Application of the Baade-Wesselink method to a pulsating cluster Herbig Ae star: H254 in IC348
V. Ripepi, R. Molinaro, M. Marconi, G. Catanzaro, R. Claudi, J. Daszyńska-Daszkiewicz, F. Palla, S. Leccia, S. Bernabei
aa r X i v : . [ a s t r o - ph . S R ] O c t Mon. Not. R. Astron. Soc. , 1– ?? (2002) Printed 6 September 2018 (MN L A TEX style file v2.2)
Application of the Baade-Wesselink method to a pulsatingcluster Herbig Ae star: H254 in IC348 ⋆ V. Ripepi † , R. Molinaro M. Marconi , G. Catanzaro , R. Claudi ,J. Daszyńska-Daszkiewicz , F. Palla , S. Leccia , S. Bernabei INAF-Osservatorio Astronomico di Capodimonte, I-80131, Napoli, Italy INAF-Osservatorio Astrofisico di Catania, I-95123, Catania, Italy INAF-Osservatorio Astronomico di Padova, I-35122, Padova, Italy Instytut Astronomiczny, Uniwersytet Wrocawski, ul. Kopernika 11, PL-51-622 Wrocaw, Poland INAF-Osservatorio Astrofisico di Arcetri, I-50125, Firenze, Italy INAF-Osservatorio Astronomico di Bologna, I-40127, Bologna, Italy
ABSTRACT
In this paper we present new photometric and radial velocity data for the PMS δ Sct star H254, member of the young cluster IC 348. Photometric V,R C ,I C light curveswere obtained at the Loiano and Asiago telescopes. The radial velocity data was ac-quired by means of the SARG@TNG spectrograph. High-resolution spectroscopy al-lowed us to derive precise stellar parameters and the chemical composition of the star,obtaining: T eff = 6750 ±
150 K; log g = 4.1 ± ± V bandA V =2.06 ± ± R ⊙ .This result was used in conjunction with photometry and effective temperatureto derive a distance estimate of 273 ±
23 pc for H254, and, in turn for IC 348, thehost cluster. This value is in agreement within the errors with the results derivedfrom several past determinations and the evaluation obtained through the Hipparcosparallaxes. Finally, we derived the luminosity of H254 and studied its position in theHertzsprung–Russell diagram. From this analysis it results that this δ –Scuti occupiesa position close to the red edge of the instability strip, pulsates in the fundamentalmode, has a mass of about 2.2 M ⊙ and an age of 5 ± Key words: stars: pre-main-sequence – stars: variables: T Tauri, Herbig Ae/Be –stars: variables: δ Scuti – stars: fundamental parameters – stars: abundances – openclusters and associations: individual: IC 348.
Herbig Ae/Be stars (Herbig 1960) are intermediate-massstars (1.5 M ⊙ < M . ⊙ ) experiencing their pre-main- ⋆ Based on observations made with the Italian TelescopioNazionale Galileo (TNG) operated on the island of La Palma bythe Fundación Galileo Galilei of the INAF (Istituto Nazionale diAstrofisica) at the Spanish Observatorio del Roque de los Mucha-chos of the Instituto de Astrofisica de Canarias † Please send offprint requests to [email protected] sequence (PMS) phase. Observationally, these stars show: i)spectral type B, A or early F; ii) Balmer emission lines in thestellar spectrum; iii) Infrared radiation excess (in compari-son with normal stars) due to circumstellar dust. Addition-ally, often these objects show significant photometric andspectroscopic variability on very different time-scales. Vari-able extinction due to circumstellar dust causes variationson timescales of weeks, whereas clumps (protoplanets andplanetesimals) in the circumstellar disk or chromospheric ac-tivity are responsible for hours to days variability (see e.g.Catala 2003). c (cid:13) V. Ripepi et al.
