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Double-mode pulsation

Description: Double mode pulsation is a very pervasive phenomenon in stars all over the Hertzsprung-Russell diagram. In order of increasing radius, examples are: ZZ Ceti stars, the sun, the delta Scuti stars, RR Lyrae variables, the ..beta.. Cephei variables and those related to them, Cepheids, and maybe even the Mira stars. These many modes have been interpreted as both radial and nonradial modes, but in many cases the actual mode has not been clearly identified. Yellow giants seem to be the most simple pulsators with a large majority of the RR Lyrae variables and Cepheids showing only one pulsation period. We limit this review to those very few cases for classical Cepheids and RR Lyrae variables which display two modes. For these we know many facts about these stars, but the actual cause of the pulsation in two modes simultaneously remains unknown.
Date: July 30, 1982
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

Nonlinear hydrodynamics. Lecture 9

Description: A very sophisticated method for calculating the stability and pulsations of stars which make contact with actual observations of the stellar behavior, hydrodynamic calculations are very simple in principle. Conservation of mass can be accounted for by having mass shells that are fixed with their mass for all time. Motions of these shells can be calculated by taking the difference between the external force of gravity and that from the local pressure gradient. The conservation of energy can be coupled to this momentum conservation equation to give the current temperatures, densities, pressures, and opacities at the shell centers, as well as the positions, velocities, and accelerations of the mass shell interfaces. Energy flow across these interfaces can be calculated from the current conditions, and this energy is partitioned between internal energy and the work done on or by the mass shell. We discuss here only the purely radial case for hydrodynamics because it is very useful for stellar pulsation studies.
Date: March 14, 1983
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

Linear nonradial pulsation theory. Lecture 7

Description: Many of the upper main-sequence stars pulsate in spheroidal nonradial modes. We know this to be true in numerous cases, as we have tabulated for the ..beta.. Cephei and delta Scuti variables in previous lectures. However, we cannot identify the actual mode for any star except for the low-order pressure p and f modes of our sun. It remains a great challenge to clearly state what really is occurring, in the process we learn more about how stars evolve and pulsate.
Date: March 14, 1983
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

Modes, masses, metallicities, and magnitudes of RR Lyrae variables

Description: The author reviews past and recent developments in the study of RR Lyrae variables. He provides supporting evidence for a large helium content but remains uncertain as to their masses and luminosities. Time dependent convection is offered as a probable explanation for the double mode pulsations of these stars. 25 refs., 8 figs., 3 tabs.
Date: July 1, 1987
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

Stellar-opacity calculations. I. Lecture 2

Description: In this study of stellar structure, evolution, stability, and pulsation or explosion, there are three very vital pieces of physical information needed. We assume the composition is known from observations of assumption. To construct a model of a star we then need to know the nuclear generation rates which give the luminosity the star emits, the pressure and energy equation of state which determines the flow of radiation through the star. It is the equation of state and opacity that we will be discussing in the next two lectures.
Date: March 14, 1983
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

RR lyrae variable pulsations and the Oosterhoff groups

Description: It is concluded that Oosterhoff group I clusters have 0.55 M/sub sun/ stars and group II clusters have 0.65 M/sub sun/ stars. The Y value is always about 0.29. Mean log L/L/sub sun/ values are 1.66 and 1.78 giving M/sub bol/ = 0.60 and 0.30 for the RR Lyrae variables in these two groups of clusters. For field RR Lyrae variables at M = approx. 0.5 M/sub sun/ or less, perhaps M/sub bol/ = 0.90 or even larger as Clube and Jones propose. Apparently all evolution is blueward for RR Lyrae variables, and the color overlap of F and 1H pulsators is not real. (GHT)
Date: January 1, 1981
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

