Introduction.
In Almagest VIII 2 Ptolemy gives a description of the Milky Way, as seen from his Alexandrian observing location. In it, he mainly focuses on three aspects of his theme: first, the location of the limits of the bands which constitute the Milky Way. He points these limits by selecting certain stars which are at or close to, the point in which the milk ceases to be perceptible. Second, he gives us some vague indications about the density of the milk along its path. These variations are conveyed through ambiguous phrases such as the indication that the milk is “somewhat denser” (ἠρέμα πυκνότερα) in some place, or with a “smoky” (καπνώδης) appearance in other. While we cannot get a very precise image from these sentences, they nevertheless allow us to have a general picture of what he was looking at, and sometimes even relate his description to modern labels given to some regions of the galactic belt.1 Third, in his description Ptolemy also gives us a general description of the structure of the Milky Way, distinguishing between two main sections. One continuous to the south, and one which is located between the regions of Ara and Cygnus. This second, northern belt is itself cut in two parts by a dark region, which today we call “the Great Rift”, and Ptolemy described as “[…] considerable gap of open space […]”2.
The description of the Milky Way is given after Ptolemy’s stellar catalogue in VIII 1, and before his instructions to build a solid globe in VIII 3. The order makes sense: he needs to have the stellar labels and coordinates in order to use the stars themselves to describe and locate the milk in a meaningful way. Because the milk itself moved together with the rest of the fixed stars, it was natural to depict it together with them in the physical representations of the celestial sphere, such as the solid globes which were crafted in those days.
Although much work has been devoted to the stellar catalogue of the Almagest, and also to the extant evidence of ancient celestial spheres, there is no substantial scholarly work devoted to Ptolemy’s description of the Milky Way. We can just barely, for example, find a couple of mentions in (Pedersen, 2010: 259 and Neugebauer, 1975: 890). I expect that this work will serve as a monograph that makes an initial survey of the topic, and provides the necessary groundwork to foster future studies.
The first section of the paper deals with the location of the Milky Way in Ptolemy’s times for an Alexandrian observer. One of the more striking features of the text is that Ptolemy describes the entire Milky Way, beginning in Centaurus, moving towards the galactic center in Sagittarius, and going all the way round up to Argo. This would not be possible for an observer today. I will show, via a brief argument, how the effect of precession account for the difference, and how the milk was positioned in ancient times with respect to an observer in those parts of the world.
The second section, which is the longest, is focused on Ptolemy’s description properly. First, I will give a general account of the structure Ptolemy gives: the aforementioned two main belts, and how they are divided. Then, following the order of the Almagest, I will begin by the southern belt in Centaurus, and continue towards Sagittarius, all the way around. After that, I will focus on the two main parts of the northern belt, one on each side of the Great Rift. Finally, I will give some concluding remarks.
The paper follows Ptolemy’s order, describing the appearance of the milk in successive constellations, starting in Centaurus. My analysis is made according to the following pattern: first, I reproduce Ptolemy’s description in a given region. Ptolemy indicates the stars (mostly) following the labels he assigned to them in his catalogue. Therefore, I in turn indicate the corresponding star number for the catalogue.3 In most cases this is a straightforward procedure. Then, I also give modern identifications for the stars in Ptolemy’s catalogue. For this, I mostly use the identification given in Toomer’s edition. After this, I identify the location of each of the stars in a high-resolution image of the Milky Way. To avoid excessively big labels which would hinder a clear visualization, I number them in the image following the order of appearance in Ptolemy’s text. The caption of these images correlates these numbers with the modern names of the stars. Then, I do the same thing in Pannekoek’s diagrams of the Milky Way (more on this below). Finally, I compare Ptolemy’s description with the depictions in the high-resolution photograph and Pannekoek’s diagrams and analyze how they relate to each other.
