We devised a straightforward procedure to derive the atmosphere fundamental
parameters of stars across the different MK spectral types by comparing
mid-resolution spectroscopic observations with theoretical grids of synthetic
spectra.The results of a preliminary experiment, by matching the Gunn and
Stryker and Jacoby et al. spectrophotometric atlases with the Kurucz models,
are briefly discussed. For stars in the A-K spectral range, effective
temperature is obtained within a 1-2% relative uncertainty (at 2 sigma
confidence level). This value raises to 4-5% for the hottest stars in the
samples (O-B spectral types). A poorer fit is obtained throughout for stars
cooler than 4000 K mainly due to the limiting input physics in the Kurucz
models.Comment: 6 pages, 3 figures; Proc. of the 1st COROT-MONS Ground-Support
  Observations Workshop (Ghent 11-12/01/2001), Ed. C. Sterken, Brussel Univ.,
  2001, in preparatio

Bertone, E.

Buzzoni, A.

English

arXiv

We devised a straightforward procedure to derive the atmospheric fundamental parameters of stars across the different MK spectral types by comparing mid-resolution spectroscopic observations with theoretical grids of synthetic spectra

BUZZONI, Alberto

OA@INAF - Istituto Nazionale di Astrofisica

2001Publication Year2024-01-30T14:29:11ZAcceptance in OA@INAFSpectral classification of stars using synthetic model atmospheresTitleBertone, E.; BUZZONI, AlbertoAuthorshttp://hdl.handle.net/20.500.12386/34661Handle7NumberSpectral classification of stars usingsynthetic model atmospheresEmanuele BertoneOsservatorio Astronomico di Brera, via Bianchi 46, 23807 Merate, ItalyAlberto BuzzoniTelescopio Nazionale Galileo, A.P. 565, 38700 S/Cruz de La Palma (Tf), SpainABSTRACT. We devised a straightforward procedure to derive the at-mospheric fundamental parameters of stars across the different MK spectraltypes by comparing mid-resolution spectroscopic observations with theoreticalgrids of synthetic spectra.The results of a preliminary experiment, by matching the Gunn & Stryker(1983) and Jacoby et al. (1984) spectrophotometric atlases with the Kurucz(1995) models, are briefly discussed. For stars in the A–K spectral range,effective temperature is obtained within a 1–2% relative uncertainty (at 2-σ confidence level). This value raises to 4–5% for the hottest stars in thesamples (O–B spectral types). A poorer fit is obtained throughout for starscooler than 4000K mainly due to the limiting input physics in the Kuruczmodels.1. IntroductionA confident estimate of the atmosphere fundamental parameters of stars is of crucialimportance in a number of physical problems dealing with the study of the stellarpopulations in the Milky Way and the other external galaxies. As a complement ofthe natural approach, that relies on high-resolution spectroscopy of single objects,one could also try to take advantage of the piece of information provided by mid-resolution observations. The latter can in general probe spectral energy distribution(SED) of stars over a wider wavelength range, and allow us to collect data in a muchshorter observing time. Physical information on target stars would derive in thiscase from a “suitable” comparison with reference spectra (both theoretical and/orempirical ones) searching for a best fit over the whole observed SED.In this work we propose a simple procedure to derive stellar fundamental para-76 Bertone & Buzzonimeters (i.e. Teff , log g, [M/H]) by matching mid-resolution (∼ 5 Å FWHM) obser-vations with a grid of theoretical model atmospheres. The fitting algorithm will bepresented in Sec. 2 while some preliminary results of our method will be discussedin Sec. 3.The Gunn & Stryker (1983, hereafter GS83) and the Jacoby et al. (1984, JHC84)spectrophotometric atlases provided the wide sample of target stars (336 in total)for our experiment, with different spectral type (from O to M) and MK luminosityclass (from I to V). This allowed us to test our procedure across the whole HRdiagram.The 175 GS83 SEDs are defined in 503 points between 3160 and 10620 Å, witha step of 10 or 20 Å. This coarse sampling basically sets also the intrinsic spectralresolution of the data. Absolute fluxes are given in the AB magnitude scale (Oke &Gunn 1983). The 161 JHC84 SEDs are sampled in 2799 points between 3510 and7427 Å, by steps of 1.4 Å. They have been obtained at a resolution of 4.5 Å FWHM.Both samples of stars were originally corrected for interstellar reddening.As a reference framework for our procedure, we relied on the ATLAS 9 syntheticmodels by Kurucz (1995). Other theoretical databases could in principle be used,of course, like for instance the recent and more elaborated NextGen 5 models byHauschildt et al. (1999a, 1999b; see