If there were any other planets, did they also have the necessary surface conditions to support some form of life? There were many questions but few answers. The main obstacle lay in the inability to directly observe these unknown bodies.
The Hubble Space Telescope has perhaps spoiled us all — we have now come to expect to frequently see images of distant galaxies and nebulae. Taking an image of an extrasolar planet therefore should not be any more difficult than taking an image of a distant galaxy. However, the problem arises due to the fact that the host star completely outshines its small, and rather faint, planet. In most cases the planets are too close to their respective stars to be directly imaged, especially from Earth’s surface, given the disturbing effect of our atmosphere.
It was only in 1995 that the first definitive detection of an extrasolar planet was reported by Michel Mayor and Didier Queloz of the University of Geneva. Although a few other detections had been made some years earlier by radio astronomers Aleksander Wolszczan and Dale Frail, they had not been found around an ordinary star but around a pulsar - the superdense remnant of a massive star that had exploded as a supernova. Mayor and Queloz's announcement of the exoplanet 51 Pegasi b in October 1995 in Geneva was essentially considered to be the first unambiguous exoplanet detection. Over the years, there have been several other discoveries that could be regarded as milestones, such as the detection of multiple planet systems and the first detection of planetary atmosphere.
Since 1995, there has been astonishing progress in this field. New discoveries and significant developments continue to be announced roughly on a monthly basis, an unprecedented level of advancement in any field of science. As of November 2019, a grand total of 4128 exoplanets had been identified with the use of several different methods of detection. The search for exoplanets has rapidly become a respectable domain of scientific research and a field of astronomy capable of standing on its own. The advance in this domain has not only been accompanied by the publication of several thousand scientific papers but has also seen improvements in optical astronomical instrumentation which led to the launch of the Kepler telescope and new techniques of detection.
The Methods of Detection
Over the past two decades several different techniques have been employed to detect exoplanets. As mentioned earlier, the light emitted by a parent star always washes out the little light reflected by its planet(s). Hence, scientists had to come up with alternative and indirect methods to detect exoplanets, since observing them directly is almost impossible. This chapter gives an overview of the most established methods that have yielded success and also the logic and science behind them, while discussing the advantages and disadvantages of each method.
Radial Velocity Method
Also called the RV method, it has been the most successful technique used to date. Michel Mayor and Didier Queloz found the first acknowledged exoplanet using this method in 1995. It has since been used to locate 863 extrasolar planets (as of November 2019).
As seen in Graph 1, scientists have been able to detect a large variety of planets over the years. The mass of exoplanets are expressed in relation to the mass of Jupiter, as Jupiter Mass. However, mass measurements of the planets are uncertain up to a factor of sin(i), where i is the angle of inclination of the planets that orbit around its star. Hence mass is plotted as M*sin(i), and not just M. Over the years, the technology has improved in sensitivity and accuracy and scientists have now found many planets with Jupiter masses lower than 0.1, a feat not achieved till around 2004.
This technique is most effective for detecting massive planets that orbit close to their parent stars. It is worth noting that this method only provides a lower limit on the planet’s mass, which is its biggest disadvantage. A planet’s true mass can only be determined when a combination of this technique and the Transit Method, described later, are used together.
The RV method is based on the natural system of gravity and orbits, defined by Newton’s law of Universal Gravitation.
As mentioned previously, a planet’s gravitational force makes its parent star wobble in its own small orbit. Although the force that the star and planet exert on each other is the same, the difference between their accelerations is huge because of the difference between the mass of the star and planet, which is equal to 10^3 at least. Since the acceleration of the planet is based on the mass of the star, which is very high, the planet moves a lot. Conversely, the star’s acceleration is small, as it is based on the planet’s mass, which is relatively small. This feeble acceleration is what causes the star to “wobble” in its small orbit.
This ‘wobble’ causes small perturbations in the observable properties of the star, such as its angular position on the sky with regard to the Earth. A more important change is the variation in the speed with which the star moves towards or away from Earth, where it is being observed. To better understand the RV method, we first need a basic understanding of the Doppler effect and general spectroscopy, as both are used in combination to detect exoplanets.
