Cyclic variability of the circumstellar disk of the Be star zetaTau - I. Long-term monitoring observations
S. Stefl, Th. Rivinius, A.C. Carciofi, J.B. LeBouquin, D. Baade, K.S. Bjorkman, E. Hesselbach, C.A. Hummel, A.T. Okazaki, E. Pollmann, F. Rantakyrö, J.P. Wisniewski
AAstronomy & Astrophysics manuscript no. sstefl c (cid:13)
ESO 2018November 2, 2018
Cyclic variability of the circumstellar disk of the Be star ζ Tau
I. Long-term monitoring observations (cid:63)
S. ˇStefl , Th. Rivinius , A. C. Carciofi , J.-B. Le Bouquin , D. Baade , K.S. Bjorkman (cid:63)(cid:63) , E. Hesselbach (cid:63)(cid:63) ,C. A. Hummel , A. T. Okazaki , E. Pollmann , F. Rantakyr¨o , and J.P. Wisniewski (cid:63)(cid:63) European Organisation for Astronomical Research in the Southern Hemisphere, Casilla 19001, Santiago 19, Chile Instituto de Astronomia, Geof´ısica e Ciˆencias Atmosf´ericas, Universidade de S˜ao Paulo, Rua do Mat˜ao 1226, Cidade Universit´aria,S˜ao Paulo, SP 05508-900, Brazil European Organisation for Astronomical Research in the Southern Hemisphere, Karl-Schwarzschild-Str. 2, 85748 Garching beiM¨unchen, Germany University of Toledo, Department of Physics & Astronomy, MS111 2801 W. Bancroft Street Toledo, OH 43606, USA Faculty of Engineering, Hokkai-Gakuen University, Toyohira-ku, Sapporo 062-8605, Japan Emil-Nolde-Str.12, 51375 Leverkusen, Germany Gemini Observatory, Southern Operations Center, c / o AURA, Casilla 603, La Serena, Chile NSF Astronomy & Astrophysics Postdoctoral Fellow, Department of Astronomy, University of Washington, Box 351580, Seattle,WA 98195, USAReceived: < date > ; accepted: < date > ; L A TEXed: November 2, 2018
ABSTRACT
Context.
Emission lines formed in decretion disks of Be stars often undergo long-term cyclic variations, especially in the violet-to-red( V / R ) ratio of their primary components. The underlying structural and dynamical variations of the disks are only partly understood.From observations of the bright Be-shell star ζ Tau, the possibly broadest and longest data set illustrating the prototype of thisbehaviour was compiled from our own and archival observations. It comprises optical and infrared spectra, broad-band polarimetry,and interferometric observations.
Aims.
The dense, long-time monitoring permits a better separation of repetitive and ephemeral variations. The broad wavelengthcoverage includes lines formed under di ff erent physical conditions, i.e. di ff erent locations in the disk, so that the dynamics can beprobed throughout much of the disk. Polarimetry and interferometry constrain the spatial structure. All together, the objective is abetter understand the dynamics and life cycle of decretion disks. Methods.
Standard methods of data acquisition, reduction, and analysis were applied.
Results.
From 3 V / R cycles between 1997 and 2008, a mean cycle length in H α of 1400 - 1430 days was derived. After each minimumin V / R , the shell absorption weakens and splits into two components, leading to 3 emission peaks. This phase may make the strongestcontribution to the variability in cycle length. There is no obvious connection between the V / R cycle and the 133-day orbital period ofthe not otherwise detected companion. V / R curves of di ff erent lines are shifted in phase. Lines formed on average closer to the centralstar are ahead of the others. The shell absorption lines fall into 2 categories di ff ering in line width, ionization / excitation potential, andvariability of the equivalent width. They seem to form in separate regions of the disk, probably crossing the line of sight at di ff erenttimes. The interferometry has resolved the continuum and the line emission in Br γ and HeI 2.06. The phasing of the Br γ emissionshows that the photocenter of the line-emitting region lies within the plane of the disk but is o ff set from the continuum source. Theplane of the disk is constant throughout the observed V / R cycles. The observations lay the foundation for the fully self-consistent,one-armed, disk-oscillation model developed in Paper II. Key words.
Stars: circumstellar matter, emission line, Be – Stars: individual: ζ Tau
1. Introduction
Circumstellar disks of classical Be-stars have been known fordecades as the place of origin of their characteristic Balmeremission lines. Polarimetric (McLean & Brown 1978) and
Send o ff print requests to : S. ˇStefl, e-mail: [email protected] (cid:63) Based partly on observations collected at the European SouthernObservatory, Chile (Prop. Nos. 073.D-0234, 074.D-0240, 078.D-0542,and 081.D-2005; as well as archival data from programs 074.D-0573and 076.B-0055) (cid:63)(cid:63)
Visiting Astronomer at the Infrared Telescope Facility, whichis operated by the University of Hawaii under cooperative agree-ment NNX08AE38A with the National Aeronautics and SpaceAdministration, Science Mission Directorate, Planetary AstronomyProgram. combined interferometric and spectro-polarimetric observations(Quirrenbach et al. 1997; Vakili et al. 1998) have brought thelong discussion of the geometry of the disks to a definitive con-clusion. These observations confirm directly that the disks aregeometrically thin with low opening angles of about 5 −
15 de-grees. The outer radius of the H α emission was estimated at typ-ically 10 −
20 stellar radii.The detailed dynamics of Be-star disks, however, is not asclearly known. Various hypotheses exist, but the observationshave not so far yielded fully unambiguous results. The relationsbetween (a) stellar v sin i (Hanuschik 1989) and (b) disk size(Quirrenbach et al. 1997), and separation of the emission peaks,details of circumstellar line shapes (Hummel & Vrancken 2000),and the occurrence of central quasi-emission peaks in shell stars a r X i v : . [ a s t r o - ph . S R ] J u l ˇStefl et al.: Cyclic disk variations of the Be star ζ Tau (Rivinius et al. 1999) are all consistent with Kepler-like rotation,in which the rotation velocity varies as r − j , where r is the dis-tance from the star. For a strictly Keplerian disk with circularorbits the exponent j is equal to 0.5. Analyses of spectral lineprofiles (Hummel & Vrancken 2000) suggests that j < . / s. However, the angular momen-tum in a Keplerian disk increases with r / , Be disks are formedfrom matter outflowing from the star, and at least part of the diskeventually escapes from the star’s gravity. Therefore, there mustbe a net angular momentum transfer from the star to the disk andthen outwards through the disk. The mechanism for this momen-tum transfer, albeit not yet conclusively identified, is most likelyrelated to dynamical viscosity. A viscous decretion disk model(Lee et al. 1991; Porter 1996; Okazaki 2001) has recently beensuccessfully applied to the circumstellar disk of the Be star δ Sco(Carciofi et al. 2006) and, at present, is the strongest candidateto describe the structure of Be-star disks.Purely circular Keplerian disks are also unable to explain thecomplex variability of the Balmer emission lines, notably theso-called V / R (the violet-to-red flux ratio of the emission peaks)variations. Most observations of V / R variations concern lowerBalmer lines, but they can also be seen in virtually all otheremission lines. Often, V / R variations are cyclic with timescalesof 5 −
10 years (Okazaki 1991). The amplitudes can be large tospectacular. Nevertheless, many V / R cycles look strongly per-turbed because of concomitant large variations in the emission-line strength relative to the continuum and, presumably, the un-steady character of the mass loss from the central star.The first models for the V / R variations, a precessing ellipti-cal ring (Huang 1973), spheroidal / ellipsoidal variable-mass loss(Doazan 1987), and a variable stellar wind causing expansionsand contractions of the disk (Mennickent & Vogt 1991) were notphysically self-consistent. They were finally made obsolete byOkazaki’s model of one-armed density oscillations in the disk(Okazaki 1991, 1997). It is based on work by Kato (1983), whoshowed that the only possible global oscillation mode in an oftenthin Keplerian disk has m =
