Creating and using large grids of precalculated model atmospheres for a rapid analysis of stellar spectra
J. Zsargo, C. R. Fierro-Santillan, J. Klapp, A. Arrieta, L. Arias, J. M. Valencia, L. Di G. Sigalotti, M. Hareter, R. E. Puebla
AAstronomy & Astrophysics manuscript no. manuscript38066 c (cid:13)
ESO 2020September 24, 2020
Creating and using large grids of precalculated modelatmospheres for a rapid analysis of stellar spectra
J. Zsargó , , C. R. Fierro-Santillán , J. Klapp , e-mail: [email protected] , A. Arrieta , L. Arias , J. M.Valencia , L. Di G. Sigalotti , M. Hareter , and R. E. Puebla , Environmental Physics Laboratory (EPHYSLAB), Facultad de Ciencias, Campus de Ourense, Universidad de Vigo, Ourense 32004,Spain Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Avenida Instituto PolitécnicoNacional S / N, Edificio 9, Gustavo A. Madero, San Pedro Zacatenco, 07738 Ciudad de México, Mexico Departamento de Física, Instituto Nacional de Investigaciones Nucleares (ININ), Carretera México-Toluca km. 36.5, La Marquesa,52750 Ocoyoacac, Estado de México, Mexico, Universidad Iberoamericana, Prolongación Paseo de la Reforma 880, Alvaro Obregon, Lomas de Santa Fe, 01219 Ciudad deMéxico, Mexico, Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana-Azcapotzalco (UAM-A), Av. San Pablo 180, 02200Ciudad de México, Mexico Facultad de Ingeniería, Ciencias Físicas y Matemática, Universidad Central del Ecuador, Ciudadela Universitaria, Quito, Ecuador Centro de Física, Universidad Central del Ecuador, Ciudadela Universitaria, Quito, EcuadorReceived MM DD, 2020; Accepted MM DD, 2020
ABSTRACT
Aims.
We present a database of 43,340 atmospheric models ( ∼ M (cid:12) , covering the region of the OB main-sequence and Wolf-Rayet (W-R) stars in the Hertzsprung–Russell(H–R) diagram. Methods.
The models were calculated using the ABACUS I supercomputer and the stellar atmosphere code CMFGEN.
Results.
The parameter space has six dimensions: the e ff ective temperature T e ff , the luminosity L , the metallicity Z , and three stellarwind parameters: the exponent β , the terminal velocity V ∞ , and the volume filling factor F cl . For each model, we also calculatesynthetic spectra in the UV (900-2000 Å), optical (3500-7000 Å), and near-IR (10000-40000 Å) regions. To facilitate comparisonwith observations, the synthetic spectra can be rotationally broadened using ROTIN3, by covering v sin i velocities between 10 and350 km s − with steps of 10 km s − . Conclusions.
We also present the results of the reanalysis of (cid:15)
Ori using our grid to demonstrate the benefits of databases of precal-culated models. Our analysis succeeded in reproducing the best-fit parameter ranges of the original study, although our results favorthe higher end of the mass-loss range and a lower level of clumping. Our results indirectly suggest that the resonance lines in theUV range are strongly a ff ected by the velocity-space porosity, as has been suggested by recent theoretical calculations and numericalsimulations. Key words. astronomical databases: miscellaneous — methods: data analysis — stars: atmospheres
1. Introduction
The self-consistent analysis of spectral regions from the X-ray to the IR is now possible because of the fertile combina-tion of the large amount of observational data and the avail-ability of sophisticated stellar atmosphere codes, such as CMF-GEN (Hillier 2013; Hillier & Miller 1998, 1999; Puebla et al.2016), PHOENIX (Hauschildt 1992), TLUSTY (Hubeny &Lanz 1995), WM-BASIC (Pauldrach et al. 2001), FASTWIND(Santolaya-Rey et al. 1997; Puls et al. 2005; Rivero Gonzálezet al. 2011; Carneiro et al. 2016), and the Potsdam Wolf-Rayet(W-R) code (PoWR, Gräfener et al. 2002; Hamann & Gräfener2004; Sander et al. 2015). As a result, significant advances havebeen made in our understanding of the physical conditions in theatmospheres and winds of massive stars. In parallel with theseadvances, stellar atmosphere codes were also improved and be-came even more sophisticated.For example, early far-UV observations (Fullerton et al.2000) showed inconsistencies between the optical e ff ective tem- perature scale and the temperature that was implied by the ob-served wind ionization. Studies by Martins et al. (2002) andothers showed that the neglect of line blanketing in the atmo-spheric models resulted in a systematic overestimate of the ef-fective temperature derived from optical H and He lines. Afterthese e ff ects were introduced into the stellar atmosphere models,the inconsistencies were eliminated. Studies by Crowther et al.(2002), Hillier et al. (2003), and Bouret et al. (2003), who si-multaneously analyzed FUS E , HS T , and optical spectra of Ostars with the corrected models, were able to derive consistente ff ective temperatures using a wide variety of diagnostics.Another crucial development was the recognition of the im-portant e ff ects of the line-deshadowing instabilities (LDI orclumping) on the spectral analyses of O, B, and W-R stars. Forexample, Crowther et al. (2002) and Hillier et al. (2003) wereunable to reproduce the observed P V λλ α .The only way in which the P V and H α profile discrepancies Article number, page 1 of 22 a r X i v : . [ a s t r o - ph . S R ] S e p & A proofs: manuscript no. manuscript38066 could be resolved were either to assume substantial clumpingor to use unrealistically low phosphorus abundances. As a con-sequence of the introduction of clumping, the mass-loss rateswere lowered by significant factors (from 3 to 10). The analysisof the high-resolution X-ray observations of the
Chandra and
XMM − Newton
X-ray observatories provided further support tothe idea of a reduced mass-loss rate. The strong emission linesproduced by H and He-like ions of O, Ne, Mg, and Si are farless strongly absorbed by the cold wind than previously expected(e.g., Cassinelli et al. 2001; Kahn et al. 2001). For example, Co-hen et al. (2006, 2010), Cohen et al. (2014), and Gagné et al.(2005) analyzed the bound-free absorption by the wind in mas-sive stars observed by
Chandra and found mass-loss rates thatwere up to ten times lower than previous estimates.Including X-ray regions into self-consistent stellar atmo-spheric models also resulted in the introduction of the non-vacuum interclump medium in the wind models. The only wayZsargó et al. (2008) were able to reproduce the strong O VI andN V lines in the far-UV (FUV) spectra of ζ Pup were to abandonthe assumption of vacuum between clumps. Now, we know thatthese super-ions are primarily produced by Auger ionization byX-rays in the rarified interclump medium (see also Puebla et al.2016). Furthermore, ideas to explain the low wind absorptionon the X-ray emission lines by Oskinova et al. (2004) that in-voked optically thick clumping, although they were refuted byOwocki & Cohen (2006) and Sundqvist et al. (2012), led to therecognition of the importance of velocity-space porosity (voros-ity) e ff ects on strong UV lines (Sundqvist et al. 2014; Sundqvist& Puls 2018, and references therein).Unfortunately, the ever improving sophistication of themodel calculations also means that running these codes and per-forming a reliable analysis is rather di ffi cult and requires muchexperience, which many researchers do not have enough timeto gain. It is therefore useful to develop databases of precalcu-lated models. Such databases will free up valuable time for as-tronomers who could study stellar atmospheres with reasonableaccuracy but with fewer time-consuming simulations. Further-more, these databases will not only accelerate the studies of thelarge number of observed spectra that are in line for analysis, butalso ensure that they are made in a uniform manner (e.g., usingthe same atomic data). This uniformity will also help to identifyand correct possible shortcomings in the codes that were used toproduce the database.The basic parameters of such databases of precalculatedmodels are the surface temperature ( T e ff ), the stellar mass ( M ),and the surface chemical composition. An adequate analysis ofmassive stars also has to take into account the parameters asso-ciated with the stellar wind, such as the terminal velocity ( V ∞ ),the mass-loss rate ( ˙M ), and the clumping. When the variationsof all necessary parameters are taken into account, the numberof precalculated models that are needed will increase exponen-tially. Production of such databases is therefore only possibleusing clusters of computers or supercomputers.A few databases of synthetic stellar spectra are currentlyavailable, but only with a few dozen or some hundred stellarmodels (see, e.g., Fierro et al. 2015; Hamann & Gräfener 2004;Palacios et al. 2010; Hainich et al. 2019). On the other hand,we here generate a database with tens of thousands of models(Zsargó et al. 2017) that will be publicly available in about Jan-uary 2021. It will be impossible to manually compare an ob-served spectrum with this many model calculations. It is there-fore imperative to develop tools that allow the automation ofthis process, but without compromising the quality of the fitting.Fierro-Santillán et al. (2018) presented FIT spec , the first of these tools, that searches our database for models that best fit the ob-served spectrum in the optical. It uses the Balmer lines to mea-sure the surface gravity (log g ) and the equivalent width ratiosof the He II and He I lines to estimate the surface temperature( T e ff ).In this article we describe the development state of our gridof precalculated models and the results of a test analysis to verifythe usefulness of the grid. In § 2 and § 2.1 we briefly describe thestellar atmosphere code (CMFGEN) that we use to produce ourmodels. Next, in § 3 we describe our model grid, and § 4 presentsa simple test analysis to demonstrate the benefits that our grido ff ers. Finally, in § 5 and 6 we summarize our conclusions.
