Rotation in the ZAMS: Be and Bn stars J. Zorec, Y. Frémat, C. Martayan, L. Cidale, A. Torres

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J. Zorec, Y. Frémat, C. Martayan, L. Cidale, A. Torres. Rotation in the ZAMS: Be and Bn stars. 2006. ￿hal-00016423￿

HAL Id: hal-00016423 https://hal.archives-ouvertes.fr/hal-00016423 Preprint submitted on 4 Jan 2006

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. ccsd-00016423, version 1 - 4 Jan 2006 S ofrneSre,Vl *OUE* *ERO PUBLICAT OF EDITORS** **YEAR OF **VOLUME**, **NAMES Vol. Series, Conference ASP TITLE** **FULL o oaigsasw eemndtems n g ftestudi the of each age From and mass 2005). the determined al. we stars rotating for 05.Uigtesm oesw acltdtetdytu rot true today the calculated we models same V the Using 2005). osraino Mfor AM of conservation A)ls u oms-ospeoeai tr ihmass with stars in phenomena mass-loss 2) to radius; due stellar loss equ time-dependent of (AM) the evolution by the affecting induced effects variation order first four account otegaiainldreigeetwt the with effect darkening gravitational the to hr sana asdpnetlmtn cut limiting mass-dependent neat a is there .ZM oainlvlcte fB stars Be observed of The velocities rotational ZAMS 1. tr nahg eoiysco.Ti niae htsasne stars that indicates This sector. velocity high a in stars oes h obtained Meyn The from models. o parameterized redistribution scale internal time barotrop 4) circulation 2D 1988); meridional using al. rotation et the (Zorec to structure and effects evolutionary to V V etrdsrbstedsrbto of distribution the describes better × trM ouain ic oeta 0 fM -yesasmus of stars out B-type stars MS of of 80% roughly than 17% more Since the only population. concerns MS histogram star The tail. h ubro eetdB tr sgvnb:d by: given is stars Be detected stars of number Be The of frequency Mass-independent distribution 2. general a population. of MS tail B-star a whole possibly but distribution, ZAMS min N fec trb eemnn t nlnto angle inclination its determining by star each of ( V T obcm ei h Spae o ahms-nevlw divide we mass-interval each For phase. MS the in Be become to ZAMS eff 1 4 3 2 .Zorec J. stars Bn and Be ZAMS: the in Rotation ASrttoa eoiishge hnagvnlmtmgtb might limit given a than 2 higher mass; velocities the Thi rotational of MS. ZAMS independent the is N(Be)/N(Be+B) in fraction distribution number velocity rotational star B-type Abstract. by ntttdAtohsqed ai,UR05CR,Ui.P&M Univ. CNRS, UMR7095 Paris, de d’Astrophysique Institut bevtied ai-edn France Paris-Meudon, de Observatoire Belgium of Observatory Royal sin ) autdd inisAto´mcsyGo´scs NP Ar Geof´ısicas, Astron´omicas UNLP, y Ciencias de Facultad V /V min i min d V τ 1 n bandtegoa itga hw nFg b h ttha fit The 2b. Fig. in shown histogram global the obtained and sin .Fr´emat Y. , d ∼ < i where , i nevl tipista esasd o omaseparate a form not do stars Be that implies it interval, 1 eso htB tr eogt ihvlct alo single a of tail velocity high a to belong stars Be that show We f17glci esaswr orce o netite du uncertainties for corrected were stars Be galactic 127 of V V ZAMS M eetmtdtecorresponding the estimated we P 2 ∼ < Be .Martayan C. , gis h tla asaesoni i.2,where 2a, Fig. in shown are mass stellar the against 15 stems-needn rbblt fbecoming of probability mass-independent the is M ⊙ V )cagso h nrilmmnu due momentum inertial the of changes 3) ; ZAMS 1 ( 3 M V .Cidale L. , min ) N /V fastrot ( ( M min e i Be, htcnnsalsuidBe studied all confines that ) i ( iheouinr tracks evolutionary With . M ) 4 bandi Gaussian a is obtained ) .Torres A. , ∝ h Mi em fthe of terms in AM the f oes(rea tal. (Fr´emat et models P V htecmassthe encompasses that t&Mee’ (2000) Maeder’s & et ZAMS Be dt have to ed tra eoiis 1) velocities: atorial nua momentum angular mle ht )the 1) that: implies s ION** cmdl fstellar of models ic E dsas(oe et (Zorec stars ed M cm estars. Be ecome Hα nsashaving stars Bn ) toa velocity ational ytkn into taking by ∼ > ( 4 T h hl B whole the hnb in be then t eff gentina 15 ,i τ, , V M ZAMS ⊙ Curie the d ) φ and ( τ ∼ > e ) t 2 Zorec et al.