It is now well established that intermediate-mass PMSstars during contraction towards the main sequence cross theinstability strip for more evolved stars. These young, pulsat-ing intermediate-mass stars are collectively called PMS δ Sctand their variability, similarly to the evolved δ Sct variables,is characterized by short periods ( ∼ ÷ δ Sct in-stability strip based on nonlinear convective hydrodynamicalmodels was carried out by Marconi & Palla (1998). In thisseminal paper, these authors calculated the instability striptopology for the first three radial modes and showed thatthe interior structure of PMS stars crossing the instabilitystrip is significantly different from that of more evolved MainSequence stars (with the same mass and temperature), eventhough the envelope structures are similar.The subsequent theoretical works by severalAuthors (see e.g. Suran et al. 2001; Marconi et al.2004; Ruoppo et al. 2007; Di Criscienzo et al. 2008;Guenther & Brown 2004, and references therein) showedthat, when a sufficient number of observed frequencies areavailable for a single object (usually a mixture of radial andnon-radial modes), the asteroseismic interpretation of thedata allows to estimate with good accuracy the positionof these variables in the HR diagram and to get insightsinto the evolutionary status of the studied objects. Fromthe observational point of view, multi-site campaigns (e.g.,Ripepi et al. 2003, 2006; Bernabei et al. 2009) and spaceobservations with MOST and CoRoT (e.g., Zwintz et al.2009, 2011, for NGC2264) were progressively able to pro-vide improved sets of frequencies to be interpreted at thelight of asteroseismic theory. Eventually, the comparisonbetween theory and observations allows to obtain stringentconstraints on the stellar parameters and the internalstructure of these objects.On the other hand, the asteroseismic techniques arenot suitable for monoperiodic pulsators, for which it isdifficult to discern whether the observed mode is ra-dial or not, making it almost impossible to use stellarpulsation theory to constrain the stellar parameters ofthe star. As demonstrated by various authors (see e.g.Daszyńska-Daszkiewicz, Dziembowski & Pamyatnykh 2003,2005, and references therein), this problem can be facedby considering amplitude ratios and phase differences frommulti-colour photometry and comparing these with models.This procedure allows to estimate the value of the harmonicdegree ℓ . However, for monoperiodic pulsators, an additionalpossible test to discriminate between radial and non-radialmodes is potentially represented by the so-called Baade-Wesselink test. As well known, the Baade-Wesselink methodcombines photometric and radial velocity data along the pul-sation cycle producing as output an estimate of both the ra-dius and the distance of the investigated pulsating star (seeGautschy 1987, for a review). For radially oscillating stars,the line-of-sight motion (responsible for the radial velocitycurve) and the subtended area of the star (responsible forthe light curve) are in phase, so that the method gives a rea-sonable estimate of the stellar radius. This occurrence doesnot hold in the case of non-radial pulsation. In fact, for a p -mode with l = 2 , we would obtain a negative value for theradius, while for l = 1 the result would be an unrealisticallylarge radius (Unno et al. 1989).In this context, among the already known PMS δ Scutivariables, the IC 348 cluster member H 254 (Herbig 1998)is an ideal candidate. Indeed, this pre-main sequence star isfairly bright (V=10.6 mag) and it has already been found byRipepi et al. (2002, Paper I hereinafter) to be a monoperi-odic pulsator with f = 7 . c/d (period ≈ V amplitude of ∼ M ⊙ or a 2.3 M ⊙ pulsating in thefirst overtone or in the fundamental mode respectively. Theapplication of the Baade-Wesselink method to this pulsatorwould allow us to test this result. Moreover, such an analysiswould also provide an estimate of both the radius and thedistance of this star, and in turn, its position in the HR Di-agram, as well as an independent estimate of poorly knowndistance to the parent cluster IC 348, the parent cluster,which is poorly known (see Herbig 1998, for a discussion onthis topic).At variance with the case of RR Lyrae and especiallyClassical Cepheids, Baade-Wesselink application to δ Sctstars is extremely rare in the literature, and concerned onlywith High Amplitude δ Sct stars (see e.g. Burki & Meylan1986). This occurrence is probably due to the limited useof δ Sct as distance indicators for extragalactic objects, aswell as to the availability of precise Hipparcos parallaxes forseveral close objects. In addition, there is an observationaldifficulty in obtaining high precision radial velocity measure-ments with the short time exposures needed to avoid lightcurve smearing for these fast pulsators. Hence in this paperwe present the first attempt to apply the BW technique toa low amplitude δ Sct star.The organization of the paper is as follows: in section 2we present the photometric and spectroscopic observations;in section 3 we discuss the determination of the stellar pa-rameters and the abundance analysis; section 4 reports onthe technique used to discriminate between radial and non-radial pulsation in H254; in section 5 we apply the CORSmethod to derive the linear radius of our target; section 6discusses the inferred distance and position in the HR dia-gram; in section 7 we summarize the main achievements ofthis paper.
The Baade-Wesselink method relies on both photometricand radial velocity (RV) observations. To minimize possi-ble phase shifts between light and RV curves, that couldrepresent a significant source of uncertainty in the applica-tion of the method, we aimed at obtaining photometric andspectroscopic observations as simultaneous as possible. Thiswas achieved only partially, as shown in Tab.1 , where thelog of the observations is shown. Indeed, due to the adverseweather conditions, we were able to gather useful photomet-ric data during only two nights, one of which was luckily veryclose to the spectroscopic ones so that we are confident that c (cid:13) , 1– ?? pplication of the Baade-Wesselink method to H254 in IC348 Figure 1.
Folded light curve in V for H254. Top panel showsthe light curves obtained using H83 (filled circles) and H89 (opencircles) as comparison stars, respectively. Bottom panel shows thelight curved obtained with the Asiago (filled circles) and Loiano(open circles) telescopes, respectively. our results are not hampered by the above quoted possiblephase shifts. Photometric data were acquired in the Johnson-Cousins sys-tem
V, R C and I C with the AFOSC and BFOSC instru-ments at the 1.8m Asiago and 1.54m Loiano telescopes, re-spectively. The [email protected] instrument was equippedwith a TK1024AB 1024x1024 CCD, with a pixel size of0.47 ′′ and a total field of view of about 8.1 ′ × . ′ . [email protected] was equipped with a EEV CCD 1300x1340pixels of individual size 0.58 ′′ , and a total field of view of13 ′ × ′ .The data were reduced following the usual procedures(de-biasing, flat-fielding) and using standard IRAF rou-tines.To measure the light variations of H254, we adoptedthe differential photometry technique. We know from PaperI that the stars H83 and H89 are isolated, constant, andbright enough to provide a very high S/N, and hence arethe ideal comparison stars.The aperture photometry was carried out using custom http://archive.oapd.inaf.it/asiago/2000/2300/2310.html IRAF is distributed by the National Optical Astronomy Obser-vatories, which are operated by the Association of Universities forResearch in Astronomy, Inc., under cooperative agreement withthe National Science Foundation.
