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Tuc, from Da Costa & Armandroff(1990). Notice that the model RGB issomewhat redder than the observedone. This disagreement, which is largerfor the fainter RGB stars, is known toexist from other comparisons betweenobservations and the Padova stellarevolutionary models. It has no effect onour major conclusion that the Z(t )shown in Figure 5 is compatible withthe morphology of the Fornax CMD. Aquantitative derivation of the star for-mation history from a thorough fit of theCMD will add further confidence in thereconstruction of the history of Fornax.It will be presented in Gallart et al.(2002).

Acknowledgements. This researchis part of a Joint Project betweenUniversidad de Chile and YaleUniversity, funded partially by theFundación Andes. C.G. acknowledgespartial support from Chilean CONICYTthrough FONDECYT grant number1990638. R.Z. was supported by NSFgrant AST-9803071 and F.P. by theSwiss National Science Fund andFONDECYT grant number 3000056.

References

Aaronson, M., Olszewski, E.W. & Hodge,P.W. 1983, ApJ, 267, 271

Aaronson, M. & Mould, J. 1980, ApJ, 240, 804Aparicio, A., Carrera, R. & Martínez-Del-

gado, D. 2001, AJ, 122, 2524Bertelli, G., Bressan, A., Chiosi, C., Fagotto,

F. & Nasi, E. 1994, A&AS, 106, 275 Bertelli, G. et al. 2002, in preparation Bonifacio, P., Hill, V., Molaro, P., Pasquini,

L., Di Marcantonio, P., & Santin, P. 2000,A&A, 359, 663

to Gallart et al. (1999b). The complete-ness and error simulation has beenperformed using a preliminary crowdingtest table obtained from the deep VLTimaging for Fornax presented in Gallartet al. (2002).

The resulting synthetic CMD is dis-played in Figure 6, to the right of the ob-served CMD. The synthetic CMD suc-cessfully reproduces the major mor-phological features of the observedCMD, namely the RGB, the horizontalbranch, the red-clump and the main-se-quence. Particularly important is theagreement between locations of theyoung main-sequence stars (a set oflines have been drawn in both the ob-served and model CMDs to guide theeye). Its position is very sensitive tometallicity of the stars younger thanabout 2 Gyr. If their metallicity werelower than that given by the Z(t) rela-tion, for example, lower than [Fe/H] ≤–0.7, as one could deduce from the col-or of the RGB without correction for theyoung ages of the stars, then the posi-tion of this part of the main sequencewould be substantially too blue. Thereis also striking agreement between themodel and observed CMDs for theplume of stars above the red-clump,which is composed of metal rich youngstars (younger than 1 Gyr and with Z �0.006–0.008) undergoing their He-burning loop phase of stellar evolution.The most obvious disagreement be-tween the model and the observedCMDs is in the color of the RGB. To il-lustrate this we have plotted in both di-agrams the fiducial RGBs of the globu-lar clusters M15, M2, NGC 1851 and 47

The ups and downs of a stellar surface: Nonradialpulsation modelling of rapid rotatorsTHOMAS RIVINIUS, DIETRICH BAADE, ESO, Garching b. München, GermanySTANISLAV ŠTEFL, Astronomical Institute, Academy of Sciences Ondřejov, Czech Republic, MONIKA MAINTZ, Landessternwarte Heidelberg, GermanyRICHARD TOWNSEND, University College London, United Kingdom

