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A New VLA-Hipparcos Distance to Betelgeuse and its Implications

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The distance to the M supergiant Betelgeuse is poorly known, with the Hipparcos parallax having a significant uncertainty. For detailed numerical studies of M supergiant atmospheres and winds, accurate distances are a prerequisite to obtaining reliable estimates for many stellar parameters. New high spatial resolution, multiwavelength, NRAO33The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. Very Large Array (VLA) radio positions of Betelgeuse have been obtained and then combined with Hipparcos Catalogue Intermediate Astrometric Data to derive new astrometric solutions. These new solutions indicate a smaller parallax, and hence greater distance (197 ± 45 pc), than that given in the original Hipparcos Catalogue (131 ± 30 pc) and in the revised Hipparcos reduction. They also confirm smaller proper motions in both right ascension and declination, as found by previous radio observations. We examine the consequences of the revised astrometric solution on Betelgeuse's interaction with its local environment, on its stellar properties, and its kinematics. We find that the most likely star-formation scenario for Betelgeuse is that it is a runaway star from the Ori OB1 association and was originally a member of a high-mass multiple system within Ori OB1a.
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The Astronomical Journal, 135:1430–1440, 2008 April doi:10.1088/0004-6256/135/4/1430
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2008. The American Astronomical Society. All rights reserved. Printed in the U.S.A.
A NEW VLA–HIPPARCOS DISTANCE TO BETELGEUSE AND ITS IMPLICATIONS
Graham M. Harper1, Alexander Brown1, and Edward F. Guinan2
1Center for Astrophysics and Space Astronomy, University of Colorado, Boulder, CO 80309, USA; graham.harper@colorado.edu,alexander.brown@colorado.edu
2Department of Astronomy and Astrophysics, Villanova University, PA 19085, USA; edward.guinan@villanova.edu
Received 2007 November 2; accepted 2008 February 8; published 2008 March 10
ABSTRACT
The distance to the M supergiant Betelgeuse is poorly known, with the Hipparcos parallax having a significant
uncertainty. For detailed numerical studies of M supergiant atmospheres and winds, accurate distances are a pre-
requisite to obtaining reliable estimates for many stellar parameters. New high spatial resolution, multiwavelength,
NRAO3Very Large Array (VLA) radio positions of Betelgeuse have been obtained and then combined with
Hipparcos Catalogue Intermediate Astrometric Data to derive new astrometric solutions. These new solutions
indicate a smaller parallax, and hence greater distance (197 ±45 pc), than that given in the original Hipparcos
Catalogue (131 ±30 pc) and in the revised Hipparcos reduction. They also confirm smaller proper motions in
both right ascension and declination, as found by previous radio observations. We examine the consequences of
the revised astrometric solution on Betelgeuse’s interaction with its local environment, on its stellar properties,
and its kinematics. We find that the most likely star-formation scenario for Betelgeuse is that it is a runaway star
from the Ori OB1 association and was originally a member of a high-mass multiple system within Ori OB1a.
Key words: astrometry – radio continuum: stars – stars: individual (αOri) – stars: kinematics – supergiants –
techniques: interferometric
1. INTRODUCTION
The study of stellar activity, and in particular mass loss, in-
volves a combination of detailed numerical studies of individual
stars together with broader surveys of similar stars that measure
a variety of atmospheric diagnostics. To gain physical insight,
quantitative studies require accurate stellar parameters: for ex-
ample, the distance leads to the luminosity and when combined
with an angular diameter gives the physical radius and effec-
tive temperature; luminosity and isotopic abundances provide
estimates of the stellar age and mass. Except for ζAurigae
eclipsing binary systems, e.g., Bennett et al. (1996) and Harper
et al. (2005), accurate stellar parameters for cool supergiants are
not available.
The M supergiant Betelgeuse (αOrionis, HD 39801, HIP
27989) is bright, has a large wavelength-dependent angular
diameter, and has been the subject of many observational,
theoretical and modeling efforts. However, its distance and
therefore most of its other parameters are not well determined.
Prior to the Hipparcos Catalogue the most up-to-date published
parallax for Betelgeuse was π=9.8±4.7mas(d102 pc)
from the Fourth Edition of the Yale Trigonometric Parallaxes
(van Altena et al. 1995), while the Hipparcos Input Catalogue,
Version 2 (ESA 1993) gives a trigonometric parallax of π=
5±4mas(d200 pc). A summary of pre-Hipparcos stellar
motions and parallax is given in Table 1. The significance of
the Hipparcos parallax is not sufficient to derive the distance
or stellar peculiar velocity with confidence, and a wide range
of distance estimates have also been adopted by researchers.
For example, White (1980) used a CN index to derive Mv
which, with a visual extinction of Av=0.7, gave a photometric
distance of 96 pc, and Lambert et al. (1984) combined a mean
apparent magnitude of mv=0.8andAv=0.7 with an assumed
Mv=−5.85 to derive a distance of 155 pc, noting that a range
3The National Radio Astronomy Observatory is a facility of the National
Science Foundation operated under cooperative agreement by Associated
Universities, Inc.
of 0.3<A
v<0.8 was likely. A value of 400 pc was invoked
by Knapp & Morris (1985) to explain a discrepancy between
their circumstellar CO observations and models. This extreme
distance would imply that Betelgeuse is overluminous for its
spectral type (Huggins 1987), and this distance can likely be
discounted as independent observations of C Inow indicate that
CO is not fully associated in the stellar wind (Huggins et al.
1994).
The Hipparcos Catalogue (ESA 1997) provided a great
improvement in the distance estimates for many nearby stars
that have been studied in detail spectroscopically at multiple
wavelengths, and have interferometric angular diameters (e.g.,
van Belle et al. 1999; Mozurkewich et al. 2003). Unfortunately,
the Hipparcos astrometric solution for Betelgeuse (given in
Table 2) has significant uncertainties in both the parallax and
proper motions.4
In angular units (mas), following the Hipparcos nomencla-
ture, the uncertainties in R.A., the proper motion in R.A., and
the uncertainty in the proper motion are indicated by (αcos δ),
µαcos δ,and(µαcos δ), respectively. The Hipparcos solution for
Betelgeuse is a stochastic solution of type X (Hipparcos Cata-
logue: Section 2.3.6). The normal single star 5-parameter solu-
tion was found to be unsatisfactory because the χ2was larger
than expected based on the predicted measurement standard er-
rors. The Hipparcos astrometric solution is derived from 1D
position measurements (abscissae) of meridians whose posi-
tions are accurately known—the position of the star along the
individual meridians, however, is not well known. The astro-
metric solution is found by fitting astrometric models to these
abscissae. A detailed discussion is given in van Leeuwen &
Evans (1998).
In the case of Betelgeuse an additional error (noise) term was
added in quadrature (stochastic solution type X) to the abscissa
4The five astrometric parameters are: right ascension (R.A.) =α; declination
(decl.) =δ; parallax=π; proper motion in R.A. =µα, and proper motion in
decl. =µδ.
1430
No. 4, 2008 VLA–HIPPARCOS DISTANCE TO BETELGEUSE 1431
Tab l e 1
Pre-Hipparcos Proper Motions and Parallax, and the Stellar Radial Velocity
Parameter Value Uncertainty Units Source
µαcos δ25.73 0.30 mas yr1FK5 (J2000.0); Fricke et al. (1988)
µδ8.70.33 mas yr1FK5 (J2000.0); Fricke et al. (1988)
π9.84.7 mas van Altena et al. (1995)
vrad +20.70.4kms
1(heliocentric) Sanford (1933); Jones (1928)
Tab l e 2
Hipparcos Astrometric Solution: ICRS Epoch 1991.25
Parameter Value Units Error Units Comment
α88.79287161 deg 1.51 mas error in αcos δ
δ7.40703634 deg 1.13 mas error in δ
Parallax π7.63 mas 1.64 mas 131 ±30 pc
µαcos δ27.33 mas yr12.30 mas yr1
µδ10.86 mas yr11.46 mas yr1
Cosmic error 3.36 mas 0.62 mas stochastic type-X
Tab l e 3
Betelgeuse Proper Motions
Parameter Value Uncertainty Source
(mas yr1) (mas yr1)
µαcos δ27.33 2.30 Hipparcos;ESA(1997)
µδ10.86 1.46 Hipparcos;ESA(1997)
µαcos δ25.0 0.4 FK5 Rotated to Hipparcos 1151 stars
µδ9.0 0.4 FK5 Rotated to Hipparcos 1151 stars
µαcos δ23.98 1.04 VLA ICRF; Boboltz et al. (2007)
µδ10.07 1.15 VLA ICRF; Boboltz et al. (2007)
errors, σ, i.e.,
σ=σ2+2,
where is referred to as the cosmic error.Thevalueof
the cosmic error adopted is that required so that the reduced
χ21 and hence reflects the excess noise in the solu-
tion and may be related to the positional movement of the
stellar photocenter. For Betelgeuse the mean of the abscissa
standard errors is 2.2 mas, whereas the additional cosmic error
is 3.36 ±0.62 mas (Hipparcos Catalogue: Double and Multiple
Systems Annex). These larger errors lead to larger uncertainty
in the parallax than might otherwise have been expected. The
origin of this cosmic error, whether it is stellar (photocenter
motions on short timescales) or instrumental (resulting from
large bright sources), is under investigation,5buthasyettobe
understood.