1. The idea of density waves was de-veloped further by Papaloizou et al. (1992), Okazaki (2000), andPapaloizou & Savonije (2006). A few scattered interferometricobservations detected decentered density enhancements in cir-cumstellar disks of ζ Tau (Vakili et al. 1998) and γ Cas (Berioet al. 1999).The wide acceptance of the model is based mainly on qual-itative comparisons. Its detailed application to specific sets of V / R curves and emission line profiles has been pending to date.A strong reason is the poor repetitiveness of V / R cycles, whichmakes it di ffi cult to decide what the model can be expected toreproduce. Furthermore, the typically long duration of the cy-cles has kept the statistics at a low level. Also, detailed compar-isons between model and observations have only become feasi-ble with the advent of three-dimensional radiative transfer codes(Carciofi & Bjorkman 2006). The generic theoretical model-ing combining the dynamics of m = V / R variations in five Be-shellstars with a companion star. They find that in some stars the V / R variability is phase-locked to the orbital motions. In others it isnot. A peculiarity seemingly limited to binary Be-shell stars (butnot exhibited by all of them) is the appearance of triple-peak H α emission profiles (which may also be described by a doublingof the self-absorption in the disk). ζ Tau is one of the examples presented by ˇStefl et al. (2007). The occurrence of such profilesseems restricted to a narrow phase interval at the beginning ofthe transition from V (cid:28) R to V ∼ R . They are not reproduced bypresent versions of the disk-oscillation model.The star ζ Tau (123 Tau, HR 1910, HD 37 202; B2 IV) isamong the most suitable targets for an in-depth observationaland theoretical test of the disk-oscillation model. The presentemission state, which started in 1990 (Guo et al. 1995, theirFig. 2), shows very stable V / R variations with a cycle length ofabout 1500 days (Rivinius et al. 2006). Compared to other V / R -variable Be stars, secular and ephemeral variations have recently(see below) been small enough that observations obtained in dif-ferent cycles can be fairly safely assembled into one picture.For decades, ζ Tau has been known as a spectroscopic binary.A comprehensive set of radial velocity measurements was com-piled and analyzed by Harmanec (1984), who derived a periodof 132.9735 d.Being a bright object reachable from both northern andsouthern latitudes, ζ Tau is one of the most observed Bestars. At the distance of 417 light years (corresponding tothe Hipparcos parallax of 7.82 mas) not only the circumstellardisk can be resolved with present-day interferometers but alsospectro-interferometry extends this resolution to the disk dy-namics. The limb-darkened photospheric diameter is estimatedat 0.4 mas (see e.g. Tycner et al. 2004; Gies et al. 2007). At theHipparcos distance, this corresponds to a radius of 5.5 to 6 R (cid:12) .The major axis of the H α emitting disk was measured byQuirrenbach et al. (1997) to 4.53 mas, corresponding to a radiusof 11.3 R (cid:63) and by Tycner et al. to 3.14 mas (almost 8 R (cid:63) ). Gieset al. (2007) derived the major axis of 1.99 mas (about 5 R (cid:63) ) forthe K-band continuum emitting disk. These values were derivedfrom the full width at half maximum (FWHM) of a Gaussianfit. The di ff erences can be reconciled by assuming that the diskwas less fully developed during the later observations as is alsosuggested by a lower H α emission strength (see below). In the K-band continuum, Gies et al. measured the semi-major axis of thedisk to 1.79 mas or 4.5 R (cid:63) (Gaussian FWHM). All these valuesare lower than the estimated Roche-lobe radius for the primaryof the system, which Tycner et al. compute as 5.3 mas (26.5 R (cid:63) )at a binary separation of 9.2 mas (46 R (cid:63) ).This first paper of the series summarizes the extended obser-vational material (see Sect. 2) and focuses on a detailed phe-nomenological description of the variability corresponding tothe V / R cycle. The variations in the visible part of the spec-trum are analyzed in Sect. 3. The variability in emission linesin the JHK -bands is described in Sect. 4. Sect. 5 is devoted tothe VLTI / AMBER spectro-interferometry and contemporaneousoptical and IR spectroscopy, and Sect. 6 deals with new and pre-viously published polarimetric observations. The last two sec-tions discuss and summarize the observational results.The second paper (Carciofi et al., this volume) presents a de-tailed self-consistent physical model of the observations. It com-bines the 2D global oscillation model of Okazaki (1997) andthe 3D radiative-transfer code HDUST of (Carciofi & Bjorkman2006, 2008).
2. Observations
In order to maximize the coverage of the V / R H α cycles, newobservations were combined with data from the literature, theESO Science Archive, and from the BeSS database (see below).Table 1 summarizes the spectroscopic data sets used for this Stefl et al.: Cyclic disk variations of the Be star ζ Tau 3
Table 1.
Spectroscopic datasets in the visual range
Data Observing JD No. of Resolving Spectralset season 2400000 + Telescope Instrument spectra power range [Å] Ref.A 1991 48 347 Heidelberg 0.9m FLASH 1 20 000 4050-6780 oB 1992 – 2007 49 049 – 51 486 Ondˇrejov 2m slit spectr. 43 8 500 6300-6700 1C 1994 & 2000 49 592 & 51 572 OHP 1.93m E lodie eros
23 20 000 3700-8600 1E 2005 – 2008 53 399 – 54 714 ESO / MPI 2.2m F eros
25 48 000 3700-9000 1,oF 2000 – 2008 51 850 – 54 174 Schmidt-Cassegrain Slitless-Grating 129 14 000 6500-6700 3G 2006 – 2007 54 005 – 54 515 SCT 0.3m LHIRES 12 13 425 6520-6700 4H 2006 54 387 & 54 083 Celestron 11 LHIRES 3 17 000 6520-6620 5I 2006 54 169 & 54 200 Takahashi TSC225 LHIRES 7 17 000 3000-7000 6J 2007 – 2008 54 162 – 54 550 Schmidt-Cassegrain Slitless-Grating 32 14 000 6500-6700 7K 2007 & 2008 54 442 & 54 527 Newton LHIRES 2 7 000 6490-6700 8L 2008 54 532 Celestron C14 LHIRES 2 17 000 6520-6610 9M 2007 – 2008 54 406 – 54 515 Meade LX200 LHIRES 10 17 000 6520-6610 10N 2008 54 106 – 54 359 C11 LHIRES 3 17 000 4000-8000 11O 2007 54 331 OHP ED120 LHIRES 1 17 000 6400-6800 12P 2006 – 2008 54 021 – 54 714 ESO / MPG 2.2m F eros
18 48 000 3700-9000 oQ 1999 – 2007 51 489 – 54 433 Ritter 1m echelle 61 26 000 4600-6700 oR 2007 54 384 OPD / LNA ECASS 1 16 000 6500-6620 oReferences: 1 – Rivinius et al. (2006), 2 – BeSS,observer: C. Neiner, 3.– E. Pollmann, data used in Pollmann & Rivinius (2008), privatecommunication 4 – BeSS observer: B. Mauclaire, 5 – BeSS observer: C. Buil, 6 – BeSS observer: E. Barbotin, 7 – BeSS observer:E. Pollmann, 8 – BeSS observer: J. Guarro Fl´o, 9 – BeSS observer: J. Ribeiro, 10 – BeSS observer: J.-N. Terry, 11 – BeSS observer:O. Thizy, 12 – BeSS observer: V. Desnoux, o – this paper study. The description of the H eros and F eros spectrographs canbe found in Kaufer (1998) and Kaufer et al. (1999), respectively.The F lash instrument is an earlier version of the H eros spectro-graph with only one spectral arm (covering the range from 4050to 6700 Å) and a somewhat lower resolution due to the use of alarger fiber, which determines the e ff ective slit width.The OPD / LNA observation was made with a Cassegrainspectrograph, equipped with a 1200 grooves / mm grating blazedat 6562 Å and a 1024x1024 pixel CCD. Observations at theRitter observatory were done with an echelle spectrograph inthe Cassegrain focus of the 1-m telescope, using the old cam-era equipped with a 1200x800 pixel CCD (cf. Sect. 2.4).In recent years, the technological progress has broughtbright stars like ζ Tau within reach of quite a few amateurtelescopes and spectrographs. Spectra of many Be stars areregularly deposited in, and conveniently available from, BeSS(http: // basebe.obspm.fr). As Table 1 shows, they account for alarge fraction of the total optical spectroscopy used in this paper. Fourteen infrared (IR) spectra were obtained between March5, 2004 and October 9, 2007 using the SpeX spectrograph atthe 3.0-m NASA Infrared Telescope Facility (IRTF) on MaunaKea (Rayner et al. 2006). With a 0 . (cid:48)(cid:48) . (cid:48)(cid:48) ∼ µ m. The observing and data reduction techniques mirrored thoseused in previous SpeX programs to study classical Be stars (see,e.g., Wisniewski 2005, Wisniewski et al. 2007). Observations of ζ Tau were immediately followed by observations of a nearbyA0V star located at a similar air mass, to facilitate optimal tel-luric correction (Vacca et al. 2003), along with a series of quartz-tungsten-halogen flat field and argon arc lamp exposures. TheIDL-based Spextool software was used to perform the basic data reduction and spectral extraction using the techniques describedin Cushing et al. (2004).
