Mass derivation of planets K2-21b and K2-21c from transit timing variations

While various indirect methods are used to detect exoplanets, one of the most effective and accurate methods is the transit method, which measures the brightness of a given star for periodic dips when an exoplanet is passing in front of the parent star. For systems with multiple transiting planets, the gravitational perturbations between planets affect their transit times. The difference in transit times allows a measurement of the planet masses and orbital eccentricities. These parameters help speculating on the formation, evolution, and stability of the system. Using transit timing variations (TTVs), we measure the masses and eccentricities of two planets orbiting K2-21, a relatively bright K7 dwarf star. These two planets exhibit measurable TTVs, have orbital periods of about 9.32 and 15.50 d, respectively, and a period ratio of about 1.66, which is relatively near to the 5:3 mean motion resonance. We report that the inner and outer planets in the K2-21 system have properties consistent with the presence of a hydrogen- and helium-dominated atmosphere, as we estimate their masses to be $1.59^{+0.52}_{-0.44}$ and $3.88^{+1.22}_{-1.07}\, \mathrm{ M}_\oplus$ and densities of $0.22^{+0.05}_{-0.04}$ and $0.34^{+0.08}_{-0.06}\, \rho _\oplus$, respectively (M⊕ and ρ⊕ are the mass and density of the Earth, respectively). Our results show that the inner planet is less dense than the outer planet; one more counterintuitive exoplanetary system such as Kepler-105, LTT 1445, TOI-175, and Kepler-279 systems.