Pope St. Julius, St. Athanasius, and the Council of Sardica

St. Athanasios appealed his deposition at the hands of the Arians to Pope St. Julius and the Apostolikos Thronos. What exactly did St. Athanasius believe this appeal entailed as regards the power of the papacy, and what can his appeal tell us about how we Orthodox should think about the rightly ordered authority of St. Peter’s heirs?