Prior to Hipparcos, accurate proper motions were available
from the Fifth Fundamental Catalogue FK5 (Fricke et al. 1988)
(see Table 1). The formal errors on these proper motions are
much smaller (0.3masyr
1) than those given in the Hip-
parcos Catalogue (2masyr
1). The Hipparcos positions and
proper motions are tied to the International Celestial Refer-
ence System (ICRS) through a link between the Hipparcos Ref-
erence Frame and the ICRS with an uncertainty in the link
of 0.6 mas in the alignment of the axes (at J1991.25) and
0.25 mas yr1in the relative rotation of the systems (Hip-
parcos Catalogue: Section 1.2.2). The FK5 and Hipparcos cat-
alogs are not tied to each other so that reference frame rota-
tions between FK5 and the Hipparcos realization of ICRS must
5C. Babusiaux & A. Jorissen, presentation at the 4th Gaia Variable Star
Working Group (July 2005).
be considered before the proper motions can directly be com-
pared. The required angular rotation rates have been obtained
by comparing FK5 and Hipparcos proper motions for signifi-
cant stellar samples, e.g., Mignard & Froeschl´
e(2000), Schwan
(2001), and Walter & Hering (2005). The internal errors on
these derived rotations are 0.1 mas and we can convert Betel-
geuse’s FK5 proper motions into the Hipparcos frame using
Equations (7) and (8), and the 1151 star rotation rates given in
Walter & Hering (2005).6The rotated proper motions are given
in Table3andaresmallerthantheHipparcos values. Positions of
Betelgeuse also have been measured at radio wavelengths with
the NRAO Very Large Array (VLA) and these measurements
use phase (position) calibrators whose positions are accurately
known in the International Celestial Reference Frame (ICRF)
(Boboltz et al. 2007). The derived VLA proper motions are
alsogiveninTable3and suggest that the proper motions in
R.A. and decl. are overestimated by Hipparcos and therefore
the Hipparcos astrometric solution is not optimal. While these
independent proper motions are significantly different from the
nominal Hipparcos values, the large Hipparcos uncertainties do
not invalidate its astrometric solution.
Fortunately, the Hipparcos Catalogue also contains Interme-
diate Astrometric Data that provide the means to improve and
revise the astrometric solution when other measurements, such
as radio measurements, are available (van Leeuwen & Evans
1998). We have been undertaking a detailed multi-wavelength
and temporal study of the shape and brightness of Betelgeuse’s
6Walter & Hering (2005) also point out that the rotation rates can differ at
the 1 mas level in extreme cases depending on position with those expected
from the luni-solar precession correction; so additional systematic errors may
be present.
1432 HARPER, BROWN, & GUINAN Vol. 135
Tab l e 4
Radio Positions of Phase Calibrators, and their separation from Betelgeuse (From the Current VLBA Phase Calibrator List)
IAU name VLA calibrator R.A. Decl. Position error Reference Separation
name (J2000) (J2000) (J2000) (mas) (deg)
J0532+0732 0532+075 05 32 38.998475 07 32 43.34547 1.06 Ma et al. (1998)5.6
J0552+0313 0552+032 05 52 50.101502 03 13 27.24314 1.01 Beasley et al. (2002)4.2
extended atmosphere with the VLA in A configuration and the
VLBA Pie Town antenna to obtain maximum spatial resolution.
As part of this radio study we have also obtained new multi-
epoch radio positions.
In this paper we combine radio positions from our observ-
ing programs and archival data, published VLA positions, and
the Hipparcos Intermediate Astrometric Data (IAD) to obtain
new astrometric solutions and parallaxes for Betelgeuse. In
Section 2we present our new radio positions together with
previous measurements, and in Section 3we discuss the Hip-
parcos IAD for Betelgeuse. In Section 4we combine all
these datasets to find an improved astrometric solution, and in
Section 5we discuss the implications of the new astrometric
solutions for Betelgeuse, including its stellar parameters, the
wind–interstellar medium (ISM) bow shock identified in IRAS
images by Noriega-Crespo et al. (1997), and the likely birthplace
of Betelgeuse. Conclusions are given in Section 6.
2. VLA STELLAR POSITION MEASUREMENTS
The large cosmic error/noise term in the Hipparcos solu-
tion may be of stellar origin, perhaps related to movements
of the photocenter, of order 3.4 mas, in the Hipparcos pho-
tometric Hpband (Bessell 2000). In M supergiants this pass-
band and also the Vband contain TiO opacity which is sen-
sitive to changes in surface temperature. One can imagine
that above the photospheric granulation pattern there are re-
gions of different temperature with differing contributions to
the flux in the Hpband. The convective turn-over timescale
is 150–350 days (see Josselin & Plez 2007); however, most
of the Hipparcos measurements occur over two intervals each
spanning <92 days, so photocenter jitter is an unlikely expla-
nation for the source of cosmic error.
The thermal continuum emission at radio wavelengths pro-
vides a different view of the star, covering the outer photosphere,
chromosphere, and the base of the stellar wind (Harper et al.
2001). The collisional source function is the Planck function
on the Rayleigh–Jeans tail, which is linear in electron temper-
ature, and the specific intensity is therefore less sensitive to
surface temperature inhomogeneities on the stellar disk than
the Planck function at optical wavelengths at Teff 3600 K.
The VLA therefore provides new 2D position measurements
which possess different kinds of systematic uncertainties, such
as non-random extended structures related to non-radiative heat-
ing and mass loss. However, centimeter continuum radio opacity
is a well-defined function of frequency and temperature, so that
by considering multiwavelength positions obtained at the same
epoch we can examine and quantify these potential systematic
uncertainties.
2.1. New Multiwavelength VLA Observations
We have obtained a sequence of high spatial resolution VLA
observations of Betelgeuse in 2002–4 (programs AH0778 &
AH0824) to study the temporal evolution of Betelgeuse’s re-
solved atmosphere and to constrain thermodynamic changes
that occur when mechanical energy is deposited to form the
chromosphere and to drive the stellar outflow. The hot chro-
mosphere is visible in the ultraviolet and confined to a small
volume filling factor (Harper & Brown 2006), while the bulk of
the extended atmosphere is cool (Lim et al. 1998).
We have used the highest spatial resolutions available with
the VLA, i.e., A-configuration with the Pie Town VLBA
antenna, and these allow us to obtain positional uncertainties
comparable to Hipparcos. Good uvcoverage was obtained for
six frequency bands (Q,K,U,X,C,L)7at five epochs. For
each band we used two 50 MHz continuum channels recording
full Stokes polarizations. The analysis of these datasets provides
source size and intensity as functions of wavelength and epoch.
In this paper we present the positions of Betelgeuse, while the
thermodynamic study will be presented in a later publication.
The VLA observations were made by repeatedly interleav-
ing observations of Betelgeuse, which is slightly offset from
the field center by a couple of synthesized beam widths in
order to avoid potential errors at phase center, with a pri-
mary phase calibrator over a long enough range of time to
ensure good uvcoverage. Typically, each 11.5 h observation
provided 7 h of on-source data for αOri. Our observing se-
quence cycled through the full set of frequency bands roughly
every 2 h. The primary phase calibrator (J0532+0732, see
Table 4for calibrator details) has an accurate position in the
ICRF (Ma et al. 1998), and the phase solutions from this cal-
ibrator are used to correct for temporal tropospheric phase
fluctuations which are then transferred to the Betelgeuse field.
