Editing Betelgeuse (section)

=== Diameter ===
{{See also|List of largest stars}}
[[File:Arcturus to Betelgeuse comparison.jpg|thumb|Size comparison between [[Arcturus]], [[Rigel]], [[S Doradus]], [[Antares]], and Betelgeuse]]
[[File:Mukyv354.png|thumb|upright=1.15|Size comparison of Betelgeuse, [[Mu Cephei]], [[KY Cygni]], and [[V354 Cephei]], according to [[Emily Levesque]]<ref>{{Cite journal |last1=Levesque |first1=Emily M. |last2=Massey |first2=Philip |last3=Olsen |first3=K. A. G. |last4=Plez |first4=Bertrand |last5=Josselin |first5=Eric |last6=Maeder |first6=Andre |last7=Meynet |first7=Georges |date=August 2005  |title=The Effective Temperature Scale of Galactic Red Supergiants: Cool, But Not As Cool As We Thought |journal=The Astrophysical Journal |volume=628 |issue=2 |pages=973–985 |doi=10.1086/430901 |issn=0004-637X|arxiv=astro-ph/0504337 |bibcode=2005ApJ...628..973L }}</ref>]]

On 13 December 1920, Betelgeuse became the first star outside the Solar System to have the angular size of its photosphere measured.<ref name="MICHELSON" /> Although interferometry was still in its infancy, the experiment proved a success. The researchers, using a uniform disk model, determined that Betelgeuse had a diameter of {{val|0.047|u="}}, although the stellar disk was likely 17% larger due to the [[limb darkening]], resulting in an estimate for its angular diameter of about 0.055".<ref name=MICHELSON/><ref name=TOWNES1>{{cite journal
 | title= A Systematic Change with Time in the Size of Betelgeuse
 | last1=Townes |first1=C.H.   | last2=Wishnow |first2=E.H.
 | last3=Hale   |first3=D.D.S. | last4=Walp    |first4=B.
 | journal=The Astrophysical Journal Letters
 | volume= 697
 | issue= 2
 | pages= L127–28
 | year=2009
 | bibcode=2009ApJ...697L.127T
 | doi=10.1088/0004-637X/697/2/L127| doi-access=free
 }}</ref> Since then, other studies have produced angular diameters that range from 0.042 to {{val|0.069|u="}}.<ref name=BONNEAU1973/><ref name=WEINER/><ref name=BALEGA>
{{cite journal
 | last1=Balega   |first1=Iu.       | last2=Blazit   |first2=A.
 | last3=Bonneau  |first3=D.        | last4=Koechlin |first4=L.
 | last5=Labeyrie |first5=A.        | last6=Foy      |first6=R.
 | title=The angular diameter of Betelgeuse
 | journal=Astronomy and Astrophysics
 |date=November 1982
 | volume=115
 | issue= 2
 | pages=253–56
 | bibcode=1982A&A...115..253B
}}
</ref>
Combining these data with historical distance estimates of 180 to {{val|815|u=ly}} yields a projected radius of the stellar disk of anywhere from 1.2 to {{val|8.9|u=AU}}. Using the Solar System for comparison, the orbit of [[Solar System#Mars|Mars]] is about {{val|1.5|u=AU}}, [[Solar System#Ceres|Ceres]] in the [[asteroid belt]] {{val|2.7|u=AU}}, [[Solar System#Jupiter|Jupiter]] {{val|5.5|u=AU}}—so, assuming Betelgeuse occupying the place of the Sun, its photosphere might extend beyond the Jovian orbit, not quite reaching [[Solar System#Saturn|Saturn]] at {{val|9.5|u=AU}}.
[[File:Betelgeuse radio wavelengths.jpg|thumb|right|upright=1.35 |Radio image from 1998 showing the size of Betelgeuse's photosphere (circle) and the effect of convective forces on the star's atmosphere]]

