1.6 Detection Methods
1.6.2 Transit Method
A newer method than measuring RVs for detecting exoplanets is to detect dips in intensity of stars over time – these dips being indicators for a planet crossing the face of its host star. As a planet orbits a star, if the observer is positioned in such a way that the orbit is ‘edge-on’ (or almost) then it is possible that the shadow of the planet may be seen as it passes the face of the star. This is seen even within our own Solar System, when Venus and Mercury have transited across the Sun. However, we cannot easily resolve the stellar disc of other stars like we can for the Sun, therefore we do not see the actual shadow of the planet. But by measuring how bright the star appears to be over time, we can detect that brightness dropping due to the planet blocking some of the light. This was first demonstrated byCharbonneau et al.(2000);Henry et al.(2000) for the planet HD 209458b.
By monitoring a star for a significant length of time, there are four parameters which describe the transit (see Figure 1.12): ΔF, the transit depth in units of the intensity; tT, the total duration of the transit; tF, the duration of the flat portion of the transit; and Porb, the orbital period of the planet. Combinations of these and known stellar parameters can provide a great deal of insight into the system (Seager & Mallén-Ornelas 2003), so long as you have at minimum two transits (to accurately derive the orbital period, assuming the eccentricity is zero):
Figure 1.12: Illustration of the transit method, showing the key points of transit (marked 1-4) and definition of key transit parameters. The period of the planet is the time between each transit. As a planet crosses in front of the stellar face, a decrease in stellar brightness occurs. This will appear differently depending on the exact orbital properties of the planet with respect to the observer. This does not include the effects of stellar limb darkening.
ρ∗≡ M∗ R∗3 =
4π2 Porb2 G
1+√
ΔF2
−b2
1−sin2(tTπ/Porb) sin2(tTπ/Porb)
3/2
. (1.10)
Equations1.7to1.10introduce seven new parameters: Rp, the planetary radius;a, the semi-major axis of the planet;b, the impact parameter;i, the orbital inclination (the same as for radial velocities); ρ∗,M∗andR∗, the stellar density, mass and radius respectively. However, Eq. 1.8-1.10 are relatively complex. They can be simplified by making one reasonable assumption (Seager & Mallén-Ornelas 2003) – that for the vast majority of planets, the transit duration will be significantly smaller than the orbital period, tTπ/Porb 1 andtFπ/Porb 1. This then allows sinx ≈ x, and if xis very small it also allows for 1−sinx ≈1. Therefore Eq.1.8-1.10 can be transformed into
b=
1−√ ΔF2
−(tF/tT)2 1+√
ΔF2 1−(tF/tT)2
1/2
, (1.11)
a
R∗ = 2Porb π
ΔF1/4
tT2 −t2F1/2 (1.12)
and
ρ∗= 32
GπPorb ΔF3/4
tT2 −t2F3/2. (1.13) These are significantly simpler, which also aids in analysing data. And as can be seen in Figure 1.12, it is possible to measure the majority of the orbital parameters from transits.
One key measurement which cannot be determined is the planetary mass, which is why it is incredibly common to take targeted “follow-up” RV observations which can determine the mass.
The transit method has been heavily used since the first transiting planet was observed, both with telescopes on the ground and ones sent into space. Large ground-based programs such as the HATNet, the Hungarian Automated Telescope, a network of twelve telescopes (situated in both the northern and southern hemispheres), have discovered dozens of planets, such as HAT-P-11: a super-Neptune around a bright and active K star (Bakos et al. 2010). Similar networks were also deployed: TrES (Trans-Atlantic Exoplanet Survey, Alonso et al. 2004), a network of three 10cm telescopes; OGLE, originally designed for observing gravitational lensing (Udalski et al. 2002), can also detect planets like OGLE-TR-56 (Konacki et al. 2003);
and WASP, the Wide-Angle Search for Planets (Pollacco et al. 2006) consists of two wide-field arrays of eight CCD cameras in both the northern and southern hemispheres and to date have well almost 200 planets to their name. There have also been a handful of single-site surveys such as MEarth (Nutzman & Charbonneau 2008;Irwin et al. 2009), the Siding Spring Observatory WFI (Bayliss et al. 2009) and NGTS, the Next Generation Transit Survey (Wheatley et al.
2013).
Transiting exoplanets have not only been discovered from the ground, but also from space.
