Quantitative studies of the optical and UV spectra of Galactic early B supergiants I. Fundamental parameters
Samantha C. Searle, Raman K. Prinja, Derck Massa, Robert Ryans
aa r X i v : . [ a s t r o - ph ] J a n Astronomy&Astrophysicsmanuscript no. 7125 c (cid:13)
ESO 2018October 27, 2018
Quantitative studies of the optical and UV spectraof Galactic early B supergiants
I. Fundamental parameters
Samantha C. Searle , Raman K. Prinja , Derck Massa , and Robert Ryans Department of Physics & Astronomy, University College London, Gower Street, London WC1E 6BT England, UKe-mail: [email protected], [email protected] SGT, Inc., Code 665.0, Nasa Goddard Space Flight Center, Greenbelt, MD 20771, USAe-mail: [email protected] Department of Physics & Astronomy, The Queen’s University of Belfast, BT7, 1NN, Northern Ireland, UKe-mail: [email protected]
Accepted January 3, 2008
ABSTRACT
Aims.
We undertake an optical and ultraviolet spectroscopic analysis of a sample of 20 Galactic B0 – B5 supergiants of luminosityclasses Ia, Ib, Iab, and II. Fundamental stellar parameters are obtained from optical diagnostics and a critical comparison of the modelpredictions to observed UV spectral features is made.
Methods.
Fundamental parameters (e.g., T e ff , log L ∗ , mass-loss rates and CNO abundances) are derived for individual stars usingCMFGEN, a nLTE, line-blanketed model atmosphere code. The impact of these newly derived parameters on the Galactic B supergiant T e ff scale, mass discrepancy, and wind-momentum luminosity relation is examined. Results.
The B supergiant temperature scale derived here shows a reduction of about 1 000 – 3 000 K compared to previous resultsusing unblanketed codes. Mass-loss rate estimates are in good agreement with predicted theoretical values, and all of the 20 B0 –B5 supergiants analysed show evidence of CNO processing. A mass discrepancy still exists between spectroscopic and evolutionarymasses, with the largest discrepancy occurring at log ( L / L ⊙ ) ∼ v and C iv P Cygni profiles. This problem arises because the models are not ionised enough and fail toreproduce the full extent of the observed absorption trough of the P Cygni profiles.
Conclusions.
Newly-derived fundamental parameters for early B supergiants are in good agreement with similar work in the field.The most significant discovery, however, is the failure of CMFGEN to predict the correct ionisation fraction for some ions. Suchfindings add further support to revising the current standard model of massive star winds, as our understanding of these winds isincomplete without a precise knowledge of the ionisation structure and distribution of clumping in the wind.
Key words. stars: early type – stars: supergiants galaxies: Milky Way – stars: atmospheres stellar winds – stellar evolution – massloss – abundances
1. Introduction
The study of luminous, massive stars is fundamental to im-proving our understanding of galactic evolution, since theradiatively driven winds of these stars have a tremendousimpact on their host galaxies. This huge input of mechanicalenergy is responsible for creating H II regions, making asignificant contribution to the integrated light of starburstgalaxies and providing star formation diagnostics at both lowand high redshifts. They substantially enrich the local ISMwith the products of nucleosynthesis via their stellar winds andsupernovae explosions and are a possible source of gamma raybursts. It is therefore imperative to obtain accurate fundamentalparameters for luminous massive stars since they contribute tomany currently active areas of astrophysical research.
Send o ff print requests to : S. C. Searle, e-mail: [email protected] However there are still some uncertainties regarding the post-main sequence evolution of massive stars since their evolutionis controlled by variable mass loss from the star as well asrotation, binarity and convective processes, the latter leadingto surface enrichment as the products of nuclear burning arebrought to the surface. Until recently, stellar evolution modelsfailed to predict the correct amount of CNO processing inmassive stars. However, new evolutionary tracks that accountfor the e ff ects of rotation (Maeder & Meynet 2001) show betteragreement between predicted and observed amounts of CNOenrichment in massive stars. A far greater problem in stellarastrophysics is the determination of accurate observed mass lossrates. Recent research (e.g., Fullerton et al. 2006; Prinja et al.2005; Massa et al. 2003; Puls et al. 2006; Repolust et al. 2004),has shown that current OB star mass loss rates might be over-estimated by at least a factor of 10. Such large uncertaintiesin the mass loss rates of massive stars suggest that our under-standing of their winds is incomplete. It is now widely accepted S. C. Searle et al.: Fundamental parameters of Galactic B supergiants that the winds of both O and B stars are highly structured andclumped and therefore our assumptions that they are smoothand homogeneous are invalid. Evidence to support this claimhas come from hydrodynamical, time-dependent simulationsof stellar winds (e.g. Owocki et al. 1988; Runacres & Owocki2002), the latter of which proposed the idea that instabilites inthe line-driving of the wind can produce small-scale, stochasticstructure in the wind. Further evidence for the inhomogeneityof stellar winds comes in the form of various observationalstudies (e.g., Puls et al. 2006; Bouret et al. 2005; Massa et al.2003; Prinja et al. 2002; Bianchi 2002). Time-series analyses ofboth Balmer and metal spectral lines (e.g., Prinja et al. 2004)in OB stars highlight clear, periodic patterns of variability thatcorrespond to the evolution of structure in the wind. Puls et al.(2006) demonstrated that the discrepancy between values of˙ M H α and ˙ M radio implies the presence of di ff erent amounts ofclumping at the base of and further out in the wind. Massa et al.(2003) showed that for a sample of O stars in the LMC, theempirical ionisation fractions derived were several orders ofmagnitude lower than expected, indicating a lack of dominantions in the wind. Similar results were found by Prinja et al.(2005) for early B supergiants. More recently, Fullerton et al.(2006) demonstrated that the ionisation fraction of P v , whichis dominant over a given range in T e ff in the O star spectralrange, never approaches a value of unity. They subsequentlyshowed that a reduction in mass loss rate of at least a factor of100 is required to resolve the situation. We intend to re-addressthe issue of the ionisation structure of early B supergiants,following on from Prinja et al. (2005), in a forthcoming paper(Searle et al., 2007b, in preparation; hereafter Paper II). Suchdrastic reductions in OB star mass loss rates would have severeconsequences for the post-main-sequence evolution of thesestars; in particular it would a ff ect the numbers of Wolf-Rayetstars produced and the ratio of neutron stars to black holesproduced in the final stages of massive star evolution.Early type B supergiants are particularly important since theyare the most numerous massive luminous stars and are idealcandidates for extra-galactic distance indicators, essential forcalibrating the Wind-Momentum-Luminosity Relation (WLR)(e.g., Kudritzki et al. 1999). Research into this WLR calibrationhas highlighted a spectral type dependence for Galactic OBAtype stars (e.g., Kudritzki et al. 1999; Repolust et al. 2004;Markova et al. 2004), whilst others have explored the e ff ect ofmetallicity on the WLR by studying OB stars in the metal-poorenvironment of the Magellanic Clouds (e.g., Kudritzki & Puls2000; Trundle et al. 2004; Evans et al. 2004b). Accuratelyderived mass loss rates are essential in calibrating the WLR,yet discrepancies still exist between observed mass loss ratesobtained from di ff erent wavelength regions (i.e. optical, UVor IR). Furthermore acknowledged discrepancies of up to30 % have been found between observational and theoreticallypredicted mass loss rates (Vink et al. 2000). Vink has remarkedthat these discrepancies for the mass loss rates of B stars canbe attributed to systematic errors in the methods employed toderive the observed values. Good agreement was found betweenobserved and predicted mass loss rates for O stars in Vink et al.(2000). Additionally, Puls et al. (2006) recently derived valuesof both ˙ M H α and ˙ M radio , highlighting a discrepancy of roughly afactor of two between both values.The layout of this paper is as follows. § § § §
5. Finally theconclusions are given in §
2. Observations
Optical and UV spectra have been collected for a sample of 20Galactic B supergiants, covering the spectral range of B0–B5and including Ia, Ib, Iab and II luminosity classes as well as ahypergiant. Stars were only included in the sample if both opti-cal and
IUE data were available for them. Where possible, starswere selected such that there would be 2 di ff erent luminosityclasses at each spectral sub-type. The details of observationaldata for each star are given in Table 2.1. Fourteen of the chosenB supergiants belong to OB associations (Humphreys 1978),so for these stars, the absolute magnitude given in Table 2.1is based on the distance to the relevant association; for theremaining six stars M V and therefore the distance modulus isderived from photometry.For fifteen of the twenty B supergiants in our sample, the opticalspectra were taken from an existing data set (see Lennon et al.1992 for further details). The blue spectra were observed usingthe 1-m Jacobus Kapteyn Telescope (JKT) at the Observatoriodel Roque de los Muchacos, La Palma in October 1990 with theRichardson-Brealey Spectrograph and a R1200B grating. Theyhave a wavelength coverage of 3950 – 4750 Å, a spectral resolu-tion of 0.8 Å and a signal-to-noise ratio ∼ > λ c of 4300 Å, whereas the R600R grating wasused for the red spectra, giving λ c ∼ >
100 and the spectral resolution was 0.7 Å. Finallyhigh resolution time-averaged blue and red spectra of HD 64760were provided by RKP (see Kaufer & Stahl 2002 for more de-tails). These spectra were taken in 1996 on the HEROS fiber-linked echelle spectrograph, which was mounted on the ESO50-cm telescope at the La Silla, Chile. The blue spectra havea range of 3450 – 5560 Å whilst the red have 5820 – 8620 Å.Both had a resolving power of 20 000. The signal-to-noise ra-tio varied with lambda but for a red spectrum with a 40-minuteexposure it was typically > As previously mentioned, our sample covers a range of B0–B5supergiants with luminosity classes varying from Ia down toII in a couple of cases. Spectral type classifications have beentaken from Lennon et al. (1992), which includes some recentrevisions. HD 204172 has been changed from B0 Ib to B0.2Ia due to the strength of its Si iv lines and narrowness of itsH lines. Comparing its UV resonance lines to those of the B0Ib star HD 164402 supports the change to a more luminousspectral type (Prinja et al. 2002). Also both HD 164353 and HD191243 have been reclassified from B5 Ia to B5 II stars. It isalso worth noting that de Zeeuw et al. (1999) has questioned themembership of the stars HD 53138 and HD 58350 to Collinder . C. Searle et al.: Fundamental parameters of Galactic B supergiants 3 Table 1.
