Answer:
To depict and remember his service in a Union cavalry unit during the civil war
Step-by-step explanation:
Given that, during the American Civil War, this Pawnee warrior, often referred to as Loots-Tow-Oots (Rattlesnake) or George Esaw, took part as a member of the Calvary unit on the side of the Union. He thereafter, together with his wife, took a photograph in 1868, which he appeared to be wearing Partial Native Dress, that is, Partial Civil War Uniform, sat on a chair carrying a sword in his hand.
Therefore, the reason Pawnee warrior Loots-Tow-Oots hold a sword in the photograph taken of him and his wife in 1868 is "to depict and remember his service in a Union cavalry unit during the war."