Pulsations of B stars: A review of observations and theories

Description: The observational and theoretical status are discussed for several classes of variable B stars. The older classes now seem to be better understood in terms of those stars that probably have at least one radial mode and those that have only nonradial modes. The former are the ..beta.. Cephei variables, and the latter are the slowly rotating 53 Persei and the rapidly rotating zeta Ophiuchi variables. It seems that in this last class there are also some Be stars that show nonradial pulsations from the variations of the line shapes and their light. Among the nonradial pulsators, we must also include the supergiants which show pulsations with very short lifetimes. A review of the present observational and theoretical problems is given. The most persistent problem of the cause for the pulsations is briefly discussed, and many proposed mechanisms plus some new thoughts are presented. 57 refs., 4 figs.
Date: January 1, 1986
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

Solar opacities constrained by solar neutrinos and solar oscillations

Description: This review discusses the current situation for opacities at the solar center, the solar surface, and for the few million kelvin temperatures that occur below the convection zone. The solar center conditions are important because they are crucial for the neutrino production, which continues to be predicted about 4 times that observed. The main extinction effects there are free-free photon absorption in the electric fields of the hydrogen, helium and the CNO atoms, free electron scattering of photons, and the bound-free and bound-bound absorption of photons by iron atoms with two electrons in the 1s bound level. An assumption that the iron is condensed-out below the convection zone, and the opacity in the central regions is thereby reduced, results in about a 25 percent reduction in the central opacity but only a 5 percent reduction at the base of the convection zone. Furthermore, the p-mode solar oscillations are changed with this assumption, and do not fit the observed ones as well as for standard models. A discussion of the large effective opacity reduction by weakly interacting massive particles also results in poor agreement with observed p-mode oscillation frequencies. The much larger opacities for the solar surface layers from the Los Alamos Astrophysical Opacity Library instead of the widely used Cox and Tabor values show small improvements in oscillation frequency predictions, but the largest effect is in the discussion of p-mode stability. Solar oscillation frequencies can serve as an opacity experiment for the temperatures and densities, respectively, of a few million kelvin and between 0.1 and 10 g/cm/sup 3/. Current oscillation frequency calculations indicate that possibly the Opacity Library values need an increase of typically 15 percent just at the bottom of the convection zone at 3 /times/ 10/sup 6/K. 41 refs., 15 figs., 1 tab.
Date: August 15, 1989
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

Constraints on stellar evolution from pulsations

Description: Consideration of the many types of intrinsic variable stars, that is, those that pulsate, reveals that perhaps a dozen classes can indicate some constraints that affect the results of stellar evolution calculations, or some interpretations of observations. Many of these constraints are not very strong or may not even be well defined yet. In this review we discuss only the case for six classes: classical Cepheids with their measured Wesselink radii, the observed surface effective temperatures of the known eleven double-mode Cepheids, the pulsation periods and measured surface effective temperatures of three R CrB variables, the delta Scuti variable VZ Cnc with a very large ratio of its two observed periods, the nonradial oscillations of our sun, and the period ratios of the newly discovered double-mode RR Lyrae variables. Unfortunately, the present state of knowledge about the exact compositions; mass loss and its dependence on the mass, radius, luminosity, and composition; ;and internal mixing processes, as well as sometimes the more basic parameters such as luminosities and surface effective temperatures prevent us from applying strong constraints for every case where currently the possibility exists.
Date: January 1, 1983
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

PG1159 variables

Description: A 0.6 solar mass model is discussed that has a temperature ranging from 100,000 K for its surface effective temperature to a maximum of almost 200 million K, and then a decrease to about 85 million K at the center. This temperature inversion is caused by strong neutrino losses at the high central densities. These internal densities range from 10/sup -6/ to 10/sup +6/ g/cm/sup 3/ from the surface to the center. For luminosities considerably lower than the 1.075 x 10/sup 35/ erg/sec for this model, the central temperature inversion disappears and the central density grows larger. For the PG1159 class of stars however, there is always this inversion.
Date: January 1, 1985
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

