A physical interpretation of the ‘red Sirius’ anomaly

Abstract

The controversy over whether the brightest star, Sirius (α CMa; HR 2491), was red in visual appearance some 2000 years ago, as suggested by Ptolemy amongst others, is re-examined from a physical perspective. Objections to hypotheses based on evolutionary events within the Sirius binary system itself are briefly reviewed. Scenarios that invoke reddening caused by foreground extinction in the interstellar medium or in the Earth's atmosphere are examined in detail to determine whether they offer viable alternatives. It is deduced that only atmospheric extinction is capable of producing appropriate changes in the colour and brightness of Sirius. This result concurs with the findings of Ceragioli, who deduced, from a re-evaluation of the historical evidence and the cultural role of Sirius in Greek and Roman society, that ‘red Sirius’ refers to observations made at the heliacal risings and settings of the star. Both physical and historical evidence are thus consistent with an interpretation of the ‘red Sirius’ anomaly based on reddening in the terrestrial atmosphere.

1 Introduction

Sirius A, the brightest star in the night-time sky, appears white to the unaided eye, consistent with its classification as an A1 V star with negligible interstellar reddening. Historical evidence that Sirius appeared red (comparable in colour to stars such as Aldebaran, Arcturus and Betelgeuse) as recently as 2000 years ago has been widely discussed in the literature in recent years (e.g. Brecher 1979; Schlosser & Bergmann 1985; Tang 1986, 1991; van Gent 1989; Gry & Bonnet-Bidaud 1990; Bonnet-Bidaud & Gry 1991; Ceragioli 1995, 1996; see Ceragioli 1995 for a guide to earlier literature). This phenomenon, which I refer to as the ‘red Sirius’ anomaly, appears to have stimulated interest and scepticism in almost equal measure. The evidence is based on interpretations of ancient texts from several cultures, including Babylonian, Greco-Roman, Chinese and early-medieval European sources, over a total time-span of approximately 1400 years (800 bc to ad 600: e.g. Brecher 1979; Schlosser & Bergmann 1985; Bonnet-Bidaud & Gry 1991). Some of the claims have been disputed on grounds of misidentification or misinterpretation: as an example of the former, the star supposed to be Sirius in the early-medieval Lombardic text discussed by Schlosser & Bergmann (1985) may be identified more reasonably as Arcturus (McCluskey 1987; van Gent 1987). Ancient Chinese texts have been re-evaluated in detail by Jiang (1993), who concludes that all such reliable sources are consistent with Sirius being white [see also Tang (1991), who draws the same conclusion]. However, other historical evidence for a red Sirius seems both reliable and unambiguous [see Ceragioli (1995) for a critical, in-depth review]. Babylonian cuneiform texts, and the writings of classical Greco-Roman authors, including Cicero, Horace, Seneca and Ptolemy, refer consistently to Sirius as a red or reddish star. Seneca (c.ad 25) stated the redness of Sirius to be ‘deeper than that of Mars’. Ptolemy described Sirius as ‘hipokeros’ (reddish) in the Almagest (c.ad 150), and likened it in colour to Aldebaran, Antares, Arcturus, Betelgeuse and Pollux — stars that are, of course, known to be red today.

Physical explanations of the red Sirius anomaly may be grouped into two categories: intrinsic and extrinsic. Intrinsic hypotheses postulate a real change in the Sirius system over the past two millennia, of which the most widely discussed is the proposal that the white dwarf Sirius B was a red giant as recently as 2000 years ago. Extrinsic hypotheses are concerned with the possibility of transient reddening in an intervening medium through which the star is observed, such as might be caused by dust in the interstellar medium, or by particles in the Earth's atmosphere. Proposals based on terrestrial atmospheric extinction gain credence from the fact that ancient observers were much preoccupied with the heliacal rising and setting of Sirius, and therefore naturally tended to focus their attention on the star when it was low in the sky (Ceragioli 1996).

An intrinsic explanation of the red Sirius anomaly, if proven to be correct, would severely challenge existing theories of stellar evolution: the arguments are summarized in Section 2. The primary aim of this paper is to examine in detail the plausibility of the relevant extrinsic physical processes — interstellar or telluric extinction — as the cause of the anomaly (Section 3). It is concluded that only telluric extinction offers a physically reasonable explanation. The question of whether this result is consistent with the historical evidence is discussed in the final section.

