Download Betelgeuse: an unauthorized biography

Betelgeuse
Betelgeuse: an
unauthorized biography
B
etelgeuse owes its name to Arab
astronomers. Due to translation error,
the original Arabic yad al-jawza – “hand
of Orion” – eventually became corrupted to bat
al-jawza and then Bedelgeuze – the somewhat
more unfortunate “armpit of Orion” (Heuter
1986), a position which it occupies in some
colourful constellation maps (e.g. Barlow
1790). Rather more picturesque is “The front
leg of the white-belted sheep” (Burnum 1978).
The conventional “α Ori” hints at greater
brightness in the past: it is currently outshone
by about 0.25 magnitudes in the visible by
Rigel, β Ori, although exceptions are known to
the rule of listing stars in constellations by
decreasing apparent brightness. It is HD 39801,
HR2061, classified as spectral type M2 Iab or
M1-M2 Ia-Iab (Keenan and McNeil 1989).
Betelgeuse is a Long Period Variable. The visible magnitude has been observed to vary by
about 0.6 to 1.1 (with occasional smaller and
larger – 1.2 mag – excursions) and the radial
velocity of individual spectral lines can vary by
up to about 10 km s–1. The variations appear
random on timescales of 100 to 400 days, but
are superimposed on a clear period of 5.78
years (Goldberg 1984), to which Dupree et al.
(1987) have added a 420-day period. The position angle of linear polarization of direct light
from the star also changes on a ~2/3 year
timescale (Hayes 1984, Tinbergen et al. 1981).
Changing aspects of giant convective elements
(Stothers and Leung 1971) or other surface features might be responsible for short-term variation, as might veiling due to the formation of
dust. Bester et al. (1996) attribute a steep
decline in magnitude, and changes in the interferometric infrared fringe pattern, in late 1994
to dust formation close to the star (0.1 seconds
of arc – within a few stellar radii of the surface
– see below). As well put by Goldberg (1984)
“it is as though gaseous matter were ejected
from the star, then diffused outward and condensed into grains, which became optically
thick at visible wavelengths” – something that
he thought had already happened at least three
times in the 60 years up to 1984. Bester et al.
argue that temperature changes are responsible
for most of the visible variations from
1989–1995, since the 11.15 µm magnitude was
comparatively constant – implying little significant change in radius. But pulsation of the star
December 1997 Vol 38 Issue 6
Mike Edmunds delves into
Betelgeuse, reviewing its
birth, life and death.
complicated radial velocity behaviour (Goldberg 1979, Boesgaard 1979) implying both
inflow and outflow with radial velocities of
tens of km s–1 . Betelgeuse has flared in radio
wavelengths during the mid-1960s (Newell and
Hjellming 1982), but I am not aware of any
reports of major flares since then.
Distance and bolometric magnitude
s one of the brightest stars in
the sky, and one of the very few
whose surface can be resolved by
current interferometric techniques,
Betelgeuse is a much-studied
object. But how much is actually
known about this huge, cool
supergiant and its life history? I
attempt a brief review of this
complex and fascinating star,
touching on its vital statistics,
both fixed and variable.
A
is also a possibility. The classic period-mean
density timescale 1/G
is of order 100 days,
while Fox and Wood (1982) give Po = 386 days,
P1 = 178 days for the fundamental and first
overtone radial pulsation periods in a model
whose parameters (solar chemical composition,
16 M , L/L = 5 ×104) are very close to those of
Betelgeuse. There is no obvious pulsation mode
for the 5.78 year (2111-day) period.
Variations in ultraviolet emission line fluxes
and wavelength shifts correlate with shortterm visual brightness variations (Dupree et al.
1987, Joras 1989), implying a causal link
between photosphere and chromosphere –
such as pulsation that might lead to shocks and
heating of the chromospheric regions. Emission lines from these regions certainly show
The Hipparcos database gives the parallax as
7.63 ± 1.64 mas. This would formally give a
distance of 131 pc, but assuming that the errors
are Gaussian implies a most likely distance of
138 pc, and we adopt 138 ± 30 pc from the
68% probability that the distance lies between
108 and 165 pc. This is rather nearer than the
200 pc typically adopted in modern literature.
