Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.mrao.cam.ac.uk/projects/OAS/publications/fulltext/spie4838-95-letter.ps Äàòà èçìåíåíèÿ: Wed Feb 20 16:40:51 2013 Äàòà èíäåêñèðîâàíèÿ: Sat Mar 1 03:28:06 2014 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: t tauri

Astrophysical results from COAST
John S. Young, John E. Baldwin, Alastair G. Basden, Nazim Ali Bharmal, David F. Buscher,
Amanda V. George, Christopher A. Hani#, James W. Keen, Bridget O'Donovan, Debbie
Pearson, Hrobjartur Thorsteinsson, Nathalie Thureau, Robert N. Tubbs, and Peter J. Warner
University of Cambridge, Astrophysics Group, Cavendish Laboratory, Madingley Road,
Cambridge CB3 0HE, UK
ABSTRACT
The first­generation COAST array is now primarily operated as a tool for astrophysics, with any development
work aimed at improving observing e#ciency and at prototyping hardware for future arrays. In this paper we
summarise the full range of astrophysical results obtained with COAST in the previous two years. Results of a
programme to investigate hotspots on red supergiant stars are presented in detail.
Keywords: Closure phase, hotspots, supergiants, symbiotic stars, Be stars, limb­darkening
1. LATEST RESULTS
The full five­telescope COAST array has been in operation since mid­1998, and has been used for a variety
of astrophysical programmes. These include measurements of diameter changes and limb­darkening of Mira
variables, observations of binary stars, investigations of hotspots and limb­darkening in supergiants, imaging of
the hydrogen envelopes of Be stars, and imaging of symbiotic stars.
There is insu#cient space to describe the latest results from all of these programmes in detail here. Therefore
we have chosen to present an in­depth treatment of one topic that makes use of the imaging capability of
COAST, that of hotspots on late­type supergiants. This treatment is given in Sec. 2, in which our latest results
on # Herculis are described. In this section we highlight recent results from our other programmes.
1.1. Symbiotic stars
Preliminary results from our programme on the symbiotic star CH Cygni were reported previously. 1 We have
since secured data during 2000 and 2001, to complement the original data from 1999. As the nine­milliarcsecond
resolution images in Fig. 1 show, the asymmetry detected in 1999 has persisted. We do not detect the purported
second red giant proposed by Skopal and co­workers. 2
There is clear evidence that the observed disc (assumed to be that of the primary red giant) is asymmetric.
The significant improvements in reduced # 2 in going from a circularly­symmetric to an elliptical disc model are
shown in Tab. 1. There is some evidence from the best­fit position angle values that the extension is rotating
with period # 15 yr, but further measurements are needed to confirm this.
No further measurements were secured in 2002, as the array was configured for other projects (in particular
the supergiant programme described in Sec. 2). We expect to publish a full account of the measurements obtained
thus far.
1.2. Be star envelopes
We have secured images in H# of the circumstellar envelopes of # Cassiopeiae and # Tauri, at two di#erent
epochs (an image of # Tau from 2001 January is shown in Fig. 2). The data include the first closure phase
measurements in H# for these stars, and so provide constraints on the apparent symmetry of their hydrogen
envelopes. More details of the measurements will be available in Ref. 3.
Further author information:
J.S.Y. (correspondence): E­mail: jsy1001@cam.ac.uk
COAST world­wide­web pages: http://www.mrao.cam.ac.uk/telescopes/coast/

Table 1. Results of fitting Gaussian disc models to the 905 nm visibility amplitude measurements on CH Cyg. Each
data­set consists of about 60 independent points. Elliptical disc models with axial ratio # 0.8 fit better than circular discs
in each case.
Data­set Red. # 2 Maj. axis /mas Axial ratio Maj. axis PA / #
1999 Aug/Sep 3.3 6.2 ± 0.1 1.0 --
2.0 6.7 ± 0.1 0.75 ± 0.04 135 ± 4
2000 Jun/Jul/Aug 3.6 6.1 ± 0.1 1.0 --
3.2 6.2 ± 0.1 0.84 ± 0.06 161 ± 7
2001 Jun/Jul/Aug/Sep 4.1 6.7 ± 0.1 1.0 --
3.1 7.1 ± 0.1 0.87 ± 0.03 176 ± 10
1.3. Stellar limb­darkening
In addition to limb­darkening measurements for Mira variables, not mentioned here, we have obtained visibility
measurements up to the second null for the red giant # Bootis (Fig. 3). The data were secured between 2000
March 21 and 2000 April 10. The waveband for the measurements was centred on 905 nm, with FWHM 50 nm.