Figure 2.
Top panel: folded radial velocity curve of H254. Secondto fourth panels show the smoothed folded light curves in I c , R and V , respectively. In all panels the solid line represent asinusoidal least-squares fit to the data (see text) routines written in the MIDAS environment with aperturesof about 17 ′′ for both data sets. To join the Asiago andLoiano observations, we have first calculated the differencesin average magnitude between the two set (of differentialmagnitudes) due to long term photometric variation notcaused by pulsation (see Paper I). The correction was ofthe order of a few hundredths of magnitudes for all the fil-ters. Due to the largest data set, we retained the Loianophotometry as reference and corrected the Asiago one.To secure the absolute photometric calibration we havefirst calibrated the comparison stars H83 and H89, usingthe V R C I C photometry by Trullols & Jordi (1997) and thenfor each star and filter, we added the magnitude differenceswith respect to H254. In this way we obtained two distinctcalibrated time series for each band, as reported in Tab. 2,which is published in its entirety in the on-line version of thepaper. The quality of the data at varying the comparisonstar or the telescope is shown in Fig 1 in the case of the V band, but similar results are obtained for R C and I C . Havingverified that all the data we gathered are compatible to eachother, the next step was to merge all the data sets (at varyingthe comparison star and the telescope) for each filter. Wethen smoothed the resulting light curves by applying a boxcar-like smoothing algorithm, making it easier to perform aleast-squares fit to the data. The smoothed light curves werethen fitted with a Fourier series: mag ( φ ) = A + n X i =1 A i sin(2 πiφ + Φ i ) . (1)Typically only one harmonic (n=1 in the formula above) is (cid:13) , 1– ?? V. Ripepi et al.
Table 1.
Log of the observations. Starting from the left, the dif-ferent columns report: the observing mode; Heliocentric JulianDay (HJD) of start and end observations; the length of the timeseries; the exposure times (in
V, R, I C , respectively for photome-try). Note that HJD=HJD-2454000.Mode Obs. HJD-s HJD-e Length Exptimed d h sPhot. Loiano 415.308 415.437 3.1 12,9,8Phot Asiago 434.395 434.547 3.6 10,5,6Spec. TNG 431.695 431.759 1.5 1020Spec. TNG 432.338 432.747 9.8 1020 Table 2.
V, R C , I C photometry for H254. From left to right wereport: HJD (in days); magnitude; filter; comparison star used.Note that HJD=HJD-2400000.HJD Mag filter Comparison54434.39491 10.6400 V H8954434.40091 10.6389 V H8954434.40693 10.6386 V H8954434.41081 10.6387 V H8954434.42263 10.6413 V H8954434.42652 10.6419 V H8954434.43035 10.6440 V H8954434.43444 10.6425 V H8954434.43831 10.6439 V H89Table 2 is published in its entirety only in the electronic editionof the journal. A portion is shown here for guidance regarding itsform and content. sufficient to describe the sinusoidal shape data of the target.The goodness of the photometry is testified by the very lowrms of the residuals around the fits: . mag, . magand . mag for V, R c and I c bands, respectively.The result of all these steps is reported in the last threepanels of Fig. 2, where, as in Fig.1, we have phased the pho-tometry using the period given in Paper I, and redeterminedthe epoch of the minimum light (which was better definedwith respect to the maximum) on the Loiano data set. Table 3.
Observation log for spectroscopic data. The B star(HD5394) as well as the target template (the spectrum withoutthe iodine cell) were observed during each night to determine thebest instrumental profile modelling.Star Nr. spectra Iodine cell T exp [s] S/NHD5394 2 Yes 180 > > > The spectroscopic observations were carried out with theSARG instrument, which is a high-resolution (from R =29000 to R = 164000 ) cross dispersed echelle spectrographcovering a spectral range from λ = 370 nm to 1000 nm(see Gratton et al. 2001, for details) mounted at TelescopioNazionale Galileo (TNG, La Palma, Canarie, Spain) .Using the yellow grism (spectral range − nm)it is possible to insert in the light path a I -cell and have,in this way, a superimposed (and stable) wavelength refer-ence on the spectrum of the star useful for accurate stellarDoppler shifts measurements. The majority of the spectrain our data sample were acquired in this configuration witha resolution of R = 164000 during two observing nights (seetable 1). A few spectra of the target were acquired withoutthe I -cell for calibration purposes. The reduction of thespectra (bias subtraction and flat fielding correction) wasperformed using the common IRAF package facilities. To un-veil the radial velocity information hidden in the star spec-tra, we need to reconstruct the spectra of the star togetherwith the superimposed I spectrum, using the measured in-strumental profile, a very high resolution I spectrum anda high resolution and high signal to noise spectrum of thestar. To model the instrumental profile, it is necessary toobtain a spectrum for a fast rotating B star acquired withand without the iodine cell. A detailed description of thespectra available is shown in Tab. 3.Besides, using the high resolution I spectra we obtainthe instrumental profile deconvolving it by the B star spec-trum. After that the observed spectrum of the star is com-pared with a modeled spectrum of the star using all obtainedelements.The reconstruction of the spectra and the comparisonwith the observed one are performed using the AUSTRALcode by Endl et al. (2000). This code takes in account theinstrumental profile changes among the spectrum subdivid-ing it in 80-120 pixel chunks. For each of these chunk aradial velocity is measured. Usually the spectrum is subdi-vided in 400-600 chunks to which correspond a radial ve-locity measurement. The final radial velocity measure is ob-tained by the mean and standard deviation of all the resultsof the chunks. The results of the measurement are reportedin Fig. 2 and Tab. 4. The same spectroscopic data used to build the referencespectrum for radial velocity determination can be used toestimate the intrinsic stellar parameters for the target star.