The Hipparchos solution is a stochastic one,
implying some variability problems; this might
be attributed to the wax and wane of surface
features causing variation (of a few mas) in the
centroid of the disk. But it would be particularly bad luck if this caused systematic errors.
Between the approximate extremes 0.1 to
1.2, we take mV = +0.5 as a representative value
for the apparent visual magnitude. A plot of
the bolometric corrections for K and M supergiants given by Flower (1977), Lee (1970) and
Elias et al. (1985) suggests values of –1.27,
–1.09, –0.9 for effective temperatures Teff of
3600 K, 3700 K, 3800 K respectively, with
probable errors around ±0.05. For our chosen
Teff = 3600 ± 100 K (see below), we therefore
adopt –1.27, although the bolometric correction implied by di Benedetto’s (1993) values
would be –0.2 magnitudes brighter. The
extinction to the star is not very well determined, but the careful review in the appendix
of Lambert et al. (1984) suggests 0.3 < AV < 0.8,
and we adopt 0.5 with them. The result is
Mv = –5.7, Mbol = –7.0 ± 0.5, equivalent to
log(L/L)=4.69±0.2 for solar Mbol of 4.75. The
latest in a series of flux measurements and
interpolations (Dyck et al. 1974, 1992, 1996)
gives a total at Earth of 1.15 × 10–11 W cm–2,
(which may only vary by a few percent, Dyck
et al. 1974), assuming a very similar extinction
(0.48), giving log(L/L) = 4.84 ± 0.16. We use
log(L/L) = 4.8 ± 0.2.
The effective temperature of Betelgeuse has
been a subject of considerable debate. Formally, this should be defined by the black-body
27
Betelgeuse
relation L = 4πσR2*Teff4 where L is the luminosity and R* is the stellar radius. In practice, several methods may be applied, including the
“infrared flux” method. This relies on knowledge of the angular diameter α of the star and
the flux F of its radiation at Earth. The distance to the star cancels to give Teff = 4F/σα1/2.
The problem with the extended atmosphere
of a cool supergiant is that the angular diameter depends on wavelength. Infrared angular
diameters for Betelgeuse (e.g. 56 mas at 11 µm
from long-baseline interferometry, Bester et al.
1996) are larger than the blue (e.g. 45 mas at
405 nm from speckle, Balega et al. 1982,
42 mas for a central core with a halo, from the
compilation of Cheng et al. 1986), and may
also be larger at wavelengths of molecular
bands formed high in the photosphere. Such
differences of tens of percent in apparent
radius are indeed seen in spherical-geometry
model atmospheres (Scholz 1985, Scholz and
Takeda 1987), and are at least partially due to
the decrease in limb darkening in the red.
The observational situation is made even
more complicated by the dependence of
derived angular diameters on what model is
assumed for limb darkening – certainly significant for Betelgeuse at optical wavelegths – and
on the presence or absence of surface structures like hot or cool spots. Early measurements were also apparently confused by scattering from a circumstellar dust shell (Tsuji
1978), and an early compilation by White
(1980) even suggests an 18% variation in
diameter over the 5.8 year photometric variability period. With the advent of optical aperture synthesis (Burns et al. 1997) and the higher resolution of 8 m telescopes, a better picture
of the size of the “surface” (or, rather, “surfaces”!) of the star should emerge – but such
information may be accurate only for a particular wavelength and epoch. Mean values will
emerge, but it is clearly dangerous to try and
define a single effective temperature from the
formula given above. A modest change of α
from 56 mas to 51 mas would raise the derived
effective temperature by 180 K. We are therefore not too disturbed by a range in Teff derived
by these methods from 3190 K (Bester et al.
