# Betelgeuse: a Review

J. Craig Wheeler  Department of Astronomy, University of Texas at Austin,
Austin, Texas, USA  Emmanouil Chatzopoulos  Department of Physics & Astronomy,
Louisiana State University, Baton Rouge, 70803, Louisiana, USA  Institute of
Astrophysics, Foundation for Research and Technology-Hellas (FORTH),
Heraklion, 70013, Greece J. Craig Wheeler<EMAIL_ADDRESS>
(Received 2023 March 31)

###### Abstract

Betelgeuse has fascinated people since they first looked at the sky. Here we
present a contemporary summary of the observations and theory that lead to
current understanding of Betelgeuse as a massive red supergiant doomed to
eventual collapse and explosion, probably $\sim$ 100,000 years from now.
Although it lies only $\sim 200$ parsecs from Earth, and hence can be
spatially resolved with appropriate instrumentation, uncertainties in its
distance remain a critical impediment to deeper understanding.

The surface of Betelgeuse is rent with a complex structure as deep convective
eddies arise to the surface affecting the photosphere, chromosphere, mass
loss, the formation of dust and molecules, and the surface magnetic field
structure. The global effective temperature has some irreducible uncertainty
because of associated temperature variations in the atmosphere. The surface
gravity is not precisely known, leading to further uncertainties in the
current mass. Determination of the equatorial rotation velocity is critical
since some current estimates indicate that Betelgeuse is rotating anomalously
rapidly, near rotational breakup, a property that cannot be explained by basic
single-star evolutionary models. Betelgeuse is also moving through space at
high, though not unprecedented, velocity that indicates that it received a
boost, perhaps through collective interaction with other stars in its birth
cluster, though disruption of an original binary system has been suggested. A
bow shock and other structure in the direction of the motion of Betelgeuse
suggests that it has affected the organization of the distant circumstellar
and interstellar medium. Betelgeuse varies in brightness on a variety of time
scales with $\sim 200$ d, $\sim 400$ d and $\sim 2000$ d being prominent.
Models of this variability may be in conflict with historical records
suggesting that Betelgeuse was yellow in color, not red, only two millennia
ago.

Betelgeuse is also subject to a rich variety of theoretical studies that
attempt to understand its observational properties and current evolutionary
state. Betelgeuse is statistically probable to have been born in a binary
system, and the high space velocity and apparent rotation have been related to
binary star evolution. One possibility is that Betelgeuse has been subject to
common envelope evolution in which a companion star plunges into the primary
and becomes tidally disrupted as it nears the core of the primary. This
interaction is complex in three dimensions and not sufficiently well
understood. Such merger models have been invoked to account for the apparently
anomalous rotation velocity.

Betelgeuse underwent a Great Dimming in 2020 that caught the attention of
astronomers and the general public world wide. Explanations have focused on
large cool spots on the surface and the expulsion of a cloud of dust that
obscured the surface.

We finally sketch the nature of the explosion to come and finish with
perspectives for further research.

††journal: Astronomy & Geophysics, June 1 2003, Volume 64, Issue 3††software:
mesa (Paxton et al., 2011; Paxton et al., 2013, 2015, 2018)

##  1 Introduction

Betelguese ($\alpha$ Orionis) is a nearby, massive red supergiant (RSG) that
is most likely destined to explode as a classic Type IIP supernova (SN IIP)
and leave behind a neutron star. Study of Betelgeuse thus promises insight
into a broad range of issues of the structure, evolution, rotation, magnetic
fields, mass loss, stellar winds, circumstellar medium, dust formation,
atmospheres, chromospheres, radiative transfer, nucleosynthesis, and,
eventually, the explosion of massive stars. Betelgeuse is special because its
propinquity allows its image to spatially be resolved. Betelgeuse also has
properties such as its runaway kinematics that may be special to it. Most
massive stars arise in binary systems and there are hints this may have been
true for Betelgeuse despite its current apparently solo state, which seems
typical of SN IIP. Betelgeuse shows a 420-d period that is most likely a first
over-tone radial pulsation mode and variance on time-scales of 2000 d that is
associated with overturn of convective plumes. Then, just to keep us guessing,
Betelgeuse staged the “Great Dimming" of 2019/2020, the detailed origin of
which is still debated. Figure 1 gives some sense of scale of Betelgeuse.

Figure 1: Schematic showing the scale of the red supergiant Betelgeuse and its
circumstellar medium compared to that of the Solar System (AU = Astronomical
Units). Art by L. Calçada, by permission of the European Southern Observatory.

Despite the relatively small distance from Earth, and in some sense because of
it, it has been difficult to obtain tight constraints on the distance,
luminosity, radius, current and Zero Age Main Sequence (ZAMS) masses, and
information about the internal rotational state and associated mixing and
hence on the evolutionary state of Betelgeuse and when it might explode. The
best current guess is that Betelgeuse is in core helium burning and will not
explode for about a hundred thousand years, but it will be a tremendous
spectacle from the Planet Earth when it does.

##  2 Observations

Valuable summaries of basic observational properties of Betelgeuse are given
by Dolan et al. (2016) and Joyce et al. (2020). Here we summarize some key
aspects.

###  2.1 Distance

Even recently the distance to Betelgeuse has been known to only 20% ($D\approx
197\pm 45$ pc; Harper et al. 2008, 2017), a situation that was not improved by
the Gaia mission that provided accurate parallaxes but that saturates on such
a bright star or is rendered less certain by transient star spots (Chiavassa
et al., 2022). Key properties such as radius and luminosity were thus
significantly uncertain, $R$ to within 20% and $L$ to only 40%. Estimates of
mass that determine the evolution depend sensitively on $L$ and $R$ and thus
also remained uncertain. The effective temperature that can be determined
independent of distance has its own intrinsic uncertainties. Dolan et al.
(2016) estimated $T_{eff}=3500\pm 350$ K. Within these uncertainties, models
of contemporary Betelgeuse could be brought into agreement with observations
of $L$, $R$, and $T_{eff}$ all the way from the minimum–luminosity base of the
giant branch to the tip of the red supergiant branch (RSB) (Wheeler et al.,
2017). Recent work has proposed ways to reduce the uncertainly in distance,
but with conflicting solutions converging on either the base (§2.13) or the
tip of the RSB (§2.12).

###  2.2 Spatial Resolution

A special characteristic of Betelgeuse is that its relatively small distance
allows its surface to be spatially resolved with appropriate instrumentation
as shown in Figure 2. The photosphere of Betelgeuse subtends an angle of $\sim
40$ milliarcseconds that can be resolved with ground-based interferometry in
the optical and infrared (Haubois et al., 2009; Montargès et al., 2016; López
Ariste et al., 2022) and submillimeter (O’Gorman et al., 2017; Kervella et
al., 2018; Haubois et al., 2019) or from space with the Hubble Space Telescope
(HST) (Gilliland & Dupree, 1996; Uitenbroek et al., 1998).

Figure 2: Spatially-resolved H band image of Betelgeuse. From Haubois et al.
(2009) by permission of X. Haubois, ESO/Observatoire de Paris, and Astronomy &
Astrophysics.

Gilliland & Dupree (1996) resolved Betelgeuse spatially by obtaining images
with the HST Faint Object Camera in 10 resolution elements across the surface.
They found the ultraviolet diameter of Betelgeuse to $108\pm 4$ mas, a factor
of 2.2 larger than the optical diameter, suggesting an extended chromosphere
in analogy to the hot temperature inversion in the Sun. A single bright,
unresolved area was 200 K hotter than the mean value. Gilliland & Dupree
(1996) suggested this surface inhomogeneity might be due to magnetic activity,
atmospheric convection, or global pulsations that produce shock structures
that heat the chromosphere. Spatially resolved spectroscopy with the Goddard
High Resolution Spectrograph suggested the complicated dynamics of outflowing
material in the chromosphere (Lobel & Dupree, 2001).

Haubois et al. (2009) undertook H-band interferometry with the Infrared-
Optical Telescope Array (IOTA) at the Whipple Observatory to measure the
diameter ($44.28\pm 0.15$ mas), effective temperature ($3600\pm 66$ K), limb
darkening, and bright or dark patches in the photosphere and surroundings.

Montargès et al. (2016) did H-band interferometry on the VLT to explore mass
loss driven by strong convective motions by mapping the shape of the envelope
and following the structure of the wind from the photosphere out through the
nearby circumstellar medium and into the interstellar medium. They detected a
hot spot on the photosphere comparable in size to the radius of the star.

O’Gorman et al. (2017) used submillimeter observations with the Atacama Large
Millimeter Array (ALMA) to study the free-free emission in the extended
atmosphere of Betelgeuse. They found that the mean temperature at 1.3 stellar
radii was 2760 K, a value that is less than both the photospheric temperature
they gave as $T_{eff}=3690$ K and the temperatures at 2 solar radii, implying
an inversion of the mean temperature in the atmosphere. The emission showed
evidence for inhomogeneous localized heating in the atmosphere of Betelgeuse,
perhaps related to magnetic activity generated by large-scale convection.

We will return to the power of interferometry in §4.

###  2.3 Convection and Plumes

The extended outer envelope of Betelgeuse engenders appreciable superadiabatic
temperature gradients that lead to strong convection Schwarzschild (1975).
Both direct observations (Gilliland & Dupree, 1996; Uitenbroek et al., 1998;
Haubois et al., 2009; Dupree & Stefanik, 2013; Montargès et al., 2016;
O’Gorman et al., 2017; Kervella et al., 2018; Haubois et al., 2019; López
Ariste et al., 2022) and models (Chiavassa et al., 2010; Goldberg et al.,
2022) indicate that the convective structure of the envelope of Betelgeuse is
characterized by large plumes of upwardly rising hot material and inwardly
cascading cooler material. The plumes in turn lead to hot and cold patches on
the surface that are substantially large compared to the radius of the star
(Montargès et al., 2016). This leads to complications in determining basic
quantities like the global effective temperature (Levesque & Massey, 2020).

###  2.4 Atmosphere, Photosphere, Chromosphere

Driven by the irregular convective plumes, the outer layers of Betelgeuse
reveal a complex atmospheric structure as the optically-thick convective
envelope yields to a wavelength-dependent and position-dependent photosphere
and chromosphere (Bernat & Lambert, 1976; Lim et al., 1998; Plez & Lambert,
2002; Montargès et al., 2016; O’Gorman et al., 2017; López Ariste et al.,
2022). O’Gorman et al. (2017) established a temperature inversion between the
photosphere and chromosphere (§2.2).

###  2.5 Mass and Mass Loss

The ZAMS mass is a fundamental property that determines the evolution of a
star. In the case of Betelgeuse, the uncertainty in distance and other factors
yields intrinsic uncertainty in the ZAMS mass. Betelgeuse qualifies as a
massive star, but estimates of the ZAMS mass vary from 10 to 25 M⊙. In recent
estimates, Dolan et al. (2016) gave 17 - 25 M⊙ whereas Joyce et al. (2020)
found 18 - 21 M⊙. This mass range destines Betelgeuse to succumb to iron core
collapse and a likely catastrophic explosion. Direct collapse to a black hole
is a remote possibility (§3).

The subsequent evolution of Betelgeuse is not determined solely by its ZAMS
mass, but also depends on abundances, rotation, stellar winds, the presence of
a binary companion, and the possibility of a merger.

Mass loss on the main sequence is estimated to be less than 0.1 M⊙, a small
effect compared to other uncertainties. Harper et al. (2001) and Le Bertre et
al. (2012) determined the current mass loss rate to be $\sim 1-4\times
10^{-6}$ M⊙ y-1. Dolan et al. (2016) adopted $2\times 10^{-6}$ M⊙ y-1.
Estimates of the current wind velocity of Betelgeuse range from 3 to 14 km
s-1. Dolan et al. (2016) adopted a range of $9\pm 6$ km s-1(their Table 5).
The wind accelerates, so a single wind velocity may not be appropriate.

As for other RSGs, mass loss from Betelgeuse in its current configuration is
episodic (Decin et al., 2012; Massey et al., 2023), a factor often neglected
in prescriptions for mass loss rates. This variability is probably linked to
the sporadic convective plumes and to the intrinsic pulsational properties.
Magnetic fields may play a role (§2.11).

López Ariste et al. (2022) sought to understand convection and the mechanisms
that trigger mass loss by using linear spectropolarimetry of the atomic lines
to provide velocity and hence depth information in addition to spatial
distribution. The result was images of the photosphere of Betelgeuse that
provide information about the 3D distribution of brightness in the atmosphere.
The data revealed the velocity of vertical convective flows at different
heights in the photosphere that showed that non-gravitational forces are
present in the photosphere of Betelgeuse that allow plasma to reach velocities
close to the escape velocity. These forces may trigger mass loss and sustain
large stellar winds.

Humphreys & Jones (2022) argue that Betelgeuse gives evidence for discrete,
directed clumpy outflows as suggested by circumstellar gas knots detected in
the submm region that are related to magnetic fields and surface activity.
They argue that this clumpy outflow analogous to solar coronal mass ejections
is a major contributor to mass loss from RSGs, including Betelgeuse.

###  2.6 Molecules and Dust

Plasma recombining to gas continues to cool as it is ejected from the surface
of Betelgeuse. If it gets sufficiently cool, the gas can form molecules
through complex non-equilibrium chemistry. The molecules can then serve as
nucleation sites where inorganic dust can form. Dust grain surfaces in turn
provide an environment to form yet other molecules.

Jennings & Sada (1998) discovered water in the atmosphere of Betelgeuse. Tsuji
(2000) confirmed the presence of water in data taken 35 years previously with
the balloon-borne telescope Stratoscope II (Woolf et al., 1964). He proposed a
molecular shell, a MOLsphere, in the atmosphere of Betelgeuse. Perrin et al.
(2007) subsequently identified a geometrically thin shell between 1.31 and
1.43 $R_{star}$ with a typical temperature of 1550 K that contained H2O, SiO,
and Al2O3. Ohnaka et al. (2009, 2011) spatially resolved the macroturbulent
gas motion in the photosphere and MOLsphere of Betelgeuse for the first time.

Models presented by Harper et al. (2001) suggested that dust formed at about
33 $R_{star}$ at a temperature of $\sim 360$ K. Kervella et al. (2018) argued
that convective cells lead specifically to the production of molecular plumes
and dusty knots in the north polar region of Betelgeuse. Related notions came
to the fore during the Great Dimming of 2019/2020 (§4).

Haubois et al. (2019) did near-IR interferometry to explore the connection
between dust formation and mass loss from Betelgeuse. They found a halo of
fosterite (Mg2SiO4) dust beginning about 0.5 $R_{star}$ above the photosphere,
much lower than suggested by the models of Harper et al. (2001). The height of
molecule and dust formation may vary inhomogeneously over the surface of
Betelgeuse.

###  2.7 Surface Gravity

The gravitational acceleration at the surface of Betelgeuse, the surface
gravity, $g=GM/R^{2}$, provides an independent constraint on the ratio $R/M$.
This quantity is determined from the analysis of line structure in the
photosphere and is typically presented as the logarithm in base 10 of $g$
measured in the cgs system. Lambert et al. (1984) observed forbidden O I
lines, vibration-rotation bands of second-overtone CO near 1.6 micron, NH
bands between 3 and 4 microns, OH fundamental bands near 3 microns, and CN red
lines near 8000 Å and 2 microns, and employed sophisticated model atmospheres
designed for supergiant stars. For Betelgeuse, Lambert et al. (1984) adopted
$log~{}g=0.0\pm 0.3$. Lobel & Dupree (2000) used near-UV, optical, and near-IR
high-dispersion spectra analyzed with non-LTE radiative transfer calculations
to obtained $log~{}g=-0.5$ that is somewhat less, even given the nominal
uncertainties. Neither Lambert et al. (1984) nor Lobel & Dupree (2000)
considered the plume structure of the envelope and departures from spherical
symmetry.

Neilson et al. (2011) employed limb-darkening laws and grids of spherical
model stellar atmospheres to determined $R/M=82^{+13}_{-12}$ R⊙/M⊙. From their
best-fitted models, Dolan et al. (2016) obtained $R/M=40$ R⊙/M⊙, substantially
less than Neilson et al. (2011), and $log~{}g=-0.05$ for their Eggleton-based
code and $log~{}g=-0.10$ with the stellar evolution code Modules for
Experiments in Stellar Astrophysics (mesa; Paxton et al. 2011; Paxton et al.
2013, 2015, 2018). The latter estimates for $log~{}g$ are roughly consistent
with Lambert et al. (1984) but appreciably larger than found by Lobel & Dupree
(2000).

In principle, the effective gravity at the surface of a star is reduced by the
centrifugal effects of rotation that is substantial in Betelgeuse (§2.8). For
a 20 M⊙ model rotating at velocities typical of Betelgeuse, Wheeler et al.
(2017) found $log~{}g=+0.42$ at the luminosity minimum at the base of the RSG
branch and $log~{}g=-0.48$ during carbon burning when the model had slowed due
to envelope expansion. The former is somewhat beyond the upper limit set by
Lambert et al. (1984) and the latter in close agreement with the determination
of Lobel & Dupree (2000). For their models with a 16 M⊙ primary merging with a
4 M⊙ secondary, Chatzopoulos et al. (2020) found post-merger surface gravity
for models merging at 300 and 250 R⊙ to be $4.67-6.65$ cm s-2, corresponding
to $log~{}g=0.67-0.82$.

There are thus significant uncertainties in both observations and models of
$log~{}g$ for Betelgeuse. Constraints on $log~{}g$ come into play in
considering pulsational properties (§2.12) and the possibility of a recent
color change in Betelgeuse (§2.13).

###  2.8 Rotational Velocity

The rotation of Betelgeuse at the surface and at depth has implications for
estimates of the current age, the current mass, the ZAMS mass, the current
evolutionary state, and the time to explosion.

Betelgeuse appears to have an anomalously large rotational velocity. Long slit
spectroscopy across the minimally resolved disk of Betelgeuse obtained with
the Hubble Space Telescope (HST) yielded an estimated surface rotational
velocity $v_{\rm rot}\sin(i)\sim 5$ km s-1 at an inclination of $i\approx 20$o
(Dupree et al., 1987; Gilliland & Dupree, 1996; Uitenbroek et al., 1998;
Kervella et al., 2009). These data imply an equatorial rotational velocity of
$\sim 15$ km s-1. The uncertainty in this quantity is itself uncertain.

More recent observations appear to further support this result even within the
uncertainties imposed by large–scale convective motions on the star’s surface.
Kervella et al. (2018) used ALMA to resolve the surface velocity and
determined that Betelgeuse rotates with a projected equatorial velocity of
$v_{\rm eq}\sin(i)=5.47\pm 0.25$ km s-1 with an estimated rotation period of
$36\pm 8$ yr (see §2.8). They confirmed that the chromosphere is co-rotating
with the star up to a radius of 1.5 times the continuum radius. They found
that the position angle of the polar axis of Betelgeuse coincided with a hot
spot in the ALMA data, suggesting that focused mass loss was currently taking
place in the polar region. They proposed that a particularly strong convection
cell was driving a focused molecular plume that could subsequently condenses
into dust at a few stellar radii thus contributing to anisotropic mass loss
(§2.3, §2.5, §2.6, §2.8, §4).

High rotation during the supergiant phase is not found in stellar evolution
calculations of single massive stars (§3.1) – including those that are rapid
rotators at the Zero Age Main Sequence (ZAMS) – nor expected by simple
arguments of angular momentum conservation (Wheeler et al., 2017).

Single massive stars lose a fraction of their mass and angular momentum
through winds already during the main sequence (MS) phase. O stars with
initial rotation velocities of $\sim 200$ km s-1 evolve through rapid mass and
angular momentum losses to become much slower rotating B stars with $v\sin
i\leq$ 50 km s-1 (Maeder & Meynet 2000; Higgins & Vink 2019 and references
therein). Simple analytic arguments (Chatzopoulos et al., 2020) and stellar
evolution calculations (Claret & Gimenez, 1989) suggest that a star rotating
at $\sim$ 200 km s-1 at the ZAMS is likely to decrease to $\leq$ 50 km s-1 at
the Terminal Age Main Sequence (TAMS). Similar estimates and detailed
simulations of the evolution of massive stars, including mass and angular
momentum losses from the ZAMS to the supergiant stage typically yield an upper
limit to the equatorial rotational velocity of $v_{\rm eq}<1$ km s-1 on the
RSB (Ekström et al., 2008; Ekström et al., 2012a; Brott et al., 2011a, b).
Measurements of giant and supergiant star rotation rates support this argument
(Ceillier et al., 2017). Wheeler et al. (2017) and Chatzopoulos et al. (2020)
found a velocity of $\sim 0.1$ km s-1 high on the RSB.

Kepler observations of low-mass giant stars ($<3$M⊙) showed 17 with rotational
speeds up to $\sim$ 18 times that of the Sun (Costa et al., 2015). It is
possible that a yet unknown mechanism, perhaps transfer of angular momentum
from inner regions by g-mode acoustic waves (§2.14), could account for this
rapid rotation (Fuller et al., 2014; Townsend et al., 2018), but it is not
clear that even such mechanisms can account for the rotation of a massive RSG
like Betelgeuse.

Taken at face value, Betelgeuse is thus rotating too rapidly by a factor
$\sim$ 15 and perhaps as much as 150 compared to basic single-star models high
on the RSB (Wheeler et al., 2017; Chatzopoulos et al., 2020; Joyce et al.,
2020). Models of Betelgeuse on the RSB give a critical Keplerian velocity of
$\sim 65$ km s-1(Wheeler et al., 2017); the observed rotational velocity is
thus a substantial fraction of the escape velocity. Such a rotation may cause
measureable oblateness that could complicate interpretation of the
observations (Tatebe et al., 2007; Haubois et al., 2009).

There are concerns that the deduced rotational velocity is not correct,
perhaps confused by the complex large scale convective flows at the
photosphere. Gray (2001) found a macroturbulence Gaussian dispersion $\sim 15$
km s-1 with a FWFM of $\sim\pm 50$ km s-1 consistent with many convection
cells appearing on the stellar disk but with no evidence for giant convection
cells. More recently, López Ariste et al. (2018) found characteristic upflow
and downflow speeds of 22 and 10 km s-1, respectively. Jadlovský et al. (2023)
argued that the projected rotational velocity $v_{\rm rot}\sin(i)$ is not
trustworthy, as both edges of Betelgeuse seem to be moving towards Earth at a
similar velocity.

An accurate measurement of the equatorial rotational velocity of Betelgeuse is
important in order to constrain models. Single–star rotating models give
$v_{rot}\sim 15$ km s-1 only in a brief phase near the base of the RSB that
would last for a few thousand years at most. It is conceivable that Betelgeuse
might currently reside in this portion of the Hertzsprung Russell Diagram
(HRD) by appropriately pushing $3\sigma$ error bars on $R$, $L$, and $T_{eff}$
(Wheeler et al., 2017). The historical color changes of Betelgeuse
characterized by Neuhäuser et al. (2022) may demand that Betelgeuse is
currently in this lower portion of the HRD where massive stars can change
$T_{eff}$ on timescales of 1000 y (§2.13). This conclusion conflicts with the
results from the careful study of the pulsation period given by Joyce et al.
(2020) that places Betelgeuse higher on the RSB (§2.12).

One possibility to account for the high rotation velocity is that Betelgeuse
has undergone a merger as it expanded and evolved up the RSB (§3.3). Another
pathway to form a rapidly-rotating supergiant is presented in de Mink et al.
(2013). They propose that Case A Roche lobe overflow mass transfer from a
$\sim 20$ M⊙ primary is enough to spin up a $\sim 15$ M⊙ secondary to high
rotational velocity if the transfer occurs right after the TAMS before the
ascent up the RSB (their Figure 2). This possibility requires considerable
fine tuning of the binary evolution parameters and the timing of the onset of
mass transfer.

Both the merger model and the Case A transfer model should be examined for
testable observational consequences.

###  2.9 Observed Abundances

Photospheric abundances are yet another clue to the evolutionary history and
state of Betelgeuse. The measured N/C (nitrogen to carbon) and N/O (nitrogen
to oxygen) surface abundance ratios for Betelgeuse are 2.9 and 0.6,
respectively, compared to solar values of N/C$=$0.3 and N/O$=$0.1 and the
ratio ${}^{12}C/^{13}C$ is much lower than solar (Lambert et al., 1984). These
ratios vary as massive stars burning hydrogen on the CNO cycle settle into CNO
equilibrium, with N being produced at the expense of C and O. CN-equilibrium
is achieved before an inhibiting gradient in mean molecular weight is
established between the core and the envelope, so the excess N can quickly be
transported to the stellar surface thus producing large N/C ratios. Full CNO-
equilibrium is achieved only after significant hydrogen burning, so surface O
depletion only occurs later.

The observation of enhanced nitrogen at the surface of Betelgeuse may be
indicative of enhanced mixing, perhaps triggered by rotation (Meynet et al.,
2013). The effects of rotational mixing are more pronounced at lower
metallicity, higher ZAMS mass, and higher rotational velocity (Brott et al.,
2011a). Rotational mixing may need to be supplemented by other effects such as
binary evolution and magnetic fields to understand the abundance distributions
in evolved massive stars (Brott et al., 2011b).

Luo et al. (2022) have used surface abundances to constrain the nature of
Betelgeuse in terms of initial mass, rotation, and overshoot. They find the
acceptable range of ZAMS masses is slightly larger for rotating models than
non-rotating models, 12 - 25 M⊙ versus 15 - 24 M⊙, respectively. They find
that the initial rotation on the ZAMS must be restricted to 0.3 of the
Keplerian velocity in order to fit the surface abundances of Betelgeuse as an
RSG and find that some of their models could be in the phase of carbon burning
or beyond.

The observed abundances in Betelgeuse are consistent with material that has
been mixed to the surface in the first dredge-up phase when the convective
hydrogen envelope penetrates the helium core (Lambert et al., 1984; Dolan et
al., 2016). This constrains Betelgeuse to have passed the base of the RSB and
to be ascending the RSB, consistent with the results of Joyce et al. (2020)
but perhaps in contradiction with the conclusions of Neuhäuser et al. (2022)
(§2.13).

###  2.10 Kinematics, Nearby CSM, ISM, Bowshocks

Figure 3: Structure in the large scale CSM surrounding Betelgeuse observed by
the Herschel mission. Note the prominent bow shock at 7 arcmin that is in the
direction of the spatial velocity of Betelgeuse. From Decin et al. (2012).
Adapted by permission of L. Decin and Astronomy & Astrophysics.

In addition to perhaps being a rapid rotator, Betelgeuse is also a known
runaway star with a measured space velocity of $\sim$ 30 km s-1 and a
kinematic age of $\sim$ 7–11 Myr (Harper et al., 2008, 2017).

As shown in Figure 3, the flight of Betelgeuse through the interstellar medium
is also illustrated by HST and Herschel observations of a bow shock forming a
swept–up shell of material of $\sim$ 0.14 $M_{\odot}$ at a radius of $\sim$
6–7 arcmin corresponding to a physical distance of $\sim$ 0.8 pc using a
distance to Betelgeuse of $\sim$ 400 pc (Noriega-Crespo et al., 1997; Decin et
al., 2012) (current estimates of the distance are less by a factor of two or
three; §§2.1,2.12). The prominent bow shock is in the same direction as the
kinematic motion, indicating a peculiar velocity with respect to the local
standard of rest of $v\approx 25$ km s-1 (Harper et al., 2008) or perhaps as
much as 35 km s-1 (van Loon, 2013). The morphology of this structure is
attributed to wind from the star sweeping up interstellar medium in the
direction of motion (Mohamed et al., 2012; Decin et al., 2012; Mackey et al.,
2014). The observations also show a smaller ring of material with a diameter
of about 4 arcmin (Le Bertre et al., 2012). One explanation is that this is
wind mass that is radiation–impeded by external radiation (Mackey et al.,
2014). There is also an odd, very linear feature about 9 arcmin away, beyond
the bow shock, that remains unexplained (Noriega-Crespo et al., 1997; Decin et
al., 2012). Wheeler et al. (2017) noted that a merger event might have some
relation with the interstellar shells of higher density in the vicinity of
Betelgeuse. The strangely linear feature at 9 arcmin might be related to the
square axisymmetric circumstellar nebula recently discovered around the B9 Ia
star HD93795 by Gvaramadze et al. (2020). Such a connection might in turn
suggest that Betelgeuse had undergone some previous mass expulsion.

Proposals to account for the high space velocity of Betelgeuse include
multi–body stellar interactions in its birth cluster and the possibility that
a binary companion underwent a supernova explosion (Blaauw, 1961; van Loon,
2013). In a study of the 30 Doradus region of the Large Magellanic Cloud, Sana
et al. (2022) conclude there are two different populations of massive runaway
Main Sequence O stars: a population of rapidly spinning ($v_{\rm
eq}\sin(i)>200$ km s-1) but slowly moving ($v=25-60$ km s-1) runaway stars and
a population of slowly rotating ($v_{\rm eq}\sin(i)<200$ km s-1) rapidly
moving ($v>60$ km s-1) stars. They found no rapidly spinning, rapidly moving
stars in their sample. Sana et al. (2022) argue that slowly moving rapidly
spinning stars result from binary ejections, while rapidly moving slowly
spinning stars result from dynamical ejections, with slowly moving rapidly
spinning stars and hence binary evolution dominating the current massive
runaway star population in 30 Doradus. Betelgeuse nominally belongs in the
slowly moving rapidly spinning runaway category.

Backwards extrapolation of the current trajectory of Betelgeuse has led some
to suggest that its possible birthplace is the Orion OB1a association (Briceño
et al., 2005). Others have argued that a backward extrapolation of its known
space velocity does not appear to bring Betelgeuse close to any plausible
sub–association of OB1 as its birth place (Bally, 2008). (Bally, 2008)
suggests a two step process: (1) a dynamical ejection of a binary within the
first few million years after the formation of Betelgeuse’s birth cluster, and
(2) a subsequent merger of the binary or a supernova explosion of the more
massive component, releasing the surviving now single Betelgeuse at some post
MS stage of its evolution.

Work on the kinematic effects of supernovae in massive star binary systems
tends to discourage the conjecture of the previous explosion of a companion to
Betelgeuse. Renzo et al. (2019a) confirm that of order 20 - 50% of massive
star binaries merge rather than undergoing disruption. They also find that by
far the largest fraction of binaries disrupted by the collapse and explosion
of the primary result in “walkaway" rather than “runaway" stars. The velocity
distribution of the ejected companion peaks at about 6 km s-1. For secondaries
more massive than 15 M⊙, as likely applies to Betelgeuse, only $\sim 0.5\%$
have velocities of 30 km s-1 and above, as appropriate to Betelgeuse.

These results suggest that, while non-zero, the likelihood that the space
motion of Betelgeuse resulted from the previous explosion of a companion is
small. The results depend on assumptions about primordial binaries, among
other things, but the general result is that it is easier to generate walkaway
stars than runaway stars. A runaway binary is likely to be rare, but is not
precluded.

As discussed above, a reasonable alternative is that the proper motion of
Betelgeuse arises from stellar dynamics in its natal cluster (Poveda et al.,
1967; Oh & Kroupa, 2016; Schoettler et al., 2019). Early ejection as a single
star either by the disruption of a cluster binary or dynamical escape from a
cluster are unlikely to yield a rapid rotator in the present supergiant stage.
Even if spun up on the ZAMS, its rotation on the RSB would be slow. If a
previous binary companion exploded, then it clearly could not have merged with
the current Betelgeuse as discussed in §3.3.

The origin of the space motion of Betelgeuse is thus one more fascinating open
question about this tantalizing star. Whether Betelgeuse attained its proper
motion from the explosion of a companion or from cluster dynamics, if it
emerged as a single star then the apparent observed equatorial velocity
remains an issue.

A possible way to account for both the space motion and the equatorial
velocity would be to provide the space motion by cluster dynamics and ejection
of a binary, of which the star we currently observe as Betelgeuse was the
primary, and a subsequent merger along the RSB. This is, admittedly, an
improbable string of events. Oh & Kroupa (2016) find that a majority of
ejected massive binaries have a period shorter than $10^{5}$ days. Supergiant
branch merger models have a typical presumed orbital period of about 30 years
or $10^{4}$ days (Wheeler et al., 2017). Having a rather massive companion
might increase the likelihood that the binary remains intact upon ejection
from the natal cluster. Current results allow for that possibility.

We note that while Betelgeuse may have moved hundreds of pc during its main
sequence lifetime, it is expected to have moved only $\sim 2$ pc during the
100,000 years or so it has been in core helium burning as a RSG.

###  2.11 Magnetic Fields

The atmosphere of Betelgeuse is observed to harbor magnetic fields of $\sim 1$
G as as measured by circular polarization (Mathias et al., 2018) and as
inferred from the Zeeman effect (Aurière et al., 2010). These fields are
thought to originate from local low-scale convective activity and associated
non-linear dynamo action in Betelgeuse or perhaps from giant convective cells
on its surface (Dorch, 2004).

We have noted earlier that magnetic fields may play a role in localized hot
spots on the surface of Betelgeuse, in the formation of the chromosphere, and
in clumpy mass loss. Thirumalai & Heyl (2012) addressed the effects of
magnetic fields on winds, dust, and the structure of the photosphere and
chromosphere of Betelgeuse.

###  2.12 Pulsation Periods

We noted in §2.7 that measurement of the surface gravity provides a constraint
on $R/M$, given an independent measurement of $R$. Stellar pulsation modes
also depend on gravity, giving yet another constraint on $R/M$. Betelgeuse
displays a range of periodic behavior.

Studies of Betelgeuse have long revealed a variety of pulsation modes. Of
particular value is the record of optical photometry compiled by amateurs and
professionals for nearly 100 years and recorded by the American Association of
Variable Star Observers (AAVSO). These data reveal at least two different
timescales, $\sim 388$ d and a “long secondary period" (LSP) of $\sim 2050$ d
(5.6 yr) (Kiss et al., 2006; Chatys et al., 2019). The LSP might be related to
the rotation, but the rotation period is apparently significantly longer
(§2.8).

Joyce et al. (2020) analyzed the most recent $\sim 40$ years of data from the
AAVSO complemented with data incidentally produced by Solar Magnetic Ejection
Imager (SMEI) observations. They find periods of $185\pm 13.5$ d, $416\pm 24$
d, and $2365\pm 10$ d, cautioning that these periods could evolve with time.
U-band observations are relatively rare. Ogane et al. (2022) presented 23
years of UBVRI data obtained at the private Ogane Hikari Observatory and found
periods of $\sim 405$ d and $2160$ d. (Jadlovský et al., 2023) presented an
analysis of spectroscopic and photometric variability in the UV and optical,
finding photometric periods of $417\pm 17$ d and $2190\pm 270$ d and radial
velocity periods from spectroscopy of $415\pm 11$ d and $2510\pm 440$ d. The
radial velocity determined from ultraviolet spectra show longer periods of
variability that may be related to the outflowing wind.

Models of RSGs show that pressure-mode or p-mode radial pulsations can be
driven by the opacity or $\kappa$-mechanism in the hydrogen ionization zone.
In this mechanism, the opacity varies out of phase with the luminosity, being
lower when the star is compressed and hot releasing radiant energy and
allowing more compression and higher when the star expands and cools thus
blocking radiant energy and driving more expansion. Simulations yield mass-
dependent periods of the fundamental of years in both linear and nonlinear
models (Li & Gong, 1994; Heger et al., 1997; Yoon & Cantiello, 2010; Paxton et
al., 2013; Dolan et al., 2016; Goldberg et al., 2022). Modeling pulsation
processes may require 3D, time-dependent convection, or otherwise more
sophisticated physical formalisms that are beyond the scope of typical 1D
stellar evolution programs, but 1D analyses already provide useful insights.

Joyce et al. (2020) used 1D hydrodynamical models and the GYRE pulsation
module of mesa to analyze the pulsations and provide new constraints on $R/M$
for Betelgeuse. They deduced that the 416 day period represents oscillation in
the fundamental mode, driven by the opacity mechanism, and that the 186 day
period represents the frequency of the first overtone of radial pulsations.
Joyce et al. (2020) also used the period information to provide a tighter
constraint on the radius of Betelgeuse, $R=750^{+62}_{-30}$ R⊙ ($3\sigma$),
compared to the previous estimate of 887 R⊙. Surprisingly, this led to a
tighter constraint on the distance and parallax than previous methods,
$D=165^{+16}_{-8}$ pc with <10% uncertainty compared to the previous estimate
of 197 pc with 20% uncertainty, and tighter constraint on the ZAMS mass, 18 -
21 M⊙ and the current mass, 16.5 – 19 M⊙. Joyce et al. (2020) do not give a
surface gravity to compare with atmospheric observations (§2.7). They give an
extensive discussion of model degeneracies that make estimates of L and
$T_{eff}$ uncertain.

With the new constraints, Joyce et al. (2020) concluded that Betelgeuse is in
core helium burning, with $\sim$ 100,000 years to go before explosion.

###  2.13 Recent Change in Color?

Another approach to determining the mass, luminosity, radius, distance,
effective temperature, age, and current evolutionary state of Betelgeuse is to
study the color evolution from the historical record. In a recent rigorous
analysis of extensive multi-cultural historical literature including Tycho
Brahe’s comparison of Betelgeuse to his supernova of 1572 and to Aldebaran,
Neuhäuser et al. (2022) [and new summary in Astronomy and Geophysics] argue
that Betelgeuse has significantly changed color over the last two millennia.

Contemporary Betelgeuse is, as can be verified by casual naked eye
observation, red, with a formal color of $B-V=1.78\pm 0.05$ mag. Neuhäuser et
al. (2022) argue that 2000 years ago Hyginus in Rome reported Betelgeuse to
have a color similar to Saturn that is equivalent to $B-V=1.09\pm 0.16$ mag
and that Sima Qian in China independently reported Betelgeuse to be “yellow,"
a condition that Neuhäuser et al. (2022) quantify to be $B-V=0.95\pm 0.35$
mag. Neuhäuser et al. (2022) estimate that these historical estimates of color
differ from the contemporary color by $5.1\sigma$. In contrast, Antares has
always been reported as red for over 3000 yr.

Taken at face value, this color change of Betelgeuse represents a strong
constraint on evolutionary models. Neuhäuser et al. (2022) compare their
estimates of historical and contemporary colors of Betelgeuse to the mesa
Isochrones and Stellar Tracks (MIST) of Choi et al. (2016). They deduce that
Betelgeuse is likely to be near the cool end of the Herzsprung Gap and less
than 1000 yr past the minimum of the RSB when relatively rapid changes in
color are expected. Neuhäuser et al. (2022) specifically argue that the color
evolution and location in the color-magnitude diagram constrain the ZAMS mass
to be $\sim 14$ M⊙ with a current age of $\sim 14$ Myr. This deduction is in
distinct contrast with the location in the Hertzsprung-Russell Diagram, the
ZAMS mass (18 - 21 M⊙), and the evolutionary state deduced by Joyce et al.
(2020) .

In their study of the rotation of Betelgeuse, Wheeler et al. (2017) noted that
the radius increases and the surface velocity plummets as models proceed
across the Hertzsprung gap and up the RSB. The only position in the
Hertzsprung-Russell Diagram for which single star models could plausibly give
the observed equatorial rotation of $\sim 15$ km s-1 (§2.8) is when the models
first approach the base of the red supergiant branch (RSB), having crossed the
Hertzsprung gap but not yet having ascended the RSB. This condition is similar
to that deduced by Neuhäuser et al. (2022). Wheeler et al. (2017) argued that
because that phase is so short ($\sim 100$ yr), that possibility is highly
unlikely. Rather, they suggested, Betelgeuse may have been in a binary system
that merged (§3.3), producing the observed rotation near the upper tip of the
RSB, the condition deduced by Joyce et al. (2020). If Neuhäuser et al. (2022)
are correct in their interpretation of the historical data, their results are
a challenge to models, including merger models, that attempt to place
contemporary Betelgeuse in the upper reaches of the RSB.

At this writing, the conflict between Joyce et al. (2020) and Neuhäuser et al.
(2022) is unresolved. Wheeler et al. (2017) noted that a solution near the
base of the RGB, as advocated by Neuhäuser et al. (2022), would yield an
excessively large surface gravity, $log~{}g\approx+0.42$ (§2.7). This may
mitigate against the solution of Neuhäuser et al. (2022), but a proper
resolution would involve identifying a flaw in either the analysis of Joyce et
al. (2020) or that of Neuhäuser et al. (2022).

Once again, an important factor is the distance. Neuhäuser et al. (2022) favor
a distance of $151.5\pm 19$ pc as determined from Hipparchos data (van
Leeuwen, 2007) rather than greater distance of $197\pm 45$ pc determined by
Harper et al. (2008), for which they consider the ALMA distance less certain.
With the larger distance, Neuhäuser et al. (2022) find a ZAMS mass of 17 or 18
M⊙, closer to the result of Joyce et al. (2020). On the other hand, Joyce et
al. (2020) favor a distance of $\sim 165$ pc, closer to the preferred value of
Neuhäuser et al. (2022) despite their other disagreements. More accurate
determinations of the surface gravity by spectral analysis and modeling would
also be useful.

Given the uncertainties, it is possible that Neuhäuser et al. (2022) and Joyce
et al. (2020) could be brought into agreement in terms of ZAMS mass, L, and
$T_{eff}$ but still disagree on the corresponding evolutionary state, near the
end of the Hertzsprung Gap, or substantially up the RSB.

Another possibility is that other surface activity analogous to the recent
Great Dimming (§4) may have caused color changes. It would be interesting if
such a possibility could be ruled out.

###  2.14 Asteroseismology

Section 2.12 dealt with the fundamental global pulsation properties. There
could, in principle, be other temporal signals coming from the depths of
Betelgeuse that give yet more evidence of the inner structure and evolution,
perhaps of unorthodox evolution such as a merger.

Over the last two decades there has been tremendous progress in using the
technique of asteroseismology to explore the depths of stars from the Sun to
evolved giants. High precision $\mu$-magnitude space–based photometry from the
$\it CoRoT$ and Kepler missions showed complex but interpretable variations
due to acoustic signals arising from deep within stars that is analogous to
exploring the core of the Earth with seismic signals (Aerts et al., 2010).
Study of these signals revealed the inner rotation of the Sun and
understanding of the structure, rotation, and inner magnetic field
distribution of thousands of stars from the ZAMS to the red giant branch,
especially those of low mass that are technically easier to analyze.

The question then arises as to whether such asteroseismology techniques can be
applied to Betelgeuse and other RSB stars. The potential is great. The inner
structure of evolved massive stars is suspected to yield complex convective
regions that will generate acoustic signals in the form of pressure modes and
gravity waves. These should get especially intense late in the evolution near
core collapse when the convective timescales become comparable to the nuclear
burning timescales (Arnett & Meakin, 2011; Couch et al., 2015; Chatzopoulos et
al., 2016). Convective regions should hammer on the inside of the star with
increasing violence and decreasing timescale as the star nears core collapse.
In practice, it is difficult to do asteroseismology of RSB stars because
typical oscillation periods are long and because the oscillations are affected
by complex processes in the atmosphere and wind (§§2.3, 2.4, and 2.5) that
affect the boundary conditions employed in the analysis but that are not well
understood (Aerts, 2015). In addition, Betelgeuse is too bright to study with
traditional telescopes on the ground or in space due to instrument saturation.

In principle, asteroseismology could be used to determine the evolutionary
stage of Betelgeuse since interior acoustic activity should get more intense
with time and carry signals specific to certain stages of evolution,
especially oxygen and silicon burning in the years or days before core
collapse. The added mass and angular momentum and associated plumes and mixing
might give evidence of a merger (§3.3). The key question is whether some of
that acoustic power reaches the surface. Could one see small perturbations on
the surface of Betelgeuse given the extensive convective envelope?

The potential of asteroseismology to glean an understanding of the interior
structure of Betelgeuse in particular and RSG in general has been explored
theoretically. Following Shiode & Quataert (2014), detailed stellar models can
be used to estimate characteristic acoustic frequencies driven by inner
convection as $\omega=v_{conv}/H_{p}$, where $v_{conv}$ is a convective
velocity and $H_{p}$ is an appropriate scale height associated with a given
convective region. The outer extended convective envelope has a characteristic
cutoff frequency, $\omega_{cut}=c_{s}/H_{p}$, where $c_{s}$ is the sound
speed, below which any acoustic signal cannot effectively propagate.

Typical signals from late in the evolution are potentially observable, but the
envelope cutoff, propagation efficiency, wave effervescence, damping, and
shock dissipation probably muffle all the inner convective noise (Fuller,
2017; Ro & Matzner, 2017; Nance et al., 2018). The largest envelope pressure
waves may arise from wave heating during core neon burning and a third carbon
shell burning phase a few years before core collapse because later, more
intense waves associated with oxygen and silicon burning do not have time to
reach the surface before core collapse (Fuller, 2017). The shock dissipation
of the acoustic luminosity generated in the very late stages of burning may
eject some mass into the CSM (Fuller, 2017; Ro & Matzner, 2017; Morozova et
al., 2020).

Most of the work on the issues described here have been done with spherically-
symmetric codes, albeit ones that can treat angular momentum and its
transport. Some work has been done in 2D (Leung & Fuller, 2020), but a more
complete understanding probably requires 3D studies (Tsang et al., 2022).
Beside effects on late-time ejection of mass from the extended envelope,
effective 3D porosity of the envelope may mitigate some of the wave damping
effects and allow some asteroseismological signals to percolate to the surface
causing diagnostic brightness variations even at earlier evolutionary phases.

##  3 Evolutionary Models

###  3.1 Single Star Models

The evolution of single massive stars, both non-rotating and rotating, has
been discussed extensively in the literature (Brott et al., 2011a, b; Ekström
et al., 2012b; Branch & Wheeler, 2017; Wheeler et al., 2017; Sukhbold et al.,
2018; Chatzopoulos et al., 2020) Models of these stars show that hydrogen is
burned on the CNO cycle in a convective core yielding a helium core of about
1/3 the original ZAMS mass. The helium core contracts and heats, and a thin
hydrogen-burning shells forms at its surface. The shell sits at a node in the
structure such that as the core contracts, the outer envelope expands becoming
large in radius and convective.

Helium eventually ignites in the center, forming a core of carbon and oxygen.
Contraction of this core results first in carbon burning and then the burning
of heavier elements as the inner core contracts and heats. Shells form burning
helium, carbon and other elements. Convection in these shells is expected to
produce intense acoustic waves (§2.14).

Near the end of the star’s lifetime, a core of silicon forms. Burning of
silicon yields a core of iron. Iron is endothermic in terms of its
thermonuclear properties. Within days of the formation of the iron core, it
will absorb thermal energy from the star, reduce the pressure, and trigger
catastrophic dynamical collapse to form a neutron star, or perhaps a black
hole.

For the case of a neutron star, most likely for Betelgeuse, most of the
kinetic energy of collapse will be lost to neutrinos but of order 1% will be
deposited in the inner regions, sufficient to cause a violent explosion of the
star, ejecting the outer layers, and leaving behind the neutron star (§5).

###  3.2 Common Envelope Evolution

It has been well established that a majority of O and B stars are in binary
systems (Sana et al., 2012; de Mink et al., 2014; Dunstall et al., 2015; Costa
et al., 2015; Renzo et al., 2019b; Zapartas et al., 2019), so it is a priori
likely that Betelgeuse began as a binary system. The implication is that many
RSG – including Betelgeuse – that appear to be single now have undergone
mergers.

An important implication of the potential that Betelgeuse arose in a binary
system is that Betelgeuse may have undergone common envelope evolution (CEE)
sometime during its history. CEE is expected when the two stars in a binary
are sufficiently close they interact as the more massive star evolves,
expands, fills its Roche Lobe, and transfers mass to its lower-mass companion.
In some circumstances, the companion cannot ingest the transferred material as
rapidly as the primary loses it, and the excess mass forms a red giant like
envelope surrounding the secondary and the evolving core of the primary. The
secondary orbiting within the common envelope (CE) will undergo drag and
spiral inward toward the evolved core. While the details are complex, there is
then a potential for the secondary to merge with the core of the primary
(§3.3). The result could appear to be a single star, but with an inner
structure rather different than would be expected of a single star of the same
luminosity, radius, and $T_{eff}$.

CEE can result in several types of anomalous mixing within the core and
between the core and the surface of the star. The inspiral phase leads to
increased equatorial rotation and thus chemical mixing via rotational
mechanisms. Plume mixing and nucleosynthesis occur during the moment of the
final tidal disruption of the secondary, and merger with the core of the
primary will affect the structure of the material inside and around the core
of the primary. Details depend on whether the plume mixing is strong enough to
rejuvenate hydrogen burning in the core. On longer timescales, rotational
mixing can dredge some $\alpha$-enhanced material from the inner regions to
the surface (§2.9).

Ivanova & Nandez (2016) (see also Morris & Podsiadlowski 2007; Taam & Ricker
2010; Ivanova et al. 2013; Ivanova et al. 2015; MacLeod et al. 2018;
Chatzopoulos et al. 2020; Roepke & De Marco 2022) describe the basic phases of
CEE and the mechanisms for treating it in 3D and 1D. There are three stages to
the process, each with associated loss of mass and angular momentum: 1) a
precursor phase when the stars begin to interact and co-rotation is lost; 2) a
plunge-in phase with a large rate of change of orbital separation and a
timescale close to dynamical, at the end of which most of the mass of the CE
is beyond the orbit of the companion; and 3) a self-regulated slow inspiral of
the companion. There are two basic endpoints to CEE: formation of a compact
binary system and merger. For mergers, Ivanova & Podsiadlowski (2003a)
differentiate three outcomes: a quiet merger, a moderate merger, and an
explosive merger. Only the former leaves behind an RSG and hence is pertinent
to Betelgeuse.

An important aspect of the problem is the deposition of the mass and orbital
angular momentum of the secondary. In 3D simulations most of the initial
angular momentum of the secondary is deposited in the outer layers of the
primary envelope. Mass and angular momentum are lost by dynamical interaction,
outflow driven by recombination, and shrinking of the orbit. The surface
layers are “shock heated" and quickly ejected prior to the plunge-in (Zhao &
Fuller, 2020). The slow inspiral often begins with an envelope that is
significantly reduced in mass and angular momentum. In some cases,
recombination outflow can eject nearly all the envelope during the slow
inspiral. The exception to these cases of extreme mass loss is when the
primary is substantially more massive than the secondary. For small secondary
masses, the fraction of mass lost in the precursor phase and the plunge-in
phase is of order $q$, the mass ratio of secondary to primary.

In their treatment of a red giant of modest mass (1.8 M⊙), Ivanova & Nandez
(2016) find that companions of mass less than 0.10 M⊙, corresponding to about
5% of the primary mass, undergo merger. The time to merger is about 1000 d,
long compared to the dynamical time of the CE but short compared to the
thermal or evolutionary time of the primary. While these results do not
necessarily scale with mass, this suggests that for many cases of interest
here, a companion of about 1 M⊙ undergoing CEE with a primary of about 20 M⊙
is likely to quickly undergo merger while sustaining a substantial envelope,
as Betelgeuse is observed to have.

The plunge-in phase is expected to induce very asymmetric structures and the
slow inspiral to yield appreciable departures from spherical symmetry that can
be simulated in 3D but are beyond the capacity of 1D models. In 3D there is a
significant density inversion in the vicinity of the companion and rather
little material near the center of mass of the binary. On the other hand, the
3D simulations often treat the companion star and the red giant core as point
sources. In 1D, the primary core, at least, can be modeled in more detail. A
1D code like mesa conserves energy and angular momentum within expected
numerical accuracy. mesa also automatically handles energy released by
recombination as the envelope expands and the angular momentum is lost in
winds. In some 1D simulations of CEE, the companion is treated in a “thin
shell" approximation.

Chatzopoulos et al. (2020) argue that for massive primaries with mass ratios
$q~{}<q_{\rm blue}$ (where 0.25$~{}<q_{\rm blue}<~{}$0.33) and initial period,
$P_{\rm i}$, greater than a few tens of days, mass transfer starts in early
Case B mass transfer. This situation arises when hydrogen is exhausted in the
primary, so the primary has evolved off the main–sequence but not yet ignited
helium, and while the secondary is still on the main-sequence. This mass
transfer is rapid and results in the primary envelope engulfing the much-lower
mass secondary. The secondary spirals inward producing a merger.

In this scenario, the helium core of the primary is surrounded by a H–burning
shell. When the secondary reaches the critical tidal disruption distance from
the core of the primary, a tidal stream will form that transports fresh H fuel
toward the core (Ivanova, 2002; Ivanova et al., 2002b; Ivanova &
Podsiadlowski, 2003b) as shown in Figure 4. Mixing can thus happen if the mass
transfer stream can penetrate the core (Ivanova et al., 2002a). The depth of
penetration of the stream into the core depends on the direction, entropy,
width, and angular momentum of the stream, the rotation, orientation, and mass
of the secondary, on the density structure and relative rotation of the core,
and on fluid instabilities.

Figure 4: Density profile from a 2D simulation of a 16 M⊙+1 M⊙ merger
occurring at an initial separation of 12 R⊙ showing the formation of the tidal
stream (teardrop shape to the right of center) within the common envelope
(outer green and blue green) as the secondary fills its Roche Lobe and is
disrupted by the core of the primary (large red dot in the center). From
Chatzopoulos et al. (2020).

The penetration depth of the stream into the core of the primary determines
the extent of its rejuvenation; if fresh fuel reaches the core then core
H–burning will be re–ignited and the star may evolve toward the blue
supergiant (BSG) phase. If, on the contrary, the stream does not penetrate
deeply into the core but rather converges with the H–burning shell, then the
star will continue to evolve toward the RSG stage. Chatzopoulos et al. (2020)
confirm, by using the arguments presented in Ivanova et al. (2002b), that none
of the models they explored (secondaries in the range 1–4 $M_{\odot}$ merging
with primaries in the range 15–17 $M_{\odot}$) undergo stream–core
penetration.

These results suggest that the “quiet merger" described above is more relevant
to the case of Betelgeuse. In that case, the amount of orbital angular
momentum depends mostly on the binary separation when the primary overflows
its Roche lobe. The total angular momentum deposited in the envelope of the
primary depends on the radius of the primary when it engulfs the secondary
during its crossing of the Hertzsprung gap.

###  3.3 Merger Models

Of primary interest for Betelgeuse is how and under what circumstances a
merged system could end up rotating at $\sim 23$% of the critical velocity, as
observations suggest (§2.8). Merger models provide a reasonable “natural"
explanation for why Betelgeuse has a large, but sub-Keplerian equatorial
velocity (Wheeler et al., 2017; Chatzopoulos et al., 2020; Sullivan et al.,
2020). These results do not prove, but do allow that Betelgeuse might have
merged with a lower mass companion. Betelgeuse might look substantially the
same whether it merged with a 1 or 10 M⊙ companion. Joyce et al. (2020)
concluded that Betelgeuse merged prior to the later carbon-burning phases, but
see Luo et al. (2022).

While the hypothesis that Betelgeuse might have merged with a companion is
credible and consistent with the a priori estimate that Betelgeuse has a
probability of $\sim 20$% of being born in a binary system (de Mink et al.,
2014), it raises a number of interesting issues involving common envelope
evolution, the fate of the companion and its angular momentum, and effect on
the post-merger structure of the primary.

The luminosity of an evolved massive star is typically a function of the mass
of the helium core and rather independent of the mass of the envelope. If a
companion merged with the core of Betelgeuse, then the current luminosity may
be a measure of the core mass ($\sim$ 5 to 6 M⊙), but the mass of the envelope
would be rather unconstrained and probably smaller than the estimates given
based on single–star models that attempt to reproduce the luminosity, radius
and effective temperature. If there were a coalescence, there would be some
mass ejected.

The mass lost from the system during the merger may be substantial. The 3D
16$M_{\odot}$+4$M_{\odot}$ merger model of Chatzopoulos et al. (2020) lost 0.5
M⊙. This model accounted for rotation, but not radiative effects nor
recombination. Sullivan et al. (2020) found up to 5 M⊙ lost. The mass loss is
a combination of the loss of mass accreted from the secondary plus loss of
mass from the primary itself. The latter is due to winds prior to the
accretion event and then the rotationally-induced mass loss after the
accretion.

A main sequence companion of about a solar mass would have a mean density of
about 1 g cm-3. That density is characteristic of the base of the hydrogen
envelope in the RSG models, implying that a companion might not be dissolved
until it reaches the edge of the helium core (see discussion of common
envelope evolution and plume penetration in §3.2). If the companion merged
with the core, the evolution of the primary might be severely altered by
anomalous burning and mixing effects, and surface abundances might be
affected.

Sullivan et al. (2020) used the mesa code to study the merger problem in a
rudimentary way that nevertheless gave some insights to the relevant physical
processes. They did not attempt to treat the companion as a corporeal entity,
but allowed for its effects by adding the relevant mass and associated angular
momentum to the outer envelope of the primary, a computational process
identified as “accretion" to distinguish it from the more complex behavior of
a true merger. The HRD of all the models of Sullivan et al. (2020) were
qualitatively similar. The accretion events resulted in irregular transient
loci before settling down to a rather normal evolution up the RSB to the point
of collapse of the models. The models suggest that the rotation of Betelgeuse
could be consistent with a primary of ZAMS mass somewhat less than 15 M⊙
accreting between 1 and 10 M⊙ in the core helium burning and core carbon
burning epochs. The observed equatorial velocity might also be attained by
accreting a broad range of masses onto a primary of ZAMS mass somewhat more
than 20 M⊙ in the later carbon shell burning epoch.

Chatzopoulos et al. (2020) used the mesa code to compute the 1D rotating
post–merger evolution of systems with mass ratio 0.06 $<q<$0.25 that suffer an
early Case B merger. In this case, unstable mass transfer occurs during during
the crossing of the Hertzsprung gap. A “stellar engineering" approach was
adopted by incorporating a perturbation term that captures the effects on the
specific angular momentum and entropy. This term was used to re–adjust the
post–merger structure of the envelope of the primary star during the in-spiral
prior to the dynamic disruption of the secondary around the He core of the
primary. The magnitude of the perturbation applied is proportional to $q$ and
the structure of the primary (their Equation 13). In their mesa simulations,
the mass of the secondary was added to the core plus hydrogen-burning shell.
The composition was not adjusted as done by Menon & Heger (2017) in their
models of SN 1987A (§3.4). Post-merger profiles were computed for different
primary radii corresponding to the time when the envelope of the primary
engulfed the secondary (200-700 $R_{\odot}$). The initial primary radii
represented initial separations corresponding to binding energies that enabled
the binary progenitor system to survive a possible past ejection from its
birth cluster, to be consistent with the borderline “runaway" nature of
Betelgeuse (§2.10). The resulting models were used to investigate the rotation
rate of the post–merger object.

The models explored by Chatzopoulos et al. (2020) were able to reproduce the
overall observed properties of Betelgeuse, including its position in the HRD,
its surface rotation rate, and its surface abundances, especially the observed
overabundance of nitrogen (§2.9). Their 16$M_{\odot}$+4$M_{\odot}$ merger
occurring at $\sim$ 200-300$~{}R_{\odot}$ yielded the best fit. These models
had a sustained high equatorial rotation for a few hundred thousand years
after the merger.

Chatzopoulos et al. (2020) also presented a 3D simulation of the merger
between a 16$M_{\odot}$ primary and a 1$M_{\odot}$ secondary that occurred
when the primary reached a radius of $\sim$12$R_{\odot}$, right after the end
of its TAMS. The simulation was performed with the 3D OctoTiger Adaptive Mesh
Refinement (AMR) hydrodynamics code developed by the LSU Center for
Computation and Technology (CCT) (Marcello et al., 2021). Post–processing of
the 3D internal structure of the post–merger object confirmed that the
envelope of the primary was spun–up by a significant amount during the in-
spiral phase.

The degree of envelope spin–up is, however, proportional to the primary’s
radius at the onset of the merger. Three–dimensional simulations of mergers
occurring at larger primary radii are needed to compute post–merger structures
that evolve to become rapidly–rotating supergiants. The limitation in
simulating the CEE evolution of such systems in 3D is purely of computational
nature; the in-spiral timescale for a 15$M_{\odot}$+1$M_{\odot}$ merger
occurring at $\sim$ 300$R_{\odot}$ is $\sim$1000 years, requiring a very long
simulation time. In addition, the density contrast between the compact
secondary and the low-density outer regions of the envelope of the primary as
well as the large simulation box that would be required to include the entire
system makes it difficult to adequately resolve the full structure of the
secondary, its tidal disruption plume, and the dense core of the primary,
requiring billions of zones rendering such calculations prohibitively
expensive.

Despite these computational challenges, there are on-going efforts involving
the use of point masses to represent the secondary and the core of the
primary. The merger can be accelerated by the removal of a constant, yet
small, amount of angular momentum per orbit. This allows the long–term
evolutionary calculation of post–merger angular momentum profiles for the
primary.

An example of such a simulation involving the merger between a 15$M_{\odot}$
primary and a 4$M_{\odot}$ secondary initiated with a separation between the
secondary and the core of the primary of 50 $R_{\odot}$ is shown in Figure 5.
This model lost $\sim 0.4$ M⊙ in the “mergeburst" (Soker & Tylenda, 2006)
phase right after the merger when the surface equatorial velocity was $\sim$
60 km s-1. The simulation focused on the angular momentum of the remaining
bound object and did not quantify the amount of angular momentum lost.

The spherical, mass-weighted, angle–averaged profiles for internal energy,
density, and temperature and the cylindrical mass-weighted profile for
specific angular momentum of the post–merger object resulting from this
simulation are shown in Figure 6. Note that the x-axis is q, the normalized
mass-coordinate variable. The specific angular momentum, j, decreases with q,
but increases in radius, so the bulk of the structure is dynamically stable. A
minor decrease/instability develops in the very outer regions that contain
very little mass. That behavior is in agreement with Ivanova & Nandez (2016).

This simulation was long and expensive. It used a sufficiently large box to
follow the unbound material after the merger for as long as possible in order
to characterize the mergeburst transient and also with sufficient zones to
resolve enough of the secondary structure and the primary core such that they
are dynamically stable in the grid. This balance did not allow sufficient
resolution to resolve the stream-core interaction in detail but such
simulations will be done in the future. These proposed simulations will allow
a comparison to the 3D models of Ivanova & Nandez (2016) for lower mass
systems. For related work on the effect of radiation pressure and
recombination energy in the ejection of mass in the CEE of an RSG star see Lau
et al. (2022).

Figure 5: The initial (upper panel) and final (immediately prior to the merger
of the secondary with the core of the primary (lower panel) density structure
of a 15$M_{\odot}$+4$M_{\odot}$ system with an initial core/secondary
separation of 50 $R_{\odot}$ simulated with the 3D AMR OctoTiger code. The
core of the primary and the secondary are treated as point masses. The color
bar on the right represents density in g cm-3. Dashed lines represent
equipotential surfaces. In the upper panel, arrows with length proportional to
magnitude represent the velocity field. Velocities beyond the primary core and
secondary are typically 50 km s-1. The numbers 8.1 and 39.8 in the lower left
corners represent the “orbit number" that was used in OctoTiger (even after
the merger) to represent the time/phase of the simulation. From Chatzopoulos
et al. 2023, in preparation. Figure 6: Energy density, specific angular
momentum, density, and temperature profiles of the post–merger object
following the merger of a 15$M_{\odot}$+4$M_{\odot}$ system occurring at 50
$R_{\odot}$. The original 3D profiles have been mass–weighted and angle-
averaged. From Chatzopoulos et al. 2023, in preparation.

####  3.3.1 Insensitivity of Final Equatorial Velocity to Accreted Mass

The original motivation of Wheeler et al. (2017) for hypothesizing that
Betelgeuse might have merged with a companion was the difficulty of accounting
for the nominal currently-observed equatorial rotation velocity, $\sim 15$ km
s-1, allowing for inclination. A companion mass of $\sim 1$ M⊙ was estimated
from simple arguments based on conservation of angular momentum. Subsequent
work showed that, broadly, the final rotational velocities of the models were
rather independent of the companion mass accreted.

Although the treatment of the post-merger system by Sullivan et al. (2020) and
by Chatzopoulos et al. (2020) is rather different, the results for the final
equatorial rotational velocity are very similar. This gives confidence that
this quantity is somewhat robust against the details of the merger process and
depends primarily on a global quantity such as the pre-merger orbital angular
momentum.

If a merger occurred in Betelgeuse, the product must have settled into a state
for which the rotation is sub-Keplerian. This global criterion is independent
of the masses of the primary and secondary involved in the merger. The
implication is that the loss of mass and angular momentum must adjust to meet
this criterion rather independently of the masses involved and the epoch of
accretion. This also serves to constrain the final rotation of the envelope to
potentially large, but finite values.

For these studies to have any relevance to Betelgeuse, it is important that
the structure remain that of an RSG after the proposed merger. As mentioned in
§3.2, a “quiet merger" can leave behind an RSG, depending on pre-merger
conditions. Ivanova & Podsiadlowski (2003a) suggest that this condition favors
secondary masses $>2$ M⊙ and a primary close to carbon ignition so that strong
gradients inhibit core/envelope mixing. Ivanova & Nandez (2016) note that
during a slow spiral-in, the angular velocity becomes constant in most of the
CE and the value of the angular velocity is significantly smaller than the
local Keplerian velocity in the envelope, so the approximation of spherical
symmetry is reasonable.

####  3.3.2 Angular Momentum

During the merger and redistribution of density, angular momentum, and
composition, some angular momentum is lost to the surroundings in the
rotation-enhanced wind, and some is retained to propagate inward toward the
primary core. In the 1D “accretion" models explored by Sullivan et al. (2020),
the angular momentum that is retained is redistributed by an inward diffusive
wave of angular momentum. The profiles of the specific angular momentum and
angular velocity quickly evolve to stable forms delineated by an inward
propagating front with the specific angular momentum increasing outward beyond
the front and the angular velocity being nearly constant.

A few years after accretion, the ingoing wave of angular momentum propagated
to the boundary between the outer envelope and the H/He shell. The wave of
angular momentum was halted at the composition boundary at the edge of the
helium core leaving behind an envelope of constant angular velocity and a
monotonically rising angular momentum per unit mass. By the epoch of collapse,
the angular momentum distribution in the outer envelope had scarcely changed.
The wave of angular momentum swept through the H/He shell, but was halted at
the outer boundary of the He shell at 7 M⊙ for both the 20M⊙+1M⊙ and the
20M⊙+10M⊙ models. The composition distribution remained virtually unchanged.

All the final models of Sullivan et al. (2020) have inner regions of negative
gradient in $j$ in regions of sharp composition gradients. These must be
stabilized against the Rayleigh instability by the associated composition
gradients. This condition has not been investigated in detail.

Ivanova & Nandez (2016) presented a model of a primary of 1.8 M⊙ and secondary
of 0.1 M⊙(model M10; their figure 7). While the mass scale is smaller than
considered by Sullivan et al. (2020) and Chatzopoulos et al. (2020), the mass
ratio, $\sim 0.05$, is about the same as for their 20M⊙+1M⊙ models. The
angular velocity as a function of mass for model M10 50 days after the plunge-
in is basically flat throughout the model. The value of the angular velocity,
$\sim 3\times 10^{-7}$ rad s-1, is close to that of Sullivan et al. (2020),
perhaps fortuitously, but the peak value of the angular momentum per unit mass
for model M10 is about a factor of 30 less than found by Sullivan et al.
(2020). The flat angular velocity profile in the 3D simulations seems to arise
naturally in mesa simulations.

Significant departures in behavior between Ivanova & Nandez (2016) and
Sullivan et al. (2020) are found in the innermost and the outermost regions.
Ivanova & Nandez (2016) do not consider the inner core, so they do not explore
the distribution of angular momentum in the core. On the other hand, Ivanova &
Nandez (2016) and the upper right panel of Figure 6 find a distinct decrease
in both the specific angular momentum and the angular velocity in the outer 10
% of the mass of the envelope that the models of Sullivan et al. (2020) do not
reveal. This difference probably arises in the loss of mass and angular
momentum in the dynamical plunge-in phase that Sullivan et al. (2020) do not
treat accurately.

####  3.3.3 Composition

In their 1D calculation with a fully-resolved primary core, Sullivan et al.
(2020) found the composition distribution of the inner core to be only
slightly affected even by the accretion of a companion of large mass. Thus
while the inner structure might be somewhat perturbed by accretion of
substantial mass, there may be rather little effect on the outside to indicate
that the accretion occurred. The implication is that the inner composition
structure of Betelgeuse could be rather different depending on the mass
accreted with basically no indication reflected in the outer, directly
observable structure.

Evidence of internal mixing due to a merger (or other effects) can be revealed
by anomalous surface abundances (§2.9). Chatzopoulos et al. (2020) were able
to reproduce surface abundances of Betelgeuse, especially the observed
overabundance of nitrogen (Lambert et al., 1984). Brott et al. (2011a, b) and
Ekström et al. (2012b) find N/C surface enhancements that are similar to those
found in the merger simulations of Chatzopoulos et al. (2020) due to the
enchanced rotation from the spiraling-in phase.

####  3.3.4 Entropy

Ivanova & Nandez (2016) give an extensive discussion of the treatment of
entropy in CEE. They argue that the evolution of the entropy of the common
envelope material differs between 3D and 1D simulations. In 1D, the entropy is
generated because the energy is added as heat. Since the radius at which the
recombination energy release overcomes the potential well depends on the
entropy of the material, the entropy generation observed in 1D codes will
likely predict different outcomes than 3D CE evolution. Ivanova & Nandez
(2016) argue that 1D stellar codes should add the energy as mechanical energy
rather than “heat" that moves the material to a higher adiabat.

Chatzopoulos et al. (2020) find relatively little heating effects in their 3D
merger simulation of Betelgeuse. We note, however, that heating during merger
can lead to non-linear envelope pulsations and to potentially large mass loss
(Clayton et al., 2017).

####  3.3.5 Recombination

The role of hydrogen and helium recombination in abetting CE mass loss is
discussed by Ivanova et al. (2015), Ivanova & Nandez (2016), and Lau et al.
(2022). These reservoirs of energy can help to trigger envelope instability
depending on where and when the recombination energy is released. The time-
scale of recombination runaway can be up to several hundred days and gets
longer as the mass of the companion decreases. In such cases, radiative losses
can become important so that 3D simulations that lack radiative transfer are
no longer appropriate. For all their limitations, 1D stellar evolution codes
like mesa can handle this aspect of the physics.

####  3.3.6 Magnetic Fields

As noted in §2.11, Betelgeuse displays various effects of magnetic fields. The
magnetic properties are often omitted in CEE simulations. Sullivan et al.
(2020) and Chatzopoulos et al. (2020) included magnetic effects as treated by
the mesa Spruit/Tayler algorithm in some cases, but did not include magnetic
effects of the magnetorotational instability (Wheeler et al., 2015; Moyano et
al., 2023). The omission of the latter will undoubtedly alter the
quantitative, if not qualitative results. The Spruit/Tayler mechanism gives
results that typically weight the radial component, $B_{r}$, orders of
magnitude less than the toroidal component, $B_{\phi}$. The magnetorotational
instability tends to give the radial component about 20 per cent of the
toroidal component. Another important caveat is that mesa computes the
magnetic field structure based on the instantaneous structure of the model. In
reality, the field only decays on a dissipation timescale that might in some
circumstances be long compared to the evolutionary timescales. This would lead
to fossil magnetic field in a region that made a transition from being
unstable to stable to the Spruit/Tayler instability. mesa has no means to
treat the existence and decay of such fossil fields. The magnetic structure
computed by Sullivan et al. (2020) is thus interesting, but should not be
given any quantitative weight.

Sullivan et al. (2020) found that accretion has little effect on the
production of magnetic fields by the Spruit/Tayler mechanism. Their models
show a more substantial field in the outer part of the helium shell, reaching
up to the base of the hydrogen envelope. The peak fields are of order 1 G and
1000 G for the radial and toroidal fields, respectively, with considerable
variation with radius that is likely to be affected by issues of numerical
resolution. Below an inward gap where the fields are very small the fields
become large, but variable, in the innermost layers of the oxygen core. The
radial fields peak at $\sim$ 1000 G and the toroidal fields at $\sim 10^{6}$
to $10^{7}$ G. In the models, the fields peak off center and the toroidal
field declines to about 1 G in the center. The accretion appears to have a
quantitative, but not qualitative, effect on the field strength and
distribution just prior to collapse. Subsequent core collapse by a factor of
$\sim 100$ in radius would amplify the field by compression alone by a factor
of $\sim 10^{4}$. The resulting field of $\sim 10^{11}$ G would not be
dynamically significant, but would give ample seed field for growth of the
field in the proto-neutron star by the MRI (Akiyama et al., 2003;
Obergaulinger et al., 2009; Mösta et al., 2018)

###  3.4 Lessons from SN 1987A

To account for the circumstellar nebular rings, many studies of the mergers of
massive stars have focused on the prospect that the progenitor of SN 1987A may
have undergone a merger (Morris & Podsiadlowski, 2007). Merger models can also
account for why the progenitor was a blue rather than red supergiant by
invoking mixing of helium from the core into the outer envelope (Menon &
Heger, 2017).

In the case of Betelgeuse, a contrasting conclusion applies. While some
discuss the possibility that Betelgeuse will explode as a blue supergiant (van
Loon, 2013), Betelgeuse is still a red supergiant. If one accepts the basic
ansatz that a merger is required to account for the observed rotational
velocity of Betelgeuse, then it follows that a merger did not produce a
compact blue envelope and thus, by the arguments of Ivanova et al. (2002a) and
Menon & Heger (2017), little to no helium could have been mixed outward from
the core, consistent with the simulations of Sullivan et al. (2020) and
Chatzopoulos et al. (2020).

The modeling of a putative Betelgeuse merger by Chatzopoulos et al. (2020)
(§3.3) concluded that the plume from the disrupted secondary would not
penetrate the helium core and induce substantial helium mixing according to
the prescription of Ivanova et al. (2002a). Mixing may be more likely for more
massive secondaries, so the results of Sullivan et al. (2020) and Chatzopoulos
et al. (2020) may be less reliable for larger mass secondaries. Plume mixing
is a complex hydrodynamical problem that deserves more study if we are to
understand both Betelgeuse and SN 1987A as products of massive star mergers.

##  4 The Great Dimming

While Betelgeuse is known to display a wide range of fascinating behavior, it
surprised the Betelgeuse community and fascinated people world wide when it
went through a phase of anomalously low optical luminosity beginning in
October 2019 and lasting through March 2020 that became known as the Great
Dimming. The brightness decreased by over a factor of two and was easily
noticed by even casual observers of the night sky. Twitter alit with rampant
speculation that Betelguese was about to explode, thus requiring some effort
by supernova experts to tamp that particular hyped fever.

The Great Dimming was dramatic enough on its own (Guinan et al., 2020;
Levesque & Massey, 2020; Harper et al., 2020a; Dupree et al., 2020;
Dharmawardena et al., 2020; Harper et al., 2020b; Safonov et al., 2020;
Montargès et al., 2021; Levesque, 2021; Harper et al., 2021; Alexeeva et al.,
2021; Kravchenko et al., 2021; Dupree et al., 2022; Matthews & Dupree, 2022;
Taniguchi et al., 2022; Cannon et al., 2023). Both professionals and amateurs
had monitored the brightness of Betelgeuse for about a century. Much of that
data is stored in the valuable records of the American Association of Variable
Star Observers (AAVSO) (Figure 7). These studies had established that
Betelgeuse was a variable star with regular pulsations on a variety of time
scales as discussed in §2.12. The decrease in V band amplitude corresponding
to the $\sim 400$ day pulsation is typically 0.3–0.5 mag. In the Great
Dimming, the decrease was over 1 mag.

Figure 7: Century long record of the visual and V band brightness of
Betelgeuse compliled by the American Association of Variable Star Observers
supplemented by data from the Solar Magnetic Ejection Imager (SMEI). The final
large dip is the Great Dimming of 2020 (§4). From Joyce et al. (2020) by
permission of Meridith Joyce, László Molnár, and the Astrophysical Journal.

There is some suggestion in the AAVSO records that Betelgeuse underwent other
periods of anomalously large dimming, perhaps in the early 1950s and the late
1980s (Joyce et al., 2020). Dimming with a period of about 30 - 40 years might
be related to the rotation period of Betelgeuse (§2.8), but uncertainties in
the early photometry and in the radius and rotational velocity and hence the
period of Betelgeuse make that difficult to determine. There is also some
concern that individual AAVSO observers in the 1950s and 1980s showed a
tendency to report anomalously faint data that might have biased the mean
AAVSO values and produced a false impression of minima (T. Calderwood, private
communication, 2023).

There was no missing the Great Dimming of 2019/2020, but the attention to it
may have been amplified by an initiative of Andrea Dupree of the Center for
Astrophysics who convened many of the world’s experts on Betelgeuse to
participate in an intense global, multi-instrument, multi-wavelength
coordinated study of Betelgeuse beginning in April, 2018, when Betelgeuse was
especially well situated for studies with the HST, a project she named the
Month of Betelgeuse (MOB). Forty-four astronomers joined the MOB. A month was
not, of course, sufficient to address all the mysteries of Betelgeuse, the
project was rapidly renamed Months of Betelgeuse. Because of the MOB activity,
attention to Betelgeuse was still focused as the Great Dimming got underway.
Dupree et al. (2020) witnessed a UV enhancement from Sept-Nov. 2019 with HST
that may have been a precursor event to the Great Dimming prior to any
substantial decrease in brightness.

Ed Guinan of Villanova had been doing careful photometry and other studies of
Betelgeuse for over 25 years. Guinan et al. (2019) reported V-band, Wing TiO-
band, and NIR photometry on 7 December, 2019. They presented one of the first
interpretations of the Great Dimming, noting that “The light variations are
complicated and arise from pulsations as well from the waxing and waning of
large super-granules on the star’s convective surface.” They predicted a
minimum on 21 February, 2020 $\pm$ a week, based on the assumption that a 420
day period was in a fortuitous concatenation with longer-term (5 - 6 yr) and
shorter term (100 - 180 d) brightness changes and perhaps a super-granule
upwelling of a cool plume. This estimate turned out to be remarkably close to
the observed light minimum of $1.614\pm 0.008$ mag during 07-13 February 2020
(Guinan et al., 2020).

Levesque & Massey (2020) reported optical spectroscopy on 15 February, 2020.
They also examined the TiO bands and reported a $T_{eff}$ of 3600 K compared
to a typical value $\sim$ 3660 K. They argued that the small change in
$T_{eff}$ was not commensurate with the large change in V-band luminosity and
that a temporary cool period on the surface of Betelgeuse due to convective
turnover was likely not the primary cause of the Great Dimming. Rather, they
proposed an increase in large-grain gray dust.

Guinan et al. (2020) and Levesque & Massey (2020) thus framed the extremes of
the possible explanations of the Great Dimming that continues to be debated.
Early discussions of $T_{eff}$ during the Great Dimming assumed spherical
symmetry. While the assumption of spherical symmetry was an obvious starting
point, subsequent consideration of spots, super-granules, and circumstellar
dust call that assumption into question. The question of how accurately a
global value of $T_{eff}$ can be determined if $T_{eff}$ varies over the
surface of the star remains to be determined.

Montargès et al. (2021) illustrated this conundrum by producing dramatic
spatially-resolved interferometric images of Betelgeuse obtained with the
SPHERE instrument on the VLT in December 2019 and January 2020 that showed
that the southern half of the star had become markedly fainter than in January
2019, indicating that a major change has occurred in, or near, the photosphere
(Figure 8). Montargès et al. (2021) attributed this dark patch to “a dusty
veil."

Figure 8: Resolved images of Betelgeuse through the Great Dimming. January
2019 was prior to the dimming; December 2019 was somewhat after the onset of
the dimming; January 2020 was near the minimum of the dimming; and March 2020
was after the maximum dimming. From Montargès et al. (2021) by permission of
M. Montargès and ESO.

Harper et al. (2020b) reported Wing three-filter (A, B, and C band) TiO and
near-IR photometry that showed that portions of the photosphere had a mean
$T_{eff}$ that was significantly lower than that found by Levesque & Massey
(2020). They interpreted the image of Montargès et al. (2021) to be a large
patch in the photosphere that could be 250 K cooler than surroundings. They
concluded that no new dust was required and emphasized the interpretation of
Guinan et al. (2019) that the Great Dimming resulted from a coincidence of the
430 day and 5.8 year periods of Betelgeuse. They suggested that the cooling of
a large portion of the surface was produced dynamically by photospheric
motions due to pulsation and large-scale convective motions (Figure 9).

Figure 9: Schematic of gigantic cool dim patches on the surface of Betelgeuse
that were proposed as contributing to the Great Dimming. By permission of T.
Dharmawardena and Max Planck Institute for Astrophysics, Heidelberg. Credit:
Judith Neidel, MPIA graphics department.

Dharmawardena et al. (2020) reported 13 years of submillimeter observations of
Betelgeuse including the epoch of the Great Dimming obtained with the James
Clerk Maxwell Telescope and the Atacama Pathfinder Experiment. These long
wavelength observations were significant because they were not expected to be
obscured by dust as the optical observations could be. Dharmawardena et al.
(2020) found that Betelgeuse had also dimmed by $\sim$ 20% at these longer
wavelengths during the optical minimum. They concluded that the dimming was
due to changes in the photospheric luminosity as opposed to obscuration by
surrounding dust. See also Matthews & Dupree (2022) for 1.3 cm and 7 mm
observations with the VLA on August 2, 2019, just prior to the onset of the
optical dimming and Harper et al. (2021) for observations of circumstellar [O
I] 63.2 $\mu$m and [C II] 157.7 $\mu$m emission profiles and [O I] 63.2
$\mu$m, [O I] 145.5 $\mu$m, and [C II] 157.7 $\mu$m fluxes obtained shortly
after the Great Dimming with SOFIA.

Dupree et al. (2022) presented a synthesis of observations and an
interpretation of the Great Dimming that was a variation on the picture first
presented by Kervella et al. (2018). Dupree et al. (2022) outlined a scenario
in which the UV burst reported by Dupree et al. (2020) represented a surface
activity perhaps catalyzed by an upwelling that ejected a blob of matter. That
matter cooled as it expanded away from the surface allowing dust to form. The
resulting clump of dust crossed the line of sight to Betelgeuse resulting in
the dim patch observed by Montargès et al. (2021) and the resulting Great
Dimming (Figure 10).

Figure 10: Schematic of model of the Great Dimming in which a blob of gas is
ejected, cools to form dust, and passes through the line of sight to cause the
Great Dimming. Courtesy Ray Villard, STScI and NASA, art by E. Wheatley,
STScI.

Alexeeva et al. (2021) presented high-resolution high S/N ratio near-infrared
spectra obtained at Weihai Observatory on four epochs in 2020 during and after
the Great Dimming. They argued that a decrease in the overall mean $T_{eff}$
by at least 170 K on 2020 January 31 could be attributed to the emergence of a
large dark spot on the surface of Betelgeuse. Levesque (2021) argued for a
synthesis in which the dark patch of Montargès et al. (2021) and the Great
Dimming were caused by dust forming over a cold patch in the southern
hemisphere. Cannon et al. (2023) presented VLTI Multi AperTure mid-Infrared
SpectroScopic Experiment (MATISSE) observations in the N-band (8 - 13 $\mu$m)
near brightness minimum. They explored a model invoking multiple clumps of
dust close to the star and another considering a large cool spot on the
stellar surface with no dust. They found that both the dust clump and the cool
spot models are compatible with the data, noting that the extinction and
emission of a localised dust clump in the line of sight compensate each other
making the clump undetectable. They concluded that the lack of infrared
brightening during the Great Dimming (Dharmawardena et al., 2020) does not
exclude extinction due to a dust clump as one of the possible mechanisms.

Spectropolarimetry provides yet another tool to explore the geometry of the
surface of Betelgeuse (López Ariste et al., 2018; Haubois et al., 2019; Cotton
et al., 2020). Safonov et al. (2020) argued that to address the challenges of
the Great Dimming it was fundamentally important to employ methods to resolve
an inhomogeneous stellar atmosphere. They presented a set of differential
speckle polarimetric observations of Betelgeuse obtained at the 2.5 m
telescope of the Caucasian Mountain Observatory operated by the Sternberg
Astronomical Institute of Moscow State University. Observations on 17 days at
wavelengths 465, 550, 625 and 880 nm spanned the Great Dimming event. The
envelope was found to be highly inhomogeneous but correlated, with features
varying on a timescale of two or three months (Figure 11). An animation
captured the dramatic variablility registered in the polarization
111http://lnfm1.sai.msu.ru/kgo/mfc_Betelgeuse_en.php. The net polarized
brightness of the envelope remained constant as the $V$ band flux approached
its minimum. After the minimum, the polarized flux of the envelope rose a
factor of two as the optical flux was restored. Safonov et al. (2020)
concluded that the Great Dimming was caused by the formation of a dust cloud
located on the line of sight.

Figure 11: Speckle polarimetry of the surface of Betelgeuse on 27 October 2019
at the very beginning of the Great Dimming (left panel) and on 5 February 2020
at the extreme of the dimming (right panel). From Safonov et al. (2020) by
permission of B. Safanov, Caucasian Mountain Observatory, and the Sternberg
Astronomical Institute of Moscow State University.

Kravchenko et al. (2021) used high resolution spectroscopy to do a tomographic
study of the structure during the Great Dimming. This analysis suggested that
two shocks propagated in the upper atmosphere, one generated in February 2018
and one in January 2019 with the second amplifying the effects of the first.
Kravchenko et al. (2021) suggest that this shock structure modified by
underlying convection or outward gas motion altered the molecular opacity in
the line of sight.

Mittag et al. (2023) have engaged in long-term studies of the chromosphere of
Betelgeuse since 2013, including the epoch of the Great Dimming when they
determined the absolute and normalized excess flux of the Ca II H&K lines.
They found a behavior similar to that during a previous decrease in the visual
brightness of Betelgeuse in 1984 and 1985. Unlike the Mg II emission (Dupree
et al., 2022), the Ca II emission attributed to the lower chromosphere of
Betelgeuse did not change significantly between November 2019 and February
2020, but did vary after the Great Dimming. Mittag et al. (2023) argue that
this delay of the chromospheric reaction suggests that the cause for the great
dimming is located in the photosphere.

Himawari-8 is a Japanese geostationary meteorological satellite orbiting
35,786 km above the equator at 140.74oE. Several bright stars, including
Betelgeuse, occasionally fortuitiously appear in the images. Taniguchi et al.
(2022) used the 16-band photometry from 0.45 to 13.5 $\mu$m from Himawari-8 to
construct a light curve of Betelgeuse spanning 4.5 yr from 2017 to 2021 with a
sampling that averaged once per 1.72 d. Taniguchi et al. (2022) used the
infrared optical depth in contrast to variations in the visual extinction,
A(V), to directly trace the amount of circumstellar dust. The IR optical depth
increased during the Great Dimming with a small delay between the peak in IR
optical depth and the extinction in the visual. Taniguchi et al. (2022) argue
that their data suggest that a clump of gas produced dust that obscured the
photosphere of Betelgeuse and contributed to the Great Dimming and that the
enhancements of visual extinction and IR optical depth during the Great
Dimming may have occurred very close to the photosphere. They conclude that
their results support a scenario in which the Great Dimming was caused by a
combination of a decrease in $T_{eff}$ and an increase in A(V) in roughly
equal amounts consistent with the change in polarization reported by Cotton et
al. (2020) and Safonov et al. (2020).

The Great Dimming was clearly a complex phenomenon. It seems unlikely that its
alignment with the phase of the $\sim 400$ d pulsation period was a
coincidence, but that alone cannot account for the magnitude and spatial
inhomogeneity of the obscuration. There seems to be solid evidence that dust
with an inhomogeneous spatial distribution played a role. A decrease in
$T_{eff}$ occurred, perhaps in the form of large, cooler patches. Such patchy
structure in surface temperature calls into question the meaning of a global
$T_{eff}$ and at least sets upper limits on the precision with which a global
$T_{eff}$ can be determined.

In an epilogue, after the Great Dimming, Betelgeuse has shown repeated minima
at an interval of $\sim 200$ d and has steadily increased in mean brightness
to reach an historic maximum of V $\sim 0$ in April, 2023 (M. Montargès,
private communication, 2023).

##  5 The Explosion to Come

Betelgeuse will eventually explode, most probably still as a red supergiant
and thus producing a Type II supernova (Branch & Wheeler, 2017). The details
will be affected by the intense convection in the late shell-burning phases
less than a year before explosion that may also produce significant outward
acoustic flux and mass loss. The convection seeds turbulence in the collapsing
material that is expected to enhance the subsequent explosion (Arnett &
Meakin, 2011; Couch et al., 2015; Chatzopoulos et al., 2016).

At the expected iron-core collapse, $10^{53}$ ergs of neutrinos will be
produced that emerge from the envelope about an hour after collapse and flood
into space. About 600 years later, detection of those neutrinos will give
humans on Earth (if there are any 100,000 + 600 years from now) their first
hint of the events to come. At that time, a human body would receive $\sim$
100 trillion neutrinos, vastly less than a lethal dose of radiation.

The shock wave generated by the explosion carrying $\sim 10^{51}$ erg of
kinetic energy will take about a day to reach the surface. A blast of UV
lasting about an hour will then occur. The resulting UV flux will be less than
the flux of the Sun at Earth but perhaps sufficient to cause some disruption
of atmospheric chemistry.

In two weeks, the explosion will be producing a billion times the solar
luminosity. At the Earth, Betelgeuse will appear as a pinpoint about as bright
as a quarter Moon lasting for $\sim$3 months. The explosion will then fade,
but remain visible at the Earth for many years and to scientific instruments
for centuries. The explosion of Betelgeuse is likely to produce a pulsar that
will also be visible for a million years or more.

The supernova blast wave will propagate out through the surrounding CSM and
ISM and interact with any mass lost in the next 100,000 years and eventually
with the complex CSM illustrated in Figure 3. The shock wave will propagate at
$\sim 5000$ km s-1 and hence collide with the bow shock in about 60 y and the
odd linear structure about 20 y later, assuming a distance to Betelgeuse of
165 pc (Joyce et al., 2020).

By the time the supernova shock reaches the Earth more than 100,000 years
after the explosion, the Solar magnetosphere should easily deflect it. The
Earth immersed within the supernova remnant may witness an increase in cosmic
ray flux.

##  6 Summary, Conclusions, and Future

As nearby and well studied as it is, Betelguese still presents a host of
outstanding issues: its irregular surface; the manner in which it ejects
matter to form a chromosphere, wind, dust, and molecules; how it came to move
through space and spin so rapidly; the nature of its variability and magnetic
fields; and the possibility that it underwent a significant change in color
within historical times. Statistics suggest that it was likely to have been
born in a binary system and undergone complex common envelope evolution. Are
the distant circumstellar structures related to the interaction of winds with
the interstellar medium or the products of the dramatic turmoil of a merger?

A pertinent question is the structure and condition of Betelgeuse as we see it
today, gracing Orion. While uncertainties in the distance remain troubling,
Betelgeuse is most likely near the tip of the RSB. Since core helium burning
is far longer than subsequent burning phases, Betelgeuse is most likely in
core helium burning. The pulsation period likely constrains the radius and
distance and the evolutionary state to core helium burning (Joyce et al.,
2020), but there are arguments to the contrary (Neuhäuser et al., 2022; Lau et
al., 2022).

Estimates of the surface gravity of Betelgeuse span a rather large range. The
inclination angle is uncertain. A more accurate measurement of $log~{}g$,
radius, and distance could yield new constraints on the current total mass.
Comparison to the luminosity that most directly measures the core mass could
reveal hints of the current mass of the outer hydrogen envelope, past mass
loss, and the current evolutionary state. Continued exploration of atomic,
isotopic, and molecular abundances may yield more information on internal
mixing processes.

The notion that Betelgeuse may have undergone a merger remains viable. The
extra angular momentum may have come from merger with a companion in the red
supergiant phase, nearly independent of the mass of the secondary. Once a
transient phase of merging has settled down and substantial mass and angular
momentum have been ejected, there is rather little external difference in
models in late core helium burning and subsequent phases. This frustrates
attempts to determine the internal structure and state of the star. How can we
prove Betelgeuse has undergone a merger?

There remain great challenges in understanding the associated physical
processes if Betelgeuse underwent a merger. These must be explored with
extensive, highly–resolved 3D studies of the formation and evolution of tidal
plumes as any secondary is disrupted near the core of the primary. How deeply
does the plume penetrate? What abundances are mixed to the surface? What is
the level of envelope enrichment with helium that may determine whether the
star remains red or moves back to the blue? What is the expected structure of
the inner core as it evolves, rapidly rotating, beyond core helium burning?

The Great Dimming of 2019/2020 did not portend imminent explosion. The origin
of the dimming might have been related to a resonance of pulsation periods,
expulsion of a dust cloud, and extra large star spots.

How can we test the current evolutionary state of Betelgeuse with observations
of pulsations and surface irregularities? Are there faint signals from
acoustic waves generated internally that carry information about the core
structure that would prove or disprove the hypothesis of a merger?

What are the clues to imminent collapse that might pertain now, or in the far
future if Betelgeuse is in core helium burning now? Models predict extensive
mass loss shortly before collapse driven by rapid convection in the inner
burning shells and there are hints of such pre-collapse mass loss in Type II
supernovae that are thought to arise in red supergiants like Betelgeuse.

Mysteries abound!

##  7 Addendum: Post-publication Notes

Andrea Dupree’s Month of Betelgeuse project, MOB, that helped to focus
attention on the Great Dimming was promptly renamed Months of Betelgeuse as
the work of the group continued after April 2018.

Tom Calderwood (private communication, 2023) pointed out that possible deep
minima in the light curve of Betelgeuse registered in AAVSO visual estimates
in the early 1950s and mid to late 1980s came from only one or two amateur
observers. Those data and hence the depth of any minima may be suspect.

After the Great Dimming, Betelgeuse brightened to near historic highs,
oscillating with a dominant timescale closer to 200 days rather than 400 days
(Sigismondi et al. 2023; Astronomer Telegram #16001: Monitoring Betelgeuse at
its brightest).

Saio et al. (2023; arXiv:2306.00287) presented an argument that the 2000 day
“long secondary period” of Betelgeuse was the fundamental radial oscillation
period, and that Betelgeuse may already be in carbon burning with only years
to live. Both these points of view were contested by Molnár et al. (2023;
Research Notes of the AAS, Volume 7, Number 6).

## Acknowledgments

We are grateful to Natasha Ivanova for discussions of common envelope
evolution and to the Aspen Center for Physics for providing the environment to
do so. We also thank Ed Guinan, Meridith Joyce, and Andrea Dupree and the
Month of Betelgeuse (MOB) team for discussions of Betelgeuse and mergers. We
thank Ralph Neuhauser, Brad Schaefer, and Anita Richards for discussions of
the historical color evolution of Betelgeuse. We are especially thankful for
the ample support of Bill Paxton and the mesa team. JCW is grateful to the
group of enthusiastic undergraduates at The University of Texas at Austin who
catalyzed his interest in Betelgeuse: Sarafina Nance, Jamie Sullivan, Manuel
Diaz, Steven Smith, Justin Hickey, Li Zhou, Maria Koutoulaki, and Julia
Fowler. The research of JCW was supported in part by the Samuel T. and Fern
Yanagisawa Regents Professorship in Astronomy and by NSF AST-1813825. EC is
grateful to Dr. Juhan Frank, Dr. Sagiv Shiber, and Dr. Bradley Munson for
insightful discussions and for their collaboration. The research of EC was
supported in part by the National Science Foundation Grant AST-1907617 and in
part by the Department of Energy Early Career Award DE-SC0021228.

; OctoTiger Adaptive Mesh Refinement (AMR) hydrodynamics code developed by the
LSU Center for Computation and Technology (CCT) (Marcello et al., 2021).

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