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

# Betelgeuse is a pulsating star, so its diameter changes with time;
# The star has no definable "edge" as limb darkening causes the optical emissions to vary in color and decrease the farther one extends out from the center;
# Betelgeuse is surrounded by a circumstellar envelope composed of matter ejected from the star—matter which absorbs and emits light—making it difficult to define the photosphere of the star;<ref name=UCBERKELEY2009/>
# Measurements can be taken at varying [[wavelengths]] within the [[electromagnetic spectrum]] and the difference in reported diameters can be as much as 30–35%, yet comparing one finding with another is difficult as the star's apparent size differs depending on the wavelength used.<ref name=UCBERKELEY2009/> Studies have shown that the measured angular diameter is considerably larger at ultraviolet wavelengths, decreases through the visible to a minimum in the near-infrared, and increase again in the mid-infrared spectrum;<ref name=GILLILAND1/><ref name=PERRIN2>
{{cite journal
 |last1=Perrin |first1=G. |last2=Ridgway |first2=S.T.
 |last3=Coudé du Foresto |first3=V. |last4=Mennesson |first4=B.
 |last5=Traub |first5=W.A. |last6=Lacasse |first6=M.G.
 |year=2004
 |title=Interferometric observations of the supergiant stars {{nobr|{{mvar|α}} Orionis}} and {{nobr|{{mvar|α}} Herculis}} with FLUOR at IOTA
 |journal=[[Astronomy and Astrophysics]]
 |volume=418 |issue=2 |pages=675–685
 |doi=10.1051/0004-6361:20040052
 |arxiv=astro-ph/0402099  |s2cid=119065851
 |bibcode=2004A&A...418..675P
 |quote=Assuming a distance of {{val|197|45|u=pc}}, an angular distance of {{val|43.33|0.04|u=mas}} would equate to a radius of {{val|4.3|u=AU}} or {{solar radius|920}}
}}
</ref><ref name=YOUNG>
{{cite press release
 | last=Young  | first=John
 | date=24 November 2006
 | title=Surface imaging of Betelgeuse with COAST and the WHT
 | publisher=[[University of Cambridge]]
 | quote=Images of hotspots on the surface of Betelgeuse taken at visible and infra-red wavelengths using high resolution ground-based [[astronomical interferometer|interferometers]]
 | url=http://www.mrao.cam.ac.uk/telescopes/coast/betel.html
 | access-date=21 June 2007
 | url-status=dead
 | archive-url=https://web.archive.org/web/20070614111315/http://www.mrao.cam.ac.uk/telescopes/coast/betel.html
 | archive-date=14 June 2007
 | df=dmy-all
}}
</ref>
# [[Scintillation (astronomy)|Atmospheric twinkling]] limits the resolution obtainable from ground-based telescopes since turbulence degrades angular resolution.<ref name=BUSCHER/>

The generally reported radii of large cool stars are [[Rosseland optical depth|Rosseland radii]], defined as the radius of the photosphere at a specific optical depth of two-thirds. This corresponds to the radius calculated from the effective temperature and bolometric luminosity. The Rosseland radius differs from directly measured radii, with corrections for [[limb darkening]] and the observation wavelength.<ref name=dyck>{{cite journal |doi=10.1086/300453 |title=Radii and effective temperatures for K and M&nbsp;giants and supergiants. II |journal=The Astronomical Journal |volume=116 |issue=2 |page=981 |year=1998 |last1=Dyck |first1=H.M. |last2=van&nbsp;Belle |first2=G.T. |last3=Thompson |first3=R.R. |bibcode=1998AJ....116..981D |citeseerx=10.1.1.24.1889 |s2cid=16674990 }}</ref> For example, a measured angular diameter of 55.6&nbsp;[[milliarcsecond|mas]] would correspond to a Rosseland mean diameter of 56.2&nbsp;mas, while further corrections for the existence of surrounding dust and gas shells would give a diameter of {{val|41.9|u=mas}}.<ref name=dolan2016/>