1. Introduction

Usually one thinks of stars as stableobjects, taking at least millions of yearsto evolve significantly. While it is truethat stars take such timescales to age,they need not be “stable” in a staticsense over all that time. Many stars infact undergo pulsations on timescalesbetween minutes and years, as for in-stance the Be stars Baade, Riviniusand Štefl reported about in a recentMessenger issue (No. 107, p. 24). Themost obvious pulsation mode is theradial one, where the star becomes big-ger and smaller periodically, and like

any expanding/compressing gas alsocooler and hotter again. We seethese stars varying in brightness andcolour, and their spectra cyclically ap-proaching and receding. The wellknown Mira in the constellation CetusP = 330 day), or the Cepheids (P =1…50 day), which help in measuringextragalactic distances, are such ob-jects. Stars may not only pulsate radial-ly, however. Imagine a free-floatingblob of water in a Space Shuttle, or abig soap bubble. Before reaching astable spherical shape (or popping)they undergo damped wobbles. This,in a sense, is externally excited non-

radial pulsation (nrp) in a multitude ofmodes.

Nonradially pulsating stars behavesimilarly. But since these pulsations areexcited from inside the star and are go-ing on for millions of cycles, they ap-pear more ordered as most modes aredamped, and typically only one or fewhigh-amplitude modes are excited in annrp star. The excitation process resem-bles a Carnot process (as in an idealsteam engine) where the role of thevalve is played by a layer inside the starthat turns opaque with increasing tem-perature due to ionization processesand becomes transparent again during

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trated towards the equator. BRUCE, oth-er than most codes before, can com-pute the surface wave pattern up to thecritical rotation limit. It is therefore ide-ally suited to Be stars, that typically ro-tate at about 70 to 80% of their criticalspeed.

Also, BRUCE is one of the few codesoptimized for relatively long oscillationperiods (i.e. longer than the fundamen-tal radial oscillation mode), for whichhorizontal motions are the most impor-tant. These are called g-modes (sincegravity is the most important restoringforce) and are comparable to waterwaves in an ocean. Most other codesspecialize in short period pulsationmodes, where radial motions dominate,called p-modes (from pressure) andrather resembling sound waves.

The input parameters required byBRUCE are stellar quantities (mass,temperature, radius, rotation, and incli-nation), and the pulsational parame-ters. At first look, this seems to be a dis-advantage of the code, because othercodes require only the pulsational pa-rameters, but also only compute thevariability of the residuals from themean, not the line profiles themselves.However, this is in fact a major advan-tage, since the variability dependsstrongly on properties of the spectralline modelled, which in turn are deter-mined by the stellar parameters. Theextended wavelength range of echelledata allows one to make use of the dif-ferences of individual spectral linesformed at different stellar latitudes tofurther constrain the model parameters.Therefore, the reproduction of the vari-ability and the mean profile, for asmany different lines as possible, notonly gives the pulsational parameters,but also the stellar ones.

circumstellar origin, and the strong,narrow absorption “spikes” seemed torequire severe distortions of the stellarsurface (see Fig. 1 for an example).However, as will be shown, these fea-tures could be modelled without anyadditional assumptions with a general-purpose non-radial pulsation modellingcode.

Other hypotheses proposed to ex-plain the line profile variability (lpv) ofBe stars, and especially of ω CMa, in-clude starspots and co-rotating clouds.However, for none of them was a satis-fying model able to reproduce the ob-served variations of more than a singlespectral line.

Ever since the discovery of periodiclpv in Be stars one has wonderedwhether it could be the same processthat is responsible for building up thecircumstellar disk. Since the mass lossmodulations of early type stars are notvery well understood in general, theidentification of the cause of the lpv inBe stars also would be a step forwardin hot star physics in general.

2. A new model-code

When the HEROS project started,none of the hypotheses introducedabove was clearly favoured. At thispoint, however, a new nrp modellingcode, the BRUCE/KYLIE-package, waspublished by Rich Townsend. Severaladvantages made it the first choice toattempt modelling the lpv of ω CMa(and other pulsating Be stars).

