The Heliacal Rising of Sirius

Full text

Published in “Ancient Egyptian Chronology”, Handbook of Oriental Studies Vol. 83, E. Horning, R. Krauss and
D.A. Warburton eds., Brill, Leiden, 432-438 (2006)
THE HELIACAL RISING OF SIRIUS
Teije de Jong
The heliacal rising of Sirius, the brightest star in the sky, was used in antiquity, both in
Egypt and in Mesopotamia, to synchronize the calendar to the solar year. On the day of its
heliacal rising Sirius is seen again for the first time in the morning twilight sky after having
been invisible for about 70 days (at the geographical latitude of Memphis). On that day it
appears a few degrees above the Eastern horizon and disappears again after about 15 minutes
due to the brightening of the sky just before sunrise. The date of heliacal rising depends on
the relative positions of Sirius and the Sun with respect to the horizon and on atmospheric
conditions.
According to Parker in the ancient Egyptian lunar calendar an additional 13th month was
intercalated in the next year whenever the first visibility of Sirius (associated with the
Goddess Sothis) occurred during the last 11 days of the last month Wep renpet of the lunar
year.1 In this way the Egyptians could make sure that the first month Toth of their lunar
calendar always began shortly (within one lunar month) after the first visibility of Sirius. The
heliacal rising of Sirius plays a crucial role in Egyptian chronology because it is supposed to
fix the zero-point of the Egyptian civil calendar of 365 days by postulating that at the time of
its installation the first visibility of Sirius occurred on the first day of the first month.
One of the earliest references to the use of Sirius for intercalation in the Mesopotamian
lunar calendar is found on Tablet II of MUL.APIN where we are told that if Sirius rises in the
month Du’uzu (the 4th month) this year is normal but if it rises in the month Abu (the 5th) an
extra month has to be intercalated that year.2 On Tablet I the nominal date of the first
visibility of Sirius in the lunar calendar is given as “the 15th of Du’uzu” (the 4th month) as part
of a list of first visibility dates of about 30 stars. This list was based on observations carried
out in Babylon during the 13th century BC.3 Later (during the 5th to 1st centuries BC) dates of
the first appearance of Sirius are given in the Astronomical Diaries.4 Sachs has shown that in
the Babylonian 19-year calendar cycle, introduced in the early 5th century BC and used
without any further change during five centuries throughout the ancient near-East, the
intercalation pattern was arranged in such a way that Sirius always rose in the 4th lunar month
Du’uzu.5
Starting with Ptolemy (~130 AD) in his Almagest (Book VIII.6),6 astronomers have
discussed the heliacal rising (also referred to as first visibility or first appearance) of stars and
planets in terms of the so-called arcus visionis, the distance between a star/planet and the sun,
measured in degrees perpendicular to the horizon when it becomes visible again for the first
time in the morning twilight sky. In the second book of his U1seis δplanzn δst6rzn kaœ
synagzgλ ™pishmasi0n Ptolemy gives the dates of first and last visibility of some 30 bright
stars at different geographical latitude zones (kl5mata) from which values of the arcus
visionis can be deduced.7 For Sirius Ptolemy apparently uses a value of about 11°.
1 R.A. Parker, “The Calendars and Chronology”, in: The Legacy of Egypt, J.R. Harris (ed.), (Oxford,
1971), 13-26.
2 H. Hunger & D. Pingree, MUL.APIN: An Astronomical Compendium in Cuneiform, AfO Beiheft 24
(1989).
3 T. de Jong, “A New Attempt to Date the Observations of Rising Stars in MUL.APIN”, paper
presented at the 7th Notre Dame Workshop on the History of Astronomy (July 2005).
4 Sachs & Hunger, Diaries.
5 A. Sachs, “Sirius Dates in Babylonian Astronomical Texts of the Seleucid Period”, JCS 6 (1952),
105-114.
6 See Toomer, Almagest.
7 H. Vogt, “Griechische Kalender V. Der Kalender des Claudius Ptolemäus”, Sitzungsberichte der

In the 1920’s Carl Schoch was the first to attempt to determine values of the arcus
visionis for Sirius and for the planets from Babylonian observations.8 He derived a value of
7.7° degrees for Sirius. The recent edition of the Astronomical Diaries by Sachs and Hunger
allows a reanalysis of the Babylonian observational material. We now know that the number
of genuine observations of the date of first visibility of Sirius in the Diaries is quite small
since Sachs showed that almost all dates during the Seleucid Era (last three centuries BC) are
computed rather than observed.9 This is probably the reason that Schoch’s value is rather
small, because the Babylonian computational scheme is apparently based on dates observed
under optimal atmospheric conditions.
