Cyclic Period Changes Research Articles

Cyclical Period Changes in Cataclysmic Variables: A Statistical Study

We report the results of a statistical study of cyclical period changes in cataclysmic variables (CVs). Assuming the third-body hypothesis as the cause of period changes, we estimate the third-body mass, m 3, and its separation from the binary, a 3, for 21 CVs showing cyclical period changes from well-sampled observed-minus-calculated diagrams covering more than a decade of observations. The inferred a 3 values are independent of the binary orbital period, P orb, whereas the m 3 values increase with P orb by 1 order of magnitude from the shortest period (oldest) to the longest period (youngest) systems, implying significant mass loss from the third body with time. A model for the time evolution of the triple system is not able to simultaneously explain the observed behavior of the m 3(P orb) and a 3(P orb) distributions because the combined mass loss from the binary and the third body demands an increase in orbital separation by factors ∼140 as the binary evolves toward shorter P orb's, in clear disagreement with the observed distribution. We conclude that the third-body hypothesis is statistically inconsistent and cannot be used to explain cyclical period changes observed in CVs. On the other hand, the diagram of the amplitude of the period change versus the CV donor-star mass is consistent both with the alternative hypothesis that the observed cyclical period changes are a consequence of magnetic activity in the solar-type donor star, and with the standard evolutionary scenario for CVs.

Control-oriented thermal model and load identification for circulating cooling water system in precision process applications

With the increasing precision in machining and measurement, there is a growing demand for improved temperature stability in cooling water systems used in industrial processes. Accurate thermal models and load states are essential for developing efficient controllers to enhance temperature performance. This paper focuses on the development of thermal models for various components of circulating water systems in precision water-cooling processes. It presents a control-oriented thermal model framework that segregates the water circulation cycles and defines system inputs and processes. A novel identification algorithm is proposed to address thermal inertia and cyclic nonlinearity by extracting the cyclic period and cycle change rate. The algorithm can simultaneously estimate the state–space model and unmeasurable load disturbances. A validation experimental setup was constructed, and the results demonstrate that, for different flow scenarios, the estimated load and thermal model parameters align well, with correlations exceeding 0.85 and error ratios close to 10%. Additionally, the circulating water output temperature can be accurately predicted. The fitting degrees surpass 84% within five cycles, with correlations exceeding 0.97 and error standard deviations below 0.22 °C.

Detection of a cyclic period change in the contact binary TU UMi

This study aims at timing the eclipses of the binary star TU UMi. The times of minima are taken from the literature, from our observations in April 2004 and from TESS observations between 2019 and 2022. The orbital period analysis of the system indicates that there is a cyclic oscillation with an amplitude of 0.0081d and a period of 9.03 yr, accompanied by a continuous decrease at a rate of $dP/dt =-1.12 \times 10^{-7}\,\mathrm{d}\, \mathrm{yr}^{-1}$. We study the secular evolution of the orbital period of the system and the possibility of the existence of a third companion or the magnetic activity cycle of the primary component in the system.

Reanalysis of c-type RR Lyrae variable BE Dor, period modulations and possible mechanism

ABSTRACT We reanalysed the c-type RR Lyrae star BE Dor (MACHO 5.4644.8, OGLE-LMC-RRLYR-06002) that had been discovered to show cyclic period changes. The photometric data of several sky surveys (DASCH, MACHO, OGLE, ASAS-SN, and TESS) were used for analyses. The O − C diagram and pulsation period obtained from Fourier analysis show significant period modulations in BE Dor. However, different from the previous viewpoint, the changes are quasi-periodic and abrupt. Therefore, the light-traveltime effect caused by the companion motion cannot explain the changes. Noting a same subtype star KIC 9453114 with similar phenomena has a high macroturbulent velocity, and the degree of O − C changes seem to be positively correlated with these velocities, we consider that the mechanism leading to period modulation should be caused by the interaction between turbulent convection and magnetic field activity in the ionization zone, i.e. the viewpoint of Stothers. It may not explain the general Blazhko effect but should explain such period modulations in BE Dor and those other c-type RR Lyrae stars. We hope our discoveries and viewpoints can provide some information and inspiration for relevant research.

