Constraints on Stellar Evolution from Pulsations [chapter]

Arthur N. Cox
1984 Observational Tests of the Stellar Evolution Theory  
Perhaps the greatest successes for the constraints of pulsation theory are for the classical Cepheids, the RR Lyrae variables, and the popula tion II Cepheids (BL Her and W Vir variables) . Masses derived by some pulsation-based methods agree well with evolution theory, but there are 421 A. Maeder and A. Renzini (eds.). Observational Tests of the Stellar Evolution Theory, 421-440. © 1984 by the 1AU. available at
more » ... 074180900031259 Downloaded from IP address:, on 11 Mar 2020 at 16:00:12, subject to the Cambridge Core terms of use, 422 A. N. COX problems that still exist. These problems might eventually be bonafide constraints to be settled by changes in our current ideas of the internal composition structure. It seems that, except for much needed accurate surface effective temperatures for Mira variables and for the extremely hot dwarf stars and more periods for double-mode RR Lyrae variables in the field and in globular clusters, the next advances in these pulsation-based constraints will come from theoretical calculations of internal mixing and element separation and from nonlinear pulsation calculations. (1972) . We ignore for this discussion the problems for the double-mode and bump Cepheids that can indicate internal helium enhancements or magnetic fields. For periods longer than 10 days, there has been a remaining problem that the Wesselink masses used with the period-mean density relation produce masses too small by typically a factor of 0.6-0.7. Cepheid masses have been shown by Cox (1979) to be consistent with evolution calculations using the new larger distance scale of Hanson (1977) and the cooler effective temperatures of Pel (1978), Flower (1977) and Bell and Parsons We here propose as Burki (1983) recently has done, that these Wesselink radii indicate mass loss rates that can be used as a constraint on evolution calculations which include mass loss. The measured Wesselink radius has been discussed by Burki, who shows that the presence of a companion star can greatly affect the derived radius. Therefore, it is better that only truly single Cepheids be considered. Solution of three equations, the period-mean density relation, the definition of the surface effective temperature, and a fit for the pulsation constant Q as a function of mass, radius, luminosity, and effective temperature, are solved for three unknowns, Q, luminosity and mass when the period, effective temperature and Wesselink radius are given. The Cepheids RS Pup, 1 Car, U Car, and SV Vul (possibly a binary) are shown to have a mass as small as 0.3 the so-called theoretical mass. Burki shows that the Maeder (1981) evolution tracks with moderate to large mass loss (cases B and C) bracket the current masses for these four Cepheids. Figure 1 gives these Burki masses versus luminosity for these Cepheids together with the case A (no mass loss), B and C relations for the initial masses of 9 and 15 M . It appears that the mass loss rate almost as high as given for case C is indicated for these four variables. Actually both RS Pup and SV Vul have measured luminosities and effective temperatures, allowing the calculation of their pulsation masses. RS Pup shows little mass loss in Figure 1 , and indeed the Wesselink and pulsation masses agree at 10 M within about 2 M . For SV VuL, however, it appears that evolution, theoretical and pulsation masses yield about 12 M , but the Wesselink value is less than 4. It may be that indeed SV Vul is a binary star with a blue companion which wrongly reduces its Wesselink radius by an appreciable amount and therefore reduces the Wesselink mass to a very low, incorrect value. We do not have luminosity data for the two other Carina stars to available at https://doi.
doi:10.1007/978-94-010-9570-9_76 fatcat:dusvybfzeng5tohxbb4wayu7be