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Fourier method of determining the rotational velocities in OB stars Aims.We present a comprehensive study that applies the Fourier transformto a sample of O and early B-type stars (either dwarfs, giants, orsupergiants) to determine their projected rotational velocities. We thencompare them with previous values obtained with other methods and seekevidence of extra broadening in the spectral lines Methods: The Fouriertechnique, extensively used in the study of cooler stars, has only beenmarginally applied to early-type stars. The comparison of v sin i valuesobtained through the ft and FWHM methods shows that the FWHM techniquemust be used with care in the analysis of OB giants and supergiants andwhen it is applied to He I lines. In contrast, the ft method appears tobe a powerful tool for deriving reliable projected rotational velocitiesand separating the effect of rotation from other broadening mechanismspresent in these stars. Results: The analysis of the sample of OB starsshows that while dwarfs and giants display a broad range of projectedrotational velocities, from less than 30 up to 450 km s-1,supergiants have in general values close to or below 100 kms-1. The analysis has also definitely shown that, while theeffect of extra broadening is negligible in OB dwarfs, it is clearlypresent in supergiants. When examining the behavior of the projectedrotational velocities with the stellar parameters and across the HRdiagram, we conclude, in agreement with previous researchers, that therotational velocity should decrease when the stars evolve. On thecontrary, macroturbulence may be constant, therefore resulting in anincreasing importance as compared to rotation when the stars evolve.The int and wht telescops are operated on the island of La Palma by theRGO in the Spanish Observatorium of El Roque de los Muchachos of theInstituto de Astrofísica de Canarias. Tables 2-10 are onlyavailable in electronic form at http://www.aanda.org
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