CSS J075415.6+191052 and NW Leo: Two Contact Binaries at Different Evolutionary Stages

Multi-color light curves of CSS J075415.6+191052 and NW Leo are presented and the photometric solutions suggest that CSS J075415.6+191052 is an A-subtype contact binary with low mass ratio (q = 0.178) while NW Leo has a high mass ratio (q = 0.707). For CSS J075415.6+191052, the RI light curves show weakening around the left shoulder of the secondary minimum, which indicates that there may be a dark spot on the secondary component. However, the light curves of BV bands are totally symmetric. It is unreasonable if the dark spot is caused by magnetic activity or mass transfer between the two components. Therefore, weakening of the light curves in this contact binary is caused by something else. A possible explanation is mass transferring from the primary component to the common convective envelope through the inner Lagrangian point, and this part of the mass, for some reason, weakens the RI bands of light from the secondary component. O − C analysis of NW Leo reveals a cyclic period change with a modulation period of 4.7 yr, which may be caused by the light travel time effect of a third body. The positions of CSS J075415.6+191052 and NW Leo in the P–J′orb diagram indicate that CSS J075415.6+191052 mainly abides by the angular momentum loss theory while NW Leo is dominated by the thermal relaxation oscillation theory.

First photometric investigation of two short-period eclipsing binaries ASAS J105115-6032.1 and GDS J1056047-604149

ASAS J105115-6032.1 (hereafter ASAS J1051) and GDS J1056047-604149 (hereafter GDS J1056) are two short-period contact binaries close to each other in the Antarctica sky area. By analyzing the light curves from AST3-1, the first photometric solutions are presented using the Wilson–Devinney (W–D) method. It is detected that both systems are W-type contact binaries with mass ratios of q = 3.2621(0.0083) and q = 4.843(0.014), respectively. Both of them have a moderate degree of contact factor of f = 46.9(1.2)% and f = 43.9(1.2)%. The asymmetries in the light curve of the intermediate-contact system GDS J1056 (strong O’Connell effect) are interpreted by a dark spot on the more massive component. For the first time, we carried out the O−C diagram analysis based on many photometric data. The results indicate an orbital period increase at a rate of dP/dt=+5.28×10−7d⋅yr−1 for ASAS J10511. As for GDS J1056, a period decrease of dP/dt=−5.41×10−7d⋅yr−1, superimposed with a cyclic period change with a semi-amplitude of 0.00744 d and a period of 11.97 yr, is discovered. The cyclic period change may be caused by the light travel-time effect via the presence of a tertiary companion with a lowest mass of M3 = 0.35(0.03)M⊙. The period increase in ASAS J1051 can be explained by the mass transfer from the less massive component to its companion. In contrast, the period decrease in GDS J1056 reveals an opposite direction of mass transfer. The facts suggest that these two intermediate-contact binaries will evolve into shallow- and deep-contact binary systems.

Orbital period changes in IO Cep, IM Cep and TX Ari: Path to masses of distant components

Three Algol-type binary systems (IO Cep, IM Cep and TX Ari) showing cyclic orbital period changes are studied. The combination of time of minimum data from the ground-based observations together with high precision photometric data from the TESS satellite enabled us to estimate the basic light curve elements of binary systems and mass functions for distant components around the systems. The relation of mass ratio to the system geometry in semi-detached binary stars allowed us to determine the mass ratio of the binary components without using spectra. By using the color and distance information from the GAIA EDR3 and light contributions of the components from the light curve analysis, the astrophysical parameters of the binary components as well as the minimum masses of the distant components are obtained with an uncertainty of ∼10–20 per cent indicating that the method can be a good guide for those studying with faint systems where spectra with sufficient resolution and S/N ratio are difficult to acquire.

