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Multiperiodicity in the Light Variations of the Beta Cephei Star Beta Crucis

High-resolution spectroscopic observations have led recently to the discovery that the P Cephei star Beta Crucis (Mimosa) is multiperiodic with at least three non-radial pulsation modes. Data obtained by the star tracker of the WIRE satellite have now allowed us to confirm this multiperiodicity in the light variations. A total of five million observations covering 17 days was analyzed and the three main periods we find in this work are in perfect agreement with the results derived from the line profile variations. The photometric amplitudes are small (3, 2.7 and 0.6 millimag for the dominant modes), but this is not surprising in view of the mode identifications derived earlier from the line profiles. Additional periods of low-amplitude modes (between 0.2-0.3 mmag) are also derived, including one suggested earlier by the radial velocity data.

Cuypers, J.

Multiperiodicity in the Light Variations of the Beta Cephei Star Beta Crucis

High-resolution spectroscopic observations have led recently to the discovery that the beta Cephei star beta Crucis (Mimosa) is multiperiodic with at least three non-radial pulsation modes. Data obtained by the star tracker of the WIRE satellite have now allowed us to confirm this multiperiodicity in the light variations. A total of 5 million observations covering 17 days was analyzed and the three main periods we find in this work are in perfect agreement with the results derived from the line profile variations. The photometric amplitudes are small (3, 2.7 and 0.6 millimag for the dominant modes), but this is not surprising in view of the mode identifications derived earlier from the line profiles. Additional periods of low-amplitude modes (between 0.2-0.3 mmag) are also derived, including one suggested earlier by the radial velocity data.

Cuypers, J.

Hercules X-1 = HZ Herculis - A multiperiod variable

Fundamental rotation properties of the free modes of oscillation of a star are employed to account for the various periodicities observed in the X-ray binary system HZ Her/Her X-1. The various rotation rates may be taken as defining a set of beat periods associated with the quasiregular flareups of HZ Her. This analysis, involving only one free parameter, provides a single physical mechanism to explain five observed periods of the binary system, including periods of 1.7 days, 35 days and 10 to 12 years.

Wolff, C. L.

Multiperiodic irradiance changes caused by r-modes and g-modes

More than 20 real periodicities ranging from 20 days to 2 years modulate the solar irradiance data accumulated since November 1978 by Nimbus 7. Many are quite strong during the first three years (solar maximum) and weak after that. There is a high correspondence between periods in irradiance and 28 periods predicted from the rotation and beating of global solar oscillations (r-modes and g-modes). Angular states l = 1, 2, and 3 are detected as well as some unresolved r-mode power at higher l. The prominence of beat periods implies a nonlinear system whose effective nonlinear power was measured to be about 2. This analysis constitutes a detection of r-modes in the sun, and determines from them a mean sidereal rotation rate for the convective envelope of 459 + or - 4 nHz which converts to a period of 25.2 days (27.1d, synodic).

Wolff, Charles L.

Multiperiod-grating surface-emitting lasers

Surface-emitting distributed feedback (DFB) lasers are disclosed with hybrid gratings. A first-order grating is provided at one or both ends of the active region of the laser for retroreflection of light back into the active region, and a second-order or nonresonant grating is provided at the opposite end for coupling light out perpendicular to the surfaces of the laser or in some other selected direction. The gratings may be curved to focus light retroreflected into the active region and to focus light coupled out to a point. When so focused to a point, the DFB laser may be part of a monolithic read head for a laser recorded disk, or an optical coupler into an optical fiber.

Lang, Robert J.

Multiperiodicities in the photometric variability of RS CVn binaries - What we know after 15 years

An overview of the behavior of the RS CVn binaries is presented. It is argued that chromospherically active stars vary in brightness on a variety of different time scales, each involving very different physics. Some of them are literally periodic, some are quasi-periodic or cyclical, and some can be described only in terms of a time scale. Connections between some of the different periods, cycles, and time scales are explained. Attention is given to orbital period, rotation period, migration, spot lifetimes, magnetic cycles and flares.

Hall, Douglas S.

White-dwarf variability and the rotation of g-modes

The multiperiodic behavior clearly evident after Fourier analysis of many DA white-dwarf light curves is interpreted as arising from outbursts whose timing is regulated by the rotation and oscillation of the star. A model is proposed on the basis of three main assumptions: (1) a broad array of g-mode oscillations is taking place all the time in DA white-dwarf variables; (2) slow rotation permits most of the g-modes to couple and form a small group of nonlinear modes, each characterized by one of the indices of the spherical harmonic functions involved; and (3) the observed brightenings of the star are produced by upwelling of convection on a large horizontal scale when the antinodes of the nonlinear oscillation patterns periodically rotate into alignment and cause a temporary local enhancement of energy per unit volume. This model is used to match precisely almost every strong periodicity observed in the complex light curves of the DA white dwarfs G207-9, G38-29, G29-38, and HL Tau 76. If the model has been applied correctly, the results indicate that all four of these variables are rotating slowly with periods in the range from 250 to 500 sec.

Wolff, C. L.

Wheat forecast economics effect study

A model to assess the value of improved information regarding the inventories, productions, exports, and imports of crop on a worldwide basis is discussed. A previously proposed model is interpreted in a stochastic control setting and the underlying assumptions of the model are revealed. In solving the stochastic optimization problem, the Markov programming approach is much more powerful and exact as compared to the dynamic programming-simulation approach of the original model. The convergence of a dual variable Markov programming algorithm is shown to be fast and efficient. A computer program for the general model of multicountry-multiperiod is developed. As an example, the case of one country-two periods is treated and the results are presented in detail. A comparison with the original model results reveals certain interesting aspects of the algorithms and the dependence of the value of information on the incremental cost function.

