Double-mode Behavior Research Articles

The Czochralski growth and characterization of a dual-wavelength Raman gain crystal Sr(MoO4)x(WO4)1−x

Crack-free Sr(MoO4)x(WO4)1−x (x=0.3,0.45,0.7) solid solution single crystals with high optical quality and large dimensions have been successfully grown by the Czochralski method for the first time. The unit cell parameters and the density change linearly on the composition x that all obey Vegard’s law, indicating an ideal isomorphous substitution of W6+ by Mo6+. The refractive index functions and the average thermal expansion coefficients are precisely measured. As the concentration of [MoO4]2− increases, the refractive indices have a monotonous increasing trend, while the thermal expansion coefficients follow a parabolic trend. In the pontaneous Raman spectra, the double-mode behavior of v1(Ag) band has been observed. The Raman shifts at 886 and 921cm−1 with narrow line widths and high peak intensities indicate Sr(MoO4)0.45(WO4)0.55 crystal a potential uncontested dual-wavelength Raman gain medium.

Optical phonons in CdGa2S4x Se4(1 − x) alloys

The Raman spectra of CdGa2S4xSe4(1 − x) alloys (x = 0.1, 0.2, … 0.9) are studied. Both the singlemode and double-mode behavior of optical phonons are observed in CdGa2S4xSe4(1 − x) alloys. The observed optical mode at 138 cm−1 is independent of the composition. It seems likely that this mode is the “breathing mode” and is caused by atomic motion in the anion sublattice relative to vacancies. It is shown that the high-frequency modes of symmetry B1(LO, TO) and B2(LO, TO) are caused by the in-phase motion of atoms in the anion sublattice along the tetragonal axis c relative to trivalent Ga atoms. The doubly degenerate symmetry modes E1(LO, TO) and E2(LO, TO) are caused by the in-phase motion of atoms in the anion sublattice relative to trivalent Ga atoms of the cation sublattice in the xy plane (dipole 2Ga–4C), where C is S, Se. The optical symmetry modes B3(LO, TO) and B4(LO, TO) are associated with the motion of atoms in the anion sublattice relative to Cd atoms along the tetragonal axis c. The doubly degenerate modes E3(LO, TO) and E4(LO, TO) are associated with the motion of atoms in the anion sublattice relative to Cd atoms (dipole Cd–4C). The low-frequency modes B5(LO, TO) and E5(LO, TO) are the analogs of acoustic phonons at the edge of the Brillouin zone of sphalerite.

The Czochralski growth and structural investigations of Ba(MoO4)x(WO4)1−x solid solution single crystals

Ba(MoO4)x(WO4)1−x (x=0; 0.05; 0.1; 0.25; 0.5; 0.7; 0.95; 1) single crystals were grown by the Czochralski technique for the first time. A complete mutual solubility of the entire solid solution concentration range with tetragonal scheelite structure at room temperature was established by XRD analysis and Raman spectroscopy of as-grown crystals. By comparison of the differential-thermal analysis data and the high temperature Raman spectra, the existence of a cubic α-modification of the solid solutions is identified at x>0.5 in the temperature region above 1200°С. The double-mode behavior of the ν1(Ag) band in the vibration spectrum, weak broadening and high peak cross section of the ν1(Ag) vibration modes make these single crystals a promising material for dual-line SRS-conversion with a Raman shift of 889 and 925cm−1.

Double-Mode RR Lyrae Variables in the Globular Cluster M3

We present new B-band CCD photometry for five double-mode RR Lyrae (RRd) variables (V68, V79, V87, V99, and V166) in the globular cluster M3. The pulsational behavior of the RRd variables is described. V68 and V87 have been known as RRd variables since 1982, V79 was recently discovered as an RRd (Clement et al.), and our data have identified V99 and V166 as RRd variables (Corwin et al.). Earlier studies of V79 and V166 do not show double-mode behavior, which indicates that these stars have only recently become RRd stars. V166 changed its dominant pulsation mode from fundamental to first overtone in the interval 1992 to 1993. The candidate double-mode variables V28 and V126 do not exhibit clear RRd behavior in the 1992–1993 data.