A full account of these measurements is in preparation.
2. HOTSPOTS ON SUPERGIANT STARS
The primary aim of the ongoing COAST programme on red supergiants is to test and refine the model for hotspot
formation proposed by Young et al. 4 In this model, the large hotspots seen at optical wavelengths correspond
to areas of elevated temperature in the stellar photosphere, whose apparent contrast with the surrounding disc
is enhanced by a local reduction in opacity. The locally raised temperatures, and corresponding reduction in
molecular opacity, are most likely due to convection --- this o#ers a convenient explanation for changing hotspot
locations and brightnesses.
Young et al. used a simple blackbody parametrization of this model to fit multi­wavelength data on # Orionis.
The hotspots were represented by unobscured areas at a given temperature, and the wavelength­dependent
opacity obscuring the remaining parts of the stellar disc was modelled by allowing the disc angular diameter and
temperature to vary as a function of observing wavelength.
Figure 1. 905 nm­wavelength images of the symbiotic star CH Cyg. The maps were reconstructed using the standard
self­calibration/CLEAN procedure used in radio astronomy. Contours are plotted at ­8, ­4, ­2, 2, 4, 8, 16, 32, and 64 per
cent of the peak flux.

The opacity­enhanced model for hotspots leads to two predictions:
. Large changes in hotspot contrast should be seen when crossing deep spectral features
. Temporal variations in hotspot contrast and TiO band strength should be correlated
For the 2002 observing season, we planned to test the first prediction, by making simultaneous imaging ob­
servations using narrow (# 5 nm) bandpasses in both strong TiO absorption features and the nearby continuum.
The two brightest northern supergiants, # Orionis (M2Iab) and # Herculis (M5II), were selected as targets (only
data on # Her is presented here). To match the angular resolution of the observations with the expected size of
the stellar discs and hotspots, three of the COAST telescopes were arranged in the most compact configuration
possible, with a maximum baseline of six metres.
Figure 2. Reconstructed image of # Tau in H#, from 2001 January. Contours are plotted at ­1, 1, 2, 5, 10, 15, 20, 25,
30, 35, 40, 50, 60, 70, 80, 90, and 99 per cent of the peak flux.
­0.2
0
0.2
0.4
0.6
0.8
1
0 5000 10000 15000 20000 25000
Calibrated
visibility
Projected baseline /mm
Alpha Boo
Figure 3. Visibility measurements at 905 nm for # Boo. In the case of a symmetric disc, the complex visibility is purely
real, and its sign can be inferred from closure phase measurements. The signs of the plotted points were determined in
this manner.

Table 2. Log of COAST observations of # Her. Dates refer to the start of each night. N vis and N cl give the number of
successful visibility and closure­phase measurements made. Each ``measurement'' corresponds to 60--200 seconds of data,
in one or more colours simultaneously.
Date(s) Baseline N vis N cl [#/nm] / [##/nm]
range /m
2002/03/27 2.1 2 -- 782/5 750/13
2002/03/28 2.3--5.6 17 4 782/5 750/13
2002/03/29 2.5--6.0 11 4 782/5 750/13
2002/04/03 2.6--4.7 3 2 782/5 750/13
2002/04/04 2.5--5.7 12 5 782/5 750/13
2002/04/16 2.7--6.0 20 5 782/5 750/13
1996/04/01 2.8--7.9 14 10 940/60 905/50 880/11
1996/04/03 2.2--8.5 22 11 940/60 905/50
1996/05/04 3.0--8.5 9 7 940/60 905/50 830/40 750/13
1996/05/05 2.6--8.4 9 12 940/60 800/11 750/13
1996/05/06 2.6--8.5 25 10 940/60 905/50
1996/05/07 2.0--7.3 20 7 940/60 905/50
1996/05/20 3.0--8.2 7 -- 940/60 830/40
1996/06/14 4.0--8.4 9 4 940/60
1996/06/24 4.0--8.4 17 8 940/60 800/11 780/30
Archive data from 1996 was also found to be useful in testing the model predictions. The measurements are
described in more detail below.
