This document summarizes observations of the red supergiant star Betelgeuse taken over several years using spectroscopy. It finds: 1) Temperature variations on the star's surface of around 100 K on timescales of hundreds of days, along with correlated but not identical brightness variations. 2) Radial velocity variations covering a range of around 9 km/s with a characteristic timescale of 400 days. 3) Little variation in the shapes of spectral lines despite larger velocity shifts, requiring large turbulent motions within the star's photosphere.

1. The Astronomical Journal, 135:1450–1458, 2008 April doi:10.1088/0004-6256/135/4/1450
c 2008. The American Astronomical Society. All rights reserved. Printed in the U.S.A.
MASS MOTIONS IN THE PHOTOSPHERE OF BETELGEUSE
David F. Gray
Department of Physics & Astronomy, University of Western Ontario, London, Ontario N6A 3K7, Canada; dfgray@uwo.ca
Received 2007 November 27; accepted 2008 February 2; published 2008 March 10
ABSTRACT
Spectroscopic observations of Betelgeuse, taken at the Elginfield Observatory, show velocity and temperature
variations delineating the systematic, but generally chaotic, rise and fall of photospheric material. The characteristic
timescale of the variations is 400 days, while velocities cover a range of ∼9 km s−1
. Macroturbulence is constant
to about 13% and does not result from motions on the largest scales, but from motions within the large structures.
The line bisectors have predominantly a reversed-C shape. Variations in the shapes of bisectors occur on the
1 km s−1
level and are not obviously connected to their shifts in wavelength. A likely explanation of the observations
is granulation and giant convection cells accompanied by short-lived oscillations they trigger. Random convection
events may account for radial-velocity jitter seen in many highly evolved stars.
Key words: convection – stars: individual (Betelgeuse) – stars: oscillations – stars: variables: other – supergiants –
techniques: spectroscopic
Online-only material: color figures
1. BACKGROUND
Betelgeuse is a red supergiant star (α Ori, HR 2061, HD
39801, M2 Iab, B − V = 1.86). The star varies in brightness,
surface features, radial velocity, and line depths, but shows
only small variation in the shapes of the spectral lines. A
detailed description of the star’s characteristics and photospheric
line-strength variations was given in an earlier publication
(Gray 2000; G1 hereafter). It was shown there that the star’s
brightness is often in phase with the changes in line depths:
deeper lines, brighter star. Bright spots that frequently appear
in interferometric imaging of the star are sometimes taken
as evidence of large granulation cells (e.g., Wilson et al.
1997; Young et al. 2000; Freytag et al. 2002; but see G1
for an alternative interpretation). Naturally one presumes long
timescales and large convection cells based on dimensional
arguments applied to a star like Betelgeuse, with its radius
∼800 solar radii and the low surface gravity of a supergiant
star (Schwarzschild 1975; Boesgaard 1979). I will use the terms
“granulation,” “supergranulation,” and “giant convection cell”
in analogy with the solar usage. Solar granules have dimensions
∼1 Mm, supergranules ∼10 Mm, and giant convection cells
span the dimension of the convection zone or ∼200 Mm. The
dimensions of each of these will be scaled up in supergiants
such as Betelgeuse, but the hierarchy remains the same. In the
1975 paper, Schwarzschild considered mainly the scaling of
solar granulation and supergranulation to giant and supergiant
stars. Some hydrodynamical models of Betelgeuse showed 3–
5 cells on the visible disk (Freytag et al. 2002). However,
previous spectroscopic evidence indicated ∼600 cells on the
visible surface of Betelgeuse (Gray 2001; G2 hereafter). This
was deduced from the ∼4% variation seen in the widths of
the spectral lines (but see updated material below). Hundreds
of granules are also predicted by the scaling relation given
by Freytag et al. (2002). While such cells would certainly
be large, ∼40 Mm across or about 40 times the dimensions
of solar granules, they fall short of being the predicted large
granulation cells by an order of magnitude. Past investigations
were therefore inconclusive on the existence or the behavior of
large granulation cells.
Many, perhaps a third of, highly evolved stars show periodic
light variations (e.g., Percy et al. 2003), while others are irregu-
lar or semi-regular (e.g., Lebzelter et al. 2005), and Betelgeuse
has been placed in the latter category. Semi-regulars seem to
show two dominant periods, one of a few hundred days and
a second of a few thousand days (Wood et al. 2004). Since
the documentation of the unstable radial velocity of Betelgeuse
by Plummer (1908), periods have been sought in radial veloc-
ity measurements as well (e.g., Sanford 1933; Goldberg 1984;
Dupree et al. 1987; Smith et al. 1989; Uitenbroek et al. 1998a).
