The Total Solar Irradiance variability in the Evolutionary Timescale and its Impact on the Mean Earth's Surface Temperature

TL;DR

This study models the long-term evolution of solar irradiance and its impact on Earth's surface temperature, predicting significant temperature increases and Earth's potential transformation into a liquid planet as the Sun ages.

Contribution

We developed a mass-loss dependent analytical model of TSI evolution over 8.23 Gyrs and assessed its impact on Earth's mean surface temperature using a zero-dimensional energy balance model.

Findings

TSI increases by 10% in 1.42 Gyrs, 40% in 3.4 Gyrs, and 120% in 5.229 Gyrs.

Earth's surface temperature rises to about 299 K in 3.4 Gyrs and peaks at 2319.2 K as the Sun becomes a red giant.

Earth may become a liquid planet due to extreme surface temperatures in the distant future.

Abstract

The Sun is the primary source of energy for the Earth. The small changes in total solar irradiance (TSI) can affect our climate in the longer timescale. In the evolutionary timescale, the TSI varies by a large amount and hence its influence on the Earth's mean surface temperature (T$_{s}$) also increases significantly. We develop a mass-loss dependent analytical model of TSI in the evolutionary timescale and evaluated its influence on the T$_{s}$. We determined the numerical solution of TSI for the next 8.23 Gyrs to be used as an input to evaluate the T$_{s}$ which formulated based on a zero-dimensional energy balance model. We used the present-day albedo and bulk atmospheric emissivity of the Earth and Mars as initial and final boundary conditions, respectively. We found that the TSI increases by 10\% in 1.42 Gyr, by 40\% in about 3.4 Gyrs, and by 120\% in about 5.229 Gyrs from now, while the T$_{s}$ shows an insignificant change in 1.644 Gyrs and increases to 298.86 K in about 3.4 Gyrs. The T$_{s}$ attains the peak value of 2319.2 K as the Sun evolves to the red giant and emits the enormous TSI of 7.93$\times10^{6} Wm^{-2}$ in 7.676 Gys. At this temperature Earth likely evolves to be a liquid planet. In our finding, the absorbed and emitted flux equally increases and approaches the surface flux in the main sequence, and they are nearly equal beyond the main sequence, while the flux absorbed by the cloud shows opposite trend.