The mass loss rate of planetary atmosphere is an important physical quantity to characterize the atmospheric escape. YAN Dongdong and GUO Jianheng from Yunnan Observatories of the Chinese Academy of Sciences recently published their new finding about the exoplanets’ mass loss rates and the modified energy-limited equation in The Astrophysical Journal.

The planet receives intense X-ray and extreme ultraviolet (XUV) radiation from its host star, and its atmosphere can be heated and expand to overcome the planetary gravitational potential and escape with continued mass loss.

The mass loss of escaping particles per unit of time is called the mass loss rates. The energy-limited equation is a convenient way to estimate the mass loss rates, indicating that the mass loss rate is proportional to the ratio of the XUV radiation flux received by the planet to the planet mean density.

In this study, the researchers investigated nearly 450 exoplanet systems using a one-dimensional hydrodynamics model of atmospheric escape, and obtained the hydrodynamic mass loss rate, heating efficiency and XUV absorption radius. On this basis, they compared the energy-limited mass loss rate with the hydrodynamic ones.

They found that when the planet receives a higher XUV radiation flux (Fxuv) than a certain value, the energy-limited equation estimates a higher mass loss rate than the hydrodynamic model.

After considering the change of kinetic energy and thermal energy of the escaping particles in the energy-limited equation (modified energy-limited equation), the mass loss rate of the energy-limited equation is basically consistent with hydrodynamic results. This is because as the product of the planetary gravitational potential and Fxuv increases, the sum of the changes in the kinetic energy and thermal energy of the particles will gradually increase to be comparable to the changes in the potential energy of the planet.

Besides, the researchers gave the applicability of the energy-limited equation and proposed that the energy-limited equation should be modified when the XUV radiation flux is higher than a certain value. It is essential to accurately estimate the mass loss rate of planets in order to study the formation and evolution of planets and the combination of large samples.