Phase Dispersion Minimization Research Articles

Rotation Periods of Nine ROSAT Selected Solar-Type Stars

We monitored 16 X-ray selected young solar-type stars for light variation and found appreciable periodic light variability with amplitudes of a few hundredths of a magnitude in nine of the objects. Using the method of Phase Dispersion Minimization (PDM) and Fourier analysis (software PERIOD04), the rotation periods of these stars were determined from the photometric data. The rotation periods of all nine stars are shorter than about 3 days. It is suggested that, as with the Pleiades cluster, small amplitude light variations are quite common among young solar-type stars with rotation periods around 3 days or less. This gives further evidence for the spin up of solar-type stars predicted by models of angular momentum evolution of pre-main sequence stars.

Photometric study of the short-period RS Canum Venaticorum binary RT Andromedae

Context. Long-term photometric observations of cool stars can reveal the evolution and activity cycles of the stellar active region. Furthermore, studying the stellar activity provides opportunities for understanding of stellar dynamo and valuable constraints for stellar dynamo theory. Aims. We analyze our observational data and discuss light-curve variability due to starspots on both a short and long time scale, especially the short-term variation. At the same time, we accumulate some results from the literature to discuss active-region evolution and activity cycles. Methods. By analyzing the light curves using the Wilson-Devinney program, the photometric solution of the system is obtained and the starspot parameters are also derived. Using the phase-dispersion minimization method, we infer the activity cycle of RT And. Results. The case of two spots being on the primary is most successful in reproducing the light curve distortion of RT And in 2004. Although the light curves in 1999 and 2005 do not have sufficient phase coverage, we still could use the spot model to explain their light-curve variation successfully based on the photometric solution in 2004. Comparing the light curves of 1999, 2004, and 2005, the light curve distortion changes on both short and long time scales, especially the significant variation around the secondary minimum on a time scale of two months. Analysis of the longitude of spots within the belt around 270 degrees suggests that the activity cycle of RT And may be 6.69 +/- 0.80 years.

Photometric monitoring of the ROSAT selected late type stars

We monitored the light variations of 16 solar-type stars recently discovered in the X-ray wave-length range during the ROSAT all-sky survey. We find that 9 out of 16 stars showed appreciable light variability with amplitudes of a few hundredths of a magnitude. They are all proved to be in periodic variations. Using the methods of the phase dispersion minimization (PDM) and Fourier Analysis (PERIOD04), we derive the photometric periods for these stars. The rotational periods are found range from 0.471 to 17.31 days and the period of stars most (of 7 stars) being shorter than 3 days. Apart from binaries system, the results give further evidence for the spin up of solar-type stars as predicted by models of angular momentum evolution of pre-main sequence stars.

Photometric Monitoring of ROSAT-Selected Weak Line T Tauri Stars

We monitored the light curves of 22 weak-line T Tauri stars (WTTSs) discovered among the X-ray sources in the field of the Taurus-Auriga clou d. For 12 of the 22 WTTSs photometric periodic variability is confirmed and their rot ational periods are determined using Phase Dispersion Minimization (PDM) and Fourier analysis. Most of them are found to have periods shorter than one day. This gives further evidence for the spin up of solar-type stars predicted by the models of angular momentum evolution of pre-main sequence stars.

Periodic radial velocity variations in RU Lupi

Context. RU Lup is a Classical T Tauri star with unusually strong emission lines, which has been interpreted as manifestations of accretion. Recently, evidence has accumulated that this star might have a variable radial velocity. Aims. We intended to investigate in more detail the possible variability in radial velocity using a set of 68 high-resolution spectra taken at the VLT (UVES), the AAT (UCLES) and the CTIO (echelle). Methods. Using standard cross-correlation techniques, we determined the radial velocity of RU Lup. We analysed these results with Phasedispersion minimization and the Lomb-Scargle periodogram and searched for possible periodicities in the obtained radial velocities. We also analysed changes in the absorption line shapes and the photometric variability of RU Lup. Results. Our analysis indicated that RU Lup exhibits variations in radial velocity with a periodicity of 3.71 days and an amplitude of 2.17 km/s. These variations can be explained by the presence of large spots, or groups of spots, on the surface of RU Lup. We also considered a low-mass companion and stellar pulsations as alternative sources for these variations but found these to be unlikely.