2. CMFGEN
CMFGEN (Hillier 2013; Hillier & Miller 1998, 1999; Pueblaet al. 2016) is a sophisticated and widely-used nonlocal thermalequilibrium (non-LTE) stellar atmosphere code. It models thespectrum from the FUV to the radio wavelength range and hasbeen used successfully to model O and B stars, W-R stars, lumi-nous blue variables, and even supernovae. Recently, an experi-mental version of the code has been developed that included theX-ray region in the analysis (Zsargó et al. 2008; Puebla et al.2016), but this version has not yet been made public. CMF-GEN determines the temperature, the ionization structure, andthe level populations for all elements in the stellar atmosphereand wind. It solves the spherical radiative transfer equation in thecomoving frame in conjunction with the statistical equilibriumand radiative equilibrium equations. The hydrostatic structurecan be computed below the sonic point, allowing the simultane-ous treatment of spectral lines formed in the atmosphere, in thestellar wind, and in the transition region between the two. Suchfeatures make it particularly well suited to the study of massiveOB stars with winds. However, there is a price for this sophisti-cation: a typical CMFGEN simulation takes anywhere between24 and 36 hours of microprocessor time to complete.For atomic models, CMFGEN uses the concept of super lev-els, by which levels of similar energies are grouped together andtreated as a single level in the statistical equilibrium equations(see Hillier & Miller 1998, and references therein for more de-tails). The atomic model used in this project includes 37 ex-plicit ions of the di ff erent elements, which are summarized inTable 1 together with the levels and super levels included in ourmodel. The atomic data references are given in Herald & Bianchi(2004).To model the stellar wind, CMFGEN requires values for themass-loss rate ˙M , terminal velocity V ∞ , β parameter, and the vol-ume filling factor F cl . The profile of the wind speed is modeledby a β -type law (Castor et al. 1975), v ( r ) = V ∞ (cid:32) − rR (cid:63) (cid:33) β . (1)The β parameter controls how fast the stellar wind is acceleratedto reach the terminal velocity (see Fig. 1), while the volume fill-ing factor F cl is the standard method with which the atmosphericmodels introduce optically thin clumping in the wind (see, e.g.,Sundqvist et al. 2014, and references therein). In short, F cl givesthe average fraction of a volume element that is filled with ma-terial at the outer regions of the wind, where v ( r ) ∼ V ∞ . Betweenthese regions filled with material, called the clumps, CMFGENassumes a vacuum. Because of this assumption, we should notexpect that our models can reproduce the strong UV lines of thesuper-ions O VI and N V (see §1 for an explanation). Because Article number, page 2 of 22sargó et al.: Large grids of model atmospheres
Table 1.
Super levels and levels for the di ff erent ionization stages included in the models. Element I II III IV V VI VII VIIIH 20 /
30 1 / · · · · · · · · · · · · · · · · · · He 45 /
69 22 /
30 1 / · · · · · · · · · · · · · · · C · · · /
92 51 /
84 59 /
64 1 / · · · · · · · · · N · · · /
85 41 /
82 44 /
76 41 /
49 1 / · · · · · · O · · · /
123 88 /
170 38 /
78 32 /
56 25 /
31 1 / · · · Si · · · · · · /
33 22 /
33 1 / · · · · · · · · · P · · · · · · · · · /
90 16 /
62 1 / · · · · · · S · · · · · · /
44 51 /
142 31 /
98 28 /
58 1 / · · · Fe · · · · · · / /
540 50 /
220 44 /
433 29 /
153 1 / * v ( r ) / V ∞ β=0.5β=0.8 β=1.1β=1.4β=1.7β=2.0β=2.3 Fig. 1.
Examples of β -type velocity laws. The curves and the corre-sponding β values are color-coded. the continuity equation requires that the average wind densityis defined as (cid:104) ρ (cid:105) = ˙M / [4 π r v ( r )] = ρ cl f cl ( r ), the volume fillingfactor also tells us how the degree of overdensity in the clumpscompares to (cid:104) ρ (cid:105) . In CMFGEN the radial distribution of the vol-ume filling factor is described by the relation f cl ( r ) = F cl + (1 − F cl ) · exp (cid:34) − v ( r ) V cl (cid:35) , (2)where the parameter V cl controls how fast F cl is reached in thewind. The lower V cl , the faster and closer to the stellar surfacedoes the volume filling factor reach the value of F cl . During thegeneration of our models in the grid, we used the generic value V cl = . V ∞ . The auxiliary program CMF_FLUX of the CMFGEN package(Hillier 2013) computes the synthetic observed spectrum in theobserver’s frame, which is one of the most important outputsof our models. To simulate the e ff ects of rotation on the spectrallines, the synthetic spectra can also be rotationally broadened us-ing the program ROTIN3, which is part of the TLUSTY package(Hubeny & Lanz 1995).For each model in the grid, we calculate the normalizedspectra in the UV (900-3500Å), optical (3500-7000 Å), and IR(7000-40 000 Å) range. Then, we can apply rotation by samplingthe range between 10 and 350 km s − with steps of 10 km s − .