It turns out that there are only two genuinely observed dates of the first appearance of
Sirius listed in the Diaries: day 18, month IV, year 12 of Darius III (22 July 325 BC) and day
13, month IV, SE 22 (20 July 290 BC). An analysis of these data results in arcus visionis
values of 11.0° and 8.6°, respectively.
To determine the best value of the arcus visionis of Sirius for the purpose of calibrating
the Egyptian civil calendar in studies of Egyptian chronology L. Borchardt and P.V.
Neugebauer in 1926 organized an observing program of the first visibility of Sirius in Egypt.
Results of this study are summarized and discussed in a recent paper by Pachner.10 He shows
that the 1926 program resulted in the determination of arcus visionis values for Sirius of 8.7°
- 9.2°.
The problem was discussed again by Schaefer without taking the results of Pachner into
account.11 He suggested a value of the arcus visionis for Sirius of about 11°, similar to the
value derived by Vogt from Ptolemy’s Phaseis. His analysis was based on a theoretical model
of stellar visibility adopting a visual extinction for the atmosphere near ancient Memphis of
0.35 magnitudes per air mass (one air mass is a measure of the thickness of the atmosphere at
zenith). This extinction estimate was based on data for Jerusalem. In his paper he also listed
the expected dates of heliacal rising of Sirius between 3500 BC and 500 AD for his adopted
value of the extinction.
To put things into perspective I have computed values of the arcus visionis and dates of
the heliacal rising of Sirius in Egypt using the model of de Jong and Inklaar12, which is an
improved and updated version of the earlier model of Inklaar13. In this model the visibility of
stars and planets is computed based on the brightness of the twilight sky as a function of the
depression of the Sun below the horizon, on the transparency of the atmosphere and on the
sensitivity of the human eye in twilight conditions. The physical principles underlying this
model are similar to those adopted in the earlier models of Bruin14 and of Schaefer15 but some
of the assumptions and parameters used are different.
Heidelberger Akademie der Wissenschaften, Phil.-Hist. klasse, 15. Abh. (1920), 1-61
8 C. Schoch, The Arcus Visionis in the Babylonian Observations, (Oxford, 1924); idem, “The Arcus
Visionis of the Planets in the Babylonian Observations”, Monthly Notices of the Royal Astronomical
Society 84 (1924), 731-734.
9 See n. 5.
10 N. Pachner, “Zur Erfassung der Sichtbarkeitsperioden ekliptikferner Gestirne”, Ä&L 8 (1998), 125-
136
11 B.E. Schaefer, “The Heliacal Rise of Sirius and Ancient Egyptian Chronology”, JHA (2000), 149-
155
12 T. de Jong & F. Inklaar, “A New Method to Compute First and Last Visibilities of Stars and
Planets” (2006), in preparation.
13 F. Inklaar, Een Nieuwe Methode voor de Berekening van Heliakische Opkomsten, doctoraalscriptie,
(Universiteit van Amsterdam, 1989).
14 F. Bruin, “The heliacal setting of the stars and planets” I & II, Proceedings of the Koninklijke
Nederlandse Akademie van Wetenschappen, Series B, Vol. 82 (1979), 385-410.
15 B.E. Schaefer, “Predicting Heliacal Risings and Settings”, Sky and Telescope 70 (1985), 261-263;

Using this model I have computed the parameters in Table 1 characterizing the heliacal
rising of Sirius in 1000 BC for a location at geographical latitude 30º North, representative for
ancient Memphis along the Nile. Visual magnitude, position and proper motion of Sirius
were taken from The Bright Star Catalogue16 and precession was calculated according to
algorithms in the Explanatory Supplement to the Astronomical Almanac.17 Results are given
for three different values of the visual atmospheric extinction k(V) in column (1) by averaging
over 4 years around 1000 BC. Values of the apparent altitude of Sirius above the horizon
when it first becomes visible are given in column (2) and of its true altitude (without
atmospheric refraction) in column (3) as well as the true solar depression below the horizon in
column (4). In column (5) I list the actual average arcus visionis <h>, the distance between
Sun and Sirius perpendicular to the horizon at first visibility (column (4) subtracted from
column (3)). In columns (6) and (7) I list the Julian date and the local time of the first
visibility of Sirius and in column (8) the duration of its visibility. The averaging takes
account of the fact that the ecliptic longitude of the Sun at sunrise on any Julian date varies
from year to year and returns to the same value every four years (due to Julian intercalation).