Double-Mode RR Lyrae Stars in the Globular Cluster M15

view Abstract Citations (20) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Double-Mode RR Lyrae Stars in the Globular Cluster M15 Purdue, Patricia ; Silbermann, N. A. ; Gay, Pamela ; Smith, Horace A. Abstract We have reinvestigated the pulsational behavior of seven previously known or suspected double-mode RR Lyrae stars in the globular cluster MiS using the V and R band photometry of Silbermann & Smith [AJ, 110, 704 (1995a)]. Five of these stars (v17, v30, v31, v39, and v53) continued to exhibit double-mode behavior in the years 1991-1992, while we were unable to confirm double-mode pulsation in vS 1 and v54 during those years. Comparison of our results with those of previous investigations demonstrates that v17, v3 1, and v39 have shown no significant changes in period ratio or amplitude ratio during the past half century. The ratio of first overtone to fundamental mode pulsation in v30 and possibly v53 has changed during the past half century. The evidence that v54 was at one time a double-mode pulsator is doubtful. The evidence for past double-mode behavior of vS 1 is stronger, but still uncertain. For the confirmed double-mode RR Lyrae stars the amplitude of the fundamental mode pulsation can be as large as about half the amplitude of the first overtone pulsation. Publication: The Astronomical Journal Pub Date: October 1995 DOI: 10.1086/117643 Bibcode: 1995AJ....110.1712P Keywords: GLOBULAR CLUSTERS: INDIVIDUAL: M15; STARS: VARIABLES: RR LYRAE; STARS: OSCILLATIONS full text sources ADS | data products SIMBAD (10)

Nonlinear RR Lyrae models with new livermore opacities

A. N. Cox recently showed that a 20% opacity decrease in the 20,000-30,000 K region as indicated by the new Livermore OPAL opacities reconciles the discrepancy between pulsation and evolution masses of double-mode RR Lyrae variables. Nonlinear hydrodynamic calculations were performed for RR Lyrae models of mass 0.75M ⊙, 51L ⊙, andZ = 0.0001 (Osterhoff II type) including this opacity decrease. The Stellingwerf periodic relaxation method was used to converge the models to a limit cycle, and the Floquet matrix eigenvalues calculated to search for a tendency of the fundamental mode to grow from the full-amplitude overtone solution, and the overtone mode to grow from the full-amplitude fundamental solution, thereby predicting double-mode behavior. Models ofT eff < 7000 K with the opacity decrease have positive fundamental-mode growth rates in the overtone solution, in contrast to earlier results by Hodson and Cox (1982), and models withT eff > 7000 have positive 1st overtone growth rates in the fundamental-mode solution, but double-mode behavior was not found.

Double-mode pulsation in radiative RR Lyrae models

Tests made with a standard, purely radiative hydrodynamical code show that sustained double-mode pulsations of RR Lyrae models with the observed periods are possible. The basic difference with our previous simulations is that the new ones have less dissipation due to reduced artificial viscosity. As a result, some models have larger amplitudes than those given by the observations. The double-mode behavior is demonstrated for several models in a sequence that is representative of Oosterhoff II variables. Similar results are also found for Oosterhoff I stars

Double-Mode Stellar Pulsation

AbstractThe current observational and theoretical status of the double-mode variables is reviewed. Focusing mostly on the RR Lyrae stars, we address the question of the observational evidence of modal stability. The problem of stationarity is a crucial issue in the modelling of these stars.We mention past efforts in hydrodynamical and analytical modelling together with a detailed discussion of some very recent results. It is suggested that stochastic forcing due to turbulent convection may play a crucial role in exciting some marginally stable modes in the limiting pulsation. The latest hydrodynamical results first demonstrate that purely radiative models are able to show permanent double-mode behavior in the relevant period regime of RRd stars. The reason for the previous lack of double-mode behavior is attributed to the large dissipation, i.e. artificial viscosity, generally used in the codes to ensure numerical stability and to obtain amplitudes comparable to the observed ones.We think that better models should include some physical dissipation, most probably turbulent convection, and a more accurate numerical treatment of the radiative hydrodynamics.