Any attempt devoted to a detailed characterization of thechemical abundance pattern in stellar atmospheres is strictly Note that SARG was dismissed at TNG and replaced with theHARPS-N spectrograph. c (cid:13) , 1– ?? pplication of the Baade-Wesselink method to H254 in IC348 Table 4.
Radial velocities for H254 measured with SARG. Notethat HJD=HJD-2400000.HJD RV σ RV d Km/s Km/s54431.69459 0.246 0.23554431.70765 0.705 0.32754431.72033 0.214 0.19454431.73337 0.495 0.32254431.74605 0.361 0.49554432.40098 0.452 0.25754432.41366 0.205 0.30054432.42647 -0.652 0.49054432.43916 -0.061 0.44254432.45197 -0.015 0.32454432.46467 0.103 0.41254432.47749 -0.330 0.35454432.49018 -0.359 0.39554432.54718 0.258 0.34054432.60579 -0.305 0.37854432.61846 -0.645 0.34754432.72134 -0.530 0.45454432.73436 -0.142 0.313 linked with the accuracy of effective temperature and surfacegravity determination.In this study, we derived the effective temperature byusing the ionization equilibrium criterion. In practice, weadopted as T eff the value that gives the same iron abundanceas computed from a sample spectral lines both neutral andin first ionization stage.First of all, we selected from the TNG spectrum a sam-ple of iron lines with the principal requirement that they donot show any sensitivity to the gravity (this condition hasbeen checked using spectral synthesis) i.e. synthetic linescomputed for a wide range of gravities did not show any ap-preciable variations. We found six lines belonging to Fe i andonly two to Fe ii . The list of these lines with their principalatomic parameters is reported in Tab. 5.For each line, the equivalent width and the centralwavelength have been measured with a Gaussian fit us-ing standard IRAF routines. As the main source of errorsin the equivalent width measurements is the uncertain po-sition of the continuum, we applied the formula given inLeone et al. (1995), which takes into account the width ofthe line and the rms of the continuum. According to the S/Nof our spectrum and to the rotational velocity of our target( v sin i = 85 ± − , see next section), we found that theerror on the equivalent widths is ≈
20 mÅ.Then, once fixed the observed equivalent widths, wecomputed for each spectral line the theoretical curves in thelog Fe/N tot - T eff plane. Since our target is reported in theliterature as a F0 star (SIMBAD database), we explored therange in temperature between 6500 K and 7000 K. Calcula-tions have been performed in two separate steps: • use of ATLAS9 (Kurucz 1993) to compute the LTEatmospheric models • use of WIDTH9 (Kurucz & Avrett 1981) to deriveabundances from single lines.The locus in common with all the curves showed in Table 5.
List of iron lines used for temperature determinations, log gf and relative reference are also reported.Sp. line log gf ReferenceFe i λ − i λ − i λ − i λ − i λ − i λ − ii λ − ii λ − Figure 3.
Behaviour of iron abundances as a function of effectivetemperature. The black curves refer to neutral iron, while the redones to single ionized.
Fig. 3 represents the effective temperature and iron abun-dance of H254. To give a realistic estimation of the er-rors on these values, we repeated the same calculationsas before, but varying the EW by a quantity equal toits experimental error. In practice the value of T eff and log N Fe /N Tot derived for EW ± δ EW gave us the extensionof the error bars. Finally, we adopted T eff = 6750 ±
150 Kand log N Fe /N Tot = − ± For early F-type stars, one of the method commonly usedin literature for the determination of the luminosity classof stars is to estimate the strength of the ratios betweenthe spectral blend at λλ ii and Ti ii lines, and the one at λ i lines.(Gray & Garrison 1989).Since the TNG spectra do not cover the spectral re-gion of interest for this purpose, we used the Loiano tele- c (cid:13) , 1– ?? V. Ripepi et al.
Figure 4.