3. Model grid
In order to properly constrain the input parameters, we usedthe evolutionary tracks and isochrones of Ekström et al. (2012)calculated with solar metallicity ( Z = . ff erent evolution-ary tracks with initial masses between 0.8 and 120 M (cid:12) as wellas 37 isochrones for both rotating and stationary models. Therotating models start on the ZAMS with an equatorial rotationalvelocity V eq = crit that is later evolved as the star loses an-gular momentum through mass loss or magnetic braking. Thedi ff erential rotation within these stars gives rise to meridionalcirculation that enhances the surface chemical composition bymoving CNO-processed material from the interior to the surface.The theory of rotation is described in a series of papers by theGeneva group (Maeder 1999; Maeder & Meynet 2000, and ref-erences therein). We refer to these papers for more information.The predictions of Vink et al. (2001) were used to calcu-late mass loss for normal early-type stars and lower mass W-Rstars, and the recipe of Gräfener & Hamann (2008) was usedfor massive W-Rs. The evolution was computed until the end ofthe central carbon-burning phase, the early AGB phase, or thecore helium-flash for massive, intermediate, and low- and verylow-mass stars, respectively. The initial abundances were thosededuced by Asplund et al. (2009), which best fit the observedabundances of massive stars in the solar neighborhood. For eachtrack, Ekström et al. (2012) calculated 400 evolutionary stagesand provided the luminosity L , the surface temperature T e ff , andthe mass M together with mass-loss rates ˙M , the surface chemi-cal composition, and the parameters that describe the stellar in-terior (see Ekström et al. 2012, for more details). This coversall parameters that our models need, except for those that de-scribe the structure of the wind. For the stellar radius and log g we calculated values that are consistent with their published lu-minosities L , surface temperatures T e ff , and masses M by usingthe Stefan-Boltzmann law and the assumption of spherical sym-metry.The elements included in our models are H, He, C, N, O, Si,P, S, and Fe. The abundances of H, He, C, N, and O were takenfrom the tables of Ekström et al. (2012). For consistency, weassumed solar metallicity as reported by Asplund et al. (2009)for Si, P, S, and Fe in all models.We only had to improvise to describe the wind structure, thatis, to determine values for the terminal velocity V ∞ , β parameter,and volume filling factor F cl . These parameters have no rele-vance in the evolutionary calculations, therefore no values werereported in Ekström et al. (2012), but they are very important toreproduce observed spectra. The terminal velocity is thought tobe related to the escape velocity for hydrodynamical considera-tions. We therefore used V esc to estimate its values (where V esc Article number, page 3 of 22 & A proofs: manuscript no. manuscript38066 β l o g ( T e ff ) l o g ( L / L ⊙ ) β l o g ( T e ff ) l o g ( L / L ⊙ ) β l o g ( T e ff ) l o g ( L / L ⊙ ) β l o g ( T e ff ) l o g ( L / L ⊙ ) β l o g ( T e ff ) l o g ( L / L ⊙ ) β l o g ( T e ff ) l o g ( L / L ⊙ ) Fig. 2.
Hyper-cube plane formed by 3D datacubes. The dimensions of this plane are the di ff erent values of the volume filling factor ( F cl = β parameter. has its usual meaning). For β and F cl , we simply used the rangeof values reported in previous studies of massive stars to definethe grid.The grid is organized as hyper-cube data of dimensions thatcorrespond to V ∞ , F cl , and the metallicity, as illustrated in Fig. 2.For V ∞ we plan to use two values, a low- ( V ∞ = . V esc ) and ahigh- ( V ∞ = . V esc ) velocity model, to cover the range of ter-minal velocities reported in the literature. However, up to thepreparation of this paper we have only generated models for thehigher velocity. The hyper-cube in Fig. 2 therefore has only twodimensions, given by F cl and the metallicity. Each value of thevolume filling factor ( F cl = β , T e ff , and L , as illustrated by Fig. 2. Theplanes generated by each β parameter (with β = L and T e ff are restricted by theevolutionary tracks.In Figs. 3 to 5 (see also Fig. A.3 in the appendix) we showa sample of the H-R diagrams formed by our models in the dat-acubes. Obviously, during the generation of our grid we onlyconsider the region in the complete H-R diagram that is relevantfor massive stars with line-driven winds (O / B-types and W-Rs),therefore only the upper left part of the full H-R diagram is cov-ered by our models. We do not generate CMFGEN model foreach evolutionary stage that is shown in the figures (we do nothave the computing resources for this), only for the models thathave ˙M > − M (cid:12) yr − . The large blue stars in the figures mark Article number, page 4 of 22sargó et al.: Large grids of model atmospheres eff )3.54.04.55.05.56.06.5 l o g ( L / L ⊙ )
12 15 20 25 32 40 60 85120 : 3.2 Myr: 5.0 Myr: 7.9 Myr: 12.6 Myr: 20.0 Myr
WR O3 O5 O7 O9.7 B0.5 B2.5 β=2.0 F cl =0.05 Fig. 3.
Hertzsprung-Russel diagram for β = F cl = (cid:15) Ori. The numbers left of the evolutionary tracks are the initial masses of the tracks (in M (cid:12) ). They also markthe approximate location of the ZAMS. The red symbols below selected isochrones indicate their ages (in 10 years). At the top of the figure weindicate the approximate locations of selected spectral classes. the location of the models that best-fit the observations of (cid:15) Ori.We discuss the implication of the position of these models in §5.The coverage of the relevant part of the H-R diagram for thewind parameters is quite diverse, and generally better for inter-mediate masses than for the extremes. It is also quite clumpy,with clusters of models separated by gaps; this is not ideal forspectral analysis. The reason for this is technical, and it is the consequence of our strategy of optimizing the production of ourmodels. CMFGEN, like any other code that relies on iterativemethods to solve a nonlinear system of equations, needs goodinitial estimates to achieve secure convergence in reasonabletime. Because it is di ffi cult to produce such estimates, the firstmodels (the seed models) in a new region of the parameter spacecan be quite troublesome. They often fail to converge and can Article number, page 5 of 22 & A proofs: manuscript no. manuscript38066 eff )3.54.04.55.05.56.06.5 l o g ( L / L ⊙ )
12 15 20 25 32 40 60 85120 : 3.2 Myr: 5.0 Myr: 7.9 Myr: 12.6 Myr: 20.0 Myr
WR O3 O5 O7 O9.7 B0.5 B2.5 β=2.0 F cl =0.30 Fig. 4.
Same as Fig. 3, but for models with F cl = . run 3-4 times longer than a normal model. It is therefore wiseto minimize the number of seed models during the generation ofthe models and grow the grid around existing seed models thatcan provide good initial conditions for the next generations ofmodels. We use this strategy to optimize the usage of the com-puting facilities; however, this results in the clumpy distributionof models described above.We do not show any models for F cl =
1. The reason for this isclear from Figs. 6 and 7, which show the number distribution ofthe models as functions of the F cl and β parameters. Our cover-age for all other F cl volume filling factors is decent and we havemany models (43,340), but not for F cl =
1. The coverage for this volume filling factor is so low that it is pointless to show anyH-R diagrams. Fortunately, it is highly unlikely that modelersencounter a wind that has no density structures (clumps) at all.Calculations with F cl = ff er to use it. It will be freelyavailable for any interested researcher by the end of 2020. Article number, page 6 of 22sargó et al.: Large grids of model atmospheres eff )3.54.04.55.05.56.06.5 l o g ( L / L ⊙ )
12 15 20 25 32 40 60 85120 : 3.2 Myr: 5.0 Myr: 7.9 Myr: 12.6 Myr: 20.0 Myr
WR O3 O5 O7 O9.7 B0.5 B2.5 β=2.0 F cl =0.60 Fig. 5.
