In answering this question we must first appreciate the difficulty historians face in discovering the real truth of the early Arab invasions, a fact well demonstrated in the varying estimates of Arab invasion forces (ranging from 1,700-9000 in current publications). Scant contemporary evidence exists beyond a short narrative present in a Spanish chronicle of 754, a vital surviving Islamic administrative document of the time, and some archaeological remains. Our knowledge of the invasions is largely founded on the works of later Islamic historians, the Ajbar Machmua text for example and the works of Ibn Idhari and al Maqqari. Unfortunately there are fewer Christian documents available. Julian's History of Wamba' is one of few Visigothic texts to be found, further information has therefore been gained from later monastic chroniclers.
For religious Muslim contemporary's the success of the 711 invasion was attributed to the will of Allah as part of Islam's rapid expansion. Likewise for the Christian author of the 9th century chronicle of Alfonso III the Visigoths' defeat had been punishment for disobeying God's commandments. To the majority of medieval men divine intervention was a valid explanation for occurrences, however even then secular minded writers appreciated more practical explanations; principally the unrest which existed within the Visigothic kingdom. The political and social problems which faced Iberia at the time are seen by many modern historians as vital to the conquest's success. In 710, supposedly the year of the first major Muslim incursion into Spain under Tarif (whether Tarif's raid even occurred is disputed by some historians ) the new King Roderic succeeded the throne. He was in a vulnerable position from the outset as controversy existed over his succession. It was argued that he had apparently usurped the throne from the rightful heir Akhila son of the old King Wittiza.
Bibliography: Chejne, Anwar G: Muslim Spain, its history and culture (Minneapolis,1974) Collins, Rodger: Early Medieval Spain, University in Diversity, 400-1000 (Basingstoke 1995) Collins, Rodger: The Arab Conquest of Spain 710-797 (Oxford 1989) Fletcher, Richard: Moorish Spain (London,1992) Kennedy, Hugh: Muslim Spain and Portugal: a political history of al-Andalus (London 1996) Read, Jan: The Moors in Spain and Portugal (London,1974) Watt, W. Montgomery: A history of Islamic Spain (Edinburgh, 1996)