Nonlinear RR Lyrae Models with New Livermore Opacities

AbstractA. N. Cox recently showed that a 20% opacity decrease in the 20,000–30,000 K region as indicated by the new Livermore OPAL opacities reconciles the discrepancy between pulsation and evolution masses of double-mode RR Lyrae variables. Nonlinear hydrodynamic calculations were performed for RR Lyrae models of mass 0.75M⊙, 51L⊙, andZ= 0.0001 (Osterhoff II type) including this opacity decrease. The Stellingwerf periodic relaxation method was used to converge the models to a limit cycle, and the Floquet matrix eigenvalues calculated to search for a tendency of the fundamental mode to grow from the full-amplitude overtone solution, and the overtone mode to grow from the full-amplitude fundamental solution, thereby predicting double-mode behavior. Models ofTeff&lt; 7000 K with the opacity decrease have positive fundamental-mode growth rates in the overtone solution, in contrast to earlier results by Hodson and Cox (1982), and models withTeff&gt; 7000 have positive 1st overtone growth rates in the fundamental-mode solution, but double-mode behavior was not found.

Nonlinear Radiative RR Lyrae Models: A Search for Double-Mode Behavior

Cox (1991), Kovacs, Buchler, and Marom (1991), and Kovacs et al. (1992) showed that opacity changes indicated by the Livermore OPAL opacities increase the pulsation masses of double-mode RR Lyrae variables. We calculated limiting amplitude solutions for radiative RR Lyrae models of 0.75 M⊙, 51 L⊙, and Z=0.0001 (Oosterhoff II) to investigate the effects of the mass increase and opacity changes suggested by the OPAL opacities. In particular, we modified the Stellingwerf analytical fit (1975) to the Cox-Tabor (1976) tables to decrease the opacity by 20% between 20,000 and 30,000 K. The Stellingwerf periodic relaxation method was used to converge the models to a limit cycle, and the Floquet matrix analysed to search for a tendency of the fundamental mode to grow from the full-amplitude overtone solution, and the overtone to grow from the full-amplitude fundamental mode solution, thereby predicting double-mode behavior.

INFRARED REFLECTION SPECTRA OF Y1-xPrxBa2Cu3O7+δ

The infrared refleotion spectra of Y1-xPrxBa2Cu3O7+δ(x = 0,0.1,0.2,0.4,0.5, 0.6, 1.0) are measured in the temprature range of 4.2 to 300K. The measurements show that Ba mode has double mode behavior, the strength of which inverses with increasing x, and that the position of the reflection peak at 194cm-1, which has been identified as Y mode of YBa2Cu3O7+δ, is indenpendent of the density of Pr, i. e, the position of the peak does not change whether the Y is partially or totally substitued by Pr. This indicates that in Y1-xPrxBa2Cu3O7+δ the valence of Pr is tetra-valent. The substitution of Pr make the mobile holes localize around Pr, thereby lead to the suppression of superconductivity.

The Masses and Pulsation Modes of Classical Cepheids

AbstractRecent general observations pertaining to the masses and pulsation modes of classical Cepheids are reviewed. Certain special ones of these variables that display unusual behavior such as long term amplitude variations, overtone pulsations, and double-mode behavior, including one Cepheid in the first and second overtones as well as those in the fundamental and first overtone, are discussed in some detail. I suggest that the amplitude varying supergiant Cepheid HR 7308, which seems to be pulsating in the second radial overtone, is alternating between states where there is enough helium to barely give kappa and gamma effect driving, and where the helium has settled too deep for this driving. Reestablishment of the helium may be due to rapid levitation of the CNONe elements which cause convection and which then dredge-up the helium again to suppress the convection and also to drive pulsations. The use of Fourier fitting to the light and velocity curves have revealed some features that are interesting and are discussed, such as the pulsation mode discrimination and the derivation of accurate Wesselink radii. The seven methods of determining the masses of these stars are presented with a short critique of each. Evolution and pulsation masses depend on uncertain observed luminosities, and these have been revised recently. Evolution masses also depend on the blue looping yellow giant evolution tracks that may need revision because of convective core overshooting and possible opacity, Z, or Y abundance increases. The most discrepant masses, however, are those that depend on period ratios – the “bump” and “beat” masses. The possibility that the Cepheid internal structure can be modified enough by doubling the material opacity seems unlikely. It is suggested, though, that perhaps the period ratio mass anomaly solution can be found in CNONe element enhancement by radiation absorption levitation that would give higher opacities by abundance effects instead of any revisions in the opacity calculations. Some details for this mass anomaly “solution” are presented.