Same as Fig. 3, but for models with F cl = . Finally, we would like to justify our choices of parametersand comment on future expansions of the grid. It might right-fully be argued that we ignore some important parameters in thegrid. The most consequential omission is the turbulent velocitybecause it a ff ects the analysis of optical He lines. Instead of ex-ploring these e ff ects, we simply use a generic V turb =
20 km s − throughout the wind. Furthermore, we should not really use thesame ionic species for the hottest O-type and for the B-type starsbecause the ionization level of elements can be di ff erent for thesestars (the most notable example is Fe). However, we have lim-ited access to the computational resources, and compromises andhard choices have to be made. With our selection of parameter space, we intend to create a grid that is sophisticated enough tobe useful in the analysis of observed spectra, but the computa-tional requirements of its production stay within the limits. It isnot a trivial task to achieve this compromise because the limitscan easily be exceeded by introducing a seemingly minor adjust-ment in the parameter space.Nevertheless, if there is future demand for an expansion ofthe parameter space (e.g., have a range in turbulent velocity), wewill address it with a follow-up project. The grid can be aug-mented in the future, and not only by us, if su ffi cient computingresources are available. Furthermore, there are ways to improveour grid that do not involve running more models on supercom- Article number, page 7 of 22 & A proofs: manuscript no. manuscript38066 β F c l N u m b e r o f m o d e l s Fig. 6.
Distribution of the 24,423 models with no rotational enhancement that are currently available as functions of wind parameters. The color-coding is to help visualize the models that correspond to the same F cl volume filling factor. β F c l N u m b e r o f m o d e l s Fig. 7.
Same as Fig. 6, but for the 18,917 models with rotational enhancement that are currently available in the grid. puters. We can, for example, appeal to the users of CMFGENto donate their no longer needed models to the grid. We suspectthat there are hundreds or even thousands of models sitting idlein computers around the world. Including such a diverse set ofmodels into our grid will be challenging, but might be feasible.We describe our choice of parameter space in the context ofthe intended purpose of the grid. We wish to provide a tool foreasy and rapid analysis of the stellar spectra that will serve wella variety of special applications where the need for rapid analy-sis outweighs the need for high-accuracy parameter determina-tion. Examples of such applications include statistical analysesof large stellar samples or population synthesis models. How-ever, we do not mean to replace the traditional modeling by using only the grid for a detailed analysis of a particular star. In suchcases, the investigators still have to fine-tune the parameters byrunning models with the code of their preference (which doesnot have to be CMFGEN) to complete the task. Using the gridwill speed up the analysis by eliminating the need to run numer-ically costly seed models in the early phases of the investigation,and will provide good initial conditions for the fine-tuning phase.The time saving is very significant. For example, our reanalysisof (cid:15)
Ori lasted only about two days, while the duration of theoriginal work by Puebla et al. (2016) was several weeks. We aretalking about a five- to tenfold decrease in the required time.
Article number, page 8 of 22sargó et al.: Large grids of model atmospheres
4. Simple test to demonstrate the usefulness of ourgrid
We demonstrate the benefits that our grid o ff ers by reanalyzing (cid:15) Ori. This B0 Ia supergiant was recently studied by Puebla et al.(2016) in the traditional way, that is, by producing every modelthat was needed for the analysis. Some members of our teamwere part of the group that performed this study, and so they hadaccess to the observational data used in the work of Puebla et al.(2016). It is therefore convenient and very useful to see the resultwe would obtain by using the models available in our grid andwithout running CMFGEN at all. Before presenting our results,we have to mention some limitations that our reanalysis has incomparison with the original study. For example, Puebla et al.(2016) used the experimental version of CMFGEN and includedhigh-resolution X-ray observations in the analysis to augmentthe UV and optical spectra. Because we are used the commonlyavailable version of CMFGEN, we cannot reproduce their re-sults in the X-ray range and so we cannot verify the additionalinformation gained by using this spectral range (e.g., additionalconstraints on the mass-loss rate and abundances). Furthermore,our models assume vacuum in the interclump medium, as op-posed to theirs, which included tenuous but not empty regionsbetween the clumps. By doing so, they successfully reproducedthe FUV O VI and N V lines, which we were not able to do.Nevertheless, in the following sections we demonstrate that wecan reproduce their results quite well and that process in a spec-tral analysis can be made by using our grid and before runningany simulation.Finally, we note that because we used the very same obser-vations in our analysis as Puebla et al. (2016) did, we omit thedescription of the data reduction and the observations in this pa-per. We refer to the relevant sections of Puebla et al. (2016) formore information on this subject. (cid:15) Ori (HD37128)
This supergiant star is the central star of the Orion belt and be-longs to the Orion OB1 association. It has been studied manytimes in the past. The most recent works include Kudritzki et al.(1999), who found T e ff = ,
000 K and log g = .
00 for this starusing the code FASTWIND, as well as a series of CMFGENstudies by Crowther et al. (2006), Searle et al. (2008), and Pueblaet al. (2016). The first two authors found very similar e ff ectivetemperatures, that is, 27,000 and 27,500 K, respectively, but theydiverged significantly in the value of log g (2.9 and 3.1, respec-tively). Previous studies also reported a wide range of mass-lossrates, but in general, lower than 5 . × − M (cid:12) yr − . The majorityof these studies assumed smooth wind (no clumping).However, the most relevant results for our analysis are thosefound by Puebla et al. (2016). They reported T e ff = , ±
500 K, log g = . ± .
05, a mass-loss rate of ˙M ∼ − M (cid:12) yr − , V ∞ ∼ − , and a highly clumped and slowly accelerat-ing wind ( F cl = . β > .
0) for (cid:15)
Ori. However, their volumefilling factor is not really well defined because of uncertaintiesin considering the degree to which the UV lines are a ff ected bythe velocity-space porosity. If they are not a ff ected too much, thewind has to be very clumped and the mass-loss rate has to be lowin order to fit the S IV λλ V λλ F cl = .
01, 0.05, 0.1, and 1.0as their best models, each with mass-loss rates adjusted to con-serve the ratio ˙M / √ F cl ∼ . × − M (cid:12) yr − . We refer to theirTables 4 and 5 to learn more about their best results. Table 2.
Weights used by FIT spec for (cid:15)
Ori.