There is consternation in the literature as investigators strug-
gle to understand pulsations with a variable period, variable
amplitudes and phases, and non-unique connections among ob-
served variables. The “long” period for Betelgeuse is ∼2100 ±
400 days, while a “short” period of ∼400 days is frequently
quoted, although values half as large and twice as large have
also been found or suspected. Radial pulsation, orbital motion
(Karovska et al. 1986), shock waves, rotational modulation, and
convection cells have been suggested as explanations.
More generally, a number of radial-velocity investigations
have documented excess scatter or random variability in the
measurements of stars at the tip of the red-giant branch, a
phenomenon termed “jitter” (Gunn & Griffin 1979; Pryor et al.
1988: Carney et al. 2003; among several others). The Betelgeuse
measurements presented below document wavelength shifts and
related characteristics, and their similarity to velocity jitter is
striking.
An interesting step was taken by Bedding (2003) and Kiss
et al. (2006) who found evidence supporting the idea that
the semi-regular light variations of red supergiants arise from
oscillations excited by convection cells. In their analyses and
for some stars, the power peaks are resolved into closely spaced
frequencies analogous to what is seen in the solar 5 min
oscillations. This implies that the oscillations are powered by the
convection and not by the ionization/opacity process that drives
oscillations in the instability strip of the HR diagram. With this
interpretation, the chaotic nature of the variations stems from
the relatively few convection cells that excite the oscillations,
i.e., we see only one or two modes at any one time. The
observations presented below amplify and confront this idea and
1450

2. No. 4, 2008 BETELGEUSE PHOTOSPHERE MASS MOTIONS 1451
6220 6230 6240 6250 6260 6270
0.0
0.5
1.0
α Ori HR 2061 M2 Iab
F/Fc
Fe I 6219.29 V I 6251.83
Fe I 6252.57
Ti I 6261.11
Wavelength
Figure 1. This typical exposure of Betelgeuse illustrates the shallow broad lines and identifies the specific lines used in the analysis. F/Fc denotes flux normalized to
nominal continuum flux.
(A color version of this figure is available in the online journal)
give some information about the physical characteristics of the
processes.
This paper also expands on G1 and G2, giving additional
information on the shapes and broadening of line profiles,
their bisectors, and their wavelength positions. Line shifts or
radial-velocity-type motions are found to be several times larger
than profile shape variations. The observed behavior requires
large macroturbulence within the material showing the velocity
excursions.
2. OBSERVATIONS AND MEASUREMENTS
The coude spectrograph at the Elginfield Observatory was
used to acquire the 338 exposures reported on here. Two
detector systems were used. From 1996 March 23 to the end
of 1999, the observations were recorded on a Reticon self-
scanned array mounted in a Schmidt camera of focal length
559 mm (see Gray 1986). From 1999 October 6 onward (three-
month overlap with the Reticon), a CCD detector was used on a
simple camera having a focal length of 2080 mm. The resolving
power is ∼100,000. The dispersion is ∼0.039 Å per pixel on the
Reticon and ∼0.013 Å per pixel on the CCD detector. Signal-
to-noise ratios in the continuum are estimated from the photon
count and range from 154 to 885 with a median of ∼500.
Figure 1 shows a sample CCD spectrum. The three lines, V i
6251.83 Å, Fe i 6252.57 Å, and Ti i 6261.11 Å identified in
the figure, are those used for most of the work described here.
The excitation potentials of the first two lines are 0.29 eV and
2.40 eV respectively, making the ratio of their line depths a good
indicator of temperature (Gray & Brown 2001). The Ti line is
used to study line bisectors and line-width variations. All other
lines are either blended or too shallow. As can be discerned in
Figure 1, the spectral lines are shallow and highly broadened,
indicating substantial macroturbulence with a dispersion of
∼11 km s−1
if an isotropic Gaussian velocity distribution is
assumed (G1). Rotational broadening probably contributes 2.0–
2.5 km s−1
to the broadening (Uitenbroek et al. 1998b; G1).
An important part of these observations from 2002
September onward is their absolute wavelength scale, estab-
lished using the telluric absorption inside the spectrograph. Tel-
luric measurements are taken both before and after the stellar ex-
posure. Details are described in Gray & Brown (2006). Barycen-
tric corrections are made using the precepts of Stumpff (1979,
1980). The final absolute scale given here is generally good to
50 m s−1
or better, which is more precise than one can mea-
sure the positions of broad spectral lines such as those of
Betelgeuse.
