Blue Supergiants as a Tool for Extragalactic Distances - Empirical Diagnostics

25 Pages·0.54 MB·English

by  Fabio Bresolin

Blue Supergiants as a Tool for Extragalactic Distances –
Empirical Diagnostics⋆
FabioBresolin
InstituteforAstronomy,UniversityofHawaii,HonoluluHI96822,USA
[email protected]
3
0
0 Abstract. Bluesupergiantstarscanbeexceptionallybrightobjectsintheoptical,makingthem
2 primetargetsforthedeterminationofextragalacticdistances.Idescribehowtheirphotometric

n and spectroscopic propertiescan be calibratedto provide ameasurement of theirluminosity. I
a first review two well-known techniques, the luminosity of the brightest blue supergiants and,
J withtheaidofrecentspectroscopicdata,theequivalentwidthoftheBalmerlines.NextIdiscuss

0 somerecentdevelopmentsconcerningtheluminositydependenceofthewindmomentumandof
1 theflux-weightedgravity,whichcanprovide,ifproperlycalibrated,powerfuldiagnosticsforthe
determinationofthedistancetotheparentgalaxies.

1
v
9 1 Introduction
7
1
1 Massive stars can reach, duringcertain phases of their post-main sequenceevolution,
0 exceptional visual luminosities, approaching M ∼−10 in extreme cases. It is thus
V
3 naturaltotryandusethemasstandardcandlesforextragalacticstudies,aswasrealized
0
long ago by Hubble. For this contribution I will concentrate on the blue supergiants,
/
h a ratherbroadbutusefuldefinitionforthe stars containedin the upperpartof theH–
p R diagram and with spectral types O, B and A. This includes ‘normal’ supergiants
o- (Ia)and hypergiants(Ia+), as well as moreexoticobjectssuch as the LuminousBlue
r Variables(LBV’s).Verybrightstarscanalsobefoundamongtheyellowhypergiants,
t
s howevertheiridentificationinextragalacticsystemsismoreproblematic,becausetheir
a
intermediatecolorcoincideswiththatofnumerousGalacticforegrounddwarfs.
:
v Fromthepointofviewoftheextragalacticdistancescale,itisnotthemostmassive,
Xi intrinsicallymostluminousO-typestars(Mbol≤−11)whichareappealing.Becauseof
thedecreaseofthebolometriccorrectionwithtemperaturefromOtoAstarsdownto
r
a ∼7000K, the visually brightest supergiantsfound in galaxies are mostly 25–40M⊙
mid-Btoearly-Atypestars,withM between−8and−9[48].Thiscanbeseenfrom
bol
Table1, which is a (probably incomplete) compilation of the visually brightest blue
stars in the Milky Way, LMC and SMC, excludingin general LBV’s with maximum
lightamplitudeslargerthan0.5mag.ThelabelLBVinthelastcolumnidentifiesknown
or suspected LBV’s, from the compilation of [87]. Sources for the photometry and
spectraltypesaregivenasafootnotetothetable,howeverinafewcasesthedatahave
been updated with more recent determinations. The absolute visual magnitudes have
⋆Invited review at the International Workshop on Stellar Candles for the Extragalactic Dis-
tance Scale, held in Concepcio´n, Chile, December 9–11, 2002. To be published in: Stellar
Candles, Lecture Notes in Physics (http://link.springer.de/series/lnpp), Copyright: Springer-
Verlag,Berlin-Heidelberg-NewYork,2003
2 FabioBresolin
generallybeen correctedfor extinctionby assuming the spectraltype vs. B−V color
index relation in the MK system given by [45] and AV =3.1×EB−V. Stars brighter
thanM =−8.0inallthreegalaxiesareplottedinthecolor-magnitude(c-m)diagram
V
ofFig.1,togetherwiththelociofIa+,IaandIabstars,andstellartracksfor60,40,25
and20M⊙from[52].