Our near-IR interferometric observations with AMBER (Petrovet al. 2007) and three 8-m telescopes (UT 1, 2, and 4) of ESO’sVLTI interferometer were made during the night of December12, 2006. Interferometric fringes from all 3 pairs of telescopes(hereafter called baselines) were measured across the K-band, atmedium spectral resolution of R ≈ γ (2.16 µ m) and He i (2.06 µ m) lines.The ζ Tau observations were interlaced with observations of thecalibration stars HD 39 699 and HD 59 686, for which diametersof 1.03 mas and 1.30 mas, respectively (M´erand et al. 2005),were adopted.In principle, three distinct quantities can be extracted foreach spectral channel of the AMBER spectro-interferometer: thefringe visibility (measuring the spatial extension of the emittingmaterial), the fringe phase (measuring the position of emittingmaterial), and the closure-phase (the sum of the 3 phases ob-tained for the 3 interferometric arms, sensitive to asymmetriesin the source brightness distribution). In AMBER data sets, thesignal-to-noise ratio on the closure-phase is very low and onlyvisibilities and phases were used for the analysis.The data reduction was done using the amdlib-2.2 pack-age, which employs the P2VM algorithm (Tatulli et al. 2007).In a first step, the instrumental calibration matrix with the stan-dard calibration files provided by ESO was computed. This ismandatory in order to properly convert the raw individual framesinto raw interferometric visibilities and phases (about thousandmeasurements per observation). The next steps consist of aver-aging these di ff erent frames into individual measurements, andperforming the final calibration. Based on our past experience ˇStefl et al.: Cyclic disk variations of the Be star ζ Tau
Fig. 1. H α V / R variations (lower panel) and emission peak separation (upper panel)of ζ Tau in the period 1992-2008 showing thedetailed character of more than 3 V / R cycles since 1996. The symbols correspond to the following data sets: ( + ) Ondˇrejov slitspectrograph, (O) OHP 1.93m, (x) Pollmann, (H) H eros , (F) F eros , ( (cid:52) ) Ritter Observatory, ( · ) BeSS database, ( (cid:3) ) A. Carciofi, seealso Table 1. Phases with triple-peaked emission line profiles are indicated by solid horizontal barsof spectro-interferometry with AMBER, two di ff erent strategieswere adopted. In the following they are distinguished as absolutereduction and di ff erential reduction . Only a brief description isincluded here, as both methods are now considered to be stan-dard data reduction steps for AMBER. Absolute data reduction:
The objective of this method is toprovide an absolutely calibrated estimation of the fringe visibil-ity (the fringe phase cannot be determined in an absolute man-ner). It requires the multiplicative e ff ect of the atmospheric tur-bulence (generally called transfer function) to be properly esti-mated. – For each observation, the top 20% of the frames with the bestsignal-to-noise ratio were averaged. This ratio provides themost stable transfer function, see discussion in Tatulli et al.(2007) and Millour et al. (2007). – The transfer function was estimated by averaging all obser-vations of the calibration stars. Their scatter is a measure forthe uncertainty of the transfer function. The resulting stabil-ity is very poor, with temporal fluctuations as large as 30%,partially due to the atmospheric turbulence and to the Unit Telescope infrastructures, which generate non-stationary vi-brations. – Absolutely calibrated quantities were derived by dividing –separately in all spectral channels – the raw visibilities of ζ Tau by the derived transfer function. Error bars on thetransfer function completely dominate the final uncertainties. – Finally, all spectral channels were averaged (avoiding theHe i and Br γ lines) to provide a single visibility across theband for each observation. Formally it introduces a smallamount of wavelength smearing, which is however negligi-ble at the level of precision.It is worth noting that this observation strategy has been opti-mized for di ff erential interferometry, not for absolute calibrationof the fringe visibility. Only a single calibration star has been ob-served for each AMBER instrument setup, and the observationsof the calibration stars do not bracket properly the observationsof the science target. Therefore it is hard to asses the reliabil-ity of the absolute calibration (usually done by comparing val-ues obtained using di ff erent calibration stars). Consequently, thefringe visibility derived with this method should be interpretedcarefully. Stefl et al.: Cyclic disk variations of the Be star ζ Tau 5
Differential data reduction:
This method aims mainly at a pre-cise measurement of the di ff erential quantities (visibility andphase) in the Br γ and He i lines with respect to the adjacentcontinuum. Compared with the previous method, a significantlyhigher SNR can be obtained because the atmosphere a ff ects allspectral channels in very nearly the same way. The main draw-back is that the continuum level is obviously lost. – First, as many as possible individual frames were averaged.To do so, all consecutive observations with the same instru-ment setup were merged together before averaging the 70%of the frames with the best signal-to-noise. It was tested thatthis method provides the best final accuracy on the di ff eren-tial quantities. – The here presented AMBER data were corrupted by rippleswith low beat frequency in the spectral direction (few cy-cles along the complete K-band spectrum) ). These artifactsmainly a ff ect the phases and not the visibilities, explainingwhy they are not of a big concern regarding the absolute datareduction. To correct them, a high-pass filter along the spec-tral direction was applied to the phases. Di ff erent methods(high-pass filter, optimal filtering at the corrupted frequen-cies, manual fit of the continuum ripples) were tested butdi ff erences in the resulting He i and Br γ phase profiles couldbe seen. – At that stage, the continuum levels for both the phase andthe visibility are arbitrary. The brightness distribution of theK-band continuum emitting region has already been con-strained by Gies et al. (2007). Because they used longer base-lines and more precise absolute calibration, their results aresignificantly better than the AMBER measurements for thecontinuum (see previous paragraph). Therefore the AMBERcontinuum level around the Br γ and He i lines was forced toto match the CHARA model of Gies et al. (2007), which isdisplayed in Fig. 10 . The polarimetric data are from observations made with theHalfwave Polarimeter (HPOL; Nordsieck & Harris 1996). Theinstrument was used primarily on the 0.9-m telescope at thePine Blu ff Observatory (PBO), operated by the University ofWisconsin (UW). The data are available through the HPOL website (http: // / HPOL) developed by M.R. Meadeand B.L. Babler, and data prior to 1995 are also available throughthe NASA MAST archive. The database includes a wide rangeof hot stars, the polarimetric variability of which has been dis-cussed in Bjorkman & Meade (2005).Data from 1989-1994 were obtained using a dual Reticonarray detector, which provided spectropolarimetry over a wave-length range of 3200-7600 Å, with a spectral resolution of 25 Å(Wol ff et al. 1996). In 1995, the HPOL detector was upgradedto a 400 × ff et al. (1996).As described by Wol ff et al. (1996), the data were processedand analyzed using REDUCE, a specialized spectropolarimetric The interferences between the light beams reflected inside theAMBER polarizers created “Moir´e fringes” in the spectral direction.The optics responsible for these artifacts was identified and properlyreplaced in October 2008.
Fig. 2. V / R data from Fig. 1, phase binned with JD + × E . Horizontal lines indicate the triple-peak phases (3-pk)from Table 2, which introduce a higher scatter in the correspond-ing phase interval because they make the definition of the V and R emission components doubtful. The letters in the upper partof the figure mark the phases of the AMBER observation and ofrepesentative visual and infrared spectra used in Sects. 3.5 and 4(see also Tables 4 and 5)software package developed at UW. Instrumental polarization ismonitored regularly as part of the observing program at PBO,and all data are fully calibrated for instrumental e ff ects to an ac-curacy of 0.025% in the V band.For the purposes of this study of ζ Tau, the spectropolarimet-ric data were binned to approximate broad-band
U BVRI results.The individual uncertainty of an HPOL measurement was esti-mated by a statistics over a series of data of polarized standards:It is about 0.01 % for the polarization degree and 1 deg for thepolarization angle in
BVRI , and about two to three times as highin the U -band.
3. Visual spectral line variability ζ Tau circumstellar disk andits V / R variations Harmanec (1984, his Fig. 2) showed that the present well-pronounced V / R variations were absent in earlier decades: Atleast from 1920 to about 1950 there was no V / R cyclicity. A V / R -variable phase started in the mid-1950s and lasted for aboutthree cycles until 1980. From 1980 to 1990 the star was againstable with V ≈ R . From 1980 to 1985 the equivalent width(EW) of the H α emission decreased from about −
23 to −
12 Åwhile the star brightened by 0.3 to 0.4 magnitudes in the
U BV passbands, also getting slightly bluer. This behavior is typical ofBe-shell stars as described observationally by Harmanec (1983)and predicted before by Poeckert & Marlborough (1978, theirFig. 33) for the case of decreasing base density of the disk.From 1985 to 1990 the disk was in a low-density state (Guoet al. 1995, their Figs. 2 and 3). The V / R variability was notwell sampled observationally. But short-term (days) variabilityprobably dominated (Guo et al. 1995, their Fig. 5). It would,then, have resembled a phase observed in µ Cen by Hanuschiket al. (1993), in which rapid V / R variations were due mainly todiscrete mass loss events and the subsequent circularization ofthe ejected matter. ˇStefl et al.: Cyclic disk variations of the Be star ζ Tau
Fig. 3.
