Download A physical interpretation of the `red Sirius` anomaly

Mon. Not. R. Astron. Soc. 310, 355±359 (1999)
A physical interpretation of the `red Sirius' anomaly
D. C. B. Whittetw
Department of Physics, Applied Physics & Astronomy, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
Accepted 1999 July 1. Received 1999 May 24; in original form 1998 November 13
A B S T R AC T
The controversy over whether the brightest star, Sirius (a 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.
Key words: history and philosophy of astronomy ± atmospheric effects ± stars: evolution ±
stars: individual: Sirius ± dust, extinction.
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,
w
E-mail: [email protected]
q 1999 RAS
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 GrecoRoman 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
356
D. C. B. Whittet
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 T H E E V O L U T I O N A R Y S TAT U S O F T H E
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 (,25 000 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
12
C(p, g )13N reaction is plausible in hydrogen-rich white dwarf
atmospheres with temperatures of , 27 000±30 000 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 & TornambeÁ 1998), in conflict with observations. I conclude
that no intrinsic model appears to offer a convincing explanation
of the red Sirius anomaly.
3 R E D D E N I N G B Y A N I N T E RV E N I N G
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 2 V† ˆ 0:00 ^ 0:01
(SIMBAD data base), consistent with the intrinsic colour
…B 2 V†0 ˆ 0:01 expected for an unreddened A1 V star (SchmidtKaler 1982); hence the formal value of the reddening is
E…B 2 V† ˆ …B 2 V† 2 …B 2 V†0 ˆ 20:01 ^ 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 & BonnetBidaud 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
1
Prior discussion of this topic by Stephanides (1976) and Whittet (1977)
appears to have been overlooked by subsequent authors.
q 1999 RAS, MNRAS 310, 355±359
The `red Sirius' anomaly
Figure 1. Plot of visual magnitude V against colour index …B 2 V† for
Sirius and five other stars described by Ptolemy as reddish in colour. Data
are from the Bright Star Catalogue (Hoffleit & Jaschek 1982). The
diagonal arrows show displacements in magnitude and colour that would
occur if Sirius were to pass behind an interstellar cloud containing either
`normal' …RV ˆ 3:05† or `dark cloud' …RV ˆ 4:3† interstellar grains. Note
that Sirius becomes significantly dimmer than the other stars before it
acquires a similar degree of redness.
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 welldetermined, so a quantitative evaluation can be made. Fig. 1 plots
V magnitude against …B 2 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 2 V† < 1:5 [Bonnet-Bidaud
& Gry 1991 adopt E…B 2 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 2 V†, to total visual
extinction, AV, we must assume a value for the total-to-selective
extinction, RV ˆ AV =E…B 2 V†. RV depends physically on
the optical properties of the dust, and is evaluated from the
shape of the extinction curve in the long-wavelength limit
[RV ˆ E…V 2 l†=E…B 2 V† for l ! 1; see Whittet (1992) for a
comprehensive review]. The mean value of RV for typical
interstellar environments is approximately 3.05, and most lines
of sight have values in the range 2.9±3.3; RV 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 RV (mean diffuse interstellar medium: RV ˆ 3:05; typical dark
cloud: RV ˆ 4:3; see Martin & Whittet 1990) are shown in
Fig. 1. A simple calculation shows that, if Sirius were reddened to
E…B 2 V† < 1:5 by a cloud containing `average' interstellar
grains, it would suffer extinction AV < 4:6, i.e. it would be
dimmed from the current prominence of V ˆ 21:46 to the relative
obscurity of V ˆ 3:14. For no assumed value of E…B 2 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 RV (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 2 V†.
q 1999 RAS, MNRAS 310, 355±359
357
Figure 2. As Fig. 1 but for telluric extinction. The long diagonal arrow
shows the displacement of Sirius as it approaches the horizon, assuming
standard atmospheric extinction coefficients from Kilkenny (1995). The
short arrows show the displacements of the comparison stars for a constant
airmass of X ˆ 1:31.
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 ˆ 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 …Al / l24 †
in the Rayleigh limit, whereas extinction caused by aerosols is less
strongly wavelength-dependent and can be almost neutral (e.g.
TuÈg, 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
2
b And (V ˆ 2:06; B 2 V ˆ 1:58) is a good test case.
