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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. References Balega Y et al. 1982 A & A 115 253. Barlow J c1790 Southern Celestial Hemisphere reproduced in Maps of the Heavens G S Snyder, A Duetsch 1984 p131. Barbon R et al. 1979 A. & A. 72 287. Basri G S et al. 1981 Ap.J. 251 162. Bedding T R et al. 1997 MNRAS 286 957. Bernat A P et al. 1979 Ap.J. 233 L135. Bester M et al. 1996 Ap.J. 463 336. Blaauw A 1991 in The Physics of Star Formation and Early Stellar Evolution eds C J Lada and N D Kylafis Kluwer p125. Boesgaard A M 1979 Ap.J. 232 485. Bowers P F and Knapp G R 1987 Ap.J. 315 305. Bowen G H 1988 Ap.J. 329 299. Brandt J C et al. 1996 Astron. J.109 2706. Bressan A et al. 1993 A & A Supp. 100 647. Brown J A et al. 1989 Ap.J.Supp. 71 623. Burnham R J 1978 Celestial Handbook Vol. 2 Dover, New York. Burns D et al. 1997 MNRAS (in press). Busher D F et al. 1990 MNRAS 245 7. Carpenter K G et al. 1994 Ap.J. 428 329. Carpenter K G and Robinson R D 1997 Ap.J. 479 970. Cheng A Y S et al. 1986 Ap.J. 309 737. Christou J C et al. 1988 Ap.J. 327 894. Cuntz M 1997 A&A 325 709. Cuntz M and Dorfi E A 1997 in Cosmic Winds and the Heliosphere eds J R Jokipii et al. Univ. Arizona Press (in press). de Jager C 1980 The Brightest Stars D. Reidel, Dordrecht. de Jager C et al. 1991 A&A 244 131. de Jager C 1993 Observatory 113 43. de Jager C et al. 1988 A.& A.Supp. 72 259. de Jager C and Nieuwenhuijzen H eds 1992 Instabilities in evolved super- and hypergiants North Holland, Amsterdam. di Benedetto G P 1993 A. & A. 270 315. Doherty L R 1986 Ap.J. 307 261. Draine B 1981 in Physical Processes in Red Giants eds I Iben and A Renzini, D. Reidel p317. Dravins D and Nordlund Å 1990 A. & A. 228 184. Dupree A K et al. 1987 Ap.J. 317 L86. Dyck H M et al. 1974 Ap.J. 189 89. Dyck H M et al. 1992 Astron.J. 104 1982. Dyck H M et al. 1996 Astron.J. 111 1705. Dyck H M and Simon T 1975 Ap.J. 195 689. El Eid M F 1994 A & A 285 915 Elias J H et al. 1985 Ap.J.Supp. 57 91. Esslinger O M 1997 Ph.D. Thesis, Univ. Wales, Cardiff. Esslinger O M and Edmunds M G 1997 A. & A. Suppl (in press). Flower P J 1977 A. & A. 54 31. Fox M W and Wood P R 1982 Ap.J. 259 198. Frank A 1995 Astron.J. 110 2457. Garcia-Berro E and Iben I 1994 Ap.J. 434 306. Goldberg L et al. 1977 Ap.J. 199 427. Goldberg L 1979 QJRAS 20 361. Goldberg L 1984 PASP 96 366. Gilliland R L and Dupree A K 1996 Ap.J. 463 29. Glassgold A E and Huggins P J 1986 Ap.J. 306 605. Guilain Ch and Mauron N 1996 A. & A. 314 585. Haas M R and Glassgold A E 1993 Ap.J. 410 111. Haisch B et al. 1991 Ap.J. 383 L15. Harris M J and Lambert D L 1984 Ap.J. 281 739. Hartmann L and Avrett E H 1984 Ap.J. 284 238. Hayes D P 1984 Ap.J.Supp. 55 179. Hebden J C et al. 1987 Ap.J. 314 690. Heuter G 1986 Vistas in Astron. 29 237. Hinke K H et al. 1976 Ap.J. 210 684. Huggins P J 1995 Astrophys.Sp.Sci. 224 281. Huggins P J et al. 1994 Ap.J. 424 L127. Hutchinson R B 1971 Ap.J. 170 551. Joras P 1989 in Evolution of Peculiar Red Giants eds H R Johnson and B Zuckerman CUP p299. Jordan C 1967 Solar Physics 2 141. Judge P G and Stencel R E 1991 Ap.J. 371 357. Karovska M et al. 1986 Ap.J. 308 260. Karovska M et al. 1988 Bull.Am.Astr.Soc. 19 755. Karovska M et al. 1993 Ap.J. 402 311. Karovska M et al. 1997 Ap.J. 482 L175. Keenan P C and McNeil R C 1989 Ap.J.Supp. 71 245. Klückers V A et al. 1997 MNRAS 284 711. Knapp G R et al. 1980 Ap.J. 242 L25. Knapp G R et al. 1982 Ap.J. 252 616. Kodaira K et al. 1979 PASJ 31 667. Lambert D L et al. 1984 Ap.J. 284 223. Lee T A 1970 Ap.J. 162 217. Mauron N 1990 A. & A. 227 141. Mauron N et al. 1984 A. & A. 130 341. Marson R G 1997 Ph.D. Thesis Univ. Sydney. Marson R G et al. (1998) MNRAS (to be submitted). Means H 1953 The Psychoed (Antigonish) quoted in The Oxford Dictionary of Quotations OUP p335. Newell R T and Hjellming R M 1982 Ap.J. 263 L85. Nordlund Å and Dravins D 1990 A. & A. 228 155. Noriega-Crespo A et al. 1997 Astron.J. 114 837. Perrin G, Coude de Foresto V, Ridgway S T, Mariotti J M, Traub W A, Carleton N P and Lacassen M G 1997 Private communication. Pijpers F P and Hearn A G 1989 A. & A. 209 198. Roddier F et al. 1986 Ap.J. 305 L77. Rogers B and Glassgold A E 1991 Ap.J. 382 606. Ritossa C et al. 1996 Ap.J. 460 489. Schaller G et al. 1992 A. & A.Supp. 96 269. Scholz M 1985 A. & A. 145 251. Scholz M and Takeda Y 1987 A&A 186 200. Schwarzschild M 1975 Ap.J. 195 137. Shklovski I S 1968 Supernovae J Wiley p377. Skinner C J and Whitmore B 1987 MNRAS 224 335. Skinner C J et al. 1997 MNRAS 288 295. Stothers R and Leung K 1971 A. & A. 10 290. Thielemann F-K et al. 1996 Ap.J. 460 408. Tinbergen J et al. 1981 A. & A. 95 215. Tsuji T 1976 PASJ 28 567. Tsuji T 1978 PASJ 30 435. Tsuji T 1979a N.Z.Journ.Sci. 22 415. Tsuji T 1979b PASJ 31 43. Tuthill P G et al. 1997 MNRAS 285 529. Vaiana G S et al. 1981 Ap.J. 244 163. White N M 1980 Ap.J. 242 646. Wilson R W et al. 1992 MNRAS 257 369. Wilson R W et al. 1997 MNRAS (in press). 31