The use of images deserves some additional clarifications. The high-resolution photograph was produced by the European Southern Observatory as part of their GigaGalaxy Zoom Project, in association with astrophotographer Serge Brunier. Regarding Pannekoek’s diagrams, they are taken from Die Nördliche Milchstrasse (1920) and from Die Südliche Milchstrasse (1928). They are isophotic charts4 that depict the constellations around the galactic equator, together with a numeric representation of the brightness of each region. The method he uses to measure the brightness of the milk is an adaptation of Argelander’s method for measuring the brightness of stars (Pannekoek, 1920: 2; 1928: 11). It is based on a fairly sophisticated procedure that takes many normalpunkte or normalstelle, and produces a common measurement system, which is later combined with visual descriptions to produce accurate diagrams. A full explanation of the reasoning behind the values given to each region is beyond the scope of this paper. It can be found in (Pannekoek, 1920: 2-5). The inclusion of Pannekoek’s diagrams in this paper serves as an additional support to the presence of modern photographs, and as an objective instrument to evaluate the consistency of Ptolemy’s indications of brightness, particularly regarding the determination of the limits of the milk.
Finally, I will assume a division of the celestial sphere by the galactic equator, where the north will be the hemisphere in which the north galactic and celestial poles are located, and south will be the other hemisphere. This is not always the convention used by Ptolemy, who is not consistent in this regard. Thus, while he sometimes talks about north and south, in other instances he refers to my northern and southern limits of the milk as the eastern and western limits, or the equivalent more advanced or rearmost limits.
Position of the Milky Way as seen from Alexandria in Ptolemy’s times.
The equatorial position of the galactic north for B1950.0 is 192;15° for RA, and 27;24° north for declination (Meeus, 1998: 94). This means that the northernmost latitude from which the entire Milky Way’s equator is visible today is about 27;30°. Because Alexandria’s latitude is 31;12° north, this shows that today it is not the case that the entire galactic plane is visible from Alexandrian latitudes: the declination of the galactic north pole would have to be at least around 31°.
While the effect of the variation of the obliquity of the ecliptic is negligible when it comes to the inclination of the galactic equator to the celestial equator, this is not the case with the effect of precession. The B1950.0 ecliptic position of the galactic north is 179;19,29° for longitude, and 29;48,43° north for latitude. If we assume a value of 50’’ per year for precession, we get a longitude for 140 of 154;11,9°. This means a declination of the galactic north for 140 of 37;23,50°.
So, in Ptolemy’s times, an observer at Alexandria would have been able to observe the entire equator of the Milky Way (“[…] the great circle drawn approximately along the middle of it […]” Toomer, 1984: 400) throughout one year. Nevertheless, because the varying width of the Milky Way spans several degrees on both sides of the galactic equator, the visibility of the entire galactic equator does not assure that the Milky Way itself will be wholly observable in all its details, particularly some sections near its rims. As we saw, Ptolemy would have been able to see up to about 37.5° - 31° = 6° to the south of the southernmost point of the galactic equator. This is a region some 4° southeast of the intersection of the two lines in Crux, almost in the center of the Coalsack (point SP in Figure 1). The relation between maximum altitude and distance to this southernmost point in the galactic equator follows a sinusoidal curve, with a maximum altitude of about 37.5° + 31° = 68.5° at the northernmost point of the galactic equator, which is about 1.5° to the northwest of the middle star in the “W” of Cassiopeia (point NP in Figure 1). However, the altitude reached by each point of the galactic equator is not the only variable relevant to study the visibility of the belt of the Milky Way. The angle between the galactic equator and the horizon varies throughout the day. For an observer at Alexandria in 140 the maximum would have been, of course, 68.5°. This means that while some points of the galactic equator might never rise more than 8° or 12° above the horizon, the band of the Milky Way which is about 15° in width on each side might still be mostly or entirely visible, due to the fact that at that moment the angle between the galactic equator and the horizon is large enough. In Figure 1 points I (in the constellation of Vela) and II (in the constellation of Ara) indicate the limits of the southern region where the visibility of the band is always less than 15° to the south of the galactic equator.