Photometric Variability of Be/X-Ray Pulsar Binaries in the Small Magellanic Cloud

We have studied the photometric variability of 10 SMC Be/X-ray pulsars using MACHO and OGLE-II data. For some of these systems we have found periodic behavior, including orbital outbursts and/or nonradial pulsations of the Be star. For others we were unable to identify any clear photometric periodicity, although their long-term light curves show significant structure. We present periodograms, phase dispersion minimization variances, and folded light curves for the systems that exhibit periodic photometric variability.

New near-aphelion light curves of Comet 2P/Encke

We present new, near-aphelion, time series of photometry of Comet 2P/Encke in Cousins-R band. With these light curves we find that the dominant, synodic rotational periodicity is either P 0 = 11.079 ± 0.009 h or 2 P 0 = 22.158 ± 0.012 h . This is in contrast to data from the 1980s published by others that are consistent with 15.08- and 22.6-h periods. Those periods do not satisfy our phased light curves, and also the 1980s data are not easily reconciled with our periods. This could be due to P/Encke having non-principal axis rotation or due to a drift in the rotation period caused by outgassing torques. We observed the comet at five epochs: July, August, September, and October 2001, and September 2002, and the comet was at times intrinsically brighter than expected for a bare nucleus, due to an apparent contribution from an unresolved coma. Three-quarters of the data were obtained in the second and fifth epochs, and we analyzed these two time series using both the phase-dispersion minimization and “WindowCLEAN” techniques. At both epochs and with both techniques strong periodicities were found near frequencies f 0 = 2.16 d −1 and f 1 = 4.35 d −1 . By then using visual inspection of the phased light curves to corroborate these frequencies, and by using the data from the other three epochs to properly align light curve features, we were able to derive P 0 and 2 P 0 as the only solutions that satisfy all our observations. The periodicity due to f 1 is clearly seen in our data, but we cannot tell from our data alone whether it is a manifestation of the nucleus's shape, non-principal axis rotation, or both.

Variable Star Identification in the BATC Field of M67

We present the result of photometric variability investigation for stars in the field of M67. The old open cluster M67, one of the most studied open clusters, shows the sign of significant main-sequence binary population in its color-magnitude diagrams. Identification of eclipsing binaries and follow-up studies will enable us to study the nature of binary population in most direct manner. We used approximately 350 images from the BATC (Beijing-Arizona-Taipei-Connecticut) data archive to examine variability within one square degree field centered on M67. A total of 18 stars were classified to be real variables. Our new discoveries include seven eclipsing binary systems of which two are likely to be W UMa systems. All of these variables were found using the phase dispersion minimization (PDM) method developed by Shin and Byun[11].

Periodicities of Radio Flares in RS CVn and Algol Binaries

Periodicities of radio flaring activity from the Algol systems β Per and δ Lib and the RS CVn systems V711 Tau and UX Ari were determined from a continuous 5-year survey. The radio continuum fluxes at 2.3 GHz and 8.3 GHz were monitored with the NRAO—Green Bank Interferometer for 2096 days from 1995 January to 2000 October. The maximum detected flare strengths at 8.3 GHz were 1.17 Jy for β Per, 0.034 Jy for δ Lib, 1.44 Jy for V711 Tau, and 0.82 Jy for UX Ari. Power Spectrum Analysis and Phase Dispersion Minimization were used to determine the periodicity of flaring activity in each binary. The strongest periodicities found were 48.9 days for β Per, 120.7 days for V711 Tau, and 141.4 days for UX Ari. No significant periodicities were found for δ Lib. The continuous survey has demonstrated that there are active and quiescent flaring cycles in V711 Tau and β Per.

Period-K magnitude relations of variable stars in the LMC

AbstractWe cross-correlated the OGLE-II database with the SIRIUS JHK survey data in the Large Magellanic Cloud (LMC). After eliminating obvious spurious variables, we determined the pulsation periods for 9 681 stars by applying the Phase Dispersion Minimization (PDM) technique to the OGLE-II data. Based on these data, we studied the period-K magnitude (PK) relations of variable stars in the LMC and found a new sequence. Comparison between the theoretical pulsation model (Wood & Sebo 1996) and observational data suggests that the variable stars on the new sequence are Mira variables pulsating in the first overtone mode.