1996) to 3605 K (Dyck et al. 1996). Photometric comparisons suggest 3620 ± 90 K (Di
Benedetto 1993), some atmospheric analyses
and fluxes 3900 ± 150 K (Tsuji 1976)
3800 ± 100 K (Kodaira et al. 1979). In a molecular line analysis, Lambert et al. (1984)
adopted 3800 ± 100 K, which gave a sum of C,
N and O of close to solar. The fit of this sum is
not very sensitive to temperature, but by
3600 K, the implied oxygen abundance is a little (–0.2dex) lower than might be expected for
a star that formed fairly recently out of the
interstellar medium, and perhaps too low to be
accounted for by the effects of CNO cycling.
28
As a reasonable compromise estimate, we
adopt Teff = 3600 ± 200 K, log Teff = 3.56 ± 0.3,
but note that this may be too low for the effective temperature used in fitting photospheric
models for abundance analysis.
As will be apparent from the discussion
above, uncertainty about the definition of
angular diameter, as well as the uncertainty in
the distance estimate, makes a radius determination difficult. Formally, 42 mas implies
650 R and 56 mas implies 950 R. For
50 ± 5 mas, and distance errors of 30 pc, the
radius is 780 ± 20 R. Our adopted effective
temperature of 3600 is not entirely consistent
with this since a black-body estimate with the
adopted luminosity of log (L/L) = 4.8 gives the
lower value 3275 i.e. log Teff = 3.52. The best
compromise seems to be to adopt a nominal
radius of 650 R (i.e. 42 mas angular diameter,
a value which interestingly has also recently
been obtained in K-band fibre-linked interferometry, Perrin et al. 1997). This will give
Teff = 3590 K, consistent with our adopted Teff .
Mass and evolutionary status
Despite the uncertainties, Log (L/L) = 4.8 ± 0.2,
Log Teff = 3.57+0.03
–0.05 serve well enough to place
the star on evolutionary tracks. The solarcomposition models of Schaller et al. 1992,
which include mass loss, place it (see figure 1)
squarely in the red supergiants, with an initial
(i.e. main sequence) mass 15+2
–5 M, the 15 M
corresponding (with mass loss rates from
Schaller et al.) to about 13.7 M now. This
mass, combined with a radius of 780, 700 or
640 R implies a surface gravity of
log g = –0.20, –0.11 and –0.04 respectively, very
much in line with the value 0.0 (with probable
errors around ±0.3) assumed in spectrographic
analysis (e.g. Lambert et al. 1984, Tsuji 1979a).
The detailed evolution of the star, according to
the Schaller et al. tracks, is rather dependent on
the mass. At 15 M the star is undergoing central helium burning, ascending the supergiant
branch without looping away across the H~R
diagram and back as an asymptotic giant
branch star, before central carbon burning.
For the lower masses (i.e. ≤12 M) loops in
evolution are possible, and even for 15 M
under different assumptions about opacities etc
(Bressan et al. 1993). Garcia-Berro and Iben
(1994) and Ritossa et al. (1996) follow the evolution and structure of a 10 M AGB star in
considerable detail, although their model only
reaches log (L/L) = 4.37, rather short of our
adopted log (L/L) = 4.8 ± 0.2, which suggests
that a lower mass limit of 12 M might be a
better guess. We adopt 15+2
–3 M. Betelgeuse’s
main sequence lifetime as a B0–B1 V star (for
15 M) would be 1.2 × 107 years from the
Schaller et al. tracks, and a total of
1.2 × 106 years as a giant. For 12 M the main
sequence lifetime is 1.6 × 107 years, and
1.7 × 106 years as a giant – although in the
12 M case its luminosity suggests that the star
must be very near the end of its asymptotic
giant branch life, and the whole AGB phase
may last less than 105 years. Our adopted age
7
for Betelgeuse is 1.2+0.5
–0.2 × 10 years.
