Final answer:
T Tauri stars do not have nuclear reactions in their core, which is the characteristic that is not applicable to them.
Step-by-step explanation:
The property that is NOT characteristic of T Tauri stars is C) nuclear reactions in the core. T Tauri stars are a class of very young stars that have not yet started hydrogen fusion in their cores; instead, they are primarily characterized by their variability, mass ejection, and strong emission lines in their spectrum. While they do show significant activity and interaction with their surroundings, including mass ejections and variations in brightness, their core has not reached the necessary conditions for nuclear fusion of hydrogen into helium, which is a characteristic of main-sequence stars, not T Tauri stars.