Doppler Effect
Let us take the example of the sirens of a firetruck to understand this concept. Let us imagine an immobile fire truck that has its sirens on. This stationary source produces sound waves λ at a constant frequency ƒ which move outward at the constant speed of sound c = 340 [m/s]. Since the sound waves propagate away from the source in all directions, they would appear as circles if they were visible, and all observers will hear the same frequency, which is, in this case, the actual frequency of the source. In other words, the observed frequency ƒ is equal to the emitted frequency ƒ_0.
However, if the firetruck starts moving in a direction, the sound waves become uneven due to the difference of wave lengths. The sound waves emitted by the sirens are at the same frequency in both cases. However, since the source is now moving, the centre of each new wave is slightly displaced in the direction of the firetruck (as shown in the figure on the right). As a result, the sound waves start to collect on the front of the firetruck, and spread apart behind it. This phenomenon is called the Doppler effect. As the wavelength of the sound waves is different, the observed frequency is affected as well. Therefore, an observer in front of the source will hear the sirens at a higher frequency, while another observer behind it will hear is at a lower frequency. The change of observed frequency is what causes the audible change of pitch of the sirens. The observed frequency can be calculated using the following formula:
Where:
- c is the velocity of the waves in the medium, in our case air, which is approximately equal to 340 [m/s].
- v_observer is the velocity of the observer, expressed in [m/s]. It will be positive if the observer is moving towards the source, and negative if moving away from it.
- v_source is the velocity of the source, also expressed in [m/s]. It will be positive if the observer is moving towards the source, and negative if moving away from it. Similarly, it will be positive if the source is moving away from the receiver, and negative if moving towards it.
- ƒ_0 is the frequency emitted b the source, expressed in [Hz].
In order for this effect to be observed, the relative motion must be along the line joining the observer and the source of the waves, i.e. either towards or away from the observer. The motion that is directed along this line is called the Radial Motion, and the velocity of this motion is called the Radial Velocity. If the observer, in relation to the wave source, is neither approaching nor receding, there is no effect. The Doppler effect is a phenomenon that affects the wavelength and frequency of any form of wave motion such as sound waves, water waves, light waves, and indeed all electromagnetic waves.
Now let us make our analogy more relevant to astronomy. Instead of a fire truck emitting sound waves, let us imagine a star emitting light waves. We, the humans on planet Earth, are the observers, and the star is the source of the light waves. If this star is without an exoplanet, it would have no apparent radial velocity, as it would be stationary. However, as mentioned previously, when a planet is orbiting a star, the latter also moves in its very small orbit in response to the former’s gravitational force. Or rather, both of them orbit their common centre of mass, which happens to be within the star itself, causing it to wobble slightly. Therefore, if we can observe this ‘wobble’, then we can conclude that an actual exoplanet is likely orbiting it. This ‘wobble’ is actually the variations in the radial velocity of the star. Astronomers can detect these variations by applying spectroscopy to the Doppler effect.
Spectroscopy
Now let us imagine that our above mentioned star does have an exoplanet orbiting it, causing variations in its radial velocity, which are ‘seen’ by us, the observers. Just like the firetruck, when the star appears to be moving towards us, the wavelengths it is emitting will be smaller i.e. more compressed and bunched up, and therefore of higher observed frequency. Conversely, when it moves away from us, the wavelengths will be larger i.e. more stretched and spread out, and the observed frequency lower. However, light waves behave slightly differently from sound waves: instead of a change in their audible pitch, light waves change in their spectral colour. In other words, the frequency, wavelength and spectral colour of light waves are all inter-related.
The wavelengths corresponding to the visible spectrum are as following:
When the light waves have small wavelengths and a high frequency, the light waves are blueshifted, meaning they have a blue spectrum colour. When the light waves have large wavelengths and low frequency, they are redshifted, meaning they have acquired a red spectrum colour.
Because of the Doppler effect, we know that when light waves are redshifted, they are moving away from us in radial motion, because of their increase in wavelength (and therefore decrease in frequency). In the same vein, when the light waves are blueshifted, we know that they are moving towards us, because of the decreasing wavelength and increase in frequency.
So when we observe the spectrum colour of the light waves emitted by our chosen star, we see that they continuously change from red to blue. This periodic spectrographic shifting occurs because the star is continuously moving on its small orbit, and thus periodically reducing and increasing its distance to us, the observers.