Tracing back the proper motion on the sky
gives a path that lies right across the Ib and Id
OB associations of Orion (Blaauw 1991). But
Betelgeuse cannot have come from the Orion
star formation region. The timescale is wrong
– it passed over the area some 1 to 2 × 106 years
ago, long after its birth. A late ejection is
impossible, since its radial velocity relative to
Orion is too small to allow it to cover the 300
or so parsecs between the associations and its
present position in the available time.
There seems little need to question the
assumption of approximately solar chemical
composition, although no full analysis including the iron group has been carried out. Lambert et al. 1984 suggested an overall slight
metal richness of +0.1 dex relative to the Sun
and CNO abundances relative to the Sun of
[C] = –0.4, [N] = +0.6, [O] = –0.2, where
sun sun
[A] = Log10(nAstar⁄nstar
H ) – Log10(nA ⁄n H ) for element abundances n by number. Realistic errors
on these abundances must be at least ± 0.2 dex,
but the significantly decreased carbon and
enhanced nitrogen are consistent with the mixing to the surface (by the deep convective structure of the giant) of material that has undergone CN cycling, i.e. the hydrogen to helium
reaction chains that would be expected as the
main energy source for most of the life of a star
of this mass. There was some initial controversy over the 12C/13C isotope ratio (measured
from relative strengths of CN or CO molecular
bands), but a value of about 6 ± 1 seems to
have been established both in photospheric
material (Hinke et al. 1976) and in cool circumstellar material (Bernat et al. 1979). This
low value presents some problems when compared to the 17–20 expected from stellar evolution calculations (e.g. Ritossa et al. 1996, El
Eid 1994). Oxygen isotope ratios (Harris and
Lambert 1984) may show some rotationallyinduced mixing of CNO-cycle material to the
surface (Garcia–Berro and Iben 1994).
Photosphere and chromosphere
Models relevant to the photosphere are the
Teff = 3600 and 3800, log g = 0.0 models of
Brown et al. (1989) and model B1 of Wanatabe
and Kodaira (1978). The probable (azimuthal)
inhomogeneity of the atmosphere implies that
multi-component models are needed (cf the
models of Nordlund and Dravins 1990) but
with perhaps only a few distinct regions. The
derived microturbulence in the photosphere is
not very high (~3 km s–1) but this would need
re-interpretation in multi-component models
(cf Dravins and Nordlund 1990) and increases
December 1997 Vol 38 Issue 6
Betelgeuse
3
10 000
9 M
–4
7 M
3
2
5 M
4 M
04 07 09 B0 B1 B2 B3
100
B8
1011
1
2
1014
1015
1016
10
102 r/R 103
*
104
multiple scattering in the stronger transition
blocks the exit of radiation, and the energy
“leaks” out through the weaker transition
(Carpenter and Robinson 1997, Jordan 1967)
1 arcsecond
–0.2
1013
1012
0.5 pc
r (m)
4.8 4.7 4.6 4.5 4.4 4.3 4.2 4.1 4.0 3.9 3.8 3.7 3.6 3.5
log Teff
December 1997 Vol 38 Issue 6
0.5 1.0
dust shells
1 AU
A0 A3 A7 F1 F8 G2
rapidly in the upper regions (9.9 ± 2.0 km s–1
from the OH line, Hutchinson 1971) and in
the chromosphere (UV emission lines have
FWHM ~24 ± 5 km s–1, Carpenter et al. 1974).
It seems appropriate to adopt de Jager’s
(1980) definition of the chromosphere as “an
envelope with T > Teff , which is optically thin
in the greater part of the continuous radiation,
and optically thick in at least some of the
strong lines”. Betelgeuse’s chromosphere was
first identified from emission lines, or emission
line cores, showing variable, multi-velocity
components (e.g. Goldberg 1979), with both
up- and down-flows (e.g. Boesgaard 1979). Its
existence has been amply confirmed at ultraviolet wavelengths in emission lines and continuum, for example the extensive Hubble
Space Telescope observations (Carpenter et al.