J0532+0732 is separated by 5.6from Betelgeuse and provides
accurate positions of Betelgeuse in the ICRF. The phase calibra-
tor (J0552+0313), which is fainter and separated by 4.2from
Betelgeuse, was used by Lim et al. (1998). Atmospheric phase
errors are proportional to frequency so that at shorter wave-
lengths a more rapid cycle between the source and the phase
calibrator, which established the source position, is required. At
the three shortest wavelength bands (Q,K,andU) an efficient
source–phase calibrator fast-switching technique was employed
(Carilli & Holdaway 1997). These three bands were observed
only at elevations greater than 20. Source–phase calibrator
fast-switching cycle times of 2–3 min were used depending on
the weather conditions. Reference pointing on the phase cali-
brator at Xband was performed prior to each section of fast
switching. At the longer wavelengths a conventional calibrator–
object–calibrator sequence was used with the Betelgeuse obser-
vations lasting between 8 and 12 min. Each 11.5 h observation
provided on-source data for Betelgeuse of roughly 0.5 h at Q,
1.0 h at Kand U, and 1.5 h at X,C,andLbands. The Qband
was not observed in our 2002 datasets.
The data were calibrated and edited within the Astronomical
Image Processing System (AIPS). Time intervals with instru-
mental problems or poor phase stability were identified using
the tasks TVFLG and CALIB and flagged. The calibrated data
7These bands have nominal wavelengths: Q=0.7 cm, K=1.3 cm,
U=2.0 cm, X=3.6 cm, C=6 cm, and L=20 cm.
No. 4, 2008 VLA–HIPPARCOS DISTANCE TO BETELGEUSE 1433
Tab l e 5
J2000 Radio Positions of Betelgeuse
Epoch R.A. Error Decl. Error Reference
Julian Year (J2000) (mas) (J2000) (mas)
2004.829 05 55 10.31227 2.5 07 24 25.4615 3.3 AH0824: Q, K, U, X, C, L
2004.805 05 55 10.31225 2.0 07 24 25.4616 4.8 AH0824: Q, K, U, X, C, L
2003.609 05 55 10.31045 4.1 07 24 25.4574 2.4 AH0824: Q, K, U, X, C, L
2003.4356 05 55 10.3097 5 07 24 25.461 12 AF0399: X, Boboltz et al. (2007)
2002.280 05 55 10.30752 1.8 07 24 25.4383 4.9 AH0778: K, U, X, C, L
2002.132 05 55 10.30725 1.7 07 24 25.4362 3.1 AH0778: K, U, X, C, L
2000.991 05 55 10.30519 1.2 07 24 25.4193 1.3 AL0525: Q, K
2000.943 05 55 10.3061 13 07 24 25.432 26 AF0376: X, Boboltz et al. (2003)
1998.241 05 55 10.30147 3.1 07 24 25.4014 5.7 AL0436: Q, K
1996.971 05 55 10.29911 8.9 07 24 25.3983 5.9 AL0398: Q, K, U, X
1987.655 05 55 10.28378 15 07 24 25.2867 15 AB0446: U
1982.4261 05 55 10.27623 30 07 24 25.2663 30 C, Johnston et al. (2003)
1982.4181 05 55 10.27564 30 07 24 25.2293 30 C, Johnston et al. (2003)
Notes.
The VLA program numbers are given for the new positions. The R.A. and decl. include guard figures. These positions
were used to derive astrometric solution No. 4, while solution 3 includes our X-band data and thus the relevant epochs
have slightly different positions and errors.
were CLEANed and imaged using IMAGR for comparison to
our uvplane fitting results.
Positions of extended sources are frequently measured from
radio maps using a simple function for the source specific
intensity such as a 2D Gaussian or a 2D uniform ellipse.
Since Betelgeuse is neither a Gaussian nor a uniform ellipse,
we have created a custom 2D specific intensity profile that is
a function of wavelength. This intensity function is derived
from the semi-empirical 1D spatially-resolved thermodynamic
model of Harper et al. (2001). The relationships between the
radio opacity and source function at adjacent wavelengths are
accurately known, so that multiwavelength observations allow
the temperature and mean density distributions, and hence the
wavelength-dependent specific intensity distributions, to be very
well constrained. The specific intensity distributions are shown
in Brown & Harper (2004), and have been generalized to have
a 2D elliptical form for greater flexibility.
This empirical multiwavelength approach to derive the spa-
tial specific intensity profiles is necessary because the source
is resolved and there are no theoretical models for the bright-
ness distributions resulting from the processes that extend the
atmospheres and drive mass loss from evolved cool stars like
Betelgeuse. These phenomena are the result of energy and mo-
mentum being deposited into the atmosphere so that the energy
balance and thermal structure are not known apriori.Notethat
in the absence of sufficient observational constraints additional
assumptions must be made, e.g., a prescribed temperature struc-
ture for Mira stars (Reid & Menten 1997).
The 2D intensity model fits are made on both the individual
visibilities and on a grid of binned data with different uv
cell sizes which allows the goodness of fit to be established.
The formal error of the 2D fits for individual wavebands are
smaller than the difference in position between the bands. We
also find that the positions measured with different uvbin
sizes are very similar, and that the positions measured in the
image map with JMFIT are very close to those measured in
the visibility data. Boboltz et al. (2003) find that their formal
fitting errors are typically smaller than the scatter of individual
position measurements made at a given frequency. These trends
suggest that some residual phase errors remain.
2.2. Published VLA Positions
Radio positions of Betelgeuse have been published by
Johnston et al. (2003), Boboltz et al. (2003), and Boboltz et al.
(2007). The two 1982 positions were obtained at Cband (6 cm)
with a single 50 MHz channel (Johnston et al. 2003), while the
2000 and 2003 Boboltz et al. observations were made with two
50 MHz channels at Xband (3.6 cm) in A configuration with
the Pie Town antenna. Boboltz et al. (2003,2007) have taken
advantage of the long time interval (21 yr) to derive a proper
motion (see Table 3). Their µαcosδand µδare about 1.5σand
0.5σbelow the nominal Hipparcos values, respectively. The
accuracy of these VLA positions is sufficient to constrain the
proper motions, but not the parallax directly.
2.3. Archival Observations
To increase the number of epochs with radio positions
we calibrated and measured several less comprehensive
datasets from the NRAO archive, including the data described
by Lim et al. (1998). The program numbers are given in
Table 5. The high frequency observations of Lim and colleagues
(programs: AL) also used the fast-switching technique.
2.4. VLA Positions
For each epoch where we have more than one wave-
length observation, we use the formal errors of the centroid
position fits for each band to form a weighted mean position.
The size of these errors reflects the quality of the phases, the uv
coverage, and deviations in source intensity from that which is
symmetric by a rotation of 180. We estimate the uncertainty
in the epoch positions by taking the standard deviation of the
positions measured in each band about the weighted mean po-
sition and adding in quadrature the mean formal fitting error
and phase calibrator uncertainty. For the 1987 single-frequency
U-band position we assign an uncertainty of 15 mas. In
Table 5we give the measured positions of Betelgeuse and their
1σuncertainties. The Julian date is given for the mid-time of
the observing session, or that from the published sources. The
positions we have measured have been corrected to the phase
calibrator positions given in Table 4, especially for J0552+0313
1434 HARPER, BROWN, & GUINAN Vol. 135
because the position given for this calibrator in the VLA Cal-
ibrator List has changed significantly over time. This results
in the phase center used for the calibrator being slightly offset
from its true position and this then introduces a corresponding
positional offset in the calibrated Betelgeuse data.