Observational data for the sample of 20 Galactic B Supergiants. Spectral types and V magnitudes are taken fromLennon et al. (1992) for all stars except HD 192660, HD 185859, HD 190066 and HD 64760. The references for the spectraltypes of these 4 stars are as follows: HD 192660 from Walborn (1971); HD185859 from Lesh (1968); HD 190066 from Hiltner(1956) and HD 64760 from Ho ffl eit & Jaschek (1982) (from which the V magnitude of HD 64760 was also taken). V magnitudesfor the remaining 3 stars were obtained from Fernie (1983). Values of ( B − V ) taken from Fitzgerald (1970). Absolute visual mag-nitudes, distance moduli and cluster associations have been taken from: 1. Brown et al. (1994), 2.Garmany & Stencel (1992) or 3.Humphreys (1978). For stars not associated with a cluster, an absolute visual magnitude scale based on spectral type (Egret 1978)was used. L1992 refers to archive data obtained from Lennon et al. (1992), INT2003 denotes data taken on the 2.5m INT and RKPmarks data supplied by R.K. Prinja. HD no. Alias Sp. Type V B-V M V Association m-M Optical
IUE ǫ Ori B0 Ia 1.70 -0.19 -6.95 Ori OB1b 7.8 L1992 SWP30272192660 - B0 Ib 7.38 0.67 -7.0 Cyg 0B8 11.8 INT2003 SWP44625204172 69 Cyg B0.2 Ia 5.94 -0.08 -6.2 Cyg OB4 6.2 L1992 SWP4890038771 κ Ori B0.5 Ia 2.04 -0.18 -6.51 Ori OB1c 8.0 L1992 SWP30267185859 - B0.5 Ia 6.48 + + κ Cas BC0.7Ia 4.16 + L1992 SWP5403813854 V551 Per B1 Iab(e) 6.47 + L1992 SWP02737190066 - B1 Iab(e) 6.53 + + + + L1992 SWP5271614818 V554 Per B2 Ia 6.25 + L1992 SWP18658206165 V337 Cep B2 Ib 4.74 + .30 -6.44 Cep OB2 13.2 L1992 SWP06336198478 55 Cyg B2.5 Ia 4.84 + L1992 SWP3868842087 3 Gem B2.5 Ib 5.75 + L1992 SWP0864553138 24 CMa B3 Ia 3.01 -0.11 -7.1 - 10.11 L1992 SWP3027158350 η CMa B5 Ia 2.41 -0.07 -7.0 - 9.41 L1992 SWP30198164353 67 Oph B5 II(Ib) 3.97 + + INT2003 SWP07737
121 on account of insignificant proper motion and smallparallax respectively. Seven of the twenty stars in our samplehave been examined for H α variability by Morel et al. (2004),who obtained both photometric and spectroscopic data on theseobjects in order to ascertain the amount of variability present intheir light-curves and H α profiles. Morel et al. (2004) quantifythe amount of spectral and photometric variability observed aswell as determining periods where cyclic behaviour is observed.The sample includes a rapid rotator, HD 64760 (discussedin detail in the following section) and a hypergiant, the B1.5Ia + star HD 190603. Furthermore, there are several objects ofinterest in the sample for which a significant amount of re-search has already been undertaken and merit further discussion. – ǫ Ori : There are several intriguing aspects of this starthat are worth mentioning. Firstly it has been noted asmoderately nitrogen deficient by Walborn (1976). Secondlyit is known to undergo significant variations in H α , withMorel et al. (2004) reporting variations of 81.9 %. Furtherstudies by Prinja et al. (2004) have revealed variability innot only H α but also H β , He absorption and metal lineswith a 1.9 day period. A modulating S-wave pattern hasbeen discerned in the weaker lines, which cannot be fullyexplained by current non-radial pulsation models (Townsend1997). These results highlight a direct connection betweenphotospheric activity and perturbations in the stellar wind.Finally this star is the only normal early B supergiant tohave a measured thermal radio flux (Blomme et al. 2002),from which a radio mass loss rate of log ˙M = − .
72 was derived. – κ Ori : Like ǫ Ori, κ Ori also exhibits spectral variability inH α . Its H α profile was studied in detail by Rusconi et al.(1980) who described it as a double-peaked absorptionprofile with a central emission core and broad profilewings, with variations on long (of the order of days) andshort (of the order of minutes) time scales. More recentlyMorel et al. (2004) reported changes in the profile amplitudeand morphology of 32.6 %. Walborn (1976) noted it as anexample of a morphologically normal B supergiant in termsof the relative strengths of its CNO spectral lines. – HD 192660 : Bidelman (1988) noted that this star showed a“faint H α emission with a slight P Cygni absorption”, basedon observations taken at the Lick observatory in 1957. Ourspectrum of this star shows a very similar H α profile that isalso only weakly in emission. Walborn (1976) and Schild(1985) both noted that HD192660 displays evidence fornitrogen deficiency. – HD 64760 : This star is classified as a rapid rotator, havinga v sin i of 265 km / s. Many interesting studies have beencarried out regarding the periodic and sinusoidal mod-ulations of its optical and UV lines (Massa et al. 1995;Fullerton et al. 1997; Kaufer & Stahl 2002), which haveturned HD 64760 into a key object for improving ourunderstanding of the spatial structure and variations of hotstar winds. More recently, Kaufer et al. (2006) found, for S. C. Searle et al.: Fundamental parameters of Galactic B supergiants the first time, direct observational evidence for a connectionbetween multi-periodic non-radial pulsations (NRPs) in thephotosphere and spatially structured winds. More specifi-cally, they can use the interference of multiple photosphericpulsation modes on hourly timescales with wind modulationperiods on time scales of several days. A beat period of6.8 days seen in the photosphere and base of the winddoes not match with the derived periods of 1.2 and 2.4days for wind variability, being closer to the longer 5-11day repetitive timescales observed for discrete absorptioncomponents (DACs) in the
IUE data sets. Evidently theprecise nature of the wind-photosphere connection in thisstar is a complex one. Using hydrodynamical simulations,Cranmer & Owocki (1996) succeeded in confirming theexistence of co-rotating interaction regions (CIRs). Theseare spiral structures in the wind that are produced throughthe collisions of fast and slow streams rooted in the stellarsurface. – κ Cas : Walborn (1972) classified this star as carbon rich,giving it a spectral type of BC0.7 Ia, when comparing itsoptical spectrum with that of HD 216411, a B0.7 Ia star. Hefound that the nitrogen lines in κ Cas were barely detectable,whereas the O II - C III blends were very prominent.Since Walborn also recognised that HD 216411 possessesa well developed nitrogen spectrum, he described κ Casas carbon-rich, rather than nitrogen-weak, with respectto a morphologically-normal B supergiant. Walborn hadpreviously suggested that all OB stars begin their post-main-sequence evolution with an enhancement of carbon(Walborn 1971), which then becomes depleted as the starevolves and produces nitrogen as a by-product of the CNObi-cycle. Therefore the implication of classifying κ Cas as aBC 0.7 Ia star is that it is less evolved than other stars in thesample. Please consult Section 4.5 for a discussion of thecarbon rich status of this star based on the results presentedin that section. – HD 13854 : McErLean et al. (1999) describe this star as‘highly processed’ i.e. displaying a large amount of CNOprocessing in its spectrum. Its H α profile is seen mostly inemission, assuming a P Cygni shape. Morel et al. (2004)found that not only does the H α profile of this star varyby 47.3 %, but that these variations have a period of 1.047days ± . Hipparcos light curves also show evidence forperiodic behaviour. – HD 14818 : possesses an H α profile with a P Cygni profile.Morel et al. (2004) report variations of 34.8 % in the H α profile and, like HD 13854, they find that this star alsoshows periodic behaviour in its Hipparcos light curve. – HD 42087 : also has its H α profile in emission but moreimportantly Morel et al. (2004) reported significant H α variability of 91.2 % ( greater than the percentage variabilitythat they found for ǫ Ori), for which they find strongevidence of cyclic behaviour on a periodicity of 25 days ± α variability correlates withvariability in the He i α emissionincreases, He i Hipparcos light curve. – HD 53138 : Walborn (1976) notes that this star showsa morphologically normal CNO spectrum, despite other
Fig. 1.
Temperature structure against Rosseland optical meandepth for the hydrostatic density structure produced from com-bining the subsonic TLUSTY velocity structure with the super-sonic CMFGEN velocity structure, such that the velocity and ve-locity gradient are constant. The above example is for the B0.5Ia star HD 185859 ( T e ff =
26 000 K, log g = / OBC groups. Itundergoes 66.4 % H α variability (Morel et al. 2004).
3. Derivation of fundamental parameters
Fundamental parameters were derived for this sam-ple of stars using the nLTE stellar atmosphere codesTLUSTY (Hubeny & Lanz 1995; Lanz 2003) and CMFGEN(Hillier & Miller 1998). The application of TLUSTY, a plane-parallel photospheric code that does not account for the presenceof a stellar wind, to modelling supergiants is valid as long as it isused solely to model purely photospheric lines. An existing gridof B star TLUSTY models (Dufton et al. 2005) was used as abase for this work and the grid (originally incremented in stepsof ∼ T e ff and 0.13 in log g ) was refined further byRR in the range 15 000 K ≤ T e ff ≤
23 000 K to cover the sameparameter space as the CMFGEN grid. The TLUSTY modelsprovide a hydrostatic structure that can be input into CMFGEN,since the latter code does not solve for the momentum equationand therefore requires a density / velocity structure (see e.g.,Hillier et al. 2003; Bouret et al. 2003; Martins et al. 2005). TheTLUSTY input provides the subsonic velocity structure andthe supersonic velocity structure in the CMFGEN model isdescribed by a β - type law. The two structures are joined to ahydrostatic density structure at depth, such that the velocity andvelocity gradient are consistent. The resulting structure is shown . C. Searle et al.: Fundamental parameters of Galactic B supergiants 5 in Fig. 1, which shows the change in Rosseland mean opacity, τ Ross ,with temperature and ensures that the model is calculatingdeep enough into the photosphere to sample the regions wherethe appropriate photospheric lines form (around -2 ≤ log τ Ross ≤ β -type velocity law of the form: v ( r ) = v + ( v ∞ − v )(1 − R ∗ / r ) β + v v core e R ∗− rh e ff (1)where v is the photospheric velocity, v core is the core velocity, v ∞ is the terminal velocity, h e ff is the scale height expressed interms of R ∗ and β is the acceleration parameter. The value of β is normally determined from fitting the H α profile, as discussedin § . ≤ β ≤ . v core = / s and v = / s are adopted for B supergiants as suggested by D.J. Hillier(priv. comm.). All parameters except log g were derived usingCMFGEN and the precise details of the methods employed willbe discussed next. The general method employed was to producea grid of CMFGEN models of varying temperatures and lumi-nosities (all other parameters were kept constant), incrementedin steps of 1 000 K in T e ff and 5 in log ( L / L ⊙ ), and compare thesesynthetic spectra to observed spectra in order to constrain thesetwo parameters ( § β velocity law, turbulent velocity ( v turb ) ( § § j that form superlevel J have the same nLTE departure co-e ffi cient (i.e., each component j is in Boltzmann equilibrium withrespect to the other components). Details of the model atoms,including their full level and superlevel groupings, are given inTable 2. T e ff , log ( L / L ⊙ ) , log g and CNOabundances In B stars, the silicon lines are used as the primary tempera-ture diagnostics, having the advantage that the abundance is wellknown as silicon is una ff ected by nuclear processing. For B0 -B2 supergiants the Si iv iii iv T e ff ∼
18 000 K. At this point the Si ii iv iii Table 2.