1994, Brandt et al. 1995, Carpenter and
Robinson 1997) showing a UV spectrum
rather atypical of late-type stars. At radio
wavelengths the chromosphere is seen as a fine
fit to free-free emission at a temperature of
order 104 K (Newell and Hjellming 1982),
which dominates over the Rayleigh–Jeans tail
of the photosphere below about 90 GHz.
Extended spatially irregular Hα emission has
been seen out to 95 mas (4.5 R*) in speckle
observations (Hebden et al. 1987), and it is
surprising that more high-resolution imaging
in this line has not yet been reported. There
have been several theoretical or semi-empirical
models of the chromosphere (e.g. Basri et al.
1981, Hartmann and Avrett 1994, Skinner et
al. 1987, 1997), with the temperature rising
from a photospheric minimum around 2710 K
at a Rosseland mean opacity of 10–4 up to a
maximum of about 8000 K near 3 R* , and
then declining outwards. A schematic illustration of the gas temperature as a function of distance outwards is given in figure 3. The
chromosphere is extended, with UV observations showing 108 mas (FWHM*, Gilliand and
Dupree 1996), extent 125 mas (i.e. out to
3 R*) and 6 cm radio an extent of 0.36, out to
T α r 1/2
10
–2
B5
chromosphere
1000
photosphere
–6
gas temperature (K)
4
–8
25 M
20 M
15 M
12 M
Mbol
log L/ L 5
stellar
interior
dust shell
bow shock
1
Dusty envelope and mass loss
0.0
0.2
0.4
0.6
0.8
1 The position of Betelgeuse in the HR
diagram, with the stellar evolution tracks of
Schaller et al. 1992.
2 A 6 cm wavelength radio emission map of
the chromosphere of Betelgeuse from the
MERLIN array. (Courtesy of R J Davies.)
3 Schematic representation of the average
gas temperature as a function of radius from
the photosphere to the edge of the envelope.
(Freely adapted from Hartmann and Avrett
1984, Rodgers and Glassgold 1991.)
8.5 R* (Skinner et al. 1997 and figure 2). Large
spatial inhomogeneity exists in both wavelength regions, in roughly the same direction.
Judge and Stencel (1991) have estimated the
chromospheric energy losses, but the heating
mechanism remains controversial. Possible
schemes for transporting energy from below
the photosphere and to the chromosphere or
beyond, to replace energy losses and initiate
mass loss include: (i) Alfvén waves (Hartmann
and Avrett 1984), (ii) acoustic waves (Pjipers
and Hearn 1989), (iii) stochastic interaction of
shocks in waves of periods of order 12 days
(Cuntz 1997, Cuntz and Dorfi 1997).
Interesting phenomena are observed in the
chromosphere. A comparable or greater
strength of an emission line (e.g. OI) can occur
for the weaker transition that shares an upper
energy level with a much stronger transition.
This happens because the optical depth due to
Betelgeuse is losing mass at about 1 to
2 × 10–6 M yr–1, and we adopt 1 × 10–6. This
estimate is based on rough adjustments of various observational estimates to a distance of
138 pc (HI, Bowers and Knapp 1987; CI, Huggins et al. 1994; CO, Knapp et al. 1980, 1982;
KI, Rogers and Glassgold 1991, Guilain and
Mauron 1996). The mass loss rate is exactly
what is expected for the star’s luminosity and
temperature in the compilation of stellar mass
loss rates by de Jager et al. 1988. The details of
the mass loss mechanism are not established,
although many models invoke the effect of
radiation pressure on newly-formed dust to
drag the gas outwards. For dust formation, the
spatial or temporal inhomogeneity may be crucial. Nucleation of condensates and subsequent
growth of dust cannot happen if the temperature (effectively that of the dust grain, strongly
influenced by its radiation balance) is too high.
Draine (1981) suggested a minimum radius of
1.8 R* for nucleation. Plausibly a large area of
lower surface temperature on the disk, and/or
the sequence pulsation → shocks → density
increase → grains → radiation pressure → wind
(cf Mira models, Bowen 1988), may lead to
periodic or irregular conditions favouring dust
formation. Indeed, it may be difficult to understand the formation of dust as close as 0.1
(reported by Bester et al. 1996) without considerable spatial inhomogeneity.