One potential source of variation of apparent stellar posi-
tion with wavelength is the presence of large-scale structures
in the stellar atmosphere. In that case the positions at adjacent
wavelengths should vary smoothly because the flux contribution
functions have significant physical (spatial) overlap. To inves-
tigate the potential magnitude of this effect we have examined
the 3D radiative hydrodynamic simulations of Betelgeuse by
B. Freytag and collaborators (Freytag et al. 2002; Chiavassa
et al. 2006). While there are no models that describe the ther-
mal structure of the extended M supergiant atmospheres, the
Freytag models describe the convective structure of the under-
lying photosphere. We find that the photocenter changes with
viewing angle at the fraction of a milliarcsecond level, while
the change with VLA frequency in a given snapshot is smaller.
The temperature contrast between the real hot chromosphere
and cool wind is larger than in the photosphere and there-
fore radio photocenter changes of order 1 milliarcsec would
not be unexpected. It is possible that some of the subtle Q
KUposition drifts seen in the 2004 data may be stellar in
origin.
Many of the more recent datasets have good uvcoverage
and long observation times and the source is sufficiently re-
solved that the formal fitting errors of the intensity centroid
are <1 mas and the positional uncertainties are 3 mas and thus
comparable to those obtained for point sources with the VLBA.
For the highest S/N data one is struck by the high repeatability of
the radio positions, for example the 2000.991 datum is a mean
of Q-andK-band observations taken a week apart, yet their
individual positions are within a fraction of a milliarcsecond in
both R.A. and decl. While the precision of many of the observa-
tions is very high our results are likely dominated by systematic
uncertainties with respect to the position of the center of mass
of the star. Our two 2004 datasets were obtained a week apart
and these have small formal errors. In R.A. both datasets show
a small decline in position with increased wavelength: QK
UXwith a 9 mas range, while in declination a similar decline
is seen in QKUbut the Xband increases by 10 mas. We
find a similar jump in declination in all our X-band data, but not
the Lim et al. (1998) 1996 data. Another advantage of the mul-
tiwavelength datasets is that the atmospheric phase errors are
proportional to frequency, so that different wavelengths should
be affected systematically to different degrees. The X-band data
were not obtained with fast switching and we may be detecting
signs of systematic error in the X-band radio positions. The
ionosphere can affect X-band positions and more so C-band.
We therefore compared our C-band positions and found that
they clustered nearer to the Q-, K-, and U-band positions rather
than following the trend observed in the Xband. We can offer no
explanation for the behavior of our X-band data, so in Section
4we consider the effect of including and excluding our X-band
data on the new astrometric solutions.
3. HIPPARCOS ASTROMETRIC SOLUTION
We have derived new astrometric solutions for Betelgeuse by
combining the VLA radio positions with the Hipparcos IAD,
which are described below. The IAD are given with respect
to the Hipparcos astrometric solution (ESA 1997)(givenin
Table 2) and we used the Hipparcos solution as the reference
solution in the following.
3.1. Intermediate Astrometric Data
The IAD are described in detail by van Leeuwen & Evans
(1998). The Hipparcos Catalogue (ESA 1997) represents the
merged results of two independent data reduction consortia,
NDAC (Lindegren et al. 1992)andFAST(Kovalevskyetal.
1992). For Betelgeuse, there were 18 NDAC and 20 FAST great
circle reductions and the results were merged to obtain the final
astrometric solution. The abscissa residuals v, the 1D offset
from the final solution that is shown in Table 2, are given in the
IAD provided by the two consortia in the catalog, along with
the partial derivatives that define
v=dv
da
a
where a=anew aHipparcos.TheHipparcos astrometric
solution is that which minimizes the square of the residuals.
The NDAC and FAST abscissa residuals for a given great
circle are correlated and the correlation coefficient is also
provided in the IAD. The IAD provides all the information
needed to decorrelate and properly weight the pair of great
circle solutions (van Leeuwen & Evans 1998). The resulting
equations can then be combined with other measurements, such
as the 2D radio positions, in a least-squares solution to improve
the overall astrometric solution, which we do in Section 4.
As discussed in Section 1, Betelgeuse required a signifi-
cant additional error source (cosmic noise) to obtained the ex-
pected χ2. The actual nature of this cosmic noise is not known
but it may be related to photocenter movement which is un-
likely to be random in position on short timescales and would
likely provide a systematic error in the astrometric solution.
The position angle of the star’s rotation axis has been mea-
sured from spatially resolved ultraviolet Hubble Space Tele-
scope spectra. Uitenbroek et al. (1998) found 55(measured
East of North) from absorption features in Goddard High Res-
olution Spectrograph data, and Harper & Brown (2006) found
65from emission features in multi-epoch Space Telescope
Imaging Spectrograph data. The distribution of photocenters,
perhaps driven by convective and Coriolis terms, may have a
special relation to the rotation axis. The stellar proper motion
vector also has a position angle of 68and brightness fluctua-
tions that occurred preferentially near the stellar equator might
induce scatter in the parallax displacements, although fluctua-
tions due to stellar rotation itself, would be unlikely because
of the 17 yr rotational period (Uitenbroek et al. 1998).
The position of the stellar image on the Hipparcos detector
is a function of effective wavelength that has been calibrated
in the Catalogue using non-contemporaneous Cousins VI
colors. A constant VI=2.32 was used for Betelgeuse in the
Hipparcos solution. Changes in the actual stellar VIduring
the Hipparcos mission could, therefore, lead to movement
of the apparent stellar positions induced by color variability.
This was seen in Mira stars whose colors change significantly
on timescales near 1 yr (Pourbaix et al. 2003). Betelgeuse
shows irregular photospheric variations on 5.78 yr (Sanford
1933) and 420 day (Dupree et al. 1987; Smith et al. 1989)
timescales. The shorter of these periods may potentially cause
some color induced movement in the apparent stellar position,
or an offset caused by differences in adopted and actual mean
VIcolor may lead to a slight systematic error. Platais
No. 4, 2008 VLA–HIPPARCOS DISTANCE TO BETELGEUSE 1435
-200 -100 0100 200 300 400
∆αcosδ (mas)
-150
-100
-50
0
50
100
150
200
∆δ (mas)
1982 Jan 1
2005 May 27
Figure 1. The predicted and observed positions of Betelgeuse. The positional
data considered in this paper are shown with the predicted positions of
Betelgeuse (black curve) based on astrometric solution No. 4. The begin and end
dates of the black curve are given. The circles show typical angular diameters
of the source: blue (optical: 45 mas) and red (radio 7 mm: 87 mas). The red
lines link the measured positions (blue) to the predicted positions. 1σerrors are
shown. The Hipparcos data are shown in more detail in Figure 2.
et al. (2003) derived relationships between contemporaneous
Hipparcos/Tycho photometry and Cousins VIcolors that
allow one to derive approximate corrections to the abscissa
residuals based on photometry obtained at the same epoch.
We combined the Hpand VTepoch photometry from the
Hipparcos Photometry Annexes with NDAC calibration data
(kindly provided by L. Lindegren) to estimate changes in
the abscissa residuals for both consortia following Pourbaix
et al. (2003). The astrometric solution was little affected, with
the cosmic noise dominating the small changes in abscissa
residuals, and we conclude that color induced abscissa errors
are not the cause of the cosmic noise.
4. REVISED VLA & HIPPARCOS ASTROMETRIC
SOLUTION
We now combine the 2D radio positions (α,δ) with the
1D Hipparcos IAD to derive new five-parameter astrometric
solutions for Betelgeuse. The square of the residuals for twice
the number of radio positions + 38 IAD decorrelated equations
were minimized. The Hipparcos cosmic error value was retained
for the IAD, although the expected change in proper motion
would actually lead to a slight increase in its value. The JPL
planetary ephemeris was used to calculate the apparent stellar
position for a given set of five astrometric parameters. Using
the IAD data and the cosmic error, the Hipparcos solution and
covariance matrix were reproduced.
The earlier radio positions of Boboltz et al. (2003)and
Johnston et al. (2003) have larger uncertainties than the IAD
abscissa residuals and cosmic noise, but they do cover a long
time span (21 yr) and clearly demonstrate the need for a down-
ward revision in both components of the proper motion. They
do not, however, constrain the parallax. Our multiwavelength
radio positions have smaller uncertainties (from the weighted
multiwavelength positions) and these provide significant new
constraints on the parallax and proper motion.