2.1. Observations and data reduction
2.1.1. Observations in 2002
# Her was observed on six nights during March and April 2002, using three of the COAST telescopes, which were
arranged in a compact configuration (foundations C W2 E1). Standard observing procedures were employed,
including interleaving of fringe measurements on # Her and measurements on an unresolved calibrator star
(# Ophiuchi).
The visible (# < 1µm) beam­combiner was used, with the observing wavebands selected using filters mounted
in front of the four avalanche photodiode (APD) detectors. Filters centred on 782 nm with 5 nm half­power
bandwidth were used with two of the APDs, and a 750/13 nm filter with the third (continuum filters can be
slightly wider, as the e#ective bandpass is flux­weighted). A broad (30 nm) filter centred on 780 nm was used
with the fourth APD, to give a high signal­to­noise channel for fringe finding. The 40 cm COAST siderostats
were typically stopped down to 16 cm (# 2.5r 0 ), to match the seeing conditions.
Data were recorded using each of the three sub­array baselines in turn, followed by one or more recordings
of fringes on all three baselines simultaneously to measure the closure phase. This sequence was repeated for
the calibrator star, before returning to the target. The number of measurements of visibility amplitude and
closure phase made on each night are given in Tab. 2. Each recording was of length 60--200 s, to fully sample the
visibility fluctuations caused by the atmosphere, and to ensure adequate signal­to­noise.
2.1.2. Observations in 1996
The observing procedure used in 1996 di#ered only in detail. The filters used with the four APDs varied from
night to night (and were sometimes changed during the night) --- details are given in Tab. 2. At the time of the
observations only three COAST telescopes were operational, and these were laid out in a slightly larger (C W3
E1) configuration than that used in 2002. Table 2 gives the range of projected baselines obtained on each night.

2.1.3. Data reduction
All of the data were reduced using the same standard techniques. These techniques are described in more detail
in Refs. 5 and 6. Squared visibility amplitudes were estimated from the single­baseline data by averaging the
power spectra of scans through the fringe envelope, and estimating the fringe power by integrating over the
noise­subtracted fringe peak.
Uncertainties in these uncalibrated squared amplitudes were estimated from the scatter in values obtained
from di#erent segments of the same recording, and hence include contributions from visibility fluctuations during
the recording and from photon noise. The squared amplitudes were calibrated by dividing them by the system
squared visibility, obtained from an adjacent measurement of the calibrator star. Additional uncertainties (five
or ten per cent of the amplitude) were added in quadrature, to account for potential changes in seeing between
the observations of target and calibrator.
Closure phases were estimated from the three­baseline data, by dividing the data into ``coherent intervals''
of duration # 2t 0 , and estimating the bispectrum from each interval. The complex bispectrum estimates were
summed over the recording, the phase of the resultant being the adopted closure phase value. The error in
the closure phase was calculated from the scatter in the interval estimates projected perpendicular to the mean
bispectrum vector. Uncertainties on the final closure phases were in the range 5--20 degrees.
2.2. Results
2.2.1. Analysis procedure
We have followed very similar procedures to those described in Ref. 4, except that here the Fourier plane coverage
was always insu#cient to allow model­independent image reconstructions. Hence we have relied solely on fitting
relatively simple parametrizations of the sky brightness distribution to the visibility amplitudes and closure
phases measured at a particular wavelength and epoch.
The parametrizations consisted of a limb­darkened disc (using the empirical model of Hestro#er 7 ) plus some
number of smaller disc components, representing superimposed bright spots. A conjugate­gradient algorithm
was used to find the model parameters that minimized # 2 , using a range of starting conditions to improve the
chance of identifying a global minimum. Uncertainties in the best­fitting parameters were estimated from the
curvatures of the # 2 hyper­surfaces around minima, having accommodated any correlations between the di#erent
parameters.
2.2.2. Evidence for asymmetries in 2002
The 2002 data considered here were obtained over a period of 20 days. Changes in surface morphology on a
timescale of three weeks are typically small. 8 Hence, after checking for consistency between nights as far as
possible, all of the 2002 data in a particular waveband were combined for the analysis described here.
The visibility amplitudes at both 782 nm (Fig. 4) and 750 nm are consistent with a uniform disc model (and
hence with any reasonable limb­darkened model) on baselines shorter than about 7 M#. Beyond this projected
baseline, there is an excess of visibility compared with the prediction of the simple model.
