The glimpse that brought the flood

The star is noticed for the first time, in the brightness above the dawn horizon. This is the star’s heliacal rising, the beginning of its annual career across the night sky.

Heliacal rising is a major subject, asking to be visualized, and important in history. I’ve long been wanting to tackle it. There is much to say, so we’ll break it into two halves.

Ancient Egyptians watched for the heliacal rising of the brightest star. That star was called by them Sopdet, later rendered in Greek as Sothis; the Greeks called it Seirios, the “scorching,” later Latinized as Sirius.

In the morning twilight of the days of the first half of summer, priests stared at the eastern horizon: the line of highlands along the right bank of the Nile. They had come to know that with or soon after the first glimpse of the star came the first stirring of the water. Sirius’s revealing of itself heralded the Nile’s annual flood.

That flood was vital to Egypt. Indeed it had created Egypt. It laid down the black silt that made the narrow valley floor fertile. Also it filled the channels dug among the fields so that those could continue to be irrigated after the flood had subsided. In years when the flood failed or was weak, the fields were poor and parched. In years when the flood was too strong it tore soil away.

In the cover picture story for Astronomical Calendar 1978 I described the vast hydrological system that governs this flooding of the Nile: the weather that comes from the Atlantic over Africa to the mountains of Ethiopia and sends water at different times and volumes down the rivers that join, south of Egypt, to make the Nile. Also the discovery that the interval between heliacal risings of Sothis was 365 days – the year. And that it became more than that by a quarter of a day over a Sothic cycle of 1460 years, giving rise to the myth of the Phoenix reborn after that time. And the Canicular or Dog Days of heat that the scorching star, in its dog-shaped constellation, also brought. And the slightly lesser Dog Star that precedes the rising of Sirius: Procyon, “fore-dog.” And even the cat that was first domesticated in Egypt’s granaries and worshipped as Bast.

What I did not then try to fix was:

When does a heliacal rising happen?

It’s fairly simple at first approximation: for a given location on the Earth (latitude and longitude), find the first day in the year when, at sunrise, Sirius has also risen – has altitude of zero or more.

Let’s use the year 2000 as the “present” epoch, so as to compare with round numbers of centuries in the past. There would be little difference for 2022. Then, for a representative American location of 40° north and 90° west, Sirius is first above the sunrise horizon on August 2.

See the end note about enlarging illustrations.

As for Egypt: the land is long (stretching from latitude 32° to 22°) and the ancient history was long, from around 3150 BC to 340 BC (the end of the 30th and last native dynasty). Let’s choose 2000 BC, near the beginning of the Middle Kingdom and the 11th dynasty, which moved the capital from Memphis, in the north near the pyramids and modern Cairo, to Thebes, in Upper Egypt, at latitude 26°.

(There were three ancient cities that the Greeks called Thebes, in three continents; Egypt’s “Hundred-Gated Thebes” was the greatest. It was also the capital during the height of Egyptian civilization in the 18th dynasty around 1500 BC.)

In our own time, at Thebes, Sirius heliacally rises on July 22.

Because Thebes is 14° farther south, the celestial equator stands up more steeply. Put another way, the horizon is tilted more down at the right in relation to the Sun, and the occasion when Sun and Sirius reach it simultaneously comes  11 days sooner.

Precession from ancient time

Adjusting for the remote past (or future) is another matter, mainly because of the precession of the equinoxes. This is an almighty phenomenon, “Vaster than empires and more slow,” to quote Andrew Marvell, though he was talking about love, not precession.

Because our rotating Earth wobbles like a spinning top, with a period of 25,800 years, the map of the sky continually changes. What stays (essentially) fixed is the ecliptic, the plane of Earth’s orbit. The celestial equator tilts around in relation to it. The equinox points – where the equator crosses the ecliptic – keep sliding westward along the ecliptic. So do the solstice points, where ecliptic and equator are widest apart. Thus the map position of any star, measured from the vernal or March equinox point, moves by a certain amount each year.

So here is the sky for Thebes, precessed backward four thousand years.

We are in the time of pharaoh Mentuhotep III. Falcon-headed Mentu or Montu was the patron god of Thebes. We might call this the Mentuhotep picture.

There are many things to be pointed out in this picture of an ancient sky.

First, and least important: the year chosen, 2000 BC, is arithmetically -1999, because the year before 1 AD was not 0 but 1 BC. So the span between our 2000 BC and AD pictures is not 4,000 but 3,999. If we choose to talk about “round” years, we’re not talking about an exactly “round” span of years. Never mind.

In these four millennia of precession, the equinox and solstice points have slid almost 56° westward. That is how the celestial equator has re-tilted, like a hula hoop, transforming the relation of everything to the Sun’s position along the ecliptic at a given time in the year.

Sirius, four thousand years ago, came level with the rising Sun – rose heliacally – 19 days earlier in the year, on July 3.

The detail that most clearly moves, between the 2000 BC and AD pictures, is the solstice point, where the Sun is northernmost. In our own time it is between Gemini and Taurus. In 2000 BC it was in Leo – on the Sun’s other side in the picture, below the horizon! The Sun apparently had not yet reached it by the date of the heliacal rising. And yes, I find that back then the “June” solstice was on July 10! (And the “December” solstice, Jan. 5; the “March” and “September” equinoxes, April 7 and October 9.) I’d be happier if we had magister Jean Meeus to confirm this. His 3,000-year list of equinox and solstice dates in his Astronomical Tables starts with the year 1. We carefully speak of the June solstice, since “summer solstice” is not true for the southern hemisphere; if it was anciently in July, we might have to rename it the northern solstice.

As noticeable, or more so because actually visible, is Procyon. In ancient time it was indeed the Fore-Dog, the precursor to Sirius; now, for Thebes, it is below the horizon when Sirius rises.

Proper motion

Precession is the largest but not the only factor in the change of stars’ positions. They also have “proper motion”: real motion in space, relative to our Sun.

You may have noticed in the 2000 BC picture that Sirius is shown in two places. One, the smaller white dot, is used as a point in the drawing of the constellation formlines, and is not shifted for proper motion; the other is. Sirius is one of the nearest stars (8.6 light years away), so its map position changes relatively rapidly. It appears to shift per year 1.2 seconds south and about 0.04 second of right ascension west.

I’ve let this difference between positions with and without proper motion show, for Sirius and some other stars that are bright and relatively near, because it’s interesting to see. (But also, I should confess, because I realized that applying proper motion to the formline stars would require reconstructing a whole catalog!) It does allow you to see that, compared with precession, proper motion makes little difference for the timing of a star’s climb into view.

Second half will follow; mainly about the Pleiades.

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

ILLUSTRATIONS in these posts are made with precision but have to be inserted in another format.  You may be able to enlarge them on your monitor.  One way: right-click, and choose “View image” or “Open image in new tab”, then enlarge.  Or choose “Copy image”, then put it on your desktop, then open it.  On an iPad or phone, use the finger gesture that enlarges (spreading with two fingers, or tapping and dragging with three fingers).  Other methods have been suggested, such as dragging the image to the desktop and opening it in other ways.