Heliacal rising – Part Two

Part One showed the heliacal rising of Sirius in our time and in the Egypt of 2000 BC.

Hazy horizon

So July 3 was (for Middle Kingdom Egypt) the first morning when Sirius was at or above the eastern horizon at or before the rising of the Sun. But was it seen?

If an Egyptian was looking across the Nile from a mortuary temple on the left bank, the horizon of the Red Sea Hills had a certain height; if he was looking from Luxor or Karnak (the two parts of Thebes) on the right bank, the horizon was nearer and higher. And a shrub or rock or hut on the skyline could happen to be in front of the star!

And the low sky is brighter, reducing contrast with the star. And atmospheric extinction means that the length of the light’s travel through the atmosphere reduces the brightness of a star by 3 magnitudes at altitude 1°; by 2 at 4°; by 1 at 10°.

However, the density of the low atmosphere also refracts the star’s light upward by nearly half a degree if its true altitude is 0°; 0.2° if 4°; 0.1° if 10°.

A dominating factor is elongation: angular distance from the glaring Sun. At sunrise at Thebes on 2000 BC July 3, Sirius was 40° rightward along the horizon from the Sun. That was its difference in azimuth (angular distance around the horizon). Next day, Sirius was not only a bit farther from the Sun but also a bit higher at sunrise; both the azimuthal difference and the altitude difference had increased. The line from Sun to Sirius was not horizontal but sloped up slightly. So this is quite a complex factor: the difficulty of seeing the star changes not only with the length of the line between them but also the angle of that line.

Some of these factors can be different for different times and places, and for stars of different brightness. So it would be tricky to calculate how long after the geometrical heliacal rising comes the observable heliacal rising. We could guess; or find records of sightings; or experiment, by going out and looking. (See Part Three.) Sirius is so piercing that it is sometimes seen down almost to the horizon – its white light split into the many colors that sometimes led to its being called red.

We’ll refer to heliacal risings in the geometrical sense, and guess that the star was actually seen within the next four days.

As those days approached, Egyptian priests perhaps began to watch the eastern sky’s almost-as-bright precursor stars – Aldebaran, Betelgeuse, finally Procyon – knowing roughly how far below Procyon lurked Sirius. But the Sun intervened. Until the morning when the Sun intervened late enough to give time for Sirius to be glimpsed, and the water began to lap higher against the temple steps.

Sudden change?

Since the change in the date of the helical rising is caused mainly by precession, we expect it to be similar to the general rate of precession. And, from July 3 in 2000 BC, the Thebes Sirius date did advance gradually, to July 8 in 1500 AD. Then it seems to have taken a wide jump to the July 22 of our own time.

But that is because of the change of the calendar we use for dates before and after 1582, when October 5 Julian was immediately followed by October 15 Gregorian. The Thebes Sirius heliacal rising was on 1582 July 8 Julian; then 1583 July 19 Gregorian.

If we were to use the Gregorian calendar (closer to the sidereal year) for all dates, instead of only those after 1582, then 2000 BC July 3 would be June 16. (I think.) This explains why the Sun in the picture for 2000 BC, at July 3, has not yet reached its “June” solstice position.

Heliacal setting

Each day after Sirius’s heliacal rising, the Sun has moved on and Sirius rises about 4 minutes sooner, therefore in a darker sky and easier to see. As the months go on, Sirius is rising in full darkness and is seen in the middle of the night sky. Then it is rising after midnight; then in the twilight hours before dusk. There comes the last evening on which Sirius can be seen before sunset.

This occasion, when a star is last above the horizon when the Sun has gone below, is the heliacal setting of the star. The last time the star is actually seen may be some days before it geometrically sets along with the Sun.

The heliacal setting of Sirius is, for modern time and the American location, on May 27.

From then until the August 2 heliacal rising (68 days), Sirius is below the horizon all night.

For Thebes in 2000 BC, the heliacal setting was on May 19 or 20.

You can see that in this instance proper motion could have made the heliacal setting a day later.

The span of daytime-only Sirius was 45 days – shorter because of the angle of the ecliptic: the Sun was more rapidly moving northward.

We can compound our giddiness by positing yet further kinds of event:

The heliacal setting of a star in the west, at or just before the rising of the Sun in the east. And the heliacal rising of a star in the east, just at or after the setting of the Sun in the west!

Elsewhere in sky and vocabulary

We distinguish the geometrical and observed heliacal rising (or setting). Other terms have been used: “true” for the geometrical events; or “cosmical” for the geometrical rising in the morning and setting in the evening, “acronycal” for the geometrical rising in the evening and setting in the morning, leaving “heliacal” for the others… They seem inconsistent, confusing, and unneeded.

Greek hêlios, “Sun”; kosmos, “ornament” or “arrangement” or “that which is perfectly arranged, the universe.” And akro-, “top” or “end”; nyx, “night” – the two limits of the night.

A star has to be within a certain wide band around the sky for it to experience heliacal rising or setting. Circumpolar stars cannot, because they either never set or never rise. If you are at latitude 40° north, stars above declination 50° north are north-circumpolar and never set; stars south of 50° south are south-circumpolar and never rise. But these sets of stars change gradually with precession, because the declination of all the stars changes.

I think we’d better pause here and keep the Pleiades for Part Three.

__________

This weblog maintains its right to be about astronomy or anything under the sun.

Sometimes I make improvements or corrections to a post after publishing  it.  If you click on the title, rather than on ‘Read more’, I think you are sure to see the latest version.  Or you can click ‘Refresh’ to get the latest version.