No explanation has been given to what properties Soul Gauge energy holds, although its name would imply it is derived from one's soul. In gameplay, the player can gather Soul Gauge energy during Missions which is stored in the Soul Gauge. With Soul Gauge energy, the player is able to pull off special, extra powerful maneuvers. When these actions are used however, the player's gathered Soul Gauge energy will deplete. The player will also lose some Soul Surge energy when taking damage.
Sonic Storybook series
Sonic and the Secret Rings
In Sonic and the Secret Rings, Soul Gauge energy made its debut, where it is just referred to as Soul. In this game, the player can gather Soul from collecting Pearls, Rich Pearls and defeating enemies. There are also Skills that allow the player to gather or better sustain Soul when certain conditions are met. Other Skills can also improve or assist with gameplay performance at the cost of Soul.
Sonic and the Black Knight
In Sonic and the Black Knight, Soul Gauge energy can be gathered from collecting red fairies and attacking enemies. There are also Skills that allow the player to gather or better sustain Soul Gauge energy when certain conditions are met. Additionally, there is the "Soul Resurrection" Skill, where Soul Gauge energy is used for health when Rings are gone.