We examined liquidus phase relations in Fe-O±H at ~40 and ~150 GPa, and in Fe-H at 45 GPa. While it has been speculated that Fe and FeH form continuous solid solution to core pressures, our experiment on Fe-H showed that FeH_0.20 forms with the hcp structure, different from fcc for stoichiometric FeH, and melts at temperature lower than that for FeH, suggesting eutectic melting between Fe and FeH. It is consistent with the liquidus phase diagram in Fe-O-H, which implies the Fe-FeH binary eutectic liquid composition of FeH_0.42 at ~40 GPa. We estimated the outer core liquid composition to be Fe + 2.9–5.2% O + 0.03–0.32% H + 0–3.4% Si + 1.7% S by weight, based on the liquidus phase relations, solid-liquid partitioning, and outer/inner core densities and velocities, indicating that O and either H or Si are important core light elements.