On The Masses And Luminosities Of RR Lyrae Stars

Some results are given from the comparison with observations of a large number of hydrodynamic pulsation models: (1) Linear pulsation calculations are adequate for the determination of the masses of RRd stars; (2) the Fourier phase parameter ϕ31 measures the luminosity-to-mass ratio L/M1.81 for RRc stars; (3) most of the Ѡ Cen RRc stars seem to be evolved, as has previously been suggested; (4) the masses of the w Cen RRc stars agree with the masses of RRd stars in other clusters; and (5) a hint emerges of a mass-helium abundance relation among the RRc stars in Ѡ Cen. New CCD observations will be needed to extend our analysis to additional globular clusters

On The Short-Period Type II Cepheid Field Stars

Fourier decomposition parameters for the photoelectric light curves of 20 short-period type II Cepheids in the field are compared with the models of Hodson, Cox, and King, also subjected to Fourier analysis. The hydrodynamic light curves display sequences in the Fourier phases very reminiscent of the resonance progressions among classical Population I Cepheids with periods less than 10 days. However a handful of type II models with small radii and relatively high period ratios, P2/P0, give Fourier phases which do not seem to follow the resonance sequence. Comparing the models with the type II Cepheid observations, we find very good agreement in both the phase-period and phase-phase diagrams. As in the models, there are a number of observed stars which obviously display a resonance progression and others which may not. Thus, based on the Fourier diagrams, we are led to distinguish three classes of short-period type II Cepheids with periods and period ratios as follows: type II S (1.d0 ≤ P ≤ 1.d6; P2/P0 ≥ 0.53); type II M (1. d 4 ≤ P0 ≤ 2. d0; P2/P0\u3c 0.53); and type II L (P ≥ 2.d0d; P2/P0 ≤ 0.49). An apparent resonance sequence among the II M stars leads us to propose that the resonance center (P2/P0 = 0.5) occurs near 2 days, rather than 1.6 days as suggested previously. We discuss the problems posed for theories of stellar and galactic evolution by the existence of disk, halo, and cluster pulsators with very similar light curves. Comparison of our results with the work of Carson, Stothers, and Vemury, Carson and Stothers, and Petersen and Diethelm, finds a number of points of agreement as well as some contradiction. Further calculations and additional observations, particularly CCD photometry of globular cluster Cepheids, will be necessary to resolve these problems

Nonlinear Period Ratios for the RRd Stars

The RR Lyrae stars play a role in the investigation of many important astronomical problems. For example, the slope of the luminosity - metallicity relation for RR Lyraes in globular clusters leads to relative cluster ages and thus to a chronology of the formation of the galactic halo. However, it is necessary to know fundamental parameters for the RR Lyrae stars, and these remain controversial. The masses of these objects can be determined in a number of ways, including the use of pulsation theory to model the RRd stars, and the calculation of horizontal branch evolutionary tracks. The RRd stars pulsate simultaneously in the first overtone and fundamental modes, enabling masses to be inferred from the period ratio vs. period diagram. These masses have the range 0.55 \u3c M/Mʘ \u3c 0.65, which disagrees with the masses M/Mʘ ≥ 0.70, determined from recent evolutionary tracks. However, the RRd masses quoted here depend upon pulsation periods obtained from linear models. Since the mass determination requires very high accuracy in the periods, it is necessary to ask whether the linear periods reflect the true theoretical values (i.e., the nonlinear periods) to the precision necessary. To answer this question, we constructed two hydrodynamic models with canonical RRd parameters and integrated them for well over 1000 periods in both the fundamental and overtone modes

Hydrodynamic Models Of RR\u3ci\u3eab\u3c/i\u3e Variables: Comparison Of Observed And Theoretical Light Curves

Eight fundamental-mode RR Lyrae models are integrated using a new code, TGRID, with dynamic zoning in the hydrogen ionization region (HIR). The models have a variety of parameters, in order to supplement an earlier group of calculations due to R. Stothers. When the light curves from these models are Fourier decomposed, it is found that the Fourier phases ϕ21 and ϕ31 agree with those from the earlier calculations but disagree with the values obtained from the observed light curves of RRab pulsators. Taken together, the past and present models cover perhaps the entire range of reasonable parameters for RR Lyrae stars and also encompass different opacities and a number of different artificial viscosity parameters. Thus the discrepancy between calculations and observations is thought to involve some basic physical or numerical aspect of the calculations. Searching the literature, we Fourier decompose a light curve from a convective model due to Stellingwerf, but find values of ϕ21 and ϕ31 similar to those for the radiative models. We also investigate two models published by Hill-one with a detailed treatment of radiative transfer, and another with both detailed radiative transfer and an extended atmosphere capable of treating the propagation of shock waves. The latter model produces a ϕ21 and ϕ31 in the middle of the range of observed values. We put forward some further evidence favoring the idea that the theoretical-observational disagreement may be due to the use of the diffusion approximation and the neglect of atmospheric shocks, and we close with a discussion of this problem

Three Interesting Stars

CO Aur is a Pop. I Cepheid, pulsating in two modes with periods Pl = 1.78 days and P2 = 1.53 days. The ratio of these periods indicates radial pulsation in the first and second overtones. Antonello and Mantegazza (1984) Fourier decompose the light curve of CO Aur and offer further evidence favoring overtone pulsation, based upon the Fourier diagrams of Simon and Lee (1981). Mantegazza (1983) estimates a temperature for CO Aur of log Te = 3.825±0.023. Employing the Lagrangian code described by Aikawa and Simon (1983), we have constructed two linear nonadiabatic (LNA) pulsation models for CO Aur, both with normal Pop. I composition X = 0.70, Z = 0.02) and an evolutionary mass-luminosity relation. The first model has M = 5.2 Mʘ, L = 1500 Lʘ and Te = 6700 K, corresponding to the temperature quoted above. The periods and growth rates (P,n) for the three lowest radial modes of this model are (2.41, -6.55E-3). (1.81, -1.26E-2) and (1.45, -1.51E-2). Although the periods of the first and second overtones match those of\u27 CO Aur quite well, all of the modes are linearly stable and thus not expected to appear at finite amplitude