For instance, the pulsational surfacewave pattern depends not only on l andm, but also on stellar rotational velocity.With increasing rotation, the wave pat-tern becomes more and more concen-

the following expansion phase. Whensuch a layer is close to the stellar sur-face, stellar pulsation may be excited.On the stellar surface nrp manifestsitself as a global wave pattern, whichtravels along the stellar surface par-allel to the equator and causes theperiodic behaviour. This global wavepattern can be described by means ofquantum numbers l and m, charac-terizing the number of oscillation nodesalong the equator and across it, sim-ilar to the two-dimensional oscillationsof a drumskin (or of the VLT primarymirror, being exploited for the activeoptics).

Such nrp might be very subtle, as inour Sun, which pulsates in numerouslow-amplitude modes with P = 5 min. Inother stars, like the Be stars, how-ever, the induced variability may lookso violent, that it was first claimed that,if this were pulsation, the star would bedisrupted. In fact, browsing the spectraof the early type Be star ω CMa afterthe observations taken during theHEROS project (Fig. 1, see also Baadeet al., op. cit.), we were convinced thatthe periodic variability could not bemodelled without taking into accountalso shocks and other non-linear ef-fects. Most notably, the variability canbe observed out to higher velocitiesthan the projected stellar rotational ve-locity, which would normally suggest a

Figure 1: The pulsational variability ofω CMa in the Mg II 4481 line. The phase(i.e. time) increases from bottom to top.The mean profile, which is averaged overall pulsation phases, is shown in red, theprojected rotation velocity of the star isplotted as dotted lines, shifted to the stellarsystemic velocity. The range of variabili-ty exceeds the rotational range by about40 km s–1 with a ramp-like form. The lineprofile variability, well seen also in the asym-metric “spikes” at the most extreme blue andred phases, is among the strongest ever ob-served.

Figure 2: The pulsational variations of the stellar surface as computed by BRUCE for an l = 2,m = 2 mode. This sectorial mode has two node-lines in longitude l = 2), thus the nrp-patternrepeats twice along the equator. The same model is shown for equator-on (upper row) andalmost pole-on orientation, like ω CMa is seen from Earth (lower row, the “+” marks the rota-tional pole). The radial motions are a factor of almost 10 slower than the horizontal ones, whilethe ϕ- and θ-amplitudes are about equal. These three velocity fields are co-added and pro-jected onto the line of sight, before KYLIE computes the observed spectrum (see also Fig. 3).The temperature changes are caused by the varying pressure.

22

nificantly (see Fig. 3). But it is onlyabout 15% of the true rotational veloci-ty, so the physical effects on the stellarsurface are much less severe. This waythe polar inclination amplifies the con-trast of the observed variability for g-mode pulsation.

Figure 3 demonstrates how underthese conditions ramps and spikes re-sult from the generic properties of anonradially oscillating, rotating sphere,without the necessity to customize themodel code for the specific case ofω CMa.

The final parameter set to reproducethe spectral variability of ω CMa wassearched by computing and testingtens of thousands of models againstthe observations. The recent Mes-senger article by Baade et al. (op. cit.)has already presented an example of

onto the line of sight. In the equatorialview, the ϕ-velocity would dominate thevisible variability at the stellar limbs.The θ-component is almost perpendi-cular to the line of sight, and thus sup-pressed by projection effects in theequatorial view. For a polar orientationof the star, the situation is reversed,however. The θ-velocity is now domi-nant, while the visibility of the ϕ-com-ponent is suppressed. Since the rota-tional velocity is also in ϕ-direction, itunderlies the same projection.

The excess of 40 km s–1, by whichthe variability is seen beyond the rota-tional range (such features are alsocalled ramps), is therefore the truemaximal velocity of the θ-field. Sincethis is 40% of the projected rotationalvelocity at the small inclination of ωCMa, it alters the visible line profile sig-

BRUCE computes the surface param-eters (such as temperature, gravity,and projected velocity) of the pulsatingstar for a mesh of about 25,000 pointson the visible surface (Fig. 2 has beenconstructed from the BRUCE output).For each surface point the local spec-trum is taken from an input grid of pre-computed data and shifted by the pro-jected velocity. The KYLIE program thenco-adds these local spectra to the onethat would be observed from Earth.

