Secular Period Research Articles

Orbital period changes of YY Coronae Borealis

Abstract By using all available times of light minimum, the orbital period changes of a W UMa eclipsing binary YY CrB have been investigated. Two possible orbital period variations are found: (1) a secular period decrease with a rate of dP/dt = −6.727 × 10−7 d yr−1, on which a sinusoidal oscillation with a period of P = 12.68 yr is superposed, or (2) an abrupt period change with a sudden period decrease of −0.7862 s around the year 2005. The secular period decrease is discussed in terms of (1) the mass transfer from the more massive companion to the less massive one with a mass transfer rate of dM2/dt = 2.8096 × 10−7 M⊙ yr−1, and (2) the mass loss via stellar wind from the system. The sinusoidal oscillatory can be interpreted as a result of the magnetic activity cycles of the system. In addition, the abrupt period decrease of the system might be due to the sudden mass transfer between the components.

THE ACTIVE CONTACT BINARY TY UMA REVISITED: IS IT A QUADRUPLE STAR?

TY UMa is an F-type eclipsing binary star. Four-color light curves and radial velocities of this system were presented and simultaneously analyzed using the W-D code. It is found that TY UMa is a W-subtype shallow contact binary system (f = 13.4%) with a mass ratio of q = 2.523. In order to explain the asymmetric light curve of this binary, a dark spot on the less massive component was employed. Our newly determined 31 times of minimum light, including those collected from the literature, have been used to analyze orbital period changes of TY UMa. The complicated period variation could be sorted into a secular period increase at a rate of dp/dt = +5.18(+/- 0.21) x 10(-7) days yr(-1), a 51.7 yr periodic modulation (A(3) = 0.0182 days), and a very small amplitude cyclic oscillation with a period of 10.0 yr (A(4) = 0.0015 days). The long-term increase of the period can be explained by mass transfer from the less massive component to the more massive one. The Applegate mechanism may impossibly explain the two cyclic components in the period. The two cyclic variations are very likely caused by the light travel time effect of third and fourth components, suggesting that TY UMa is a quadruple system.

A Suggestion: The Malinvestment Index

According to the Austrian Business Cycle Theory, malinvestment is the key concept for understanding the transmission mechanism of the business cycle and the main determinant of its length and amplitude especially during a recession. This paper attempts to construct a malinvestment index to measure the degree of malinvestment in the U.S. economy for the period of 1974:01-2013:12. Four different stage-of-processing price indexes are used for constructing the malinvestment index and tracking the transmission of price changes across successive stages of economic activity in the U.S. economy. The findings of the malinvestment index suggest that the U.S. economy had been in a strong malinvestment period during the pre and post 2008 global crisis. Furthermore, the malinvestment periods all resulted in recessions in the U.S. economy with the exception of the 2008 global crisis. Lastly, the malinvestment index indicates technology-induced growth or secular growth periods.

PHOTOMETRIC SOLUTION AND FREQUENCY ANALYSIS OF THE oEA SYSTEM EW BOO

We present the first photometric solution and frequency analysis of the neglected oscillating Algol-type (oEA) binary EW Boo. B- and V-band light curves of the star were obtained on 11 nights in 2014. Using the Wilson–Devinney code, the eclipsing light curves were synthesized and the first photometric solution was derived for the binary system. The results reveal that EW Boo could be a semi-detached system with the less-massive secondary component filling its Roche lobe. By subtracting the eclipsing light changes from the data, we obtained the intrinsic pulsating light curves of the hotter, massive primary component. Frequency analysis of residual light shows multi-mode pulsation with the dominant period at 0.01909 days. A preliminary mode identification suggests that the star could be pulsating in non-radial (l = 1) modes. The long-term orbital period variation of the system was also investigated for the first time. An improved orbital period and new ephemerides of the eclipsing binary are given. The O−C analysis indicates a secular period increasing at a rate of dP/dt=2.9×10{sup −7} days yr{sup −1}, which could be interpreted as mass transfer from the cooler secondary to the primary component.