The closure phase data are also shown in Fig. 4. At both wavelengths, the closure phase is small (< 20 # )
when the projected baselines making up the triangle are all shorter than 6.8 M#, and somewhat larger (up to
# 70 # at 782 nm; up to # 50 # at 750 nm) when the longest projected baseline exceeds this length. Closure
phase values inconsistent with zero or 180 # are unambiguous evidence of asymmetry. Centro­symmetric models
were unable to fit the data, the lowest reduced # 2 value obtained for the 782 nm data being 6.9.
The Fourier coverage of the data is insu#cient to unambiguously determine the nature of the asymmetry.
However, adequate fits (# 2
# 2) were obtained by modelling the flux distribution as a limb­darkened disc plus a
single superimposed bright feature. The parameters of this model could be determined unambiguously for both
colours: the best­fit radial coordinate of the ``hotspot'' was the same in both cases, and the values for its position
angle were marginally consistent (being 119±22 # at 782 nm and 157±19 # at 750 nm). The fit obtained at 750 nm
by fixing the hotspot in the 782 nm location was not significantly worse, hence the hotspots were assumed to be
coincident for the subsequent analysis.

0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10
Calibrated
Visibility
Projected Baseline /Ml
782nm
37mas FDD
­100
­80
­60
­40
­20
0
20
40
­3.5 ­3 ­2.5 ­2 ­1.5 ­1 ­0.5 0 0.5
Closure
Phase
/deg
HA /h
750nm
782nm
Figure 4. Visibility amplitudes at 782 nm for # Her in 2002 (left panel), and closure phase values at both 782 and 750 nm
(right panel). The predictions of the appropriate models from Tab. 3 are also shown in the right­hand panel.
The Hestro#er limb­darkening parameter # is hardly constrained by the 2002 data --- discs with # in the
range 0--4 are practically indistinguishable on the baselines measured. A value of unity was adopted (this model
is abbreviated to ``FDD'' --- for Fully­Darkened Disc --- in some of the figures). The size of the hotspot is
also indeterminate. Results are presented for moderately­resolved hotspots (Gaussian FWHM of 10 mas), for
consistency with the 1996 results below.
2.2.3. Evidence for asymmetries in 1996
The entire 1996 data­set spans 84 days. Significant changes would certainly be expected over this period. In
fact di#erent sub­sets of the wavebands were used on di#erent nights, so only the timespans for 940, 905, and
800 nm exceed the typical hotspot evolution time of 20 days. 8 The 905 nm closure phase values from April are
not consistent with those from May, whereas all of the 940 and 800 nm data is self­consistent.
As the number of data points in some wavebands is barely su#cient to constrain the surface structure, all
of the data in a particular waveband were combined for model­fitting, except at 905 nm where only the data
from May were considered. Mean dates for each waveband are given in Tab. 3, and the reader should bear in
mind that those for 880 nm and 780 nm di#er significantly from the dates for the other five wavebands. Changes
occurring within the timespan of the data­set at a particular wavelength could also lead to badly­fitting models
compared with single­epoch data.
The 940 nm data­set, being the largest, gives the best constraints on the flux distribution. The closure phases
are obviously not consistent with zero or 180 # (Fig. 6) --- the best # 2 obtained for a symmetric disc model was
6.9 (# 2 = 20 for the closure phases alone) for a Hestro#er disc with # = 2. Adding a single hotspot could
significantly improve the # 2 (to # 5 for the closure phases, # 3 overall), provided the hotspot was resolved
(Gaussian FWHM # 10 mas). This is necessary to fit the small visibilities close to the ``null'' (Fig. 5), while still
reproducing the closure phase signature (Fig. 6).
Non­zero closure phases were also measured at the other wavelengths, bar 880 nm. Only the 940 nm data
could constrain both the radial and azimuthal coordinates of the hotspot (with a prior forcing it to be on the
disc --- hotspots were modelled as sharp­edged discs to facilitate the application of this condition). Assuming the
position angle from the 940 nm data, the 750 nm data could unambiguously constrain the radius of the hotspot.
The 905 nm data could constrain the position angle but not the radius. Importantly, in no case was it possible
to fit a data­set with a much brighter or fainter hotspot than that given in Tab. 3.