Possible substellar companions in dwarf eclipsing binaries

We present the new results of our long-term observational project to detect the small variations in the orbital periods of low-mass and short-period eclipsing binaries. About 120 new precise mid-eclipse times were obtained for three relatively well-known dwarf eclipsing binaries: SDSS J143547.87+373338.5 (P = 0.126 d), NSVS 07826147 (0.162 d), and NSVS 14256825 (0.110 d). Observed-minus-calculated diagrams of these systems were analyzed using all accurate timings, and, where possible, new parameters of the light-time effect were calculated. For the first time, we derive (or improve upon previous findings with regard to) the short orbital periods of 13 and 10 years of possible third bodies for SDSS J143547.87+373338.5 and NSVS 07826147, respectively. In these binaries, our data show that period variations can be modeled simply on the basis of a single circumbinary object. For the first two objects, we calculated the minimum mass of the third components to be 17 MJup and 1.4 MJup respectively, which corresponds to the mass of a brown dwarf or a giant planet. For NSVS 14256825, the cyclical period changes caused by a single additional body cannot be confirmed by our recent eclipse time measurements. More complex behavior connected with two orbiting bodies, or yet unknown effects, should be taken into account.

A cautionary tale of interpreting O−C diagrams: period instability in a classical RR Lyr Star Z CVn mimicking as a distant companion

We present a comprehensive study of Z CVn, an RR Lyrae star that shows long-term cyclic variations of its pulsation period. A possible explanation suggested from the shape of the O-C diagram is the light travel-time effect, which we thoroughly examine. We used original photometric and spectroscopic measurements and investigated the period evolution using available maximum times spanning more than one century. If the binary hypothesis is valid, Z CVn orbits around a black hole with minimal mass of $56.5$ $\mathfrak{M}_{\odot}$ on a very wide ($P_{\rm orbit}=78.3$ years) and eccentric orbit ($e=0.63$). We discuss the probability of a formation of a black hole-RR Lyrae pair and, although we found it possible, there is no observational evidence of the black hole in the direction to Z CVn. However, the main objection against the binary hypothesis is the comparison of the systemic radial velocity curve model and spectroscopic observations that clearly show that Z CVn cannot be bound in such a binary. Therefore, the variations of pulsation period are likely intrinsic to the star. This finding represents a discovery/confirmation of a new type of cyclic period changes in RR Lyrae stars. By the analysis of our photometric data, we found that the Blazhko modulation with period of 22.931 d is strongly dominant in amplitude. The strength of the phase modulation varies and is currently almost undetectable. We also estimated photometric physical parameters of Z CVn and investigated their variations during the Blazhko cycle using the Inverse Baade-Wesselink method.

A possible giant planet orbiting the cataclysmic variable LX Ser

Abstract LX Ser is a deeply eclipsing cataclysmic variable with an orbital period of 0.1584325 d. 62 new eclipse times were determined by our observations and the AAVSO International Data base. Combining all available eclipse times, we analyzed the O − C behavior of LX Ser. We found that the O − C diagram of LX Ser shows a sinusoidal oscillation with a period of 22.8 yr and an amplitude of 0.00035 d. Two mechanisms (i.e., the Applegate mechanism and the light-travel time effect) are applied to explain the cyclic modulation. We found that it is difficult to apply the Applegate mechanism to explain the cyclic oscillation in the orbital period. Therefore, the cyclic period change is most likely to be caused by the light-travel time effect due to the presence of a third body. The mass of the tertiary component was determined to be M3 ∼ 7.5 MJup. We supposed that the tertiary companion is plausibly a giant planet. The stability of the giant planet was checked, and we found that the multiple system is stable.

Nonradial and radial period changes in theδScuti star 4 CVn

The nature of period and amplitude changes in nonradial pulsators is presently unknown. It is therefore important to examine the correlations between these changes in stars with a large number of simultaneously excited pulsation modes. However, the small amplitudes require extensive high-precision photometry covering many years. We present 702 nights of high-precision photometry of the evolved Delta Scuti variable 4 CVn obtained from 2005 - 2012 with a dedicated telescope. We detected 64 frequencies, of which 38 can be identified as combinations and harmonics. The relative amplitudes of the combination frequencies are similar to those found in 44 Tau and show no evidence for resonant mode coupling. Significant period and amplitude changes are detected for the dominant modes. The known prograde and retrograde modes show period changes with opposite signs, while the radial mode exhibits only small, cyclical period changes. For each mode, the period changes are constant over the eight years and range from (1/P)dP/dt = -16 to +13 parts per million. On the other hand, the amplitude variations show no systematic behavior between different pulsation modes. The behavior of the prograde, axisymmetric, and retrograde modes indicates a constant decrease in the rotational splitting over the eight years.

