halacha - Until what time in the morning may you eat on a fast day?

On fast days that begin in the morning, (Asara B'Teves, Taanis Esther, Shiva Asar B'Tamuz, Tzom Gedalya) if you intend to eat when you awake, until what time may you eat in the morning? Does it depend on Shaos Zemanios?