CMFGEN model atomic data, showing the numberof full levels and superlevels treated as well as the number ofbound-bound transitions considered for each ion included in aCMFGEN model.
Ion Full Levels Superlevels b-b transitionsH I 30 20 435He I 59 41 590He II 30 20 435C II 53 30 323C III 54 29 268C IV* 18 13 76N I 22 10 59N II 41 21 144N III* 70 34 430O I 75 18 450O II 63 22 444O III* 45 25 182Mg II 45 18 362Al II 44 26 171Al III 65 21 1452Si II 62 23 365Si III 45 25 172Si IV 12 8 26S II 87 27 786S III 41 21 177S IV* 92 37 708Ca II 12 7 28Fe II 510 100 7501Fe III 607 65 5482Fe IV 272 48 3113Fe V* 182 46 1781 He i lines at 4144 Å, 4387 Å, 4471 Å and 4713 Å and Mg ii line at 4481 Å can also be used as secondary criteria for bothtemperature and luminosity, since they are sensitive to changesin both parameters. The principal luminosity criteria used inspectral classification of B stars is the ratio of Si iv i / or 4144 Åfor B0 - B1 supergiants,whereas for stars later than B1 the ratio of Si iii i T e ff , log ( L / L ⊙ ), log g and CNO abundances isthe same method adopted by Hillier et al. (2003); Crowther et al.(2006); Bouret et al. (2003); Martins et al. (2005) and is as fol-lows:1. An optical stellar spectrum of a chosen star is compared to agrid of CMFGEN models which di ff er in values of Te ff andluminosity (all other parameters are kept constant).2. A value of Te ff is selected for the star by finding the modelthat provides the best fit to the temperature sensitive siliconlines. The diagnostic lines are Si iv iii ii iii ii (but these lines were not used to derive the initialvalue of T e ff ) to ensure it provided a reasonable match to alltemperature-sensitive lines.3. Once a value of T e ff has been chosen, an inital estimate oflog ( L / L ⊙ ) is made by selecting the model from the grid(at the chosen value of T e ff ) whose value of M V (outputfrom the model) best matches the observed value of M V S. C. Searle et al.: Fundamental parameters of Galactic B supergiants for the star in question. The luminosity is then constrainedfurther by taking observed values of M V , the absolute visualmagnitude and V , together with the estimate of A ( V ), wereused to obtain an initial estimate of the distance modulus.Optical photometry and ultraviolet spectroscopy were thende-reddened with respect to the model spectral energydistribution to obtain revised estimates of E(B-V) and M V .This M V derived from the model was then compared to anobserved M V , if the values matched then the model lumi-nosity was correct. If not, the value of M V was translatedinto a bolometric correction to obtain an estimate of thecorrected luminosity for the model, which was then rerunwith this value for the luminosity. This iterative process wascontinued until the observed and model values of M V werein reasonable agreement and then the resulting model waschecked against the T e ff diagnostic lines (Si ii , Si iii , Si iv )and derived value of T e ff was adjusted if necessary.4. Estimates of log g were then made from TLUSTY fits to theH γ lines of the observed spectra. H γ is normally chosen asthe log g diagnostic since H α and H β su ff er from too muchwind fill emission; H δ was used as a secondary diagnosticto check for consistency with values of log g derived fromH γ . Since H γ is a ff ected by an O ii blend around 4350 Å andH δ has a blend with N iii g values so we can have confidencethat the derived log g values are not a ff ected by these blends.The adopted log g value was then incorporated into theCMFGEN model and again the derived T e ff and log ( L / L ⊙ )values were revised if necessary.5. Next CNO abundances were derived by varying the abun-dance of each element until the appropriate diagnostic lineswere fitted by the model. For nitrogen, we use the N iii δ ) and theN ii ii ii blends at 4070 Å, 4317 – 4319 Å and 4650 Å, theO ii lines at 4590 Å, 4596 Å and 4661 Å and the C ii dou-blet at 6578, 6582 Å. The errors on constraining the CNOabundances using this method were typically up to ∼ The stellar wind parameters ˙ M , β and v turb were then con-strained using the usual method outlined below (again thesame procedure used by Hillier et al. 2003; Crowther et al. 2006;Bouret et al. 2003; Martins et al. 2005). CMFGEN allows fora treatment of turbulence in the stellar wind by assuming aradially-dependent microturbulent velocity, defined as v turb = v min + ( v max − v min ) v ( r ) v ∞ (2)where v min is the minimum turbulent velocity occurring inthe photosphere and v max is the maximum turbulent velocity.Hillier et al. (2003) found that varying the turbulent velocity hadlittle e ff ect on the temperature structure calculated by CMFGEN.In this work, values of v min =
10 km / s and v max =
50 km / s areadopted as limits. Typically v reaches the value of v turb around r = R ∗ . 1. Values for the mass loss rate of each star were constrainedby fits to the H α profile, with each fit aiming to reproducethe overall profile shape and amplitude.2. Values of v ∞ are best determined from the UV so values ob-tained through UV line synthesis modelling (see Prinja et al.2005; Paper II) are used here.3. The value of β is also varied in order to improve the shapeof the model profile fit with respect to the observed profile,but this has no e ff ect for H α profiles in absorption, in whichcase values obtained from SEI analysis were used.4. Estimates of the microturbulent velocity, v turb , were thenmade by fitting the Si iii α in emission,six in absorption and the remainder displaying a more complexmorphology. In the last case, the profiles are partly in absorptionwith some emission component also detectable, implying thatthe profile has been filled in by stellar wind emission. TheB2 - B5 supergiants display H α profiles with a P Cygni profileshape, which implies that line scattering is playing a significantrole in the line’s formation, though this is not normally observeduntil late B / A supergiants. The majority of stars in this samplehave no record of H α variability so that any changes in the lineprofile morphology and amplitude can be considered negligiblefor the purpose of this analysis. However ǫ Ori, HD 13854,HD 14818 and HD 42087 all display significant H α variabilityaccording to Morel et al. (2004). In view of this problem,for ǫ Ori we have assumed a radio mass loss rate, ˙ M radio , of1 . × − M ⊙ yr − , as measured by Blomme et al. (2002),thereby avoiding the inaccuracies involved in deriving ˙ M froma variable H α line. An estimate of the error in fitting the H α profile of this star is given nonetheless is Table 8. Unfortunatelythis approach is not possible for the other 3 stars since there areno reliable ˙ M radio values available in the literature. The problemsassociated with deriving ˙ M from the H α profiles of these starsare discussed in the next section.
4. Results T e ff scale Model fits to the optical spectra of HD 192660 (B0 Ib), HD213087 (B0.5 Ia), HD 13854 (B1 Iab), HD 193183 (B1.5 Ib),HD 14818 (B2 Ia), HD 198478 (B2.5 Ia), HD 53138 (B3 Ia)and HD 58350 (B5 Ia) are shown in Fig. 2 (4050 – 4250 Å),Fig. 3 (4250 – 4450 Å) and Fig. 4 (4450 – 4650 Å). OverallCMFGEN has succeeded in providing excellent fits to theobserved spectrum of each star. The models succeed in repro-ducing the H, He, Si and Mg lines quite accurately. However,some individual spectral lines are more di ffi cult to model thanothers. The Si iv ff ect being most pronouncedin B1 - B2 supergiants, which might be partly due to a blendwith O ii . It is also noticeable that the model Si iv line displays . C. Searle et al.: Fundamental parameters of Galactic B supergiants 7 Fig. 2.
Overall CMFGEN fit to the optical spectrum of B0 – B5 supergiants (4050 Å - 4250 Å). The solid black line is the observedspectrum and the red line denotes the CMFGEN model fit.a slight sensitivity to mass loss. Hillier et al. (2003) also notedthat some model photospheric lines can be a ff ected by mass lossand more importantly, Dufton et al. (2005) noted when usingFASTWIND that Si iv iii multiplet 4552,4568, 4575 Å were a ff ected by the stellar wind. However, whilstusing CMFGEN, we have not observed any significant stellarwind e ff ects on the Si iii multiplet. The values of T e ff derived forthese stars can still be justified since the model spectrum still fitsthe rest of the spectrum, including the Si iii , Mg ii and He i lines,very well. In the cases where the model does underestimate theSi iv T e ff thatprovided a better fit to the Si iv line would provide a worse fitto the rest of the observed spectrum. Note that the values of T e ff obtained in these cases were still derived using the siliconionisation balance and the e ff ect of the compromise attainedbetween fitting the Si iv line underestimated by the model andthe rest of the spectrum is reflected in the value of ∆ T e ff quotedin Table 3. It is also intriguing to note that CMFGEN predictstwo absorption lines at 4163 Å (see in B1.5 – B5 supergiants)and 4168.5 Å (seen in all B0 – B5 supergiants) that are not observed in any of the sample stars. These predicted linesalso appear in the CMFGEN models of Crowther et al. (2006),where it appears that they have identified the line at 4168.5 Å asHe i but no explanation is given for the line at 4163 Å. We canconfirm the identify of the line at 4168.5 Å and also add that theline at 4163 Å is Fe iii .The values of T e ff , log g , log ( L / L ⊙ ), E(B-V) and M V derivedfor each of the 20 B supergiants in the sample are listed in Table3. These results show that B0 – B5 supergiants have a rangein T e ff of 14 500 – 30 000 K, in log ( L / L ⊙ ) of 4.30 – 5.74 andthat their stellar radii vary from about 20 - 71 R ⊙ . They alsoexhibit a range of − . ≤ M V ≤ − .
26 in brightness, con-firming their status as some of the brightest stars in our Galaxy.The temperature scale for B supergiants derived here is shownin Fig. 5, plotted against spectral type. A drop of up to 10 000 Kin temperature is witnessed between B0 – B1, whereas at lowerspectral types, the T e ff scale shows a more gradual decrease in T e ff . The Galactic O star T e ff scale published by Repolust et al.(2004) ranges from an O2 If star with T e ff =
42 500 K down to
S. C. Searle et al.: Fundamental parameters of Galactic B supergiants
Fig. 3.