Overall, the envelope has gas density falling
approximately as r–2 (as would be expected in
a constant velocity wind outflow; Skinner et al.
1997, Rogers and Glassgold 1991, Tsuji
1979b), with temperature falling as shown in
figure 3. The gas-to-dust mass ratio in the
envelope implied by its infrared emission is not
the typical interstellar value of about 100, but
29
Betelgeuse
much higher, perhaps 1000–2000 (Bowers and
Knapp 1987, Skinner et al. 1997). This is not a
chemical abundance effect, for example the
carbon abundance as measured by the CI
609 µm emission line (Huggins et al. 1994) is
compatible with the photospheric value, which
is only slightly lower than solar. The low dust
fraction most likely reflects nucleation and
growth conditions. Enhanced shells of gas have
been seen at 0.5 (24 R*) and 1.0 (48 R*) in
11 µm radiation (Bester et al. 1996; and Skinner et al. 1997 give a list of other detections).
The characteristic 9.7 µm dust emission feature is prominent, and possibly variable. Cool
shells are also seen in molecular CO absorption, with rotation temperatures of 500 K
(Carpenter et al. 1994) and 200+50
–10 K, 70 ± 10 K
(Bernat et al. 1979), the latter two being seen
at the outflow velocities of 11 and 18 km s–1
respectively that are also seen in the KI 769 nm
line (Goldberg et al. 1977).
Resonance line scattering in Na I extends out
to at least 17 (810 R*, Mauron 1990) and in
KI out to at least 63 (3000 R*, Mauron et al.
1984), again indicating an r–2 density structure.
Polarization is seen in dust-scattered continuum light (in optical B band out to 90,
4300 R*, McMillan and Tapia 1978). The variation of the direction of position vector of linear polarization of light directly from the star
(or its very close environs) on a ~2/3 year
timescale (Hayes 1984) might be due to illumination changes, rather than structural ones,
although “hot spots” on the surface may not
cause big enough polarization changes (Doherty 1986). We note in passing that any significant variation of properties due to the rotation
of the surface of the star cannot occur on
timescales of less than about 550 days (based
on 1/6 rotation with vrot < 10 km s–1 from line
widths, and note that more likely rotation of
<2 km s–1 implies variation timescales of longer
than 2700 days. An outward propagation with
speed 15 km s–1 (a typically quoted outflow
velocity) gives a timescale of order 350 days in
moving through a distance of 1 R* .
The outer edge of the envelope is visible
(Noriega-Crespo et al. 1997) in IRAS 60 µm
and 100 µm maps as a shell of 1 thickness and
about 6 radius (corresponding to 17 000 R*,
0.26 pc), with a bow shock in the direction of
Betelgeuse’s proper motion through the interstellar medium. Scaling Noriega-Crespo et al.’s
mass estimate from the 60 µm flux to a distance of 138 pc, and using a gas-to-dust ratio
of 1000 rather than 10, gives a shell mass of
about 0.15 M . This could rise considerably if
their assumed temperature is too high: some
models imply much lower temperatures in the
outer envelope (Rogers and Glassgold 1991).
Betelgeuse shows no evidence of an X-ray
corona, with (X-ray flux/visible flux) ≤ 10–6.8,
which may be compared with 10–1 –10–3 for M
30
dwarfs and 10–4.5 for solar-type dwarfs (Vaiana
et al. 1981). This is consistent with its position
in the HR diagram on one side of the apparent
dividing line between stars with and without
coronae (Haisch et al. 1991). Whether significant mass loss quenches corona formation, or
whether the respective generation mechanisms
for coronae and strong mass loss require very
different conditions, is still not clear.
The companion
“As I was going up the stair
I met a man who wasn’t there.
He wasn’t there again today.
I wish, I wish he’d stay away.”
(Means 1953)
This light verse seems rather appropriate for
the elusive companion(s) of Betelgeuse.