Properties and nature of Be stars

Reliable determination of the basic physical properties of hot emission-line binaries with Roche-lobe filling secondaries is important for developing the theory of mass exchange in binaries. It is a very hard task, however, which is complicated by the presence of circumstellar matter in these systems. So far, only a small number of systems with accurate values of component masses, radii, and other properties are known. Here, we report the first detailed study of a new representative of this class of binaries, BR CMi, based on the analysis of radial velocities and multichannel photometry from several observatories, and compare its physical properties with those for other well-studied systems. BR CMi is an ellipsoidal variable seen under an intermediate orbital inclination of ∼ 51°, and it has an orbital period of 12919059(15) and a circular orbit. We used the disentangled component spectra to estimate the effective temperatures 9500(200) K and 4655(50) K by comparing them with model spectra. They correspond to spectral types B9.5e and G8III. We also used the disentangled spectra of both binary components as templates for the 2D cross-correlation to obtain accurate radial velocities and a reliable orbital solution. Some evidence of a secular period increase at a rate of (1.1 ± 0.5) s per year was found. This, together with a very low mass ratio of 0.06 and a normal mass and radius of the mass gaining component, indicates that BR CMi is in a slow phase of the mass exchange after the mass-ratio reversal. It thus belongs to a still poorly populated subgroup of Be stars for which the origin of Balmer emission lines is safely explained as a consequence of mass transfer between the binary components.

A period study and revised photometric model for the eclipsing binary ZZ Cyg

We present new photometry of the eclipsing binary ZZ Cyg. From all accumulated eclipsing times, we constructed the (O–C) curve, which can be described by a downward parabola with a possible light-time orbit. The period decrease rate is dP/dt=-5.73(±0.18)dyr-1. The modulated period, semi-amplitude and eccentricity for the light-time orbit are Pmod=71.4(±1.1)yr, A=0.0071(±0.0005)day and e=0.420(±0.053), respectively. After removing effects of the magnetic activity, this kind of cyclic oscillation may be attributed to light-time effect via an additional companion. By using the W-D code, the photometric model was updated, which identified that ZZ Cyg is a near-contact binary. We find that a hot spot may occur on the primary that explains the asymmetric light curve. The secular period decrease may possibly cause the fill-out factor of the primary to increase. Finally it will finally fill its Roche lobe. This kind of binary, ZZ Cyg, may evolve into contact binary star.

Mean Element Propagations Using Numerical Averaging

The long-term evolution characteristics and stability of an orbit are well characterized using a mean element propagation of the perturbed two body variational equations of motion. The averaging process eliminates short period terms leaving only secular and long period effects. In this study, a non-traditional approach is taken that averages the variational equations using adaptive numerical techniques and then numerically integrating the resulting equations of motion. Doing this avoids the Fourier series expansions and truncations required by the traditional analytic methods. The resultant numerical techniques can be easily adapted to propagations at most solar system bodies.

Why Currency-Hedge Foreign Developed Equities?

When investors allocate to foreign stocks, they typically assume a secondary currency exposure on top of their local equity market returns and usually do so without having a strong conviction in the direction of the underlying currency. The authors believe the reason why investors fail to hedge their currency exposure is the result of a few common myths. In this article, they address three of the most common myths: 1) It is expensive to hedge foreign currencies; 2) currencies are a good hedge against purchasing power; and 3) currency returns are a wash in the long run. The authors explain why they believe these myths cause investors to take on additional currency risks, which depending on their currency outlook, may lead to suboptimal allocation decisions. The authors argue that investors who do not have strong conviction in the potential direction of the underlying currency should hedge at least a portion of their exposure to these currencies. They also discuss why the U.S. dollar may be entering a longer secular trend period where it increases in value against other major developed currencies. This view is based on changes unfolding in relative central bank policies, as well as likely changes in relative interest rate policies developing among Europe, Japan, and the United States. Ultimately, if this view proves accurate, the case for hedging foreign currency exposure against the dollar may become even more powerful.

Orbital-period variations of the close binaries with late-type components TY Del and RY Cnc

A detailed study of orbital-period variations was performed for TY Del and RY Cnc, which are both Algol-type eclipsing binaries with late-type second aries; for RY Cnc, this is the first study of this kind. The period variations of both stars can be considered a superposition of a secular period increase and cyclic changes of this period. The secular period increase can be explained as the effect of a uniform transfer of mass from the lower-mass to the higher-mass component, with the total angular momentum conserved. The mass-transfer rate is about 1.25 × 10⊙M⊙/year for TY Del and (0.68−1.02) × 10−8M⊙/year for RY Cnc. The cyclic period variations of the eclipsing binaries TY Del and RY Cnc could be due to either the presence of a third body in the system or the influence of magnetic activity of the secondary.