Overall CMFGEN fit to the optical spectrum of B0 – B5 supergiants (4200 Å - 4450 Å). The solid black line is the observedspectrum and the red line denotes the CMFGEN model fit.an O9.5 Ia star with T e ff =
29 000 K and an O9.5 Ib star with T e ff =
32 000 K, meaning that the B supergiant T e ff scale pre-sented here carries on smoothly from the Galactic O supergiant T e ff scale. Similarly the B supergiant T e ff scale ends with B5Ib stars having T e ff ≈
15 000 K and the Galactic A supergiant T e ff scale derived by Venn (1995) begins with a T e ff of 9950 K.A gap between the B and A supergiant T e ff scales is expectedsince none of the recently published B star T e ff scales includeB6-9 stars. The B supergiant temperature scale derived here alsodemonstrates the di ff erence in T e ff between B Ia and B Ib / Iab / IIstars. B0 – B2 Ib / Iab stars are found to be up to 2 500 K hot-ter than B0 – B2 Ia stars, with the exception of the stars HD190603 (B1.5 Ia + ) and HD 193183 (B1.5 Ib). However, a lesssignificant di ff erence of 500 K in T e ff is found between B2 –B5 Ia and B2 – B5 Ib / II stars, with the B Ib stars again beinghotter than their more luminous counterparts; this discrepancyis well within the margins of error in deriving T e ff as typically ∆ T e ff =
500 - 1 000 K. We have compared our Galactic B super-giant T e ff scale to other published values (Trundle et al. 2004;Trundle & Lennon 2005; McErLean et al. 1999; Crowther et al.2006) in Table 4. Where each author has several stars with thesame spectral type, the values are averaged and marked with an asterisk in the table. Note that the results of McErLean et al.(1999) were obtained with an unblanketed stellar atmospherecode. If we compare our derived T e ff values with those of the un-blanketed McErLean et al. (1999) T e ff scale, the use of a stellar-atmosphere code with a full treatment of line blanketing hasthe e ff ect of lowering T e ff by 1 000 - 3 000 K for Galactic Bsupergiants. This is not as drastic as the reduction found forO supergiants, which can be as high as 7 000 K for extremestars (Crowther et al. 2002). If we compare our derived T e ff ’s tothose of McErLean et al. (1999), with whom we have 10 targetstars in common (HD 37128, HD 38771, HD 2905, HD 13854,HD 193183, HD 14818, HD 206165, HD 42087 and HD 53138),we find reasonably good agreement except for B1 Ia / Iabs, wherethe McErLean et al. (1999) results imply that a B1 supergiantis 2500 - 3 000 K hotter than our values. The SMC B super-giant temperature scale (Trundle et al. 2004; Trundle & Lennon2005) also implies a much hotter B1 supergiant, but it is ex-pected that SMC stars will be hotter than Galactic stars (see e.g.the O star temperature scales of Massey et al. (2005) (SMC) andRepolust et al. (2004) (Galactic) where the SMC stars are up to4 000 K hotter than the Galactic ones). . C. Searle et al.: Fundamental parameters of Galactic B supergiants 9
Fig. 4.
Overall CMFGEN fit to the optical spectra of B0 – B5 supergiants (4450 Å - 4650 Å). The solid black line is the observedspectrum and the red line denotes the CMFGEN model fit. g estimates An example of a TLUSTY log g fit to the H γ profile of HD164353 is shown in Fig. 7. Fits to the H γ and H δ profilesof all 20 B supergiants can be found online. TLUSTY is apurely photospheric code therefore the model Balmer linesare also photospheric; however in B supergiants the observedBalmer lines su ff er from wind contamination, where hydrogenphotons emitted in the wind at the same wavelengths as H γ and H δ ‘fill in’ the absorption profile. This makes it appearmore ‘shallow’ when compared to a photospheric profile andexplains the di ff erence in depth between the two profiles shownin Fig. 7. Values of log g derived from H γ and H δ were ingood agreement in general and no discrepancies larger than themargin of error on log g were found. Only small discrepancieswere found for B0 – B0.5 stars where a model with a log g value 0.13 dex higher than the adopted value might providea slight better fit to the H δ profile. However this ambiguitycan be attributed to the influence of a large N iii blend on theblue wing of H δ masking where the actual wing of the profileshould really lie. In these cases a very good fit is made to H γ so the value derived from H γ is taken. Some di ffi culties wereencountered when trying to fit the H γ and H δ profiles of HD192660, HD 64760, HD 190603, HD 13854 & HD 190066 dueto the observed asymmetry of the H γ and H δ profiles. This isparticularly evident in the HD 190603, a B1.5 Ia hypergiant witha strong wind evident from the P Cygni shape of its H β profile.The T e ff – log g scale derived from this work is shown in Fig.6, where higher log g values are found for B Ib stars. The log g values derived for B Ia stars are 0.1 - 0.2 dex higher than thoseobtained by Kudritzki et al. (1999); Crowther et al. (2006) fora sample of Galactic B supergiants, whereas the Trundle et al.(2004); Trundle & Lennon (2005) values for SMC B super-giants are generally higher than those for Galactic B supergiants. Using our estimates of log g , spectroscopic masses have beenderived for each of the 20 B supergiants and imply a rangeof 8 ≤ M ∗ ≤
52. Estimates of the evolutionary mass, M evol , Table 3.
Fundamental parameters ( T e ff , log g , log ( L / L ⊙ ), R ∗ ( R ⊙ ), E(B-V) M V and M evol ) derived for the sample of 20 Galactic Bsupergiants.Values of v e sin i are taken from Howarth et al. (1997) and are expressed in km / s.HD no. Sp. type T e ff (K) log g log (L / L ⊙ ) R ∗ ( R ⊙ ) E(B-V) M V v e sin i M evol ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± + ± ± ± ± ± ± ± ± ± ± ±
500 2.38 5.40 ± ± ± ± ±
500 2.50 5.18 ± ± ± ± ±
500 2.25 5.26 ± ± ± ± ± ± ± ± ± ±
500 2.25 5.30 ± ± ± ± ±
500 2.13 5.18 ± ± ± ± ± ± ± ± ± ± ± ± ± ± Fig. 5.
The Galactic B supergiant T e ff scale as a function of spec-tral type. B Ia stars are indicated by an asterisk, whilst B Ib starsare marked by a plus sign.were then obtained using our derived stellar parameters and thestellar evolutionary tracks of Meynet & Maeder (2000). The po-sitions of our 20 Galactic B supergiants on the Hertzsprung- Fig. 6.
The Galactic B supergiant T e ff - log g scale.Russell diagram, along with other Galactic B supergiants(Crowther et al. 2006), SMC B supergiants (Trundle et al. 2004;Trundle & Lennon 2005) and Galactic O stars (Repolust et al.2004), are shown in Fig. 8. Here, the Meynet & Maeder (2000)stellar evolutionary tracks have been used, which include the . C. Searle et al.: Fundamental parameters of Galactic B supergiants 11 Table 4.
Values of T e ff (expressed in terms of 10 K) obtained in this thesis work and from Trundle et al.(2004); Trundle & Lennon (2005); Kudritzki et al. (1999);McErLean et al. (1999). Values marked with an asterisk denotewhere values from one author have been averaged and are quotedto 1 decimal place. † the B0.5 Ib star HD 64760 has been omittedhere because it is a rapid rotator. Sp type This work Trundle McErlean CrowtherB0 Ia 27.5 27.0* 28.5 27.4*B0 Ib 30.0 - - -B0.2 Ia 28.5 - 28.5 -B0.5 Ia 26.0 27.3* 27.5 26.0*B0.5 Ib 27.0 † - 26.5* -B0.7 Ia 23.5 - 24.0 22.9B1 Ia - 23.8* - 22.0B1 Iab / Ib 20.5* - 23.3* 21.8*B1.5 Ia 19.5 21.3* 21.25 18.17B1.5 Ib 18.5 - 22.3* -B2 Ia 18.0 19.0 19.83 18.6*B2 Ib 18.0 - 20.8* -B2.5 Ia 17.5 16.5 18.0 16.5B2.5 Ib 18.0 - 20.5 -B3 Ia 16.5 14.0 17.9* 15.8*B4 Iab - - 16.5 -B5 Ia 15.0 14.5* 15.4* -B5 Ib / II 15.0* - 15.8* - e ff ects of rotation and are therefore more appropriate for OBsupergiants. In order to demonstrate the e ff ect of di ff erent stel-lar parameters on a star’s precise position on the HR diagram,Galactic B supergiants common to both our sample and that ofCrowther et al. (2006) are joined by a dotted line. A compar-ison of both masses is shown in Fig. 9. For 14 out of the 20B supergiants, M evol > M spec as found by Herrero et al. (2002).However, for the 5 other stars, which (excluding the rapid ro-tator HD 64760) have log ( L / L ⊙ ) ≥ M evol < M spec . Thedependence of the mass discrepancy with luminosity is exam-ined further in Fig. 10 and compared to the mass discrepancyfor SMC B supergiants investigated by Trundle et al. (2004);Trundle & Lennon (2005). Both data sets exhibit a peak in themass discrepancy at 5 . ≤ log ( L / L ⊙ ) ≤ . ff quiterapidly. A calibration of stellar atmosphere parameters (i.e., T e ff , log L ∗ ,log g , M ∗ , R ∗ ) according to spectral type has been carried out,using the fundamental parameters derived for our sample andthat of Crowther et al. (2006). A linear regression was applied tothe trend of T e ff with spectral type; once the T e ff scale had beenestablished, linear regressions were made to the trends of log T e ff vs. log L ∗ and log T e ff vs. log g , from which the values of R ∗ and M ∗ were then calculated. The resulting values of T e ff , log L ∗ , log g , M ∗ and R ∗ for each spectral type are shown in Table 5. As previously mentioned, it was Walborn (1976) who firstsuggested that the nitrogen and carbon anomalies found in OBstars can be explained by their evolutionary status, with OBCstars being the least evolved. It therefore follows that a typicalOB supergiant should display some partial CNO processing, inthe form of nitrogen enrichment accompanied by CO depletion.
Fig. 7.
Example of a TLUSTY log g fit to H γ profile of the B5Ib / II star HD 164353. A value of log g = ǫ Ori) arenitrogen deficient due to the weakness of the N iii ii iii ii ii multiplets at 6578 and 6582 Å, due to their strong sensitivityto nLTE e ff ects and the adopted stellar parameters (see e.g.,Nieva & Przybilla 2006). A combination of high-resolution andhigh signal-to-noise spectra, along with su ffi ciently- detailedmodel atoms, are required to attempt to resolve this problem. Table 6.
Derived CNO abundances for the sample of Galactic B supergiants (expressed as log (cid:18) N x N H (cid:19) + (cid:18) N x N H (cid:19) ∗ − log (cid:18) N x N H (cid:19) ⊙ . HD no. Sp. type T e ff v e sin i C N O N / C N / OSUN G2 V 5770 - 8.39 7.78 8.66 -0.61 -0.8837128 B0 Ia 27500 91 7.66 7.31 8.68 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + / II 15500 44 7.78 7.89 8.53 + + / II 14500 38 7.70 7.65 - + Table 7.