In Table 6we provide the astrometric solutions based on
different criteria and data sets. The first two use the Hipparcos
data with fixed proper motions. The solutions are: (1) IAD with
fixed FK5 proper motions; (2) IAD with the proper motion given
by Boboltz et al. (2007); (3) all VLA positions and IAD, and
(4) VLA positions (excluding our X-band data) and IAD. The
1σerrors of the new astrometric solutions have been scaled
(increased) to obtain a reduced χ2=1. The goodness-of-fit
measure shows that systematic errors are present in the radio
-40 -20 0 20 40
∆αcosδ (mas)
-20
-10
0
10
20
∆δ (mas)
New VLA-Hipparcos Soln.
-40 -20 0 20 40
∆αcosδ (mas)
-20
-10
0
10
20
∆δ (mas)
Original Hipparcos Soln.
Figure 2. Top: Enlargement of the new astrometric solution showing the
Hipparcos IAD. These are a 2D representation of the 1D abscissa data from the
FAST (green bar) and NDAC (blue bar) consortia. The measured source position
is offset from the astrometric solution by the length of the red connecting line,
but its position along the bar is unknown. For most great circle solutions there
are matching FAST and NDAC solutions. The total length of the green and blue
bars is arbitrarily shown with 2×the additional cosmic error/noise given in the
Hipparcos solution (i.e., 2 ×3.36 mas). The instrumental abscissa error is only
2.2 mas. Bottom: The original Hipparcos solution is shown for comparison.
data; however, we have not added any cosmic radio noise to
the radio positional uncertainties as was done in the Hipparcos
solutions.
Figure 1shows all the data included in astrometric solution
No. 4 and emphasizes the 24 yr span of the datasets. Figure 2
(top) shows an enlargement of the solution and shows how the
IAD fit the new combined solution, and (bottom) the original
Hipparcos solution. Figure 3shows enlargement of the recent
VLA radio positions.
Fixing the proper motions in solutions (1) and (2) does
not change the parallax significantly. However, when the radio
positions are included the parallax decreases. Because the IAD
data favors a larger parallax the Hipparcos and VLA datasets
are in tension. As noted in Section 2.4, there is an indication
that X-band is systematically offset in declination in our data
from the Q-, K-, and U-band positions, so in solution No. 4 we
further exclude our X-band positions from the weighted epoch
positions. In this solution the positions errors on decl. and this
is our preferred solution.
Solution No. 4 provides a distance of 197 ±45 pc to
Betelgeuse, which is greater than the original Hipparcos values
of 131 ±30 pc. The inclusion of the radio positions into the
combined astrometric solution has reduced both proper motions,
as found previously from VLA only data by Boboltz et al.
(2007). The parallax, however, is reduced by 2σfrom the
original Hipparcos value leading to a greater stellar distance,
size, luminosity, and space motion. The combined solution for
the parallax is in a sense a mean of the original Hipparcos
value and that from the radio data alone. The radio data are
not currently sufficient to define a reliable parallax, but they
1436 HARPER, BROWN, & GUINAN Vol. 135
150 200 250 300 350
∆αcosδ (mas)
40
60
80
100
120
140
∆δ (mas)
2005 May 27
Figure 3. Enlargement of the post-Hipparcos VLA radio positions which exclude our X-band data. The small errors on the VLA positions provides sufficient weight
in the combined solutions to reduce the parallax from its original Hipparcos value. The two largest error bars are the single frequency X-band Boboltz et al. positions.
The epoch 2000.991 position has a very small estimated uncertainty and provides tension in the proper motions with the 2002 and 2004 positions. Increasing the
uncertainty of the 2000.991 position to that of the smallest of our uncertainties leads to an increase in distance to 220 pc, i.e., 0.5σ.
Figure 4. Schematic representation of Betelgeuse’s position as a function of age
in galactic coordinates, compared to the positions of the young Orion Nebula
Cluster (ONC) and the older Ori OB1 association. The motion of Betelgeuse is
very different from the ONC which has a small velocity in the Z-direction (W).
The most likely formation scenario for Betelgeuse is as a runaway star from the
extended Ori OB1 association which has a similar age. Betelgeuse’s Wthen
would likely be the result of expulsion from a high mass multiple system.
suggest a value 330 pc (with a large uncertainty). New
multiwavelength radio observations are needed to improve the
parallax.
4.1. Comparison with the New Hipparcos Reduction
A new reduction of the Hipparcos raw data has very recently
become available (van Leeuwen 2007). One feature of this
reduction is significantly smaller astrometric formal errors for
bright stars. The new Hipparcos solution for Betelgeuse is given
in Table 7and compared with the original and our No. 4 solution.
It can be seen that the formal errors for proper motions are
decreased by more than a factor of 2. Both the revised µαcos δand
µδare >2σdifferent from our new combined result. The revised
Hipparcos parallax leads to a larger distance (152±20 pc) than
the original; however, the astrometric solution still requires a
significant cosmic noise of 2.4 mas. Given these results it is
clear that the Hipparcos data still contain systematic errors of
unknown origin.
The radio data also suffer from unknown systematic errors
and it is our hope that by combining these two datasets the new
solution mitigates the effect of these errors on the solution.
5. DISCUSSION
Now we discuss some of the implications of different distance
estimates for Betelgeuse’s interaction with its local environ-
ment, stellar parameters, and its place of birth. In the following
we adopt our new nominal distance of 200 pc.
5.1. Betelgeuse’s Wind-ISM Bow Shock
As Betelgeuse travels through its local interstellar environ-
ment, its massive M supergiant wind plows up material forming
an asymmetric arc observable in high-resolution IRAS 60 µm
and 100 µm images (Noriega-Crespo et al. 1997). The apex
of the arc has a position angle of 60±10, a mean thickness
of 1.5 arcmin, and an inner radius of 5 arcmin from the star
(Noriega-Crespo et al. 1997) which at 200 pc corresponds to a
mean physical projected radius of 0.33 pc. Within 2NE of the
arc there is a straight bar that may be cirrus, i.e., interstellar dust
heated by the ambient radiation field.
The radial velocity of Betelgeuse is best determined from
photospheric radial velocity observations when the 5.78 yr
pulsation signature is most stable, i.e., when the radial velocities
are least stochastic (Goldberg 1984). In Table 1we give the
mean of the Jones (1928) and Sanford (1933) values, i.e.,
Vrad =+20.7±0.4kms
1(heliocentric) moving away from
the Sun. The tangential velocities (in km s1) at a distance
Dare Vαcos δ=23.7[D(pc)/200] and Vδ=9.1[D(pc)/200],
with a position angle of 69.0east of north, which is consistent
with the infrared arc’s orientation. The new astrometric solution
corresponds to a galactic space velocity of U=−21.7,V =
11.5,W =+21.2kms
1,whereUis positive towards the
Galactic center. Correcting for the solar motion, the space
motion in the local standard of rest (LSR) is U=−12.7,V =
+0.5,W =+28.2kms
1.
If the arc is a result of a wind bow shock, the standoff distance
(Rso) is where the ram pressure of the wind balances that of the
No. 4, 2008 VLA–HIPPARCOS DISTANCE TO BETELGEUSE 1437
Tab l e 6
New Astrometric Solutions for Betelgeuse
Solution αcos δError δError πError µαcos δError µδError
(mas) (mas) (mas) (mas) (mas) (mas) (mas yr1) (mas yr1) (mas yr1) (mas yr1)
(0) Hipparcos 0.00 1.51 0.00 1.13 7.63 1.64 27.33 2.30 10.86 1.46
(1) Hipp + FK5 µ’s 0.51 1.38 0.85 0.91 7.11 1.51 25.0 ... 9.0 ...
(2) Hipp + VLA µ’s 0.52 1.39 0.55 0.91 7.32 1.51 23.98 ... 10.07 ...
(3)Hipp+AllVLA(Q,K,U,X) 0.20 1.77 0.85 1.20 4.32 1.29 24.93 0.10 9.42 0.18
(5) Hipp + VLA (Q, K, U, X)0.06 1.80 0.60 1.21 5.07 1.10 24.95 0.08 9.56 0.15
Notes.
ICRF Epoch 1991.25. R.A. and decl. are given with respect to the Hipparcos Solution (given in Table 1). Xdenotes that we have
excluded our X-band data.