To overcome these challenges, researchers have employed various solutions. Astronomical interferometry, first conceived by [[Hippolyte Fizeau]] in 1868, was the seminal concept that has enabled major improvements in modern telescopy and led to the creation of the [[Michelson interferometer]] in the 1880s, and the first successful measurement of Betelgeuse.<ref name=PERRIN1>
{{cite journal
 | last1=Perrin | first1=Guy | last2=Malbet | first2=Fabien
 | title=Observing with the VLTI
 | journal=EAS Publications Series
 | year=2003
 | volume= 6
 | bibcode=2003EAS.....6D...3P
 | page=3
 | doi=10.1051/eas/20030601| doi-access=free
 }}
</ref>
Just as human [[depth perception]] increases when two eyes instead of one perceive an object, Fizeau proposed the observation of stars through two [[apertures]] instead of one to obtain [[Interference (wave propagation)|interferences]] that would furnish information on the star's spatial intensity distribution. The science evolved quickly and multiple-aperture interferometers are now used to capture [[Speckle imaging|speckled images]], which are synthesized using [[Fourier analysis]] to produce a portrait of high resolution.<ref name=APOD1>
{{cite APOD
 | title=3 ATs
 | date=21 April 2012
 | access-date=17 August 2012
 | quote=Photograph showing three of the four enclosures which house 1.8&nbsp;meter Auxiliary Telescopes (ATs) at the [[Paranal Observatory]] in the [[Atacama Desert]] region of [[Chile]].}}</ref> It was this methodology that identified the hotspots on Betelgeuse in the 1990s.<ref name=WORDEN>
{{cite magazine
 | last=Worden | first=S.
 | title=Speckle Interferometry
 | magazine=[[New Scientist]]
 | year=1978
 | volume=78
 | pages=238–40
 | bibcode=1978NewSc..78..238W
}}
</ref>
Other technological breakthroughs include [[adaptive optics]],<ref name=RODDIER1>
{{cite conference
 | last=Roddier | first=F.
 | year=1999
 | title=Ground-based interferometry with adaptive optics
 | book-title=Working on the Fringe: Optical and IR interferometry from ground and space 
 | series=ASP Conference
 | volume=194 | page=318
 | publisher = [[Astronomical Society of the Pacific]]
 | isbn=978-1-58381-020-0
 | bibcode=1999ASPC..194..318R
}}
</ref> [[Space observatory|space observatories]] like Hipparcos, [[Hubble Space Telescope|Hubble]] and [[Spitzer Space Telescope|Spitzer]],<ref name=GILLILAND1/><ref name=NASA1>
{{cite press release
 | title=Top five breakthroughs from Hubble's workhorse camera
 | date=4 May 2009
 | series=[[NASA Jet Propulsion Laboratory]]
 | publisher = [[California Institute of Technology]]
 | place = Pasadena, CA
 | url=http://www.jpl.nasa.gov/news/features.cfm?feature=2132
 | access-date=28 August 2007 | url-status=dead
 | archive-url=https://web.archive.org/web/20090507102643/http://www.jpl.nasa.gov/news/features.cfm?feature=2132
 | archive-date=7 May 2009
}}
</ref>
and the [[AMBER (Very Large Telescope)|Astronomical Multi-BEam Recombiner (AMBER)]], which combines the beams of three telescopes simultaneously, allowing researchers to achieve milliarcsecond [[spatial resolution]].<ref name=MELNICK>
{{cite press release
 | last1=Melnick | first1=J. | last2=Petrov | first2=R.
 | last3=Malbet | first3=F.
 | date=23 February 2007
 | url=http://www.eso.org/public/news/eso0706/
 | title=The Sky Through Three Giant Eyes, AMBER Instrument on VLT Delivers a Wealth of Results
 | publisher=[[European Southern Observatory]]
 |access-date=29 August 2007
}}
</ref><ref name=WITTKOWSKI>
{{cite journal
 |last = Wittkowski |first = M.
 |date = 23 February 2007
 |journal = [[New Astronomy Reviews]]
 |title = MIDI and AMBER from the user's point of view
 |volume = 51  |issue = 8–9  |pages = 639–649
 |bibcode = 2007NewAR..51..639W
 |doi= 10.1016/j.newar.2007.04.005
 |url = http://www.vlti.org/events/assets/1/proceedings/2.4_Wittkowski.pdf
 |access-date = 29 August 2007 |url-status = dead
 |archive-url = https://web.archive.org/web/20110728164017/http://www.vlti.org/events/assets/1/proceedings/2.4_Wittkowski.pdf
 |archive-date = 28 July 2011
 |df = dmy-all
}}
</ref>