Comparison of mean published CNO abundances for OBA supergiants (expressed as log (cid:18) N x N H (cid:19) + Author Stellar group C N 0 N / C N / + + + + + + + + + + It is unlikely that our data is of a suitable resolution andsignal-to-noise to attempt to solve this discrepancy, but wewill nonetheless discuss our findings as appropriate. For oursample of B supergiants, the C ii multiplets at 6578 and 6582Å are not prominent for B0 – B1 supergiants; however forB1 – B5 stars the lines are distinguishable. The fits to the C ii ii iii ii ii iii ii ii ii κ Cas, which hasbeen defined as a carbon-rich star (Walborn 1976) has verysimilar CNO abundances to the stars HD 64760, HD 213087which have not been noted as carbon rich by any other authors.The original criteria for classifying κ Cas as a carbon-rich star were based on the weakness of its nitrogen lines as well as thestrength of its carbon lines; this makes sense since (as Walborn1976 explains) it is expected that nitrogen deficiency will beaccompanied by carbon enrichment. In order to resolve thisdiscrepancy, the
IUE spectrum of κ Cas has been comparedto the
IUE spectrum of the B0.7 Ia star HD 154090 (see Fig.11). Looking at the C ii iii line at 1247 Å. However, both stars appear tobe nitrogen weak (see e.g., the N v wind resonance line around1240 Å). Therefore on the basis of this evidence, it appears thatthe κ Cas should be defined as a nitrogen weak star, rather thancarbon rich. Crowther et al. (2006) found similar results for κ Cas, citing it as having the ‘least nitrogen enriched abundance’in their sample as well as the lowest values for the N / C and N / Oratios.The CNO abundances derived here for the sample of 20 Bsupergiants are compared in Table 7 to values obtained byother authors (Trundle et al. 2004; Trundle & Lennon 2005;Evans et al. 2004a; Crowther et al. 2006; Venn 1995, 1999)for OBA supergiants. The results from Trundle et al. (2004);Trundle & Lennon (2005) SMC B supergiants have been com-bined to obtain mean CNO abundances based on a sample of18 stars (but only 13 were used for the mean oxygen abundance . C. Searle et al.: Fundamental parameters of Galactic B supergiants 13
Fig. 8.
Position of the sample of Galactic B supergiants onthe Hertzsprung-Russell diagram, along with other GalacticB supergiants Crowther et al. (2006), SMC B supergiantsTrundle et al. (2004); Trundle & Lennon (2005) and Galactic Ostars Repolust et al. (2004). Evolutionary tracks are taken fromMaeder & Meynet (2001) and imply 15 M ⊙ < M evol ≤ M ⊙ forthe sample of 20 Galactic B supergiants presented in this work.Galactic B supergiants that are common to both our sample andthat of Crowther et al. (2006) are joined by a dotted red line toillustrate the e ff ect of di ff erent stellar parameters on a star’s pre-cise location on the HR diagram.since oxygen abundances were not derived for some B2.5 - 5stars due to weak, unmeasurable O ii lines). The data fromEvans et al. (2004a) were purely based on CNO abundancesderived from OB supergiants so that the results for nebularand H ii regions included by the authors for comparison wereomitted. It is clear from Table 7 that more CNO enrichmentoccurs in stars belonging to the Magellanic Clouds than Galacticstars. This is in accordance with Evans et al. (2004a), who foundthat OB supergiants in the LMC display a nitrogen enrichmentthat is greater than the nitrogen enrichments in Galactic Bsupergiants. Evans et al. (2004a) conclude that their sample ofMagellanic Cloud stars show significant nitrogen enrichmentdue to e ffi cient rotational mixing. The CNO abundances showno clear trend with e ff ective temperature or v e sin i . The mass loss rates obtained for this sample of 20 GalacticB supergiants are based on matches to the H α profile and theresulting values are listed in Table 8. All of these B supergiants Fig. 9.
Comparison of evolutionary and spectroscopically-derived stellar masses for the sample of B supergiants. The dot-ted line indicates 1:1 correspondance.have mass loss rates ranging between − . ≤ log ˙ M ≤ − . / Ib star HD 164353 for which ˙ M = × − was derived. The errors quoted in Table 8 reflect the ambiguityinvolved in fitting H α ‘by eye’ (and therefore represent themaximum and minimum values of ˙ M that fit H α reasonably) andare no greater than a factor of 2. In some cases an upper or lowererror limit only is quoted where the model fit over- or under-estimates the observed H α profile, meaning that a larger / smallermass loss rate would not be appropriate. CMFGEN fits to theH α profiles of κ Cas, HD 190603, HD 14818, HD 190066,HD 193183 and HD 164353 are given in Fig. 12. In general,good fits are obtained for each star, but several di ffi cultieshave been encountered in trying to reproduce the observed H α profiles. It is clear that all the observed profiles are asymmetricand it is likely that this is caused by the influence of resonantline scattering that is too weak to produce a ‘P Cygni’-typeprofile so merely results in a slightly asymmetric profile. Insome stars e.g., HD 213087, it appears to be a redward emissioncomponent that partly fills in the profile, to such an extent that insome stars this red component is visible as a separate emissioncomponent (e.g., HD 206165) and the H α profile begins toresemble a P Cygni profile (e.g., HD 14818). In the majorityof stars, the peak / trough of the H α profile has shifted from theline centre as observed in κ Cas. This e ff ect is particularly clearon comparing the H α profile of κ Cas with that of HD 190603,whose peak is much more central resulting in only a slightasymmetry to the overall profile. It is also of interest to note thatCMFGEN predicts a ‘bump’ in the blueward wing of the H α profile of HD 190603 that is not present in the observed profile; Fig. 10.
Comparison of M evol M spec with luminosity (B5 Ib / II starsomitted). Values obtained for the 20 Galactic B supergiants (as-terisks) are plotted with those derived for SMC B supergiants(diamonds) Trundle et al. (2004); Trundle & Lennon (2005).The dotted line indicates 1:1 correspondance.
Table 5.
Calibrations of fundamental parameters by spectraltype for Galactic B supergiants, based on this work and that ofCrowther et al. (2006)
Sp. type T e ff log ( L / L ⊙ ) R ∗ ( R ⊙ ) log g M ∗ ( M ⊙ )B0 Ia 28.1 5.60 26.9 2.99 25B0 Ib 29.7 5.66 23.8 3.24 37B0.2 Ia 26.7 5.62 30.4 3.04 36B0.2 Ib 28.5 5.65 27.8 3.23 49B0.5 Ia 24.7 5.58 33.8 2.90 33B0.5 Ib 25.4 5.58 32.2 3.09 47B0.7 Ia 23.6 5.53 35.1 2.72 23B0.7 Ib 24.4 5.51 33.9 2.93 37B1 Ia 22.0 5.44 36.5 2.41 12B1 Ib 21.7 5.38 34.9 2.67 22B1.5 Ia 19.9 5.44 44.5 2.41 18B1.5 Ib 19.3 5.29 39.7 2.50 19B2 Ia 18.3 5.41 51.0 2.32 19B2 Ib 18.1 5.27 44.4 2.46 21B2.5 Ia 17.2 5.39 56.5 2.24 19B2.5 Ib 17.6 5.25 46.2 2.43 22B3 Ia 16.4 5.37 60.4 2.16 19B3 Ib 17.5 5.23 45.5 2.39 19B4 Ia 15.8 5.34 63.5 2.06 16B4 Ib 17.4 5.18 43.2 2.27 13B5 Ia 15.7 5.33 63.0 2.03 15B5 Ib 15.2 5.09 51.7 2.11 13 Fig. 11.
Comparison of the relative strengths of the N and C linesin κ Cas and HD 154090
Fig. 12.
Examples of CMFGEN fits to H α profiles of κ Cas, HD190603, HD 14818, HD 190066, HD 193183 and HD 164353,along with the mass loss rate adopted for each star. The red, dot-ted line represents the CMFGEN model fit to each H α profileand the solid, black line indicates the observed H α profile.a similar phenomenon is observed for HD 193183.A small, preliminary investigation into the e ff ects of includingclumping on the morphology of the model H α profile was un-dertaken. Hillier & Miller (1999) assume the winds are clumped . C. Searle et al.: Fundamental parameters of Galactic B supergiants 15 Table 8.
Stellar wind parameters ( ˙ M , β , v ∞ , v turb ) derived fora sample of 20 Galactic B supergiants. The errors given on ˙ M reflect the errors in fitting each individual H α profile. HD no. Sp type ˙ M (10 − M ⊙ yr − ) β v ∞ (km / s) v turb (km / s)37128 B0 Ia 1.90 + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . + + . − . + . − . + . − . + . − . + . − . + . − . + . − . + . − . / II 0.06 + . − . / II 0.83 + . − . with a volume filling factor f and that no inter-clump medium ispresent. The volume filling factor, is defined as: f = f ∞ + (1 . − f ∞ ) e − vvcl (3)where f ∞ is the filling factor at v ∞ and v cl is the velocity at whichclumping is ‘switched on’ in the wind. However, to carry outa fair comparison between clumped and homogeneous modelsinvolves a larger parameter space than merely varying f ∞ and v cl . For example, it is important to check for consistency in theatmospheric structure of both models i.e., that they sample thesame optical depth in the photosphere and have the same densitystructures, which can include some fine tuning of the velocitylaw and the point at which the TLUSTY hydrostatic structurejoins the CMFGEN density structure. It is also important tocheck that the same computation options are selected for bothmodels to ensure that the density structure is computed usingthe same methods (e.g, the same number of Λ iterations arespecified). This is important as computational parameters mayhave been changed for individual models in order to easeconvergence. For these reasons, a rigorous comparison ofhomogeneous and clumped models will be postponed to a laterdate.These mass loss rates have been compared to those predictedby the theoretical mass loss prescription of Vink et al. (2000),as shown in Fig. 13, where the values of T e ff , log L ∗ and M ∗ derived in the previous section have been input into the relevantmass loss recipes (equations 12 and 13) quoted in the paper. Fig. 13.
Comparison of CMFGEN derived mass loss rates withtheoretical mass loss rates predicted by the Vink et al. (2000)mass loss prescription. The dotted line indicates 1:1 correspon-dance.We find that the ˙ M ’s derived here are in good agreement withthe Vink et al. (2000) predictions, with discrepancies of a factorof 2-3 on average and the maximum discrepancy a factor of 6.Trundle et al. (2004); Trundle & Lennon (2005) found that thevalues of ˙ M vink were a factor of five lower than observed massloss rates for early B supergiants, whereas for mid B supergiants˙ M vink was a factor of seven higher than observed values. Noconsistent discrepancy is found in our results but generally ˙ M vink ≤ ˙ M H α for B0 – B1 supergiants and the reverse is truefor B2 – B3 supergiants. Our values of ˙ M obtained here werecompared to those of Crowther et al. (2006), with who we have8 stars in common, and the mass loss rates are in very goodagreement. A comparison has also been made to the valuesobtained by Kudritzki et al. (1999), since there are again 8 starscommon to both data sets (Fig. 14). With the exception of ǫ Ori, κ Cas and HD 206165, all the B supergiant mass loss ratesderived by Kudritzki et al. (1999) are smaller than our values bytypically a factor of up to 5. The values derived for ǫ Ori and κ Cas are well within the errors of our derived values; however alarger discrepancy of a factor of ∼
10 is found for HD 206165.Initially this is puzzling since in both cases good fits have beenobtained to the observed H α profile of HD 206165 and do notsuggest such a large discrepancy in ˙ M . However, quite di ff erentstellar parameters have been adopted in terms of T e ff ( T e ff =
18 000 K in our analysis cf. 20 000 K from Kudritzki et al.1999), log ( L / L ⊙ ), R ∗ and v ∞ ; more importantly Kudritzki et al.(1999) adopt a much higher β value of 2.5 compared to 1.5 inthis work. Fig. 14.
