How we find planets around other stars

The first planet caught crossing its star was never seen. What was measured was a star that got very slightly dimmer for several hours, twice, a week apart. Everything we know about that planet's size comes from how much light went missing.

What is being claimed

When a planet passes between us and its star, it blocks a small patch of the star's glowing disk. This passage is called a transit. The star's measured brightness drops, stays low while the planet is in front, and recovers when the planet moves off. The fraction of light lost is the transit depth, and for a planet that crosses fully inside the disk it depends mainly on one thing: how big the planet's disk is compared with the star's.

Why it is worth knowing

Before these results, the close-in giant planets of nearby stars were known through one method only: the wobble each planet gives its star, measured as a shifting speed along our line of sight (the radial velocity). That method gives the orbit and a lower limit on the mass, but it says nothing about the planet's size. A transit supplies the size. Put the two together and you can work out what the planet is made of, at least roughly: a dense rock or a puffed-up ball of gas.

A shadow measured by area

The blocked light is the planet's disk area divided by the star's disk area. Areas go as the square of the radius, so if k is the planet's radius divided by the star's, the depth is about k². Joshua Winn's review of transits gives exactly this and adds the catch: the light curve “reveals the planet-to-star radius ratio” but “not the planetary radius, and says nothing about the planetary mass.”

The square matters twice. A planet twice as wide makes a dip four times deeper. Put the same planet in front of a star of double the radius and the dip shrinks to a quarter. A dip does not tell you how big the planet is until someone tells you how big the star is. Winn puts the scale plainly: the loss of light is only 1% for a Jupiter-sized planet crossing a Sun-like star, and 0.01% for an Earth-sized one.

The first one: HD 209458 b

The star HD 209458 was already known, from its wobble, to have a giant planet on a 3.52447-day orbit. David Charbonneau, Timothy Brown, David Latham and Michel Mayor used that orbit to predict when a transit could happen and watched the star with a camera designed to search for transits. On 9 and 16 September 1999 it dimmed, on schedule. Another team, Henry and colleagues, reported catching part of a transit of the same star at about the same time.

Fitting the shape of the dip, and assuming the star is 1.1 times the Sun's radius and mass, they found a planet 1.27 times Jupiter's radius on an orbit inclined at 87.1°, within 3° of exactly edge-on, 0.0467 astronomical units from its star. The paper does not print a depth. Our arithmetic from its own numbers: k is about 0.116, so the depth is about 1.35%, in line with Winn's 1%. The paper also shows why the star matters: a larger assumed star needs a larger planet to fit the same data, and the star's radius is their largest modelling uncertainty.

Most planets never transit

A transit needs the orbit to be seen nearly edge-on, so that the planet's path runs across the star's disk. Winn gives the chance for a randomly tilted orbit as the star's radius divided by the orbit's radius, about 0.005 times the star's radius in solar radii, divided by the orbit's radius in astronomical units. For the Earth and the Sun that is about 0.5%. For HD 209458 b, the exact ratio of 1.1 solar radii to 0.0467 AU is about 11% (our arithmetic), close to Charbonneau's rough 10% for such a tight orbit. So a star that shows no transit may still have planets; we are simply seeing their orbits from the wrong angle.

Size plus wobble gives substance

Because the transit fixes the tilt of the orbit, the wobble, together with the star's assumed mass, now gives the true mass rather than a lower limit: 0.63 Jupiter masses. With both mass and radius the authors could calculate an average density of about 0.38 grams per cubic centimetre, which they note is well below Saturn's, the least dense of the Sun's gas giants. The planet is a gas giant.

In short

A transit is not a picture of a planet. It is a star's light dipping by the fraction of its disk the planet covers, the square of the planet-to-star radius ratio. Turning that ratio into a size needs the star's radius, and seeing the dip at all needs an orbit lined up almost edge-on to us.