Observations in different regions of the electromagnetic spectrum—the visible, near-infrared ([[Infrared#Astronomy division scheme|NIR]]), mid-infrared (MIR), or radio—produce very different angular measurements. In 1996, Betelgeuse was shown to have a uniform disk of {{val|56.6|1.0|u=mas}}. In 2000, a [[Space Sciences Laboratory]] team measured a diameter of {{val|54.7|0.3|u=mas}}, ignoring any possible contribution from hotspots, which are less noticeable in the mid-infrared.<ref name="WEINER" /> Also included was a theoretical allowance for limb darkening, yielding a diameter of {{val|55.2|0.5|u=mas}}. The earlier estimate equates to a radius of roughly {{val|5.6|u=AU}} or {{solar radius|1,200}}, assuming the 2008 Harper distance of {{val|197.0|45|u=pc}},<ref name=SMITH2009>
{{cite journal
 |last1=Smith  |first1 = Nathan
 |last2=Hinkle |first2 = Kenneth H.
 |last3=Ryde   |first3 = Nils
 |date=March 2009
 |title=Red supergiants as potential type&nbsp;IIn supernova progenitors: Spatially resolved 4.6&nbsp;μm CO emission around VY&nbsp;CMa and Betelgeuse
 |journal=The Astronomical Journal
 |volume=137 |issue=3 |pages=3558–3573
 |arxiv=0811.3037 |doi=10.1088/0004-6256/137/3/3558
 |bibcode=2009AJ....137.3558S |s2cid=19019913
}}
</ref>
a figure roughly the size of the Jovian orbit of {{val|5.5|u=AU}}.<ref name=ASTRONOMYMAG2009>
{{cite news
 | title=Red giant star Betelgeuse in the constellation Orion is mysteriously shrinking
 | date=June 2009
 | magazine=[[Astronomy Magazine]]
 | url=http://www.astronomy.com/en/News-Observing/News/2009/06/Red%20giant%20star%20Betelgeuse%20in%20the%20constellation%20Orion%20is%20mysteriously%20shrinking.aspx
 | access-date=14 September 2012
}}
</ref><ref name=APOD2>
{{cite APOD
 |title=The spotty surface of Betelgeuse
 |date=6 January 2010
 |access-date=18 July 2010
}}
</ref>

In 2004, a team of astronomers working in the near-infrared announced that the more accurate photospheric measurement was {{val|43.33|0.04|u=mas}}. The study also put forth an explanation as to why varying wavelengths from the visible to mid-infrared produce different diameters: The star is seen through a thick, warm extended atmosphere. At short wavelengths (the visible spectrum) the atmosphere scatters light, thus slightly increasing the star's diameter. At near-infrared wavelengths ([[K band (infrared)|K]] and [[L band (infrared)|L bands]]), the scattering is negligible, so the classical photosphere can be directly seen; in the mid-infrared the scattering increases once more, causing the thermal emission of the warm atmosphere to increase the apparent diameter.<ref name=PERRIN2/>
[[File:Orion's Big Head Revealed in Infrared.jpg|thumb|right|Infrared image of Betelgeuse, [[Meissa]] and [[Bellatrix]] with surrounding [[nebula]]e]]