3. TEMPERATURE AND BRIGHTNESS VARIATIONS
The ratio of the line depths of V i 6251.83 to Fe i 6252.57
(Figure 1) is a measure of the temperature, with larger ratios
indicating cooler temperatures (Gray & Brown 2001). Although
no calibration exists in this range to convert the line-depth ratios
to temperature, one can make an order-of-magnitude estimate. If
the lines were weak, the ratio of their strengths would vary with
the ratio of their Boltzmann excitation factors. For these lines,
χ = 0.29 and 2.40 eV respectively, and for the observed range
in line-depth ratios, a temperature change ∼100 K would be
implied. Since the lines are not weak and the light is integrated
over the stellar disk, this is a lower limit to the real temperature
variations.
Figure 2 shows the line-depth ratio as a function of time.
Measurement errors are ∼0.005, smaller than the symbol size,
as estimated from repeated exposures taken minutes apart. As
can be seen in the figure, variations occur on many timescales.
In some time intervals, there is a hint of oscillation, but there is
no one period that stands out. A period of 388 days (±30) was
deduced by Kiss et al. (2006) from photometric observations
obtained from the American Association of Variable Star Ob-
servers (AAVSO). Some of the AAVSO observations (Henden
2007, private communication) are compared to the line depths
in Figure 2. The magnitudes were binned in 10 day intervals
and these averages, aside from the occasional erratic point, typ-
ically have errors of ∼0.1 mag or less. Also shown are the
more precise measurement of Krisciunas & Luedeke (1996),
where the typical error is a few thousandths of a magnitude. The
agreement between these two independent photometric studies
is very good, with differences in overall trends, rates of change,
and amplitudes of variation rarely exceeding 0.1 mag. Earlier
measurements by Krisciunas (1990, 1992, 1994) also agree with
AAVSO data to this level.
In a rough sense, the photometric variation is seen to mimic
the line-depth ratio variation. There are times when the photome-
try tracks the line-depth ratio rather well, as in the 11000–11300
and 12650–12750 intervals in Figure 2. But more often there are
significant differences, for example near 10500, 10750, 10850,
11600, 12000, and 12550. Similar conclusions have been drawn

3. 1452 GRAY Vol. 135
10000 10500 11000 11500
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Line-DepthRatio
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(b)
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13000 13500 14000 14500
1.4
1.3
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(c)
JD - 2440000
Line-DepthRatio
Magnitude
1.0
0.5
Figure 2. The line-depth ratio of V i 6251.83 to Fe i 6252.57, a temperature index, is shown as a function of time (◦). Superimposed are the AAVSO visual magnitudes,
binned in 10 day intervals (+). The photometric observations of Krisciunas & Luedeke (1996) are also shown (×).
(A color version of this figure is available in the online journal)
in the past (e.g., Sanford 1933). Apparently the temperature
variations account for the bulk of the brightness variations, but
the effective photospheric radius is frequently an independent
variable, i.e., the phenomenon is not simply pulsation on a global
scale.
A Fourier analysis or periodogram of the line-depth ratio
is shown in Figure 3, panel (a). The window patterns have
relatively small sidelobes so each large peak is a true frequency.
For frequencies higher than ∼0.02 cycles day−1
, there is only
noise. At lower frequencies, there is signal. In particular, the
highest signal corresponds to a period of 427 days, but there
are also several other frequencies present. The second panel
(b) in Figure 3 shows the periodogram of the AAVSO data
over the same time interval used in panel (a). Here again
several frequencies show up, with one corresponding to 418
days, essentially the same as for the line-depth ratio. Both
these periods are somewhat longer than the 388 days found
by Kiss et al. (2006), but as they emphasize, a range of period
is expected if oscillations are driven by convection with its
stochastic characteristics.
To probe a step further, panel (c) in Figure 3 shows peri-
odograms of AAVSO data for eight independent time spans,
each having a duration approximately the same as for panels
(a) and (b). There are clumps of peaks near 0.0025 (400 days),
the variations being emphasized in this paper, 0.0005 (2000
days), and possibly 0.0001 (10,000 days). The last set is long
enough to correspond to rotational modulation. One of these
eight spans (JD2433997 to 2438048) shows no peak at all in the
0.0025 region. In fact, the middle half of the data, JD2429801
to JD2446199, shows no peak in this region. Another interest-
ing result from this figure is the Gaussian envelope shown by
the peak heights. A Gaussian envelope in the frequency domain
implies convolution with a Gaussian, i.e., Gaussian smooth-
ing, in the time domain. The e−1
width in Figure 3 is 0.0062
cycles day−1
. The corresponding e−1
width of the smoothing is
(0.0062 × π)−1
= 51 days. Perhaps this gives an indication of
the thermal relaxation time of the material.