To sum up, by using high precision spectroscopy instruments, we can effectively detect a periodic spectrographic shift in the spectral colours of the host star, implying a periodic change of wavelength in its visible light waves, in turn indicating an apparent radial motion, which can only be caused by the gravitational force of an exoplanet as it compels the star to move around the combined centre of mass of both the bodies, thereby confirming its existence.
Transit Method
Another method that has produced results in detecting exoplanets is the transit method, which is mostly known due to the space based missions such as CoRoT and Kepler. The basics of this technique are simple: if a planet passes in front of the star it is orbiting, the intensity of the light that is being received on Earth will see a small drop.
By observing the variations in the brightness of the star’s light caused by the transits of the planets, one is able to detect exoplanets. Although the drop in luminosity depends on the relative size of the star and planet, the typical amount is estimated to be between 0.01% and 1.7%. The duration of the transit also depends on the planet’s distance from the star and the star’s size.
This technique has one obvious flaw: it is only applicable when the planet’s orbital plane is aligned with our line of sight, so that we can witness the planet blocking some of the star’s light.
A planet orbiting a sun-sized star at Earth-Sun distance (1 AU) will have a probability of 0.47% of producing a transit to an observable alignment. One could therefore deem this method as potentially impractical and unproductive. However, by scanning for stars in large areas of the sky which contain several thousands of them, one can, in principle, find extrasolar planets at a pace which could potentially exceed that of the Radial Velocity Method. It is in this hope that many missions have been launched, notably the Kepler mission. In December 2012, 291 planets had been found using this method and over 2000 candidate exoplanets found by Kepler are awaiting confirmation. Today, the number of confirmed planets stands at 2966 confirmed planets and 2428 candidates using the transit method.
Another disadvantage with the transit method is the length of time necessary to confirm the authenticity of planet candidates. Indeed, observation of a single transit is not enough to be fully accepted as a planet due to the high rate of false detections. Hence, it can take many years for a candidate to be confirmed as an extrasolar planet, as one has to wait for it to orbit several times. This method is also more biased towards detecting large planets with small orbits, designated as Hot Jupiters, as they transit more frequently and are therefore easier to detect.
On the other hand, one of the advantages of the transit method is that the dip in light provides an estimate of the planet size. But by far, the biggest advantage is that we can determine the atmospheric composition of the exoplanet which is vital in ascertaining its potential for habitability. When the planet is transiting the star, the starlight goes through the planet’s atmosphere before reaching the Earth, giving us the opportunity to detect whether elements such as oxygen are present in it.
The dip in the emitted light of a star is more when the planet transiting it has an atmosphere, as the elements present in it absorb some of the light waves in addition to those that were already blocked by the body of the planet. The atmosphere of the planet essentially acts like a filter to the light waves of the star, blocking some and letting go of some, depending on the atmospheric elements.
The elements present in the atmosphere block the wavelengths that correspond to them, which result in the appearance of black lines in the spectrum, and are called absorption lines.
Each element is associated with a specific set of wavelengths that it blocks because of its chemical properties. So when we find absorption lines in the light spectrum of a star that has a planet transiting it, we know that the planet in question has an atmosphere. By analysing the absorption lines, we can determine the chemical composition of the atmosphere by looking at the element(s) corresponding to the wavelengths. If the absorption lines of the stellar spectrum correspond exactly to the absorption spectrum of an element, then it indicates its presence.
For example, by finding absorption lines in the spectrum of a star that match those of oxygen, we could determine whether the exoplanet orbiting it could potentially be habitable or not.
Further reading:
- Part II: Interpretation of Data
- Part III: Habitability and Conclusion
- Original report: https://eklavyafcb.github.io/exoplanets.html
References:
- L. Calçada, ESO. https://luiscalcada.com/
- NASA’s Imagine the Universe, Doppler Shift. (2013)
- NASA, Visible Light Waves. (2013).
- Las Cumbres Observatory Global Telescope Network, Transit Method. (2013).
Wikipedia, https://www.wikipedia.com [accessed in 2013]:
- Redshift
- Radial Velocity
- Light