Fig.1. In thiscolor-magnitude diagram thebrightest starshaving MV <−8 inthe Milky Way
(squares),LMC(circles)andSMC(triangles)areshownwiththelargersymbols.Opensymbols
refertoconfirmedorcandidateLBV’swithmagnitudevariationssmallerthan0.5mag.Thesmall
pointsrepresentGalacticstarsfainterthanMV =−8and/orofspectraltypeFandlater.Schematic
evolutionarymodelsatsolarmetallicityandvariousZAMSmassesfrom[52]areshownbythe
thicklines.Thegridgivingluminosityclassesandspectraltypesisfrom[45]
Extragalacticstellarastronomyhasquicklyevolvedfromtheidentification,viapho-
tometryandqualitativespectroscopy,ofindividualbrightstarsmostlywithingalaxies
oftheLocalGroup,tothequantitativeanalysisofstellarspectrawellbeyondthebound-
ariesoftheLocalGroup.Theobservationandanalysisofextragalacticsupergiantshas
importantramificationsforthestudyofmassivestellarevolutionwithmassloss,super-
novaprogenitors,stellarinstabilitiesneartheupperboundaryofthestellarluminosity
distribution,andchemicalabundances.HereIreviewfourdifferenttechniquesconcern-
BlueSupergiantsasaToolforExtragalacticDistances 3
Table1.ThevisuallybrightestbluestarsintheMilkyWay,LMCandSMC
StarID MV,0 SpectralType
MilkyWay MV,0≤−8.0
HD other
CygOB2-12 −10.4 B5IeLBV
80077 −9.4 B2/3Ia+LBV
92693 −8.73 A2Ia
152236 z 1Sco −8.70 B1.5Ia+
WRA977 −8.7 B1.5Ia+
92207 −8.55 A0Ia
197345 a Cyg −8.45 A2Iae
168607 −8.4 B9Ia+LBV
316285 He3-1482 −8.4 BIeLBV
169454 −8.29 B1Ia+
MWC314 −8.2 <B2LBV
92964 −8.17 B2.5Iae
223385 6Cas −8.00 A3Iae
LMC MV,0≤−8.5 m−M=18.5
HD Sk
33579 −6744 −9.57 A4Ia+
269902 −69239 −9.34 B9Iae
32034 −6717 −9.03 B9Iae
270086 −69299 −8.91 A1Ia+
269546 −6882 −8.89 B3Iab
269923 −69247 −8.85 B6Iab
269857 −68131 −8.80 A9Ia
269781 −67201 −8.77 A0Iae
269331 −6993 −8.67 A5Ia
268654 −697 −8.63 B9Iae
268835 −6946 −8.60 B8p
269128 −6863 −8.6 B2.5Ia+LBV
269661 −69170 −8.56 B9Ia+
268718 −6916 −8.52 B9Iabe
268946 −6658 −8.51 A0Ia
37836 −69201 −8.5 BpecLBV
SMC MV,0≤−8.0 m−M=19.0
AV Sk
475 152 −9.15 A0Ia+
136 54 −8.41 A0Ia
56 −8.32 B8Ia+
315 106 −8.30 A0Ia
78 40 −8.30 B1.5Ia+
443 137 −8.21 B2.5Ia
56 31 −8.17 B2.5Ia
65 33 −8.15 B8Ia+
48 27 −8.08 B5Ia
76 39 −8.07 B9Ia+
SOURCES —MILKYWAY-[34].DistancetoHD92207,HD92693,HD92964andHD223385:[23].CygOB2-12:[49].
LBVdatafrom[87].LMC-[67].SMC-[6],[47].