Tab l e 7
Comparison of New and Original Hipparcos Results with the New Hipparcos Reduction
Parameter Value Uncertainty Source
(mas yr1or mas) (mas yr1or mas)
µαcos δ27.33 2.30 Old Hipparcos;ESA(1997)
µαcos δ27.54 1.03 New Hipparcos; van Leeuwen (2007)
µαcos δ24.95 0.08 This work
µδ10.86 1.46 Old Hipparcos;ESA(1997)
µδ11.32 0.65 New Hipparcos; van Leeuwen (2007)
µδ9.56 0.15 This work
π7.63 1.64 Old Hipparcos;ESA(1997)
π6.56 0.83 New Hipparcos; van Leeuwen (2007)
π5.07 1.10 This work
surrounding material, i.e.,
Rso =˙
MV
4πρV 2
(1)
(Wilkin 1996), where Vis the peculiar motion of the star
with respect to the local medium of density ρ,andVand
˙
Mare the wind outflow speed (in the frame of the star) and
mass-loss rate, respectively, at the distance Rso from the star.
Circumstellar absorption features indicate V17 km s1
(Bernatetal.1979), and a representative estimate of the
mass-loss rate is ˙
M3×106Myr1(Harper et al.
2001). Betelgeuse has a small radial velocity in the LSR, and
the Sun’s peculiar motion is directed away from Betelgeuse
contributing most of the observed heliocentric radial velocity.
If the environs near Betelgeuse are at rest in the LSR, we can
estimate the star’s peculiar velocity with respect to the LSR as
VV2
αcos δ+V2
δ25 km s1and the bow shock will be
viewed close to edge on. These values then provide an estimate
of the density of the material surrounding the star.
When the stellar motion in and out of the plane of the sky is
small, the hydrogen density of the material being swept-up by
the stellar wind (nH)isgivenby
nH
cm33.7×107
ΣD
pc2θ
arcmin2˙
M
106Myr1
×V
km s1 V
km s12
(2)
where Σis the mean mass per hydrogen nucleus (1.4) of the
surrounding material, and θis the observed angle between the
star and the bow shock. Since VD,thennHis a strong
function of distance, nHD4.
The initial analysis of the enhanced resolution IRAS images
by Noriega-Crespo et al. (1997) assumed a stellar distance of
D=400 pc and adopted a mean shell distance of θ7arcmin,
and obtained nH0.1cm
3which is typical of the local ISM.
(This should have been nH0.05 cm3because the power
of the mean mass has an incorrect sign in Equations (1) of van
Buren & McCray 1988 and Noriega-Crespo et al. 1997)
The original and revised Hipparcos distances of 131 pc and
152 pc, respectively imply a major change in the inferred
hydrogen density. The large reduction in distance by a factor
of 3 leads to a large increase to nH23cm
3,whichis
inconsistent with the picture of the local ISM towards galactic
coordinates l=200,b=−9, namely, a hydrogen column
density of NH1019 cm2with ¯nH0.05 cm3(Paresce
1984), and ¯nH0.3cm
3for material in front of the Orion
OB association (Frisch et al. 1990).
The wind-ISM bow shock model with our new VLA-
Hipparcos distance implies a smaller but still high local density
of nH1cm
3. For distances greater than 75 pc, beyond the
Local Bubble (Lallement et al. 2003), Betelgeuse lies near the
edge of a cavity of low neutral hydrogen density and close to a
steep gradient in ISM column density between l=180–200.
It is possible that the increase in ISM column density in this
region is associated with larger particle densities. Visual inspec-
tion of the IRAS images reveals an interesting detail: the shape
of the 60 µm and 100 µm arcs are rather circular. However, the
ratio of the angular separation of the arc apex and the arc at 90
to the apex in this idealized wind-ISM bow shock model should
be close to 1/3 (Wilkin 1996), which is smaller than observed
and the discrepancy gets worse if there is a radial velocity com-
ponent with respect to the LSR. This may mean that the arcs
are shaped by an interaction of stellar mass loss at past and
present epochs rather than direct interaction with the interstellar
medium.
1438 HARPER, BROWN, & GUINAN Vol. 135
Tab l e 8
Stellar Properties Inferred as a Function of Distance
Property Distance
150 pc 200 pc 250 pc
Bolometric luminosity (ergs s1) 4.87 5.12 5.31
Initial mass (M)17 20 24
Age (106Yr) 13 10 8
Space velocity (LSR)[U,V,W](kms
1)[12, 2, 22] [13, 0, 29] [13, 1, 35]
Note. For the space motions the proper motions are held constant.
In the bow shock scenario, the flow velocities are low enough
that the post-shock cooling length is smaller than the shell
thickness and the wind-ISM shock is potentially unstable. The
isothermal stellar wind bow shock instabilities examined by
Blondin & Koerwer (1998) have length scales of the order of
the standoff distance, which is larger than suggested by the IRAS
images. The ratio of Betelgeuse’s peculiar velocity to the wind
speed is only V/V1.5 and as a consequence it might only
be modestly unstable (Dgani et al. 1996). New AKARI, and
future higher spatial resolution and more sensitive far-infrared
images, may help clarify the nature of the infrared arcs and any
substructure they contain.
5.2. Stellar Properties
αSco (M1 Iab + B3 V: Antares) and CE Tau (M2 Iab-Ib:
119 Tau) are both nearby M supergiants with spectral types
close to that of Betelgeuse (M1-M2 Ia-Iab). The MK desig-
nations are from Keenan & McNeil (1989), and change by a
sub-type during the erratic pulsation cycle. Betelgeuse might be
slightly more luminous than αSco which has a similar angular
diameter and pulsation period. αSco also has a large uncer-
tainty in its Hipparcos parallax, 5.40 ±1.68 mas, and it also
has essentially the same cosmic error 3.37 ±0.59 mas. CE Tau
is more distant (π=1.70 ±0.80 mas), and although it has a
smaller parallax uncertainty its distance is also uncertain. The
paucity of local M supergiants makes it difficult to calibrate ob-
servational diagnostics that might provide additional constraints
on the stellar distances.
Different estimates of Betelgeuse’s observed (de-reddened)
integrated bolometric flux are in reasonable agreement, in part
because of the low interstellar and circumstellar extinction near
the stellar flux peak: i.e., FBol =1.0±0.1×104erg cm2s1
(Harper et al. 2001), and FBol =1.1±0.1×104erg cm2s1
(Perrin et al. 2004), and the luminosity is then given directly in
terms of distance by
log L
L=5.12 + 2 log D
200pc.
At a distance of 197 pc with the uncertainty from our parallax
measurement Betelgeuse would have a bolometric luminosity
of log L/L5.10 ±0.22 (1σ). This corresponds closely
to the 20 Mstellar evolution model of Meynet & Maeder
(2003) which would have a main-sequence spectral-type of O9
V. This set of models, which includes the effects of mass loss and
rotation, are probably the most appropriate set for comparison to
Betelgeuse (see Levesque et al. 2005). Table 8shows the implied
properties of Betelgeuse for different assumed distances. The
radius of Betelgeuse is then 950 Rboth from the observed
near infrared photospheric angular diameter (φ=45 mas, e.g.
Perrin et al. 2004) and from the measured luminosity and an
effective temperature of 3650 K (Levesque et al. 2005). The
evolutionary models suggest that the current mass of the star is
18 Mwhich corresponds to a surface gravity of 0.5cms
1.
At the 2σupper bound to the distance of 300 pc the bolometric
luminosity is log Lbol =5.47, which is close to the 25 M
model of Meynet & Maeder (2003).
Indirect estimates of the luminosity can be made using
period–luminosity relations. Turner et al. (2006) presented an
empirical period–luminosity relation for semi-regular (SRc) M
supergiant variables in Per OB1 and Berkeley 87, and found that
the relation was consistent with selected linear non-adiabatic
pulsation models of Guo & Yi (2002). Betelgeuse shows at
least two periods and both the 5.78 yr and 400 day periods
are observed in radial velocity and light curves, although the
radial velocities and light curves are not tightly correlated. The
Turner et al. (2006) relation for Betelgeuse’s shorter period,
similar to BU Per, T Per, and SU Per (Kiss et al. 2006; Stothers
1969) implies log L/L4.75, which is consistent with the
Hipparcos distance, while the Kiss et al. (2006) period–K-
magnitude relation gives 200 ±40 pc which is close to our
preferred distance.