2 The Evolutionary Status of the Sirius System

Sirius A and B form a unique pair. The 2.1-M_⊙ primary is one of the earliest known main-sequence stars to exist in a binary system containing a white dwarf, and the main-sequence progenitor of the 1.0-M_⊙ secondary must have been even earlier in spectral type [Holberg et al. (1998) propose B5, with a main-sequence mass of 6–7 M_⊙]. A possible third component has been proposed from time to time by various authors [see Benest & Duvent (1995) for a detailed orbital analysis and a review of the previous literature]. A conservative upper limit on the mass of the putative Sirius C is ∼0.1 M_⊙: such a low-mass object, should it exist, seems unlikely to have any direct relevance to the red Sirius anomaly [but see Bonnet-Bidaud & Gry (1991) for an alternative point of view].

As a red giant, Sirius B would have easily exceeded the current primary in luminosity. However, the hypothesis that a conventional red giant phase of Sirius B can explain the red Sirius anomaly suffers two fatal objections.

• (i)

  Sirius B must have undergone very substantial mass loss since leaving the main sequence. The lack of any detectable nebular matter in the vicinity of the Sirius system (Bruhweiler, Kondo & Sion 1986; Bonnet-Bidaud & Gry 1991) is inconsistent with core—envelope separation as recently as ∼2×10³ yr ago. The time-scale for dissipation of an ejected envelope such as a planetary nebula is at least two orders of magnitude higher.

• (ii)

  The current physical properties of Sirius B are highly inconsistent with recent core—envelope separation (Bruhweiler et al. 1986; Joss, Rappaport & Lewis 1987; Holberg et al. 1998). The predicted time-scale for the temperature, luminosity and radius of a newly exposed, degenerate ∼1-M_⊙ core to reach the currently determined values for Sirius B is ∼10⁷—10⁸ yr, enormously large compared with the time-scale of the red Sirius anomaly. If standard single-star models are applicable, Sirius B has been a white dwarf throughout human history.

These objections might be alleviated somewhat if significant interaction occurred within the Sirius binary system. Its orbital dimensions are comparable to those of a lobe-filling red giant with a 1-M_⊙ core, suggesting that at least the final stages of mass loss from Sirius B may have occurred via lobe overflow on to Sirius A (Joss et al. 1987). This might explain the lack of external nebulosity, but the current mass of Sirius A seems inconsistent with the notion that it was the recipient of much of the mass loss of its companion. Mass transfer might shorten appreciably the time-scale for transition from a red giant to a hot white dwarf. The second objection remains, however, as no known mechanism is capable of explaining the current surface temperature (∼25000 K) and other physical characteristics of Sirius B on time-scales much less than 10⁷ yr.

An alternative hypothesis postulates that a transient thermonuclear event on the surface of the white dwarf caused it temporarily to mimic the colours of a red giant (D'Antona & Mazzitelli 1978; Bruhweiler et al. 1986). Such events might be triggered by accretion or by thermal instability in the atmosphere. Accretion-induced ignition seems unlikely in the case of Sirius B, however, as its companion is well within its Roche lobe. Bruhweiler et al. (1986) argued that spontaneous ignition of the ¹²C(p, γ)¹³N reaction is plausible in hydrogen-rich white dwarf atmospheres with temperatures of ∼27000–30000 K, similar to that of Sirius B. This reaction is highly temperature-sensitive, suggestive of the possibility that thermal pulses induce transient flashes which lead to a short-lived (∼250 yr) expansion of the atmosphere, during which a quasi-red giant photosphere might appear. However, it seems unlikely that an event of this nature can occur without ejecting appreciable mass from the system (Cassisi, Iben & Tornambè 1998), in conflict with observations. I conclude that no intrinsic model appears to offer a convincing explanation of the red Sirius anomaly.

3 Reddening by an Intervening Medium

Small particles in the line of sight to a star produce reddening by wavelength-selective absorption and scattering. The light from the star is inevitably dimmed as well as reddened, and the ratio of total extinction to reddening is critically dependent on the nature of the particles, their composition, their shape, and, especially, their typical size. Dust grains large in comparison with the wavelength produce neutral extinction (extinction without reddening), whereas those of dimensions comparable to or smaller than the wavelength are efficient inducers of reddening. Three possible locations of dust in the line of sight to Sirius may be considered: the circumstellar environment of the binary system; the intervening interstellar medium; and the terrestrial atmosphere. However, the first of these can be discounted immediately: observations indicate a lack of infrared excess emission that would signal the presence of circumstellar dust (Aumann et al. 1984) — Sirius is clearly not a ‘Vega-type’ star with a remnant disc, and the absence of detectable nebulosity in the line of sight (Bruhweiler et al. 1986) suggests that no circumstellar material has been dissipated in the relatively recent past. In this section, I compare and contrast the merits of interstellar and telluric reddening as models for the red Sirius anomaly.