4. LINE PROFILE SHAPE AND POSITION VARIATIONS
The line profiles appear to be highly variable, as shown in
Figure 4, left-hand panels (a) and (c), where the data are plotted
on an absolute wavelength scale and with no renormalization
of line depths. However, the variations are primarily in the
positions of the lines and their depths, with only small changes
in shape and broadening, in agreement with G2. For example,
if the profiles are repositioned in wavelength and re-scaled in
depth (but not width), the variations appear much smaller, as
shown in right-hand panels (b) and (d) of Figure 4. Rescaling
in depth amounts to changing the continuous opacity, and this
thesis was presented in G1. A variation on this hypothesis is that
a light-scattering shell surrounds the photosphere and its opacity
varies with time, but given the tight correspondence shown in
G1 between the line depth (which might be affected by a shell)
and line-depth ratio (which is highly unlikely to be affected by
a shell), this hypothesis can be ruled out for the timescales we
are considering.
The small variation in the widths of the lines is illustrated
in Figure 5, where the full half width of the λ6261 line is
shown as a function of time. Measurement errors are estimated
to be ±0.3 km s−1
or approximately the size of the symbols in

4. No. 4, 2008 BETELGEUSE PHOTOSPHERE MASS MOTIONS 1453
0.0
0.5
1.0
Frequency, cycles/day
Power
AAVSO ∆JD ~ ∆JD of LDR
0.000 0.005 0.010 0.015 0.020
Gaussian
0.0
0.5
1.0 AAVSO ∆JD for LDR
Power 0.0
0.5
1.0 LDR ( ∆JD = 4059)
Power
(c)
(b)
(a)
Figure 3. (a) Periodogram of the line-depth ratio (LDR) shows several peaks at these low frequencies. The observations cover a time window of 4059 days.
(b) Periodogram of AAVSO magnitudes over the same time interval used in (a). (c) Periodograms of AAVSO magnitudes for eight time windows having a similar
length to the one used in (a). The peaks lie under a Gaussian envelope.
(A color version of this figure is available in the online journal)
6251 6252 6253
(b)
6251 6252 6253
0.6
0.7
0.8
0.9
1.0
F/Fc
(a)
6260 6261 6262
0.5
0.6
0.7
0.8
0.9
1.0
F/Fc
Wavelength
(c)
6260 6261 6262
(d)
Wavelength
Figure 4. The left-hand panels, (a) and (c), show spectral lines on an absolute wavelength scale with only continuum normalization. The right-hand panels, (b) and
(d), show the same profiles shifted in wavelength and scaled to the same central depth. In panel (b), the V i λ6251.83 line was used for the depth normalization; the
Fe i λ6252.57 line differs in depth owing to temperature differences. Any of the recorded spectral lines could have been used for this illustration.
(A color version of this figure is available in the online journal)

5. 1454 GRAY Vol. 135
(c)
(f)(e)
(a)
10000 11000 12000 13000 14000
25
30
HalfWidth,km/s
JD - 2440000
Betelgeuse λ6261
(d)
100 d
(b)
Figure 5. The full half width of Ti i λ6261.11 is shown as a function of time. The outlying panels have expanded time dimensions so more detail can be seen. The
vertical scale of the outlying panels is the same as for the main panel (d) but are offset in some cases to center the data in the panel.
(A color version of this figure is available in the online journal)
12500 13000 13500 14000
-10
-5
0
5
Velocity+constant,km/s
JD - 2440000
2003 2004 2005 2006 2007
Figure 6. Mean core velocity of V i 6251.83, Fe i 6252.57, and Ti i λ6261.11 (plus an unknown constant) is shown as a function of time.
(A color version of this figure is available in the online journal)
the plots. The variations are, therefore, many times larger than
the measurement errors. The half width varies from about 27 to
30
1
2 km s−1
, or some 13% over the course of these observations.
Apparently the large macroturbulence of this star is constant to
that level. A similar stable and isotropic macroturbulence was
found in the chromospheric study by Lobel & Dupree (2001),
but see Carpenter & Robinson (1997) who found evidence for
non-isotropic velocity fields. Freytag et al. (2002) also found
large velocities in their hydrodynamical models, “. . . often
exceeding 20 km s−1
. . . .” As can be seen in the various panels of
Figure 5, changes occur on many timescales. A periodogram
shows no outstanding peaks, but for frequencies below about
0.005 cycles day−1
, or periods longer than about 200 days,
there is a signal.
The wavelength positions of the line cores of the three lines,
λ6251.83, λ6252.57, and λ6261.11, were estimated by eye.
Within the uncertainty of measurement and variable blending,
estimated to be 100 m s−1
, all three lines show the same
pattern of shifts. Their mean is shown as a function of time in
Figure 6. The wavelength shifts were converted to velocities
using nominal rest wavelengths, but since the center-of-mass
velocity of the star is not known to the precision being discussed,
true zero velocity remains unknown. Notice the shorter time
base compared to previous figures; no absolute wavelength scale
was available for earlier observations. Naturally, this severely
restricts the study of velocity variations on a many-year scale.