Betelgeuse’s radial velocity amplitude, when present, is
similar for both periods so that the longest period leads to
the largest change in radius and may be the fundamental
mode. Wasatonic et al. (2005) also found dual photometric
periods of 350–450 days and 6.16 yr for TV Gem (M1 Iab)
and concluded that the 6.16 yr period was the fundamental
mode. Only the models more massive than 18Min Guo &
Yi (2002) have fundamental and first overtone periods that
have these range of values and luminosities consistent with
our revised distance. However, from their analysis of brightness
variations in M supergiants, Kiss et al. (2006) conclude that
the long secondary periods (i.e., >1000 days) are not radial
pulsations in accord with Stothers & Leung (1971). Clearly
period–luminosity relations, observational or theoretical, are not
yet sufficiently well understood to help constrain Betelgeuse’s
distance, and we note that the large fractional radius changes
associated with the longer periods have yet to be fully addressed
by theoretical pulsation models.
Some previous estimates of the distance have used the
Vmagnitude. We do not anticipate significant interstellar
reddening in Betelgeuse’s line-of-sight, but there will be some
visual extinction associated with the circumstellar dust shell.
Betelgeuse is oxygen rich, and its dust shell has been modeled
with silicate grains, e.g., Rowan-Robinson et al. (1986). Silicates
grains with characteristic radius 0.1µm have a high albedo in
the Vband and in the ultraviolet between 2000–3000 Å. We can
estimate the visual dust absorption by noting that low intrinsic
optical depth ultraviolet emission lines observed in International
Ultraviolet Explorer (IUE) spectra are not systematically red-
shifted with respect to the star (Carpenter 1984). The emission
No. 4, 2008 VLA–HIPPARCOS DISTANCE TO BETELGEUSE 1439
line Doppler line widths are comparable to the gas wind speed
(i.e., 17 km s1), and the R12,000 resolution IUE spectra
obtained through the 10 ×20 large aperture would collect
most of red-shifted backscattered dust emission. Using the dust
grain constants and size distribution described in Harper et al.
(2001) and requiring that the scattering optical depth in the
ultraviolet be τuv
sca 3 to allow for the forward scattering phase
function and dust absorption, e.g., Lef`
evre (1992), we estimate
that the circumstellar dust shell has V absorption optical depth
of τV
abs 0.2. Adopting an MV5.85 for an M1-2 Iab star,
which is consistent with the value for the M supergiant in the
αSco binary system, and an upper-limit of AV=0.22 we find
for αOri that a mean ¯
V0.65 implies that the distance is
180 pc, which is on the near end of our new distance range
but on the far end of the Hipparcos distance.
5.3. The Life and Times
The kinematics of Betelgeuse are intriguing and not easily
explained. The space motion is [U,V,W]=[12.7,+0.5,
+28.2kms
1] for a distance of 197 pc. The current galactic
coordinates relative to the Sun are [X,Y,Z]=[182,66,
31 pc] and therefore projection of Betelgeuse’s space motion
back in time only takes the star farther from the galactic plane.
The age of an early M supergiant with an initial mass of 20 M
is 10 Myr (Meynet & Maeder 2003) and Betelgeuse would
have moved 290 pc farther from the galactic plane over that
time interval. Projecting the star’s spacemotion back in time for
10 Myr does not place it close to any likely star formation region
for any adopted distance between 150 and 300 pc.
One possible explanation is that Betelgeuse has not fol-
lowed its current space motion for all its life. If the space mo-
tion is projected backwards in time, 2.5 Myr ago Betelgeuse
passed through the extensive Ori OB1a star-formation region.
Brice˜
neno et al. (2005) find an age of 7–11 Myr for Ori OB1a de-
pending on the evolutionary tracks used (7.4 Myr results from
the Baraffe et al. (1998) tracks, while 10.7 Myr results from
those of Siess et al. (2000)). One of the clearest subassocia-
tions within Ori OB1a is the 25 Ori group which has an age of
10 Myr and a distance of 330 pc (Brice˜
no et al. 2007)and[X,Y,
Z]=[292,112,104 pc]. αOri’s projected path apparently
does not intersect precisely with the 25 Ori group but the space
motion for this group is not yet measured. However, the most
likely formation scenario is that Betelgeuse is another runaway
star from Ori OB1 (see, e.g., Hoogerwerf et al. 2000)andwas
originally a member of a high-mass multiple system within Ori
OB1a.
Formation close to the far younger Orion Nebula Cluster
(ONC, also known as Ori OB1d) is much less likely. The
distance to the ONC has been measured from VLBA astrometry
to be 389+24
21 pc (Sandstrom et al. 2007) and 414 ±7 pc (Menten
et al. 2007). The space motion of the ONC is approximately
[U,V,W]=[11.0,2.4,+1.1kms
1] (see Sandstrom
et al. 2007) and its location is [X,Y,Z]=[322,178,
129 pc]. While the ONC lies more than 100 pc from the
galactic plane, its motion orthogonal to the galactic plane is
very small unlike the motion of Betelgeuse. Figure 4shows a
representation of Betelgeuse’s position as a function of age in
comparison with the young ONC and older Ori OB1 association.
6. CONCLUSIONS
Positions of Betelgeuse from high spatial resolution multi-
wavelength VLA observations have lead to a reduction in the
parallax, and an increased distance, as compared to that mea-
sured by Hipparcos. Our new proper motions are barely consis-
tent with the latest Hipparcos solutions and the required cosmic
noise suggests that systematic errors remain in the Hipparcos so-
lution. By combining the Hipparcos and VLA positional data,
the different kinds of systematic erros may result in a more
robust result. In a sense, the derived distance of 200 pc is a
balance between the 131 pc Hipparcos distance and the radio
which tends towards 250 pc. Future new radio positions should
lead to an improved astrometric solution.
It should be borne in mind that because the angular size of
Betelgeuse is significantly greater than its parallax it is not an
ideal target for parallax studies. However, the multiwavelength
approach allows for checks on systematic errors arising from
atmospheric phase corrections and unresolved stellar structures,
and provides robust error estimates on the measured stellar
positions. Understanding the systematic behavior of the non-
fast-switched X-band declinations may allow further refinement
of the parallax, and using X-band fast-switching may elucidate
this matter. We plan to reobserved Betelgeuse at strategic epochs
in order to refine the parallax.
The Hipparcos and VLA-Hipparcos distances both suggest
that if the infrared arcs observed 7from the star are indeed a
wind-ISM bow shock then the surrounding ISM densities are not
typical of local interstellar properties, and perhaps Betelgeuse’s
mass loss is plowing into the remnants of previous epochs of hot
star mass loss. The new space motions suggest that Betelgeuse
was not formed near the ONC, but more likely was a member
of a high-mass multiple system within Ori OB1a.
We thank the referee for their careful review which materi-
ally improved this work. This research was supported by NASA
under ADP grant NNG04GD33G (GMH) issued through the Of-
fice of Space Science, by NSF grant AST-0206367 (AB,GMH),
and travel support by NRAO. We wish to thank C. Carilli and
M. Claussen for their assistance in the planning and execution
of the observations for VLA projects AH0778 and AH0824. We
also thank S. Engle for his assistance.
Facilities: VLA, Hipparcos.
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... Designated in the HRD and M-K spectral system as M2-Iab and a well-known Type C semiregular (SRc) variable, the bright pulsating RSG has been on the hot seat for popular press and astronomy aficionados caused by its deep dimming episode in November 2019 to March 2020. α Ori is characterized by a current mass of 16.5 -19 M ⊙ [8], T eff of 3600 ± 25 K with a dilemma to the massive star's position on the HRD [9], varying size at ∼ 600 -1000 R ⊙ , proximity reinforced seismically up to ∼ 130 -200 pc, and a promising candidate of being a post-merger star [8,[10][11][12][13]. ...
... Other than being a fast rotator, it is noteworthy that α Ori is among the few RSGs that are known as 'runaway stars' moving supersonically throughout the interstellar medium (ISM) with a measured space velocity of ∼ 30 km s −1 and a kinematic age of ∼ 7 -11 Myr. Backwards extrapolation of α Ori's 10 Myr trajectory reveal that it is closely linked to the high-mass multiple system within Ori OB1a as its birthplace [11,12,30]. Yet, some [31] invoke a two-step dynamic approach: 1. being ejected instead within the first few million years and 2. an ensuing merger of the binary or an SNe of the high-mass component, discharging the surviving α Ori at some post-MS phase of its evolution. ...