Lines or ratios Initial weights Final weights T e ff fit:He II / He I II / He I II / He I II / He I g fit:H I 3835 0.17 0.17H I 3889 0.17 0.17H I 3970 0.17 0.17H I 4102 0.17 0.17H I 4341 0.17 0.16H I 4861 0.17 0.16Combined fit:Ratios He II / He I I As previously mentioned, we intend to provide tools that aid thecomparison of the model and observed spectra and acceleratethe search for the best-fitting models. FIT spec , the first of thesetools, is already operational, therefore it is natural to start ourreanalysis of (cid:15)
Ori by applying this code. To start an analysis byFIT spec , the user must measure the equivalent widths (EWs) inthe observations of the λλ II λλ I λλ I + He II blend at λ spec has a complete library of the EWs for theselines measured in each model spectra of the grid. Instrumentaland rotational broadening of the observed spectra are not of con-cern because they do not a ff ect the measured EWs.FIT spec uses the EW of the Balmer lines and the EW ratiosof He II and He I lines to search for the best-fitting models in thelog g – T e ff space. The strategy is the following. First, the codecalculates the ratios ofEW(He II λ λ , (3)EW(He II λ λ , (4)EW(He II λ λ , (5)EW(He II λ λ , (6)then the relative di ff erences, or as we call them, the " errors " , arecalculated byError EW = EW obs − EW model EW obs . (7)for each H Balmer line, and byError (cid:32) He IIHe I (cid:33) = (cid:16) He IIHe I (cid:17) obs − (cid:16) He IIHe I (cid:17) model (cid:16)
He IIHe I (cid:17) obs . (8) Article number, page 9 of 22 & A proofs: manuscript no. manuscript38066
Table 3.
Models in the grid that best fit the observations of (cid:15)
Ori
Parameter Model 1 Model 2 Model 3 T e ff (K) 26,540 26,540 26,980L (10 L (cid:12) ) 4.196 4.196 4.491log g (cid:12) ) 30.62 30.62 30.65 ˙M (10 − M (cid:12) yr − ) 1.526 3.737 10.82 V ∞ (km s − ) 1,414 1,414 1,473 β F cl v sin i (km s − ) 80 80 80M ini a ( M (cid:12) ) 40 40 44Age a (10 yr) 4.47 4.47 3.98X(He) a a a a a Solar without rotational enhancement a From the evolutionary models of Ekström et al. (2012).for each He II to He I ratios defined by Eqs. (3)–(6).FIT spec then calculates the weighted averages of these er-rors, where the weights need to be specified by the user a priori.Weights are usually assigned to lines that reflect the quality oftheir signal-to-noise ratio (S / N) (see Table 2 for the weights weused for (cid:15)
Ori). Then, models with average errors smaller than30% in either the EWs of the H Balmer lines or the EW ratiosof the He lines are selected, and among these models FIT spec identifies the model that has the smallest total error,Error tot = (cid:115)(cid:88) (Error EW ) + (cid:88) (cid:34) Error (cid:32)
He IIHe I (cid:33)(cid:35) , (9)where the summation is over all H lines and He ratios. Then, theuser has the option to adjust the weights, if necessary, and restartthe procedure. After a few iterations, the best-fitting models arefound. More about the code FIT spec and the way it works canbe found in Fierro-Santillán et al. (2018).After running FIT spec , we found that models with T e ff = ± g = ± After identifying the relevant parameter ranges in T e ff and log g by FIT spec , we visually inspected the models within theseranges. This was done with another tool that we created to help inthe search for best-fitting models. The tool allows selecting spe-cific lines from any wavelength region for display on the screenand compare the observations with selected models. The displayis very similar to Fig. 9, for example. Several of our figures aresimple snapshots of this display. Then, we can browse through anumber of models and visually inspect the fit. The user has theoption of changing the parameter ranges of the models that arequeued for inspection, to apply rotational or instrumental broad-ening to the model spectra, to Doppler-shift them, zoom in andout, and the displayed lines can also be changed. The compar-ison can be made in the form of normalized or calibrated fluxspectra. Unfortunately, the interaction with the code is not yetuser-friendly, therefore we have not yet released it. However, we are developing a graphic user interface to make it user friendly.When this code is optimized and easy to apply, it will be releasedand will be a powerful tool if used in combination with FIT spec .With the help of FIT spec we were able to decrease the num-ber of models that are to be inspected visually to a few hun-dred, and then applied a rotational broadening with v sin i = − . The convolution of the model spectra with a broad-ening profile adequately accounts for the rotation and macro-turbulence for slowly rotating stars (Hillier et al. 2012). Wind-free line profiles were used to estimate the projected rotationalvelocity v sin i . After several hours of inspection, we then foundthat 26,500 K < T e ff < < log g < β = ± V ∞ ≥ − are the best values for the stellar and windparameters (see the parameters of the best-fitting models in Ta-ble 3). The error estimates are based on the ranges of acceptablemodels and on the parameter resolutions that we have in the grid.Unfortunately, we were only able to derive a lower limit for V ∞ because the coverage that our grid still has in this parameter islimited. For the mass-loss rates we found that ˙M could vary be-tween 1 . × − M (cid:12) yr − and 1 . × − M (cid:12) yr − , depending onthe adopted F cl so that ˙M / √ F cl ∼ . × − M (cid:12) yr − is approx-imately conserved. Our analysis mildly favors the combinationof ˙M = . × − M (cid:12) yr − with F cl = ff ects the UV resonance lines (see the dis-cussion in §5). These values agree well with the results of pre-vious studies. Figs. 8–13 show our best-fitting models with theobserved spectra for important H, He, C, N, O, and S lines. Inthe following, we discuss how the di ff erent parameters a ff ect thespectral diagnostics and describe our results.Fig. 8 shows how well our models fit the Balmer series ofhydrogen, especially the model with the highest mass-loss rate(Model 3 in Table 3 and the dashed black lines in Fig. 8). TheBalmer series is normally used to measure log g , but the figurereveals that other parameters also a ff ect the H lines. For exam-ple, there is a significant e ff ect due to mass loss as the absorptionprofiles of H α and H β are filled in by the emission from the wind.We also observe significant di ff erences in the synthetic profilesfor di ff erent values of F cl , especially in the case of H α . However,the line profiles should not vary with F cl if the mass-loss rate isadjusted to conserve ˙M / √ F cl . As we explain in § 5, because ofthe way in which CMFGEN introduces clumping (see Eq. (2))and the slow acceleration of the wind of (cid:15) Ori, an extended tran-sition zone exists between the smooth wind near the stellar sur-face and the outer region with constant F cl . This transition zonehas a profound e ff ect on the profiles of the lower order Balmerlines. Fortunately, the e ff ects of the wind emission are negligibleon the higher order Balmer lines, as Fig. 8 clearly shows, so wecan use them to measure log g . The good fit between the mod-els and the observations in the wings of these lines (see the toppanels of Fig. 8) suggests that the most probable value of log g is about 3.Fig. 9 shows the comparison of our best-fitting models withthe optical He I and He II lines observed for (cid:15) Ori. Although theHe II lines are very weak for this star, the comparison clearlyindicates that T e ff has to be about 27,000 K. No other parametersignificantly a ff ects the He lines, at least in the parameter spacethat we use in our grid. The derived T e ff is also consistent withthe observed C, N, O, and S lines, as illustrated by Figs. 10–13.These figures show lines that originate from consecutive ioniza-tion levels and do not suggest that T e ff needs to be revised. Thefit is surprisingly good considering the limited resolution andcovering that our grid has in the parameter space. Figs. 11–13also indicate that the abundances of N, O, and S are about rightin the best-fitting models, while Fig. 10 suggests that we should Article number, page 10 of 22sargó et al.: Large grids of model atmospheres T eff = 26980 K log(g)= 3.1 X(H )= 0.3 X(CNO)= 8.7E-03 0M=1.1E-06 M ̇.) F cl = 0.60 β= ⊙.0 T ff = ⊙6540 K l(g(g)= 3.0 X(H )= 0.3 X(CNO)= 8.7E-03 0M=1.5E-07 M ̇.) F cl = 0.05 β= ⊙.0 T ff = ⊙6540 K l(g(g)= 3.0 X(H )= 0.3 X(CNO)= 8.7E-03 0M=3.7E-07 M ̇.) F cl = 0.30 β= ⊙.0 Wav l ngth (Å) N ( ) m a li / d f l u - Fig. 8.