4 FabioBresolin
ingtheuseofbluesupergiantsinthecontextofmeasuringextragalacticdistances.Two
ofthemhavequitealonghistory:
• luminosityofthebrightestbluesupergiants
• equivalentwidthoftheBalmerlines
whilethetworemainingonesarebasedonmorerecentdevelopmentsintheanalysisof
stellarwindsandtheatmospheresofbluesupergiantstars:
• thewindmomentum–luminosityrelationship
• theflux-weightedgravity–luminosityrelationship
2 The Luminosity ofthe Brightest Blue Supergiants as
a Standard Candle
SincethepioneeringworkofHubble[29]agreatamountofeffortshavebeendevoted
tothecalibrationoftheluminosityofthevisuallybrightestblueandredsupergiantstars
in nearbygalaxiesas a distance indicator.This work culminated in a series of papers
byA.Sandage,R.Humphreysandothersinthe1970–80’sonthebrightstellarcontent
of galaxiesin the LocalGroup and in a handfulof more distant late-type spirals (see
reviewsby[70],[31]and,morerecently,[68]).Whilethebrightestredsupergiantswere
soon recognizedas a more accurate secondarystandard,thanks to the smaller depen-
denceoftheirbrightnessontheparentgalaxyluminosity,hereIwillbrieflysummarize
theworkconcerningthebrightestbluestars,generallyoftypesfromlateBtoA.Note
thataphotometriccolorselectioncriterion(B−V) <0.4isolatessupergiantsofspec-
0
tral type earlier than F5. Even if nowadaysthis method is not consideredsufficiently
accuratewhencomparedwiththebestavailableextragalacticdistanceindicators,ithas
beenadoptedalsoduringthepastdecadewheneverobservationalmaterialonmoreac-
curatedistanceindicators(Cepheids,TRGB,SNIa,etc.)waslacking.
Someofthemaindifficultiesinusingtheluminosityofthebrighteststarsingalax-
ies as a standardcandle were recognizedby Hubble himself, namely the unavoidable
confusionbetweenreal‘isolated’starsandunresolvedsmallstellarclustersorHII re-
gions,andthepresenceofforegroundobjectsin theGalaxy.While the latterproblem
is easily solved by avoiding stars of intermediate color in the c-m diagram, the for-
mer is much more subtle, eventually becoming the main criticism to the bright blue
starmethodraisedbyHumphreysandcollaborators[33],[32],who,withstellarspec-
troscopyinsomeofthenearestgalaxies,revealedthecompositenatureofmanyofthose
objectswhichwerepreviouslyconsideredtobethebrighteststars.
Hubble’soriginalcalibrationofthemeanabsolutemagnitudeofthethreebrightest
stars in a galaxy, M (3) , introduced as a more robust measure of the visually most
B 0
luminousstarsthanthesinglebrighteststar,wasflawed(headopted<M >≃−6.3,
pg
about3magnitudestoofaint),whichwaspartlyresponsibleforthelargevaluehefound
fortheexpansionrateoftheuniverse.
ThedependenceofM (3) ontheparentgalaxyluminosity[M (3) (cid:181) M(gal) ],an
B 0 B 0 0
effectalreadydiscussedbyHubbleandbyHolmberg,wasfirstinvestigatedindetailby
[71] aspartof a seriesofpaperson thebrighteststarsin resolvedspiralandirregular
BlueSupergiantsasaToolforExtragalacticDistances 5
galaxies, with distances calibrated via observations of Cepheids (see [69], and refer-
ences therein).The existence of such a correlationhampersthe use of the luminosity
of the brightestblue stars as a standardcandle.Moreover,the standarddeviationof a
singleobservationasmeasuredby[71]was≃0.5mag,muchlargerthantheirquoted
0.1mag for the standard deviation of the mean of the three brightest red supergiants.
Thelatterwerelateralsofoundtoobeyadependenceontheparentgalaxyluminosity,
albeitwithashallowerslope.
The M (3) –M(gal) relationship has been customarily interpreted as a statistical
B 0 0
effect,sincemoreluminousandlargergalaxiescanpopulatethestellarluminosityfunc-
tionuptobrightermagnitudesthansmallergalaxies.Aflatteningofthisrelationmight
be detected in galaxies brighter than M(gal) =−19 [70], correspondingto the total
0
luminosity of large spirals, in which the observed limit is simply imposed by the lu-
minosityofthebrightestpost-mainsequenceB-andA-typestarsintheH–Rdiagram.