Evolution of representative lines in the visible spectrum during the V / R cycle. See Table 4 for the properties of spectra “A”to “F”. The H α V / R can bbe read o ff Fig. 2Around 1990, the emission strength began to increase againto a high level of almost −
30 Å, together with brightness andcolour changes as expected for an edge-on disk with increas-ing base density. At the same time, the disk entered a phaseof V / R variations. Since this replenishing of the disk, the emis-sion lines became weaker (H α EW between −
15 and −
20 Å ),but the V / R variations are still ongoing. The AAVSO database indicates that the magnitude was stable over the last 8 years( < m V > ∼ . m ± . m American Association of Variable Star Observers;htpp: // / data Table 2.
Properties of individual V / R cycles Cycle Max. V / R Cycle Triple peaknumber JD 24 V / R length [d] [JD 24 range] [d]I 50 414 1.62 1419 51 137 – 51 440 303II 51 833 1.58 1527 52 580 – 53 094 494III 53 360 1.44 1230 54 005 – 54 208 203IV 54 590 1.40 N / A N / A – N / A NAStefl et al.: Cyclic disk variations of the Be star ζ Tau 7 α equivalent width Equivalent widths were measured by means of an automaticMIDAS (Grosbøl & Ponz 1990) procedure in the interval 6546 − − . −
20 Å, with a mean of( − . ± .
2) Å. After an initial increase of emission lasting fromabout 1991 to 1994 the value remained rather stable. This is afurther indicator of the validity of the assumption that the indi-vidual cycles are comparable to each other.In view of the uncertainties in the normalization of theechelle spectra with imperfectly corrected wiggles and system-atic di ff erences between spectrographs with very di ff erent spec-tral resolution, a more detailed analysis of the measured to-tal equivalent widths and their temporal variations was not at-tempted. In the visual (and higher-resolution) spectra, two types of shelllines (dubbed “narrow-” and “broad-line group”, NLG and BLG)and their associated cyclic behavior can be distinguished. PureNLG-type shell absorption is found in lines of Fe ii (near-UVlines only), Fe iii , Ni ii , O i , Na i , and He i . The cores of theBalmer lines, too, fall into the NLG category. Pure BLG-typeshell absorption is seen in some lines of Si ii , Fe ii (visual wave-lengths), Cr ii , Ti ii , Mg i , and O i . This group also includesMg ii / BLG classification of themost important spectral lines in the optical spectrum is markedin Table 3.The assignment of a line to BLG or NLG is not in allcases and not at all epochs unique. For instance, Fe ii ii V / R cycle.Other BLG lines, too, exhibit additional temporary NLG com-ponents, especially around V / R phase τ ≈ .
25 (see Sect. 3.5).Typical representatives are the strongest shell lines due to Si ii ,Ca ii , Ni ii , and Fe ii .Besides the obvious property of their widths, the two groupsalso di ff er in their variations of radial velocity and symmetry asdescribed in Sect. 7.7 V / R cycles Some confusion may occur due to di ff erent definitions of the V / R ratio in the literature. They di ff er in the reference flux level,with respect to which the peak maxima are measured. This pa-per uses the more common definition ( V / R = F V / F R , where F V and F R are the relative fluxes at the violet and red emis-sion peak maxima, respectively), according to which V / R iscomputed without prior correction for the underlying continuumlevel. Therefore, the results are less influenced by the spectrumnormalization than in the other definition, which uses only theflux above the continuum level. Consequently, this approach en-ables to combine reasonably well V / R values even in hetero-geneous databases. Since the photometric variability has beensmall (Sect. 3.1), while the H α line emission was strong, thecontinuum variability should have little e ff ect on the V / R valuesmeasured in this way. The V / R values obtained for the interval1993-2008 are visualized in Fig. 1.The observations before JD 2 450 500 are insu ffi cient to con-clude whether the V / R cycle was not yet stabilized or whetherthe sampling was too sparse to deduce a more regular V / R vari- Table 3.
Selected spectral lines in the optical spectrum andtheir classification into broad-line (BLG) and narrow-line group(NLG), respectively, as described in Sect. 3.5
Wavelength Ion Comment3187.746 He i NLG, no phot.3465.642 Ni ii NLG3468.678 Fe ii NLG3471.386 Ni ii NLG3513.987 Ni ii NLG, strong3530.505 He i pure phot.3554.412 He i pure phot.3587.268 He i pure phot.3634.238 He i pure phot.3968.469 Ca ii BLG + NLG3994.997 N ii pure phot.4002.592 Si ii BLG4067.031 Ni ii BLG + NLG4128.054 Si ii BLG + NLG4130.872 Si ii BLG + NLG4258.154 Fe ii BLG4294.099 Ti ii BLG4481.126 Mg ii BLG4824.127 Cr ii BLG5015.678 He i NLG + weak phot.5100.727 Fe ii BLG5127.387 Fe iii
NLG5156.111 Fe iii
NLG5169.033 Fe ii BLG + NLG5172.684 Mg i BLG5183.604 Mg i BLG5197.577 Fe ii BLG + NLG5226.543 Ti ii BLG5316.615 Fe ii BLG + NLG5679.558 N ii pure phot.5875.625 He i NLG + phot.5889.951 Na i NLG5895.924 Na i NLG6147.741 Fe ii BLG6149.258 Fe ii BLG6156.755 O i BLG6158.187 O i BLG6347.109 Si ii BLG + NLG6371.371 Si ii BLG + NLG6678.154 He i NLG + phot.7774.166 O i NLG ability. However, the subsequent observations define nicely threecomplete cycles marked I, II, and III in Fig. 1. Cycle IV just com-menced about JD 2 454 590. Starting Julian Dates and lengths ofthe cycles are summarized in Table 2. The cycle-averaged V / R curve is displayed in Fig. 2.The mean V / R curve is smooth and roughly symmetric ex-cept for some time shortly after the minimum. During this as-cending branch, the H α emission is split into three peaks (or theself-absorption is split into 2 components), making the definitionof ‘the’ V and ‘the’ R component ambiguous (see Sect. 3.5.4and Fig.6). An increased scatter in V / R values is the result (seeFigs. 1 and 2). Obviously, the disk variability cannot be charac-terized by a single parameter such as V / R alone.By contrast, the V / R maxima are very well defined and canbe used as fiducial marks for measuring the length of V / R cy-cles. Fourth-order polynomials fitted to the peaks over di ff erentbaselines indicate an error in their position of 5-8 days. ˇStefl et al.: Cyclic disk variations of the Be star ζ Tau
In spite of the systematic uncertainty in V / R , Fig. 1 seemsto suggests a secondary V / R maximum that coincides with thetriple-peak phases and follows the main minimum. Apparently,such secondary maxima in the cyclic V / R variations were not sofar reported for any Be star. Their height and widths vary fromcycle to cycle and the strongest secondary peak can be recog-nized in Cycle II at JD 2 452 700 – 2 453 000.A formal Fourier frequency analysis was only applied toH α V / R values not a ff ected by a third component (see Table 2for the corresponding dates). Such a restriction is suggested bythe sensitivity of most period-search methods to non-sinusoidalperturbations and to a lower accuracy of the V / R values dur-ing the triple-peak phase. The CLEAN method of the sinusoidfitting (Kaufer et al. 1996) gives periods P = (685 ±
5) dand P = (1405 ±
26) d, obviously the former one is the har-monic produced due to variable cycle lengths. Scargle’s method(Scargle 1982) is less likely to return harmonics and suggests1429 days.This mean duration of the V / R cycles is shorter than the val-ues derived by Pollmann & Rivinius (2008), 1475 days, and byRivinius et al. (2006), 1503 days. The di ff erences are well ex-plained by the di ff erent data sets used. In particular, the earlierstudies could not include the shorter-than-average triple-peakphase of Cycle III. Even more di ff erent and variable cycle lengthcan be identified during the 1955 - 1980 V / R variable phase. Thecompiled data presented by Harmanec (1984) show three max-ima, defining -in the same sense as in this paper- two completecycles of about 2290 and 1290 days.Radial-velocity (RV) measurements su ff er from the inhomo-geneity of the database in a similar fashion as the absolute emis-sion strength does. The impact of this inhomogeneity is reducedin the RV separation of the red and violet emission peaks (Fig. 1.The separation follows the V / R cycle, but with a possible phaseshift and a considerably higher scatter, which not surprisingly ismost prominent when the triple-peak profiles are present. Thedates of maxima of peak separation are delayed by 100 - 200days with respect to the V / R maxima. V / R cycle The repeatability of the V / R cycles for more than a decade justi-fies the introduction of the concept of an ephemeris and a phaseso that observations can be compared between cycles. In the fol-lowing, all phases refer to the formal cycle length of 1429 daysfrom above and adopt the V / R maximum of JD 2 450 414 as thereference epoch. The co-phased V / R curve is given in Fig. 2.In order to more completely characterize the disk variabil-ity than the V / R ratio can do, 6 optical reference spectra wereselected. Their V / R phases are marked in Fig. 2. The spectrawere sorted such that the phase of equal peak height in presum- Table 4.