358
D. C. B. Whittet
Sirius, I adopt mean extinction coefficients for the Sutherland site
of the South African Astronomical Observatory: kB ˆ 0:27 and
kV ˆ 0:15 (Kilkenny 1995). These values are similar to those
measured at other observatories sited at comparable altitudes (e.g.
Flagstaff: TuÈg et al. 1977). Although it is not customary to
describe atmospheric extinction in terms of the parameter
RV ˆ AV =E…B 2 V†, it is worthwhile to note that the adopted
coefficients imply RV ˆ 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…2h=H†, 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 ˆ 1:76 km†,
the relative contribution from aerosols will tend to be greater,
resulting in higher extinction per unit reddening (i.e. RV 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 2 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 < 408. 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 ˆ 12:5 is needed to redden Sirius to …B 2 V† ˆ 1:5,
and its visual magnitude is then dimmed only to V ˆ 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 ,58 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 Al / l21 extinction; the much steeper
…Al / l24 † 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
3
See also Ceragioli (1992) for a popular account of this work.
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.
AC K N O W L E D G M E N T S
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
Aumann H. H. et al., 1984, ApJ, 278, L23
Benest D., Duvent J. L., 1995, A&A, 299, 621
Bonnet-Bidaud J. M., Gry C., 1991, A&A, 252, 193
Brecher K., 1979, in Brecher K., Feirtag M., eds, Astronomy of the
Ancients. MIT Press, Cambridge, Massachusetts, p. 91
Bruhweiler F. C., Kondo Y., Sion E. M., 1986, Nat, 324, 235
Cassisi S., Iben I., TornambeÁ A., 1998, ApJ, 496, 376
Ceragioli R. C., 1992, Sky Telesc., 83 (June), p. 613
Ceragioli R. C., 1995, J. Hist. Astron., 26, 187
Ceragioli R. C., 1996, J. Hist. Astron., 27, 93
D'Antona F., Mazzitelli I., 1978, Nat, 275, 726
Gry C., Bonnet-Bidaud J. M., 1990, Nat, 347, 625
Hoffleit D., Jaschek C., 1982, Bright Star Catalogue, 4th edn. Yale
University Observatory, New Haven
Holberg J. B., Barstow M. A., Bruhweiler F. C., Cruise A. M., Penny A. J.,
1998, ApJ, 497, 935
Jiang X., 1993, Chin. Astron. Astrophys., 17, 223
Joss P. C., Rappaport S., Lewis W., 1987, ApJ, 319, 180
Kilkenny D., 1995, Observatory, 115, 25
Kitchen C. R., 1991, Astrophysical Techniques, 2nd edn. IoP Publishing,
Bristol, pp. 2±7
McCluskey S. C., 1987, Nat, 325, 87
Martin P. G., Whittet D. C. B., 1990, ApJ, 357, 113
Schlosser W., Bergmann W., 1985, Nat, 318, 45
Schmidt-Kaler Th., 1982, in Schaifers K., Voigt H. H., eds, Landolt±
BoÈrnstein New Series. Springer-Verlag, Berlin, Group IV, Volume 2b,
p. 1
Stephanides T., 1976, J. Br. Astron. Assoc., 87, 93
Tang T. B., 1986, Nat, 319, 532
4
Visibility differences would have arisen as a result of variations in the
aerosol content of the atmosphere (Section 3.2) and hence in the amount of
neutral extinction.
q 1999 RAS, MNRAS 310, 355±359
The `red Sirius' anomaly
Tang T. B., 1991, Nat, 352, 25
TuÈg H., White N. M., Lockwood G. W., 1977, A&A, 61, 679
van Gent R. H., 1987, Nat, 325, 87
van Gent R. H., 1989, Observatory, 109, 23
Walker G., 1987, Astronomical Observations: An Optical Perspective.
Cambridge Univ. Press, Cambridge, pp. 47±48
q 1999 RAS, MNRAS 310, 355±359
359
Whittet D. C. B., 1977, J. Br. Astron. Assoc., 87, 523
Whittet D. C. B., 1992, Dust in the Galactic Environment. IoP Publishing,
Bristol, pp. 70±71
Whittet D. C. B., Bode M. F., Murdin P., 1987, Vistas Astron., 30, 135
This paper has been typeset from a TEX/LATEX file prepared by the author.