Studies with the [[Infrared Optical Telescope Array|IOTA]] and VLTI published in 2009 brought strong support to the idea of dust shells and a molecular shell (MOLsphere) around Betelgeuse, and yielded diameters ranging from 42.57 to {{val|44.28|u=mas}} with comparatively insignificant margins of error.<ref name=HAUBOIS>
{{cite journal
 | last1=Haubois  | first1=X.        | last2=Perrin    | first2=G.
 | last3=Lacour   | first3=S.        | last4=Verhoelst | first4=T.
 | last5=Meimon   | first5=S.        | last6=Mugnier   | first6=L.
 | last7=Thiébaut | first7=E.        | last8=Berger    | first8=J.P.
 | last9=Ridgway  | first9=S.T.
 | display-authors=6
 | year=2009
 | title=Imaging the spotty surface of Betelgeuse in the H&nbsp;band
 | journal=[[Astronomy & Astrophysics]]
 | volume=508 | issue=2  | pages=923–32
 | arxiv = 0910.4167 | s2cid=118593802
 | bibcode=2009A&A...508..923H
 | doi=10.1051/0004-6361/200912927
}}
</ref><ref name=HERNANDEZ>
{{cite journal
 | last1=Hernandez Utrera |first1=O.
 | last2=Chelli |first2=A
 | title=Accurate Diameter Measurement of Betelgeuse Using the VLTI/AMBER Instrument
 | journal=Revista Mexicana de Astronomía y Astrofísica, Serie de Conferencias
 | year=2009
 | volume=37
 | pages=179–80
 | url=http://www.astroscu.unam.mx/rmaa/RMxAC..37/PDF/RMxAC..37_ohernandez.pdf
 | bibcode=2009RMxAC..37..179H
 | access-date=16 August 2010
 | archive-date=15 July 2011
 | archive-url=https://web.archive.org/web/20110715041557/http://www.astroscu.unam.mx/rmaa/RMxAC..37/PDF/RMxAC..37_ohernandez.pdf
 | url-status=dead
 }}</ref> In 2011, a third estimate in the near-infrared corroborating the 2009 numbers, this time showing a limb-darkened disk diameter of {{val|42.49|0.06|u=mas}}.<ref name=OHNAKA2011>{{cite journal|doi=10.1051/0004-6361/201016279|title=Imaging the dynamical atmosphere of the red supergiant Betelgeuse in the CO first overtone lines with VLTI/AMBER|journal=Astronomy & Astrophysics |volume=529 |pages=A163 |year=2011 |last1=Ohnaka |first1=K.|last2=Weigelt |first2=G. |last3=Millour |first3=F. |last4=Hofmann |first4=K.-H. |last5=Driebe |first5=T. |last6=Schertl |first6=D. |last7=Chelli |first7=A. |last8=Massi |first8=F. |last9=Petrov |first9=R. |last10=Stee |first10=Ph. |bibcode=2011A&A...529A.163O |arxiv=1104.0958 |s2cid=56281923 }}</ref>{{efn|
"We derive a uniform-disk diameter of {{val|42.05|0.05|u=mas}} and a power-law-type limb-darkened disk diameter of {{val|42.49|0.06|u=mas}} and a limb-darkening parameter of {{val|9.7|0.5|e=−2}}"<ref name=OHNAKA2011/>
}} The near-infrared photospheric diameter of {{val|43.33|u=mas}} at the Hipparcos distance of {{val|152|20|u=pc}} equates to about {{val|3.4|u=AU}} or {{solar radius|730}}.<ref name="KERVELLA2011">{{cite journal|doi=10.1051/0004-6361/201116962|title=The close circumstellar environment of Betelgeuse|journal=Astronomy & Astrophysics |volume=531 |pages=A117 |year=2011 |last1=Kervella |first1=P. |last2=Perrin |first2=G. |last3=Chiavassa |first3=A. |last4=Ridgway |first4=S. T. |last5=Cami |first5=J. |last6=Haubois |first6=X. |last7=Verhoelst |first7=T.|arxiv=1106.5041|s2cid=119190969}}</ref> A 2014 paper derives an angular diameter of {{val|42.28|u=mas}} (equivalent to a {{val|41.01|u=mas}} uniform disc) using H and K band observations made with the VLTI AMBER instrument.<ref name=montarges>{{cite journal |last1=Montargès |first1=M. |last2=Kervella |first2=P. |last3=Perrin |first3=G. |last4=Ohnaka |first4=K. |last5=Chiavassa |first5=A. |last6=Ridgway |first6=S. T. |last7=Lacour |first7=S. |date=2014 |title=Properties of the CO and H2O MOLsphere of the red supergiant Betelgeuse from VLTI/AMBER observations |journal=Astronomy & Astrophysics |volume=572 |pages=id.A17 |bibcode=2014A&A...572A..17M |doi=10.1051/0004-6361/201423538 |arxiv=1408.2994 |s2cid=118419296}}</ref>

