Angular momentum of stars and their planets

Abstract

To understand the distribution of angular momenta between host stars and their planets, we estimate the spin angular momentum (J spin ) of host stars that follow a power law ${10}^{(42.33\pm 5.40)}{\left(\tfrac{{M}_{\star }}{{M}_{\odot }}\right)}^{(4.18\pm 0.53)}$ with stellar mass $\left(\tfrac{{M}_{\star }}{{M}_{\odot }}\right)$. Similarly, the orbital angular momenta (L p ) of exoplanets are estimated, and the best fit yields a power law, ${10}^{(42.66\pm 1.79)}{\left(\tfrac{{M}_{p}}{{M}_{J}}\right)}^{(1.26\pm 0.05)}$, with the exoplanetary mass $\left(\tfrac{{M}_{p}}{{M}_{J}}\right)$. Furthermore, the total (spin and orbital) angular momentum J tot of the stellar planetary system is computed, and a power law of the form J tot = ${10}^{(43.11\pm 6.82)}{\left(\tfrac{{M}_{p}}{{M}_{J}}\right)}^{(0.94\pm 0.14)}$ is obtained. In addition, an analysis between specific angular momenta (I p ) of planets and planetary masses reveals that specific angular momentum is nonlinearly related with planetary mass in case of multiplanetary systems and is independent of planetary mass in case of single-planetary systems. We find that the probability of detecting Earth-like planets is more likely for host stars that have total angular momentum ≤1041 kg m2 s−1. Finally, a power-law relationship is obtained between exoplanetary masses and their orbital distances in case of multiplanetary systems and, is independent in case of single-planetary systems.