About this experiment
Most of the thousands of known exoplanets were never seen directly. Astronomers found them by watching stars very carefully and noticing that the light dipped a tiny amount, again and again, as a planet crossed in front. An Earth passing the Sun dims it by less than one part in ten thousand. Choose a star and a planet, add realistic measurement noise, stack several transits, and find out which planets a telescope can detect and what the dip tells you about the planet.
Learning goals
- Explain how a transiting planet causes a periodic dip in the brightness of its star
- Use the transit depth to estimate the radius of the planet
- Relate the time between transits to the orbital period and, with Kepler III, the size of the orbit
- Explain why only a small share of planetary systems are lined up to show transits
- Explain how noise limits detection and why stacking many transits helps
How to use it
- 1Start with Earth and Sun. Read the depth. Increase the noise to 1000 ppm. Can you still see the dip?
- 2Keep the noise at 1000 ppm and increase the number of transits stacked. How many do you need to detect the Earth?
- 3Choose Hot Jupiter. How much deeper is the dip? Why is a hot Jupiter so much easier to find?
- 4Choose Earth-sized, red dwarf. The planet is about as big as Earth. Why is the dip so much deeper than for Earth and Sun?
- 5Increase the impact parameter b from 0 towards 1.3. How do the shape and length of the transit change? When does it disappear?
- 6Compare the radius from the depth with the planet radius you set. Why is it not exactly the same?
The model
Assumptions
- Circular orbits, and the planet mass is ignored in Kepler's third law. The star has quadratic limb darkening: it is dimmer near its edge.
- The blocked light uses the overlap area of the two discs times the brightness of the star under the planet, a good approximation for small planets.
- Measurements are taken every 10 minutes with independent Gaussian noise from a seeded generator. Real data also have slow drifts, star spots and flares.
- A dip counts as detected when its signal-to-noise ratio is 7 or more, close to the threshold used by the Kepler mission.
Try this in class
- Q1A planet blocks 1 % of the light of a Sun-like star. Estimate its radius in Earth radii (the Sun is 109 times as wide as the Earth).
- Q2The same transit repeats every 12.4 days. What else can you work out about the planet?
- Q3Why do most Earth-sized planets found so far orbit small red dwarf stars?
- Q4Only about 0.5 % of Earth-like orbits around Sun-like stars are lined up to show transits. Why does a survey still have to watch so many stars?
- Q5Why does a transit with b close to 1 look V-shaped rather than flat-bottomed?
Frequently asked questions
Why is the dip curved at the bottom?
Stars are brighter in the middle than near the edge, an effect called limb darkening. When the planet is near the centre of the disc it blocks brighter light, so the dip is deepest in the middle of the transit.
Which telescopes find planets this way?
NASA's Kepler and TESS missions found thousands of planets by the transit method, and ESA's PLATO will look for Earth-like planets around Sun-like stars. Bright hot Jupiters can even be detected with good amateur telescopes.
Can a transit tell us the mass of a planet?
No, a transit gives the size. The mass is usually measured separately from the small wobble the planet causes in its star, seen as a Doppler shift in the starlight. Size and mass together give the density, which tells rocky planets from gas giants.