Phase Lags and Pulsation Modes of Classical Cepheids

The first-order phase lag between light and velocity is calculated from Fourier decompositions of the variations of 12 classical Cepheids. The phase lags have a narrow range, with maximum expansion velocity always retarded with respect to maximum light. The average value of the first-order phase lag is found to be approximately ‒0.3, close to the theoretical value obtained from the models of Simon and Davis. When the phase lag is plotted against period, two of the stars stand out. These stars are SU Cas and AZ Cen, both suspected overtone pulsators. We further investigate AZ Cen by combining the light curves of three observers and plotting the star on the ϕ21-period diagram of Simon and Lee. The tentative result is seen to strengthen both the identification of AZ Cen as an overtone pulsator and the possible role of the first-order phase lag as a discriminator of mode. We close with a discussion of our results and of the uncertainties which remain

Nonlinear Period Ratios for the RRd Stars

The RR Lyrae stars play a role in the investigation of many important astronomical problems. For example, the slope of the luminosity - metallicity relation for RR Lyraes in globular clusters leads to relative cluster ages and thus to a chronology of the formation of the galactic halo. However, it is necessary to know fundamental parameters for the RR Lyrae stars, and these remain controversial. The masses of these objects can be determined in a number of ways, including the use of pulsation theory to model the RRd stars, and the calculation of horizontal branch evolutionary tracks. The RRd stars pulsate simultaneously in the first overtone and fundamental modes, enabling masses to be inferred from the period ratio vs. period diagram. These masses have the range 0.55 \u3c M/Mʘ \u3c 0.65, which disagrees with the masses M/Mʘ ≥ 0.70, determined from recent evolutionary tracks. However, the RRd masses quoted here depend upon pulsation periods obtained from linear models. Since the mass determination requires very high accuracy in the periods, it is necessary to ask whether the linear periods reflect the true theoretical values (i.e., the nonlinear periods) to the precision necessary. To answer this question, we constructed two hydrodynamic models with canonical RRd parameters and integrated them for well over 1000 periods in both the fundamental and overtone modes

On The Short-Period Type II Cepheid Field Stars

Fourier decomposition parameters for the photoelectric light curves of 20 short-period type II Cepheids in the field are compared with the models of Hodson, Cox, and King, also subjected to Fourier analysis. The hydrodynamic light curves display sequences in the Fourier phases very reminiscent of the resonance progressions among classical Population I Cepheids with periods less than 10 days. However a handful of type II models with small radii and relatively high period ratios, P2/P0, give Fourier phases which do not seem to follow the resonance sequence. Comparing the models with the type II Cepheid observations, we find very good agreement in both the phase-period and phase-phase diagrams. As in the models, there are a number of observed stars which obviously display a resonance progression and others which may not. Thus, based on the Fourier diagrams, we are led to distinguish three classes of short-period type II Cepheids with periods and period ratios as follows: type II S (1.d0 ≤ P ≤ 1.d6; P2/P0 ≥ 0.53); type II M (1. d 4 ≤ P0 ≤ 2. d0; P2/P0\u3c 0.53); and type II L (P ≥ 2.d0d; P2/P0 ≤ 0.49). An apparent resonance sequence among the II M stars leads us to propose that the resonance center (P2/P0 = 0.5) occurs near 2 days, rather than 1.6 days as suggested previously. We discuss the problems posed for theories of stellar and galactic evolution by the existence of disk, halo, and cluster pulsators with very similar light curves. Comparison of our results with the work of Carson, Stothers, and Vemury, Carson and Stothers, and Petersen and Diethelm, finds a number of points of agreement as well as some contradiction. Further calculations and additional observations, particularly CCD photometry of globular cluster Cepheids, will be necessary to resolve these problems

Temperature-Grid Coordinates For Treating Pulsations In The Hydrogen Ionization Zone

A temperature grid is used for the description of motion in the hydrogen ionization region (HIR). This means zones are labeled by temperature rather than mass. Outside the HIR, the conventional Lagrangian grid is used, with transitional coordinates at the boundaries. Although our final object is to apply this scheme to the nonlinear periodic integration problem, we have first constructed a linear version as a test. It is found that periods and growth rates agree very well with those calculated using pure Lagrangian coordinates, but the temperature grid scheme proves less sensitive to a reduction of zones in the HIR. This property is desirable for the nonlinear problem where zoning must necessarily be coarse. As a further test of the temperature grid, we formulate the linear work integral in the new coordinates and confirm the consistency of the growth rates. Finally, it is shown that the scheme is insensitive to a change in the manner in which the transition zones are treated

A Criterion for Nuclear-Energized Pulsational Instability

This Note will present briefly some general properties of nuclear-energized pulsations of stars as treated in the linear quasi-adiabatic theory. In particular, the results will be derived from a number of detailed calculations of stellar models. It is well known that an upper limit for the fundamental eigenfrequency of radial pulsation Ѡ0 is given by Ѡmax2 = 1ʃ0(3Γ1 ‒ 4)q/x dq / 1ʃ0 x2dq, Ѡ2= (2∏/Period)2 R3/GM (e.g., Ledoux and Walraven 1958). According to this expression, Ѡmax2 increases both with decreasing radiation pressure (i.e., increasing Γ1) and with increasing central condensation as measured by the ratio of integral