Although early classification as a spectroscopic binary was probably due to the complex
variable chromospheric features, subsequent
observations are ambiguous. A companion
0.4–0.5 away and ∆m = 3.5–4 was seen in
rotation shearing interferometry (Roddier et al.
1986), and speckle observations gave similar
results (Karovska et al. 1986, 1988), with a
possible second, closer, companion. Christou et
al. 1978 saw no companion of ∆m ≤ 4.5, and
none has been seen in the Non-Redundant
Masking (NRM) observations by the Cambridge group (probable dynamic range ∆m ~ 4).
A problem with the Karovska et al. identifications is the extremely high mass that their
deduced periods would imply for the system,
and the lack of any identifiable UV continuum
or spectra feature from the companion (Carpenter et al. 1984). But there is no a priori reason why Betelgeuse should not have a companion – indeed two of the other best-observed
nearby red giants do; α Sco (M1.5 Iab) has a
7–8.5 M B2.5 V star companion (∆m = 4) 2.9
away, and Mira (M2-M7 III, and much less
massive than Betelgeuse) has a probable accreting white dwarf 0.6 away, seen in speckle
observations (Karovska et al. 1993) and by
HST (Karovska et al. 1997).
Adaptive optics observations in January
1996 in a narrow band at 2.10 µm with the
Come-On Plus system at the European Southern Observatory (Esslinger and Edmunds
1997) hint at a bright feature ∆m = 5 ± 0.5 at a
distance of 0.5 from Betelgeuse, although it is
very difficult to discount the possibility that it
is a residual artefact of the adaptive optics correction. But the position angle corresponds
almost exactly to that of the “hot spot” seen in
the UV chromospheric image by the HST
(Gilliland and Dupree 1996), especially if
slightly corrected for the ten-month difference
in observational epoch based on the most likely period of 84 ± 9 years derived from combining the adaptive optics observations with
Karovska et al.’s. The implied system mass
(Esslinger 1997), assuming a circular, face-on
orbit is 16 ± 8 M. The Hipparchos propermotion errors probably limit the motion of
Betelgeuse and hence the centre of mass to a
few mas, implying the companion must be of
low mass. If cool, at ∆mK ~ 5 the star would
have to be a red giant – but a faint and less
massive red giant would have to be much older
than Betelgeuse. If hot it would have to be a
main-sequence star of perhaps 4–5 M , but
then the lack of evidence in the ultraviolet is
strange (recall that the extinction is only
AV 0.5 to Betelgeuse) unless the object is fortuitously hiding behind a thick dust shell. Also,
the mass would be rather high for the limit on
the proper motion of the centre of mass.
The question of the companion’s existence can
certainly soon be settled by coronographic adaptive optics observations. It remains an important
issue, since its presence would certainly affect
chromosphere, envelope and variability.
Surface features
The surface of angular diameter 42 mas is only
just resolvable in the visible with a 4 m telescope (1.2λ/D ~ 31 mas at 500 nm), but use of
NRM techniques by the Cambridge group has
shown evidence for two or three bright spots
contributing up to ~25% of the total flux,
varying on a timescale of ≤ 9 months (Tuthill et
al. 1997, Wilson et al. 1992, Busher et al.
1990). Bispectrum phase reconstruction of fullaperture speckle patterns (Klückers et al. 1997)
strongly confirms the presence of significant
spatial inhomogeneity, although not matching
in detail the contemporaneous NRM maps of
Wilson et al. 1997, an example of which is
shown in figure 4. The Wilson et al. maps have
been confirmed by independent observations
by Marson 1997, Marson et al. (1998). The
first maps with the Cambridge Optical Aperture Synthesis Telescope (COAST; Burns et al.
1997) find no spots at a 4% flux level. All
these observations may not necessarily be in
conflict. Apart from time variability, the different methods used are most sensitive to different spatial scales, and the detectability of a
spot depends strongly on its position on the
disk – and this detectability variation may be
different for the different imaging methods.