Therefore, while large, late-type spiral galaxies, such as M101, may contain stars as
brightasM ≃−10,the brightestbluestarsin dwarfslike NGC6822orIC1613are
B
foundatM ≃−7.Numericalsimulationsby[73]and[25]haveprovidedsupportfor
B
thestatisticalinterpretation,makingvariationsinthestellarluminosityandmassfunc-
tionamonggalaxiesunnecessarytoexplaintheobservedtrend.
Amongthemostrecentcompilationsofthebrightestbluestarsinnearbyresolved
galaxies is that of [24], based on updated stellar photometry of galaxies included in
previousworksby[59],[38]and[68].TheresultingrelationbetweenM (3) andparent
B 0
galaxy total luminosity is shown in Fig.2, where different symbols are used for 17
standardgalaxiesandafewtestgalaxies(onlythosewithavailableCepheiddistances
fromthelistof[24]areshown,togetherwithIC4182[69]).Inthisplot,distancesfor
some of the galaxies have been updated from the results of the HST Key Project, as
summarizedby[20](asanaside,nosystematicstudyofthebrighteststarsinthewhole
sampleanalyzedbytheKeyProjecthasbeenpublished).Thestandardgalaxiesdefine
alinearregression:
M (3) =−1.76(±0.45)+[0.40(±0.03)]M (gal) (1)
B 0 B 0
with a standard deviation s (M )=0.26. The rather small dispersion is, at least
B
partly,aresultoftheparticularselectionofthe‘standard’galaxiesmadeby[24].Infact,
s (M )≃0.6 is obtainedfrom the data of [59] and [68]. Differencesin the treatment
B
offoregroundandinternalextinctionexistbetweendifferentauthors.Furthermore,[70]
hasadvocatedthe use of the irregularbluevariablesamongthe brightestblue stars, a
viewstronglyopposedby[33].Wemustalsonotethatconsensusstillhastobereached
concerningthechoiceoftheindividualbrightestbluestarsinthemostluminousgalax-
iesinFig.2.Forexample,spectroscopyofbrightobjectsinM81by[96]hasrevealed
that none of the seven brightest supergiantcandidatescould be confirmed as a single
star,imposingafainterupperlimitforM (3) .ThepointsinFig.2correspondingtothe
B 0
otherluminousgalaxies,M31andM101,arelikelytobeaffectedbysimilarproblems,
andcouldthereforealsoberevisedtolowerM (3) values.
B 0
Numericalsimulationssuchasthoseby[73],shownbythedotted(50%limitsofthe
probabilitydistribution)and long-dashed(99.5%) curves,can explain both the trend,
whichhoweverispredictednottobelinear,andthedispersionintheobservationaldata,
6 FabioBresolin
Fig.2.Therelationshipbetweentheaveragemagnitudeofthethreebrightestbluestarsandthe
magnitudeoftheparentgalaxy.Datafrom[24],withminorupdatesonthedistances.Fulldots
refertothecalibrationgalaxies,whiletheopensymbolsareusedfortheadditionaltestgalaxies
for which a Cepheid distance is available. The straight line represents the linear regression to
the calibration points. The numerical simulations showing the 50% and 99.5% limits of the
probabilitydistribution(dottedandlong-dashedlines,respectively)arefrom[73]
atleastuptothemaximumgalaxybrightnessconsideredinthemodels.Itappearsthat
removing objects with Cepheid distances from the linear regression as done by [24]
(thoseshownherebytheopensymbols)mightnotbefullyjustified,sinceaconsider-
abledispersionatthelow-luminosityendisexpectedfromtheincompletefillingofthe
stellarluminosityfunction.However,considerationsontheevolutionarystatusofsome
ofthe dwarfgalaxiesmightprovidesomejustificationforthe removalofsomeofthe
datapoints.