Mass-transfer in close binary and their companions

Secular and/or cyclical orbital period variations of close binaries can be derived by analyzing the (O-C) diagram. The secular variations are usually explained as mass transfer between components, while the most plausible explanation of the cyclic period changes is the light-travel time effect (LTTE) through the presence of a third body. Mass transfer and additional companions in close binary systems are important for understanding the formation and evolution of the systems. Here, UV light curves of several close binaries based on the Lunar-based Ultraviolet Telescope (LUT) observations are presented and analyzed with the Wilson-Devinney (W-D) method. Then, based on those light-curve solutions and new analysis of the orbital period variations, the multiplicity, geometrical structure and evolution state of targets are discussed.

THE FIRST PHOTOMETRIC ANALYSIS OF THE OVERCONTACT BINARY MQ UMa WITH AN ADDITIONAL COMPONENT

The first V Rc Ic bands light curves of MQ UMa are presented and analyzed using the Wilson-Devinney (W-D) program. It is discovered that MQ UMa is an A-subtype contact binary with a high fill-out (f=82 %) and a low mass ratio (q = 0:195), which indicates that it is in the late evolutionary stage of latetype tidal-locked binary stars. The mass of the primary and secondary stars are estimated and the evolutionary status of the two components are placed in the H-R diagram. The W-D solutions also indicates that MQ UMa may be a triple system with an F5V type additional component. A sample of sixteen high fillout, low mass ratio overcontact binaries are collected and their possible evolution scenarios are discussed. Using the five times of light minimum recently observed together with those collected from literatures, the authors find that the observedcalculate (O-C) curve exhibits a cyclic period variation. The cyclic period change also reveals the presence of a tertiary component, which may play an important role in the formation and evolution of this binary system by drawing angular momentum from the central system.

PHOTOMETRIC ANALYSIS OF THE OVERCONTACT BINARY CW CAS

New CCD photometric observations of overcontact binary CWCas were carried out in 2004 and 2011. In particular, the light curve obtained in 2004 shows a remarkable O'Connell effect. Compared with light curves in different observing seasons, variations were found. These variations can be explained by dark spot activities on the surface of at least one component. Using the Wilson-Devinney code with a spot model, we find that the photometric solutions confirm CWCas is a shallow W-subtype overcontact binary with a spotted massive component. Our new determined times of minimum light together with the others published in the literature were analyzed to find a change of orbital period. From the O - C curves, the period of the system shows a cyclic period change (P-3 = 69.9 yr, A(3) = 0.03196 days) superposed on the linear increase. The cyclic variation, if explained as the light-travel time effect, reveals the presence of a tertiary companion.

Cyclic period changes and the light-time effect in eclipsing binaries: A low-mass companion around the system VV Ursae Majoris

In this article, a period analysis of the late-type eclipsing binary VV UMa is presented. This work is based on the periodic variation of eclipse timings of the VV UMa binary. We determined the orbital properties and mass of a third orbiting body in the system by analyzing the light-travel time effect. The O−C diagram constructed for all available minima times of VV UMa exhibits a cyclic character superimposed on a linear variation. This variation includes three maxima and two minima within approximately 28,240 orbital periods of the system, which can be explained as the light-travel time effect (LITE) because of an unseen third body in a triple system that causes variations of the eclipse arrival times. New parameter values of the light-time travel effect because of the third body were computed with a period of 23.22±0.17years in the system. The cyclic-variation analysis produces a value of 0.0139day as the semi-amplitude of the light-travel time effect and 0.35 as the orbital eccentricity of the third body. The mass of the third body that orbits the eclipsing binary stars is 0.787±0.02M⊙, and the semi-major axis of its orbit is 10.75AU.

A plausible third body in RS CVn-type binary: RT Coronae Borealis

Cyclic period changes, which are usually explained as being caused by the magnetic activity of one or both components or the light travel time effect of a third body, are a typical phenomenon in the RS CVn-type binary. Combining the newly determined eclipsing times with others compiled from literature, we analyzed the cyclic period change in the RS CVn-type binary RT CrB. The result shows that the orbital period of the binary shows a period of 3.47 yr with an amplitude of 0 d .0084. The cyclic oscillation can be attributed to the existence of a third body with a lower limit mass of 1.71(±0.19) M⊙. The third body is cycling the binary at a distance of no more than 2.30(±0.19) AU which would play an important role in the evolution of this system. No detected spectral lines of the third body may suggest that the third component may itself be a close binary of 0.86 M⊙ stars, or more likely a dark star such as a neutron star.