Optical spectra representative of the V / R -cycle. F lash is the predecessor instrument of HEROS, i.e. the same instru-ment before the extension with a blue channel Spectrum [JD 24...] Instrument CommentA 53 333.8 UVES / ESO Archive nightly averageB 52 009.3 H eros / Data Set C single spectrumC 53 700.8 UVES / ESO Archive night averageD 52 364.3 H eros / Data Set C single spectrumE 52 725.3 H eros / Data Set C single spectrumF 48 347.6 F lash / LSW Archive single spectrum
Fig. 4. H α , H β (solid), and O i i ii ff erent length.Phenomenologically, “F” is actually following “E”.)This classification is restricted to the visual spectral range.For the IR spectra, which are more limited in phase coverageand spectral resolution, a separate scheme is introduced in Sect.4. The following subsections describe the main optical V / R phases and their transitions. The definition of the V / R phases isfor H α . The variability of other lines may have significant o ff setsin phase, as detailed below. V > R This phase is represented by the “A” profiles in Fig. 3. In allemission lines the violet peak is higher than the red one. Theshell absorption lines weaken and become narrower. Both NLGand BLG are red-shifted with respect to the systemic velocity.However, there are di ff erences: The red edge of BLG shell ab-sorption is very steep, and the blue edge rather asymptoticallyjoins the continuum. In the NLG, it is the blue edge which issteeper than the red one. All ionic species are present but somelow-ionization lines begin to weaken. V = R , descending to V < R , and deep absorption When the strength of the R peak in H α begins to approach theone of the V peak, the peaks in H β are already of almost equalheight, and Fe ii lines even exhibit an inverted V / R ratio (cf. spec-tra “B” and “C” in Fig. 3).Some of the low-ionization shell lines of the BLG categoryhave completely vanished, while the NLG shell lines are at max-imum depth now. The Balmer series is maximally visible up toH40 /
41. At other phases, the limit is reached around H34 / H35(see Fig. 7).While pure BLG lines such as Mg ii Stefl et al.: Cyclic disk variations of the Be star ζ Tau 9
Fig. 5. V / R variations of Br γ and δ (middle panel) and Br 12 –16 (lower panel). H α values are shown in the upper panel forcomparisonlines are far more clearly present than at other phases, phe-nomenologically belonging to the NLG. Their FWHM is onlyabout 17 to 20 km s − , i.e. about the thermal width.Shell lines of Fe ii and Si ii , however, develop a two-component structure related to both groups: a very narrow anddeep absorption core at zero velocity is superimposed on a broadand shallower absorption that has its own distinct core farther tothe blue. The two cores can be clearly identified as parts of theBLG and NLG characteristics, respectively. V < R The “D” profiles in Fig. 3 illustrate this phase. The red peakreaches its maximal strength. Both NLG and BLG lines areblue-displaced with respect to the systemic velocity. The dualNLG / BLG characteristics of some lines weakens and finallyvanishes in that NLG cores disappear while the remainder ofthe profile evolves as if belonging to the BLG. V = R , ascending to V > R , and triple-peak structure Spectra “E” and “F” in Fig. 3 o ff er a general overview of thisphase, and Fig. 6 illustrates the temporal evolution in H α . Themost intriguing property of this phase is that the H α line emis-sion strongly deviates from the classical Be star profile in that Fig. 6.
Evolution of the H α triple-peak profiles in the two mostrecent V / R cycles of ζ Tau. The shifts between the spectra cor-respond to di ff erences in phase as indicated on the left side.The phase is computed separately for each cycle, using di ff er-ent starting dates (V / R maxima) and lengths as listed in Table 2.The vertical bar indicates the 100 % continuum levelit no longer shows clear double peaks with a well-pronouncedcentral depression. Rather, the central depression is filled in (orsplit) and three peaks of similar strength co-exist. Although thecentral depression does not get filled in in the other Balmer lines,and they do not show multiple peaks, their structure is more com-plex than in other phases.The O i β and therefore usually assumed to present an optically thin tracerof the hydrogen distribution, does not show any sign of a triplepeak (see Fig. 4). Instead, the profile is double-peaked with acentral depression. Noteworthy is that the radial velocity of thered peak of the O i profile coincides with the local minimum inthe triple peaked H α and H β profiles.The shell absorption lines are strong and yet relatively broad.Lowly ionized species like Ti ii , Cr ii , or Mg ii prevail, but high-ionization species like Fe iii still produce noticeable absorption.Spectrum “F” (Fig. 3) was obtained in 1991. Since then,the shell spectrum has generally weakened. But there is nodoubt that spectrum ”F” is representative of the general V / R pat-tern about this phase. The latter includes that, between spectra“E” and “F”, BLG shell absorptions shift from zero to moder-ately positive velocities. Examples are Mg ii ii ii ζ Tau
Fig. 7.
The region of the Balmer discontinuity (upper panel) andthe narrow shell lines (lower panel) in the Balmer continuum inreference spectra “A” (lower plots) and “C” (upper plots), seeSect. 3.5.2In the NLG shell lines, however, the position of the line min-imum as well as the symmetry change in exactly the oppositeway, from low positive velocity to zero velocity in the same twoobservations. See, e.g., Fe iii i ii β , where emission stilldominates over the shell absorption, already show the V peakhigher than R . That is, the V / R phase of these lines is ahead ofthe one of H α .Fig. 6 illustrates the evolution of the triple peak profiles in thetwo most recent V / R cycles. The triple-peak interval in Cycle IIlasted for almost 500 days, while in Cycle III it was only 200days. As can be seen from Figs. 1 and 2, the onset of the triple-peak interval is typically fairly close to phase 0.5. Much strongercycle-to-cycle variations are evident for its terminal phase. Inspite of the varying time scale, however, the morphological evo-lution of the H α line profile follows approximately the same pat-tern in all cycles.
4. Infrared spectral variations
As for the optical domain, a number of phase-representative ref-erence IR spectra were selected to facilitate the description of
Table 5.
Representative infrared spectra
Spectrum Date [JD 24...] CommentI 53 722 22 days after spectrum “D”II 53 982 just before triple peakIII 54 097 contemporaneous to AMBERIV 54 281 just after triple peakV 54 382 the main variability. Their dates are marked as I through V inFig. 2, and listed in Table 5.The IR spectra (see Fig. 8) cover the JHK bands and the H α V / R phases from about 0.3 through 0.8. Although of lower res-olution, some of the conclusions already drawn from the visualspectra are confirmed: The V = R deep absorption phase hasthe same characteristics in the IR, as far as H i and He i are con-cerned. In the triple-peak phase, the shell absorption gets shal-lower in He i and even disappears completely in the higher-orderBrackett lines, leaving a pure emission profile although with apronounced central depression. All observed Brackett lines aredouble-peaked at all times. But Br γ and Br δ develop single-peakprofiles when the one in H α shows a triple-peak structure. Alsometallic lines, in particular those of Fe ii may show single peakprofiles, but at other phases. But it must be suspected that thismerger is only apparent due to the limited spectral resolvingpower.The IR lines provide the basis for a more in-depth discussionof the phase lags between H α and other lines (Sect. 3.5.4). Atsome phases, they are well visible even within H i emission ofthe Brackett series. In Spectrum III of Fig. 8 the lower Brackettlines still show V < R and, in Br γ , even V (cid:28) R , but towards theend of the series V / R reaches unity. In a spectrum taken lessthan a month later, some of the latter lines even appear with V > R while Br γ looks unchanged. The V = R state is alsoreached in He i , Fe ii , and Mg ii . These two particular observa-tions (incl. Spectrum III) were obtained almost simultaneouslywith the AMBER data described below.The phase lag between higher- and lower-order Brackettlines is also well visible in Fig. 5. Already the first IR obser-vation on JD 2 453 069 shows that, while log( V / R ) is still belowunity for H α , it is about unity for Br γ and Br δ , and still largerfor higher Brackett lines. In general, the V / R values for both Br γ and Br δ precede the V / R curve of H α , but clearly lag behind theones of the Br 12-16 lines. The V / R amplitude of the Br 12-16lines is slightly lower than the ones of Br γ and Br δ . But it islower by a factor 8-10 relative to the one of H α .Contrary to H α (see Fig. 2), a distortion of the V / R curvearound phase 0.6 due to triple-peak profiles cannot be recognizedin any IR lines. Observations at higher spectral resolution aredesirable to establish this definitively.A very conspicuous type of behavior without counterpart inthe visible range is associated with the infrared C i lines (seeupper right panel of Fig. 8). IR multiplets 1 and 24 of this speciesare seen in emission in six out of fourteen IR spectra (JD24:53 069, 53 639, 53 722, 53 723, 54 038, and 54 070) and absentin the others. Since intermediate cases were not observed, thismay constitute some type of “on / o ff ” behavior. Contrary to thetypical circumstellar lines described above, these lines have asymmetric single-peak profile and exhibit no variability otherthan their being either present or absent. No relation could befound of the presence or absence of the C i emission to the V / R cycle or the 132.9735-d orbital period. It was also checked that Stefl et al.: Cyclic disk variations of the Be star ζ Tau 11
Fig. 8.