Thegeneralconclusionwecandrawfromtheseresultsisthatdistancemodulitoin-
dividualgalaxiescannotbedeterminedfromthesimplephotometryofbrightbluestars
to betterthan atleast0.5mag(0.9magaccordingto [68]). Thisislargerthans (M ),
B
asaresultofthestrongdependenceofM (3) onM(gal) .Moreover,thenecessityof
B 0 0
spectroscopicconfirmationofthebrighteststarsmustbestressed.OutsideoftheLocal
Group,aftertheinitialeffortsatmoderateresolutionin M81,NGC2403,M101[32],
[96],high-qualityspectroscopyofthebrightstellarcontentofgalaxieshascomewithin
reachofmodernequipmenton8m-classtelescopesatincreasingdistances.Asanexam-
ple,Icitetheworkby[8]and[9]inNGC3621andNGC300,whichwillbediscussed
laterinthispaper.
BlueSupergiantsasaToolforExtragalacticDistances 7
To conclude the section on extragalactic distances based on the luminosity of the
brightestbluestars,ahandfulofworkspublishedinthelastdecadecanbehighlighted:
–brighteststarsingalaxieswithradialvelocities<500kms−1:aprojectaimingatthe
measurementofthedistanceofalargenumberof(mostlydwarf)resolvedgalaxiesin
the LocalVolume(v <500kms−1) hasbeencarriedoutsince 1994byKarachent-
rad
sev andcollaborators,usinga M (3) calibrationobtainedby [38] (see [75],[16] and
B 0
referencestherein).RecentlytheTRGBmethodisbeingused[39].
– brightest stars in Virgo galaxies: brightest star candidates have been detected from
ground-based images taken under excellent seeing conditions in two Virgo spirals,
NGC4523[74]andNGC4571[57].Distancesof13(±2)and14.9(±1.5)Mpcwere
derived, respectively,from yellow and blue supergiants. The brightest stars in a third
galaxy in Virgo, M100, were discussed by [21], based on HST WFPC2 images. The
CepheiddistancefromtheHSTKeyProjectis14.3(±0.5)Mpc.
–additionalgalaxiesinthefield(D∼7-8Mpc):thebrightestblueandredsupergiants
have been used by [77], [78] and [79] to measure distances to a few spiral galaxies,
includingNGC925andNGC628,adoptingthecalibrationof[68].
3 Spectroscopic Diagnostics:Equivalent Width of
the Balmer Lines
Thespectroscopicapproachalleviatesthemajordifficultiesofthephotometricmethod
described in the previous section. Small clusters, close companions and HII regions
can be easily identified from line profiles, compositeappearanceof the spectrum and
presenceofnebularlines.Inaddition,theanalysisofthespectraldiagnostics(equivalent
widths, line profiles, continuum fluxes) can provide detailed information on element
abundances,spectralenergydistributions,windoutflowsandstellarreddening.
Thediscoveryofarelationshipbetweenstellaropticalspectrallinesandluminosity
dates back to the 1920’s, when the character of the lines, diffuse vs. sharp, and their
strengthwerefoundtocorrelatewiththeabsolutemagnitudeofstarsoftypeAandB
[1], [2], [17], [93]. The hydrogenBalmer lines in particular were soon recognizedto
playanimportantroleinconnectionwiththeproblemofmeasuringstellarluminosities
usingspectra,a factwhichcontinuesto holdtrueevenforthemostrecenttechniques
involvingthespectralanalysisofbluesupergiants.Theluminosityeffectonthewidthof
theBalmerlinesderivesfromtheirdependenceonthepressure(Starkbroadening),as
realizedby[30]and[80],withalineabsorptioncoefficientinthewingsproportionalto
theelectronpressure(andalsodependentonthetemperature).Asaresult,narrowerand
weakerlinesareformedwithdecreasingpressureandsurfacegravity,andconsequently
withincreasingluminosity.
Iwillnotdiscusshereadditional,somewhatrelatedmethods,including:i)therela-
tionshipbetweenMV andthestrengthoftheOItripletatl ∼7774A˚,whichholdsfor
theA–Gspectraltypes[4];ii)thestrengthandtheeffectivewavelengthoftheBalmer
jump, as in the Barbier, Chalonge & Divan classification system [12], and iii) photo-
metric indexes centred on selected Balmer lines, such as the b index used by [14],
[15] and [95]. Another luminosity diagnostic for B9–A2 supergiants, the strength of
8 FabioBresolin
theSiIIll 6347,6371lines,wasproposedby[66],but[19]showedthatthisindicator
breaksdownforbrightSMCstars,asalikelyeffectofthereducedmetallicity.
