“…If this is not properly considered, the O − C diagram may show intriguing shapes, which could be misinterpreted as irregular period variations. This has already been stressed by Arellano Ferro et al () for the case of the RRLs in M5. In the present case of NGC 6171, we do not see any irregular variations but only constant periods (linear) or a few parabolic secular variations (quadratic).…”
Section: Times Of Maximum Brightness and The O − C Diagramssupporting
confidence: 61%
“…The observed minus the calculated ( O − C ) residuals of a given feature in the light curve, as an indication of miscalculations or authentic variations of the pulsation or orbital period, using a single given phase of the light curve as a reference, is a standard approach that has been in use for many decades, for example, in Cepheids, RRLs, and contact binary stars (e.g., Arellano Ferro et al ; Arellano Ferro & Rosenzweig ; Coutts & Sawyer Hogg ). Then, it is convenient to select a feature that facilitates the accurate determination of the phase.…”
Section: The O − C Approach To the Secular Period Changesmentioning
confidence: 99%
“…From the above equations, it is straightforward to demonstrate that the period change rate at N = 0 and P = P 0 is given by and that if the O − C distribution is linear, that is, A 2 = 0, then the correct epoch and period are given by E 0 + A 0 and P 0 + A 1 , respectively. A detailed derivation of the above equations can be found in Arellano Ferro et al ().…”
Section: The O − C Approach To the Secular Period Changesmentioning
confidence: 99%
“…However, measuring secular period changes from observations is difficult as accurate observations over a very long time base are required. Only a few clusters have been studied from data covering more than 60 years, for example, M3 (Corwin & Carney ; Jurcsik et al ), M5 (Arellano Ferro et al ; Szeidl et al ), NGC 6934 (Stagg & Wehlau ), M14 (Wehlau & Froelich ), M15 (Silbermann & Smith ), NGC 7006 (Wehlau et al ), and ω Cen (Jurcsik et al ). Theory predicts that blueward or redward evolution near the zero‐age HB (ZAHB) is slow and produces very small period change rates, except toward the end of the HB evolution, when the values of can be between +0.1 and +0.15 day Myr −1 (Lee ).…”
Based on photometric data obtained between 1935 and 2017, O − C diagrams were built for 22 RR Lyrae stars in the globular cluster NGC 6171, leading to the discovery of secular period changes in four variables for which we have calculated period change rates . In contrast, we find that 82% of the sample stars have stable periods over the last 82 years. For the stable-period stars, the whole database has been employed to refine their periods. Among the period-changing stars, three (V10, V12, and V16) have decreasing periods that are larger than expected from stellar evolution. Despite these individual cases of significant period change rate, the global average of the measured period changes in the cluster is basically zero, in consonance with theoretical predictions for clusters with redder horizontal branches. The hitherto unpublished observations, now brought into public domain, are employed to calculate a set of times of maximum light, which is used in the present analysis.
“…If this is not properly considered, the O − C diagram may show intriguing shapes, which could be misinterpreted as irregular period variations. This has already been stressed by Arellano Ferro et al () for the case of the RRLs in M5. In the present case of NGC 6171, we do not see any irregular variations but only constant periods (linear) or a few parabolic secular variations (quadratic).…”
Section: Times Of Maximum Brightness and The O − C Diagramssupporting
confidence: 61%
“…The observed minus the calculated ( O − C ) residuals of a given feature in the light curve, as an indication of miscalculations or authentic variations of the pulsation or orbital period, using a single given phase of the light curve as a reference, is a standard approach that has been in use for many decades, for example, in Cepheids, RRLs, and contact binary stars (e.g., Arellano Ferro et al ; Arellano Ferro & Rosenzweig ; Coutts & Sawyer Hogg ). Then, it is convenient to select a feature that facilitates the accurate determination of the phase.…”
Section: The O − C Approach To the Secular Period Changesmentioning
confidence: 99%
“…From the above equations, it is straightforward to demonstrate that the period change rate at N = 0 and P = P 0 is given by and that if the O − C distribution is linear, that is, A 2 = 0, then the correct epoch and period are given by E 0 + A 0 and P 0 + A 1 , respectively. A detailed derivation of the above equations can be found in Arellano Ferro et al ().…”
Section: The O − C Approach To the Secular Period Changesmentioning
confidence: 99%
“…However, measuring secular period changes from observations is difficult as accurate observations over a very long time base are required. Only a few clusters have been studied from data covering more than 60 years, for example, M3 (Corwin & Carney ; Jurcsik et al ), M5 (Arellano Ferro et al ; Szeidl et al ), NGC 6934 (Stagg & Wehlau ), M14 (Wehlau & Froelich ), M15 (Silbermann & Smith ), NGC 7006 (Wehlau et al ), and ω Cen (Jurcsik et al ). Theory predicts that blueward or redward evolution near the zero‐age HB (ZAHB) is slow and produces very small period change rates, except toward the end of the HB evolution, when the values of can be between +0.1 and +0.15 day Myr −1 (Lee ).…”
Based on photometric data obtained between 1935 and 2017, O − C diagrams were built for 22 RR Lyrae stars in the globular cluster NGC 6171, leading to the discovery of secular period changes in four variables for which we have calculated period change rates . In contrast, we find that 82% of the sample stars have stable periods over the last 82 years. For the stable-period stars, the whole database has been employed to refine their periods. Among the period-changing stars, three (V10, V12, and V16) have decreasing periods that are larger than expected from stellar evolution. Despite these individual cases of significant period change rate, the global average of the measured period changes in the cluster is basically zero, in consonance with theoretical predictions for clusters with redder horizontal branches. The hitherto unpublished observations, now brought into public domain, are employed to calculate a set of times of maximum light, which is used in the present analysis.
“…Also Firmanyuk (1982) supposed that cyclic period variations could rise from changes of the internal structure of a star, but without any further details. However, Arellano Ferro et al (2016) found that, at least for some stars in M5, the irregular O−C variations could be caused by improper counting of the cycles and that it must not be a real feature of a star.…”
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 M ⊙ on a very wide (P 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.
We present a comprehensive analysis of the variable stars projected on the field of the Galactic bulge globular cluster NGC 6522, offering valuable insights into their characteristics. Using proper motions from Gaia-DR3, we aim to distinguish between field stars and true cluster members. For an accurate color-magnitude diagram of the member stars, we produced a differential reddening map. We detect and discuss the peculiarities of variable stars of the types RR Lyrae, type II Cepheids, Long Period Variables (LPV) and eclipsing binaries, whose light curves are available through the OGLE III and IV databases. Notably, we explore the variable V24, which shows a prominent phase modulation resulting from period changes in a time scale of 1100 days. The variable stars among the cluster members serve as indicators of the cluster metallicity and distance; these determinations are based on their light curves. With the Fourier light curve decomposition of three RRc stars, we have derived the following cluster parameters: the metallicity in the spectroscopic scale $\text{[Fe/H]}_{\mathrm{UVES}}=-1.16 \pm 0.09$
[Fe/H]
UVES
=
−
1.16
±
0.09
; and the mean distance $D=8.77 \pm 0.16$
D
=
8.77
±
0.16
kpc.
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