3.1 Interstellar extinction

The line of sight to Sirius is currently free of detectable quantities of interstellar dust. The mean colour index of the star in the standard Johnson photometric system is (B-V)=0.00±0.01 (SIMBAD data base), consistent with the intrinsic colour (B-V)₀=0.01 expected for an unreddened A1 V star (Schmidt-Kaler 1982); hence the formal value of the reddening is E(B-V)=(B-V)-(B-V)₀=−0.01±0.01. The possibility that Sirius might have been reddened in the past by the transient appearance of an interstellar cloud in the line of sight has been proposed independently by several authors (Stephanides 1976; Brecher 1979; Bruhweiler et al. 1986; Gry & Bonnet-Bidaud 1990).¹ The transit time-scale for a compact cloud of dimensions 0.01–0.1 pc, such as a Bok globule, might have been ∼1000 yr or less, assuming reasonable values for relative proper motions (Bonnet-Bidaud & Gry 1991). Bonnet-Bidaud & Gry argue that such an event has a non-negligible probability, given the known presence of 200 or more Bok globules within 150 pc of the Sun.

The crucial test of this hypothesis is the degree of dimming of the light of Sirius that accompanies sufficient reddening (Whittet 1977). The optical properties of interstellar dust are rather well-determined, so a quantitative evaluation can be made. Fig. 1 plots V magnitude against (B–V) colour, comparing Sirius with the other bright stars (Aldebaran, Antares, Arcturus, Betelgeuse and Pollux) noted in Ptolemy's Almagest as being red. To have a colour index comparable to the mean of the other five stars, Sirius would need to suffer reddening E(B–V)≈1.5 [Bonnet-Bidaud & Gry 1991 adopt E(B–V)≈1.0, but this value raises its colour index only to the value for Pollux, the least red of the comparison stars]. To convert from reddening, E(B–V), to total visual extinction, A_V, we must assume a value for the total-to-selective extinction, R_VA_VE(B–V). R_V depends physically on the optical properties of the dust, and is evaluated from the shape of the extinction curve in the long-wavelength limit [R_VE(V–λ)/E(B–V) for λ→∞; see Whittet (1992) for a comprehensive review]. The mean value of R_V for typical interstellar environments is approximately 3.05, and most lines of sight have values in the range 2.9–3.3; R_V can be higher (up to ∼5.5) in dense clouds where the grains grow by coagulation. Reddening versus extinction vectors for two representative values of R_V (mean diffuse interstellar medium: R_V=3.05; typical dark cloud: R_V=4.3; see Martin & Whittet 1990) are shown in Fig. 1. A simple calculation shows that, if Sirius were reddened to E(B-V)≈1.5 by a cloud containing ‘average’ interstellar grains, it would suffer extinction A_V≈4.6, i.e. it would be dimmed from the current prominence of V=−1.46 to the relative obscurity of V=3.14. For no assumed value of E(B-V) does Sirius become generally similar to the comparison stars in both magnitude and colour. The situation is worse if we assume a higher value of R_V (as might be appropriate to the dense globule postulated by Bonnet-Bidaud & Gry): the brightness of the star dips even lower for a given increase in (B–V).

Such levels of dimming seem unreasonable and incompatible with the historical evidence, as has been pointed out before (Bruhweiler et al. 1986; Ceragioli 1995). However, there is a more fundamental objection that does not seem to have been discussed previously in this context: the ability of the eye to perceive colour as a function of illumination. It is well-known that the human retina contains two types of photosensitive cell, rods and cones, of which only the cones give colour perception. However, the cones become inactive at low light levels as their sensitivity is only a few per cent of the peak sensitivity of the rods in the dark-adapted eye (e.g. Kitchen 1991). Colour vision thus declines with intensity and is lost entirely for naked-eye observations of stars fainter than about V=2. One can easily verify this fact with a simple observational test: whereas the colours of bright red stars such as Betelgeuse and Antares may be discerned with relative ease, somewhat fainter red stars appear colourless to the unaided eye.² I conclude that if Sirius had been sufficiently obscured by an interstellar cloud to have a colour index appropriate to a red giant, the accompanying decline in its brightness would have rendered its redness imperceptible to the human eye.

3.2 Telluric extinction

Extinction in the Earth's atmosphere arises primarily as a result of scattering by gaseous molecules and solid particles (aerosols). As these two populations have widely differing dimensions, they produce quite different spectral dependences: molecular-sized particles give strongly wavelength-dependent extinction (A∝λ⁻⁴) in the Rayleigh limit, whereas extinction caused by aerosols is less strongly wavelength-dependent and can be almost neutral (e.g. Tüg, White & Lockwood 1977; Walker 1987; Whittet, Bode & Murdin 1987). Volcanic activity can inject dust particles into the atmosphere that are small enough to affect stellar colours (e.g. Kilkenny 1995), but such events are too short-lived to be relevant to the interpretation of the red Sirius anomaly.