One should be particularly careful not to interpret the two
minima near 12700 and 13800 as defining a cycle since any
two randomly placed minima separated by more than half the
time base will produce such a suggestive plot. Further, notice
the points near 14200 that are as low as those at 12700.
The velocities show the characteristic chaotic behavior with
variations on many timescales. The observed range in velocity
is ∼9 km s−1
with an root-mean-square scatter of 2.4 km s−1
.

6. No. 4, 2008 BETELGEUSE PHOTOSPHERE MASS MOTIONS 1455
Velocity + constant, km/s
-5 0
2005-06
12
3
4
5
6
7
8
9
10
11
12
13
0.5
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Velocity + constant, km/s
0-5
2006-07
1
2
3
4
5
6
7
8
9
10
11
0.5
0.6
0.7
0.8
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1.0
F/Fc
2004-05
1
2
3
4
5
6
7
8
910
11
12
13
14
F/Fc
0.5
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1.0 2002-03
1
2
3
4
5
6
7
8
9
10
1112
13
14
2003-04
1
2
3
4
5
6
7
8
9
1011
1213
14
15
16
(d)
(e)
(c)
(a) (b)
Figure 7. Bisectors of the Ti i λ6261.11 line are shown for individual observing seasons. Both the shape and the shifts have meaning, but the position of zero velocity
is unknown. The numbers indicate the time order of the exposures, so the time progression of positions and shape changes can be seen.
(A color version of this figure is available in the online journal)
This is consistent with observations in earlier epochs (e.g.,
Sanford 1933; Boesgaard 1979; Goldberg 1984). A periodogram
analysis again shows signal at low frequencies. The largest peak
corresponds to 365 days, which one is immediately tempted to
attribute to the seasonal sampling in the observations. However,
characteristic timescales of variation in the range of 300–400
days are seen within the 2002–2003, 2005–2006, and the 2006–
2007 seasons, and these have nothing to do with the yearly
sampling times. It should also be noted that periods of this size
are typical for semi-regular variables.
There is no simple correlation between the line width and the
wavelength shift.
5. BISECTOR SHAPES AND VARIATIONS
As seen in Figure 1, the λ6261 line is one of the very few in
these exposures that is sufficiently deep and possibly unblended
enough to yield a meaningful line bisector. Bisectors for this
line were computed for all exposures in the last five observing
seasons where absolute wavelength information is available.
They are shown in Figure 7 on an absolute velocity scale with
an unknown but constant offset owing to motion of the star
in space. Therefore both the shapes of the bisectors and their
relative shifts have significance. The bisector numbers indicate
the time order.
Bisector errors can be assessed empirically. The noise on
the individual bisector points can be seen by looking closely at
individual bisectors in Figure 7 and noting the wiggles they show
between the ∼1% F/Fc ordinate steps. This noise is ∼0.1 km s−1
or less except at the very top and bottom, where larger values can
occur (see Gray 1983, 1988). Further, by comparing bisectors
from different exposures taken relatively close together in time
one can see the degree of consistency. For example, bisectors
2 & 3 and 10 & 11 in the 2002–2003 season are two cases taken
one day apart. Both pairs show the same basic shapes and differ
by ∼0.1 km s−1
in position, and any variation of the star is
included in these differences.
Inspection of the figure shows that (1) bisectors taken on
successive nights are almost identical, (2) shape variations occur
on the 1 km s−1
level, including change in curvature, reversal of
curvature, and slope, (3) there is no consistent relation between
the shape and shift, (4) shifts are much larger than shape
variations, being on the 5 km s−1
scale, and (5) the predominant
shape is like a reversed C, mimicking what is seen for stars
hotter than the granulation boundary (Gray & Toner 1986; Gray
& Nagel 1989; Gray 2005; near G0 for the more luminous
stars). Given these variations in the bisector shape, classical
radial-velocity measurements, where one number is assigned
to the star’s line shifts, clearly loses meaning on scales below
∼1 km s−1
.
As seen in Figure 7, a C shape, or at least a positive slope,
occasionally occurs, but both the C and reversed-C shapes can
and do occur at similar velocity displacements. The shape
changes are much larger than those would be induced by
classical radial pulsation of a few km s−1
, i.e., the observed
shifts. For example, the asymmetry for a radial pulsation that
shifts the profile 3 km s−1
amounts to less than 0.1 km s−1
,
whereas the observed shape changes are ten times this. Normal
variable-star pulsation is therefore inadequate as an explanation
of the bisector variations, whereas large convection cells or
similar mass motions are compatible with the size of the shifts,
their chaotic nature, and the bisector contortions.