THE ECLIPSING SYSTEM V404 LYR: LIGHT-TRAVEL TIMES AND γ DORADUS PULSATIONS

We present the physical properties of V404 Lyr exhibiting eclipse timing variations and multiperiodic pulsations from all historical data including the Kepler observations. Detailed analyses of 2,922 minimum epochs showed that the orbital period has varied through a combination with an upward-opening parabola and two sinusoidal variations, with periods of $P_3$=649 d and $P_4$=2,154 d and semi-amplitudes of $K_3$=193 s and $K_4$=49 s, respectively. The secular period increase could be interpreted as a combination of the secondary to primary mass transfer and angular momentum loss. The most reasonable explanation for both sinusoids is a pair of light-travel-time effects due to two circumbinary objects with projected masses of $M_3$=0.47 M$_\odot$ and $M_4$=0.047 M$_\odot$. The third-body parameters are consistent with those calculated using the W-D binary code. For the orbital inclinations higher than 43$^\circ$, the fourth component has a mass within the hydrogen-burning limit of $\sim$0.07 M$_\odot$, which implies that it is a brown dwarf. A satisfactory model for the Kepler light curves was obtained through applying a cool spot to the secondary component. The results demonstrate that the close eclipsing pair is in a semi-detached, but near-contact, configuration; the primary fills approximately 93% of its limiting lobe and is larger than the lobe-filling secondary. Multiple frequency analyses were applied to the light residuals after subtracting the synthetic eclipsing curve from the Kepler data. This revealed that the primary component of V404 Lyr is a $\gamma$ Dor type pulsating star, exhibiting seven pulsation frequencies in the range of 1.85$-$2.11 d$^{-1}$ with amplitudes of 1.38$-$5.72 mmag and pulsation constants of 0.24$-$0.27 d. The seven frequencies were clearly identified as high-order low-degree gravity-mode oscillations which might be excited through tidal interaction.

Pulsation Period Change & Classical Cepheids: Probing the Details of Stellar Evolution

AbstractMeasurements of secular period change probe real-time stellar evolution of classical Cepheids making these measurements powerful constraints for stellar evolution models, especially when coupled with interferometric measurements. In this work, we present stellar evolution models and measured rates of period change for two Galactic Cepheids: Polaris and l Carinae, both important Cepheids for anchoring the Cepheid Leavitt law (period-luminosity relation). The combination of previously-measured parallaxes, interferometric angular diameters and rates of period change allows for predictions of Cepheid mass loss and stellar mass. Using the stellar evolution models, We find that l Car has a mass of about 9 M⊙ consistent with stellar pulsation models, but is not undergoing enhanced stellar mass loss. Conversely, the rate of period change for Polaris requires including enhanced mass-loss rates. We discuss what these different results imply for Cepheid evolution and the mass-loss mechanism on the Cepheid instability strip.

Secular variations of the photometric parameters of Mira Ceti variables and semiregular variables

The photometric properties of long-period variable stars and problems related to their traditional classification are analyzed. A general review of secular variations of such light-curve parameters studied in our previous papers as the period, amplitude, and mean brightness is given. Several types of Mira Ceti stars that differ in the secular period variation pattern are identified. A connection between the secular amplitude variations of certain variables with the effect of multiperiodicity is revealed. It is shown that the pattern of these variations and their numerical properties may be used to classify these variable stars.

Comprehensive photometric study of the eclipsing binary AW UMa

Due to its extreme mass ratio, the system AW UMa is considered as one of the most interesting contact binaries. In the present paper, a total of 1289 observations in VRI band were carried out from on 2006 March 7, 8, and 9 at Piszkesteto, Mountain Station of the Konkoly observatory (Hungary). VRI light curves were constructed and a photometric solution of these light curves was obtained by means of Willson-Devinney code. The results show that the primary component is more massive and hotter than the primary component by ∼140 K. A secular period decrease with a rate dP/dE=2.436×10−10 day/cycle was detected. Based on the physical parameters of the system, we investigate the evolutionary state of the components. The primary component is above the zero age main sequence (ZAMS) track, while the secondary component has a larger radius and luminosity than expected from its ZAMS mass.