THE TRIPLE BINARY STAR EQ TAU WITH AN ACTIVE COMPONENT

New photometric data of EQ Tau observed in 2010 and 2013 are presented. Light curves obtained in 2000 and 2004 by Yuan & Qian and 2001 by Yang & Liu, together with our two newly determined sets of light curves, were analyzed using the Wilson-Devinney code. The five sets of light curves exhibit very obvious variations, implying that the light curves of EQ Tau show a strong O'Connell effect. We found that EQ Tau is an A-type shallow contact binary with a contact degree of f = 11.8%; variable dark spots on the primary component of EQ Tau were also observed. Using 10 new times of minimum light, together with those collected from the literature, the orbital period change of EQ Tau was analyzed. We found that its orbital period includes a secular decrease (dP/dt = -3.63 x 10(-8) days yr(-1)) and a cyclic oscillation (A(3) = 0.0058 days and P-3 = 22.7 yr). The secular increase of the period can be explained by mass transfer from the more massive component to the less massive one or/and angular momentum loss due to a magnetic stellar wind. The Applegate mechanism cannot explain the cyclic orbital period change. A probable transit-like event was observed in 2010. Therefore, the cyclic orbital period change of EQ Tau may be due to the light time effect of a third body.

Detection of a cool stellar companion to the [formula omitted] Scuti variable star BP Peg

New CCD photometric monitoring on the high-amplitude δ Scuti variable BP Peg was carried out on November 4, 2013 by using the 1.0-m reflecting telescope of Yunnan Observatories in China as well as on December 29, 2013 by using the 85-cm telescope at Xinglong Station of National Astronomical Observatory in China. BP Peg is a new high-amplitude δ Scuti variable with a period of 0.10954357day. We have collected all the times of light maximum from the literature together with our data, and the pulsation period changes are analyzed through Observed–Calculated (O–C) method. With the available data, we discover that the pulsating period of BP Peg shows a cyclic oscillation with a period of 24.5years and an amplitude of 0.0060days. If the cyclic period changes are caused by light-time effect in a binary system, the reckoned mass of the hidden companion could be 0.20M⊙ and possibly, it is an M-type star.

The oEA stars QY Aql, BW Del, TZ Dra, BO Her and RR Lep: photometric analysis, frequency search and evolutionary status

New and complete multi-band light curves of the oEA stars QY Aql, BW Del, TZ Dra, BO Her and RR Lep were obtained and analysed with the Wilson-Devinney code. The light curves residuals were further analysed with the Fourier method in order to derive the pulsation characteristics of the oscillating components. All the reliable observed times of minimum light were used to examine orbital period irregularities. The orbital period analyses revealed secular changes for QY Aql and BW Del, while the Light-Time Effect seems to be the best explanation for the cyclic period changes in TZ Dra and BO Her. RR Lep has a rather steady orbital period. Light curve solutions provided the means to calculate the absolute parameters of the components of the systems, which subsequently were used to make an estimate of their present evolutionary status.

δ Scuti light variations as a test for choosing the mechanism of cyclic orbital period changes in Algols

The temporal behaviour of the orbital period and pulsation period of the δ Scuti type primary component is studied in the eclipsing binary AB Cas, where the secondary fills its Roche lobe. Orbital period changes observed over 80 years are a superposition of secular variations due to mass exchange between the components and cyclic variations with a quasi-period of about 46 years. At the same time, the period of δ Scuti light variations is found to remain constant to a high accuracy. This result rules out the explanation of cyclic orbital period changes in AB Cas by the presence of a third body and forces us to seek other interpretations. In view of our results, the only mechanism that currently seems to be acceptable for the observed cyclic orbital period changes in AB Cas and, possibly, many other Algols is the mechanism proposed by Applegate in 1992, which explains these modulations by the variations in the quadrupole moment of the component with a convective shell caused by its cyclic magnetic activity.