In 2009 it was announced that the radius of Betelgeuse had shrunk from 1993 to 2009 by 15%, with the 2008 angular measurement equal to {{val|47.0|u=mas}}.<ref name=TOWNES1/><ref name=COWEN>{{cite web
 | url=http://www.sciencenews.org/view/generic/id/44573/title/Betelgeuse_shrinks
 | title=Betelgeuse Shrinks: The Red Supergiant has Lost 15 Percent of its Size
 | date=10 June 2009
 | first=Ron
 | last=Cowen
 | quote=
 | archive-date=29 June 2011
 | archive-url=https://web.archive.org/web/20110629205838/http://www.sciencenews.org/view/generic/id/44573/title/Betelgeuse_shrinks
 | access-date=11 June 2009 | url-status=dead
}}
</ref>{{efn|
The shrinkage corresponds to the star contracting by a distance equal to that between Venus and the Sun, researchers reported June 9 at an American Astronomical Society meeting and in the June&nbsp;1 Astrophysical Journal Letters.<ref name=COWEN/>
}}
Unlike most earlier papers, this study used measurements at one specific wavelength over 15&nbsp;years. The diminution in Betelgeuse's [[apparent size]] equates to a range of values between {{val|56.0|0.1|u=mas}} seen in 1993 to {{val|47.0|0.1|u=mas}} seen in 2008— a contraction of almost {{val|0.9|u=AU}} in {{val|15|u=years}}.<ref name=TOWNES1/> The observed contraction is generally believed to be a variation in just a portion of the extended atmosphere around Betelgeuse, and observations at other wavelengths have shown an increase in diameter over a similar period.<ref name=montarges/>

The latest models of Betelgeuse adopt a photospheric angular diameter of around {{val|43|u=mas}}, with multiple shells out to 50–{{val|60|u=mas}}.<ref name=kervella2018/> Assuming a distance of {{val|197|u=pc}}, this means a stellar diameter of {{val|887|203|u=R_solar}}.<ref name=dolan2016/>

Once considered as having the largest angular diameter of any star in the sky after the [[Sun]], Betelgeuse lost that distinction in 1997 when a group of astronomers measured [[R Doradus]] with a diameter of {{val|57.0|0.5|u=mas}}, although R Doradus, being much closer to Earth at about {{val|200|u=ly}}, has a linear diameter roughly one-third that of Betelgeuse.<ref name=BEDDING>
{{cite journal
 | last1=Bedding |first1=T.R.
 | last2=Zijlstra  | first2=A.A.  | last3=von der Luhe  | first3=O.
 | last4=Robertson | first4=J.G.  | last5=Marson | first5=R.G.
 | last6=Barton    | first6=J.R.  | last7=Carter | first7=B.S.
 | year=1997
 | title=The angular diameter of R&nbsp;Doradus: A nearby Mira-like star
 | journal=[[Monthly Notices of the Royal Astronomical Society]]
 | volume=286  | issue=4  | pages=957–62
 | bibcode=1997MNRAS.286..957B | s2cid=15438522
 | arxiv = astro-ph/9701021
 | doi=10.1093/mnras/286.4.957  | doi-access=free
}}
</ref>