Portion of spectra modeled with v sin i = 85 km s − .The spectral lines are: Fe i λ ii λ scope spectra. We computed the λλ ± log g . After having fixed the T eff to thevalue found in Sect. 3.1, we computed ATLAS9 atmosphericmodels with gravities spanning the range between 3.5 and4.5 dex. By using this curve, we converted our measured ra-tio in a measurement of gravity, obtaining: log g = 4.1 ± To derive chemical abundances, we undertook a syn-thetic modeling of the observed spectrum. The atmosphericparameters inferred in the previous sections have beenadopted to compute an ATLAS9 LTE model with so-lar ODF. This model has been applied to SYNTHE code(Kurucz & Avrett 1981) to compute the synthetic spec-trum.The rotational velocity of H254 has been derived bymatching metal lines with synthetic profiles. The best fitoccurred for 85 ± − , where the error has been esti-mated as the variation in the velocity which increases the χ of a unit. An example of the goodness of our fit is showedin Fig. 4.Practically, we divided all the spectral range covered byour data in a number of sub-intervals ≈
100 Å wide. For eachinterval we derived the abundances by a χ minimizationof the difference between the observed and synthetic spec-trum. Line lists and atomic parameters used in our modelingare from Kurucz & Bell (1995) and the subsequent update Figure 5.
Chemical pattern derived for H254, the horizontaldashed line represents the solar abundances. by Castelli & Hubrig (2004). The iron abundance found inSect. 3.1 has been used as guess input to speed up the cal-culations. The adopted iron abundance with its error is theone reported in Tab. 6.In Table 6 and Fig. 5 we report the abundances derivedin our analysis expressed in the usual logarithmic form rel-ative to the total number of atoms N Tot . To easily comparethe chemical pattern of H254 with the Sun, we reportedin the last column the differences with the solar values astaken from Asplund et al. (2005). Errors reported in Table 6for a given element are the standard deviation on the aver-age computed among the various abundances determined ineach sub-interval. When a given element appears in one ortwo sub-intervals only, the error on its abundance evaluatedvarying temperature and gravity in the ranges [ T eff ± δT eff ] and [log g ± δ log g ] is typically 0.10 dex.Inspection of Fig. 5 suggests an almost standard atmo-sphere, with the exception of a moderate under abundance( ≈ ≈ For the following analysis it is important to evaluate the in-terstellar absorption in the direction of H254. To this aim,we firstly calculated the mean magnitudes in
V, R c and I c bands on the basis of the fitting curves illustrated in Fig. 2.Then we calculated the colours: ( V − R c ) =0.589 mag and ( V − I c ) =1.268 mag. Taking advantage of the T eff value es-timated from spectroscopy, we can now compare the ob-served ( V − R c ) and ( V − I c ) values with those tabulatedby Kenyon & Hartmann (1995, their Tab.A5) for the esti-mated T eff of H254. As a result we find that the tabulatedcolours are: ( V − R c ) =0.240 mag and ( V − I c ) =0.480 mag. c (cid:13) , 1– ?? pplication of the Baade-Wesselink method to H254 in IC348 Table 6.
Chemical abundances derived for the atmosphere ofH254. For each element we report its abundance in the form log N el /N Tot , and the difference with respect the solar values(Asplund et al. 2005).Elem. log N el /N Tot [ ǫ ( x ) ]Na − ± ± − ± − ± − ± ± − ± − ± − ± ± − ± ± − ± − ± − ± − ± Hence, the derived values of E ( V − R c ) and E ( V − I c ) are,respectively, 0.349 mag and 0.788 mag.The uncertainty on these reddening values has been es-timated by analyzing how the theoretical colors change ac-cording to the error on the spectroscopic temperature. Theresulting uncertainties are δE ( V − R c ) = 0 . mag and δE ( V − I c ) = 0 . mag.From the derived reddening values, we calculated theabsorption A V as the weighted mean of the two val-ues A V =5.956 E ( V − R c ) and A V =2.612 E ( V − I c ), wherethe numerical coefficients are obtained from Cardelli et al.(1989) assuming R V =3.1. The value we use in this work isA V =2.06 ± Identification of the mode degree, ℓ , for thedetected pulsation frequency ν = 7 . c/dof H254 has been done using the method ofDaszyńska-Daszkiewicz, Dziembowski & Pamyatnykh(2003, 2005). In this method the effective temperatureperturbation, measured by the complex parameter f , isdetermined from observation instead of relying on thelinear non adiabatic computations of stellar pulsations. Theadvantage is that we can avoid in that way uncertaintiesresulting from theoretical modelling, e.g., an impact ofsubphotospheric convection on pulsation. To apply thequoted method, the V R C I C photometric data presentedin Sect. 2 are not well suited because of the poor timesampling. Therefore, we adopted the uvby Strömgrenphotometry published in Paper I . In Fig. 6 we show thediscriminant χ as a function of ℓ , as determined fromthe fitting of the theoretical amplitudes and phases to theobservational values in all uvby passbands, simultaneously.To illustrate how robust is the method to uncertainties instellar parameters (e.g., effective temperature, luminosityand mass) we considered five models located in the errorbox of H254.Moreover, two models of stellar atmospheres were We actually published only b, y photometry in Paper I. Herewe use also the data in the u, v bands. The uvby light curves areavailable upon request. adopted. In the left panel of Fig. 6 we show results obtainedwith the Kurucz models (Kurucz 2004), whereas the rightpanel of Fig. 6 reports the same analysis based on the NEMOmodels (Nendwich et al. 2004). As we can see, in both casesidentification of ℓ is clear: the pulsational frequency of H254is associated with the radial mode. In section 4 we have show that H254 pulsate in a radialmode. In this section we aim at applying to our target aparticular realization of the Baade–Wesselink method calledCORS (Caccin et al. 1981) to derive the linear radius, R , ofthis low amplitude δ –Scuti star. To date, the CORS methodhas been applied only to Cepheid stars (see Molinaro et al.2012, and references therein), characterized by light curveswith large amplitude (typically ∼ ∼ The basic equation of the CORS method can be easily de-rived starting from the surface brightness: S V = m V + 5 log θ (2)where θ is the angular diameter (in mas) of the star and m V is the apparent magnitude in the V band. If we differentiateeq.