PHOTOMETRIC PROPERTIES FOR SELECTED ALGOL-TYPE BINARIES. VI. THE NEWLY DISCOVERED oEA STAR FR ORIONIS

New photometry of the neglected eclipsing binary FR Orionis was obtained in 2012 November and December. Using the updated Wilson–Devinney program, the photometric elements were deduced from two-color light curves. The results indicate that this system is a semi-detached binary, with a mass ratio of 0.325(±0.002) and a fill-out factor of the primary of fp = 73.5(±0.2)%. The oscillating light curves imply that FR Ori may be an oscillating EA (oEA)-type star with a rapidly pulsating, mass-accreting primary component. After we removed the theoretical light curves from the observations, Fourier analysis revealed that the more massive component possibly shows a δ Scuti type pulsation with four detected frequencies. The dominant frequency is f1 = 38.6c day −1 (i.e., Ppuls = 37.3 minutes), and the pulsation constant is Q = 0.014 days. Based on all available eclipsing times, the orbital period is undergoing a secular period increase with a rate of dP/dt = +8.85(±0.66) × 10 −8 day yr −1 , which may be interpreted by mass transfer from the secondary to the primary. We expect that the more massive component will fill its Roche lobe due to mass transfer of the secondary. Therefore, the oEA star FR Ori may evolve into a contact configuration.

Effects of Geopotential and Atmospheric Drag Effects on Frozen Orbits Using Nonsingular Variables

The concept of frozen orbit has been applied in space missions mainly for orbital tracking and control purposes. This type of orbit is important for orbit design because it is characterized by keeping the argument of perigee and eccentricity constant on average, so that, for a given latitude, the satellite always passes at the same altitude, benefiting the users through this regularity. Here, the system of nonlinear differential equations describing the motion is studied, and the effects of geopotential and atmospheric drag perturbations on frozen orbits are taken into account. Explicit analytical expressions for secular and long period perturbations terms are obtained for the eccentricity and the argument of perigee. The classical equations of Brouwer and Brouwer and Hori theories are used. Nonsingular variables approach is used, which allows obtaining more precise previsions for CBERS (China Brazil Earth Resources Satellite) satellites family and similar satellites (SPOT, Landsat, ERS, and IRS) orbital evolution.

The sunspot cycle length – modulated by planets?

The Schwabe frequency band of the sunspot record since 1700 has an average period of 11.06 yr and contains four major cycles, with periods of 9.97, 10.66, 11.01 and 11.83 yr. Analysis of the O-C residuals of the timing of solar cycle minima reveals that the solar cycle length is modulated by a secular period of about 190 yr and the Gleissberg period of about 86 yr. Based on a simple harmonic model with these periods, we predict that the solar cycle length will in average be longer during the 21st century. Cycle 24 may be about 12 yr long, while cycles 25 and 26 are estimated to be about 9 and 11 yr long. The following cycle is estimated to be 14 yr long. In all periods during the last 1000 yr, when the solar cycle length has increased due to the 190 yr cycle, a deep minimum of solar activity has occurred. This is expected to re-occur in the first part of this century. The coherent modulation of the solar cycle length over a period of 400 yr is a strong argument for an external tidal forcing by the planets Venus, Earth, Jupiter and Saturn, as expressed in a spin-orbit coupling model.

A detailed census of variable stars in the globular cluster NGC 6333 (M9) from CCD differential photometry★

We report CCD $V$ and $I$ time-series photometry of the globular cluster NGC 6333 (M9). The technique of difference image analysis has been used, which enables photometric precision better than 0.05 mag for stars brighter than $V \sim 19.0$ mag, even in the crowded central regions of the cluster. The high photometric precision has resulted in the discovery of two new RRc stars, three eclipsing binaries, seven long-term variables and one field RRab star behind the cluster. A detailed identification chart and equatorial coordinates are given for all the variable stars in the field of our images of the cluster. Our data together with literature $V$-data obtained in 1994 and 1995 allowed us to refine considerably the periods for all RR Lyrae stars. The nature of the new variables is discussed. We argue that variable V12 is a cluster member and an Anomalous Cepheid. Secular period variations, double mode pulsations and/or the Blazhko-like modulations in some RRc variables are addressed. Through the light curve Fourier decomposition of 12 RR Lyrae stars we have calculated a mean metallicity of [Fe/H]$_{\rm ZW}$=$-1.70 \pm 0.01{\rm(statistical)} \pm 0.14{\rm(systematic)}$ or [Fe/H]$_{UVES}=-1.67 \pm 0.01{\rm(statistical)} \pm 0.19{\rm(systematic)}$.Absolute magnitudes, radii and masses are also estimated for the RR Lyrae stars. A detailed search for SX Phe stars in the Blue Straggler region was conducted but none were discovered. If SX Phe exist in the cluster then their amplitudes must be smaller than the detection limit of our photometry. The CMD has been corrected for heavy differential reddening using the detailed extinction map of the cluster of Alonso-Garc\'ia et al. (2012). This has allowed us to set the mean cluster distance from two independent estimates; from the RRab and RRc absolute magnitudes, we find $8.04\pm 0.19$ kpc and $7.88\pm0.30$ kpc respectively.

