But current techniques for estimating exoplanetary mass are limited. Radial velocity is the main method scientists use — tiny wobbles in a star’s orbit as it is tugged around by the planet’s gravitational force from which scientists can derive the planet-to-star mass ratio. For large Neptune-sized planets or smaller Earth-sized planets orbiting very bright stars, radial velocity works relatively well. But the technique is less successful with smaller planets that orbit much farther from their stars, as Earth does.

Now, scientists at the Massachusetts Institute of Technology (MIT) have developed a new technique for determining the mass of exoplanets using only their transmission spectra — dips in light as a planet passes in front of its star. This data has traditionally been used to determine a planet’s size and atmospheric properties, but the MIT team has found a way to interpret it such that it also reveals the planet’s mass.

“With this method, we realized the planetary mass — a key parameter that, if missing, could have prevented us from assessing the habitability of the first potentially habitable Earth-sized planet in the next decade — will actually be accessible, together with its atmospheric properties,” said Julien de Wit from MIT.

Estimating Mass from Light

In addition to a planet’s composition, its mass can provide a glimpse of the planet’s surface and internal activity, such as any plate tectonics, its internal cooling and convection, how it generates magnetic fields, and whether gas escapes from its atmosphere.

“The mass affects everything on a planetary level,” de Wit said. “If you don’t get it, there is a large part of the planet’s properties that remains undetermined.”

Using space-based and large ground-based telescopes, scientists have been able to analyze the transmission spectra of newly discovered exoplanets. A transmission spectrum is generated as a planet passes in front of its star, letting some light through its atmosphere. By analyzing the wavelengths of light that pass through, scientists can determine a planet’s atmospheric properties, such as its temperature and the density of atmospheric molecules. From the total amount of light blocked, they can calculate a planet’s size.

To determine the mass of an exoplanet using transmission spectroscopy, de Wit relied on the effect that a planet’s mass has on its atmosphere, as transmission spectra give information on a planet’s atmospheric properties. To do that, he worked from a standard equation describing the effect of a planet’s temperature, gravitational force, and atmospheric density on its atmospheric pressure profile — the extent to which pressure changes throughout its atmosphere.

According to this equation, knowing any three of these parameters would reveal the fourth parameter. As a planet’s mass can be derived from its gravitational force, de Wit reasoned that a planet’s mass could be derived from its atmospheric temperature, pressure profile, and density — parameters that, in principle, may be obtained from a transmission spectrum.

But to get an accurate measurement of a planet’s mass, de Wit had to prove that these three parameters could be obtained independently of each other, solely from a transmission spectrum.

Unlocking a Planet’s Mass

To prove that a planet’s temperature, pressure profile, and atmospheric density may be derived independently from a transmission spectrum, de Wit had to demonstrate that each parameter has a distinctive effect on a transmission spectrum. De Wit performed new analytical derivations from the first principles of radiative transfer and found that an 18th-century mathematical constant called the Euler-Mascheroni constant helps reveal the individual effects of each parameter. In other words, this constant acted as an “encryption key” to decode the process by which the properties of a planet’s atmosphere are embedded in its transmission spectrum.

“It really helps you unlock everything and reveal, out of these crazy equations, which atmospheric properties do what and how,” de Wit said. “You find this constant in a lot of physical problems, and it’s fun to see it reappearing in planetary science.”

To test the method, de Wit applied the technique to a recently discovered exoplanet known as HD189733b that is located 63 light-years away. From his calculations, de Wit came up with the same mass measurement as obtained by others using radial velocity.

Using the specifications of future high-resolution space telescopes, such as the James Webb Space Telescope — an instrument designed to observe exoplanetary atmospheres — the authors showed that the new technique will be able to characterize the mass and atmospheric properties of smaller Earth-sized planets.