Finally a double-mode RR Lyrae model?

It is shown that in a certain range of physical parameters a proper choice of the artificial viscosity parameters can lead to double-mode pulsation of RR Lyrae models. Here we present one such model and exhibit its double-mode behavior both through the stability analysis of the periodic limit cycles and through straightforward numerical integrations.

Recent Work on Cepheid Variables

AbstractRecent work on Cepheids is reviewed in the areas of (1) the large-amplitude mode behavior, (2) convection, and (3) Cepheid masses. Initial-value type nonlinear calculations have not yet yielded true double-mode behavior. Yet we have the beginnings of a promising theory of modal selection. Theoretical calculations also yield reasonably located red edges to Cepheid (and Cepheid-like) instability regions.

Modal selection in pulsating stars

view Abstract Citations (31) References (21) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Modal selection in pulsating stars Simon, N. R. ; Cox, A. N. ; Hodson, S. W. Abstract Initial-value and periodic nonlinear pulsation integrations are carried out for a series of double-mode Cepheid models (P1/P0 equals about + 0.7) in the vicinity of the resonance omega (1) + omega (0) omega (3). None of the models tested shows persistent double-mode behavior. A new semiquantitative description of modal selection, based upon the iterative theory of Simon, is introduced to analyze the nonlinear results. In the simplest version of this description, modal section categories emerge which are identical to those of Stellingwerf. The hydrodynamic results also agree at least partially with Stellingwerf's in that a region in the red where the models approach (though never reach) simultaneous instability of both limit cycles is found. Analysis of resonant effects on modal selection in the calculations leads to the conclusion that models lying between the resonances omega (1) + omega (0) = omega (3) and P2/P0 = 0.5 may yet be viable candidates for double-mode pulsation. Publication: The Astrophysical Journal Pub Date: April 1980 DOI: 10.1086/157899 Bibcode: 1980ApJ...237..550S Keywords: Astrophysics; Cepheid Variables; Stellar Models; Periodic Variations; Time Dependence; Astrophysics full text sources ADS |

Theoretical period ratios for RR Lyrae variables and AQ Leonis

The ratio of the overtone to fundamental periods has been calculated for models of RR Lyrae variables by using the linear nonadiabatic theory. Both homogeneous envelope and helium-enriched surface-layer models have been considered in order to predict the observed period ratio for the only known Population II double-mode RR Lyrae variable AQ Leonis. It is shown that the period ratio for homogeneous models in the radial pulsation instability strip depends only on the fundamental mode period at 0.58 M/sub sun/ and 0.65 M/sub sun/ and does not depend on the luminosity or surface effective temperature. The AQ Leo period of 0/sup d/.55 and the period ratio of 0.746 can be explained with a homogeneous composition model with a mass of 0.65 M/sub sun/. No surface helium enrichment is necessary for this variable even though such enrichment seems to be necessary for the more luminous double- and triple-mode Cepheids. It appears that the double-mode behavior of AQ Leo can be explained by mode switching in its blueward or redward horizontal branch evolution. This mode switching is rapid compared with its lifetime as an RR Lyrae variable.

Recent work on Cepheid variables

Recent work on Cepheids is reviewed in the areas of (1) the large-amplitude mode behavior, (2) convection, and (3) Cepheid masses. Initial-value type nonlinear calculations have not yet yielded true double-mode behavior. Yet we have the beginnings of a promising theory of modal selection. Theoretical calculations also yield reasonably located red edges to Cepheid (and Cepheid-like) instability regions.