(2) with respect to the pulsational phase ( φ ), multiply theresult by the generic color index ( C ij ) and integrate alongthe pulsational cycle, we obtain: q Z ln n R − pP Z φφ v ( φ ′ ) dφ ′ o C ′ ij dφ − B + ∆ B = 0 (3)where q = , P is the period, v is the radial velocityand p is the projection factor, which correlates radial andpulsational velocities according to R ′ ( φ ) = − p · P · v ( φ ) . Thelast two terms, B and ∆ B , are given by: B = Z C ij ( φ ) m ′ V ( φ ) dφ (4) ∆ B = Z C ij ( φ ) S ′ V ( φ ) dφ . (5)and are connected to the area of the loop described duringpulsational cycle of the star, respectively, in the V – C ij planeand S V – C ij plane, typically with B larger than ∆ B .Equation (3) is an implicit equation in the unknownradius R at an arbitrary phase φ . The radius at anyphase φ can be obtained by integrating the radial velocitycurve. The main problem in the solution of eq.(3) is theestimation of the term ∆ B which contains the unknownsurface brightness. In the case of Cepheids the term ∆ B ,typically, assumes small values with respect to the B termand, consequently, in the original works it was neglected c (cid:13) , 1– ?? V. Ripepi et al.
M/M logT eff logL/L 2.4 3.832 1.5 2.4 3.857 1.5 2.6 3.857 1.7 2.1 3.857 1.3 2.6 3.832 1.7 2.1 3.832 1.3
2 M/M logT eff logL/L 2.4 3.832 1.5 2.4 3.857 1.5 2.6 3.857 1.7 2.1 3.857 1.3 2.6 3.832 1.7 2.1 3.832 1.3 with NEMO models with Kurucz models
Figure 6.
The discriminant, χ as a function of the mode degree, ℓ , for pulsation frequency ν = 7.406 c/d of H254 as obtained from thefit of the photometric amplitudes and phases. The five lines correspond to models consistent with the observations. Two stellar modelatmospheres were considered: the Kurucz models (left panel) and The NEMO models (right panel). (Caccin et al. 1981; Onnembo et al. 1985). However recentlyMolinaro et al. (2011) found that the Cepheid radii esti-mated by including the ∆ B term are more accurate thanthose based on the original version of the CORS method.Ripepi et al. (1997) applied the CORS method toCepheids and calculated the ∆ B term by calibrating the sur-face brightness expressed as function of the ( V − R C ) colorindex through the relation from Gieren, Barnes & Moffett(1989). In more recent works by Ripepi et al. (2000);Ruoppo et al. (2004) and Molinaro et al. (2011, 2012), theterm ∆ B has been calculated for a sample of Cepheids byexpressing it as a function of two colors using grids of mod-els. In the present work we calibrated the surface brightnessusing the relations given by Kervella & Fouqué (2008) andtaking into account the definition in eq.(2). In particular,we defined the mean surface brightness using the relationsin ( V − R c ) and ( V − I c ) color indices: S V = (0 . . V − R c ) − . V − R c ) ++0 . . V − I c ) − . V − I c ) ) (6)while the color C ij in the eq.(3) is chosen to be ( V − I c ) .We note here that the solution of the CORS method is notdependent from the reddening because the first term of theeq.(3) contains the derivative of the color C ij and the twoterms B and ∆ B are connected with the area of the loopsdescribed by the pulsating star. To solve the CORS equation we used the fitted light curvesand interpolated the radial velocity data using the same pro-cedure of photometry (see Fig. 2). The rms of residuals ofthe data around the fitted radial velocity curve is 0.3 km/s.According to our result any phase shift between the mini-mum of radial velocity and the maximum light is lower than0.1 times the period, in agreement with other authors (seee.g. Breger et al. 1976; Noskova 1992).The mean radius obtained from the CORS method isequal to R = 3 . R ⊙ . To estimate the radius uncertainty weperformed Monte Carlo simulations following the same pro-cedure by Caccin et al. (1981). These consist in varying alldata points of light and radial velocity curves using randomshifts extracted from a Gaussian distribution. The rms ofthe distribution in the case of photometry is equal to theerror on the data points (typically 0.001 mag), while for theradial velocity it is equal to 10% of the amplitude of the ra-dial velocity itself. We have performed 5000 simulations andfor each simulated photometry and radial velocity curves theCORS equation has been solved. Finally, the uncertainty hasbeen obtained from the rms of the resulting simulated radiusdistribution (clipped at 2- σ to exclude possible outliers) andis equal to 0.7 R ⊙ .The angular size in mas, θ , of H254 was obtained fromthe relations provided by Kervella & Fouqué (2008) using ( V − R c ) and ( V − I c ) colors: log θ = 0 . . V − R c ) − . V − R c ) − . V (7) c (cid:13) , 1– ?? pplication of the Baade-Wesselink method to H254 in IC348 log θ = 0 . . V − I c ) − . V − I c ) − . V (8)with uncertainty of 4.5% and 5.6%, respectively. The de-rived mean angular diameter is equal to θ = 0 . ± . mas, for the color ( V − R c ) , and θ = 0 . ± . masfor the color ( V − I c ) . Hereafter we will use the mean value . θ + θ ) = 0 . mas and, because of the evident in-consistency of the two previous measures, we have conser-vatively estimated the uncertainty as their half differences . | θ − θ | = 0 . mas. To investigate the dependence ofthe angular diameter from the reddening, we varied it withinthe uncertainty reported above and recalculated the angu-lar diameter. The resulting variations ( ∼ . mas) areincluded into the error on the mean angular diameter. In this section we derive the distance of H254 and use it toestimate its luminosity. Then, using the spectroscopic effec-tive temperature, we place H254 in the Hertzsprung–Russelldiagram to estimate its mass and age using theoretical evo-lutionary tracks and isochrones from Tognelli et al. (2011).