One last variable to remember is extinction, which is the absorbing and scattering effect that the atmosphere has on the light coming from the sky. As it is natural, the closer the object is to the horizon, the more relevant this effect becomes.
Ptolemy’s description.
Ptolemy begins his description by indicating the general structure of the Milky Way. He says that “[…] the Milky Way is not strictly speaking a circle, but rather a belt of a sort of milky colour overall (whence it got its name); moreover this belt is neither uniform nor regular, but varies in width, colour, density and situation, and in one section is bifurcated […] The bifurcated part of the belt has one of its ‘forks’, so to speak, near Ara, and the other in Cygnus. But, whereas the advance [part of the] belt is in no way attached to the other part, since it forms gaps both at the fork by Ara and at the fork by Cygnus, the rearmost part is joined to the remainder of the Milky Way and forms [with it] a single belt […] It is this belt which we shall describe first, beginning with its southernmost section.”6
The description is simple. Throughout most of the Milky Way, there is a single belt. But when we approach the center in Sagittarius from each side, we find that it bifurcates, with one belt being continuous with the rest, and another going towards the north. As Ptolemy will comment later on, this second belt is itself divided into two sections. Refer to Figure 2.
As Ptolemy says, he begins with the southern belt, and he does so by studying the milk in what was for him the southernmost constellation of the Milky Way: Centaurus.
Centaurus.
Ptolemy begins his description of the Milky Way in Centaurus by locating it as passing “[…] through the legs of Centaurus”7, and then says that in this region it is dimmer than in other parts. He then indicates that “[…] the star on the knee-bend of the right hind leg is a little further south than the line [bounding] the milk to the north […]”8. The description is identical to the star XLIV 31 in his catalogue, and the identification as γ Cru is certain. He then says that the same is true of two more stars, “[…] the star on the left front knee and the star under the right hind hock.”9 In these cases the descriptions match to XLIV 36 (β Cru) and 32 (β Cen), respectively. Next, he defines the center of the band: “[…] the star in the left hind lower leg lies in the middle of the milk […]”10 Toomer identifies it as XLIV 33 (“The star under the knee-bend of the left [hind] leg”11, or δ Cru, which is a reasonable identification. With respect to the southern rim, Ptolemy indicates that “[…] the stars on the hock of the same leg and on the right front hock are to the north of the southern rim by about 2° […]”12 These stars can be identified with certainty as α Cru and α Cen, respectively. Finally, he indicates that the milk is somewhat denser in the region near the hind legs.
Refer to Figure 3. The galactic equator passes just below 2 and above 3 (refer to Figure 4 for an accurate indication of its location). Ptolemy’s description indicates that 1, 2 and 3 are just below the northern rim of the milk, which is a strange description since their galactic latitudes are very different. If we compare this description to the photograph in Figure 3, and to Pannekoek’s corresponding chart (see Figure 4) we can see that while 1 is certainly “a little further south” of the northern rim of the band13, 2 and 3 are much more separated. The positioning of 4 “in the middle of the milk” is stranger still. This is not because it is not on the galactic equator. The determination of this great circle is somewhat arbitrary, and Ptolemy might have in mind a circle a little bit to the north of our current determination of its position. The difficulty lies in the fact that 4 is to the north of 2, which was previously used to determine the northern rim. All this confusion is nevertheless understandable: this part is, as we saw, the one with the worst visibility. Ptolemy would have not been able to see much under the Cross, and even the observations of those stars which were visible would have been much disturbed by their low altitude.
This also explains why he does not mention one of the most salient features of this region, the Coalsack (at the center of Figure 4, and whose lack of luminosity is marked by Pannekoek with a definite “00”).14 Ptolemy does, nevertheless, notice the increased brightness in the rear legs of the Centaur. He is likely referring to the bright clouds in Crux and Carina, clearly visible to the right of the Cross.