Bertone et al. 2001 for a critical discussion inthis regard).The adopted ATLAS 9 grid consists of 409 models in total, assuming a solarmetallicity, a microturbulent velocity of 2 km s−1 and a mixing-length-to-scale-heightratio L/Hp = 1.25. Effective temperature spans the range 50 000 ≥ Teff ≥ 3500Kwith a step in the model grid of 250K for stars cooler than 10 000K, increasing upto 2500K for hotter stars. Surface gravity explores the range 0.0 ≤ log g ≤ 5.0 dexat steps of 0.5 dex. All these model atmospheres and spectra are available on theInternet at the Kurucz www site (http://cfaku5.harvard.edu/).2. The fitting algorithmOur method basically consists in a measure of the likelihood function s that quanti-fies the similarity between target spectrum and each template SED of the referencegrid. As far as the quantity s is known across the grid — that is, as a function ofthe physical parameters of the model atmospheres — a formally “best” solution isidentified by the minimum of s in the (Teff , log g, [M/H]) parameter space. Theunderlying hypothesis of this choice is of course that similar spectra are producedby similar physical parameters in an univocal way.Operationally, the fiducial atmosphere parameters for the i-th star in our targetSpectral classification of stars using model atmospheres 77sample are obtained in three steps:1. We first compute a residual function, X vs. λ in the flux logarithm domainsuch asX(i,j)(λ) = [ln fi(λ) − ln fj(λ)] W (λ) (1)where fi is the SED of the target star, fj is that of the j-th reference modelatmosphere and W is a weighting factor that only depends on λ. In case awavelength resampling is necessary to consistently match target and templatespectra, this will always be done by rebinning the template spectrum at thewavelength values of the target. We also assume that the template spectrumhas been preliminarily degraded to the same resolution of the target data.2. We therefore compute the standard deviation of the statistical variable Xwithin the wavelength range of the target observations:σ(X)(i,j) =√Var(X ) (2)As in eq. (1) we worked in the natural logarithm domain, σ(X)(i,j) can beread, to a first approximation, as a mean percent deviation of the j-th templatespectrum with respect to the i-th target spectrum.3. For each template we therefore compute the corresponding likelihood function,s, defined ass(i,j) = σ(X)(i,j). (3)The minimum of the quantity s(i,j) across the grid of reference spectra willeventually identify the “best” fiducial atmosphere parameters for the i-th tar-get star. As a further refinement, to increase the accuracy of our fitting al-gorithm, we actually search for a minimum of the s(i,j) function after a splinesmoothing.An example of our procedure for star no. 35 (an F6V dwarf) and no. 100(a K3 III giant) in the JHC84 atlas is shown in Fig. 1. In order to estimate thestatistical uncertainty in the fiducial set of atmosphere parameters, for each targetstar we performed an F test on the likelihood function s (the freedom degrees inthis case are the number of SED points accounted in the fit). The resulting 2-σconfidence interval for a one-tail F test then translates into a confidence range forTeff and log g, as displayed in Fig. 1.Full details of the matching procedure for the same star no. 35 of Fig. 1 are alsoreported in Fig. 2, by comparing with Kurucz templates with different temperature78 Bertone & BuzzoniFig. 1.— Spline interpolation of the loci of the points s vs. Teff for two stars in the JHC84atlas. The solid line is the curve at the best fiducial gravity (log g = 4.0 for JHC84 no.35and log g = 2.0 for JHC84 no.100); the dashed lines are the curves at the other surfacegravity values; diamonds are the interpolated s values at the best gravity (the points atother gravities have the same abscissae); the square indicates the minimum of the curve.The horizontal dotted line shows the upper limit smax of the 2-σ confidence interval of thestandard deviation, given by the F test. This limit defines the Teff error range, indicatedby the vertical dotted lines. The error on log g is provided by the gravity value of thecurves that pass under smax.Spectral classification of stars using model atmospheres 79(left panels) and surface gravity (right panels). The central panel in the figure isthe best fit for Teff= 6500K and log g= 4.0 dex, assuming a solar metallicity.As far as the continuum emission is concerned, note that the trend in theresidual flux is much more sensitive to a change in temperature while any change ingravity would especially reflect in the ultraviolet emission shortward of the Balmerbreak.Some artificial features appear in the GS83 spectra about 7600 Å and 9400 Å.They are due to telluric