3. Reproducing spectra

How could this new code help in re-solving the seemingly contradictory be-haviour of ω CMa? The key is the al-most polar inclination of the star. Figure2 shows the three constituents of thepulsational velocity before projection

Figure 3: The projected velocity field, as seen from Earth, is dominated by the rotation and the pulsational θ-velocity for a pole-on star. At theapproaching limb of the star (blue), the co-added θ-amplitude increases the total approaching velocity, causing the extended ramp on the bluewing of the final spectrum (see also Fig. 1). At the receding limb, rotation and θ-velocity have different signs, thereby reducing the maximalprojected velocity. A large part of the receding hemisphere is, therefore, projected into a narrow velocity range, causing the spike. The mod-elled SII 5454 line is shown for illustration.

Figure 4: Comparison of observed phase-variations (black) with the modelled ones (red), including line blends. The phase averaged meanspectra are plotted above. The good reproduction, also of the absolute mean line profiles (and their anomalies, like the flat bottoms), demon-strates that the stellar parameters derived by modelling the variability provide a good estimate of the true quantities.

23

Figure 5: Periodic line profile variability (lpv) of low v sin i Be stars shown in the extreme asymmetry phase. The lpv of ωCMa is the strongest,but not in principle different from other low v sin i Be stars. See also Figure 6 for a dynamical view of the lpv of FW CMa, ωCMa, and HR4625.

Figure 6: Observed lpv of stars with different v sin i, shown as residuals from the mean line profile for two different lines. It is compared tothe ω CMa model being ‘viewed’ at inclinations between 6º and 70º to match the indicated v sin i of the observed stars. The apparently asym-metric lpv of Mg II 4481 in 28 Cyg is caused by rotational blending with HeI 4471, visible in both observations and model data.

24

observational evidence for a connec-tion between nrp and the disk forma-tion. Among other effects, the lpv pat-tern of ωCMa changes in several spec-tral lines during an outburst, whichmight provide the key to understand themass transfer mechanism between Bestars and their disks.

Just as the pulsational parametersare determined by the best fit of thevariability, the stellar parameters canbe determined by the best fit of themean absolute line profile. The model-ling method described above offers thepotential to combine these two steps ina single analysis, due to the good re-production of both residual variabilityand absolute line profile (see Fig. 6).Since nonradial pulsation breaks thesymmetry of the stellar surface w.r.t. ro-tation, one can even derive the stellarinclination angle from the modelling,while otherwise it is inseparably fac-tored into the projected rotational ve-locity v sin i. Rotation is becoming in-creasingly important for understandingstellar structure and evolution. A meth-od to derive v and i separately, utilizingthe nrp pattern on the stellar surface,bears great potential not only for Bestars, but for a much wider range of ob-jects, since nonradial pulsation is wide-spread in the Hertzsprung-Russell-Diagram.

A complementary approach focuseson the observed lpv of equator-on (highv sin i) stars. The lpv of these starslooks different from the pole-on ωCMa.But if ω CMa is proto-typical, the differ-ences should be just inclination effects.To address this expectation the modelof ωCMa was computed for a set of in-clinations, so that the resulting v sin iwould be the same as for some typicalBe stars. Then, the modelled variationswere compared to the observed ones(Fig. 6). The similarity of model and ob-servations shows that the model ofω CMa represents a typical early-typeBe star.

5. Consequences and outlook

The main result of the modellingproject is the confirmation that early-type Be stars pulsate nonradially in g-modes. Based on the detailed model-ling of ω CMa, it could be shown thatthis star is proto-typical, and that theperiodic lpv of early type Be starsin general is due to nonradial pulsa-tion.