... Despite being a touch higher by 0.6 mag, the quantity remains slightly loose compared to the pronounced stellar L though also strictly permitted by the imposed T eff range. [11] Note. -Annotated with asterisks are acting as arbitrary pulsation periods that are close to those of acquired. ...
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We conduct benchmarking analysis of the semi-regular pulsator and red supergiant α Ori. On its dimming episode last 2020, our observational results include the binned-measurements from space-based telescope SMEI collated. We report a long secondary period of PLSP = 2350 ± 10 d and a fundamental pulse of P0 = 415 d ± 30 d for the interest. Meanwhile, we also detected the first overtone component of 185 ± 10 d which supports the current literature's standing for this newly acquired pulse. At ∼2.20 ± 0.10 μm, we acquired Near-Infrared K-band photometric measurements from several catalogues and surveys in accordance of the calibration. Our assigned inherent color plays at the middle of the extremes from existing literatures. Likewise, we attained a weighted excess color index of E(B−V) = 0.340 and using a K-extinction factor of RK = 0.382 yields to an extinction of AK = 0.130. By subtracting extinction to all K-band photometry, using the linearity, and newly-derived distance from previous literatures, our effort results to a log(L/L⊙) = 5.00 ± 0.15 (+0.48, −0.45) for α Ori. In turn, this allows us to conduct the benchmarking scheme alongside the data from existing reports that are stitched together using period-luminosity relationship. This results to a best-fit of log(L/L⊙) = 7.26 ± 0.10 × log Ρ + (-14.10 ± 0.25) which reveals that α Ori can be situated into the lower bound 18 M⊙ regime caused by the current pulsation trends.
... Unfourtunately, due to the difficulty in obtaining precise distance measurements (Harper et al. 2008(Harper et al. , 2017, many of Betelgeuse's fundamental stellar properties remain uncertain. As a result, there is currently no clear consensus on Betelgeuse's evolution history, and thus we cannot immediately explain the dimming episode nor predict its future course of evolution with only observations. ...
... For ease of comparison, observational constraints for the HR diagram used in this paper will be the same as those adopted by Dolan et al. (2016), namely log L/L ⊙ = 5.1±0.22 and T ef f = 3500±200 K, where L and T ef f are luminosity and effective temperature. The adopted surface temperature is the result of an average of past studies as the surface temperature of Betelgeuse is known to vary, and the luminosity is derived from the distance measurement given by Harper et al. (2008). A new distance measurement was reported by Harper et al. (2017), but since it only differs from the 2008 results by 0.7σ, we stick with the 2008 results for ease of comparison. ...
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... Lennon et al. 2018) and less commonly in RSGs (e.g. Orionis; Harper et al. 2008). The relatively few systems that remain bound can be observed as massive stars with compact object companions (Gottlieb et al. 2020;Hinkle et al. 2020;Lennon et al. 2021), which may produce DCO binary systems (Kruckow et al. 2018;Langer et al. 2020). ...
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We developed a 3D radiative transfer code which computes emerging spectra and monochromatic maps from radiative-hydrodynamic (RHD) simulations of red supergiant stars. Computed emerging spectra show that our RHD models qualitatively reproduce the velocity amplitude and line asymmetries in observations. However, they cannot reproduce strong and weak lines simultaneously. This is explained by the shallow thermal gradient which weakens the contrast between strong and weak lines. The non-grey treatment of opacity in RHD models is planned in the near future to solve this problem. Moreover, we are now studying the possibility to detect and measure the granulation pattern with interferometers such as VLTI/AMBER, using our monochromatic intensity maps and visibility calculations.
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In the present paper we present an analytical representation of the relations between the systems of the HIPPARCOS catalogue and the Basic FK5 catalogue. These relations were used in the construction of the ``Sixth Catalogue of Fundamental Stars (FK6)'' for the reduction of the FK5 to the HIPPARCOS system. A comparison has been made between the present results and those derived by Mignard and Fr\oe schlé recently. A computer program for evaluating analytically the systematic differences will be provided via the Internet facility.
Article
We present hydrodynamical simulations illustrating the instability of stellar wind bowshocks in the limit of an isothermal equation of state. In this limit, the bowshock is characterized by a thin dense shell bounded on both sides by shocks. In a time-averaged sense the shape of this bowshock shell roughly matches the steady state solution of Wilkin (1996)[ApJ, 459, L31], although the apex of the bowshock can deviate in or out by a factor of two or more. The shape of the bowshock is distorted by large amplitude kinks with a characteristic wavelength of order the standoff distance from the star. The instability is driven by a strong shear flow within the shock-bounded shell, suggesting an origin related to the nonlinear thin-shell instability. This instability occurs when both the forward bowshock and the reverse wind shock are effectively isothermal and the star is moving through the interstellar medium with a Mach number greater than a few. This work therefore suggests that ragged, clumpy bowshocks should be expected to surround stars with a slow, dense wind (which leads to rapid cooling behind the reverse wind shock), whose velocity with respect to the surrounding interstellar medium is of order 60kms−1 (leading both to rapid cooling behind the forward bowshock and sufficiently high Mach numbers to drive the instability).
Article
Supergiant stars such as Betelgeuse have very extended atmospheres, the properties of which are poorly understood. Alfvén waves, acoustic waves,, and radial pulsations have all been suggested as likely mechanisms for elevating these atmospheres and driving the massive outflows of gas seen in these stars: such mechanisms would heat the atmosphere from below, and there are indeed observations showing that Betelgeuse's extended atmosphere is hotter than the underlying photosphere,. Here we report radio observations of Betelgeuse that reveal the temperature structure of the extended atmosphere from two to seven times the photospheric radius. Close to the star, we find that the atmosphere has an irregular structure, and a temperature (3,450 +/- 850K) consistent with the photospheric temperature but much lower than that of gas in the same region probed by optical and ultraviolet observations. This cooler gas decreases steadily in temperature with radius, reaching 1,370 +/- 330K by seven stellar radii. The cool gas coexists with the hot chromospheric gas, but must be much more abundant as it dominates the radio emission. Our results suggest that a few inhomogeneously distributed large convective cells (which are widely believed to be present in such stars) are responsible for lifting the cooler photospheric gas into the atmosphere; radiation pressure on dust grains that condense from this gas may then drive Betelgeuse's outflow.
Article
A survey of variations in the radial-velocity and visual brightness of the star Betelgeuse (alpha-Orionis) over the last six decades is presented. On the basis of a comparison of the results of several observations, it is suggested that major disturbances in Betelgeuse's atmosphere are likely to occur in the year or two following the minimum in the six-year velocity curve. A coordinated observing program is proposed to take place during and after the next minimum, which is predicted to take place in early 1984. The desirable observations include multicolor photometry (particularly in the infrared), polarization measurements, and spectroscopy.
Article
The comparison of Hipparcos and FK5 proper motions points to an inconsistency with the correction, Delta p, of the luni-solar precession derived from VLBI and LLR observations with unprecedented accuracy. An attempt is made to explain this inconsistency of approximately -1.3 mas/yr by rotational offsets of the Hipparcos and FK5 proper motion systems. In terms of right ascension and declination, these offsets give rise to proper motion offsets in the range of ±1 mas/yr on average which is not exceptional given the FK5 error budget. In the case of Hipparcos it is proven that the proper motions are not affected by rotational offsets larger than those indicated by the errors of the proper motion link to the ICRF. This result is obtained by analysing the Hipparcos proper motions in view of the existence of additional systematic motions other than those caused by galactic rotation and the parallactic motion of stars due to the solar motion with respect to the LSR. It is concluded that the Hipparcos proper motions are nearly free of unmodelled rotations, confirming that the Hipparcos frame is inertial at the accuracy level of the proper motion link to the ICRF. The gap between the estimated precessional corrections is bridged primarily by minor changes in the FK5 proper motions of the order of their errors, and only to a small extent by the elimination of a bias in the Hipparcos proper motions.