The occurrence of reversed-C bisectors on the cool side of
the granulation boundary is surprising and of some significance.
One might be tempted to dismiss the reversed-C shape as arising

7. 1456 GRAY Vol. 135
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2004-05
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2002-03
(a)
2003-04
(b)
-5 0
Generic
Velocity + constant, km/s
hotter
rising
(f)
2005-06
(d)
Figure 8. Line-depth ratio is shown as a function of the mean core velocity of V i 6251.83, Fe i 6252.57, and Ti i λ6261.11 for an individual observing season. Arrows
indicate the direction of increasing time. Panel (f) illustrates the full inferred generic behavior, including the directions of the rising temperature and rising velocity.
The symbol size indicates the full half width of Ti i λ6261.11.
(A color version of this figure is available in the online journal)
from blends in the line. There are at least two reasons to think that
the reversed-C shape is not spurious. First, there is no connection
between shape and the temperature variations discussed above.
In other words, any blending line would have to have the same
temperature dependence as the main λ6261 line; not impossible,
but unlikely. Although the Fe i 6219.29 Å line is badly blended,
the lower portion shows the reversed-C shape, mimicking λ6261
and supporting the reality of the λ6261 shape. Second, a recent
study of metal-poor red-giant branch stars (Gray et al. 2008,
in preparation) reveals that most of them cooler than 4100 K
show reversed-C bisectors (Betelgeuse is ∼3600 K). For these
red-giant branch stars, because of their low metallicity, there
is little blending and essentially all the available lines show
the same result. Betelgeuse is apparently consistent with other
stars in its region of the HR diagram. Further, since Betelgeuse
is a Population I star, the existence of the reversed-C shape
apparently does not require the low metallicity of the stars
studied in D. F. Gray et al. (2008, in preparation).
6. EXCURSIONS OF THE PHOTOSPHERE
The timescales of the larger variations are typically many
months so one can follow only a portion of the full variation
during any one observing season. Figure 8 gives a summary of
the temperature index (line-depth ratio) plotted as a function of
core velocity (as per Figure 6). The general pattern is an increase
in temperature followed by a rise of the material followed by
a cooling and finally a descending phase. Each season has
captured only a portion of this behavior, but from five seasons,
the general pattern seems clear, as constructed in panel (f).
Apparently large portions of the surface are seen rising and
falling, and this material dominates the star’s spectrum.
The size of the symbols in Figure 8 indicates the relative
half width of the λ6261 line, which I take to be a proxy for the
strength of the macroturbulence. Although there is no consistent
change in half width during any one cycle, more vigorous
excursions, such as the one in the 2005–2006 season, are hotter,
rise faster, and have stronger macroturbulence. The excursion
in the 2003–2004 season illustrates the opposite case, where the
material reaches less hot temperatures, rises more slowly, has
smaller macroturbulence, and eventually peters out.
The difference between the largest fall velocity (2003–2004
season) and the largest rise velocity (2005–2006 season) is 7–
8 km s−1
. Since the absolute zero on the radial velocity scale
is unknown, this cannot be split between rise and fall portions.
Further, the angle of rise to the line of sight is not known, so this
velocity difference is a lower limit. The variation in the line-
depth ratio during these episodes ranges from ∼1.05 to 1.30,
which is ∼100 K or more, as indicated in Section 3. Any light
from other portions of the stellar disk will dilute the true velocity
and temperature variations of the moving material. Projection
and dilution factors can be expected to vary from one excursion
to the next and cannot be separated from stochastic variations
of the excursion itself.
An estimate of the size of the displacements can be made
by approximating a typical velocity excursion in Figure 6 by a
sinusoid and integrating over half a cycle. With a semi-amplitude
of ∼2.5 km s−1
, and using a characteristic time of 400 days, the
material would move ∼40 R or ∼5% of the radius of the star.

8. No. 4, 2008 BETELGEUSE PHOTOSPHERE MASS MOTIONS 1457
7. ADDITIONAL DISCUSSION AND SUMMARY
The term “photosphere” has been used here to mean the
layers of the atmosphere from which the light we record arises.
This is no different from what is commonly meant, but in
the case of Betelgeuse, the geometry of the photosphere is
undoubtedly irregular, permeated with structure, and dynamic.
Some of the largest of these structures will move the photosphere
several percent of the stellar radius, as noted in the previous
section. Since the line profiles are dominated by velocity shifts
with much smaller alterations in shape and width, apparently
one large, or at least bright, feature dominates the spectrum
at most times. On the one hand, we might speculate that
the variations are caused by enormous convection cells with
the excursions discussed in Section 6 being the rising and
falling of the cells. On the other hand, we might imagine
the excursions are the surface trying to pulsate, but being
stochastically disrupted by other pulsation modes or large
convection cells. It may be that both processes are acting,
perhaps interacting. Do the observations allow us to identify the
dominant process?
