In response, Darius' commander on the left, Bessus, sent the rest of the Bactrian cavalry into the fight. Alexander wheeled his right wing to meet the Bactrians, and fierce fighting continued for some time. In the end, after a desperate charge by the Persian flank-guard infantry, this attempt to envelop the Macedonian right flank failed.
As Alexander had planned, the concentration of Persian troops to the right left a gap in the center of Darius' formation. Alexander reformed his line into a wedge, wheeled center and charged. According to Greek sources, Alexander himself led the leftward charge toward the gap and toward Darius. At this point, the Persian king either turned and fled, or was bundled up and hauled away by some of his own commanders and nobles, depending upon the source.
The flight of Darius did not end the battle, however. Alexander's advance had left a gap in his own front line, and a group of Persian and Indian cavalry pressed all of the way through the Macedonian forces. Rather than turning to envelop one of the flanks, however, the Persians and Indians rode to the Macedonian baggage-train and started to ransack it. They also freed all the prisoners captured by the Greeks. Macedonian infantry then about-faced and drove them away.
Meanwhile, the Persian right was attacking the Macedonian left, attempting to envelop it. The Greek commander Parmenion sent riders to Alexander asking for aid, but the king was already far away, riding hard in pursuit of Darius. Parmenion's troops finally managed to fight off the Persians unaided; word that Darius had left the battle field took the fight out of the Persians and their allies. Soon, the Persian withdrawal turned into a panic.
Alexander lost Darius' trail and turned back, only to ride right into the retreating Persian cavalry. He lost sixty of his hand-picked riders in the ensuing fracas, and his lover Hephaestion was injured. This skirmish was the last of the Battle of Gaugamela.
Oddly, the surviving sources make no mention of the Indian war elephants playing any role in the fighting.
The Aftermath of Gaugamela
After the battle ended, Alexander the Great rode out once more in pursuit of Darius III. The Macedonian general Parmenion captured the Persians' camp, taking their supplies and the elephants. Alexander's scouting force captured the Persian field-treasury of 4,000 talents at Arbela the following day; this treasure would fund much of his conquest of southern and Central Asia.
As for Darius, he hoped to rally the eastern half of his empire to fight on against the Macedonian invasion. However, his generals and nobles (satrapies) felt that it would be better to surrender and cooperate with Alexander. So, Bessus murdered his own king. Alexander would later have Bessus executed for regicide. The death of Darius marked the end of Persia's Achaemenid Empire, and the beginning of Alexander's conquest of Asia proper.
Alexander himself would live only eight more years. After his death, his generals divided up his empire, including the lands of the former Achaemenid Empire. Persia would be ruled by the ethnically-Greek Seleucid Empire from 312 BCE to 63 BCE.
Ernst Badian, Achaemenid History: The Battle of Gaugamela, Circle of Ancient Iranian Studies: School of Oriental and African Studies, University of London.
E. Badian. "Darius III," Harvard Studies in Classical Philology, Vol. 100 (2000), pp. 241-267.
Davis, Paul K., 100 Decisive Battles: From Ancient Times to the Present, Oxford University Press, 2001.
A.M. Devine. "Grand Tactics at Gaugamela," Phoenix, Vol. 29 No. 4 (Winter, 1975), pp. 374-385.
Barry Porter, Battle of Gaugamela: Alexander Versus Darius, HistoryNet.com.