Notice that if one wants to compute the date of heliacal rising based on a value of the arcus
visionis one should use a minimum value h0 which is ~ 0.5° (one half the daily motion of the
Sun) smaller than the average values listed in Table 1.
Table 1 Heliacal rising of Sirius at GB = 30o in 1000 BC
Visual Apparent Real Real Arcus Julian Local Duration
extinction stellar stellar solar visionis date Time of
k(V) altitude altitude altitude <h> visibility
0.20 1,5 1,1 -6,9 8,0 16-jul 4:25 13
0.27 2,3 2,0 -7,3 9,3 17-jul 4:24 14
0.35 3,2 2,9 -7,7 10,7 19-jul 4:22 14
mag/airmass degrees degrees degrees degrees dd-mon hrs:min minutes
The day on which the heliacal rising of Sirius (Sothis) was observed in ancient Egypt
clearly depends on the prevailing atmospheric conditions. In Table 2 I show values of the
average visual extinction as measured at different locations on Earth at different epochs. Not
surprisingly, the data show that by far the clearest skies (lowest extinction values) are found
in dry regions at high altitudes where present-day astronomical observatories are located
(McDonald Observatory on Mount Locke, Texas, USA18 and the European Southern
Observatory on La Silla, Chile19). According to the data in Table 2 much poorer atmospheric
conditions are found in humid climates at sea level (Leiden Observatory, the Netherlands20,
no longer in use) and at low altitudes (Jena Observatory in Grossschwabhausen, Germany21).
idem, “Heliacal Rise Phenomena”, Archeoastronomy 11 (1987), S19-S33.
16 D. Hoffleit, The Bright Star Catalogue, (New Haven, 1982).
17 P.K. Seidelmann (ed.), Explanatory Supplement to the Astronomical Almanac, (Mill Valley:
University Science Books, 1992).
18 R.J. Angione & G. de Vaucouleurs, “Twenty years of atmospheric extinction at McDonald
observatory”, Publications of the Astronomical Society of the Pacific 98 (1986), 1201-1207
19 F. Rufener, “The evolution of atmospheric extinction at La Silla”, Astronomy and Astrophysics 165
(1986), 275-286
20 K.K. Kwee & A.M. van Genderen, “Photo-electric Observations of 31 and 32 Cygni during
November and December 1961”, Bulletin of the Astronomical Institutes of the Netherlands 17 (1963),
53-55
21 H.-G. Reimann, V. Ossenkopf & S. Beyersdorfer, “Atmospheric extinction and meteorological
conditions: a long time photometric study”, Astronomy and Astrophysics 265 (1992), 360-369

It is instructive to realize that an increase in extinction of 0.1 magnitudes corresponds to a
small decrease in the intensity of starlight of 10% at zenith but to a large decrease by a factor
4 at 3º above the horizon.
Table 2 Atmospheric visual extinction at different locations and epochs
Location Epoch Season Altitude <k(V)>
Babylon, Mesopotamia ~ 1300 BC yearly average sea level 0,27
Babylon, Mesopotamia 647-634 BC jul - nov sea level 0,25
Uruk, Mesopotamia 577-575 BC oct - dec sea level 0,34
Leiden, the Netherlands 1961 nov - dec sea level 0,43
Grossschwabhausen, Germany 1968-1991 yearly average 350 m 0,36
Mount Locke, Texas, USA 1960-1980 yearly average 2000 m 0,17
La Silla, Chile 1975-1985 yearly average 2400 m 0,12
One important uncertainty that affects estimates of the atmospheric extinction is the
aerosol content of the atmosphere, which over the last century and a half has been noticeably
increasing due to industrial pollution. Therefore I also list in Table 2 values of the
atmospheric visual extinction in Mesopotamia during the 6th and 7th century BC derived from
an analysis of ancient observations of Saturn from Babylon and Uruk22 and during the 13th
century BC from an analysis of observations of about 20 bright stars from Babylon23. These
values are close to the present-day visual extinction for clear skies at sea level of about 0.28
magnitudes per air mass (0.02 due to Ozone absorption, 0.12 due to molecular scattering and
0.14 due to aerosols and dust)24. Contrary to Schaefer25 who adopted 0.35 magnitudes per air
mass for the Memphis area I suggest that 0.27 is a more appropriate choice since the climatic
conditions in the Nile valley near Memphis are probably quite similar to those in the
Euphrates valley near Babylon. This value is consistent with the 1926 observations
summarized by Pachner26 because arcus visionis values of 8.7º - 9.2º correspond to a visual
extinction of about 0.25 magnitudes per air mass (see Table 1). Ptolemy’s arcus visionis of
11° (corresponding to a visual extinction of about 0.35 magnitudes per air mass) is
appropriate for the much more humid conditions in Alexandria at the shore of the
Mediterranean.
