It could mean when a star, etc., comes up in the east or when it reaches a certain angle in the sky. It could mean the rise of the river or a procession in which a god was to be carried through town. But that is a conjecture. But Sirius could not be seen arising at those times when the sun was in the sky. It would have to arise at least 36 minutes before the sun came up, in order to be seen.
Alternative theories are equally feasible.
5 - A number of Egyptologists have rejected the theory entirely. 6 - The ancients did not know the correct length of the solar year. It is actually 365.2422 days in length. A true solar year would change the calculation from 1,460 to 1,507 years. That is a difference of 47 years.