Mathematical Model to Accurately Gauge Temperatures of Exoplanets

Astronomers from Cornell University observed a peculiar pattern in scientific articles—describing exoplanets as cooler than predicted. They have optimized a mathematical model to precisely estimate the temperatures of planets in distant solar systems.

Atmospheric gases recede from a “hot Jupiter,” which is a Jupiter-size, egg-shaped planet that orbits close to its own sun, in this artistic rendering. Cornell astronomers have developed a new mathematical model for determining temperatures on different parts of exoplanets, rather than averaging a planet’s temperature. Image Credit: Matthew Fondeur/Cornell University.

With the new model, researchers can collect data on the molecular chemistry of an exoplanet and understand the planetary start of the cosmos, reports a study published in Astrophysical Journal Letters on April 23rd, 2020.

Nikole Lewis, assistant professor of astronomy and the deputy director of the Carl Sagan Institute (CSI), had observed that in the last five years, scientific articles detailed exoplanets as much cooler than estimated by theoretical models.

It seemed to be a trend—a new phenomenon. The exoplanets were consistently colder than scientists would expect.

Nikole Lewis, Assistant Professor of Astronomy and Deputy Director, Carl Sagan Institute

Until now, astronomers have identified over 4,100 exoplanets. “Hot Jupiters” are among these exoplanets and a common form of gaseous giant that always orbits nearer to its host star. The overwhelming gravity of the star make the hot Jupiters to always have one side facing their star, a condition called “tidal locking.”

Thus, as one side of the hot Jupiter is extremely hot, its far side has considerably cooler temperatures. The tidally locked exoplanet’s hot side actually bulges similar to a balloon, making it look like an egg.

Viewing from tens to hundreds of light-years, astronomers have conventionally observed the temperature of the exoplanet as homogenous—by averaging the temperature—making it appear considerably colder than proposed by physics.

However, temperatures on exoplanets—specifically hot Jupiters—can differ by thousands of degrees, stated Ryan MacDonald, lead author of the study who is a researcher at CSI. MacDonald added, wide-ranging temperatures can lead to radically distinct chemistry on alternating sides of the planets.

Lewis, MacDonald, and research associate Jayesh Goyal explored scientific articles on exoplanet and solved the puzzle of apparently cooler temperatures—astronomers’ math was incorrect.

When you treat a planet in only one dimension, you see a planet’s properties—such as temperature—incorrectly. You end up with biases. We knew the 1,000-degree differences were not correct, but we didn’t have a better tool. Now, we do.

Nikole Lewis, Assistant Professor of Astronomy and Deputy Director, Carl Sagan Institute

At present, astronomers can confidently increase the size of the exoplanets’ molecules.

We won’t be able to travel to these exoplanets any time in the next few centuries, so scientists must rely on models,” stated MacDonald, elucidating that when the latest generation of space telescopes are launched in 2021, the exoplanet dataset details will have improved such that researchers can investigate the predictions of these three-dimensional models.

We thought we would have to wait for the new space telescopes to launch, but our new models suggest the data we already have—from the Hubble Space Telescope—can already provide valuable clues.

Ryan MacDonald, Study Lead Author and Researcher, Carl Sagan Institute

Astronomers can use updated models that include current exoplanet data to find out the temperatures on all sides of an exoplanet, as well as better understand the chemical composition of the planet.

When these next-generation space telescopes go up, it will be fascinating to know what these planets are really like,” MacDonald added.

This study was funded by Cornell University.


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