Comparison of our best-fitting models (dashed black, red, and blue lines) with the observed H I lines for (cid:15)
Ori (solid gray line). The relevantmodel parameters are color-coded above the panels. lower the carbon abundance by a factor of few. In this figure allsynthetic profiles are stronger than the observations, regardlessof the level of ionization. This conclusion agrees very well withthe findings of Puebla et al. (2016), who needed a C abundancea factor of 2 to 4 lower than those in our models to fit these lines.However, the objective of this paper is to show how closely wecan match the right stellar and wind parameters by using onlythe grid, therefore we did not adjust the carbon abundance.The most useful spectral region to estimate the mass-lossrate ˙M and terminal velocity V ∞ is the UV region. Here, we en-counter strong resonance lines of the dominant ionization statesin the winds of massive stars. These resonance lines often showP-Cygni profiles, which are useful for measuring ˙M and V ∞ (see, e.g., the C IV doublet around 1550 Å or the Si IV dou-blet around 1400 Å in Fig. 14). Unfortunately, we cannot repro-duce many of these lines well for various reasons. For example, we have a problem to fit the N V doublet around 1240 Å be-cause our models do not include interclump medium. The UVregion is also not useful for estimating the β -parameter and F cl because most of the P-Cygni profiles are saturated (and proba-bly strongly a ff ected by vorosity). To derive mass-loss rates, theUV spectra show a somewhat contradictory situation. While theSi IV λλ ˙M to fit theC IV λλ ˙M > . × − M (cid:12) yr − would result in H α emission,which is not observed. We therefore conclude that 1 . × − M (cid:12) yr − > ˙M > − M (cid:12) yr − is the best estimate we can have.The actual value depends on the adopted F cl . Fig. 14 also showsthat the terminal velocity has to be higher than 1,500 km s − ,but our grid does not yet have the necessary coverage in V ∞ todetermine its exact value. Article number, page 11 of 22 & A proofs: manuscript no. manuscript38066
He I
He I
He I
He I
He I
He I
He I
He I
He I
He II
He II
He II T eff = 26980 K log(g)= 3.1 X(H )= 0.3 X(CNO)= 8.7E-03 0M=1.1E-06 M ̇.) F cl = 0.60 β= ⊙.0 T ff = ⊙6540 K l(g(g)= 3.0 X(H )= 0.3 X(CNO)= 8.7E-03 0M=1.5E-07 M ̇.) F cl = 0.05 β= ⊙.0 T ff = ⊙6540 K l(g(g)= 3.0 X(H )= 0.3 X(CNO)= 8.7E-03 0M=3.7E-07 M ̇.) F cl = 0.30 β= ⊙.0 Wav l ngth (Å) N ( ) m a li / d f l u - Fig. 9.
Same as Fig. 8, but the comparison is for the He I and He II lines.
5. Discussion
In Figs. A.1 and A.2 we show the general comparisons of ourbest models (dashed black, red, and blue lines) with the obser-vations (gray lines). With these figures we intended to reproduceFigs. A1–A3 in the appendix of Puebla et al. (2016) for an easycomparison of our and their results. These figures also show thatthe overall fit in the optical range is very good, especially for themodel with ˙M = . × − M (cid:12) yr − and F cl = .
6. However, aswas mentioned earlier, there are significant discrepancies in theUV.The top panel of Fig. 14 shows that our models lack the O VI profile around 1032 Å, which is expected because our models do not take the interclump medium into account. A graver problemis that S IV around 1070 Å is too strong for our models, espe-cially for ˙M = . × − M (cid:12) yr − and F cl = .
6. The same problemled Puebla et al. (2016) to the conclusion that the wind is ex-tremely clumped ( F cl ∼ .
01) and ˙M is low. However, they havealready raised the possibility that the fact that CMFGEN doesnot yet take the velocity-space porosity into account might be re-sponsible for the anomalously strong S IV profiles in the models.Since the publication of their paper, several studies have con-cluded that the UV P-Cygni profiles should indeed be a ff ectedstrongly by the vorosity e ff ects. For example, one of the mainconclusion of Sundqvist & Puls (2018) was that velocity-spaceporosity is critical (in their words) for the analysis of UV reso- Article number, page 12 of 22sargó et al.: Large grids of model atmospheres T eff = 26980 K log(g)= 3.1 X(H )= 0.3 X(CNO)= 8.7E-03 0M=1.1E-06 M ̇.) F cl = 0.60 β= ⊙.0 T ff = ⊙6540 K l(g(g)= 3.0 X(H )= 0.3 X(CNO)= 8.7E-03 0M=1.5E-07 M ̇.) F cl = 0.05 β= ⊙.0 T ff = ⊙6540 K l(g(g)= 3.0 X(H )= 0.3 X(CNO)= 8.7E-03 0M=3.7E-07 M ̇.) F cl = 0.30 β= ⊙.0 Wav l ngth (Å) N ( ) m a li / d f l u - Fig. 10.
Same as Fig. 8, but the comparison is for selected C lines. nance lines in O stars. Taking these e ff ects into account might fixour problems because it would weaken these lines for the same ˙M . In short, the theory of velocity-space porosity assumes that asthe material is swept up in dense clumps, the process also createsgaps in the velocity distribution of the material. These gaps thenallow the escape of radiation that otherwise would be absorbedin smooth wind.A possible other solution for the weak P-Cygni profiles in theobservations could be the low abundances of the species in ques-tion. This possibility was raised and quickly dismissed when thesame problem was encountered with the P V λλ ffi cult it is to es-timate the parameters F cl and β . We have essentially one diag-nostic, H α , which is a ff ected by multiple other parameters. Fit-ting H α is also where our results di ff er the most from those ofPuebla et al. (2016). They found that the highly clumped wind( F cl < .
05) fits this line the best, while our results suggest a much lower degree of clumping ( F cl ∼ .
