Higher-order generalized uncertainty principle corrections to the Jeans mass

TL;DR

This paper explores how higher-order generalized uncertainty principle corrections influence the Jeans mass, potentially explaining star formation in smaller Bok globules by lowering the critical mass needed for collapse.

Contribution

It introduces a modified Jeans mass considering higher-order GUP effects and estimates the GUP parameter using observational data.

Findings

Higher-order GUP significantly affects gravitational potential and energy.

Modified Jeans mass is lower, facilitating star formation in small globules.

Estimated GUP parameter range is between 10^{11} and 10^{12}.

Abstract

The Jeans instability is regarded as an important tool for analyzing the dynamics of a self-gravitating system. However, this theory is challenging since astronomical observation data show some Bok globules, whose masses are less than the Jeans mass and still have stars or at least undergo the star formation process. To explain this problem, we investigate the effects of the higher-order generalized uncertainty principle on the Jeans mass of the collapsing molecular cloud. The results in this paper show that the higher order generalized uncertainty principle has a very significant effect on the canonical energy and gravitational potential of idea gas, and finally leads to a modified Jeans mass lower than the original case, which is conducive to the generation of stars in small mass Bok globules. Furthermore, we estimate the new generalized uncertainty principle parameter $\gamma _0$ by applying various data of Bok globules, and find that the range of magnitude of $\gamma _0$ is ${10^{11}} \sim {10^{12}}$.