Comparison of CMFGEN derived ˙ M with those ofKudritzki et al. (1999) for 8 stars common to both samples The concept of a Wind-Luminosity–Momentum Relation (here-after WLR) was first proposed by Kudritzki et al. (1995), usingthe prediction from the theory of radiatively driven winds thatthere is a strong dependence of the total mechanical momen-tum flow ˙ Mv ∞ of the stellar wind on stellar luminosity (e.g.,Castor et al. 1975), which can be described as˙ Mv ∞ ∝ R − ∗ L α ef f (4)The importance of the WLR lies in its potential as an extra-galactic distance indicator provided that it is reliably calibrated .The proportionality shown in Equation 4 was first confirmed ob-servationally by Puls et al. (1996) for a sample of Galactic andMagellanic Cloud O stars with 5 . ≤ log L ∗ ≤ .
5. For log L ∗ < .
5, a linear fit was not possible, demonstrating the depen-dence of the WLR on spectral type. Kudritzki et al. (1999) thenshowed that a linear fit to the WLR was also possible for galac-tic BA supergiants. Since then many authors (Repolust et al.2004; Markova et al. 2004; Massey et al. 2004; Massey et al.2005; Trundle et al. 2004; Trundle & Lennon 2005) have pub-lished values for wind momenta when deriving fundamental pa-rameters for sets of OBA stars using D mom = ˙ Mv ∞ R . ∗ (5)where R ∗ is in solar radii, ˙ M in g / s and v ∞ in cm / s to give D mom in units of cgs. Assuming a WLR of the formlog D mom = log D + x log ( L / L ⊙ ) (6) a linear regression can be used to constrain the coe ffi cients x and log D . The reciprocal of x can be thought of as the e ff ectiveexponent α e f f (see Equation 4). Applying a linear regressionto our data gives log D = .
76 and x = .
61. Looking atFig. 15, it can be seen that the hotter spectral types i.e. O starshave a steeper WLR than cooler B spectral types. This is tobe expected if, as proposed by Vink et al. (1999), Fe ii andFe iii lines are responsible for driving the subsonic part of thewind, corresponding to lower ionisation stages. Fig. 15 alsoillustrates the e ff ect of metallicity on the WLR, with the moremetal poor environment of the Magellanic Cloud hosting starswith lower values of D mom . This e ff ect is particularly notice-able between Galactic and SMC B supergiants. Our valuesof D mom are compared to those predicted by the theoreticalWLR prescription of Vink et al. (2000), using the parametersderived for our sample of stars in this chapter. It is found thatthe observational values are greater than predicted values forB0 – B0.7 supergiants (except for the B0.2 Ia star HD 204172)where T e ff ≥
23 000 K, which is expected for the hotter sideof the bi-stability jump. Conversely, B1 – B5 supergiants havesmaller, observed values of D mom compared to predicted values.This is caused by a combination of several e ff ects. Firstly, justas the predicted Vink et al. (2000) mass loss rates are a factor of5 larger on the cooler side of the bi-stability jump, ( T e ff ∼
23 000K), the predicted wind momenta will be greater for B1 – B5supergiants, causing a larger discrepancy between observed andtheoretical values of D mom . In addition to this, many B1 – B5supergiants have H α profiles in absorption, making it harderto constrain a ‘true’ observed mass loss rate. Similar resultsare found by Trundle & Lennon (2005) for their sample ofSMC B supergiants. Repolust et al. (2004) suggested that theinclusion of clumping in the derivation of mass loss rates mayhelp to alleviate the existing discrepancies between observedand theoretical wind momenta, which also exist for O stars aswell as B stars. Clumping would reduce the mass loss rate andconsequently lower wind momenta, although the precise amountof clumping present in OB star winds remains uncertain. Veryrecently Puls et al. (2006) attempted to derive better constraintson the clumping factor in hot star winds through a combinedoptical, infra-red and radio analysis of the wind. They foundthat use of clumped mass loss rates did produce much betteragreement between observed and theoretical wind momenta,since for O stars the observed wind momenta were originallyhigher than the theoretical ones, but the inclusion of clumpingreduced the value of ˙ M and consequently D mom . Unfortunately,for the case of Galactic B supergiants this may only work forB0 – B0.7 supergiants; the use of a lower, clumped ˙ M wouldnot resolve the discrepancy for B1 – B5 supergiants. This mayindicate a fundamental di ff erence between the structure andinhomogeneity of O and B star winds. At present, it is notpossible to obtain a reliable calibration of the WLR, until theproblems associated with its dependence on luminosity andmetallicity, as well as the e ff ect of clumping on observed massloss rates, are resolved.
5. Testing the UV predictions of CMFGEN
The next step of our investigation was to examine if theCMFGEN models presented in the previous section wouldalso provide a good fit to the UV silicon lines, thus confirmingthat T e ff diagnostics at both optical and UV wavelengthsimplied the same value of T e ff for each star. An example of aCMFGEN comparison to T e ff -sensitive silicon lines Si ii λ . C. Searle et al.: Fundamental parameters of Galactic B supergiants 17 Fig. 15.
The Wind-Luminosity Momentum Relation for OBAstars. Note the dependence of the WLR on spectral type andmetallicity. The theoretical WLR predicted by Vink et al. (2000)is calculated for our sample of Galactic B supergiants and is rep-resented by the orange line.Si iii λ λ T e ff =
18 000 K, L = × L / L ⊙ and ˙ M = . × − M ⊙ yr − . Two other models with T e ff =
17 500 K, L = × L / L ⊙ , ˙ M = . × − M ⊙ yr − and T e ff =
18 500 K, L = × L / L ⊙ , ˙ M = . × − M ⊙ yr − respectively are also shown to demonstrate the e ff ectsof changing T e ff on these lines (the slight di ff erences in theluminosity and mass loss of these models will not significantlya ff ect the silicon lines). A direct comparison of the observed andmodel Si ii λ ffi cult since the continuumis raised about this line, but it is apparent that the modelproduces an asymmetric profile (whereas the observed profileis symmetric) shifted by about 1 Å blue-ward relative to theobserved line profile centre. The model profile is also muchbroader than the observed profile and varying T e ff by ±
500 Khas no significant e ff ect on this line. In the case of Si ii λ T e ff are more apparent on this line,though still make no significant improvement to the overall linefit. For Si iii λ λ iii lines appear to showsome evidence of broadening due to the stellar wind despitebeing photospheric, which is also evident in the model profilesin the form of asymmetry. Additionally change in T e ff appearsto have no a ff ect on these lines; however the higher value of Fig. 16.
CMFGEN model fit to the
IUE spectrum of HD 14818(B2 Ia), focusing on the UV silicon T e ff diagnostics: Si ii λ λ iii λ λ λ T e ff =
18 000 K, L = × L / L ⊙ and ˙ M = . × − M ⊙ yr − (dashed red line). Others modelshave T e ff =
17 500 K, L = × L / L ⊙ , ˙ M = . × − M ⊙ yr − (dotted green line) and T e ff =
18 500 K, L = × L / L ⊙ , ˙ M = . × − M ⊙ yr − (dot-dashed blue line).˙ M for the T e ff =
18 500 K model (blue line) produces a deeperabsorption trough for the profile. To conclude, varying T e ff andeven ˙ M has a small a ff ect on these lines, but will not succeedin reproducing the observed lines accurately, with the correctbroadness and symmetry. A large number of UV lines are also strongly a ff ected by massloss from the wind, so it is also of interest to investigate whetherthe values of ˙ M derived from H α in § T e ff and luminosityare readily available and only depend on abundance, T e ff and / or luminosity. On the other hand, the task of identifying suitablediagnostic lines is less straightforward, since many UV lineswill be sensitive to mass loss as well as T e ff , abundance and insome cases v turb .An example of a CMFGEN fit to the IUE spectrum ofHD 190603 (B1.5 Ia + ) is shown in Fig. 17. Since the massloss rate has already been constrained from fits to the H α profile, it is interesting to see whether the derived value of ˙ M is confirmed by reasonable fits to the UV P Cygni profiles,provided that a reasonable model fit to the H α profile hasalready been achieved. Looking at the case of HD 190603shown in Fig. 17, the fit to the observed H α profile is good.However, it is clear that CMFGEN does not reproduce anyof the observed P Cygni profiles accurately, implying that adi ff erent value of ˙ M would be appropriate for the UV. Themodel fails to produce su ffi cient high velocity absorption inthe UV wind resonance lines, to the extent that the predictedC iv λλ v is not seen as aP Cygni profile in this star, but the model does not even producea distinct, weak photospheric line at 1238 Å. However, betterfits are achieved at lower ionisation: C ii λλ iv λλ iii λλ ii λλ M is required or the modelionisation is incorrect. Adopting a higher value for ˙ M thoughwould worsen the e ff ect of the model overestimating the redwings of the Si iv λλ ff ect on the Al iii λλ α would worsenif a higher value of ˙ M was adopted, illustrating the discrepancybetween the mass loss rates implied from the optical and UV.It is also noticeable when comparing the observed and modelSi iv P Cygni profiles that the model doublet components arenarrower than observed. As in the case of C iv , this is dueto the model predicting to little absorption at high veloci-ties. For HD 190603, these problems arise in spite of the factthat the value adopted for ˙ M provides a good fit to the H α profile.An example of a better CMFGEN fit to the UV wind resonancelines is given in Fig. 18 for the B2 Ia star HD 14818. Theobserved H α profile displays a P Cygni profile, which has notbeen successfully reproduced by the model (as discussed in § iv and Al iii in comparison to those obtained for HD 190603,though again a lack of high velocity absorption causes themodel to under-estimate the broadness of the absorption troughfor Si iv . However, the same failure occurs in reproducing theP Cygni profile of C iv line, whilst N v shows no evidence ofwind contamination. The fit to C ii is reasonable, although themodel predicts too much redward emission and as a result doesnot match the redward side of the absorption trough. Converselyan example of a worse fit than either of the previous casesis shown in Fig. 19 for HD 53138 (B3 Ia). Its observed H α profile is in absorption but shows a small amount of red-wardemission and is reasonably well matched by CMFGEN. Onthe other hand, the UV P Cygni profiles are in general poorlymatched by the model, with none of the five wind line profilesbeing well reproduced. The same problems seen for HD 190603and HD 14818 in matching N v , C iv and Si iv also occur here. Fig. 17.
CMFGEN fit to the IUE spectrum to the N v , C iv , Si iv ,Al iii and C ii wind resonance lines of HD 190603 (B1.5 Ia + ).Note that a good fit to H α does not guarantee the same mass lossrate will provide a good fit to the UV P Cygni profiles. Modelparameters are T e ff =
19 500 K, log ( L / L ⊙ ) = M = × − M ⊙ . Fig. 18.
