# Celestial I-spy: exoplanets

During the course of researching things for my recent blog post on Galileo’s Starry Messenger I stumbled across the exoplanet.eu catalog of exoplanets (ie planets outside of our solar system). I thought it would be interesting to take a look at some of the data. Things have progressed in the 11 and a bit years since I first learnt about exoplanets as part of an introductory astronomy course I took in my first semester at university.

Starting with the basics, below is a histogram of the number of confirmed discoveries by year (bars) and a cumulative total (line) up to the end of 2014. 43% of all confirmed exoplanets were discovered (or at least publicly announced) last year!

Two of the most interesting (and obvious) properties we can find out about an exoplanet are its mass and the distance at which it orbits its star. Since planets have elliptical orbits we should technically refer here to the semi-major axis but for simplicity I will use the term “orbital radius”. If we look only at exoplanets with known (or estimated) mass and orbital radius (click/tap on the histogram above to toggle) we see much less data for 2014. This is something of an artefact – the year of discovery refers to the first discovery, but the mass and orbital data refers to the current knowledge. For example, the first exoplanet was discovered in 1989 (and is marked as such) but not confirmed until 2003. The latest data for that planet in the database dates from August 2014. Most of the exoplanets from 2014 currently lack mass estimates. I would expect this to change with time.

So what do we know? The chart below plots the orbital radius data using a (base-10) logarithmic scale in Astronomical Units (AU) – 1 AU is the mean distance the Earth is from the Sun – against year of planet discovery. Using a logarithmic y axis makes it easier to see the wide spread in data. Since the log of 1 is 0, a y value of 0 means the orbital radius of an exoplanet is the same as that of Earth. A value of 1 means it is ten times that of Earth, 2 means 100 times that of Earth and so on. -1 means it orbits its “parent” star at a tenth of the distance the Earth does from the Sun. The majority of exoplanets discovered to date have an orbital radius less than that of Earth.

Click or tap the image above and it switches to the (more limited) mass data. Again we’re using a logarithmic scale on the vertical axis, this time the exoplanet mass in units of Earth masses. The picture is even clearer here – nearly all exoplanets discovered to date (with known masses) have masses greater than that of Earth. It isn’t entirely clear (to me at least) these should all be classified as planets. Typically, objects in excess of about 13 Jupiter masses come under the banner “brown dwarf“. This translates to a value of ~3.6 on the vertical scale. For simplicity I’ll stick to using the term exoplanet for all the objects.

So the Earth is an unusually small planet that’s further from its star than average? Selection effects mean it’s not that simple. To understand that we need to look at how exoplanets are discovered. This excellent lecture by Professor Ian Morison (who ran my course back in 2003) gives a great overview and is, I think, well worth an hour of your time (you may have to download it for it to work properly). However, I’ll try to provide quick explanations for the 7 methods that feature in the chart below. In the interest of brevity and because I’m not an expert I am avoiding any great detail or precision – these are just meant as rough descriptions:

#### Astrometry

Astrometry is literally the precise measurement of the positions and motions of stars. The gravitational pull of an exoplanet orbiting a star will cause slight deviations (a “wobble”) in the path of a star across a sky. Hence precise measurements of a stars position over time can provide evidence of the existence of an exoplanet orbiting the star.

#### Imaging

This is simply direct observation of the light reflected (and emitted) by an exoplanet. This is easier to do (though still very difficult) at infrared wavelengths because the ratio of light emitted by the star compared to light reflected and emitted by the planet is smaller.

#### Microlensing

One of the key predictions (and one of the first to be confirmed) of Einstein’s general theory of relativity was that mass bends light. This means that large masses can act like lenses, bending more light from a distant star towards an observer than they would otherwise normally see. As a star moves across the sky in front of a more distant star, lensing can lead to an increase in the brightness of the more distant star, possibly for a period of months. A planet transiting the lensing star can also have a small effect, temporarily (over the course of perhaps hours) boosting the degree of lensing. (I found this diagram quite helpful in understanding this.) The size and duration of such a microlensing event give astronomers details about the exoplanet causing the effect.

#### Primary Transit

An exoplanet transiting its parent star will lead to a drop in the amount of light from the star reaching Earth. This drop is used to infer the existence and properties of the planet.

#### Pulsar Timing

Pulsars are rapidly rotating neutron stars that emit long-wave electromagnetic radiation. Because of this they can be used as extremely precise clocks. The small gravitational pull of a planet orbiting a neutron star leads to the star undergoing a small orbit of its own around the systems centre of mass or “barycentre“. This in turn leads to small deviations in the timings of pulsar signals. By measuring these deviations or irregularities, astronomers can detect planets with masses less than tenth that of the Earth.

This method also relies on the fact that a star with a planet will orbit the barycentre of the system. In this case astronomers use the periodic Doppler shift of characteristic spectral lines of the star as it moves towards and away from the Earth to calculate the properties of the perturbing exoplanet.

#### TTV

Transit-timing variation or TTV is a method for detecting additional planets in a solar system once one can be detected through the primary transit method. In a single-planet solar system the transits of the star by the planet (as viewed from Earth) will be regularly spaced in time. However, a secondary planet will lead to small perturbations in this periodicity that can (at least in principle) be measured to determine properties of the perturbing secondary planet.

Despite the roughness and brevity of these explanations, I hope it is relatively obvious that most of these methods are biased towards detecting larger planets. For example, gravitational perturbations to the motion of a star (relevant to astrometry and the radial velocity method) are larger when the planet is larger (all else being equal). Similarly, a large (at least in radius) planet transiting its star will lead to a greater dip in light reaching us from the star than a smaller planet.

The chart below combines the mass and orbital radius data (up to mid-March 2015 and where both are known) with the method of first discovery. The most succesful methods to date (in terms of number of planets found) are clearly the primary transit and radial velocity methods. The pulsar timing method holds the record (by orders of magnitude) for the smallest exoplanet detected. Direct imaging is the one method where a large orbital radius is beneficial (since it means the light from the exoplanet won’t be swamped out).

As is, the chart above doesn’t tell the whole story. It was noted above that the rate of exoplanet detection has increased with time. The relative importance of different methods has also changed as technology has moved forwards and new satellites launched. Click on the chart to see an animation of discoveries from 1988 up to 2015.

Aside from a trio of planets discovered through pulsar timing in 1992, exoplanet discovery was almost entirely through the radial velocity method up until around 2003. Since then, and especially since about 2006, the primary transit method has started to play a bigger and bigger role, helped in part by the launch of the Kepler satellite in 2009. To date only two exoplanets have been detected through astrometry and three through TTV (two of these were last year). In terms of the hunt for Earth-like planets though, microlensing seems the most promising.