How a Star Can Hide its Earths

Autor: Xavier Dumusque, Observatory of Geneva

Let’s consider that we want to find a planet extremely similar to Earth, meaning that it’s orbiting a star similar to the Sun, with a mass equal to Earth and an orbital period of one year. Let’s also consider that we want to detect this object by measuring the gravitational effect it induces on its host star. I know what you are telling yourself; “No way, the Sun is so massive it doesn’t move!”. You are right, the Sun is extremely massive, in fact 300,000 times more than the Earth, but let’s stick to physics here. The laws of gravity (thank you Newton!) tell us that all object with mass will interact with each other, so the Sun should move. But the question is by how much? Plugging the numbers in, we arrive at a maximum displacement of the Sun’s center of 500 km over a 6-month period. This means that its displacement will be 1,500 times smaller than its radius, and that the maximum velocity the Sun will reach will be only 0.3 km/h (or the velocity of turtle going out for a walk). I agree with you that this is extremely small, but still, it moves!

Displacement of the Sun’s center induced by the gravitational pull of all the planets in the Solar System as a function of time. The Sun moves by about a solar radius, and  the major contributor to this displacement is the most massive planet of the Solar System, Jupiter (CC, Carl Smith’s derivative work)

Let’s now imagine that we build the perfect instrument to measure the tiny effect induced by an Earth twin on its host star. This instrument should therefore be capable of detecting a velocity of 0.3 km/h on a star that is a hundred thousand billion kilometers away. I do not want to go into the details here, but let’s use an analogy to get a feeling of the difficulty we are facing. Imagine that this perfect instrument is a ruler, and you want to measure the width of an object with the same precision that is required to detect an Earth twin. The required precision is 10,000 times smaller than the smallest graduation of the ruler. Not so easy right? With good eyes, you might probably get down to 1/3rd or 1/4th of the graduation, but 1 in 10,000! Today, the best instruments we use are capable of a precision of 1 in 1,000 (see HARPS and HARPS-N). We are therefore capable of detecting a planet ten times more massive than Earth if the host star is similar to the Sun and if its orbital period is one year. At the University of Geneva, where I am working, scientists are now developing a new instrument, called ESPRESSO, that will have the precision required to detect Earth twins.

Let’s now imagine that one year from now ESPRESSO can be used (this is the real timeline), and we start observing several stars to search for Earth-twins. To be confident in a detection, we need to observe at least one full orbital period of a planet, or one year in this case. If these Earth-twins exist, and we are confident there should be a lot of them out there, we should detect a Holy Grail planet before 2020. But—wait a minute!—several things can go wrong here, and I want to just highlight the biggest problem we have nowadays. This big problem is the stars.

Let me try to explain to you how stars can mess everything up. Everything starts with the Doppler effect. A fancy name that physicist like to use, but if you didn’t study physics, you probably do not know what this means, or you heard the name in high school and now it’s forgotten forever. But most of you have already encountered the Doppler effect in real life. One day you were probably walking down the street, when suddenly an ambulance passed by. You could hear the vehicle from far away with its strident siren—you focused on the sound created and could easily hear the pitch of the siren, but once the ambulance passed by you, the pitch changed. Did the driver push a button at the same moment he was passing by you? Probably not. To be sure, you asked other people in the street if they also had the same impression (well, in real life people would have wondered, “who is this weirdo?”, but this is a mental experiment; you can be as weird as you want). And yes, they all confirmed that this phenomenon happened at the moment the ambulance passed them by—confirming that the driver was not playing around. What happened is simply that before overtaking you, the ambulance was moving toward you; whilst after, it was moving away from you. And because sound-waves progress through the air with a limited speed, the difference between the velocity of the ambulance before and after passing by you creates this difference in tonality.

The radial velocity method to detect exoplanet is based on the detection of variations in the velocity of the central star, due to the changing direction of the gravitational pull from an (unseen) exoplanet as it orbits the star. When the star moves towards us, its spectrum is blueshifted, while it is redshifted when it moves away from us. By regularly looking at the spectrum of a star - and so, measure its velocity - one can see if it moves periodically due to the influence of a companion. Image credits : ESO
The radial velocity method to detect exoplanet is based on the detection of variations in the velocity of the central star, due to the changing direction of the gravitational pull from an (unseen) exoplanet as it orbits the star. When the star moves towards us, its spectrum is blueshifted, while it is redshifted when it moves away from us. By regularly looking at the spectrum of a star – and so, measure its velocity – one can see if it moves periodically due to the influence of a companion. Image credits : ESO