Selected spectral windows in the J, H, and K bands. Observing dates of spectra I through V are given in Table 5; their phasesin the mean H α cycle are marked in Fig. 2. Pa γ is blended with He i
16 600 and two magnesium lines. Spectrum III is the one closestin time to the AMBER observations. The upper right panel combines all spectra of C i multiplet 1 in the J-band, illustrating its on / o ff behavior Fig. 9.
Visual spectroscopic state of ζ Tau during the AMBER observationsthe variations cannot be produced by an overlapping OH telluricemission (Rousselot et al. 2000).
5. Interferometric results
AMBERIn Fig. 10, the left panel shows the coverage of the uv plane byour AMBER observations. Following the ESO / VLTI documen-tation, the following baseline position angles were accepted: U1- ζ Tau U3 = = = ζ Tau model derived from the CHARA K’-band ob-servations by Gies et al. (2007) are over- plotted. The AMBERcontinuum observations – in spite of the large scatter – are com-patible with the CHARA model. However their accuracy and thefact that ζ Tau is only marginally resolved by AMBER / VLTI inthe K-band continuum prevent us to test the model in more de-tail.AMBER spectro-interferometric measurements were com-bined with the CHARA model in order to derive visibilities andphases in Br γ and He i µ emission lines (see Sec. 2.3). Thedi ff erential values are shown in Figs. 11 and Figs. 12 for the re-gions around Br γ and He i µ , respectively. In all baselines,the signal is much stronger in the Br γ line (2.17 µ m), but it is alsoclearly detected in the He i line (2.06 µ m). The drops in visibilityprove that the Br γ and He i emitting regions are more extendedthan the continuum emitting region. Moreover, an asymmetryin the visibility profile is clearly seen, with the visibility in thered part being lower than in the blue part. Fitting these visibilityprofiles across the lines requires proper modeling. Such a workis presented in paper II.Apart from the visibility signature, also a phase e ff ect wasfound in all baselines for Br γ , indicating that the photocen-ter across the line is shifted with respect to the photocenterin the continuum. To allow a geometrical representation of theAMBER phases, the di ff erential-phases φ ( λ ) across the Br γ linewere converted into 2D astrometric shifts p ( λ ) by inverting thewell-known formula for marginally resolved interferometric ob-servations (Lachaume 2003): φ ( λ ) = − π · p ( λ ) · b λ (1)where b is the interferometric baseline vector projected onto thesky. Uncertainties were propagated to the astrometric vector p bystandard formulas. Neither the uncertainty in the baseline lengthnor in the spectral calibration were taken into account, becausethey a ff ect all spectral bins in the same way.Figs. 11 and 12 prove the presence of phase di ff erences ofthe V and R emission components with respect to the contin-uum. The observed (di ff erential) phases are the flux weightedvector sum of the source phases of the continuum and line com-ponents. With a physical model of the disk and radiative trans-fer, the fluxes are known and the phase di ff erences between thecontinuum and line emitting regions can be translated into theirangular separation. Such a model is presented in Paper II. Themodel-independent conclusion is that the line emitting regionsand the continuum source lie in one common plane but that theV and the R components arise from di ff erent locations that donot coincide with the continuum source.Fig. 13, left panel shows the computed relative o ff sets inangular units. The phases across the Br γ line is converted into2D photocenter shift in the plane of the sky. The photocenter isdisplaced toward the NW direction in the blue part of the line,and toward the SE direction in the red part of the line. This isthe clear signature of the rotating disk emitting the Br γ line. Theposition angle of the displacement is perfectly compatible withthe position angle of the CHARA model based on measurementsmade in the K’ continuum, as shown in the right panel of Fig. 13.Moreover, the amplitude of the photocenter displacement is sig-nificantly larger in the red wing (280 µ as, SE) than in the blue −400−200 0 200 400−200 0 200 400 Modelmajor−axisModelminor−axis
0 100 200 300 4000.00.51.01.5 −1 0 1−1 0 1
Baseline (arcsec −1 ) v i s <− East U (arcsec −1 ) V N o r t h −> Fig. 10.
Schematic comparison of the VLTI / AMBER observa-tions with the CHARA model by Gies et al. (2007). In the colourplot available in the on-line version of the paper, the green, redand blue colours correspond to the UT 3-4. UT 1-3 and UT 1-4baselines, respectively. Left panel: Coverage of the uv plane byAMBER observations of Dec 12, 2006. The sub-frame in the up-per right corner shows the CHARA model projected on the sky(before the transformation). The sub-frame covers the region ofabout 3mas x 3mas and corresponds to the K-band continuum.The squired visibility of the AMBER observations is linearlyproportional to the size of symbols, for the CHARA model (inthe sub-frame and transformed in the background) to the bright-ness. Right panel: Absolutely calibrated continuum squared vis-ibilities as a function of the baseline length. Squared visibili-ties of the major and minor disk axes derived from the CHARAmodel are overplotted.wing (120 µ as, NW). The simplest explanation is an asymme-try in the Br γ -emitting material, with the SE part being brighterand / or more extended than the NW part. Again, modeling of thissignal in the framework of the one-armed disk-oscillation modelis developed in Paper II. AMBER observations
When AMBER observed ζ Tau, simultaneous FEROS opticalspectra as well as quasi-simultaneous IRTF spectroscopy werealso obtained. Fig. 9 depicts representative visual line profiles.Further FEROS observations were made throughout December2006, which di ff er but little from the one at the time of the VLTIobservations. In the IR, Spectrum III (see Fig. 8) comes closest(12 days before) in time to the AMBER observations. A nextspectrum, obtained 16 days after AMBER data, is very similar.Therefore, the low variability in both optical and IR spectra sug-gests that the selected spectra represent well the dynamics of thedisk at the time of the AMBER observations.As IR spectrum III shows (Fig. 8), the emission is almostsymmetrical in He i µ m, so that the much lower amplitudeof the phase signature in the same line is in good agreement withthe spectroscopic data. The distribution of the He i µ m emit-ting material is symmetric with respect to both systemic velocityand location of the continuum source.The situation is di ff erent for Br γ but the reasoning is thesame: The closure phase is undoubtedly non-zero for this lineand proves a spatial asymmetry in the brightness distribution ofthe system (continuum vs. line-emitting region). At the sametime, the V / R value of Br γ is far from unity. The combinationof these two asymmetries places the bulk of the Br γ -emittingregion to the receding sector of the disk. Stefl et al.: Cyclic disk variations of the Be star ζ Tau 13 l ( m m) l ( m m) l ( m m) v i s f ( d e g ) UT1−3 (93m, 43deg) UT3−4 (52m, 99deg) UT4−1 (130m, 63deg)
Fig. 11.
AMBER visibilities and phases around 2 . µ m normal-ized to the model of Gies et al. (2007). l ( m m) l ( m m) l ( m m) v i s f ( d e g ) UT1−3 (93m) UT3−4 (52m) UT4−1 (130m)
Fig. 12.
Same as Fig. 11 but around 2 . µ m. The signal is sig-nificantly weaker but the He i line is still detectedThe scheduling of the AMBER observations was very suc-cessful in that they could be made during a triple-peak phase ofthe H α emission. However, with single-epoch data it is di ffi cultto say whether they harbor any related hidden anomaly. For adiscussion of the azimuth (in a not point-symmetric model) ofthe region of formation of this spectral structure see Sect. 7.6.