For single aperture methods the advent of the
4 times area resolution of the 8 m telescopes
should help considerably, and optical longbaseline interferometry is only just beginning.
Apart from the promise as the target of
largest angular size (now overtaken by R Dor,
Bedding et al. 1997) the search for surface features on Betelgeuse was greatly spurred on by
the seminal paper of Schwarzschild (1975) who
argued that the vertical size of convective elements in the Sun was about the thickness of the
region in which convective velocities were high.
This is only a few hundred kilometres, but scalDecember 1997 Vol 38 Issue 6
Betelgeuse
ing to a model for T= 3700, log g = –0.15 (comparable to Betelgeuse) suggested a size of
6 × 1010 m, and if the horizontal scales are of
order 3 times the vertical, one might expect
2 × 1011 m, i.e. of order R*/2 for Betelgeuse.
Stothers and Leung (1971) had previously
argued that the convective elements would be
as large as the convection zone – which in a
highly convective giant could approach R* . It
may be significant that the best-fitting spot
models so far favour spots that are hotter (by
500–1000 K) than the mean photosphere, and
could correspond to rising convective elements.
Other interpretations are possible – de Jager
(1993, see also Jager et al. 1991) suggests the
effects of R*/5 wavelength gravity waves excited by underlying convective motions.
The future
Within the next 1.7 × 106 years, Betelgeuse will
reach core carbon burning and shortly afterwards explode as a Type II supernova, leaving
a neutron star of about 1.21 M (Thielemann
et al. 1996). Assuming an absolute magnitude
MB ~ –17.4, initial (B–V) ~ –0.4 (Barbon et al.
1979 adjusted to Ho = 65 km s–1 M pc–1) and
AV unchanged at 0.5 (although it may
increase), the apparent visual magnitude will
become –10.8 (i.e. a brightening of a factor of
30 000), within an order-of-magnitude of the
brightness of the full moon, and 400 times
Venus at its brightest. Betelgeuse’s mass is not
greatly less than the precursor of SN1987A
(~18–20 M), but, due to composition differences, it is expected to explode as a red supergiant, rather than a blue one. How dangerous
will the Betelgeuse supernova be for Earth? A
greatly enhanced cosmic-ray flux may be the
most sinister aspect, but the star is over
130 parsecs away, and a calculation à la
Shklovski (1968) suggests over 10 000 supernovae at least this close to Earth over the history of the Solar System. The rate of one every
half-a-million years implies that life is not seriously threatened, but the possible effects
remain a subject for grisly speculation.
Despite its comparative nearness to us, and
despite intensive (albeit rather uncoordinated)
study, many aspects of the structure of Betelgeuse remain poorly understood. This is particularly true of the variability and structure
between 0.9 and 10 stellar radii. Much food
for thought is still provided by the book of de
Jager (1990) and conference edited by de Jager
and Niuewenhuijzen (1992). There are similar,
and not too distant, stars for comparative
study, such as Antares (α Sco).
Three feasible directions for further investigation seem likely to improve our knowledge:
(i) regular observation at optical, UV, IR and
radio wavelengths, including simultaneous
spectral and spatial resolution. (ii) Co-ordination of observations (within a few weeks) at
December 1997 Vol 38 Issue 6
Fig. 4: Betelgeuse by NRM techniques at 700 nm,
best-fit model with uniform disk and 3 Gaussian
spots. (courtesy of R Wilson et al. 1997)
different wavelengths, and with different techniques, to link cause and effect. (iii) Hydrodynamic modelling of spatially inhomogeneous
atmosphere and envelope models, a challenging problem exploiting improvements in computing speed and methods. ●
M G Edmunds, Department of Physics and Astronomy, University of Wales, Cardiff CF2 3YB. I am very
grateful for discussion or correspondence with E
Bedding, M Cuntz, R Davies, B Scott Gaudi, J Gallagher, C Haniff, N Mauron, P Murdin, O Esslinger,
G Perrin, A P Whitworth and R Wilson.
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