The behavior in Figure 8, especially when coupled with the
bisector variations of Figure 7, is highly suggestive of large
convection cells seen rising through the photosphere, indeed,
becoming the photosphere, cooling and falling back down. At
the same time, it is easy to imagine the material “ringing” to
the eruption of such a large cell. If the ∼400 day timescale
of the excursions is comparable to the “echo” time from the
bottom of the convection zone, radial oscillations are likely.
Kiss et al. (2006) found mode lifetimes for Betelgeuse to be
1140 days, or about three cycles of ringing. By the time three
cycles have passed, another major convection cell erupts and
chaotic behavior is created in the parameters we observe. The
timescales for convection-cell episodes and pulsation of the
fundamental mode may both lie near 400 days, assuring power
peaks in the 400 day region of a periodogram, but the stochastic
driving of the convection produces a wandering period, variable
amplitude, and variable phase, i.e., the characteristics of the
observations.
It should also be noted that the phase relation between velocity
and temperature (Figure 8) is very different from those of
instability-strip pulsating stars, where the temperature varies in
phase, or nearly so, with velocity (see, for example, Wesselink
1946; Walhraven et al. 1958). Nor do the Betelgeuse velocity
variations resemble the much larger ones of the cool-supergiant
Mira stars, which show a monotonic rise over the full period
followed by a discontinuous drop seen as line doubling (e.g.,
Hinkle et al. 1982; Querci 1986; Jorissen & Udry 1998; Alverez
et al. 2001). Variations of the semi-regular variable WZ Cas
were studied by Lebzelter et al. (2005). Their results show
velocity to be in anti-phase with brightness, although with poor
amplitude tracking. Even though the translation of line-depth
ratio into magnitude (Figure 2) is imperfect, Betelgeuse does
not show an anti-phase relation during the time span of my
velocity measurements. Apparently the mechanisms proposed
to explain pulsation of other evolved stars are not immediately
applicable to Betelgeuse. Recall, however, the basic variation
in the depths of photospheric absorption lines (see G1) on the
same ∼400 day timescale that is most obviously explained by
changes in the continuous opacity. It may be that the kappa
pulsation mechanism (e.g., Bedding et al. 2005) is interacting
with the convection, resulting in transient pulsations.
The quadrature phase relation seen in Figure 8 is at least
potentially compatible with convection. That is, heating is
followed by the material rising; cooling followed by it falling.
Since cooling occurs over most of the rise-velocity phases,
considerable overshoot may be implied, depending on where the
(unknown) zero velocity lies in Figure 8. The opposite portion
of the cycle may be harder to understand, namely, why do we see
the temperature increase prior to seeing rise velocities? Taken
at face value, it implies that we see the material heating up
before it rises, as if a thermal pulse entered the material rather
than the cell acquiring its velocity below the surface, prior
to its becoming visible. Perhaps the observational coverage
during heating phases is actually too incomplete to draw this
conclusion. Furthermore, since we do not know the position of
zero velocity, we cannot be certain that all the velocities we
see are not rise velocities. This could occur if most of the light,
most of the time, comes from bright rising cells, the falling cells
being so cool and faint as to contribute negligible light.
The lack of close correspondence between visual magnitude
and temperature, discussed in Section 3, is expected with giant
convection cells simply because cells will vary in size, temper-
ature, and location on the disk. In addition, limb darkening for
a star like Betelgeuse is extreme, so a cell away from the disk
center would perturb the brightness more than the same cell at
the disk center. A behavior more coherent than the observations
indicate would be expected from radial pulsations.
There is also circumstantial evidence supporting convection
cells as the source of the variations. For example, the radial
velocity of metal lines, as published by Uitenbroek et al.
(1998a), shows a systematic rise (along with many smaller
variations) of ∼6 km s−1
over a 3500 day interval. This
corresponds to a radius change of ∼1300 solar radii or ∼1.6
stellar radii, which is hardly likely and implies that such a
simple interpretation of the radial velocity is naive. Furthermore,
the AAVSO magnitude (again ignoring shorter-term variations)
has remained essentially constant over this same time interval.
This kind of inconsistency is unlikely to find an explanation
in pulsation. Convection velocities, on the other hand, might
well introduce systematic displacements of this type because
(1) the lines are asymmetric and the asymmetry changes, which
could result in a different radial velocity measurement even if
the overall position of the line has not significantly changed,
and (2) the Doppler shifts of the bright gas might reasonably be
expected to dominate the radial velocity, producing a systematic
offset from the true space motion of the star. Variation of the
offset might vary from one epoch to another, in particular on
decadal timescales.