6) and a higher mass-loss rate. Most of the di ff erence originates from the di ff erent ra-dial distribution of the true volume filling factor, f cl ( r ), in ourmodels (see Eq. (2) for its definition). While we use a genericvalue V cl = . V ∞ in Eq. (2), they used a very low value of V cl ∼
50 km s − . The value we use creates a large transitionalzone at the base of the wind for slowly accelerating models( β > . F cl is the volume filling factorat large radii, where v ( r ) ∼ V ∞ in the parameterization of CM-FGEN, and it does not mean that f cl ( r ) = F cl at every radius. InFig. 15 we show the true radial distribution of ˙M / (cid:112) f cl ( r ) calcu-lated by using our best-fitting β and V cl parameters for a typicalO star, and what these models would have if we had used the V cl value of Puebla et al. (2016). The quantity ˙M / (cid:112) f cl ( r ) is im-portant because it controls the emission by the recombination ofH II in the wind (assuming that the ionization structure of hydro-gen is similar in the models). The panels in Fig. 15 show that thevalues of ˙M / (cid:112) f cl ( r ) are always higher at every radius for modelswith smaller V cl (and with all other parameters being the same),and this excess is greater and extends to much larger radii forhighly clumped (low F cl ) and slowly accelerating (high β ) mod- Article number, page 13 of 22 & A proofs: manuscript no. manuscript38066 T eff = 26980 K log(g)= 3.1 X(He)= 0.3 X(CNO)= 8.7E-03 1M=1.1E-06 M ⊙ ̇/r F cl = 0.60 β= 2.0 T eff = 26540 K log(g)= 3.0 X(He)= 0.3 X(CNO)= 8.7E-03 ̇M=1.5E-07 M ⊙ //r F cl = 0.05 β= 2.0 T eff = 26540 K log(g)= 3.0 X(He)= 0.3 X(CNO)= 8.7E-03 ̇M=3.7E-07 M ⊙ ̇/r F cl = 0.30 β= 2.0 Wavelength (Å) N o r m a li z e d f l u x Fig. 11.
Same as Fig. 8, but the comparison is for selected N lines. els. This means that the models of Puebla et al. (2016) producemuch more emission in the crucial dense internal part of the windthan ours, especially for smaller F cl and larger β . This explainswhy our results favor a higher mass-loss rate and a lower levelof clumping when the same H α profile is analyzed. Finally, wewould like to stress that the di ff erence would be smaller if thewind of (cid:15) Ori had accelerated normally ( β < ffi cult to judge which distribution is more realistic be-cause the hydrodynamic simulations are quite fuzzy on this sub-ject (see, e.g., Runacres & Owocki 2002). The simulations sug-gest that the wind is smooth near the stellar surface and predicta transitional zone, but they are not clear about the size of thiszone. The motivation behind using an Eq. (2) type distribution isexactly to reproduce these characteristics and to recognize thatthe clumping scales with the wind velocity, that is, the faster thewind, the more clumped. The wind of (cid:15) Ori is already anomalousin the sense that it likely accelerates slowly. Theoretical calcula-tions (e.g., Castor et al. 1975) predict β -values lower than unity.The question then is that if a star has a slowly accelerating wind( β ∼
2) and if the clumping scales with the wind velocity, whywould the prescribed F cl at V ∞ be reached rapidly? Nevertheless,we are not in the position to decide which distribution is more realistic, therefore we consider all the models with F cl = . F cl = .
3, and F cl = . ff ected by vorosity.Finally, we would like to comment on the evolutionary sta-tus of (cid:15) Ori. A pleasant side-e ff ect of using actual evolutionarycalculations to create stellar atmosphere models is that the resultcomes with immediate information on the evolutionary status ofthe subject star. As shown in the H-R diagrams of Figs. 3–5 aswell as in Table 3, the locations of the best-fitting models arenear the terminal age main sequence (TAMS) of the evolution-ary track for M ini ∼ M (cid:12) . Furthermore, Table 3 shows that allthe best-fitting models are from the batch that was calculatedwithout considering the rotational enhancement in the surfaceabundances, which indirectly suggest that the star rotates slowly.This is consistent with the fact (cid:15) Ori has low v sin i .
6. Summary
We presented a mega grid of 43,340 stellar atmospheric modelscalculated by the CMFGEN package, which will soon be ex-
Article number, page 14 of 22sargó et al.: Large grids of model atmospheres
O II
O II
O II
O II
O II
O II
O III
O III
O V T eff = 26980 K log(g)= 3.1 X(He)= 0.3 X(CNO)= 8.7E-03 1M=1.1E-06 M ⊙ ̇/r F cl = 0.60 β= 2.0 T eff = 26540 K log(g)= 3.0 X(He)= 0.3 X(CNO)= 8.7E-03 ̇M=1.5E-07 M ⊙ //r F cl = 0.05 β= 2.0 T eff = 26540 K log(g)= 3.0 X(He)= 0.3 X(CNO)= 8.7E-03 ̇M=3.7E-07 M ⊙ ̇/r F cl = 0.30 β= 2.0 Wavelength (Å) N o r m a li z e d f l u x Fig. 12.
Same as Fig. 8, but the comparison is for selected O lines. tended to 80,000 models. These models cover the region of theH–R diagram that is populated by OB main-sequence and W-Rstars with masses between 9 and 120 M (cid:12) . The grid provides UV,visual, and IR spectra for each model.We used the surface temperature ( T e ff ) and luminosity ( L )values that correspond to the evolutionary traces and isochronesof Ekström et al. (2012). Furthermore, we used seven values of β ,four values of the clumping factor, and two di ff erent metallicitiesand terminal velocities. This generated a six-dimensional hyper-cube of stellar atmospheric models that we intend to release tothe general astronomical community as a free tool for analyzingthe spectra of massive stars. We have also demonstrated the usefulness of our mega-grid by reanalyzing (cid:15) Ori. Our somewhat crude but very rapidanalysis supported the stellar and wind parameters reported byPuebla et al. (2016). The only significant di ff erence is that ourreanalysis favors the high end of the acceptable mass-loss range( ˙M ∼ . × − M (cid:12) yr − ) with a lower level of clumping. Thisresult indirectly supports recent simulations that suggest that theUV resonance lines are highly a ff ected by velocity-space poros-ity. The reason for the slightly di ff erent conclusion of our reanal-ysis is that we used a generic radial distribution of clumping,while Puebla et al. (2016) customized the distribution to (cid:15) Ori. Itis not clear that our distribution is worse.
Article number, page 15 of 22 & A proofs: manuscript no. manuscript38066 T eff = 26980 K log(g)= 3.1 X(He)= 0.3 X(CNO)= 8.7E-03 2M=1.1E-06 M ̇0r ⊙ l = 0.60 β= 2.0 T eff = 26540 K log(g)= 3.0 X(He)= 0.3 X(CNO)= 8.7E-03 2M=1.5E-07 M ̇0r ⊙ l = 0.05 β= 2.0 T eff = 26540 K log(g)= 3.0 X(He)= 0.3 X(CNO)= 8.7E-03 2M=3.7E-07 M ̇0r ⊙ l = 0.30 β= 2.0 Wa.ele)gth (Å) N o r ( a li e d f l - / Fig. 13.
Same as Fig. 8, but the comparison is for selected S lines.
The reanalysis showed the benefits of having a large grid ofprecalculated models. The stellar and wind parameters for a starcan be calculated rapidly. If required, a more detailed study canthen be performed, but by starting with good initial values. Thissignificantly shortens the time that is needed to complete a spec-tral analysis.
Acknowledgements.
All models and their synthetic spectra were calculated bythe cluster Abacus I. The authors express their acknowledgement for the re-sources, expertise and the assistance provided by "ABACUS" Laboratory ofApplied Mathematics and High Performance Computing CINVESTAV-IPN,CONACyT-EDOMEX-2011-C01-165873 Project. The authors are also gratefulto D.J. Hillier, the author of the code CMFGEN, for his helpful comments duringthe production of the grid and during the preparation of this article. J. Zsargo ac-knowledges CONACyT CB-2011-01 No. 168632 grant for support. J. Klapp ac-knowledges financial support by the Consejo Nacional de Ciencia y Tecnología(CONACyT) of México under grant 283151. The authors also acknowledge theanonymous referee for his or her helpful comments and suggestions.