Now you know what the Doppler effect is, but what does the ambulance have to do with what we are speaking about here—stars and planets? Well, stars emit light, and because light also has a limited speed (thanks Albert Einstein!), a similar effect will occur. Without entering into too many details, objects emitting light that are moving towards you will appear bluer (or blue-shifted), and objects moving away from you will appear redder (or red-shifted). This Doppler effect is at the origin of the radial-velocity technique used to detect planets. If a star is moving towards you, then away, and continues to do so in a periodic way, this motion is most probably induced by a planet orbiting the star. Another famous example of the use of the Doppler effect in astrophysics is the measurement of the Universe’s expansion. Looking at all the galaxies surrounding us in the Universe, we observe that their light is redder than it should be, therefore all the galaxies in the Universe are moving away from each other; the conclusion being that the Universe is expanding.

I told you that the biggest obstacle to the detection of Earth-twins is the host stars themselves. So let’s come back to this problem. Stars are formed by the contraction of giant molecular clouds, therefore by applying the concept of momentum conservation, you arrive at the conclusion that the stars are rotating around their center, like an ice-skater bringing his arms towards his chest to accelerate his spin. Given that the Sun has a 25 day rotation period and a radius of about 500,000 km, you can do the math and calculate that the rotation velocity of the Sun at its surface is 7,200 km/h. Therefore, looking in detail at the Sun, you will see that the light coming from the approaching limb is bluer than it should be, and the light from the receding limb is redder; do you remember the Doppler effect? So, does this mean that we see half Sun moving forwards and half moving backwards because of the rotation? Yes, it’s exactly what it means, but as the blue and the red shifts are equivalent, the average velocity is zero. This makes sense as the Sun only rotates around its axis, and does not move towards or away from you.

Now, you probably know that the Sun often has dark spots on its surface, so-called sunspots. These sunspots are caused by strong magnetic fields present inside the Sun, that sometimes emerge at the surface. Because they are dark, sunspots can be seen as a mask occulting, or blocking, part of the stellar disc. Therefore, they distort the red- and blue-shift balance; the Sun will appear a little redder (or bluer) and you could mistakenly conclude that it is moving. Considering a large spot on the Sun, that is around 0.1% of the surface area, and a maximum rotational velocity of 7,200 km/h, we arrive at the conclusion that such a sunspot induces a radial velocity effect of 7.2 km/h, which is an order of magnitude larger than the 0.3 km/h required to detect Earth-twins.

Doppler velocity map of the Sun as observed by the MDI instrument on board the SOHO satellite (left image). A black dot was introduced to simulate a sunspot as observed in the solar surface (see  a real sunspot observed by SOHO on the right). The Sun’s rotation produces equivalent blue- and red-shifted hemispheres, but this balance can be broken by a sunspot. On the left image for example, the black dot masks part of the blue shift of the star, so the final flux of the whole star will appear redder than it should be (Credit: SOHO/MDI).

In conclusion, even with an instrument reaching the precision required to detect Earth-twins, perturbing signals induced by stars, such as the effect of sunspots, will significantly complicate their detection. We have been aware of the sunspot problem for nearly 20 years now, and have discovered other stellar effects more recently. Many scientists are trying to understand better these perturbations, and are looking into new techniques to correct for them. I am one of them, and I am convinced that we will manage to solve this critical problem of stellar signals in the coming years.

Dr. Xavier Dumusque.

About the author.

Dr. Xavier Dumusque’s expertise is planet detection taking into account stellar intrinsic signals. Xavier studied Astrophysics at the University of Geneva where he also obtained his PhD in 2012, in collaboration with the University of Porto. After two postdocs at the Harvard-Smithsonian Center for Astrophysics (USA), he came back to the Observatory of Geneva where he is currently working. He is the first author of the Nature article announcing an Earth mass planet orbiting Alpha Centauri B (2012) and of an article presenting the discovery of the Mega-Earth planet orbiting Kepler-10 (2014). Xavier is actively involved in the development of a solar telescope that will help characterize and understand the origin of perturbing signals in the Sun to develop new state-of-the-art techniques to mitigate their impact on the detectability of Earth-twins orbiting other stars. Among the awards he has obtained we highlight the Schläfli Prize for outstanding thesis (Swiss Academy of Science, 2014), the Yale Center for Astronomy and Astrophysics Postdoctoral Prize fellowship (2015), and the Branco Weiss fellowship (2015).

10 thoughts on “How a Star Can Hide its Earths”

    1. Hi Adam,
      Thanks a lot for your comment. I gave 500’000 km to give a rough estimate but indeed it is closer to 700’000. The 7’200 km/h for the rotational velocity is however measured with the correct solar radius.