Supergiant radial and nonradial pulsations. Lecture 10

Description: The stars that we consider here have luminosities above 10,000 solar luminosities and masses above 15 solar masses. We contact the 53 Per stars such as ..nu.. Ori, 10 Lac, and iota CMa at our lower luminosity limit, and at the most luminous limit, we have the famous stars eta Car, Cyg OB12, and P Cyg. Evolution tracks including a reasonable mass loss rate are given for 15, 30, 60, and 120 solar masses. It appears that our pulsators have masses less than 60 solar masses, but how do the most luminous stars observed survive mass loss. Do they have masses above 100 solar masses as indicated, or are these stars somehow superluminous due to their erratic mass loss behavior. Popper (1980) studying the masses in binary systems has never found one with a value greater than 27 solar masses.
Date: March 14, 1983
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

Stellar-opacity calculations. II. Lecture 3

Description: We turn to the effects on opacities of atomic lines and molecular bands. It was the realization that these atomic lines were important for the opacity and the radiation flow in stars that allowed the field of stellar evolution to greatly flower in the 1960's and 1970's. Our understanding of stellar structure and evolution is now very deep.
Date: March 14, 1983
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

Beta-Cephei variables. Lecture 1

Description: In discussing upper-main-sequence stars and their intrinsic pulsations, we need to realize that theory has not yet been able to understand these pulsations. In many discussions the character of the pulsations has been described, and in many cases these theoretical solutions of the stellar pulsation theory may be the actual ones occurring. But the specific driving mechanism, so well known for the yellow and red giants and supergiants, and very recently known for the white dwarf stars, remains the subject for intense discussion. My ideas will pervade all my discussion, but many of them concerning the details such as the cause of the pulsations have not yet been proved correct.
Date: March 14, 1983
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

Delta Scuti variables. Lecture 6

Description: The class of variables near or on the upper main sequence, the delta Scuti variables, are not only the usual ones about the masses, radii, and luminosities, but also the age, rotation, element diffusion to change the surface layer composition, the occurance of convection and the presence of radial and nonradial pulsation modes. (GHT)
Date: January 1, 1983
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

Linear radial pulsation theory. Lecture 5

Description: We describe a method for getting an equilibrium stellar envelope model using as input the total mass, the envelope mass, the surface effective temperature, the total surface luminosity, and the composition of the envelope. Then wih the structure of the envelope model known, we present a method for obtaining the raidal pulsation periods and growth rates for low order modes. The large amplitude pulsations observed for the yellow and red giants and supergiants are always these radial models, but for the stars nearer the main sequence, as for all of our stars and for the white dwarfs, there frequently are nonradial modes occuring also. Application of linear theory radial pulsation theory is made to the giant star sigma Scuti variables, while the linear nonradial theory will be used for the B stars in later lectures.
Date: January 1, 1983
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

Mythical Maia, ultrashort and 53 PSC variables. Lecture 4

Description: Moving down the main sequence from the ..beta.. Cephei variables, we come to later B-type stars. The suspicion of variability for these stars goes back to Vogel in 1891 who studied the radial velocities of Vega. Since that time there have been numerous studies of Vega (Wisniewski and Johnson 1979, Fernie 1981) and other B and early A stars which hint at variability in both radial velocity and light. Since Struve (1955) discussed these stars 28 years ago, they have been called the Maia stars after the Pleiades star that he thought was the prototype. The uncertainty in their actual variability has led Breger (1980) to call them the mythical Maia variables.
Date: March 14, 1983
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

RR Lyrae and BL Herculis variables

Description: The RR Lyrae variables are currently believed to have masses between about 0.5 and 0.8 M/sub solar mass/, effective surface temperatures between 6350 and 7500/sup 0/K, radii from about 4.0 to 6.0 R/sub solar mass/ and luminosities between log L/L/sub solar mass/ of 1.5 and 2.0. Since they are found in population II locations, they generally have Y = 0.3 and Z = 10/sup -3/, but there are exceptions for both higher Z like the sun and lower Z like 0.0002. In globular clusters the periods range from 0.25 to 0.45 day for the first overtone pulsators and 0.40 to 0.80 day for those in the fundamental mode, depending on their luminosity. At transition lines, discussed in detail, the switch from fundamental to first overtone, or maybe vice versa, involves a period change factor of about 0.74 to 0.75.
Date: January 1, 1980
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

