Question

Compare and contrast the four-planet detection techniques described during lectures. Use labelled diagrams and equations relevant to each technique to illustrate and support your statements. The methods are: Transit detection, Radial velocity method, direct imaging and microlensing

Answer 1

Transit detection : While the radial velocity method provides information about a planet's mass, the photometric method can determine the planet's radius. If a planet crosses (transits) in front of its parent star's disk, then the observed visual brightness of the star drops by a small amount, depending on the relative sizes of the star and the planet.

This method has two major disadvantages. First, planetary transits are observable only when the planet's orbit happens to be perfectly aligned from the astronomers' vantage point. The probability of a planetary orbital plane being directly on the line-of-sight to a star is the ratio of the diameter of the star to the diameter of the orbit (in small stars, the radius of the planet is also an important factor). About 10% of planets with small orbits have such an alignment, and the fraction decreases for planets with larger orbits. For a planet orbiting a Sun-sized star at 1 AU, the probability of a random alignment producing a transit is 0.47%. Therefore, the method cannot guarantee that any particular star is not a host to planets. However, by scanning large areas of the sky containing thousands or even hundreds of thousands of stars at once, transit surveys can find more extrasolar planets than the radial-velocity method.

The second disadvantage of this method is a high rate of false detections. A 2012 study found that the rate of false positives for transits observed by the Kepler mission could be as high as 40% in single-planet systems.

An example is in order:

Radial Velocity Method: A star with a planet will move in its own small orbit in response to the planet's gravity. This leads to variations in the speed with which the star moves toward or away from Earth, i.e. the variations are in the radial velocity of the star with respect to Earth. The radial velocity can be deduced from the displacement in the parent star's spectral lines due to the Doppler effect. The radial-velocity method measures these variations in order to confirm the presence of the planet using the binary mass function.

Planets with orbits highly inclined to the line of sight from Earth produce smaller visible wobbles, and are thus more difficult to detect. One of the advantages of the radial velocity method is that eccentricity of the planet's orbit can be measured directly. One of the main disadvantages of the radial-velocity method is that it can only estimate a planet's minimum mass

The posterior distribution of the inclination angle i depends on the true mass distribution of the planets.^[3] However, when there are multiple planets in the system that orbit relatively close to each other and have sufficient mass, orbital stability analysis allows one to constrain the maximum mass of these planets. The radial-velocity method can be used to confirm findings made by the transit method. When both methods are used in combination, then the planet's true mass can be estimated.

Although radial velocity of the star only gives a planet's minimum mass, if the planet's spectral lines can be distinguished from the star's spectral lines then the radial velocity of the planet itself can be found, and this gives the inclination of the planet's orbit. This enables measurement of the planet's actual mass. This also rules out false positives, and also provides data about the composition of the planet. The main issue is that such detection is possible only if the planet orbits around a relatively bright star and if the planet reflects or emits a lot of light.

An example would look like:

Direct Imaging: Direct imaging can give only loose constraints of the planet's mass, which is derived from the age of the star and the temperature of the planet. Mass can vary considerably, as planets can form several million years after the star has formed. The cooler the planet is, the less the planet's mass needs to be. In some cases it is possible to give reasonable constraints to the radius of a planet based on planet's temperature, its apparent brightness, and its distance from Earth. The spectra emitted from planets do not have to be separated from the star, which eases determining the chemical composition of planets.

Planetary-mass objects not gravitationally bound to a star are found through direct imaging as well.

For example:

Microlensing: Microlensing occurs when the gravitational field of a star acts like a lens, magnifying the light of a distant background star. This effect occurs only when the two stars are almost exactly aligned. Lensing events are brief, lasting for weeks or days, as the two stars and Earth are all moving relative to each other. More than a thousand such events have been observed over the past ten years.

If the foreground lensing star has a planet, then that planet's own gravitational field can make a detectable contribution to the lensing effect. Since that requires a highly improbable alignment, a very large number of distant stars must be continuously monitored in order to detect planetary microlensing contributions at a reasonable rate. This method is most fruitful for planets between Earth and the center of the galaxy, as the galactic center provides a large number of background stars.

Unlike most other methods, which have detection bias towards planets with small (or for resolved imaging, large) orbits, the microlensing method is most sensitive to detecting planets around 1-10 astronomical units away from Sun-like stars.

A notable disadvantage of the method is that the lensing cannot be repeated, because the chance alignment never occurs again. Also, the detected planets will tend to be several kiloparsecs away, so follow-up observations with other methods are usually impossible. In addition, the only physical characteristic that can be determined by microlensing is the mass of the planet, within loose constraints. Orbital properties also tend to be unclear, as the only orbital characteristic that can be directly determined is its current semi-major axis from the parent star, which can be misleading if the planet follows an eccentric orbit. When the planet is far away from its star, it spends only a tiny portion of its orbit in a state where it is detectable with this method, so the orbital period of the planet cannot be easily determined. It is also easier to detect planets around low-mass stars, as the gravitational microlensing effect increases with the planet-to-star mass ratio.

The main advantages of the gravitational microlensing method are that it can detect low-mass planets; it can detect planets in wide orbits comparable to Saturn and Uranus, which have orbital periods too long for the radial velocity or transit methods; and it can detect planets around very distant stars. When enough background stars can be observed with enough accuracy, then the method should eventually reveal how common Earth-like planets are in the galaxy.

This is what an example curve would look like: