Technically, "authority" is defined as a person or group's legitimate power over others. It is the power to influence the opinions of others, esp. because of one's recognized knowledge or scholarship, authoritative opinion, or acknowledged expertise. [1] Regarding research, "authority" relates to whether or not the author(s) has established their expertise. This expertise may come in many forms, from special skills (training, learned abilities, longevity at a position, etc.); to knowledge derived from formal education and current/continual research.
You can establish the authority of your sources by researching the author(s).
An expert is: