Betelgeuse

Betelgeuse (α Ori)

The pink arrow at the star on left labeled α indicates Betelgeuse in Orion.
Observation data Epoch J2000.0      Equinox J2000.0
Constellation	Orion
Pronunciation	/ˈbiːtəldʒuːz/ or /ˈbɛtəldʒuːz/[1]
Right ascension	05h 55m 10.3053s[2]
Declination	+07° 24′ 25.426″[2]
Apparent magnitude (V)	0.42[2] (0.3 to 1.2)
Characteristics
Spectral type	M2Iab[2]
U−B color index	2.06[2]
B−V color index	1.77[2]
Variable type	SR c (Semi-Regular)[2]
Astrometry
Radial velocity (Rv)	+21.91[2] km/s
Proper motion (μ)	RA: 24.95 ± 0.08[3] mas/yr Dec.: 9.56 ± 0.15[3] mas/yr
Parallax (π)	5.07 ± 1.10[3] mas
Distance	643 ± 146 [3] ly (197 ± 45 [3] pc)
Absolute magnitude (MV)	−6.05[4]
Details
Mass	~18–19[5] M☉
Radius	~1,180[6] R☉
Surface gravity (log g)	-0.5[7]
Luminosity	~180,000[8] L☉
Temperature	3,500[7][9] K
Metallicity	0.05 Fe/H[10]
Rotation	5 km/s[9]
Age	~1.0 × 108 [5] years
Other designations
Betelgeuse, α Ori, 58 Ori, HR 2061, BD +7° 1055, HD 39801, FK5 224, HIP 27989, SAO 113271, GC 7451, CCDM J05552+0724AP, AAVSO 0549+07
Database references
SIMBAD	data

Coordinates: 05^h 55^m 10.3053^s, +07° 24′ 25.426″

Betelgeuse, also known by its Bayer designation Alpha Orionis (α Orionis / α Ori), is the ninth brightest star in the night sky and second brightest star in the constellation of Orion, outshone by its brighter neighbour Rigel (Beta Orionis) almost all the time. Distinctly reddish-tinted, it is a semiregular variable star whose apparent magnitude varies between 0.2 and 1.2, the widest range of any first magnitude star.^[11] The star marks the upper right vertex of the Winter Triangle and center of the Winter Hexagon.

Classified as a red supergiant, Betelgeuse is one of the largest and most luminous stars known. If it were at the center of our solar system, its surface would extend past the asteroid belt possibly to the orbit of Jupiter and beyond, wholly engulfing Mercury, Venus, the Earth and Mars.^[12][13] However, with distance estimates in the last century that have ranged anywhere from 180 to 900 light years from Earth, calculating its size, luminosity and temperature have proven difficult. Betelgeuse is currently thought to lie around 640 light-years away,^[3][5] yielding a mean absolute magnitude of about −6.05. It was the first star after the Sun to have its angular diameter measured in 1920, yielding a result of .047 arcseconds.^[14] Since then, Betelgeuse has been measured numerous times with results ranging between 0.042" to 0.069". Because of limb darkening, the star's variable photosphere, and angular diameter estimates that vary at different electromagnetic wavelengths, the star remains a perplexing mystery. To complicate matters further, Betelgeuse has an enormous circumstellar envelope. Images taken by the ground-based Very Large Telescope in July 2009 show a huge plume of gas extending from its photosphere.

Astronomers believe Betelgeuse is only 10 million years old, but has evolved rapidly because of its high mass.^[5][15] It is thought to be a runaway star from the Orion OB1 Association, which also includes the late type O and B stars in Orion's belt—Alnitak, Alnilam and Mintaka. Currently in the later stages of stellar evolution, Betelgeuse has moved off the main sequence on the Hertzsprung-Russell diagram, and has swollen and cooled to become a red supergiant. It is expected to explode as a type II supernova.

Observational History

Betelgeuse and its red coloration have been noted since antiquity; the classical astronomer Ptolemy described its color as ὑπόκιρρος. It was described by a translator of Ulugh Beg's Zij-i Sultani as rubedinem "ruddiness".^[16]

Herschel's discovery

Portrait of Sir John Herschel by Julia Margaret Cameron a few years before his death.

Betelgeuse's variable brightness was first described in 1836 by Sir John Herschel, when he published his observations in Outlines of Astronomy, in which he noted an increase in activity from 1836–1840, followed by a subsequent reduction. In 1849, he noted a shorter cycle of variability which peaked in 1852. Later observers recorded unusually high maxima with an interval of several years, but only small variations from 1957 to 1967. The records of the American Association of Variable Star Observers (AAVSO) show a maximum brightness of apparent magnitude 0.2 in the years 1933 and 1942, with a minimum brightness fainter than magnitude 1.2 in both 1927 and 1941.^[17][18] This variability in brightness may explain why Johann Bayer designated the star alpha as it may have rivalled the usually brighter Rigel (beta).^[19]

In 1919, Albert Michelson and Francis Pease mounted a 6 metre (20 ft) interferometer on the front of the 2.5 metre (100 inch) telescope at Mount Wilson Observatory. Helped by John A. Anderson, in December 1920 Pease measured the angular diameter of α Orionis as 0.047 arcseconds. Given the then-current parallax value of 0.018 arcseconds, this resulted in an estimated diameter of 3.84 × 10⁸ km (240 million miles or 2.58 AU). However there was known uncertainty owing to limb darkening and measurement errors.^[14][20] More recent visible-light observations of Betelgeuse have found the diameter to vary between 0.0435" and 0.0690".^{[21][22] [note 1]}

Aperture masking

Betelgeuse imaged in ultraviolet light by the Hubble Space Telescope and subsequently enhanced by NASA. The bright white spot is likely one of its poles. NASA/ESA credit.^[23][24]

In the late 1980s and early 1990s, Betelgeuse became a regular target for Aperture Masking Interferometry visible-light and infrared imaging, which revealed a number of bright spots on the star's surface, thought to result from convection.^[25][26] These were the first optical and infrared images of the disk of a star other than our Sun, and generally showed one or more bright patches—indicating the location of hotspots in the star's photosphere.

In 1995, the Hubble Space Telescope's Faint Object Camera captured an ultraviolet image of comparable resolution—this was the first conventional-telescope image (or "direct-image" in NASA terminology) of the disk of another star. The image was taken at ultraviolet wavelengths since ground-based instruments cannot produce images in the ultraviolet with the same precision as Hubble. Like earlier images, this ultraviolet image also contained a bright patch, indicating a hotter region of about 2000 degrees Kelvin, in this case on the southwestern portion of the star's surface.^[27] Subsequent utraviolet spectra taken with the GHRS suggested that the hot spot was one of Betelgeuse's poles of rotation. This would give the rotational axis an inclination of about 20° to the direction of Earth, and a position angle from celestial North of about 55°.^[28]

Recent studies

AAVSO V-band light curve of Betelgeuse (Alpha Orionis) from Dec. 1988 – Aug. 2002

Recent ground-based measurements of the disk of Betelgeuse in the mid-infrared, at 11.15 μm, gave an angular diameter of 54.7 ± 0.3 milliarcseconds (mas) in November 1999, slightly smaller than the typical visible-light angular diameter. This measurement assumes a uniform disk model and ignores any possible contribution from hotspots (which are less noticeable in the mid-infrared.) Allowing for the limb darkening effect, whereby the intensity of a star's image diminishes near the edge, gives an increase of approximately 1%, to 55.2 ± 0.5 milliarcseconds (mas). It is difficult to define the precise diameter of Betelgeuse as the photosphere has no "edge"—instead the gas making up the photosphere gets gradually thinner with distance from the star.^[29]

On June 9, 2009, Nobel Laureate Charles Townes announced that the star has shrunk 15% since 1993 with an increasing rate. He presented evidence that UC Berkeley's Infrared Spatial Interferometer (ISI) atop Mt. Wilson Observatory had observed 15 consecutive years of stellar contraction. The average speed at which the radius of the star has been shrinking during this period is around 1,000 km/hr.^{[note 2]} Despite Betelgeuse's diminished size, Townes and his colleague, Edward Wishnow, pointed out that the star's visible brightness, or magnitude, which is monitored regularly by members of the American Association of Variable Star Observers (AAVSO), had shown no significant dimming over that same time frame. According to the university, Betelgeuse's diameter is about 5.5 A.U., and the star's radius has shrunk by a distance equal to half an astronomical unit, or about the orbit of Venus.^[13][30] Townes concluded it was unclear whether the shrinkage is part of a periodic process or not; if it is, then the cycle is likely to be decades long.^[31]

In July 2009, images released by European Southern Observatory, taken by the ground based Very Large Telescope, gave a more detailed view of the surface of the star.^[32] In the picture a plume of gas six times its photospheric diameter is seen extending from the star. ^[9] This is comparable to the distance between the Sun and Neptune.

A series of spectropolarimetric observations, obtained in 2010 with the Bernard Lyot Telescope at Pic du Midi Observatory, revealed the presence of a weak magnetic field at the surface of Betelgeuse, suggesting that the giant convective motions of supergiant stars are able to trigger the onset of a small-scale dynamo.^[33]

Visibility

The location of Betelgeuse near the famous "Belt of Orion".

Betelgeuse is an easy star to spot in the night sky, as it appears in close proximity to the famous belt of Orion and has a distinctive orange-red color to the naked eye. Beginning in January of each year, it can be seen rising in the east just after sunset. By mid-March, the star is due south in the evening sky and visible to virtually every inhabited region of the globe, with only a few obscure research stations in Antarctica south of 82 degrees unable to see it. Even in cities like Sydney—Down Under where one might expect Betelgeuse to be hidden—the star rises almost 49° above the horizon. Once May arrives, the red giant can be glimpsed but briefly on the western horizon just after the Sun sets.

The apparent magnitude of α Ori is listed in SIMBAD at 0.42, making it on average the ninth brightest star in the night celestial sphere—just ahead of Achernar. Because Betelgeuse is a variable star whose brightness ranges between 0.2 and 1.2, there are periods when it will surpass Procyon in brightness to become the eighth brightest star. As Rigel, with a nominal apparent magnitude of 0.12, has been reported to fluctuate slightly in brightness, by 0.03 to 0.3 magnitudes,^[34] it may also be possible for Betelgeuse to occasionally outshine Rigel and become the seventh brightest star. At its faintest, it will actually fall behind Deneb as the 19th brightest star and compete with Mimosa for the 20th position in the sky.

Image of the supergiant from ESO's Very Large Telescope showing the redness of the star and its extended atmosphere.

Betelgeuse has a color index (B–V) of 1.86—a figure which points to the advanced "redness" of this celestial object. It was the first star on which starspots were resolved in optical images using a telescope, first from ground-based Aperture Masking Interferometry and later from the Hubble Space Telescope, followed by higher-resolution observations by the ground-based COAST telescope.^[35] Betelgeuse's photosphere has an extended atmosphere which displays strong lines of emission, rather than absorption. This chromosphere has a temperature no higher than 5,500 K and may stretch outward to seven times the diameter of the star. This extended gaseous atmosphere has been observed moving both away from and towards Betelgeuse, apparently depending on radial velocity fluctuations in the photosphere. Only about 13% of the star's radiant energy is emitted in the form of visible light, with most of its radiation occurring in the infrared. If our eyes were sensitive to radiation at all wavelengths, Betelgeuse would appear as the brightest star in the sky.^[18]

Enigmatic Parallax

The uncertainty of Betelgeuse's distance has puzzled astronomers for centuries, and has made reliable estimates difficult for many other stellar parameters such as luminosity. When combined with the angular diameter of the star, one can estimate the radius and its effective temperature; luminosity combined with an understanding of isotopic abundances provides an estimate of the stellar age and mass.^[3] In 1920, when the first interferometric studies were performed, the assumed parallax was 0.180 arcseconds. That equates to a distance of 56 pc or roughly 180 ly. Since then, there has been an ongoing inquiry as to the actual distance of this mysterious star with estimated distances as high as 900 light years being proposed.^[3]

Before the publication of the Hipparcos Catalogue (1997), there were two respected publications with up-to-date parallax data on Betelgeuse. The first was the Yale University Observatory (1991) with a published parallax of π = 9.8 ± 4.7 milliarcseconds, yielding a distance of roughly 102 pc or 330 ly.^[36] The second was the Hipparcos Input Catalogue (1993) with a trigonometric parallax of π = 5 ± 4 mas, a distance of 200 pc or 650 ly—almost twice the Yale estimate.^[37] With such uncertainty, researchers were adopting a wide range of distance estimates, a phenomenon which fueled much debate—not only in terms of the star's distance, but also in terms of its many other implications.^[3]

Image showing one of NRAO's Very Large Arrays (VLA) located at Socorro, New Mexico, USA. Each of the 27 antennas weighs 209 metric tons and can be moved as needed on railroad tracks allowing the array to perform detailed studies using aperture synthesis interferometry.

The long awaited results from the Hipparcos mission were finally released in 1997. Instead of resolving the issue, a new parallax figure was published of π = 7.63 ± 1.64 mas, which equated to a distance of 131 pc or roughly 430 ly.^[38] Because stars like Betelgeuse vary in brightness, they raise specific problems in quantifying their distance.^[39] As a result, the large cosmic error in the Hipparcos solution may be of stellar origin, perhaps related to movements of the photocenter, of order 3.4 mas, in the Hipparcos photometric Hp band.^[3][40]

Where a breakthrough in this debate appears to have come is with the advances in radio astronomy. New high spatial resolution, multiwavelength, NRAO Very Large Array (VLA) radio positions of Betelgeuse have produced a more precise estimate, which combined with the recent Hipparcos data furnished a new astrometric solution: π = 5.07 ± 1.10 mas, a tighter error factor yielding a distance of 197 +/- 45 pc or 643 +/- 146 ly.^[3]

Artist's depiction of the upcoming Gaia satellite mission in 2012.

In 2012, the European Space Agency's (ESA) upcoming Gaia mission will explore the detailed physical properties of each star observed, revealing luminosity, temperature, gravity and composition. Gaia will achieve this by repeatedly measuring the positions of all objects down to magnitude 20, and those brighter than magnitude 15, to an accuracy of 24 microarcseconds—akin to measuring the diameter of a human hair from 1000 km away. On-board detection equipment will ensure that variable stars like Betelgeuse will all be detected and catalogued to this faint limit, thus addressing most of the limitations of the earlier Hipparcos mission. The nearest stars, in fact, will have their distances measured to the extraordinary accuracy of 0.001%. Even stars near the Galactic centre, some 30 000 light-years away, will have their distances measured to within an accuracy of 20%.^[41]

Rhythmic dance

Ultraviolet image of Betelgeuse showing the star's asymmetrical pulsations, expansion and contraction.

Betelgeuse is a semiregular pulsating variable, with the sub-classification "SRC": supergiants with amplitudes of about 1 magnitude and periods of light variation from 30 days to several thousand days. If we assume a distance of 197 pc (± 640 ly), its peak absolute magnitude would be −6.27, while its minimum would be −5.27, and its mean −6.05. Researchers have offered different hypotheses to explain Betelgeuse's volatile choreography. Our current understanding of stellar structure suggests that the outer layers of this supergiant gradually expand and contract, causing the surface area (photosphere) to alternately increase and decrease, and the temperature to rise and fall—thus eliciting the measured cadence in the star's brightness between its dimmest magnitude of 1.2, seen as early as 1927, and its brightest of 0.2, seen in 1933 and 1942. A red supergiant like Betelgeuse will pulsate this way because its stellar atmosphere is inherently unstable. As the star contracts, it absorbs more and more of the energy that passes through it, causing the atmosphere to heat up and expand. Conversely, as the star expands, its atmosphere becomes less dense allowing the energy to escape and the atmosphere to cool, thus initiating a new contraction phase.^[17] Calculating the star's pulsations and modeling its periodicity have been difficult, as it appears there are several cycles interlaced. As discussed in papers by Stebbins and Sanford in the 1930s, there are short term variations of around 150 to 300 days that modulate a regular cyclic variation with a period of roughly 5.7 years.^[42][43]

An illustration of the structure of the Sun showing photospheric granules :
1. Core
2. Radiative zone
3. Convective zone
4. Photosphere
5. Chromosphere
6. Corona
7. Sunspot
8. Granules
9. Prominence

In fact, the supergiant consistently displays irregular photometric, polarimetric and spectroscopic variations, which points to complex activity on the star's surface and in its extended atmosphere.^[25] In marked contrast to most giant stars that are typically long period variables with reasonably regular periods, red giants are generally semiregular or irregular with pulsating characteristics. In a landmark paper published in 1975, Martin Schwarzschild attributed these brightess fluctuations to the changing granulation pattern formed by a few giant convection cells covering the surface of these stars.^[44][45] For the Sun, these convection cells, otherwise known as solar granules, represent the foremost mode of heat transfer—hence those convective elements which dominate the brightness variations in the solar photosphere.^[44] The typical diameter for a solar granule is about 2,000 km (yielding a surface area roughly the size of India), with an average depth of 700 km. With a surface of roughly 6 trillion km² , there are about 2 million of such granules lying on the Sun's photosphere, which because of their number produce a relatively constant flux. Beneath these granules, it is conjectured that there are 5 to 10 thousand supergranules, the average diameter of which is 30,000 km with a depth of about 10,000 km.^[46] By contrast, Schwardschild argues that stars like Betelgeuse may have only a dozen monster granules with diameters of 180 million km or more dominating the surface of the star with depths of about 60 million km, which, because of the very low temperatures and extremely low density found in red giant envelopes, result in convective inefficiency. Consequently, if only a third of these convective cells are visible to us at any one time, the time variations in their observable light may well be reflected in the brightness variations of the integrated light of the star.^[44]

Schwarzschild's hypothesis of gigantic convection cells dominating the surface of red giants and supergiants seems to have stuck with the astronomical community. In 1995, the Hubble Space Telescope captured the first direct picture of the supergiant's surface. The image revealed an extended chromosphere of roughly twice the star's angular diameter with a mysterious hot spot located in the southwest quadrant of the disk that dominated the total ultraviolet flux. The hot spot appeared to be hotter than the surrounding chromosphere by at least 2000K. "Such a major single feature is distinctly different from scattered smaller regions of activity typically found on the Sun", authors Andrea Dupree and Ronald Gilliland reported, "although the strong ultraviolet flux enhancement is characteristic of stellar magnetic activity. This inhomogeneity may be caused by a large scale convection cell or result from global pulsations and shock structures that heat the chromosphere."^[17][47]

Two years later in 1997, astronomers observed intricate asymmetries in the brightness distribution of the star, revealing at least three bright spots on the stellar disk.^[26] And then in the year 2000, another team of astronomers led by Alex Lobel of the Harvard–Smithsonian Center for Astrophysics (CfA) noted that Betelgeuse exhibits raging storms of hot and cold gas in its turbulent atmosphere, a potential cause being asymmetric pulsations in the star's chromosphere. The team surmised that huge areas of the star's photosphere vigorously bulge out in different directions at times, ejecting long plumes of warm gas into the cold dust envelope. Another explanation that was also given was the occurrence of shockwaves caused by warm gas traversing cooler regions of the star.^[43][48] The team investigated the atmosphere of Betelgeuse over a period of five years between 1998 and 2003 with the STIS instrument aboard Hubble. They found that the bubbling action of the chromosphere tosses gas out one side of the star, while it falls inward at the other side, similar to the slow-motion churning of a lava lamp.

Angular anomalies

A third challenge that has confronted astronomers has been measuring this behemoth's angular diameter. As noted earlier, Betelgeuse became the first star to have its diameter measured on December 13, 1920 by means of a 20-foot beam interferometer.^[14] Although interferometry was still in its infancy, the experiment proved to be a success and the angular diameter was found to average .047 arcseconds. What was noteworthy were the astronomers' insights on limb darkening. In addition to a measurement error of 10%, Michelson and Pease estimated the actual size of the star to be about 17% larger because of the diminishing intensity of light around the edges—hence an angular diameter as large as .055".^[14][49] Since that time, there have been many other studies conducted with angles ranging anywhere from .042 to .069 arcseconds.^[29][22][50] If we simply take that data and combine it with historical distance estimates of 180 to 815 ly, the projected diameter of the stellar disk could be anywhere from 2.4 to 17.8 AU, hence radii of 1.2 to 8.9 AU respectively.^{[note 1]} That's a wide margin—hence one of the reasons Betelgeuse has been such a mystery. Using the Solar System as a yardstick, the orbit of Mars is approximately 1.5 AU, Ceres in the asteroid belt 2.7 AU, Jupiter 5.5 AU—hence a photosphere which, depending on Betelgeuse's actual distance from Earth, could well extend beyond the orbit of Jupiter but not quite as far as Saturn at 9.5 AU.

Radio image showing the size of Betelgeuse's photosphere (circle) and the effect of convective forces on the star's extended atmosphere as it expands beyond the orbit of Saturn.

The precise diameter has been hard to define for several reasons:

1. The rhythmic expansion and contraction of the photosphere, as theory suggests, means the diameter is never constant;
2. There is no definable "edge" to the star as limb darkening causes the optical emissions to vary in color and decrease the farther one extends out from the center;
3. Betelgeuse is surrounded by a circumstellar envelope composed of matter being ejected from the star—matter which both absorbs and emits light—making it difficult to define the edge of the photosphere;^[13]
4. Measurements can be taken at varying wavelengths within the electromagnetic spectrum, with each wavelength revealing something different. Angular diameters, studies have shown, are considerably larger at visible wavelengths, decrease to a minimum in the near-infrared, only to increase again in the mid-infrared.^[51][52] The difference in reported diameters can be as much as 30–35%, yet because each wavelength measures something different, comparing one finding with another can be difficult.^[13]
5. Atmospheric twinkling limits the resolution obtainable from ground-based telescopes since turbulence in the Earth's atmosphere degrades the angular resolution.^[25]

To overcome these challenges, researchers have employed a number of solutions. The concept of astronomical interferometry was first conceived by Hippolyte Fizeau in 1868.^[53] He proposed the observation of stars through two apertures to obtain interferences that would furnish information on the star's spatial intensity distribution. Since then, the science of interferometry has evolved considerably where multiple-aperture interferometers are now used consisting of a large number of images superimposed on each other. These "speckled" images are then synthesized using Fourier analysis—a method which has been used for a wide array of astronomical objects including the study of binary stars, quasars, asteroids and galactic nuclei.^[54] Space observatories like Hipparcos, Hubble and Spitzer have also produced significant breakthroughs^[24][55] and recently another instrument, the Astronomical Multi-BEam Recombiner (AMBER), is yielding new insights. As part of the VLTI, AMBER is capable of combining the beams of three telescopes simultaneously, allowing researchers to achieve milliarcsecond spatial resolution. Also by combining three baselines instead of two, which is customary with conventional interferometry, AMBER enables astronomers to compute the closure phase—an important element in astronomical imaging.^[56][57]

The current debate centers around which wavelength—the visible, near-infrared (NIR) or mid-infrared (MIR)—produces the most accurate angular measurement.^{[note 1]} The solution that has been most widely adopted, it appears, is the one performed with the ISI in the mid-infrared by astronomers from the Space Sciences Laboratory at U.C. Berkeley. In the epoch year 2000, the group, under the leadership of John Weiner, published a paper showing Betelgeuse as having a uniform disk of 54.7 ± 0.3 mas.^[29] The paper also included a theoretical allowance for limb darkening yielding a diameter of 55.2 ± 0.5 mas—a figure which equates to a radius of roughly 5.5 AU (1,180 times solar), assuming a distance of 197.0 ± 45 pc.^{[note 3]} Nevertheless, given the angular error factor of ± 0.5 mas combined with a parallax error of ± 45 pc found in Harper's numbers, the photosphere's radius could actually be as small as 4.2 AU or as large as 6.9 AU.

Crossing the Atlantic, another team of astronomers led by Guy Perrin of the Observatoire de Paris produced a document in 2004 arguing that the near-infrared figure of 43:33 ± 0:04 mas was a more accurate photospheric measurement. "A consistent scenario to explain the observations of this star from the visible to the mid-infrared can be set-up", Perrin reports. "The star is seen through a thick, warm extended atmosphere that scatters light at short wavelengths thus slighty increasing its diameter. The scatter becomes negligible above 1.3 μm. The upper atmosphere being almost transparent in K and L—the diameter is minimum at these wavelengths where the classical photosphere can be directly seen. In the mid-infrared, the thermal emission of the warm atmosphere increases the apparent diameter of the star." It's a compelling argument but one which has yet to receive widespread support among astronomers.^[13]

More recent studies done in the near-infrared with the IOTA and VLTI have brought strong support to Perrin's analysis yielding diameters that range from 42.57 to 44.28 mas with impressively tight error factors of no more than 0.04 mas.^[58][59] Of pivotal importance in this discussion, however, is a second paper published by the Berkeley team in 2009, this time led by Charles Townes, reporting that the radius of Betelgeuse had actually shrunk from 1993 to 2009 by 15%, with the 2008 angular measurement equal to 47.0 mas, not too far from Perrin's estimate.^[49][60] Unlike most papers heretofore published, this seminal paper represented a systematic study of the star over a 15 year horizon at one specific wavelength. Earlier studies have typically lasted one to two years by comparison and have explored multiple wavelengths, often yielding vastly different results. The diminution in angular separation equates to a range of values between 56.0 ± 0.1 mas seen in 1993 to 47.0 ± 0.1 mas seen in 2008—a contraction of almost 0.9 AU.^{[note 2]} What is not fully known is whether this observation is evidence of a rhythmic expansion and contraction of the star as astronomers have theorized, and if so, what the periodic cycle might be, although Townes suggests that if a cycle does exist, it is likely a few decades long.^[49] Consequently, until a full cycle of data has been gathered, we will not know whether the 1993 figure of 56.0 mas represents the maximum extension of the star or its mean, or whether the 2008 figure of 47.0 in fact represents a minimum. It will likely take another 15 years or longer (2025 C.E.) before we know with any certainty, meaning that the Jovian orbit of 5.5 AU will likely serve as the star's "average" diameter for some time.^[61]

Once considered as having the largest angular diameter of any star in the sky after the Sun, in 1997 Betelgeuse lost that distinction when a group of astronomers measured R Doradus with a diameter of 57.0 ± 0.5 mas. Betelgeuse is now considered to be in third place, although R Doradus, being much closer to Earth at about 200 ly, has an actual diameter roughly one-third that of Betelgeuse.^[62]

Properties

Hertzsprung-russel detailed diagram identifying supergiants like Betelgeuse that have moved off the main-sequence.

Betelgeuse's spectral class is listed as M2Iab in the SIMBAD astronomical database. The "ab" suffix is derived from the Yerkes spectral classification system, and signifies that it is an intermediate luminous supergiant, less bright than other supergiants like Deneb. However given some of the recent findings, this classification may be outdated, as there is evidence Betelgeuse is actually much more luminous than Deneb and other stars in its class.

If we assume an average radius of 5.5 AU and a distance of 197 pc, Betelgeuse has a luminosity in excess of 180,000 Suns at maximum. When the star contracts as it has since 1993, its luminosity diminishes to about 130,000 Suns. Either way, that amount of electromagnetic energy dwarfs Deneb's output of about 50,000 Suns.^{[note 4]} However, with most of the star's radiant energy occurring in the infrared and huge amounts of it being absorbed by circumstellar matter in the star's outer shell, we simply don't experience the star's total luminosity.

Typical of red supergiants, Betelgeuse is a cool star with a surface temperature of about 3,500 degrees Kelvin. It is also a slow rotator, with the most recent velocity recorded at 5 km/s. Depending on its photospheric radius, it could take the star anywhere from 25 to as long as 32 years to turn on its axis—extremely slow when compared with a fast rotator like Pleione in the Pleiades star cluster, which turns on its axis once every 11.8 hours.

Cryptic pathways

The kinematics of Betelgeuse are intriguing yet not easily explained. The age of a Type M supergiant with an initial mass of 20 times solar is roughly 10 million years.^[3][63] Given its current space motion, a projection back in time would take Betelgeuse around 290 parsecs farther from the galactic plane where there is no star formation region—an implausible scenario. Although the space motion for the 25 Ori group has yet to be measured, α Ori's projected path does not appear to intersect with it either. Also, formation close to the far younger Orion Nebula Cluster (ONC, also known as Ori OB1d) is doubtful. VLBA astrometry yields a distance to the ONC between 389 and 414 parsecs. Consequently, it is likely that Betelgeuse has not always had its current motion through space and has changed course at one time or another.^[3]

The most likely star-formation scenario for Betelgeuse is that it is a runaway star from the Orion OB1 Association. Originally a member of a high-mass multiple system within Ori OB1a, which includes the late type O and B stars in Orion's belt—Alnitak, Alnilam and Mintaka—Betelgeuse was probably formed about 10–12 million years ago from the molecular clouds observed in Orion, but has evolved rapidly due to its unusually high mass.^[3]

Like many of the young stars in Orion where masses greater than 10 solar can be found in abundance, Betelgeuse will use its fuel quickly and not live very long. On the Hertzsprung-Russell diagram, Betelgeuse has moved off the main sequence and has swelled and cooled to become a red supergiant. Although this only ten million years old, Betelgeuse has probably exhausted the hydrogen in its core—unlike its OB cousins born about the same time—causing it to contract under the force of gravity into a hotter and denser state. As a result, it has begun to fuse helium into carbon and oxygen producing enough radiation to unfurl its outer envelopes of hydrogen and helium. Its extreme luminosity is being generated by a mass so large that the star will eventually fuse higher elements through neon, magnesium, sodium, and silicon all the way to iron, at which point it will likely collapse and explode as a supernova ^[5][43]

Ethereal Cubed

Betelgeuse compared to other stars. Sirius (Panel 4) is the brightest star in the night sky, but is tiny compared to Betelgeuse (Panel 5). Both Sirius and Betelgeuse traverse the sky the same time of year.

As an early M-type supergiant, Betelgeuse is one of the largest and most luminous stars of its class. A radius of 5.5 AU is roughly 1,180 times the radius of the Sun—a sphere so huge that it could contain over 2 quadrillion Earths (2.15 × 10¹⁵) or more than 1.6 billion (1.65 × 10⁹) Suns. That's the equivalent of Betelgeuse being a giant football coliseum like Wembley Stadium in London with the Earth a tiny pearl, 1 millimeter in diameter, orbiting a Sun the size of a mango.^{[note 5]} Of particular interest in this respect is the impact of a 15% reduction in the star's radius as reported. That equates to a shortening of the star's radius from about 5.5 AU to 4.6 AU, and a diminution in the star's photospheric volume of approximately 41% or 680 million Suns.^{[note 6]}

Bowl Volume of Wembley Stadium. The center circle (9.15m radius) is a close analogy for the Earth's orbit around the Sun

Not only is the photosphere enormous, but the star is surrounded by a complex circumstellar environment that could take over three years just for light to escape.^[64] In the outer reaches of the photosphere, the density is extremely low. In volume, Betelgeuse exceeds the Sun by a factor of about 1.6 billion Suns. Yet the actual mass of the star is no more than 18–19 solar masses, since the star is estimated to have lost 1–2 solar masses since its birth.^[5] Consequently, the average density of this stellar mystery is less than one-sextillionth (1.116 × 10⁻²³) the density of our Sun. If we compare such star matter to the density of ordinary air at sea level, the ratio is roughly 1.286 × 10⁻⁵, a density so tenuous, one would have to get above the noctilucent clouds in the Earth's mesosphere to experience it.^{[note 7]} Such star matter is so ethereal that Betelgeuse has often been called a "red-hot vacuum".^[17][18]

Circumstellar Dynamics

In the late phase of stellar evolution, massive stars like Betelgeuse exhibit high rates of mass loss, possibly as much as 1 solar mass every 10,000 years, resulting in a complex circumstellar environment that is constantly in flux.^[32] Exactly how this mass loss occurs is a mystery that has puzzled astronomers for decades. When Martin Schwarzschild first proposed his theory of monster convection cells dominating the surface of red supergiants, he also argued that such cells could be the primary cause of stellar mass loss. Prior attempts to explain mass loss in terms of solar wind theory had proven unsuccessful as they led to a contradiction with observations involving circumstellar shells.^[44] Other theories that have been advanced include magnetic activity, global pulsations and schock structures as well as stellar rotation.^[24][65]

Artist's rendering from ESO showing Betelgeuse with a gigantic bubble boiling on its surface and a vast plume of gas being ejected to at least six photospheric radii or roughly the orbit of Neptune.

As a result of work done by Pierre Kervella and his team at the Paris observatory in 2009, astronomers may be close to solving this mystery. What Kervella noticed was a large plume of gas extending outward at least six times the stellar radius indicating that the star is not shedding matter evenly in all directions.^[9][32] The plume's presence, in fact, implies that the spherical symmetry of its photosphere, often observed in the infrared, is not preserved in its close environment. Asymmetries on the stellar disk had been reported many times at different wavelengths. However, due to the refined capabilities of the NACO adaptive optics on the VLT, these asymmetries have come into focus. The two mechanisms that could cause such asymmetrical mass loss, Kervella noted, were large-scale convection cells or polar mass loss, possibly due to rotation. ^[9] Probing deeper still with the AMBER instrument on ESO’s Very Large Telescope Interferometer, Keiichi Ohnaka from the Max Planck Institute in Bonn observed that the gas in this behemoth's extended atmosphere is vigorously moving up and down, creating bubbles as large as the supergiant itself, leading his team to conclude that such stellar upheaval is behind the massive plume ejection observed by Kervella.^[66][32]

Evidence of circumstellar shells surrounding M supergiants was first proposed by Walter Adams and Elizabeth MacCormack in 1935 when they observed anomalies in the spectral signature of such stars and concluded that the likely cause was an expanding gaseous envelope.^[67][68] The first indication of vastly extended envelopes surrounding such stars occurred in 1955 with the work of Armin Deutsch who noticed when studying the Rasalgethi system that spectroscopic peculiarities were mysteriously occurring in the G star companion, α² Her. This led him to conclude that the whole system had to be enveloped by a circumstellar shell composed of matter being ejected by the mainstar, M supergiant α¹ Her, and extending to at least 170 stellar radii.^[69][68] In the mid 1970s, Andrew Bernat undertook a detailed analysis of four circumstellar shells, Betelgeuse, Antares, Rasalgethi and Mu Cephei, concluding that red stars dominate mass return to the Galaxy.^[68]

In addition to the photosphere, researchers have now identified six other components of Betelgeuse's complex extended atmosphere. Extending outward, we find a compact molecular environment otherwise known as the MOLsphere, a gaseous envelope, a chromosphere, a dust environment and two outer shells (S1 and S2) composed of carbon monoxide (CO). Some of these elements are known to be asymmetric while others overlap.^[59]

Exterior View of ESO’s Very Large Telescope (VLT) in Paranal, Chile.

At about .45 stellar radii (~2-3 AU) above the photosphere, the closest membrane appears to be the molecular layer known as the MOLsphere. Studies show it to be composed of water-vapor and carbon monoxide with an effective temperature of about 1500 ± 500 K.^[70][59] Curiously, water-vapor had been originally detected in the supergiant's spectrum back in the 1960s with the Stratoscope project initiated by Martin Schwarzschild and others but had been ignored for decades. Recent studies suggest that the MOLsphere may also contain SiO and Al₂O₃—molecules which could explain the formation of dust particles.

Interior View of one of the four 8.2-metre Unit Telescopes at ESO’s VLT.

Between two and seven stellar radii (~10 - 40 AU) astronomers have identified another region known as an asymmetric gaseous envelope composed of elemental abundances C, N and O (Carbon, Nitrogen and Oxygen).^[71][59] The radio-telescope images taken in 1998 confirm that Betelgeuse has a dense atmosphere with a remarkably complex structure. Observations show the atmosphere to be boiling with a temperature of 3,450 +/- 850K—similar to the temperature recorded on the star's surface but much lower than surrounding gas in the same region.^[72][73] The VLA images also showed this lower-temperature gas progressively decreasing in temperature as it extends outward—a discovery which, although unexpected, turns out to be the most abundant constituent of Betelgeuse's atmosphere. "This alters our basic understanding of red-supergiant star atmospheres," explained Jeremy Lim, the team's leader. "Instead of the star's atmosphere expanding uniformly because of gas heated to very high temperatures near its surface, it now appears that several giant convection cells propel gas from the star's surface into its atmosphere."^[73] This is the same region in which Kervella's 2009 finding of a bright plume, possibly containing CN and extending at least six photospheric radii in the southwest direction of the star, is believed to exist.^[59]

The chromosphere, as mentioned earlier, was resolved in 1996 at about 2.2 times the optical disk (~10 AU) at ultraviolet wavelengths. The image was taken with the Faint Object Camera on-board the Hubble Space Telescope (HST) and also revealed a bright area in the southwest quadrant of the disk. However in 2004 observations with the STIS, Hubble's high-precision spectrometer, pointed to the existence of warm chromospheric plasma at least one arcsecond away from the star, suggesting a size to the chromosphere of almost 200 AU or seven times the Neptunian orbit. ^[74] The CfA team led by Alex Lobel concluded that the spatially resolved STIS spectra directly demonstrate the co-existence of warm chromospheric plasma with cool gas in Betelgeuse's circumstellar dust envelope.

The first attestation of a dust shell surrounding Betelgeuse was put forth by Sutton et al. when the team noted in 1977 that dust shells around mature stars often emit large amounts of radiation in excess of the photospheric contribution. Using heterodyne interferometry, the team concluded that α Ori emits the majority of its excess outside 12 stellar radii or roughly the distance of the Kuiper belt at 50 to 60 AU, depending on the assumed stellar radius.^[75][59] Since then, there have been numerous studies done of this dust envelope at varying wavelenghts yielding decidedly different results. More recent studies have estimated the inner radius of the dust shell anywhere from 0.5 to 1.0 arcseconds, hence 25 to 50 stellar radii or 100 to 200 AU.^[76][77] What these studies point out is that the dust environment surrounding Betelgeuse is anything but static. In 1994, Danchi et al. reported that Betelgeuse undergoes sporadic dust production involving decades of activity followed by inactivity. A few years later, a group of astronomers led by Chris Skinner noticed significant changes in the dust shell's morphology in just one year, suggesting that the shell is asymmetrically illuminated by a stellar radiation field strongly affected by the existence of photospheric hot spots.^[76] The 1984 report of a giant asymmetric dust shell located 1 pc (206,265 AU) from the star has not been corroborated in recent studies, although another report published the same year said that three dust shells were found extending four light years from one side of the decaying star, suggesting that, like a snake, Betelgeuse sheds its outer layers as it journeys across the heavens.^[64][78]

Although the exact size of the two outer CO shells remains elusive, preliminary estimates suggest that one shell extends from about 1.5 to 4.0 arcseconds with the other expanding as far as 7.0 arcseconds.^[79] If we use the Jovian orbit of 5.5 AU as the "average" radius for this gargantuan star, (~0.055" diameter), the inner shell would extend from roughly 50 to 150 stellar radii (~300 to 800 AU) with the outer shell extending out as far as 250 stellar radii (~1400 AU). With the heliopause estimated at about 100 AU, the size of this outer shell is almost fourteen times the size of our Solar System.

Fate

The future fate of Betelgeuse depends on its mass; as it probably contains more than 15 solar masses, it will continue to burn and fuse elements until its core is iron, at which point Betelgeuse will explode as a type II supernova. During this event the core will collapse, leaving behind a neutron star remnant some 20 km in diameter.^[19]

Celestia's computerized depiction of the constellation Orion as it will appear from Earth when Betelgeuse explodes as a supernova.

Betelgeuse is already old for its size class and will explode relatively soon compared to its age.^[80] At the current distance of Betelgeuse from the Earth, such a supernova explosion would be the brightest recorded; outshining the Moon in the night sky and becoming easily visible in broad daylight.^[80] Professor J. Craig Wheeler of The University of Texas at Austin predicts the supernova will emit 10⁵³ ergs of neutrinos, which will pass through the star's hydrogen envelope in around an hour, then reach the solar system several centuries later. Since its rotational axis is not pointed toward the Earth, Betelgeuse's supernova is unlikely to send a gamma ray burst in the direction of Earth large enough to damage ecosystems.^[81] The flash of ultraviolet radiation from the explosion will be weaker than the ultraviolet output of the Sun.

The supernova would brighten to an apparent magnitude of −12 over a two week period, then remain at that intensity for two or three months before rapidly dimming. The year following the explosion, radioactive decay of cobalt to iron will dominate emission from the supernova remnant, and the resulting gamma rays will be blocked by the expanding envelope of hydrogen. If the neutron star remnant became a pulsar, then it might produce gamma rays for thousands of years.^[82]

Star system

In 1985, Margarita Karovska, in conjunction with other astrophysicists at the Harvard–Smithsonian Center for Astrophysics, announced the discovery of two close companions orbiting Betelgeuse. Analysis of polarization data from 1968 through 1983 indicated a close companion with a periodic orbit of about 2.1 years. The team realized that the observed polarization could be caused by a systemic asymmetry created by the close companion orbiting the supergiant inside its extended dust envelope. Using speckle interferometry, the team concluded that the closer of the two companions was located at 0.06 ± 0.01 arcseconds from the main star with a position angle of 273 degrees. The more distant companion was estimated at 0.51 ± 0.01" with a PA of 278 degrees. The magnitude differences with respect to the primary, measured at 656.3 (Hα) and 656.8 nm (red continuum), were 3.4 and 3.0 for the close component and 4.6 and 4.3 for the distant component.^[83][84]

Sketch illustrating the design of an aperture mask as used by Buscher et al. in their discovery of hotspots on the surface of Betelgeuse.

In the years that followed, different teams of astronomers monitored the data in the hope of obtaining additional confirmation. In 1987, Andrea Dupree observed, "Periastron of the recently discovered close optical companion to Alpha Ori is predicted to be 1986.7; detection of atmospheric disturbances similar to those found subsequent to the last periastron (~ 1984.6) would give strong support to the presence of a companion."^[85] However, it appears that such detection never materialized. Rather, in 1990, David F. Buscher, John E. Baldwin and a team of collaborators from the Cavendish Astrophysics Group made a number of high-resolution images of the supergiant at wavelengths of 633, 700, and 710 nm using the nonredundant masking method. At all these wavelengths, they remarked, there was unambiguous evidence for an asymmetric feature on the surface of the star, which contributed 10-15 percent of the star's total observed flux. Their conclusion was that such a phenomenon could be caused by a close companion passing in front of the stellar disk, differential photospheric brightening due to the effects of stellar rotation or the more likely scenario of "large-scale convection in the stellar atmosphere" as suggested by Schwarzschild.^[25]

The Cavendish colleagues published another paper in 1992, this time under the helm of Richard. W. Wilson, noting that the brightness features on the surface of Betelgeuse appear to be "too bright to be associated with a passage of the suggested companions in front of the red giant." They also noticed that these features were fainter at the 710 than at 700 nm, by a factor of 1.8, indicating that they would have to reside within the molecular atmosphere of the star.^[86]

That same year, Karovska published a new paper reconfirming her and her colleagues' interpretation of the data, but also noting that "the correlation between the calculated position angles of the companion and the measured position angles of the asymmetries suggests that there is a possible connection between the asymmetries and the companion. The asymmetry in the images of Betelgeuse could be caused by the unresolved companion, by tidal distortion of the supergiant's atmosphere, or possibly by an unresolved bright spot on the stellar surface facing the companion. To determine the nature of the companion (which presently remains a puzzle), it is crucial to obtain further speckle observations using large aperture telescopes, coordinated with other ground-based observations and the observations from space."^[87]

Since then, researchers turned their attention to analyzing the intricate dynamics of the star's extended atmosphere and little else has been published on the possibility of orbiting companions, although as Haubois and his team reiterate in 2009, the possibility of a close companion contributing to the overall flux has never been fully ruled out.^[59] Dommanget's double star catalog (CCDM) lists at least four adjacent stars, all within three arcminutes of this stellar giant, yet aside from apparent magnitudes and position angles, little else is known.^[88] As the decade unfolds and new technologies are brought to unraveling the star's enigmatic past, we will likely see conclusive evidence, one way or another, of any potential star system. Given the planned capabilities of the upcoming Gaia mission, a confirmation could occur any time after the mission's scheduled launch in December 2012.

Ethnological influences

Etymology

Betelgeuse has been known variously as Betelgeux,^[1] and Beteigeuze^[89] in German (according to Bode^[90][91]). Pronunciations for the star are as varied as its spellings. The Oxford English Dictionary has /ˈbɛtəldʒuːz/, /ˈbiːtəldʒuːz/, and French [ˈbɛtɛlʒœz].^[1] The Royal Astronomical Society of Canada favors /ˈbɛtəldʒuːz/ BET-əl-jooz), while The Friendly Stars has /ˈbɛtəldʒəz/ BET-əl-jəz.^[92] Webster's Collegiate Dictionary suggests /ˈbiːtəldʒuːs/, as in the film Beetlejuice and The Hitchhiker's Guide to the Galaxy,^[92] or /ˈbɛtəldʒuːs/ with a final s sound, or either with a final z as in the OED. Betelgeux and Betelgeuze were used until the early 20th century, when the spelling Betelgeuse became universal.^[11]

Multiple sources with competing etymologies exist to describe the star's name. All agree that the last part of the name "-elgeuse" comes from the Arabic الجوزاء al-Jauzā', the indigenous Arabic name for the constellation Orion, a feminine name in old Arabian legend, and of uncertain meaning. Because جوز j-w-z, the root of jauzā', means "middle", al-Jauzā' roughly means "the Central One". Later, al-Jauzā' was also designated as the scientific Arabic name for Orion and for Gemini. The current Arabic name for Orion is الجبار al-Jabbār ("the Giant"), although the use of الجوزاء al-Jauzā' in the name of the star has continued.^[93]

In his 1863 work Star-Names and Their Meanings, American amateur naturalist Richard Hinckley Allen stated the derivation was from the ابط الجوزاء Ibṭ al-Jauzah, which he claimed degenerated into a number of forms including Bed Elgueze, Beit Algueze, Bet El-gueze, Beteigeuze and more, to the (then) current forms Betelgeuse, Betelguese, Betelgueze and Betelgeux. The star was named Beldengeuze in the Alfonsine Tables, and Riccioli had called it Bectelgeuze or Bedalgeuze.^[16]

Paul Kunitzsch refuted Allen's derivation and instead proposed that the full name is a corruption of the Arabic يد الجوزاء Yad al-Jauzā' meaning "the Hand of al-Jauzā', i.e., Orion. European mistransliteration into Latin during the Middle Ages led to the first character y (ﻴ, with two dots underneath) being misread as a b (ﺒ, with only one dot underneath). During the Renaissance, the star's name was written as بيت الجوزاء Bait al-Jauzā' ("house of Orion") or بط الجوزاء Baţ al-Jauzā', incorrectly thought to mean "armpit of Orion" (a true translation of "armpit" would be ابط, transliterated as Ibţ). This led to the modern rendering as Betelgeuse.^[93] Other writers have since accepted Kunitzsch's explanation.^[5] The 17th century English translator Edmund Chilmead gave it the name Ied Algeuze ("Orion's Hand"), from Christmannus.^[16]

Other Arabic names recorded include Al Yad al Yamnā ("the Right Hand"), Al Dhira ("the Arm"), and Al Mankib ("the Shoulder"), all appended to "of the giant",^[16] as منكب الجوزاء Mankib al Jauzā'. In Persian, however, the name is اِبطالجوزا, derived from the Arabic ابط الجوزاء Ibţ al-Jauzā', "armpit of Orion".

Betelgeuse was the fourth nakshatra Ardra "Moist" in Hindi, and associated with Rigvedic deity Rudra. Allen linked Orion's association with stormy weather to that of this deity of storms.^[16] Bahu was its Sanskrit name, as part of a Hindu understanding of the constellation as a running antelope or stag.^[16] Other terms included the Persian Bašn "the Arm" via Brown, and Coptic Klaria "an Armlet".^[16]

In traditional Chinese astronomy, Betelgeuse was known as 参宿四 (Shēnxiùsì, the Fourth (Star of the constellation) of Three (Stars)) as the constellation of 参宿 was at first a name only for the three stars in the girdle of Orion. Four stars were later added to this constellation, but the earlier name stuck.

In Japan, this star was called Heike-boshi (suggested by the red butterfly flag of the Heike clan), (平家星),^[94][95] "the Star of the Heike clan" or Kin-waki, (金脇), "the Gold (Star) beside (Mitsu-boshi)."

Legacy

The stars unusual name spawned the 1988 film Beetlejuice, and script writer Michael McDowell was impressed at how many people made the connection. He added they had received a suggestion the sequel be named Sanduleak-69 202 after the former star of SN 1987A. In August Derleth's take on H. P. Lovecraft's Cthulhu Mythos, Betelgeuse is the home of the 'benign' Elder Gods.^[11] There has been much debate over the identity of the red star Borgil mentioned in Lord of the Rings, with Aldebaran, Betelgeuse and even the planet Mars touted as candidates. Professor Kristine Larsen has concluded the evidence points to it being Aldebaran as it precedes Menelvagor (Orion).^[96] Astronomy writer Robert Burnham, Jr. proposed the term padparadaschah which denotes a rare orange sapphire in India, for the star.^[11]

See also

• List of brightest stars
• List of largest known stars
• List of most luminous stars
• List of most massive stars
• List of supernova candidates
• Betelgeuse in fiction

Notes

1. ↑ ^{1.0 1.1 1.2} The following table provides a non-exhaustive list of angular measurements conducted since 1920. Also included is a column providing a current range of radii for each study based on α Ori's most recent distance estimate (Harper et al) of 197±45 pc:

   Article	Year1	Telescope	#	Spectrum	λ (μm)	∅ (mas)2	Radii3 @ 197±45 pc	Notes
   Michelson	1920	Mt-Wilson	1	Visible	0.575	47.0 ± 4.7	3.2 - 6.3 AU	Limb darkened +17% = 55.0
   Bonneau	1972	Palomar	8	Visible	0.422-0.719	52.0 - 69.0	3.6 - 9.2 AU	Strong correlation of ∅ with λ
   Balega	1978	ESO	3	Visible	0.405-0.715	45.0 - 67.0	3.1 - 8.6 AU	No correlation of ∅ with λ
   	1979	SAO	4	Visible	0.575-0.773	50.0 - 62.0	3.5 - 8.0 AU
   Buscher	1989	WHT	4	Visible	0.633-0.710	54.0 - 61.0	4.0 - 7.9 AU	Discovered asymmetries/hotspots
   Wilson	1991	WHT	4	Visible	0.546-0.710	49.0 - 57.0	3.5 - 7.1 AU	Confirmation of hotspots
   Tuthill	1993	WHT	8	Visible	0.633-0.710	43.5 - 54.2	3.2 - 7.0 AU	Study of hotspots on 3 stars
   	1992	WHT	1	NIR	0.902	42.6 ± 0:03	3.0 - 5.6 AU
   Weiner	1999	ISI	2	MIR (N Band)	11.150	54.7 ± 0.3	4.1 - 6.7 AU	Limb darkened = 55.2 ± 0.5
   Perrin	1997	IOTA	7	NIR (K Band)	2.200	43:33 ± 0:04	3.3 - 5.2 AU	K&L Band,11.5μm data contrast
   Haubois	2005	IOTA	6	NIR (H Band)	1.650	44.28 ± 0.15‡	3.4 - 5.4 AU	Rosseland diameter 45.03 ± 0.12
   Hernandez	2006	VLTI	2	NIR (K Band)	2.099-2.198	42:57 ± 0:02	3.2 - 5.2 AU	High precision AMBER results.
   Ohnaka	2008	VLTI	3	NIR (K Band)	2.280-2.310	43.19 ± 0.03	3.3 - 5.2 AU	Limb darkened 43.56 ± 0.06
   Townes	1993	ISI	17	MIR (N Band)	11.150	56.00 ± 1.00	4.2 - 6.8 AU	Systematic study involving 17 measurements at the same wavelength from 1993-2009
   	2008	ISI		MIR (N Band)	11.150	47.00 ± 2.00	3.6 - 5.7 AU
   	2009	ISI		MIR (N Band)	11.150	48.00 ± 1.00	3.6 - 5.8 AU
   Harper	2004	VLA		Also noteworthy, Harper et al in the conclusion of their paper make the following remark: "In a sense, the derived distance of 200 pc is a balance between the 131 pc (425 ly) Hipparcos distance and the radio which tends towards 250 pc (815 ly)"—hence establishing ± 815 ly as the outside distance for the star.

   ¹The final year of observations, unless otherwise noted. ²Uniform disk measurement, unless otherwise noted. ³Radii calculations use the same methodology as outlined in Note #3 below ^‡Limb darkened measurement.

2. ↑ ^{2.0 2.1} Betelgeuse's reported radius of 56.0 mas in 1993 equates to 5.516 AU (1,185 ), assuming a distance of 197.0 pc. The reported angular diameter of 47.0 mas from 2008 would equate to a radius of 4.630 AU (995 ), hence a shrikange of 0.887 AU, a little more than the orbit of Venus, and just under the orbit of the Earth.
   
   To compute the average speed of contraction, the only missing variable is time. The 1993 measurement was taken on October 30th; the 2008 figure, on October 29th—hence a time frame of 5,478 days. Therefore:
   
   0.887 AU × 149,597,871 km ÷ 5,478 days ÷ 24 hours ≈ 1,008 km/hr.
   
   It should also be noted that any speed calculation is highly dependent on the estimated distance (parallax) to Betelgeuse. If we assume the Hipparcos distance to Betelgeuse (131 pc or 425 ly) in lieu of the Harper estimate, the speed drops to 671 km/hr.
3. ↑ To determine the average radius of Betelgeuse in terms of solar units, the calculations begin with the formula for angular diameter as follows:

   

   where equals the angular diameter of Betelgeuse in arcseconds, the star's diameter in AU, and the Distance from Earth in parsecs. If we know the angular diameter and the Distance, then we can solve for as follows:

   .

   To obtain Betelgeuse's radius:

   .

   However, given that:
   1. There are significant error factors in the two variables that make up this formula, the angular diameter () and distance (),
   2. The error factors yield a radius range for Betelgeuse between 4.2 to 6.9 AU, and
   3. The hypothesis that the star's radius continually expands and contracts,
   the astronomical community has selected —the orbit of Jupiter—as a conceptually elegant solution.
   
   To convert 5.5 AU into Solar units, the math is straightforward. Since 1 AU = 149,597,871 km and the mean diameter of the Sun = 1,392,000 km (hence a mean radius of 696,000 km), the calculation is as follows:

   (rounded).

4. ↑ To understand the luminosity calculations below, the first step is to clearly delineate between the two forms of luminosity: apparent luminosity (counting visible light only) and bolometric luminosity (total radiant energy), sometime's referred to as intrinsic luminosity. The formula for bolometric luminosity is as follows:

   where... B = Betelgeuse, L = Luminosity, R = Radius and T = Temperature.

   Therefore:

   

   Similarly:

   

5. ↑ The analogy is based on the computation of certain ratios — specifically the diameter, radius and volume of the 3 celestial bodies in question, Betelgeuse, the Sun and Earth. Once these ratios are derived, the relative size of each as they relate to Wembley Stadium can be easily determined. The calculations begin with the formula for angular diameter as follows:
   • Betelgeuse diameter ≈ 0.0552 arcseconds × 197.0 pc ≈ 11.000 AU (rounded up) × 149,597,871 km ≈ 1.646 ×10⁹ km,
   • Betelgeuse radius ≈ 11.000 AU ÷ 2 ≈ 5.500 AU × 149,597,871 km ≈ 8.230 ×10⁸ km ≈ 823,000,000 km,
   • Betelgeuse volume ≈ (4÷3×π) × 823,000,000³ ≈ 2.335 × 10²⁷ km³.
   Also:
   • Solar radius ≈ 696,000 km. Volume ≈ 1.412×10¹⁸ km³,
   • Earth radius ≈ 6,371.0 km. Volume ≈ 1.083×10¹² km³.
   • Wembley Bowl Volume ≈ 1,139,100 m³. Spherical radius ≈ (1,139,100m³ ÷ (4/3*π))^1/3 ≈ 64.787 m or 64,787 mm.
   Therefore:
   • Betelgeuse ≈ (2.335 × 10²⁷) ÷ (1.412×10¹⁸) ≈ 1.654 × 10⁹ Suns,
   • Betelgeuse ≈ (2.335 × 10²⁷) ÷ (1.083×10¹²) ≈ 2.156 × 10¹⁵ Earths.
   • Solar volume relative to Wembley ≈ 1,139,100 m³ ÷ (1.654 × 10⁹) × 10⁹{i.e. to convert to mm³} ≈ 689,000 mm³ (rounded up)
   • Solar diameter relative to Wembley ≈ (689,000 mm³ ÷ (4/3*π))^1/3 ≈ 55.61845 × 2 ≈ 110 mm or 4.3 inches
   • Earth volume relative to Wembley ≈ 1,139,100 m³ ÷ (2.156 × 10¹⁵) × 10⁹{i.e. to convert to mm³} ≈ 0.528 mm³
   • Earth diameter relative to Wembley ≈ (0.528 mm³ ÷ (4/3*π))^1/3 ≈ 0.501 × 2 ≈ 1.002 mm or 0.04 inches
   • Earth's orbital radius (1 AU) relative to Wembley ≈ 1AU ÷ 5.5 AU × 64.787 meters = 11.8 meters.
   Conclusion:
   • If the immense space of Wembley Stadium were Betelgeuse, the Earth would be a tiny pearl, 1.0 mm in diameter, orbiting a Sun, 11.0 cm/4.3 inches in diameter (i.e. the size of an average mango or grapefruit), with an orbital distance of about 11.8 meters.
6. ↑ Once again, the calculations begin with the formula for angular diameter as follows: Calculations for 1993 values:
   • Betelgeuse radius ≈ 0.056 arcseconds × 197.0 pc ≈ 11.032 AU ÷ 2 ≈ 5.516 AU × 149,597,871 km ≈ 825,000,000 km,
   • Betelgeuse volume ≈ (4÷3×π) × 825,000,000³ ≈ 2.352 × 10²⁷ km³.
   Calculations for 2008 values:
   • Betelgeuse radius ≈ 0.047 arcseconds × 197.0 pc ≈ 9.260 AU ÷ 2 ≈ 4.630 AU × 149,597,871 km ≈ 692,500,000 km,
   • Betelgeuse volume ≈ (4÷3×π) × 692,500,000³ ≈ 1.391 × 10²⁷ km³.
   Therefore:
   • Betelgeuse change in volume ≈ 2.352 × 10²⁷ km³ – 1.391 × 10²⁷ km³ ≈ –9.610E × 10²⁶ km³
   • Betelgeuse percent change in volume ≈ –9.610E × 10²⁶ km³ ÷ 2.352 × 10²⁷ km³ ≈ –40.86%
   • Betelgeuse volume change as a function of Solar volume ≈ –9.610E × 10²⁶ ÷ 1.412×10¹⁸ km³ ≈ –681,000,000 Suns.
7. ↑ To compute these density ratios, the first step is to calculate the mass and volume of each component from which density calculations can be made. Once we have the density of the Sun, Betelgeuse, and the Earth's atmosphere, it's but a matter of simple division to compute the appropriate ratios. Therefore: Calculations for the Sun:
   • Solar mass ≈ 1.9891×10³⁰ kg
   • Solar volume ≈ 1.412×10¹⁸ km³.
   • Solar density ≈ 1.9891×10³⁰ ÷ (1.412×10¹⁸ × 10⁹) ≈ 1.409×10³ kg/m³.
   Calculations for Betelgeuse:
   • Betelgeuse mass ≈ 18.5 x Solar × 1.9891×10³⁰ ≈ 3.680 ×10³¹ kg
   • Betelgeuse volume ≈ 2.335 × 10²⁷ km³ (from previous note)
   • Betelgeuse density ≈ 3.680 ×10³¹ kg ÷ 2.335 × 10²⁷ km³ × 10⁹ ≈ 1.576 ×10⁻⁵ kg/m³.
   Calculations for the Earth's atmosphere:
   • Atmospheric Mass ≈ 5.148 × 10¹⁸ kg
   • Atmospheric Volume ≈ 4.200 × 10⁰⁹ km³.
   • Atmospheric Density ≈ 5.148 × 10¹⁸ kg ÷ 4.200 × 10⁰⁹ km³ × 10⁹) ≈ 1.226 kg/m³.
   Ratios:
   
   • Betelgeuse/Sun ≈ 1.576 × 10⁻⁵ kg/m³ ÷ 1.409 × 10³ kg/m³ ≈ 1.116 × 10⁻²³ kg/m³
   • Betelgeuse/Earth's Atmosphere = 1.576 × 10⁻⁵ kg/m³ ÷ 1.226 × 10⁰ kg/m³ ≈ 1.286 × 10⁻⁵ kg/m³ OR 1.286 × 10⁻⁸ g/cm³
   Conclusion:
   
   • Betelgeuse's average density relative to Earth's Atmosphere is graphically represented in the NRLMSISE-00 standard atmosphere model. A density of 1.286 × 10⁻⁸ g/cm³, is roughly equivalent to the Earth's atmospheric density found at about 90 kilometers above sea level. Noctilucent clouds are found between 76 to 85 km above sea level.

References

Further reading

• Magnetic activity in late-type giant stars: Numerical MHD simulations of non-linear dynamo action in Betelgeuse
• Invisible Giant: Chandra's Limits on X-rays from Betelgeuse

External links

• Alpha Orionis (Betelgeuse) AAVSO Variable Star of the Month article, December 2000.
• Surface imaging of Betelgeuse with COAST and the WHT Interferometric images taken at different wavelengths.
• Hinode Views the Sun's Surface NASA image from the Hinode Solar Optical Telescope showing photospheric granulation.
• Near, Mid and Far Infrared Infrared Processing and Analysis Center (IPAC) webpage showing pictures at various wavelengths.
• APOD Pictures:

1. Mars and Orion Over Monument Valley Stunning skyscape showing the relative brightness of Betelgeuse and Rigel.
2. The Spotty Surface of Betelgeuse A reconstructed image showing two hotspots, possibly convection cells.
3. Simulated Supergiant Star Freytag's "Star in a Box" illustrating the nature of Betelgeuse's "monster granules".
4. Why Stars Twinkle Image of Betelgeuse showing the effect of atmospheric twinkling.
5. Canaries Sky The glowing nebulas surrrounding Betelgeuse.

• Red supergiant movie Numerical simulation of a red supergiant star like Betelgeuse.