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Uva-DARE (Digital Academic Repository) UvA-DARE (Digital Academic Repository) Over Be-sterren en de bouw en samenstelling van Wolf-Rayet-sterren Weenen, J. Publication date 1949 Link to publication Citation for published version (APA): Weenen, J. (1949). Over Be-sterren en de bouw en samenstelling van Wolf-Rayet-sterren. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl) Download date:25 Sep 2021 57 7 Onn Be stars and the structure and composition of Wolf- Rayy e t stars, SUMMARY. Inn order to explain the large colour indices for Be stars andd an anomaly in., the temperature determina- tionn from Hell and He I lines of Wolf-Rayet stars "by Zan- stra'ss method, Kosirev assumed a model of an extended pho- tospheree which appeared to produce an ultraviolet excess, thuss eliminating the difficulty. In the first part of the dissertation,, § 1-§12,Kosirev'streatment is improved upon "by as- suming,, instead of an absorption coefficient independent of wavelength,, the absorption coefficient of hydrogen,with its dependencee on £. The numerical quantities were chosen with aa view of representing a Be star, of which 48 Librae is a typicall example. Thee star is represented by a black body of a temperature of 250000 at the boundary between star and envelope. In choo- singg the density, care was taken to have a certain amount off absorption of thee star light by the envelope in the ob- servablee region, mainly due to the Balmer- and Paschen con- tinua.. The optical depth in the Lyman continuum then became veryy large. Thee equation of radiative transfer for curved layers was used.. Por that part of the envelope having temperatures of 15000°° and higher, it turned out that scattering by free e- lectronss became of much greater importance than the Rosse- landd mean of the hydrogen absorption. Assuming local ther- modynamicc equilibrium, the temperature could be determined ass a function of the radius (§ 4) choosing the thickness of thee shell equal to the radius of the star (M)• Thee intensity distribution in the spectrum was then derived. Forr the Lyman continuum the star plus surrounding shell then behavedd as a black body of a temperature equal to the out- sidee boundary temperature (§7). Other wave-lengths gave rise inn some cases to predominant absorption U3000,A 6000,A8000, §9),, in other cases to predominant scattering by electrons, U1000,;42000,A4000,§8).. As compared with a black body of the samee total radiation, the spectrum turns out to be strongly distorted:: the Lyman continuum is extremely weak, likewise thee region near the Balmer limit, while in the visual region thiss loss is compensated and the radiation is much stronger. (MO,, Fig.2 and §11). Indeed this gives rise to a large co- lourr index in the visual region, but not to Kosirev*s excess off radiation in the ultraviolet, which, to the contrary,be- comess very weak (?11). AA comparison of our theoretical results with the observation off a typical Be star like 48 Librae, showed that the obser- vedd electron concentration according to Struve is much smal- lerr than used in our model, and therefore insufficient to producee a notable absorption of the underlying star light by thee envelope (§12). The possibility naturally remains that, amongg the many known Be stars one might find a group satis- fyingg the theoretical model used, but certainly this is not soo for the large majority of cases, 58 8 Noww turning to the Wolf-Rayet stars, Kosirev»s idea of an extendedd photosphere encounters even greater difficulties . Iff these show also a large optical depth in the Lyman con- tinuum,, as in fact Kosirev assumes, a proper treatment with thee absorption coefficient dependent on I gives rise to a lackk of radiation for wavelengths shorter than X912. This howeverr is in contradiction with the observations of Wolf- Rayett stars which are surrounded "by a planetary nebula(§12) wheree always hydrogen emission is observed in the nebula. Thuss one is forced to conclude that the optical depth of Ly- mann continuum is small in the Wolf-Rayet envelope, and Ko- sirev'' s treatment can no longer be upheld. So we return to Beals** original model of a Wolf-Rayet star, viz, a hot star eventuallyy with an ultraviolet excess in itself, surrounded byy an envelope in which the mechanism of nebular luminosity iss applicable. Such a treatment of Wolf-Rayetstars is now presentedd in the following sections of the dissertation,af- terr the introductory $13. AA discussion of spectra of planetary nebulae which surround Wolf-Rayett stars shows that a concentration of radiation in emissionn lines of high ions which subsequently escapes the Wolf-Rayett envelope is unlikely (§14). The same materialpro- videss an argument in favour of Beals' hypothesis for the Wolf-Rayett envelope; ionisation from the ground state by stellarr radiation followed by recombination (mechanism of nebularr luminosity). With this mechanism the transition of thee inner Hell shell to the outer Hel shell in the Wolf-Ra- yett envelope is then investigated, and it proves to be very abrupt,, so that practically never.the spectra Hell and Hel aree emitted together (§18). The Wolf-Rayet envelope can thereforee be divided into successive shells of predominent- lyy He++ and He+ ions, eventually followed by a shell of neu- trall helium. Thiss sharpness of the ionisation limit and consequent divi- sionn of the atmosphere in subsequent layers is then used forr determining the abundance of carbon with respect to he- lium,, using Beals1 observed band intensities. This is like- wisee based on the assumption of the mechanism of nebular lu- minosityy applied to the Wolf-Rayet envelope, as in the above, butt now the assumptions are more general, since it is no longerr assumed that the star behaves like a black body, ex- ceptt in the visual region (§19) To this end two models have beenn postulated. In model I the CIII and Hell shells ter- minatee together and adjoin there the combined CII and He I shell.. By this method, which is entirely based on numbers off recombinations, the electron concentration drops in the abundancee formulae. For ions not of the hydrogen type the numberss of recombinations are also determined by means of the cilliéé factors, which approximation has some justification forr higher levels. The computations for this Model I (Fig5) aree contained in 520- {28. Inn Model II (§30 and Pig.7) it was assumed that the first transitionn layer separates the CIV from the CIII region,while fartnerr outward the Hell is separated from the Hel region, butt that then the CIII region extend to infinity. Inn addition to this, the ratios of the radii of the shells weree determined. The results for both models are summarised inn §31, tables 17 and 18 r r L L 59 9 Thee abundance ratios of carbon with respect to helium deter- minedd in this way are very high. Aller, who assumes thermal equilibriumm for various excitation temperatures derived from hiss observations, finds 10 to 20 times lower abundances for thee same stars. Finallyy the ratio of hydrogen to helium is determined in a correspondingg manner for one star for which Beals disen- tangledd the blends of hydrogen and helium lines, one finds abundancee ratio of the order 1 (§32). Neubauer and Aller, assumingg thermal equilibrium, obtained similar results for aa different Wolf-Rayet star. Thee conclusion based on the foregoing is that one should seriouslyy face the possibility that the Wolf-Rayet envelopes thee abundance ratios are quite different from those in other starss and that the abundance of carbon may even be of the samee order as that of helium and hydrogen. .
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