Work by [56] on the equivalentwidth of the Hg line, W(Hg ), led to a calibration
of its relationship with absolute magnitude, lower values of W(Hg ) being found for
high-luminositystars.AspectraltypedependenceamongtheBandAstarsofdifferent
luminosityclasseswasalsodetected.Thecut-offatthebrightendofthisearlycalibra-
tion(M >−7)wasimposedbythescarcityofsupergiantstarswithknowndistances.
V
Refinementstothecalibrationofthistechniquewereintroducedby[7]andby[37].
ThelatterusedaW(Hg )–M calibrationbasedonGalacticstarstoestimatethedistance
V
to the Magellanic Clouds, thus pioneeringstellar spectroscopyas a way to determine
extragalacticdistances(seealso[13]).Morerecentcalibrationshavebeenproposedby
[54](O–Adwarfsandgiants),[92]and[28](supergiants),accountingforthespectral
typedependence.Amongtheapplications,Irecalltheworkby[5],whousedW(Hg )to
determineluminosityclassesforalargenumberofstarsintheSMC.
Correlations between Balmer lines of blue supergiants and stellar luminosity are
not restricted to the use of Hg . A strong luminosity effect on the Ha line was found
fromnarrow-bandphotometryofGalacticearly-typestarsby[3].Later[82]turnedtheir
attentiontotheequivalentwidthoftheHa andHb linesinasampleofB–Asupergiants
intheLMCandSMC.Theavailabilityintheseextragalacticsystemsofalargenumber
ofbluesupergiantsuptoextremeluminosities,allatacommondistanceandwithsmall
reddening,isamajoradvantageforcalibrationpurposes.TheHa andHb linesarein
emissionforthevisuallybrightestbluestarsintheClouds,asrecognizedsincetheearly
stellarspectroscopicworkinthesegalaxies[18],asignatureofthepresenceofextended
atmospheresandmasslossthroughstellarwinds.Theluminosityeffectisparticularly
stronginHa ,whichinlate-Bandearly-Asupergiantsbeginstoshowaclearemission
nature,mostlywithacharacteristicP-Cygniprofile,aroundM =−7[65].Thefilling
V
of the line profiles by stellar wind becomes progressively smaller as one proceedsto
Balmerlinesofhigherorder,sothatHg ,Hd ,etc.areincreasinglybetterdiagnosticsof
stellar surface gravity.Examples of Ha , Hb and Hg line profiles are shown in Fig.3
forstarsofdifferentvisualbrightness,fromM =−9.3to−6.2intheLMC(thetwo
V
brightestobjects),theMilkyWay(HD92207)andNGC300(thethreefainterobjects),
all plotted at the same intermediate spectral resolution. Excellent examples of higher
resolution profiles of Balmer lines of B–A supergiantscan be found in the papers by
[65],[40]and[89].
Forextragalacticdistancestudiesitisessentialthatthescatter inthe relationships
between observablesbe small. In the case of the equivalentwidth of Ha and Hb vs.
magnitude,thermsscatterfoundby[82]forabout40B5–A0supergiantsintheLMC
was0.3–0.4mag.However,thescatter doublesforsimilarstars in theSMC, aneffect
attributedtoametallicitydependenceofthemasslossrate.WhenHg andHd arecon-
sidered[83]a∼0.5magdispersionisfoundintheLMC.Ontheotherhand,[92]and
[28], using their W(Hg )–M calibration, claim a probable error ≃0.2mag (standard
V
deviation≃0.3mag),forasingleobservation.However,wenotethatinthelattertwo
worksstarsbrighterthanM =−8areexcludedfromthecalibration,somewhatreduc-
V
ingitsusefulnessforextragalacticwork.
BlueSupergiantsasaToolforExtragalacticDistances 9
Fig.3. Examples of Hg (left), Hb (middle) and Ha (right) lineprofiles in blue supergiants of
different visual brightness (decreasing from top to bottom, as indicated in the legend) in the
LMC,MilkyWayandNGC300.TheLMCandGalacticspectra(courtesyN.PrzybillaandR.