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Article number, page 16 of 22sargó et al.: Large grids of model atmospheres
He IIO VI S IV
H IC III N VS IIISi III P V
C II O V Si IVFe V Fe V
He IIC IV Fe IV T eff = 26980 K log(g)= 3.1 X(He)= 0.3 X(CNO)= 8.7E-03 3M=1.1E-06 M ⊙ ̇1r F c( = 0.60 β= ⊙.0 T eff = ⊙6540 K log(g)= 3.0 X(He)= 0.3 X(CNO)= 8.7E-03 3M=1.5E-07 M ⊙ ̇1r F c( = 0.05 β= ⊙.0 T eff = ⊙6540 K log(g)= 3.0 X(He)= 0.3 X(CNO)= 8.7E-03 3M=3.7E-07 M ⊙ ̇yr F c( = 0.30 β= 2.0 W /e(eng-h (Å) N o r ) (i e d f ( . Fig. 14.
Comparison of our best-fitting models (dashed black, red, and blue lines) with the UV spectra observed for (cid:15)
Ori (solid gray line). Therelevant model parameters are color-coded above the panels, and important UV lines marked above the spectra. ⊙ r −1 , F cl =0.05(dashed) β=0.5, V cl =V ∞ /10(solid) β=2.0, V cl =V ∞ /10(dashed) β=0.5, V cl =V ∞ /40(solid) β=2.0, V cl =V ∞ /40r/R * ̇ M / √ f c l ( r ) ( − M ⊙ r − ) ⊙ r −1 , F cl =0.30(dashed) β=0.5, V cl =V ∞ /10(solid) β=2.0, V cl =V ∞ /10(dashed) β=0.5, V cl =V ∞ /40(solid) β=2.0, V cl =V ∞ /40r/R * ̇ M / √ f c l ( r ) ( − M ⊙ r − ) ⊙ r −1 , F cl =0.60(dashed) β=0.5, V cl =V ∞ /10(solid) β=2.0, V cl =V ∞ /10(dashed) β=0.5, V cl =V ∞ /40(solid) β=2.0, V cl =V ∞ /40r/R * ̇ M / √ f c l ( r ) ( − M ⊙ r − ) Fig. 15.
True value of the ratio ˙M / (cid:112) f cl ( r ) as a function of r / R (cid:63) for a typical O type star (relevant parameters are color-coded and listed above andin the body of each panel). This ratio controls the wind emission due to recombination of ionized hydrogen, i.e., the higher its value, the greaterthe emission. We used Eq. (2) with the di ff erent values of V cl (color-coded in the body of each figure) to calculate f cl .Article number, page 17 of 22 & A proofs: manuscript no. manuscript38066
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Appendix A:
Article number, page 19 of 22 & A proofs: manuscript no. manuscript38066 H I H I H e I H e I H e I H e I H e I H I H e I H e I H e II C III O II O II S i I V S i I V S i I V H I H e I H e I C II N III N III O II O II O II O II O II O III S III S III M g II T eff = 26980 K log(g)= 3.1 X(He)= 0.3 X(CNO)= 8.7E-03 2M=1.1E-06 M ⊙ ̇0r ⊙ l = 0.60 β= 2.0 T eff = 26540 K log(g)= 3.0 X(He)= 0.3 X(CNO)= 8.7E-03 2M=1.5E-07 M ⊙ ̇0r ⊙ l = 0.05 β= 2.0 T eff = 26540 K log(g)= 3.0 X(He)= 0.3 X(CNO)= 8.7E-03 2M=3.7E-07 M ⊙ ̇0r ⊙ l = 0.30 β= 2.0 Wa.ele)gth (Å) N o r ( a li e d f l - / Fig. A.1.
Comparison of our best-fitting models (dashed black, red, and blue lines) with the blue part of the optical spectra for (cid:15)
Ori (solid grayline). The relevant parameters are color-coded and listed above the figure, and important lines are indicated above the spectra.Article number, page 20 of 22sargó et al.: Large grids of model atmospheres
He II He IIC III + N III/N IIN III O II O II O IIS IV Si III Si IIISi III
H IHe I He IO II
He II C IIIN IIO III O III Si III
H I He IC II T eff = 26980 K log(g)= 3.1 X(He)= 0.3 X(CNO)= 8.7E-03 3M=1.1E-06 M ⊙ ⊙1r F c( = 0.60 β= 2.0 T eff = 26540 K log(g)= 3.0 X(He)= 0.3 X(CNO)= 8.7E-03 3M=1.5E-07 M ⊙ ⊙1r F c( = 0.05 β= 2.0 T eff = 26540 K log(g)= 3.0 X(He)= 0.3 X(CNO)= 8.7E-03 3M=3.7E-07 M ⊙ ⊙yr F c( = 0.30 β= 2.0 W /e(eng-h (Å) N o r ) (i e d f ( . Fig. A.2.
Same as Fig. A.1, but for the central region of the optical spectra. Article number, page 21 of 22 & A proofs: manuscript no. manuscript38066 eff )3.54.04.55.05.56.06.5 l o g ( L / L ⊙ )
12 15 20 25 32 40 60 85120 : 3.2 Myr: 5.0 Myr: 7.9 Myr: 12.6 Myr: 20.0 Myr
WR O3 O5 O7 O9.7 B0.5 B2.5 β=0.5 F cl =0.05 4.24.44.64.8 log(T eff )3.54.04.55.05.56.06.5 l o g ( L / L ⊙ )
12 15 20 25 32 40 60 85120 : 3.2 Myr: 5.0 Myr: 7.9 Myr: 12.6 Myr: 20.0 Myr
WR O3 O5 O7 O9.7 B0.5 B2.5 β=0.5 F cl =0.054.24.44.64.8 log(T eff )3.54.04.55.05.56.06.5 l o g ( L / L ⊙ )
12 15 20 25 32 40 60 85120 : 3.2 Myr: 5.0 Myr: 7.9 Myr: 12.6 Myr: 20.0 Myr
WR O3 O5 O7 O9.7 B0.5 B2.5 β=0.5 F cl =0.30 4.24.44.64.8 log(T eff )3.54.04.55.05.56.06.5 l o g ( L / L ⊙ )
12 15 20 25 32 40 60 85120 : 3.2 Myr: 5.0 Myr: 7.9 Myr: 12.6 Myr: 20.0 Myr
WR O3 O5 O7 O9.7 B0.5 B2.5 β=0.5 F cl =0.304.24.44.64.8 log(T eff )3.54.04.55.05.56.06.5 l o g ( L / L ⊙ )
12 15 20 25 32 40 60 85120 : 3.2 Myr: 5.0 Myr: 7.9 Myr: 12.6 Myr: 20.0 Myr
WR O3 O5 O7 O9.7 B0.5 B2.5 β=0.5 F cl =0.60 4.24.44.64.8 log(T eff )3.54.04.55.05.56.06.5 l o g ( L / L ⊙ )
12 15 20 25 32 40 60 85120 : 3.2 Myr: 5.0 Myr: 7.9 Myr: 12.6 Myr: 20.0 Myr
WR O3 O5 O7 O9.7 B0.5 B2.5 β=0.5 F cl =0.60 Fig. A.3.
Sample of H-R diagrams, similar to Fig. 3, for various F clcl