Several stars in the database, includ-ing ωCMa, were observed to replenishtheir disks via outburst events duringour campaigns. Although plain nrp can-not account for mass and angular mo-mentum transfer into the disk, there is

the resulting reproduction of the lpv ofHeI 4471 and MgII 4481. In Fig. 4, re-sults for additional lines of helium andother ions are shown, all computed withthe same set of stellar and pulsationalparameters.

4. Do all Be stars pulsate?

Since the periodic lpv of ω CMa isamong the strongest known, the ques-tion needs to be addressed whether itis a typical Be star.

ω CMa is a B2 IV star. Since it isknown that Be stars rotate almost criti-cally, its low projected rotational veloci-ty v sin i points to a pole-on orientation,which is also supported by the derivedmodel parameters. If all (or most) othersuch Be stars would show this kind ofperiodic variability (possibly weaker,but in principle the same), the lpv couldbe explained by nrp in general.

Although most Be stars are of early Bspectral type, there are not too manybright ones in the same range of v sin ias ω CMa. Searching archival data andsecuring additional observations withFEROS, we found most of them toshow spikes like ω CMa, or a similarvariability with lower amplitudes, i.e. nofully developed spikes, but globalasymmetry variations, as is shown inFigure 5.

The VLT and the most distant quasarsL. PENTERICCI and H.W. RIX (MPIA, Heidelberg), X. FAN (IAS Princeton), M. STRAUSS (Princeton University)

1. Introduction: optical surveysfor high-redshift quasars

Quasars are amongst the most lumi-nous objects in the Universe, allowingus to study them and any interveningmaterial out to very large distances,corresponding to look-back times whenthe Universe was very young. Findingand studying quasars at high redshiftsis one of the best ways to constrain thephysical conditions in the early Uni-verse. The mere existence of luminousquasars at such early times, and theimplied presence of black holes withM ≥ 109 M� place stringent limits on theepoch at which massive condensedstructures formed, thereby constrainingstructure formation models (e.g. Efsta-thiou and Rees 1988).

Most known high redshift quasarshave been found as outliers in colorspace from the stellar locus in multicol-or optical surveys (e.g. Warren et al.1994, Kennefick et al. 1995). Oneprominent survey is the Sloan DigitalSky Survey (SDSS, York et al. 2000)which is systematically mapping one-

quarter of the entire sky, producing adetailed multi-color image of it and de-termining the positions and absolutebrightnesses of more than 100 millioncelestial objects. The SDSS will alsomeasure the distance to a million of thenearest galaxies, producing a three-di-mensional picture of the Universethrough a volume one hundred timeslarger than that explored to date.

One of the principal aims of theSDSS is the construction of the largestsample of quasars ever, with more than100,000 objects spanning a large rangeof redshift and luminosities, giving usan unprecedented hint at the distribu-tion of matter to the edge of the visibleUniverse.

Thanks to the accurate 5 band pho-tometry of SDSS, high redshift quasarscan be efficiently selected by their dis-tinctive position in color-color diagrams,with characteristic colors due to themain feature of the quasar spectra, viz.,the strong Lyα emission line, the Lyαforest and the Lyman limit. During itsfirst year of operation, the SDSS has al-ready found a large number of ex-

tremely distant quasars, including morethan 200 new quasars at redshiftgreater than 4 and the most distantquasar known, SDSS J1030 + 0524 atz = 6.28 (Fan et al. 2001). Until a fewmonths ago this was also the most dis-tant object known but it has been sur-passed by a galaxy at z = 6.56 recent-ly discovered by Hu et al. (2002).

2. VLT observations of the mostdistant quasars: revealing the conditions of the early Universe

The spectra of very high redshiftquasars can tell us a great deal aboutthe conditions in the early Universe. Inparticular, we can use them as probesof the intergalactic medium (IGM) to de-termine the state of any intervening ma-terial along the line of sight.

One of the fundamental questions ofmodern cosmology is how and whenthe Universe became ionized (for acomplete review see Loeb & Barkana2001). When the Universe was very