CMFGEN fit to the IUE spectrum to the N v , C iv , Si iv ,Al iii and C ii wind resonance lines of HD 14818 (B2 Ia). Eventhough the fit to H α is not perfect, a reasonable fit is made to theUV P Cygni profiles, particularly Si iv and Al iii . Model param-eters are T e ff =
18 000 K, log ( L / L ⊙ ) = M = × − M ⊙ .The red-ward emission in C ii is grossly over-estimated andthe model produces an asymmetric Al iii profile that is notobserved. In both cases the model predicts saturated lines whenthe observed profiles are not saturated (though C ii is beginningto saturate a little). The high velocity absorption in Al iii isover-estimated to the extent that it predicts saturation to occurat a higher velocity than observed. It is therefore clear from Fig.17, Fig. 18 and Fig. 19 that a discrepancy exists between thevalue of ˙ M required to fit the H α and UV wind resonance lines(hereafter referred to as the optical / UV discrepancy ). . C. Searle et al.: Fundamental parameters of Galactic B supergiants 19 Fig. 19.
CMFGEN fit to the IUE spectrum to the N v , C iv ,Si iv , Al iii and C ii wind resonance lines of HD 53138 (B3 Ia).Although a good fit has been made to H α with the adoptedmass loss rate, CMFGEN does not reproduce the observed UVP Cygni profiles well. Model parameters are T e ff =
16 500 K,log ( L / L ⊙ ) = M = × − M ⊙ .In general, CMFGEN only succeeds in matching the C iv linewhen it is saturated in early B supergiants, at which point it isno longer sensitive to T e ff and ˙ M so a reliable fit cannot be ob-tained as altering these parameters will have no a ff ect on themodel line profile. Otherwise, CMFGEN manages to reproducemost of the observed P Cygni profile for C ii , Al iii and Si iv ,but fails to produce enough high velocity absorption to repro-duce the full extent of the observed absorption trough. As a re-sult, the model often under-estimates the blueward absorptionas well as over-estimating the redward emission, especially inthe case of Si iv . This can sometimes lead to the model givingan asymmetry to the P Cygni profile that is certainly not ob-served in the spectrum. Additionally, CMFGEN never succeedsin producing the N v P Cygni profile when present in B0 – B1supergiants and even when a weak, photospheric profile is ob-served, the model fails to produce a discernible spectral lineat the correct wavelength for N v . In the hotter B supergiants,the model grossly underestimates the photospheric Al iii and C ii lines. However when the same resonance lines are seen as PCygni profiles, the model has a tendency to reproduce them assaturated when they are observed to be unsaturated. All thesediscrepancies suggest that the problem lies within the predictedionisation structure of the models. CMFGEN fits to the overallIUE spectra of 10 B0 – B5 supergiants are available as onlinematerial (Fig.s 9, 10, 11). Very similar problems in matching theUV P Cygni profiles have also been encountered by Evans et al.(2004a) and Crowther et al. (2006) when modelling O and earlyB supergiants with CMFGEN. The CMFGEN models examined in the last section demonstratea clear discrepancy between ˙ M H α and the value of ˙ M impliedby the P Cygni profiles of the wind resonance lines. It ishardly surprising that they are unsuccessful in reproducing theobserved UV wind diagnostics accurately. In this section, the possibility of modelling a star solely from its UV spectra willbe investigated (ignoring any prior knowledge of values ofparameters from the optical) to see if the UV can be reproducedmore accurately. In order to do this, we must first identifysuitable UV diagnostic lines by which values of T e ff , log ( L / L ⊙ ),˙ M , v ∞ , β and abundances could be constrained.Looking back to the problems mentioned in the previous sec-tion, one potential di ffi culty is immediately apparent. CMFGENis unable to reproduce the C iv line accurately, which makesit hard to constrain v ∞ and β from this line. Suitable UV T e ff diagnostics also need to be found besides the photospheric Si ii and Si iii lines discussed in §
5. Si iv λλ T e ff diagnostics are Al iii and C ii which also show some sensitivity to mass loss and are thereforenot ideal. Another possible T e ff diagnostic is the photosphericSi ii iv λλ v ∞ . At this stage, we have no photospheric lines touse as reliable T e ff diagnostics, since they are not well matchedby CMFGEN. The best we can do is look at the UV lines bestreproduced by CMFGEN (i.e., Si iv , Al iii and C ii ) and analysetheir sensitivity to the main stellar parameters.In practice, another major problem materialises. It is di ffi cult todisentangle the e ff ects of T e ff and ˙ M on Si iv , Al iii and C ii , plusthey are often too saturated to be sensitive enough to these pa-rameters. When Si iv is not observed to be saturated, CMFGENstill predicts a saturated profile that is virtually insensitive to T e ff and ˙ M , making it di ffi cult to use as a T e ff and ˙ M diagnostic. Infact, the lack of a significant di ff erence between model P Cygniprofiles when varying mass loss presents a serious obstacleto any attempt to derive parameters from the UV, as we willnow show. For B0-B1 supergiants, the model often producesa saturated C iv P Cygni profile and over-estimates the Si iv PCygni profile. It may appear logical that adopting a model witha lower mass loss rate would provide a better fit to the observedC iv and Si iv lines. However, the lack of sensitivity of this lineto mass loss becomes apparent when the ˙ M adopted by themodel is altered. This is illustrated in Fig. 20, where it can beseen that lowering the value of ˙ M from 5 . × − to 2 . × − has no a ff ect on the wind resonance lines (implying that theyare still optically thick), despite producing model H α profilesin emission and absorption respectively (note that the broadfeature seen in the model between 1242 - 1247 Å is not N v butC iii , which interestingly enough does show some sensitivity tomass loss). It could still be argued that a larger decrease in massloss is required to fit these lines. However Fig. 21 disprovesthis idea as yet again no di ff erence is seen between P Cygniprofiles for models with ˙ M = × − M ⊙ yr − (red dashedline) and = . × − M ⊙ yr − (blue dotted line) respectively.This is in spite of the fact that this di ff erence in mass loss againresults in model H α profiles in emission and absorption, aswell as having a significant di ff erence on the amplitude of Ly α (1216 Å). HD 164353 presents an interesting case study forhow CMFGEN deals with the ionisation in the stellar wind,as it is a B5 Ib / II star that possesses a very weak wind with˙ M = × − M ⊙ yr − and can be thought of as a star with Fig. 20.
Comparison of UV wind resonance lines of HD 192660for models with ˙ M = . × − M ⊙ (red dashed line) and 2 . × − M ⊙ (blue dotted line) for HD 192660 (B0 Ib).negligible mass loss and stellar wind contamination. This isconfirmed by looking at the observed C ii and Al iii resonancelines (Fig. 21), which show some asymmetric broadening.However the model predicts strongly saturated profiles for bothlines despite the low mass loss rate adopted for the model,again suggesting that the predicted ionisation structure is atfault. This highlights another significant problem that, giventheir lack of sensitivity to significant changes in mass loss, theC iv and Si iv P Cygni profiles would not make suitable massloss diagnostics. It appears that the root of the problem lies inCMFGEN predicting ionisation fractions for C ii and Al iii thatare too high, resulting in a large optical depth that produces toomany absorbers at too high a velocity. The observed profileson the other hand show us that absorption is only occurringaround the rest velocity of the line. The model over-estimationof C ii and Al iii may therefore only be resolvable by loweringthe ionisation fraction of these two elements and cannot beresolved by altering the mass loss rate of the model in question.From this, we conclude that the UV wind resonance lines arenot suitable candidates for deriving T e ff and ˙ M . Even if theionisation structure was correctly predicted, more diagnosticlines would be required to determine all the necessary stellarparameters other than T e ff and ˙ M , as well as ensuring that anaccurate analysis had been carried out.In addition to the wind resonance lines, the UV subordinatelines can potentially be used to provide additional constraintson the mass loss adopted for the model. An example is theSi iv iv Fig. 21.
Comparison of UV wind resonance lines of HD 164353for models with ˙ M = × − M ⊙ yr − (red dashed line) and = . × − M ⊙ yr − (blue dotted line) respectivelyThis means that if the model over-populates the lower level ofSi iv iv iv w at fourdi ff erent T e ff ; 27 500 K, 23 500 K, 18 000 K and 15 000 K for thesix ions (N v , C iv , Si iv , Si iii , Al iii and C ii ). CMFGEN predictsthat Si iv will be dominant as expected for T e ff =
27 500 K, butshows very low levels of N v and C iv . This is hardly surprisingsince it explains the complete absence of a N v P Cygni profile(when present observationally), as well as the di ffi culties ingenerating a P Cygni profile for C iv when it is unsaturated. Itis also interesting to note that the levels of ionisation drop o ff rapidly in the model as w increases, contradicting the empiricaldeterminations of Prinja et al. (2005) where winds becamemore highly ionised at high w . This is direct evidence of themodel failing to generate enough high-velocity absorption tosustain the same level of ionisation further out in the wind.This is the reason for the ‘narrowness’ of the model C iv and . C. Searle et al.: Fundamental parameters of Galactic B supergiants 21 Fig. 22.
CMFGEN predicted ionisation structure at di ff erent T e ff ,plotted against normalised veocity w . The ions are colour-codedas follows: N v = green, C iv = red, Si iv = dark blue, Si iii = lightblue, Al iii = purple and C ii = yellow. Si iv is predicted to bedominant for B0-B2 supergiants (30 000 K ≤ T e ff ≤
18 000 K ),after which Si iii , Al iii and C ii take over as the dominant ions inthe wind for T e ff ≤
18 000 K.Si iv P Cygni profiles compared to the broad absorption troughsof the observed P Cygni profiles. If the model cannot sustainenough ionisation in the inner and outer parts of the wind, thenit will be unable to fully reproduce the blue-ward part of theprofile. CMFGEN predicts Si iv to be dominant down to T e ff =
18 000 K, at which point Si iii and Al iii take over as thedominant ions in the wind. At this T e ff , C ii has also increased instrength, becoming a dominant ion at T e ff =
15 000 K. Whereasthis approach has provided us with valuable insight into whyCMFGEN struggles to predict the P Cygni profiles correctly, ittoo fails to provide us with an alternative means of constrainingparameters due to the incorrectly-predicted ionisation structure.Given all these problems with CMFGEN mismatching theobserved UV P Cygni profiles, a investigation into the e ff ectsof clumping on these lines would not be worthwhile at present.In addition, mass loss in the UV is only sensitive to ρ , ratherthan ρ as in H α and radio-dominated regions of the wind, soit is not a particularly sensitive indicator of clumping. First themodels need to predict the correction ionisation structure for Bsupergiants. Secondly, the problems associated with investigat-ing the e ff ects of clumping on H α (as discussed in § α is an important diagnostic of clumping andcan provide important insight into its behaviour, which wouldaid a subsequent analysis of clumping in the UV. Furthermore,in comparison to O stars which possess strong indicators of UV clumping e.g., P v λλ ff ectof clumping on the UV profiles has shown that it does notimprove the fits to the observed P Cygni profiles, as expected,but can alleviate the over-estimation of emission seen in thered-ward part of the model Si iii and Al iii profiles. In the case ofthe photospheric Si iii lines around ∼ ff ect of the stellar wind onthese lines by producing slightly asymmetric profiles, but theinclusion of clumping can help to lessen this asymmetry. Thisis logical since the inclusion of clumping will increase thewind density locally, providing more absorption at the point atwhich the line forms in the wind, helping to reduce the excessred-ward emission seen in many of the model P Cygni profiles.The inclusion of clumping will have no a ff ect on saturated linesin the model as they are no longer sensitive to density changesin the wind. All the afore-mentioned issues associated withinvestigating clumping e ff ects need to be addressed before anytruly meaningful analysis of clumping in the UV can be carriedout.