The first space-based mission to observe exoplanets was CoRoT (a 0.27m telescope) led by the CNES and other European partners (Auvergne et al. 2009), launched in 2006, and was able to observe individual stars for up to 150 days at a time. During its lifetime, CoRoT found almost 30 planets before suffering a fatal computer failure in 2012. Another space mission was Kepler(Borucki et al. 2010;Koch et al. 2010) – to date it is the mission that has discovered the largest number of exoplanets (over 2000!). Launched in March 2009, it began observations a coupe of months later and continued to observe a small patch of sky continuously for 4 years.
However, during 2012 and 2013, two reaction wheels (in charge of controlling the stability of the telescope) failed, thereby stopping scientific operations. November 2013,Keplerwas given a second chance – namedK2– by balancing the remaining two reaction wheels with the solar
radiation pressure, though performing at a lower precision, it would be possible to observe transits for up to 80 days at a time (Howell et al. 2014).
1.6.2.1 Transit Timing Variations
Whilst planets typically orbit in their given period quite happily, if there is another body (or more), then the gravitational effect of that body (or bodies) can apply a small ‘tug’ to the observed planet. This will cause the time at which the transit should occur (using the centre of the transit as the reference point) to alter slightly (Miralda-Escudé 2002;Agol et al. 2005;
Holman & Murray 2005). These transit-timing variations are known as TTVs. This effect becomes significantly more sensitive if the planets are in resonant orbits (i.e. the periods are integer or fraction multiples of one another). Commonly these will be confirmed similarly to standard transiting planets, by taking radial velocity measurements.
A system which experiences TTVs was Kepler-9 (Holman et al. 2010). Kepler-9b and c are two giant-planets which had TTVs of∼ 4 and∼39 minutes respectively, thereby their orbits are roughly in a 2:1 resonant orbit.
One of the first planet discoveries from TTVs was Kepler-19c – a system with a planet in a 9.3-day orbit which exhibited TTVs of five minutes. Ballard et al.(2011) demonstrated that the likelihood that this has an astrophysical cause is very unlikely, and showed with radial velocity measurements that the mass is of a planetary nature (it was then further characterised byMalavolta et al. 2017).
1.6.2.2 Stellar Activity Effects on Photometry
As for RVs, there are important stellar activity effects to acknowledge when planet hunting with light curves; these are a mix of short-term and long term variations, as well as uncertainties induced by lack of knowledge. Short-term variations are primarily from the stellar granulation and flicker. For the granulation, hydrodynamical models can be used to predict likely jitter observed (Svensson & Ludwig 2005;Ludwig 2006; Cegla et al. 2013;Norris et al. 2017).
Flicker, photometric variability during an 8-hour scale, is a valuable stellar diagnostic and attributed to the stellar granulation (Bastien et al. 2013;Cranmer et al. 2014). It is directly correlated to the stellar surface gravity (Bastien et al. 2013) which is an advantageous stellar parameter to know for understand any star-planet system. This is, however, a continuous jitter term and therefore only introduces a uniform uncertainty.
The effect of starspots is considerable – they vary the brightness of the star which is needed to accurately determine sizes of the planets observed, as well as the transit duration. The planetary radius, measured from the change in brightness as it transits the star, is influenced
by how spotted the surface of the star is (Czesla et al. 2009;Carter et al. 2011; Walkowicz et al. 2013;Oshagh et al. 2016). In fact, using simulations,Oshagh et al.(2013b) determined that any unaccounted spots can lead to underestimating the size of the planet by up to 4%; and potentially introduce an error of ∼4% in the transit duration and as much as 200s variation in the transit time (so after only a few transits, the time of transit may have an error as high as quarter-of-an-hour!). Additionally, due to changes in the the level of magnetic activity, the photometric radius of the star will change and this further induces more uncertainty in the transit duration (Loeb 2009;Cegla et al. 2012).
As well as having an effect on the overall brightness, which in turn affects the planet, spots can physically alter the observed transit shape. There have been cases where it was clear to see a spot being eclipsed by a planet as it eclipses the star. One of the most famous cases is HAT-P-11 which shows these spot-crossings in multiple transits (Southworth 2011). Because of so many crossings over a long baseline, as well as discovering and learning about the planet, a lot has been learnt about the spots as well; to the extent that we know HAT-P-11 exhibits similar preferential latitudes for spot formation as the Sun, and with similar spot sizes and distributions to the Sun, HAT-P-11 likely has a solar-like dynamo (Sanchis-Ojeda & Winn 2011;Morris et al. 2017).
1.6.3 Other Methods