Measuring the Density of Exoplanets: Transit Photometry and Radial Velocity Methods

Astronomers use sophisticated methods to measure the density of exoplanets, two of which are vital: transit photometry and radial velocity measurements. This article will discuss the process in detail and highlight the importance of these methods in understanding the composition and structure of distant planets.

Transit Photometry

The first method, transit photometry, involves detecting transits, which occur when an exoplanet passes in front of its host star. This event causes a temporary dimming of the star's brightness. By studying these transits, astronomers can deduce the size of the exoplanet.

Detection of Transits and Calculating Radius

The amount of dimming during a transit is used to estimate the planet's radius. The calculation is based on the following formula:

Rp Rstar × sqrt{frac{Delta F}{Fstar}}

where Rstar is the radius of the star, Delta F is the change in flux, and Fstar is the original flux.

Radial Velocity Method

The second key method, radial velocity measurements, involves measuring the radial velocity of the host star. As an exoplanet orbits, it exerts a gravitational pull on its host star, causing it to move slightly. This movement can be detected as a shift in the star's spectral lines, known as the Doppler effect.

Measuring Mass and Calculating Mass

The amplitude of this shift provides the minimum mass of the planet. The mass can be estimated using the formula:

Mp sin i K left(frac{P}{2pi G}right)1/3

where K is the semi-amplitude of the radial velocity curve, P is the orbital period, and G is the gravitational constant. The inclination i is often assumed to be 90 degrees for a circular orbit.

Calculating Density

Once the radius and mass of the exoplanet are determined, the density can be calculated using the formula:

Density frac{Mp}{left(frac{4}{3} pi Rp3right)}

where Mp is the mass of the planet and Rp is its radius.

Combining Methods for Effective Density Measurement

By combining the measurements of the radius from transit observations and the mass from radial velocity data, astronomers can effectively calculate the density of exoplanets. This information is critical for understanding the composition and structure of these distant worlds.

The Role of the Kepler Mission

The Kepler mission and its extension, K2, have discovered thousands of exoplanets using the transit technique. This method measures the dip in light intensity whenever an orbiting planet moves across the face of its host star as viewed from Earth. Transits not only measure the orbital period but also often determine the size of the exoplanet from the detailed depth and shape of its transit curve and the host star's properties.

However, the transit method does not measure the mass of the planet, while the radial velocity method allows for the measurement of its mass. Knowing a planet's radius and mass enables the determination of its average density and, consequently, its potential composition.

Testing the Reliability of the Transit-Timing Variation Method

About fifteen years ago, astronomers from the Center for Astrophysics (CfA) and others discovered that in multiple planetary systems, the periodic gravitational tug of one planet on another alters their orbital parameters. Although the transit method cannot directly measure exoplanet masses, it can detect these orbital variations, which can be modeled to infer masses. The Kepler mission has identified hundreds of exoplanet systems with transit-timing variations, and dozens have been successfully modeled.

Surprisingly, this procedure seemed to find a prevalence of exoplanets with very low densities. For example, the Kepler-9 system appears to have two planets with densities of 0.42 and 0.31 grams per cubic centimeter, respectively. In comparison, the density of rocky Earth is 5.51 grams per cubic centimeter, while water is 1.0 grams per cubic centimeter and the gas giant Saturn is 0.69 grams per cubic centimeter. These results cast doubt on the reliability of the transit-timing variation methodology and created a long-standing concern.

CfA astronomers, including David Charbonneau, David Latham, Mercedes Lopez-Morales, and David Phillips, tested the reliability of the method by measuring the densities of the Kepler-9 planets using the radial velocity method. They used the HARPS-N spectrometer on the Telescopio Nazionale Galileo in La Palma. Their results confirmed the very low densities obtained by the transit-timing method and verified the power of the transit-variation method.