It was the practice of the Prophet (peace and blessings be upon him):
"When he (peace and blessings be upon him) had prayed the Fajr prayer, he would remain sitting in his place of prayer until the sun rose."
Hadith Referenceصحیح الجامع الصغیر / حرف الكاف / 4747
Hadith Gradingالألبانی:صحيح
Hadith Takhrij[حم م ٣] عن جابر بن سمرة. صحيح أبي داود ١١٧١.