6. Conclusions
A quantitative study of the optical and UV properties of B0 – B5Ia, Iab, Ib / II supergiants has been carried out, using the nLTE,line-blanketed stellar atmosphere code of Hillier & Miller(1998). A revised B supergiant T e ff scale (derived using a stellaratmosphere code that includes the e ff ects of line blanketing) hasbeen presented, giving a range of 14.5 000 K ≤ T e ff ≤
30 000 Kfor these stars. This scale shows a drop of up to 10 000K fromB0 Ia / b to B1 Iab and a di ff erence of up to 2 500 K between Iaand Ib stars. It also shows that on average the e ff ect of includingline blanketing in the model produces a modest reduction of upto 1 000 K for B0 – B0.7 and B3 – B5 supergiants, whereas alarger reduction of up to 3 000 K is seen for B1 – B2 supergiants(see Table 4). The 20 Galactic B supergiants also displayed arange of 2.1 ≤ log g ≤ α proved B supergiant winds to begenerally weaker than those of O supergiants (as expectedsince they are lower-luminosity objects) with ˙ M ranging from − . ≤ log ˙ M ≤ − .
30. All 20 B supergiants also shown signsof CNO processing, with the largest nitrogen enrichments beingseen for B1-B2 supergiants. Evidence for a mass discrepancyis found between estimates of M spec and M evol , with the largestdi ff erences peaking at a value of log ( L / L ⊙ ) ∼ ff erence in observed andtheoretical WLRs over the whole B supergiant spectral rangeby adopting clumped ˙ M as is the case for O stars. A severeproblem exists in the form of the optical-UV discrepancy,where the model fails to reproduce some of the P Cygni profilesaccurately. This highlights a failure in the model to generateenough high-velocity absorption to succeed in reproducing the observed P Cygni profile and more crucially highlights that themodels are not predicting the correct ionisation structure. Giventhat B supergiants, along with other massive stars, have theirpeak flux in the UV, it is imperative that this discrepancy is re-solved if we are to have confidence that fundamental parametersderived by this method are a true representation of the star’sproperties. Furthermore it underlines the incompleteness of ourcurrent understanding of the physics of massive star winds andthe necessity to review the standard model. A more thoroughanalysis of the ionisation structure of early B supergiant windswill be presented in Paper II. Acknowledgements.
SCS would like to acknowledge PPARC and BFWG forfinancial support. Thanks go to John Hillier for assistance in using CMFGEN aswell as Callum Wright and Jeremy Yates for computing support. We also thankthe referee for his comments.
Appendix A: Error Analysis
In this section, the errors a ff ecting each derived parameter arediscussed. The error on T e ff is estimated from the quality of theCMFGEN model fit to the diagnostic silicon, helium and magne-sium lines and therefore represents the range in T e ff over whicha satisfactory fit to the observed spectrum of the star could beobtained. Luminosity is primarily constrained through dered-dening the observed spectra with respect to the model spectraldistribution, its error depends on ∆ M V , whose errors are esti-mated from dereddening the observed spectrum with respect tothe model spectral energy distribution. ∆ log L ∗ also depends on ∆ M bol , since M bol = M V + B . C . , therefore ∆ log L ∗ is calculatedas ∆ log L ∗ = log L ∗ . ∆ M bol ( M bol − .
72) (A.1)The error on R ∗ depends on the square root of the sum of( ∆ T e ff ) and ( ∆ L ∗ ) , with ∆ L ∗ having the greatest influence on ∆ R ∗ . For 15 out of the 20 B supergiants, ∆ R ∗ is within 10%of the absolute value of R ∗ ; those stars with larger ∆ R ∗ arediscussed separately in this section. The error on log g for 16of the 20 stars star is estimated to be 0.25 dex, based on theaccuracy of line fits and the e ff ect of ∆ T e ff in determining log g .For four of the stars in our sample, we adopted ∆ log g = γ and H δ profiles, whereas forHD 64760 and HD 13854 it reflected the larger error in T e ff of2000 K (cf. to 500 - 1500 K for other stars in the sample. Theresulting uncertainty on the spectroscopic mass, M spec , due toerrors in constraining log g and R ∗ range from 0.08 ≤ ∆ M ∗ ≤ ∆ M evol is typically 5 M ⊙ as shown inFig. 8, which demonstrates the e ff ect of assuming di ff erent val-ues of T e ff and log ( L / L ⊙ ) on a star’s position in the HR diagram.Determining the error in constraining the mass loss rate ismore complicated, since it depends on both ∆ R ∗ and the errorin fitting the H α profile by varying ˙ M and β . However, theerrors incurred from uncertainties in deriving R ∗ are negligiblecompared to those arising from fitting the H α profile, so we arejustified in defining ∆ ˙ M as solely the error in fitting the H α profile, accounting for the degeneracy in varying β to fit H α profiles in emission. Values of v ∞ are taken from SEI analysis ofUV wind resonance lines (the result of which will be presentedin Paper II) and are accurate to ±
50 km / s. The values for v turb are constrained with an uncertainty of ± / s, as dictated by sensitivity of fitting the Si iii lines by eye.Some uncertainties exist in our analysis that warrant furtherdiscussion. Although for the majority of stars it was possible toconstrain T e ff within ± T e ff di ff er by1 000 K, resulting in ∆ T e ff = ± T e ff of 20 000 K is increasedto 22 000 K (keeping the same luminosity) then a much betterfit is made to the silicon lines (i.e., Si iv iii β , H γ , H δ , He i iv T e ff . HD 13854 alsohas quite a large error in M V , which consequently propagatesinto significant uncertainties in log ( L / L ⊙ ) and, combined witha larger ∆ T e ff , leads to a very large ∆ R ∗ . This arises from anoisy IUE SWP spectrum and the absence of a LWR spectrumleading to a large dereddening error; the same is true for theconsiderable errors on the values of M V and R ∗ obtained forHD 204172. Low quality IUE spectra generating higher ∆ E(B-V) also explain the ∆ log ( L / L ⊙ ) found for HD 14818 andHD 206165. However, for the B5 II (Ib) star HD 164353, it isthe value of M V = -4.2 that poses a problem; CMFGEN simplyfails to calculate a succesfully-converged model at the requiredluminosity. This explains the large values of ∆ log ( L / L ⊙ ), ∆ R ∗ and ∆ M V . The adopted value of M V has been independentlyconfirmed by several di ff erent sources in the literature so webelieve it to be correct. Furthermore, four stars (HD 37128,HD192660, HD198478 and HD 42087) have larger errors inthe observed value of M V than the value of M V derived fromdereddening, so in practise the quoted value of ∆ M V could beup to 0.2 mag larger. References
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Online Material . C. Searle et al.: Fundamental parameters of Galactic B supergiants , Online Material p 2
Fig. 1.
CMFGEN model fits (4050 – 4250 Å) to the optical spectra of 10 B Ia supergiants, with the T e ff , luminosity and CNOdiagnostic lines marked as shown. Optical spectrum is in black, CMFGEN model fit is shown in red. . C. Searle et al.: Fundamental parameters of Galactic B supergiants , Online Material p 3
Fig. 2.
CMFGEN model fits (4250 – 4450 Å) to the optical spectra of 10 B Ia supergiants, with the T e ff , luminosity and CNOdiagnostic lines marked as shown. Optical spectrum is in black, CMFGEN model fit is shown in red. . C. Searle et al.: Fundamental parameters of Galactic B supergiants , Online Material p 4
Fig. 3.
CMFGEN model fits (4450 – 4650 Å) to the optical spectra of 10 B Ia supergiants, with the T e ff , luminosity and CNOdiagnostic lines marked as shown. Optical spectrum is in black, CMFGEN model fit is shown in red. . C. Searle et al.: Fundamental parameters of Galactic B supergiants , Online Material p 5
Fig. 4.
CMFGEN model fits (4050 – 4250 Å) to the optical spectra of 10 B Ib supergiants, with the T e ff , luminosity and CNOdiagnostic lines marked as shown. Optical spectrum is in black, CMFGEN model fit is shown in red. . C. Searle et al.: Fundamental parameters of Galactic B supergiants , Online Material p 6
Fig. 5.
CMFGEN model fits (4250 – 4450 Å) to the optical spectra of 10 B Ib supergiants, with the T e ff , luminosity and CNOdiagnostic lines marked as shown. Optical spectrum is in black, CMFGEN model fit is shown in red. . C. Searle et al.: Fundamental parameters of Galactic B supergiants , Online Material p 7
Fig. 6.
CMFGEN model fits (4450 – 4650 Å) to the optical spectra of 10 B Ib supergiants, with the T e ff , luminosity and CNOdiagnostic lines marked as shown. Optical spectrum is in black, CMFGEN model fit is shown in red. . C. Searle et al.: Fundamental parameters of Galactic B supergiants , Online Material p 8
Fig. 7.
TLUSTY model fits to the H γ profile of all 20 supergiants. Optical spectrum is represented by a solid, black line; TLUSTYmodel fit is shown as a dotted black line. . C. Searle et al.: Fundamental parameters of Galactic B supergiants , Online Material p 9
Fig. 8.
TLUSTY model fits to the H δ profile of all 20 supergiants. Optical spectrum is represented by a solid, black line; TLUSTYmodel fit is shown as a dotted black line. . C. Searle et al.: Fundamental parameters of Galactic B supergiants , Online Material p 10
Fig. 9.
CMFGEN model fit to the IUE spectra of 10 B0 – B5 supergiants (1230 Å – 1480 Å). The solid red line represents the modelfits whereas the solid black line is the IUE spectrum. . C. Searle et al.: Fundamental parameters of Galactic B supergiants , Online Material p 11
Fig. 10.
CMFGEN model fit to the IUE spectra of 10 B0 – B5 supergiants (1480 Å – 1680 Å). The solid red line represents themodel fits whereas the solid black line is the IUE spectrum. . C. Searle et al.: Fundamental parameters of Galactic B supergiants , Online Material p 12