absorption and have therefore been excluded in our analysisby setting W = 0 in eq. (1) for the relevant wavelength. In addition, also the regionshortward of 3500 Å has been rejected for the same sample due to a poorer fluxcalibration of the original data in the ultraviolet wavelength range.3. Results and discussionAs our method entirely relies on the Kurucz synthetic models, its performance ismainly determined by their properties, virtues and faults. The ATLAS 9 modelsare LTE, plane-parallel and they use the mixing-length theory with overshootingfor the treatment of convection. A huge amount of atomic and molecular lines areconsidered, but triatomic molecules are not implemented in the opacity calculations,and Kurucz (1993) himself suggests not to use these models for M stars.For 293 out of 336 stars in the GS83 and JHC84 atlases our procedure convergedto an acceptable set of fiducial atmosphere parameters (namely Teff and log g, as-suming a solar metallicity). About 85% of these stars have smin < 0.07, with amean of 0.05 for the total sample. All stars with poorer fit (i.e. smin > 0.11) arecooler than 4000K. For 43 stars no solution was found as smin presumably locatedbeyond the physical boundaries of the model grid. They are mostly O and M stars— that is, at the extreme edges of the temperature scale. Molecular contributionseems the most likely responsible for the trouble with M stars, while for O starsthis seems rather to deal with the non-LTE regime affecting stellar atmospheres athotter temperature.Figure 3 gives a summary of our results by reporting the relative uncertaintyin the derived Teff for the 293 stars with fitting solution. The GS83 stars providedslightly better results compared with the JHC84 sample because of a wider wave-length baseline of the spectra that allowed a more accurate determination of Teff .The typical relative uncertainty (at 2-σ confidence level) in the temperature esti-mate for A–K stars turns about ± 1–2%, raising to 4–5% for B stars. The typicalerror box for the surface gravity estimates is ±0.5 dex.As a final remark, it is worth stressing that our procedure could in principle80 Bertone & BuzzoniFig. 2.— The SED of the star JHC84 no.35 (SAO 57199, F6 V) is compared with severalATLAS9 SEDs. In the left column, the models have same gravity and ∆Teff=250 K. Inthe right column, the models have same Teff and ∆log g=0.5 dex. The lower panels showthe value of X(i,j)(λ), see eq. (1).Spectral classification of stars using model atmospheres 81Fig. 3.— Relative error on the Teff of the stars of the two atlases. The typical 2-σ absoluteerror is ±50–100K for K–F stars, ±100–200K for A stars and ±400–1000K for B stars.work also for high-resolution spectra. Different problems would come out in thiscase, however, deserving to be preliminarily assessed in order to assure a confidentfit to the data.From the operational point of view we know, in fact, that the calibration ofechelle spectra at a high-order dispersion is a more critical task to perform over awide wavelength baseline compared to corresponding low-resolution observations.Computation of theoretical spectra at high-resolution is on the other hand verytime consuming, and template grids are usually not available for public release.Furthermore, they take a huge amount of disk space and often cannot be so easilymanaged with the current computing facilities.A suitable compromise in this sense could rely on a selective analysis of narrow-band spectrophotometric indices, like in the the Lick system (Worthey et al. 1994)or according to Rose’s (1994) studies, taking full advantage in this case of the high-resolution piece of information but restraining the analysis only to much reduced(and strategically placed) windows to probe the SED.82 Bertone & BuzzoniReferencesBertone E., Buzzoni A., Chavez M., Rodriguez L., 2001, in The link between starsand cosmology, eds. M. Chavez, A. Bressan, A. Buzzoni and D. Mayya,Kluwer, Dordrecht, in pressGunn J.E. , Stryker L.L., 1983, ApJS 52, 121Hauschildt P.H., Allard F., Baron E., 1999, ApJ 512, 377Hauschildt P.H., Allard F., Ferguson J., Baron E. , Alexander D.R., 1999, ApJ 525,871Jacoby G.H., Hunter D.A. , Christian C.A., 1984, ApJS 56, 257Kurucz R.L., 1993, in Proc. IAU Symp. 149, eds. B. Barbuy and A. Renzini, Kluwer,Dordrecht, p.225Kurucz R.L., 1995, CD-ROM n.13, revisedOke J.B. , Gunn J.E., 1983, ApJ 266, 713Rose J.A., 1994, AJ, 107, 206Worthey G., Faber S.M., González J.J., Burnstein D., 1994, ApJS 94, 687

Spectral classification of stars using synthetic model atmospheres

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Spectral classification of stars using synthetic model atmospheres

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