The distance of H254 can be obtained by using the sim-ple equation d ( pc ) = . R ( R ⊙ ) θ ( mas ) , where R is the linearradius derived from the Baade–Wesselink method, θ isthe angular diameter, obtained by using the relations byKervella & Fouqué (2008), and the constant factor takesinto account the units of measure. The distance derived inthis way is equal to 295 ±
77 pc.Assuming the validity of the Stefan–Boltzmann law L =4 πR σT e , where σ is the Stefan–Boltzmann constant and T e is the effective temperature of the star, the distance can bealso calculated from the following equation: d = 10 . V − A V + BC V − M bol ⊙ +10 log TT ⊙ +5 log RR ⊙ +5) (9)where BC V is the bolometric correction fromKenyon & Hartmann (1995), M bol ⊙ = 4 . mag is theabsolute bolometric magnitude of the Sun (Schmidth–Kaler1982), T ⊙ = 5777 K is the Sun effective temperature.The previous equation gives a distance value equal to262 ±
54 pc. The uncertainty on the previous distancevalue was obtained from the usual rules of propagation oferrors. The value obtained by the solution of the CORSequation is in good agreement with that obtained from theStefan–Boltzmann law.A weighted average of the two distance estimates re-ported above gives 273 ±
23 pc, which represents our bestestimate for the distance of the H254.We tested the consistency of this result with the dis-tance obtained by using the Period–Luminosity relation for δ –Scuti stars. Assuming that H254 pulsate in the fundamen-tal mode (this assumption is justified in the next section),using the PL relation recently derived by McNamara (2011): M V = ( − . ± .
05) log P − (0 . ± . F e/H ] − (1 . ± . and adopting our metallicity estimate for H254, we obtainan absolute magnitude M V = 1 . ± . mag. By combining this value with the apparent visual magnitude, m V = 10 . mag, obtained from the fitting procedure of the data and theextinction A V = 2 . mag, derived in Sect. 3.4, we obtain adistance equal to 292 ±
15 pc, in very good agreement withinthe errors with the value from the BW analysis.In the literature there are other estimates of the dis-tance of H254 and/or the cluster IC 348 harbouring it.Herbig (1998) reviewed all the results till 1998 ranging fromlow values such as 240 − pc (Trullols & Jordi 1997) and260 ±
16 pc (Cernis 1993) to larger values, namely 316 ±
22 pc(Strom, Strom & Carrasco 1974). In the end Herbig (1998)assumed a distance of 316 pc (no error was given).Subsequent investigations made use of the Hipparcos par-allaxes. On the basis of 9 bright members of the cluster,Scholz et al. (1999) derived a distance of 260 ±
25 pc. Con-temporaneously, de Zeeuw et al. (1999) estimated the dis-tance of the Per OB2 association, in which IC 348 is sup-posed to be embedded, and found a value of 318 ±
27 pc.Assuming that there were no mistakes due to the inclusionof non-members to the cluster and/or to the OB association,this discrepancy could mean that the Per OB2 associationand IC 348 are not at the same distance. To check this result,we recalculated the distance of IC 348 using the membershipcriterion by Scholz et al. (1999), but adopting the revisedHipparcos parallaxes by van Leeuwen (2007). The stars se-lected in this way are listed in Tab. 7 together with therelevant information coming from the satellite. The result-ing distance is 227 ±
25 pc, a result which tends to support alower value for the distance of IC348. This is confirmed evenif we include in the calculation only the four stars closer than30 arcmin to the center of the cluster, obtaining 251 ±
50 pc.Concluding, our estimate of 273 ±
23 pc is in agree-ment within the errors with the results derived from thePeriod–Luminosity relation for δ –Scuti stars by McNamara(2011) and those coming from the Hipparcos parallaxes byScholz et al. (1999) as well as with the recalculation basedon the revised Hipparcos parallaxes by van Leeuwen (2007).We are only marginally in agreement with the larger valueof the distance, i.e. 310-320 pc found by Herbig (1998) andde Zeeuw et al. (1999). Using the distance obtained in the previous section, theapparent magnitude of H254 and our estimate for theabsorption, as well as the assumed BC, we can evaluatethe intrinsic luminosity of H254. Taking into account theerrors associated to the various quantities, we obtain: logL/L ⊙ = 1 . ± . dex. The location of the star inthe Hertzsprung–Russell diagram (filled red circle in Fig. 7with the associated error bars), is evaluated combining thisluminosity estimate with our spectroscopic measurementof the effective temperature, namely T eff =6750 ±
150 K.We notice that the evaluated position of H254 is closeto the red edge of the instability strip. In the same plot,the filled blue squares mark the location of the two bestfit models, used to define the pulsational mode of H254(Daszyńska-Daszkiewicz, Dziembowski & Pamyatnykh2003, 2005). Empirical data seems to suggest that the lowerluminosity model with logL/L ⊙ = 1 . should be preferred.Using the recent results by Tognelli et al. (2011), weoverplot in Fig. 7 the evolutionary tracks for selected masses, c (cid:13) , 1– ?? V. Ripepi et al.