To investigate the effect of telluric extinction on the colour of Sirius, I adopt mean extinction coefficients for the Sutherland site of the South African Astronomical Observatory: k_B=0.27 and k_V=0.15 (Kilkenny 1995). These values are similar to those measured at other observatories sited at comparable altitudes (e.g. Flagstaff: Tüg et al. 1977). Although it is not customary to describe atmospheric extinction in terms of the parameter R_VA_VE(B–V), it is worthwhile to note that the adopted coefficients imply R_V=1.25, compared with 3.0 or more for interstellar extinction (Section 3.1). Both Rayleigh and aerosol components of atmospheric extinction scale in proportion to exp(-hH), where h is the altitude of the observer and H is the appropriate scaleheight: typical values of H for Rayleigh and aerosol extinction are 8 and 1.5 km, respectively (Walker 1987). At altitudes significantly below that of Sutherland (h=1.76 km), the relative contribution from aerosols will tend to be greater, resulting in higher extinction per unit reddening (i.e. R_V will increase). However, the Rayleigh component always dominates in a clear, fog-free atmosphere, so the difference should be small compared with the difference between the atmospheric and interstellar cases.

Fig. 2 shows the displacement of Sirius in the V versus (B-V) diagram as a function of airmass, calculated using the adopted extinction coefficients. The loci of other bright stars are shown for comparison, as in Fig. 1. Displacements for the comparison stars are shown for an airmass X≈sec z≈1.31, equivalent to a zenith angular distance of z≈40°. This is a good approximation if the comparison stars are observed at reasonably high altitude whilst Sirius is observed near the horizon.

It is immediately apparent from inspection of Fig. 2 that the telluric extinction vector is capable of displacing Sirius into a domain of the diagram where it has values of colour and brightness very similar to those of the comparison stars. An airmass of X=12.5 is needed to redden Sirius to (B-V)=1.5, and its visual magnitude is then dimmed only to V=0.42— still amply bright enough for its colour to be discerned with the unaided eye. Such large airmasses are reached when the star is within ∼5° of the horizon. The striking contrast between Figs 1 and 2 is caused by the difference in the typical size of particles responsible for visual extinction in each case: interstellar dust grains are comparable in size to the wavelength of visible light and produce roughly A∝λ⁻¹ extinction; the much steeper (A∝λ⁻⁴) dependence of atmospheric gases in the small-particle limit gives greater colour contrast per unit extinction.

4 Discussion and Conclusions

In view of the severe problems faced by evolutionary models for the red Sirius anomaly (Section 2), explanation in terms of an extrinsic effect should be favoured if a viable mechanism can be found. The main result of this paper is to show that one of the two possibilities, telluric reddening, is indeed a quantitatively plausible model. The caveat, of course, is that this mechanism only makes an appreciable difference to the colour of Sirius when it is low in the sky. Is it reasonable to suppose that the early observers would preferentially record the colour of Sirius whilst it was close to the horizon? The answer to this question, according to a thorough investigation of the historical evidence by Ceragioli (1996),³ is clearly ‘yes’. In several Mediterranean cultures, the local visibility of Sirius at heliacal rising and setting (whether it appeared bright and clear or dimmed) was thought to have astrological significance and was thus subject to systematic observation and intense interest.⁴ Thus Sirius, more than any other star, was observed and recorded whilst close to the horizon. Other contemporary cultures, such as Chinese, lacking this tradition, recorded Sirius only as white (Jiang 1993).

Why did Ptolemy, an experienced observer, list Sirius amongst red stars without qualification? The answer will probably never be known, but Ceragioli (1996) suggests two possible explanations. First, as an astrologer, Ptolemy may simply have been more concerned with the astrological significance of Sirius than with its usual physical appearance. Secondly, it has been shown that parts of the Almagest were probably not attributable to Ptolemy himself — tradition seems to have played an important role in shaping the text, and a tradition that emphasized ‘red Sirius’ may have been favoured over objective observation.

I conclude that physical evidence and historical evidence are now convergent on the view that the red Sirius anomaly was caused by atmospheric extinction arising when the star was observed near the horizon.

Acknowledgments

This research has made use of the SIMBAD data base, operated at CDS, Strasbourg, France. I am grateful to Polly-Alida Farrington for assistance with the literature search, and to an anonymous referee for helpful suggestions.

References