Searching for Variability in the Globular Cluster Messier 4

Time-series data taken with the Hubble Space Telescope of a field six core radii (~5') from the center of the globular cluster Messier 4, and covering a period of about 10 weeks in early 2001, have been analyzed in search of variable objects. Various criteria were employed to select candidate variable stars. Period searches were performed on the selected candidates using phase dispersion minimization (PDM). The reliability of the PDM search results was tested using synthetic light curves of eclipsing binary stars and sinusoidal light curves of different periods. Results from this analysis showed that there are probably no eclipsing binary stars or periodic variables in our field with periods on the order of a few hours to a few days, down to limiting magnitudes of V ~ 25 and I ~ 24, which is consistent with the absence of contact binaries such as W Ursae Majoris systems. However, one candidate variable star does show an increase in brightness of ~0.1 mag in both bandpasses, which seems to last for a few days. Possible explanations concerning the nature of this object include a binary system with a white dwarf primary and a low-mass main-sequence secondary or a BY Draconis variable star. We are able to set an upper limit to the observed fraction of photometric variability in this data set of 0.05%.

Long‐Term X‐Ray Variability of Circinus X‐1

We present an analysis of long term X-ray monitoring observations of Circinus X-1 (Cir X-1) made with four different instruments: Vela 5B, Ariel V ASM, Ginga ASM, and RXTE ASM, over the course of more than 30 years. We use Lomb-Scargle periodograms to search for the ~16.5 day orbital period of Cir X-1 in each of these data sets and from this derive a new orbital ephemeris based solely on X-ray measurements, which we compare to the previous ephemerides obtained from radio observations. We also use the Phase Dispersion Minimization (PDM) technique, as well as FFT analysis, to verify the periods obtained from periodograms. we obtain dynamic periodograms (both Lomb-Scargle and PDM) of Cir X-1 during the RXTE era, showing the period evolution of Cir X-1, and also displaying some unexplained discrete jumps in the location of the peak power.

Statistical Analysis of 5 Year Continuous Radio Flare Data from β Persei, V711 Tauri, δ Librae, and UX Arietis

We report on the longest-running continuous radio flare survey of two Algol-type systems (β Per and δ Lib) and two RS CVn systems (V711 Tau and UX Ari). All four systems have late-type components, and all were known to display radio flaring activity. The primary aim of the campaign was to determine the timescales for flaring activity in these systems. The radio continuum flux at 2.3 and 8.3 GHz was monitored with the NRAO-Green Bank Interferometer from 1995 January to 2000 October. The survey spanned 2096 days with interruptions during maintenance runs and temporary closings of the interferometer. Many strong flares were detected with continuum fluxes at 8.3 GHz as high as 1.17 Jy in β Per, 1.44 Jy in V711 Tau, and 0.82 Jy in UX Ari. Only two flares were detected from δ Lib during 1123 days of monitoring, and the continuum flux reached a maximum of only 0.034 Jy at 8.3 GHz. The independent techniques of Power Spectrum Analysis and Phase Dispersion Minimization were used to determine the periodicity of flaring activity in each binary. The strongest periodicities found were 48.9 ± 1.7 days for β Per, 120.7 ± 3.4 days for V711 Tau, and 141.4 ± 4.5 days for UX Ari, with other significant periodicities of 80.8 ± 2.5 days for V711 Tau and 52.6 ± 0.7 days for UX Ari. In the case of δ Lib, the strongest periodicities were related to the duration of the two monitoring cycles within the data set and are not real. The continuous survey has demonstrated that there are active and quiescent flaring cycles in V711 Tau and β Per. During both of these cycles, β Per had more flares than V711 Tau, but its strongest flares were typically weaker than those of V711 Tau.

A CCD Photometric Survey of Variable Stars in the Field of NGC 188

The results of a recent CCD photometry survey of variables in a 1° field covering the old open cluster NGC 188 are presented. A total of 16 short-period variables were identified during five nights, among which eight are new variables in the program field. By adopting the method of phase-dispersion minimization, the periods for seven of the eight new variables are determined. The main properties, the classifications, as well as the memberships are discussed for all of these variable stars, based on the behavior of light curves, the locations in the color-magnitude diagram, and the results of proper motions. Among the eight new objects, six are W UMa binaries, in which one definitely is and two probably are members of the cluster. A detached or semidetached eclipsing binary with an orbital period longer than 1 day is found, which is a likely cluster star. In addition, a field star with a peculiar light curve is detected, which can be classified as a RRd–type variable. Moreover, revised basic data for the eight old variables are given according to our observations. V8 can be classified as an RS CVn–type star with light variations larger than 0.2 mag.