6. Polarimetric results
Since the V / R cyclicity before JD 2 490 000 is not well con-strained by the observations and, as described in Sect. 3.2, ζ Taureached a stable disk state only after that date, only polarizationmeasurements obtained after JD 2 490 000 were taken into ac-count for the computation of the mean values shown in Table 6.The polarization angle (PA) is the same in all bands withinboth the individual uncertainty and the standard deviation.Although the standard deviation of the PA measurements isslightly higher than the uncertainty estimated for a single mea-surement, this di ff erence is not large enough to conclude a vari-
34 +/− 5deg −0.4−0.20.00.20.4−0.4−0.20.00.20.4 −1 0 1−1 0 1 <− East (mas) N o r t h ( m a s ) −> <− East (mas) N o r t h ( m a s ) −> Fig. 13.
Left: Photocenter shifts derived from the AMBER rel-ative phases across Br γ . The maximum shift is about 0.4 maswithin the plane of the circumstellar disk, while no significanto ff set perpendicular to it can be found (black line). Right: Theposition angle derived from our di ff erential data overplotted onthe model of Gies et al. (2007). Table 6.
Mean polarimetric properties, taking into account onlyHPOL data after JD 2 490 000
Spectral Pol. degree Pol. angleBand Mean [%] σ Mean [deg] σ U B V R I able polarization angle. Even after inclusion of all data, i.e. alsothe observations taken before the V / R cycle is well defined, thevalues for the PA in Table 6 would change only in the last digit,if at all, so that the conclusion about a non-changing angle isvalid over the entire period of observation.Other than the angle, however, the polarization degree doesvary. The variability shown in Fig. 14 can be disentangled intotwo components. A slow and secular change is visible well inthe VRI and, though somewhat noisy, also in the
U B bands inFig. 14. This behaviour is in agreement with the general evo-lution of the H α disk as described in Sect. 3.2: The mean po-larization degree is lower before JD 2 448 000, then rises untilJD 2 450 000, and after that remains stable again. Superimposedon that pattern is short-term variability. Unfortunately, the datado not cover the timescales required to properly constrain theshort-term component. However, the observed behavior is notin contradiction with polarimetric variability produced by a se-ries of discrete and individually rather minor ejections of matterinto the immediate stellar environment, as already suggested inSect. 3.1.In summary, neither the variability of the polarization degreenor the polarization angle, which is stable, can be connected tothe cyclic V / R variability. No modulation due to the orbital pe-riod could be detected.
7. Synopsis and discussion ζ Tau spectral type
Table 3 lists several near-UV He i lines as having purely pho-tospheric profiles. They o ff er the opportunity to shed some lighton the various discrepant spectral types that have been publishedfor ζ Tau. A comparison of the high-quality UVES data to sev- ζ Tau
Fig. 14.
Temporal behaviour of the polarization degree. Datafrom McDavid (1999) are shown as circles. The uncertainty ofthe HPOL data ( + ) is about the size of the symbols, i.e. 0.01 %eral early B-type stars in the UVES POP-library (Bagnulo et al.2003) showed unambiguously that the observed strength of theselines is inconsistent with an e ff ective temperature correspondingto a spectral type of ζ Tau later than B2. However, an exact re-determination of the spectral type is beyond the scope of thisstudy.
With ζ Tau having an unseen companion, any variability mustbe checked for a relation to the 132.9735 d orbital period estab-lished by Harmanec (1984). However, the strength of the diskduring the observations implies that the vast majority of the spec-tral lines are contaminated by line emission primarily varying ona di ff erent time scale. The other lines are mostly too shallow forradial-velocity measurements that would permit a verification ofHarmanec’s amplitude of K ≈
10 km / s to be attempted, whichwas derived from observations at more V / R -quiescent epochs.The photospheric He i lines are all in the blue spectral region,which is covered only by a small number of spectra used in thisstudy.It follows that the used dataset of optical spectra, focusedon the H α V / R variations is not suitable for a refinement of or-bital parameters. As a compromise only a check of the periodusing the He i . ± . ff ects. No other quantity investigated in thiswork shows a significant modulation with the orbital period.Even over the given large spectral range, lines due to a sec-ondary, either hot or cool, were not found. In particular, notrace of He ii In an axi-symmetric circumstellar disk the PA is in general per-pendicular to the disk plane and thus parallel to the disk positionangle ( χ ).The spectropolarimetric monitoring of ζ Tau from the PBOobservatory shows that the polarization angle has been remark-ably constant from at least 1989 to 2004 (see Sect. 6). The av-erage V -band polarization angle is PA PBO = . ± . ◦ withan individual measurement uncertainty of 1 deg. The data fromLimber Observatory, taken between 1984 and 1997 (McDavid1999), gave very similar results: PA Limber = . ± . ◦ , and atypical individual uncertainty of 0 . ◦ .Further, there are three independent measurements of theposition angle from interferometric studies. Quirrenbach et al.(1997) determined from a 2D Gaussian fit for data from the MarkIII interferometer a value of χ MarkIII = ± ◦ . Using data fromNPOI, Tycner et al. (2004) obtained χ NPOI = ± ◦ , while Gieset al. (2007) report χ CHARA = ± ◦ from their CHARA data.Finally, the VLTI data of Sect. 5 show that χ AMBER = ± ◦ The orientation of the disk on the sky, as indicated by allthese measurements, has not changed since 1984, and in particu-lar there seems to be no binary phase-locked variability through-out the V / R cycle, at least within the individual measurementuncertainties. The stability of the disk position angle is typicalfor Be stars, the only few counter-examples ever found are sus-pected to undergo precession of a non-equatorial disk (Hummel1998; Hirata 2007). V / R cycle length The analysis of the up to now most comprehensive observationaldata set of ζ Tau confirmed that its V / R variations follow a cyclewith relatively stable amplitude and length of 1405 - 1430 daysduration during the present V / R variable phase starting at thebeginning of nineties. The length is di ff erent and much morestable than during the previous V / R active phase in 1955 - 1980.Table 2 shows that the cycle length varies and suggests a cor-relation between the cycle length and the duration of the triple-peak epoch. In fact, the di ff erences in cycle length seem to bedominated by the duration of the triple-peak phase. For instance,the lengths of Cycles II and III di ff er by 291 days. But after sub-traction of the duration of the triple-peak epochs, the remaindersof the cycles are of the same length (1033 and 1027 days, respec-tively). The lack of an explanation of the variation of the durationof triple-peak phases may limit models for the basic V / R activity For very optically thick disks, the polarization can be parallel to thedisk plane.Stefl et al.: Cyclic disk variations of the Be star ζ Tau 15 as well. Fortunately, at less than ±
10 %, the quantitative e ff ect issmall.The well-observed V / R maxima in H α have been decreasingthrough Cycles I to III. This may be indicative of a decrease alsoof the amplitude of the perturbation causing the V / R variations. V / R phase differences between emission lines The relative shifts in the V / R variations of Balmer, Brackett,He i , and metal emission lines should probe the disk at de-creasing distances from the central star and so place consider-able constraints on any explanation of the cyclic V / R cyclic of ζ Tau (and other Be stars). The phase lag between H α and thehigher Brackett lines is of the order of ∆ φ ≈ .