Table 7.
Data used to recalculate the Hipparcos distance to IC 348. From left to right the different columns show the identification ofthe star, the distance from the center of IC348, the RA and DEC, the new parallaxes by van Leeuwen (2007), the proper motions in RAand DEC. name d RA DEC π µ RA µ DEC arcmin J2000 J2000 mas mas masHIP 17465 0.05 03 44 34.187 +32 09 46.14 6.58 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ranging from 2.0 M ⊙ to 2.8 M ⊙ , and three isochrones at 1, 3and 10 Myr. From this analysis we can conclude that H254has a mass of about 2.2 M ⊙ and an age of 5 ± M ⊙ evolutionary track at thetemperature of H254 is 3.4 R ⊙ , in very good agreement withthe CORS result.The solid and dashed magenta lines in Fig. 7 representthe loci of constant fundamental and first overtone periodrespectively, predicted by linear nonadiabatic models (seeMarconi & Palla 1998, for details), with period equal to theobserved one. We notice that, even taking into account theerrors on the star luminosity and effective temperature, thefundamental mode is favoured. In this paper we present new photometric and radial veloc-ity data for the PMS δ Sct star H254, member of the youngcluster IC 348. The photometric light curves were secured inthe Johnson-Cousins
V, R C , I C bands using the Loiano andAsiago telescopes. The radial velocity data was acquired bymeans of the SARG@TNG spectrograph. Some of the high-resolution spectra were specifically acquired with SARG toestimate stellar parameters and the chemical compositionof the star, obtaining: T eff = 6750 ±
150 K; log g = 4.1 ± ± eff derivedhere is cooler by more than 400 K with respect to previousliterature results based on low-resolution spectroscopy. Pho-tometric and spectroscopic data were used to estimate thetotal absorption in the V band A V =2.06 ± Figure 7.
The Hertzsprung–Russell diagram for H254: solid redcircle represents the position of H254 obtained by using thespectroscopic temperature and the luminosity derived from theBW analysis. Solid blue squares show the best fit models ofFig. 6. The dark vertical band represents the instability stripfrom Marconi & Palla (1998), while evolutionary tracks for differ-ent values of the mass (solid lines) and the isochrones for differentvalues of the ages (dashed lines) are obtained from Tognelli et al.(2011). Finally, solid and dashed green lines represent the locusof constant period (equal to 7.406 − d) for fundamental and firstovertone mode, respectively. taining a value for the linear radius of H254 equal to 3.3 ± R ⊙ . This quantity was used to measure the distance of thetarget star and, in turn, of the host cluster IC 348, obtain-ing a final value of 273 ±
23 pc. This estimate is in agree-ment within the errors with the results derived from thePeriod–Luminosity relation for δ –Scuti stars by McNamara(2011) and those coming from the Hipparcos parallaxes byScholz et al. (1999) as well as with our own recalculationbased on the revised Hipparcos parallaxes by van Leeuwen c (cid:13) , 1–, 1–
23 pc. This estimate is in agree-ment within the errors with the results derived from thePeriod–Luminosity relation for δ –Scuti stars by McNamara(2011) and those coming from the Hipparcos parallaxes byScholz et al. (1999) as well as with our own recalculationbased on the revised Hipparcos parallaxes by van Leeuwen c (cid:13) , 1–, 1– ?? pplication of the Baade-Wesselink method to H254 in IC348 (2007). We are only marginally in agreement with the largervalue of the distance, i.e. 310-320 pc found by Herbig (1998)and de Zeeuw et al. (1999).Finally, we derived the luminosity of H254 and studiedits position in the Hertzsprung–Russell diagram. From thisanalysis it results that this δ –Scuti occupies a position closeto the red edge of the instability strip, pulsates in the fun-damental mode, has a mass of about 2.2 M ⊙ and an age of5 ± ACKNOWLEDGMENTS
We thank our anonymous Referee for his/her very help-ful comments that helped in improving the paper. It is apleasure to thank M.I. Moretti for a critical reading of themanuscript. This research has made use of the SIMBADdatabase, operated at CDS, Strasbourg, France.
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