Lupus and Ara.
The next section he considers is within Lupus and Ara. He says that “[…] the northern rim of the milk is about 1.5° from the star on the rump of Lupus, and the southern rim encloses the star on the burning-apparatus of Ara, but just grazes the northernmost of the two stars close together on the brazier and the southernmost of the two stars in the base, while the star in the northern part of the brazier and the one in the middle of the brazier lie right in the milk.”15 There are six stars in this description, and they can be identified with certainty. The one determining the northern rim is XLV 10 (ζ Lup). The one enclosed by the southern rim is XLVI 7 (ζ Ara). The two which are “just grazed” by the southern rim are XLVI 6 (β Ara) and XLVI 2 (θ Ara). The last two, those which “lie in the middle of the milk”, are XLVI 4 (ε Ara) and XLVI 3 (α Ara). Ptolemy ends this part of the description indicating that “[t]hese sections are rather less dense.”16
Refer to Figure 5. From Lupus we can see ζ Lup, while we have several stars from Ara: ζ Ara, β Ara, θ Ara, ε Ara and α Ara. Ptolemy’s description is fairly consistent with the photograph in Figure 5, and with Pannekoek’s evaluation in Figure 6. While it seems that the 1½° from 1 to the northern rim was a conservative estimate, in the case of the southern rim the limit indicated by 3 and 4 seems more accurate. As in the previous case, the low altitude explains the general lack of consistency: the maximum altitude this region reached in Alexandria was about 11°. With such values, atmospheric extinction plays a major role, and indeed this region would have seemed “less dense” than others. Had Ptolemy been able to have clearer views, he might have noticed the very bright Norma Star Cloud in-between 1 and 5, whose brightness Pannekoek marks with a “73”.
Scorpius and Sagittarius.
The following section is focused on Scorpius and Sagittarius. This is the part of the Milky Way which is in the direction of the galactic center, where the stellar population is the densest, and therefore the appearance of the milk is the brightest. He references many stars: “[…] the northern part of the milk encloses the three joints before the sting of Scorpius and the nebulous mass to the rear of the sting, while the southern rim touches the star in the right front hock of Sagittarius, and encloses the star on his left hand.”17 The three stars near the sting are XXIX 17, 18 and 19 (θ, ι and κ Sco, respectively). The “nebulous mass to the rear of the sting” is M7, an open cluster which is about 0;40° across. In Ptolemy’s catalogue it is XXIX 22.18 The two stars in Sagittarius described here are XXX 25 (η Sgr) and 2 (δ Sgr), respectively. He continues explaining that “[t]he star on the southern portion of the bow is outside the milk, but the star on the point of the arrow lies in the middle of it, while the stars in the northern part of the bow also lie in it, each of them being a little more than 1° removed from one of the rims, the southern star from the southern rim, the northern star form the opposite rim.”19 These four stars are XXX 3 (ε Sgr), 1 (γ Sgr), 4 (λ Sgr) and 5 (μ Sgr), respectively. He ends the section by pointing out that “[t]he area near the three joints is somewhat denser, while the area around the point [of the arrow] is very dense indeed and appears smoky.”20
Refer to Figure 7 and Figure 8. This description shows a remarkable match to the lines in Pannekoek that indicate, in his scale, a density of 30-40. Almost all of the stars that Ptolemy references, and which are in or close to, the sting, are within such areas. If we look at the location of 5, it is remarkably close to the line, while 6 is a couple of degrees inside that limit, just as Ptolemy says. Moreover, 7 is just outside the line, and 8 is indeed “in the middle of it”, lying almost at the very center of the Large Sagittarius Star Cloud. This explains Ptolemy’s note that the area is so dense as to appear “smoky”. Finally, the indication of 9 and 10 as being “a little more than 1°” removed from the northern and southern rims also fits the 30-40 limit Ptolemy seems to be following.