DEEP, LOW MASS RATIO OVERCONTACT BINARY SYSTEMS. XIII. DZ PISCIUM WITH INTRINSIC LIGHT VARIABILITY

New multi-color photometry for the eclipsing binary DZ Psc was performed in 2011 and 2012 using the 85 cm telescope at the Xinglong Station of the National Astronomical Observatories of China. Using the updated Wilson-Devinney (W-D) code, we deduced two sets of photometric solutions. The overcontact degree is f = 89.7(+/- 1.0)%, identifying DZ Psc as a deep, low mass ratio overcontact binary. The asymmetric light curves (i.e., LC2 in 2012) were modeled by a hot spot on the primary star. Based on all of the available light minimum times, we discovered that the orbital period of DZ Psc may be undergoing a secular period increase with a cyclic variation. The modulated period and semi-amplitude of this oscillation are P-mod = 11.89(+/- 0.19) yr and A = 0.0064(+/- 0.0006) days, which may be possibly attributed to either cyclic magnetic activity or light-time effect due to the third body. The long-term period increases at a rate of dP/dt = +7.43(+/- 0.17) x 10(-7) days yr(-1), which may be interpreted as conserved mass transfer from the less massive component to the more massive one. With mass transferring, DZ Psc will finally merge into a rapid-rotation single star when J(spin)/J(orb) > 1/3.

Orbital period variation study of the low-mass Algol eclipsing binary AI Draconis

Orbital period changes for the Algol-type eclipsing binary AI Dra were studied based on the analysis of its observed times of light minimum. The period variation showed cyclic changes in the interval from JD.≈2436000 to JD.≈2447500 and a secular period increase rate (dP/dt=2.44×10−7d/year) starting from JD.≈2448500 up to 2455262, in a time scale equals to 5×106year.

PHOTOMETRIC STUDIES OF THREE NEGLECTED SHORT-PERIOD CONTACT BINARIES GN BOOTIS, BL LEONIS, AND V1918 CYGNI

We present new photometry for three short-period contact binaries, GN Boo, BL Leo, and V1918 Cyg, observed from 2008 December to 2012 April using several small telescopes in China. Photometric models were deduced from new observations using the updated Wilson-Devinney Code. The results show that GN Boo and BL Leo are W-type contact binaries, while V1918 Cyg is an A-type one. The mass ratios and fill-out factors are q = 0.320(+/- 0.002) and f = 5.8(+/- 0.1)% for GN Boo, q = 0.476(+/- 0.005) and f = 21.3(+/- 1.1)% for BL Leo, q = 0.264(+/- 0.002), and f = 49.7(+/- 0.7)% for V1918 Cyg, respectively. From the (O - C) curves, it is discovered that the orbital periods of three binaries have varied in a complicated way, i.e., cyclic oscillation for GN Boo, long-term period decrease for BL Leo, and both for V1918 Cyg. The cyclic variations for GN Boo and V1918 Cyg may probably be attributed to the magnetic activity of the primary component or light-time effect due to the third body. Meanwhile, the secular period decreases for BL Leo and V1918 Cyg may result from mass transfer from the primary to the secondary, accompanying the mass and angular momentum loss from the central system. Finally, GN Boo, BL Leo, and V1918 Cyg will evolve into deep contact binaries. Additionally, a statistical study of 37 contact binaries with decreasing periods is given. We obtained the relations of q - f and q - d ln P/dt, and preliminarily determined the mass loss rate of d ln M/dt from the binary system.