Period analysis for simultaneous multichannel photometric observations

The method of three stage weighted period analysis is generalized for simultaneous multichannel ob- servations. The new method is based on the phase disper- sion minimization over all channels simultaneously. The three stages in the full algorithm are phase dispersion minimization method (PDM), linear modeling (LM) and nonlinear modeling (NLM). Simple computational tests of the multichannel period analysis (MPA) are presented. We show that the method has advantages if compared with methods where single channels are analysed sepa- rately. We derive a general formula for spurious periods and demonstrate that the interpretation of peaks in the PDM spectra can be more complicated than in classical power spectra.

The Correct Probability Distribution for the Phase Dispersion Minimization Periodogram

The phase dispersion minimization (PDM) statistic is a popular method for searching for nonsinusoidal pulsations. The method involves comparison of the PDM value with the Fisher-Snedecor F distribution to assess the significance of pulsations. Later, it was demonstrated that the PDM statistic does not follow the F distribution and that the sensitivity of the method in its original form, based on the F distribution, is poor. In the present paper we demonstrate that the PDM statistic follows a beta distribution, which we designate PDM*. We find that the significance of a given detected pulsation according to the relevant beta distribution is higher than the corresponding significance obtained using the F distribution. In addition, we demonstrate that all methods relying on phase binning and variance estimates related to χ2 are equivalent for a given sampling, binning, and weighting pattern. We conclude by observing that with the invention of the high-performance Fourier series method, based on orthogonal projections, the original motivation for the use of phase binning for nonsinusoidal signals has weakened considerably.

Systematic Radio-Observations of UX Arietis: Analysis of Its Variability

UX Arietis is an active binary system with an orbital period of 6.44 days. The presence of long lasting large spots on the surface of the more active star has been deduced from optical observations (Vogt & Hatzes 1991).The observations presented here have been performed from December 1992 until October 1994 using the Effelsberg 100 m telescope. The instrument was available for this program in the gaps between previously scheduled observations. For this reason our observations span a frequency interval between 1.4 GHz (21 cm) and 43 GHz (7 mm), depending on the scheduled receiver at each observing time. These data, which are an extension of those published by Neidhöfer et al. (1993), are shown in Fig. 1, plotted in terms of the known orbital period (6.44 days). The search for different periodicities (by using the Phase Dispersion Minimization method) has shown the existence of two main other periods: at 156 days and at 24 days (Massi et al., in preparation).

On the validity of Davies' test for periodicity

Davies' test (1990, MNRAS, 244) for periodicity, which is based on the phase dispersion minimization method, is shown to be of limited application. In his derivation of the null distribution of the test statistic (i.e. the distribution under the null hypothesis of no periodicity), Davies assumes that the period to be tested is known a priori. Consequently, although the test can be used to test periods, that are identified by conducting a period search of the data. In the latter case, Davies uses adjustment based on Bonferroni's Inequality to compensate for the fact that multiple trial periods have been examined. Until a better solution to this difficult problem has been found, the use of the non-parametric randomization test described by Nemec & Nemec (1985, Astron. J., 90) is recommended

Rotational modulation in IUE spectra of cool dwarf chromospheres. I - Data analysis and period search techniques

Time-sequenced IUE spectra of a number of a bright F-K dwarfs have been used to investigate rotational modulation in several important chromospheric and transition emission lines. Stellingwerf's phase dispersion minimization (PDM) technique forms the basis of this time-series analysis of these sparsely sampled, irregularly spaced observational sequences, which consist of no more than 13 spectra in any one season. In such highly sample-limited time series, the resultant PDM spectrum is greatly complicated by overlapping alias orders which invariably produce strong interference effects, but the deliberately irregular sampling has proven of value in the development of techniques to identify the intrinsic stellar flux modulation period. Two stars are selected to illustrate these new techniques in detail.

Periodic variations in the activity of Comet P/Halley during the 1985/1986 apparition

A search for periodic variation in the production of gas and dust by Comet Halley has been performed using narrowband photometric measurements from four sites - Lowell Observatory, Mauna Kea Observatory, Perth Observatory, and Cerro Tololo Inter-American Observatory. The method of phase dispersion minimization was applied to observations made during 164 observing nights between September 1985 and June 1986. A clear-cut variation, with a period near 7.4 days, was present throughout the postperihelion window. Less conclusive evidence of a similar period has been found in the pre-perihelion data. No indication of a shorter period or of strong sporadic activity exists in the data. The observations require that Halley's nucleus returns to essentially the same orientation with respect to the sun approximately every 7.4 days except for longer-timescale seasonal evolution. This fact precludes certain proposed models of nuclear motion.