60

500 Gaussian 50

400

) 40 -1

(km s 300 30 ZAMS

V 20 200 no Be star Number of Be stars no Be star

10 100 (a) (b) 0 4 6 8 10 12 14 16 0.0 0.5 1.0 1.5 2.0 2.5 3.0 M/M [V/Vmin(M)]ZAMS

Figure 1. a) Distribution of the equatorial velocities in the ZAMS of the studied Be stars against the mass . b) Frequency distribution of VZAMS/Vmin and fit with a Gaussian function. No Be star has VAMS/Vmin < 1

6 1.0 (a) o = 1.0 0.9 (c) o = 1.0 5 o = 1.5 0.8 o = 1.5 o = 2.3 o = 2.3 4 0.7

)> 0.6 ,

eff 3 0.5 N(Be) 0.4

N(M) 2.2 10 30

log 2.0 20 1.8 Number of Be stars 1.6 10 log10M/M Spectral type 1.4 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 O B0 B1 B2 B3 B4 B5 B6 B7 B8 B9 A

Figure 2. a) Hα emission intensity function as a function of Teff and τo. b) Number of stars around the Sun in an apparent V=7 magnitude limited volume. c) Normalized predicted number of Be stars near the Sun. d) Com- parison of predicted with observed number of Be stars near the Sun

Be star (see Sect. 1.); EHα is the probability of detecting a Be star measured in terms of the intensity of the Hα emission produced by a disc with opacity τ shown in Fig. 1a; N(Teff) is the total number of stars with a given Teff given by the IMF function; sin i is the probability of seeing the disc at inclination i. We can integrate the indicated relation for an apparent V=7 magnitude limited volume to represent the fraction of Be stars near the Sun. The reduced apparent magnitude IMF function is shown in Fig. 1b. It comes then that the product of EHα with the ‘local’ IMF produces the curves shown in Fig. 1c, which represent Rotation in the ZAMS 3

0 70 (a) dwarfs Bn (V) Vsin i>200 km/s (b) 60 -1 ``subgiants Bn'' (IV-V+IV) ``giants Bn'' (II-III+III+III-IV) 50 -2

40 -3 30

ln-4 N(Be)/N(B) Counts of20 Bn stars

-5 10 Spectral type -6 0 O B0 B1 B2 B3 B5 B7 B9 A0-2 B0 B1 B2 B3 B4 B5 B6 B7 B8 B9 A0 A1 A2

Figure 3. a) Apparent magnitude limited counts (V=7mag) of dwarf Be stars relative to dwarf B stars. b) Apparent magnitude limited counts (V=7mag) of Bn stars. Most Bn stars are dwarfs, which may indicate that they are fast rotators in the first MS evolutionary phases the normalized predicted number N(Be) of Be stars. The comparison of the predicted (τo =1) with the actually observed number of Be stars around the Sun is shown in Fig. 1d. This shows that the apparently bi-modal distribution of Be stars around the Sun against the spectral type is entirely explained by the interplay of the probability of detecting Be stars (EHα), the shape of the IMF and PBe(M) = constant.

3. Some Bn stars might be progenitors of Be stars

Figure 3a shows the apparent V=7 magnitude limited counts of dwarf Be stars relative to dwarf B stars. There is an apparent lack of dwarf Be stars cooler than spectral type B7. This could be due to genuine Be stars whose discs are minute and/or too cool for the Hα emission be detectable and/or, to fast rotating B stars that still had not attained the required properties to become fully-fledged Be stars. According to findings in Sect. 1., which are supported by those in Sect. 2., the relation shown in Fig. 3a should be straightened, so that ln N(Be)/ ln N(B) = constant. It has been shown in Zorec et al. (2005) that there is a lack of Be stars with masses M ∼< 7M⊙ in the first half of the MS phase. However, Fig. 3b shows that apparent V=7 magnitude limited counts of Bn stars increase strongly at spectral types cooler than B7. Since most of them are dwarfs, they probably had not enough time to attain the angular velocity ratio Ω/Ωc ≃ 0.9 that characterizes Be stars (Fr´emat et al. 2005). The determination of the VZAMS of 100 Bn stars is underway. This will enable us to see which of them has the required condition VZAMS ∼> Vlim to become Be. Other related subjects can be found in http://www2.iap.fr/users/zorec/.

References

Fr´emat, Y., Zorec, J., Hubert, A.M, & Floquet, M. 2005, A&A, 440, 305 Meynet, G., & Maeder, A. 2000, A&A, 362, 101 Zorec, J., Fr´emat, Y., & Cidale, L. 2005, A&A, 441, 235 Zorec, J., Mochkovitch, R., & Divan, L. 1988, C.R. Acad. Sci. Paris, 306, 1265