Kappa effect pulsational instability for hot extreme helium stars

Description: A long standing problem for the hydrogen deficient stars has been the mechanism for the pulsation instability for the hottest members of this class. The usual {kappa} mechanism works well for stars that are in the hydrogen and helium ionization instability strip, and this strip extends to perhaps 20,000K at high luminosity. However, several stars are definitely hotter. Investigations for another ionization instability strip, such as for carbon, have always shown that there is not enough carbon to produce a rapid enough increase of opacity with temperature to give the well-known {kappa} effect. This is so even though these hydrogen deficient stars do show enhanced carbon in their spectra. A strong stellar wind can produce the observed hydrogen deficiency. Another popular mechanism is mass loss in a binary system through the Roche lobe. It now is possible that the missing pulsational instability mechanism is the rapid increase of iron lines absorption as the temperature increases above about 150,000K in the low density envelopes of these luminous stars. Recent calculations shows that the n = 3 to n = 3 transitions in iron that were assumed unimportant in the earlier Los Alamos calculations can double or triple the opacity suddenly as the iron lines appear in a very sensitive part of the spectrum of the diffusing photons. It has been proposed that these iron lines also cause the many varieties of normal B star pulsations, and the hydrogen deficient stars are merely another example of this new {kappa} effect for pulsating stars. The extreme helium star V2076 Oph at 31,900K, and 38,900 L{sub {circle dot}} for a mass of 1.4 M{sub {circle dot}} pulsates in the radial fundamental model at about 1 day period with a very large linear growth rate when the iron lines more than double the opacity, but ...
Date: January 1, 1990
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

Solar oscillation frequency and solar neutrino predictions

Description: The light and velocity variations of the Sun and solar-like stars are unique among intrinsic variable stars. Unlike all other standard classes, such as Cepheids, B stars, and white dwarfs, the pulsation driving is caused by coupling with the acoustic noise in the upper convection zone. Each global pulsation mode is just another degree of freedom for the turbulent convection, and energy is shared equally between these g{sup {minus}}-modes and the solar oscillation modes. This driving and damping, together with the normal stellar pulsation mechanisms produce extremely low amplitude solar oscillations. Actually, the surface layer radiative damping is strong, and the varying oscillation mode amplitudes manifest the stochastic convection driving and the steady damping. Thus stability calculations for solar-like pulsations are difficult and mostly inconclusive, but calculations of pulsation periods are as straightforward as for all the other classes of intrinsic variable stars. The issue that is important for the Sun is its internal structure, because the mass, radius, and luminosity are extremely well known. Conventionally, we need the pulsation constants for each of millions of modes. Unknown parameters for constructing solar models are the composition and its material pressure, energy, and opacity, as well as the convection mixing length. We treat the nuclear energy and neutrino production formulas as sufficiently well known. The presence of weakly interacting massive particles (WIMPs) orbiting the solar center affects the predicted oscillation frequencies so that they do not agree with observations as well as those for models without WIMPs. 34 refs., 4 figs.
Date: July 5, 1990
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department

Pulsations of delta Scuti stars

Description: A general review of the pulsating {delta} Scuti variables is given including the observed light curves and positions of the stars in the Hertzsprung-Russell diagram. Theoretical interpretations from evolution and pulsation calculations give their masses, radii, luminosities, and even their approximate internal compositions. Three models of these stars are discussed and used to study the nonlinear hydrodynamic behavior of these stars. The hydrodynamic equations and the Stellingwerf method for obtaining strictly periodic solutions are outlined. Problems of allowing for time-dependent convection and its great sensitivity to temperature and density are presented. Tentative results to date do not show any tendency for amplitudes to grow to large unobserved amplitudes, in disagreement with an earlier suggestion by Stellingwerf. It is found that the very small growth rates of the pulsations may even be too small to be useful in seeking a periodic solution. 15 refs., 8 figs., 3 tabs.
Date: January 1, 1989
Creator: Cox, A.N.
Partner: UNT Libraries Government Documents Department