To investigate the wavelength­dependence of the hotspot flux, we have assumed its location to be independent
of wavelength. The data do not contradict this assumption, and it has been found to be generally true for
supergiants on previous occasions when hotspots have been detected at multiple wavelengths. 4, 9--11

0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10
Calibrated
Visibility
Projected Baseline /Ml
940nm
780nm
37mas FDD
43mas FDD
Figure 5. Visibility amplitudes at 940 nm (solid triangles) and 780 nm (open circles), illustrating that at the time of the
1996 observations, # Her was significantly more resolved in the light of the TiO band at 780 nm.
­180
­120
­60
0
60
120
180
­5 ­4 ­3 ­2 ­1 0 1 2 3
Closure
Phase
/deg
HA /h
940nm
40
60
80
100
120
140
160
180
0 0.5 1 1.5 2 2.5
Closure
Phase
/deg
HA /h
780nm
Figure 6. Closure phases at 940 nm (left panel) and at 780 nm (right panel). The dotted curve in the right­hand panel
corresponds to the model for 780 nm from Tab. 3.

Table 3. Results of fitting models with fixed hotspot locations (obtained from the 782 nm data for 2002, and the 940 nm
data for 1996). The adopted hotspot locations are given in the last two columns. Refer to the text for details. The dates
correspond to the mean of the Julian days on which measurements were made in the given waveband. Hotspots were
modelled as Gaussians with 10 mas FWHM (2002 data), or Hestro#er discs with diameter 18 mas and limb­darkening
parameter # = 1 (1996 data).
Year Mean date #/nm Red. # 2 FDD diam. /mas Frac. hotspot flux r/mas #/mas
2002 04/02 782 2.4 37.4 ± 0.7 .19 ± .01 8(±5) 114(±19)
04/02 750 1.9 33.9 ± 0.5 .13 ± .02
1996 05/10 940 3.3 37.5 ± 0.1 .018 ± .001 11(±2) 199(±6)
05/06 905 3.8 36.9 ± 0.2 .019 ± .005
04/01 880 1.0 38.4 ± 0.7 < .05
05/12 830 0.9 37.6 ± 0.3 .053 ± .004
05/05 800 2.5 37.7 ± 0.4 .074 ± .006
06/24 780 3.2 42.6 ± 0.4 .030 ± .008
05/05 750 1.8 36.9 ± 0.5 .065 ± .009
A model with the hotspot fixed in the location obtained from the 940 nm data was fit to each waveband
separately. The flux of the hotspot and the disc size were allowed to vary. The resulting best­fit parameters
are given in Tab. 3. We chose a value of unity for the limb­darkening parameter # for these final model­fits.
Similarly acceptable fits to the 1996 data can be obtained with # = 2, but the hotspot fluxes are not changed
significantly.
2.2.4. Wavelength dependence
The results of fitting single­hotspot models to the 2002 data (Tab. 3) show that the contrast between hotspot
and disc is significantly enhanced in the TiO band at 782 nm, compared with the 750 nm continuum. The stellar
disc is also 10 per cent larger at 782 nm.
The wavelength­dependence of the hotspot flux (quoted as a fraction of the total flux in the model) in 1996
is plotted in Fig. 7. Here the behaviour is opposite to that seen in 2002 --- the hotspot is weaker in the TiO­
contaminated band. However, some of the apparent wavelength­dependence may be attributable to temporal
changes: the e#ective epoch of the 780 nm measurement is the latest of all the colours.
If the point at 780 nm is neglected, a general trend of decreasing hotspot flux with increasing wavelength is
seen. This is similar to the trend observed over a larger wavelength range by Young et al. 4 The disc diameter is
constant with wavelength, except at 780 nm, where it is 14 per cent larger.
2.3. Discussion
The comparison between the 1996 and 2002 data is intriguing. The generally larger disc diameters measured in
1996 suggest either a change in the intrinsic size of # Her, or more likely, higher opacities in 1996.
In the limit of extremely high opacity in the outermost photospheric layers, it is clear that any area of enhanced
temperature in the deeper photosphere can be completely masked. This kind of behaviour could explain the
observation of reduced, rather than enhanced, hotspot contrast in the TiO band. The larger enhancement in
disc size in the TiO band in 1996, despite the use of a wider filter, is further evidence for higher opacity at the
earlier epoch.