25 (see Fig. 5).Unfortunately, any quantitative modeling is somewhat hamperedby the medium spectral resolution of both the interferometry andIR-spectroscopy.From a subset of the present IR spectra, Wisniewski et al.(2007) derived the opposite V / R phase relation between IRlines and H α . The larger phase and wavelength coverage of thepresent study appears to exclude this possibility. α profiles The present compilation of spectra maps the evolution ofthe triple-peak profiles in Cycles III and IV in much detail.Qualitatively, it follows a very similar pattern in either cycle.But the duration of the triple-peak phases is variable and maylast from 200 to 500 days. They are not phase-locked to the com-panion star. However, this does not invalidate the small-numberstatistics produced by Rivinius et al. (2006), who report thattriple-peak line profiles only occur in shell stars that are both V / R variable and multiple.As is apparent from Fig. 3, the triple-peak profile in H α isaccompanied by a somewhat disturbed profile in H β . But othernon-hydrogen emission lines in the visual range are largely un-a ff ected. Although the lower resolution of the IR spectra leavessome space for undetected line profile deformations, IR emis-sion lines, too, (including those of H i ) do not seem to undergorelated variations.The absence of triple peaks from optically thin emissionlines and in particular the stability of O i α -forming region due to Ly β resonance pumping, suggest thatthe triple-peak feature does not probably correspond to an ac-tual density structure. Triple peak profiles have so far only beenreported in shell stars. This detail, too, would not easily be ex-plained by real density enhancements.This gives rise to the speculative conjecture about a changein the local escape probability due to distortions of the local ve-locity field, which of course would have an e ff ect only on op-tically thick lines, like H α . Another possibility, guided by thefinding by ˇStefl et al. (2007) that triple-peak emission lines oc-cur in binary Be stars, might be some resonance between theorbital motion of the companion stars and the orbital motion ofgas in the outer disk.H α and H β are not the only optically thick emission lines,though: It is commonly accepted that the Paschen and Brackettlines as well as some strong IR Fe ii emission lines form closerto the star than the first few lines of the Balmer series. Since onlyH α and H β show some form of triple peak, this may point at theouter regions of the disks as the locus of the physical variability.Such a region was on the line of sight at the time of the AMBERobservations. At that time, the bisector line of the H α emitting region was close to the line of sight, whereas the bisector linesof the regions of formation of emission lines requiring higherproximity to the exciting central star passed the line of sight upto one year earlier. As described in Sect. 3.3, NLG lines are formed in a broad diver-sity of ionic species and over a wide range of ionization and / orexcitation potentials beginning with O i and Na i and extendingto Fe iii . Conversely, BLG characteristics are exclusively asso-ciated with transitions expected from comparatively cool condi-tions; examples are Mg i or O i . The simultaneous, let alone long-term, presence of both Fe iii and Mg i shell absorption is veryunusual. A search of the large FLASH, HEROS, and FEROSdatabase of Be spectra (Rivinius et al. 2003) furnished no sec-ond example.The occurrence of lines with persistent mixed BLG and NLGcharacteristics suggests that the circumstellar disk does not havea simple and smoothly varying structure. Rather, NLG and BLGcomponents seem to form in two spatially separated regions withdistinct physical conditions. Simple common-sense considera-tions lead to conflicting conclusions about the location of theseregions relative to the central star.On the one hand, their higher excitation would place theNLG closer to the star and the lower-excitation BLG in the outerdisk. On the other hand, the line profiles point to the opposite,provided that the disk dynamics is crudely Keplerian: The nar-rowness of the NLG, which in some UV lines hardly exceedsthe thermal width, as well as their lower RV amplitudes suggest,then, that the region of formation of NLG lines is relatively farfrom the central star. The broader BLG lines would form in theinner disk, where the velocity ranges are larger.Apart from their width, NLG and BLG lines also di ff er in thevariation of their equivalent width with V / R phase. While BLGlines are strongest in the second half of the cycle, NLG lines arestrongest around phase 0.25.The radial-velocity variations of both groups have compara-ble amplitude through the V / R -cycle (see Fig. 3). However, thereis a phase di ff erence of about ∆ φ ≈ .
25 with the NLG trailingthe BLG.
8. Conclusions ζ Tau is a Be-shell star. Its spectral type is B2 or earlier one. Bothinterferometry and polarimetry demonstrate that its circumstel-lar disk is flat and seen edge-on. The assumption that all
Be-shell stars are observed edge- and equator-on has been vital forthe analysis by Rivinius et al. (2006) of the fractional criticalrotation rates of Be stars.The plane of the disk has remained stable for decades.Warping or tilting, as diagnosed in other Be stars by Hummel(1998), may be present but was not detected. The disk seemsto have been persistent for about a century. But the strength ofemission and shell absorption lines has varied on time scales ofyears to decades.The photocenter of the Br γ line emission lies in the plane ofthe disk but is o ff set from the continuum source. The same couldnot be diagnosed from the weaker He I 2.06 µ m emission line.This may be a data-quality issue or result from an alignment, atthe time of the observations, of the photocenter of the He I linewith the continuum source.The Br γ result may also resolve a general ambiguity in theinterpretation of V / R -asymmetric emission lines. From the spec- ζ Tau tra alone one cannot decide whether the V / R asymmetry is onlyin velocity or also in configuration space. The VLTI observationsshow that the latter is true in ζ Tau.Like some other, but by far not all, Be stars, ζ Tau is abinary. The companion remains undetected at optical and IRwavelengths. An intensive search in a dense series of multi-wavelength observations of a very broad range of electromag-netic observables did not furnish any e ff ect of the companion onthe long-term variability or orientation of the disk. The variabil-ity of the circumstellar disk can, therefore, be considered intrin-sic to the disk itself and the central B-type star.The most prominent spectroscopic signature of the disk ac-tivity is the cyclic V / R variability. Its amplitude can for decadesdrop below the level of easy detectability. Pronounced V / R varia-tions were resumed about 1992. Since 1996, three complete V / R cycles were observed. Their similarity in length and amplitudehas enabled a detailed phenomenological description of the vari-ability.The formal mean cycle length is 1405 - 1430 days, withcycle-to-cycle variations of less than ±
10 %. The basic log( V / R )curve for H α is smooth and symmetric. However, about the V / R minimum a perturbation develops, which has been qualitativelythe same in all three of the most recent cycles. The H α emissionprofile develops a comb-like structure at its top, which consistsof three small peaks separated by equally small depressions. Theduration of this phase varies from cycle to cycle, and the changesmay be the main reason of the variation in length of the maincycle. In the available observations, triple-peak profiles are re-stricted to H α , with traces showing up in H β . Therefore, the un-derlying perturbation may be confined to the outer disk.All emission lines partake in the V / R variability. But thereare line-specific shifts in phase of up to 25% of the cycle length.H α V / R lags behind Br γ , which trails the higher Brackett lines.Metallic lines typically behave like the higher Brackett lines.This supports the notion that the phase lag increases with de-creasing density and increasing distance from the central star.The shell absorption lines crudely fall into two di ff erentgroups mainly distinguished by the line widths. Low-ionizationspecies and low-excitation lines are broader than the ones involv-ing higher energies. Some lines also share the behavior of bothgroups so that each group may predominantly arise from dif-ferent locations. If the disk motions are basically Keplerian anddensity and temperature mainly drop with distance from the cen-tral star, the grouping provides seemingly contradictory diagnos-tics of these locations relative to the central star. Both groups un-dergo similar radial-velocity variations but the broad lines leadin phase by about one-quarter of a V / R cycle.The only variability apparently unrelated to both the V / R cy-cle and the binarity is the occasional presence of infrared C i emission.Discrete major mass loss events were not observed. But ob-servations of other Be stars and the relative constancy of the to-tal emission strength suggest that minor ones have likely takenplace. They may provide a partial explanation of not fully repet-itive variations.The complexity of the observations and especially the vari-ous cyclically repeating phase di ff erences show that the under-lying perturbations are not both point-symmetric and radiallymonotonic. Consequently, the perturbations are hardly reconcil-able with roughly spherically symmetric models as, e.g., the oneof Doazan & Thomas (1987). Major outbursts might temporarilylead to such a situation but the cyclic variability would probablyrequire them, too, to be cyclic. A perturbation that propagates ina spiral-like pattern has a physical foundation in global m = Acknowledgements.
The polarimetric observations were supported in part byNASA via contract NAS5-26777 with the University of Wisconsin and grantsNAG5-3447 and NAG5-8054 to the University of Toledo. We thank KenNordsieck for access to HPOL. We also thank the many members of the PBO ob-serving and data reduction teams over the years, with special thanks to MarilynMeade and Brian Babler, for assistance with data acquisition and reduction.This work has made use of the BeSS database, operated at GEPI,Observatoire de Meudon, France: http: // basebe.obspm.fr. We would like to thankthe amateur observers who obtained valuable spectra and generously made themavailable at the BeSS web page, namely to E. Barbotin, C. Buil, J. Guarroflo,B. Mauclaire, J. Ribeiro, J. Terry, O. Thizy and V. Desnoux.We thank Dr. D. Gies who provided us with their model derived from theCHARA observations, and the unknown referee for his / her very constructivecomments and suggestions.We thank the observers and sta ff at Ritter Observatory, especially NancyMorrison, for their assistance in providing data used in this paper. Observationsat Ritter Observatory are supported by the NSF under the PREST program,grant AST04-40784. JPW is supported by a NSF Astronomy & AstrophysicsPostdoctoral Fellowship under award AST-0802230. The observations atOndˇrejov Observatory were supported by the Grant Agency of the Academyof Sciences of the Czech Republic (grants AA3003001, AA 3003403). TheHeros@Ondˇrejov monitoring project was part of a joint project supported bythe German Bundesministerium f¨ur Bildung and Forschung and the Ministry ofEducation of the Czech Republic (TSE-001-009, 436 TSE 113 /
18 and 41). Thiswork was also supported by FAPESP grant 04 / References
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