Polarization measurements (Hayes 1984) show variations in
strength and position angle on timescales of months to years, i.e.,
the same timescales shown by the excursions, that do not repeat
from one episode to the next. Not only is periodicity lacking,
but fundamental-mode oscillations are not expected to produce
polarization by virtue of geometrical symmetry, whereas no
such symmetry constraints exist with giant convection cells.
Hayes concluded that giant granulation cells offered the best
explanation of his polarization data.
Further, consider solar non-radial oscillations that are be-
lieved to be powered by the granulation. These oscillations have
characteristic velocities of ∼0.4 km s−1
compared to granula-
tion velocities an order of magnitude larger. If the excursions
displayed in Figure 8 were the comparable oscillations, then
where are the larger motions that drive them? The only other
velocities detected are those producing line broadening, and
these are of the same order of magnitude as the excursions. Un-
less there is some (unknown) process that transfers the energy

9. 1458 GRAY Vol. 135
of non-resonant modes into the resonant mode, the efficiency
would have to be near unity. It therefore seems more likely that
the excursions are the driving mechanism. If there are oscilla-
tions with ∼400 day periods, rather than this time simply being
the characteristic eruption time of the cells, they may occur as a
follow-up ringing of the excursions in a manner that is natural
and expected.
For all these reasons, the conclusion seems to be that large
convection cells dominate the ∼400 day variations, while os-
cillations are secondary. But is it possible that only one con-
vection cell essentially always dominates the spectrum? That
is, following the argument of G2, since motions of several
km s−1
are involved, how is it we never see split or bumpy
line profiles of the type one might expect if 2–10 convection
cells appeared at the same time? The hierarchy of convection-
cell dimensions seen in the Sun may give us a clue. Granulation
(∼1 Mm), supergranulation (∼30 Mm), and giant convection
cells (∼200 Mm) have been identified (e.g., Beck et al. 1998;
Lisle et al. 2004). The largest of these involves dimensions the
size of the convection zone itself. If this were transferred to
Betegeuse, the giant convection cells would have dimensions
essentially equal to the size of the star. Perhaps the observed
excursions are the giant cell motions, while the line broadening
reflects the Doppler-shift distribution of the combined super-
granulation, granulation, and smaller scale motions. The down
side of this argument is that the solar giant-cell velocities are
extremely small, perhaps ∼100 m s−1
, two orders smaller than
granulation velocities. To invoke giant cells in Betelgeuse im-
plies scaling up the giant-cell velocities to the same order as
the granulation velocities. The 400 day timescale would be the
typical time between cells surfacing, not the turnover time of
one cell.
Even though these arguments suggest that the main variations
arise from convection, the result is not yet definitive.
In any case, the dominant motions associated with the
excursions are not a primary contributor to macroturbulence.
Instead, motions within the large structures form the classical
macroturbulence of the type seen in lower-luminosity stars. In
other words, the motions of the excursions produce mainly
displacements of spectral lines, while the motions within the
moving material dominate the broadening of spectral lines. Is it
possible that these characteristics are an integral part of all stars
showing reversed-C bisector shapes?
The similarity of the chaotic velocity variations of Betelgeuse
and the radial-velocity phenomenon termed “jitter” should not
be overlooked. Jitter or real, but noise-like, variations in radial
velocity measurements of high-luminosity stars, after being first
seen by Gunn & Griffin (1979), has remained a puzzle. Jitter has
been noted in many investigations dealing with evolved stars.
A summary is given by Carney et al. (2003). It seems to make
its appearance near absolute magnitudes ∼0.5 and increases to
a few km s−1
at the tip of the red-giant branch. Since such a
radial-velocity variation is precisely the type of behavior seen in
Figure 6, it seems likely that jitter is caused by stochastic
convective motions and any oscillations they engender. If so,
a study of jitter will help map out the increasing vigor of
convection, perhaps giant convection cells, as a function of
position in the H–R diagram.
Bear in mind that only a limited range of time variations
has been included in this discussion. Events on longer and
shorter timescales are no doubt present. Whether or not detailed
hydrodynamical modeling can reproduce these observations
remains to be seen, and such modeling is in progress (Piskunov
et al. 2008, in preparation).
I am grateful to the Natural Sciences and Engineering
Research Council of Canada for continued financial support.
I thank M. Debruyne for technical support at the observatory,
the observers who contributed to the data over many years, and
to Kevin I. T. Brown, Bruce W. Carney, and a referee for helpful
suggestions. My thanks also go to the work of the AAVSO and
its many contributors around the world.
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