Higher opacities are to be expected in # Her compared with # Ori, due to its later spectral type. This would
be consistent with TiO­suppressed hotspots occurring sometimes in # Her, and (perhaps) not at all in Betelgeuse.
In the high­opacity regime, the blackbody parametrization used by Young et al. will not work without
modification, as it assumes that the hotspots are unobscured. Quantitative comparison of the new data with the
convective picture of hotspot formation is needed, but more appropriate parametrizations are beyond the scope
of this paper.

0.02
0.04
0.06
0.08
750 800 850 900 950
Fractional
hotspot
flux
Wavelength /nm
Figure 7. Wavelength­dependence of hotspot flux, as measured in 1996. Only an upper limit was determined at 880 nm.
2.4. Conclusions and future work
The new data provide further evidence that hotspots are ubiquitous on late­type supergiant stars, at least at
visible wavelengths. We have identified two types of behaviour in # Her: enhancement of hotspot contrast in a
TiO band, and also suppression of hotspot contrast in the same band, at an epoch when the outer atmosphere
was probably more opaque.
Further interpretation of these data requires some modelling e#ort, both to modify the ``first­order'' blackbody
parametrization used previously, and also to compare the data with the predictions of the three­dimensional
hydrodynamic models of Freytag (these proceedings, paper 4838­93).
Monitoring of a small sample of the brightest supergiants would be desirable, to measure changes in the
wavelength­dependence of the surface structures. Such measurements are best made at frequent (# 2 week) in­
tervals. Contemporaneous spectrophotometric measurements would give an independent handle on the variations
in TiO opacity.
REFERENCES
1. J. S. Young, J. E. Baldwin, R. C. Boysen, A. V. George, C. A. Hani#, C. D. Mackay, D. Pearson, J. Rogers,
P. J. Warner, D. M. A. Wilson, and R. W. Wilson, ``Recent astronomical results from COAST,'' in In­
terferometry in Optical Astronomy, P. J. Lena and A. Quirrenbach, eds., Proc. SPIE 4006, pp. 472--479,
2000.
2. A. Skopal, M. F. Bode, H. M. Lloyd, and S. Tamura, ``Eclipses in the symbiotic system CH Cyg,'' Astron.
Astrophys. 308, pp. L9--L12, 1996.
3. A. V. George. PhD thesis, University of Cambridge, 2002. In preparation.
4. J. S. Young, J. E. Baldwin, R. C. Boysen, C. A. Hani#, P. R. Lawson, C. D. Mackay, D. Pearson, J. Rogers,
D. St.­Jacques, P. J. Warner, D. M. A. Wilson, and R. W. Wilson, ``New views of Betelgeuse: multi­
wavelength surface imaging and implications for models of hotspot generation,'' Mon. Not. R. astr. Soc.
315, pp. 635--645, 2000.
5. D. Burns, Experiments with the Cambridge Optical Aperture Synthesis Telescope. PhD thesis, University of
Cambridge, 1997.
6. D. Burns, J. E. Baldwin, R. C. Boysen, C. A. Hani#, P. R. Lawson, C. D. Mackay, J. Rogers, T. R. Scott,
P. J. Warner, D. M. A. Wilson, and J. S. Young, ``The surface structure and limb­darkening profile of
Betelgeuse,'' Mon. Not. R. astr. Soc. 290, pp. L11--L16, 1997.

7. D. Hestro#er, ``Centre to limb darkening of stars: new model and application to stellar interferometry,''
Astron. Astrophys. 327, pp. 199--206, 1997.
8. R. W. Wilson, V. S. Dhillon, and C. A. Hani#, ``The changing face of Betelgeuse,'' Mon. Not. R. astr. Soc.
291, pp. 819--826, 1997.
9. D. F. Buscher, C. A. Hani#, J. E. Baldwin, and P. J. Warner, ``Detection of a bright feature on the surface
of Betelgeuse,'' Mon. Not. R. astr. Soc. 245(1), pp. 7p--11p, 1990.
10. R. W. Wilson, J. E. Baldwin, D. F. Buscher, and P. J. Warner, ``High­resolution imaging of Betelgeuse and
Mira,'' Mon. Not. R. astr. Soc. 257, pp. 369--376, 1992.
11. P. G. Tuthill, C. A. Hani#, and J. E. Baldwin, ``Hotspots on late­type supergiants,'' Mon. Not. R. astr. Soc.
285, pp. 529--539, 1997.