Heliacal Rising: Definitions, Calculations, and Some Specific Cases
by Brad Schaefer, Yale University

Heliacal rising is a phenomenon where a star is first visible in the morning sky. On this day, a star will only be briefly and barely visible, since if you had looked a day earlier, it was too close to the Sun for visibility. . The heliacal setting of a source is its last evening of visibility as conjunction with the Sun approaches. Note that the first visibility of the thin crescent moon is just a special case of heliacal rising.

Heliacal rising is an important phenomenon for ancient calendrics since almost all old calendars included such events. Here is a partial list of ancient cultures and the celestial source on which their calendars are based:

EGYPT	SIRIUS
MAYA	VENUS
AZTEC	PLEIADES
ARABS	CANOPUS
GREEK	CONSTELLATIONS

Additionally, everyone had months based on the heliacal events of the Moon. I only know of one case (Egypt for Sirius) where architectural structures were oriented towards a heliacal event as known from historical/ethnographic evidence.

While much less important and rarer, some cultures did note achronal events. The achronal rising of a source occurs when it first appears in the eastern evening sky just after sunset. Similarly, the achronal setting is when the source last appears in the western morning sky just before sunrise. Unfortunately, this defintion is ambiguous. By choosing sunset, nautical twilight, civil twilight, or astronomical twilight as the fiducial time, the achronal date can vary by many weeks. So achronal events are intrinsically ill-defined, and a date can only be assigned with an accuracy of weeks. As such, achronal events are useful only with strong historical/ethnographic support and with an acknowledged low accuracy. I know of only two cases (old Greek and Amazon) where achronal events of whole constellations or bright stars are used as approximate seasonal markers. In the Greek case, this is well documented in Hesiod.