Kudritzki)havebeendegradedtothe5A˚ resolutionoftheNGC300data
Since the mid-1980’s not much work has been published about new applications
oftheW(Hg )–M relationship,possiblybecauseofthesomewhatuncertainresultsob-
V
tainedintheCloudsand,mostofall,becauseofthelackofhigh-qualityspectraforblue
supergiantsingalaxiesbeyondtheMagellanicClouds.Withtheavailabilityof8–10m
telescopesinrecenttimesthespectroscopyofalargenumberofstarswellbeyondthe
LocalGroupboundarieshas becomefeasible, and new calibrationsand tests of spec-
troscopic luminosity diagnostics are likely to appear in future years. Several projects
areunderwaywithinourgroupandotherstousethecurrentgenerationofmulti-object
spectrographs(FLAMES,FORSandVIMOSattheVLT,DEIMOSatKeck,GMOSat
Gemini)toobservealargefractionofthebrightstellarcontentingalaxiesoftheLocal
Groupandbeyond.
Afirst,modernversionoftheW(Hg )–M relationforBandAsupergiants,based
V
onCCDspectracollectedwithinourgroup,isreproducedinFig.4.Thesampleshown
containsobjectsfromthefollowinggalaxies:NGC300[9],MilkyWay[40],LMCand
SMC[60],M33andM31[50],[51].Ithasbeensubdivided,somewhatarbitrarily,into
threeseparateclassesaccordingtothestellarspectraltyperange:earlyB(B0–B4,full
symbols),B8–A0(opensymbols)andA1–A9(crosses).
The slope of the empirical relationship in Fig.4 becomes shallower for the later
spectral types, as indicated by the regressions corresponding to the B8–A0 (dashed
line)andA1–A9(dottedline)classes.Thistrendwithspectraltypeiswell-knownfrom
previouswork,withamaximumW(Hg )atagivenM aroundtypeF0forsupergiants
V
[37].Contrarytothecalibrationby[28],thenewdiagramispopulateduptoverybright
magnitudes,M ≃−9.TherelationshipdefinedbytheB8–A0subgroupisrathertight,
V
withastandarddeviationofabout0.3mag(bottompanelofFig.4),andisgivenby
M =−9.56(±0.15)+[1.01(±0.07)]W(Hg ). (2)
V
10 FabioBresolin
Fig.4.(Top)TheW(Hg)–M relationshipforB–AsupergiantsinNGC300,MilkyWay,Magel-
V
lanicClouds,M31andM33.Thesamplehasbeendividedintothreeclasses:B0–B4(fullsym-
bols), B8–A0 (open) and A1–A9 (crosses). The regression lines for the latter two are shown.
(Bottom)ResidualplotfromtheregressionsforB8–A0(opensymbols)andA1–A9supergiants
(crossed).Thestandarddeviationisshownbydashedanddottedlines,respectively
The scatter for the later A-type supergiants is 50% larger. A further subdivision
of thisbroadclass mightrevealtightercorrelations,butcurrentlythisis preventedby
thesmallnumberofobjectsavailable.Wenotetheratherlargediscrepancyoftheonly
A0 Ia supergiantplotted for the SMC (AV 475) from the regression line, with an Hg
linetoostrongforitsmagnitude.A metallicityeffectcannotbeexcludedatthisstage
to explain this discrepancy.The measurementsof W(Hg ) in SMC supergiantsby [5],
combined with M ’s obtained from magnitudes and spectral types in the catalog by
V
[6], are in generalagreementwith those shownin Fig.4, althoughthey show a larger
scatter.Thismightbe,atleastpartly,relatedtothenecessityofredefiningthespectral
typeclassificationatlowmetallicity,asshownby[47].
To conclude,byrestrictingthe analysisto a narrowrangein spectraltypes(B8 to
A0) the scatter aboutthe meanW(Hg )–M relationis on the orderof0.3mag,which
V