Mehra, R. K.

The pulsating white dwarfs

The characteristics of variable white dwarfs are presented through an examination of observational data. The variable white dwarfs are normal, single, DA white dwarfs. The variations are caused by pulsations, but the pulsations are nonradial rather than radial pulsations. The periods are all very long. Excluding harmonics and cross frequencies, the shortest period is 114 sec and the longest period is 1186 sec. Without exception every variable is multiperiodic. The stability of the periods varies from extremely high to very low; the low stability of many of the variables perhaps being due to incomplete data. Finally, there is a strong correlation between the amplitude of the variations and their remaining properties. The higher amplitude variables have more periods in their light curves and the periods are more unstable.

Robinson, E. L.

Two new extremely hot pulsating white dwarfs

High speed photometry of the extremely hot, nearly degenerate stars PG 1707 + 427 and PG 2131 + 066 reveals that they are low-amplitude pulsating variables. Power spectral analysis shows both to be multiperiodic, with dominant periods of 7.5 and 6.4-6.9 minutes, respectively. Together with the known pulsators PG 1159 - 035 and the central star of the planetary nebula Kohoutek 1-16, these objects define a new pulsational instability strip at the hot edge of the H-R diagram. The variations of these objects closely resemble those of the much cooler pulsating ZZ Ceti DA white dwarfs; both groups are probably nonradial g-mode pulsators. Evolutionary contraction of the PG 1159 - 035 variables may lead to period changes that would be detectable in as little as 1 year. The optical and IUE spectra of the PG 1159 - 035 variables are characterized by absorption lines of C IV and other CNO ions, indicating radiative levitation of species heavier than helium. He II is also present in the spectra, but the hydrogen Balmer lines are absent. Effective temperatures near 100,000 K are required, and the He II 4686 A profiles indicate log g greater than 6. These helium-rich pulsators form the hottest known subgroup of the DO white dwarfs.

Bond, H. E.

Radial pulsations in DB white dwarfs?

Theoretical models of DB white dwarfs are unstable against radial pulsation at effective temperatures near 20,000-30,000 K. Many high-overtone modes are unstable, with periods ranging from 12 s down to the acoustic cutoff period of approximately 0.1 s. The blue edge for radial instability lies at slightly higher effective temperatures than for nonradial pulsations, with the temperature of the blue edge dependent on the assumed efficiency of convection. Models with increased convective efficiency have radial blue edges that are increasingly closer to the nonradial blue edge; in all models the instability persists into the nonradial instability strip. Radial pulsations therefore may exist in the hottest DB stars that lie below the DB gap; the greatest chance for detection would be observations in the ultraviolet. These models also explain why searches for radial pulsations in DA white dwarfs have failed: the efficient convection needed to explain the blue edge for nonradial DA pulsation means that the radial instability strip is 1000 K cooler than found in previous investigations. The multiperiodic nature of the expected pulsations can be used to advantage to identify very low amplitude modes using the uniform spacing of the modes in frequency. This frequency spacing is a direct indicator of the mass of the star.

Kawaler, Steven D.

CoCoSim, a Code Generation Framework for Control/command Applications: An Overview of CoCoSim for Multi-Periodic Discrete Simulink Models

We present CoCoSim, a framework to support the design, code generation and analysis of discrete dataflow model expressed in Simulink. In this work, we specifically focus on the analysis and code generation of multi-periodic systems. For that CoCoSim provides two complementary approaches: the first amounts to encode the multiperiodic semantics in a pure-synchronous one – à la Lustre–, enabling the use of model checker for verifying properties. The second provides a faithful code generation into multiple communicating (mono)synchronous components – à la Prelude– that can be then simulated or embedded in the final platform with any real-time scheduler. These approaches have been experimented in various settings.

Bourbouh, Hamza

Rotation of Low-mass Stars in Upper Centaurus-Lupus and Lower Centaurus-Crux with TESS

We present stellar rotation rates derived from Transiting Exoplanet Survey Satellite (TESS) light curves for stars in Upper Centaurus–Lupus (UCL; ∼136 pc, ∼16 Myr) and Lower Centaurus–Crux (LCC; ∼115 pc, ∼17 Myr). We find spot-modulated periods (P) for ∼90% of members. The range of light-curve and periodogram shapes echoes that found for other clusters with K2, but fewer multiperiod stars may be an indication of the different noise characteristics of TESS, or a result of the source selection methods here. The distribution of P as a function of color as a proxy for mass fits nicely in between that for both older and younger clusters observed by K2, with fast rotators being found among both the highest and lowest masses probed here, and a well-organized distribution of M-star rotation rates. About 13% of the stars have an infrared excess, suggesting a circumstellar disk; this is well matched to expectations, given the age of the stars. There is an obvious pileup of disked M stars at P ∼ 2 days, and the pileup may move to shorter P as the mass decreases. There is also a strong concentration of disk-free M stars at P ∼ 2 days, hinting that perhaps these stars have recently freed themselves from their disks. Exploring the rotation rates of stars in UCL/LCC has the potential to help us understand the beginning of the end of the influence of disks on rotation, and the timescale on which stars respond to unlocking.

L M Rebull