For chronological purposes the actual date of heliacal rising of Sirius is the crucial
quantity. In Table 3 I list dates of heliacal rising of Sirius computed for geographical latitudes
25° North (Elephantine) and 30° North (Memphis) for different values of the atmospheric
visual extinction at different epochs in antiquity. These dates are averages over four
consecutive years. As argued above atmospheric conditions in arid upper Egypt (Elephantine
and Memphis) are probably best characterized by a visual extinction k(V) = 0.27 magnitudes
per air mass, while for the more humid climate of lower Egypt (Alexandria) k(V) = 0.35
magnitudes per air mass may be more appropriate.
The atmospheric extinction varies due to changing weather conditions. On some days
this will make Sirius unobservable and it may cause variations in the date of heliacal rising of
22 T. de Jong, “Early Babylonian Observations of Saturn: Astronomical Considerations”, in: Under
One Sky, J.M. Steele & A. Imhausen (eds.), (Münster: AOAT 297, 2002), 175-192
23 See n. 3.
24 See M.S. Bessell, “UBVRI passbands”, Publications of the Astronomical Society of the Pacific 102
(1990), 1181-1199.
25 See n. 11.
26 See n. 10.

Sirius of up to about ± 3 days, corresponding to extreme values of k(V) ranging from 0.15 to
0.40 magnitudes per air mass.27
Table 3 Julian dates of the heliacal rising of Sirius and of summer solstice
k(V) 0.20 0.27 0.35 0.20 0.27 0.35 Summer
Epoch solstice
3500 BC 8-jul 10-jul 11-jul 14-jul 16-jul 17-jul 22-jul
3000BC 8-jul 10-jul 11-jul 14-jul 16-jul 17-jul 18-jul
2500 BC 9-jul 11-jul 12-jul 14-jul 16-jul 18-jul 14-jul
2000 BC 9-jul 11-jul 12-jul 15-jul 17-jul 18-jul 10-jul
1500 BC 10-jul 12-jul 13-jul 15-jul 17-jul 18-jul 7-jul
1000 BC 11-jul 12-jul 14-jul 16-jul 17-jul 19-jul 3-jul
500 BC 11-jul 13-jul 14-jul 16-jul 18-jul 19-jul 29-jun
1 AD 12-jul 14-jul 15-jul 17-jul 18-jul 20-jul 25-jun
500 AD 13-jul 14-jul 15-jul 17-jul 19-jul 20-jul 21-jun
Geographical latitude = 30°Geographical latitude = 25°
The data in Table 3 also show that in the course of 4000 years the date of the heliacal
rising of Sirius moves forward with respect to the summer solstice by one day in about 120
years. This is due to precession but tempered by the fact that Sirius lies far (~ 40°) south of
the ecliptic. For a star in the ecliptic this forward motion would be one day in about 75 years,
as expected for a rate of precession of 1° in 72 years. The rather large proper motion of Sirius,
which causes a displacement in the sky of about 1.5° in 4000 years, only causes a minor shift
in the date of heliacal rising of about one day over that period. Notice that the inaccuracy of
the Julian calendar causes the summer solstice to recede by about one month in 4000 years
rather than two months as expected for an accurate solar (Gregorian) calendar.
Acknowledgements
I am grateful to Rolf Krauss and Peter Huber for several useful comments and
suggestions for improvement.
27 See n. 22.