Lomb-Scargle Method Research Articles

Exploring the nature of an ultraluminous X-ray source in NGC 628

Aims. In this work, we study the X-ray spectral and temporal properties of an ultraluminous X-ray source (ULX) in NGC 628 by using multi-epoch archival X-ray data. The physical parameters were estimated in each epoch in order to constrain the nature of the compact object in the system. Also, the optical counterpart candidates of the ULX were examined using the archival Hubble Space Telescope (HST)/Wide Field Camera 3 (WFC3) data. Methods.XMM-Newton, Chandra, and Swift data were used to create the long-term light curve (which covers a period of 22 years) and perform the spectral analysis. Lomb-Scargle periodograms of the source were constructed to examine the short-term variability in each epoch. In order to search for an optical counterpart in the HST/WFC3 images, a relative astrometric correction was initially applied to the Chandra and HST/WFC3 images. Results. The X-ray flux of the source changes by a factor of ∼200 throughout the observations. The previously detected quasi-periodic signal (in the range of 0.1−0.4 mHz) was confirmed by using the Lomb-Scargle method. After astrometric correction, two optical counterpart candidates were detected for the source. The obtained spectral energy distributions in the optical band for both candidates indicate that the optical emission is dominated by the irradiation of the accretion disc. Considering the best-fit model parameters of the multi-colour disc black-body model, we derived the mass of the black hole in the system as being in the range of (5−28) M⊙. Nonetheless, the long-term variability and the spectral transitions in the hardness–luminosity diagram make it difficult to rule out the neutron star scenario.

Search for Periodic Time Variations of the Solar B8 Neutrino Flux between 1996 and 2018 in Super-Kamiokande

We report a search for time variations of the solar B8 neutrino flux using 5804 live days of Super-Kamiokande data collected between May 31, 1996, and May 30, 2018. Super-Kamiokande measured the precise time of each solar neutrino interaction over 22 calendar years to search for solar neutrino flux modulations with unprecedented precision. Periodic modulations are searched for in a dataset comprising five-day interval solar neutrino flux measurements with a maximum likelihood method. We also applied the Lomb-Scargle method to this dataset to compare it with previous reports. The only significant modulation found is due to the elliptic orbit of the Earth around the Sun. The observed modulation is consistent with astronomical data: we measured an eccentricity of (1.53±0.35)%, and a perihelion shift of (−1.5±13.5) days. Published by the American Physical Society 2024

Trends of Key Greenhouse Gases as Measured in 2009–2022 at the FTIR Station of St. Petersburg State University

Key long-lived greenhouse gases (CO2, CH4, and N2O) are perhaps among the best-studied components of the Earth’s atmosphere today; however, attempts to predict or explain trends or even shorter-term variations of these trace gases are not always successful. Infrared spectroscopy is a recognized technique for the ground-based long-term monitoring of the gaseous composition of the atmosphere. The current paper is focused on the analysis of new data on CO2, CH4, and N2O total columns (TCs) retrieved from high resolution IR solar spectra acquired during 2009–2022 at the NDACC atmospheric monitoring station of St. Petersburg State University (STP station, 59.88°N, 29.83°E, 20 m asl.). The paper provides information on the FTIR system (Fourier-transform infrared) installed at the STP station, and an overview of techniques used for the CO2, CH4, and N2O retrievals. Trends of key greenhouse gases and their confidence levels were evaluated using an original approach which combines the Lomb–Scargle method with the cross-validation and bootstrapping techniques. As a result, the following fourteen-year (2009–2022) trends of TCs have been revealed: (0.56 ± 0.01) % yr−1 for CO2; (0.46 ± 0.02) % yr−1 for CH4; (0.28 ± 0.01) % yr−1 for N2O. A comparison with trends based on the EMAC numerical modeling data was carried out. The trends of greenhouse gases observed at the STP site are consistent with the results of the in situ monitoring performed at the same geographical location, and with the independent estimates of the global volume mixing ratio growth rates obtained by the GAW network and the NOAA Global Monitoring Laboratory. There is reasonable agreement between the CH4 and N2O TC trends for 2009–2019, which have been derived from FTIR measurements at three locations: the STP site, Izaña Observatory and the University of Toronto Atmospheric Observatory.

Stellar activity and differential rotation of HD 111395

Aims. Stellar activity cycles and rotation periods are important parameters for characterising the stellar dynamo, which operates in late-type main-sequence stars. However, the number of stars with well-known cycle and rotation periods is rather low, so new detections are still important. Methods. To find activity cycles and rotation periods, we utilised the TIGRE telescope to monitor stars for periodic variations in chromospheric activity indicators. We employed the widely used CaII H&K lines and the CaII infrared triplet lines as stellar activity indicators. To verify a periodic variation and to determine the corresponding period, we performed a frequency analysis via the generalised Lomb-Scargle method of the taken time series. Results. We studied CaII data of the G5V star HD 111395 and derive an activity cycle period of 949 ± 5 d (≈2.6 yr). This cycle is coincident with coronal measurements from the X-ray telescope eROSITA on board SRG. Furthermore, the TIGRE CaII time series show a long-term trend that indicates an additional long-term cycle. Using the few available literature S-index data points, we estimate a probable cycle length of 12–15 yr for this potential long-term cycle. Finally, we determined rotation periods from each observation season. We computed a mean rotation period of 16.76 ± 0.36 d averaged over all observation seasons and chromospheric indicators. However, we also find a strong variation in the mean seasonal rotation periods, which follows the derived cycle period; therefore, we interpret this behaviour as a sign of surface differential rotation.

Multi-band optical variability on diverse timescales of blazar 1E 1458.8+2249

Abstract This study presents an analysis of the optical variability of the blazar 1E 1458.8+2249 on diverse timescales using multi-band observations, including observations in the optical BVRI bands carried out with the T60 and T100 telescopes from 2020 to 2023 and ZTF gri data from 2018 to 2023. On seven nights, we searched for intraday variability using the power-enhanced F-test and the nested ANOVA test, but no significant variability was found. The long-term light curve shows a variability behaviour in the optical BVRI bands with amplitudes of $\sim$ 100% and in the gri bands with amplitudes of $\sim$ 120%, including short-term variability of up to $\sim$ 1.1 mag. Correlation analysis revealed a strong correlation between the optical multi-band emissions without any time lag. From 62 nightly spectral energy distributions, we obtained spectral indices between 0.826 and 1.360, with an average of $1.128\pm0.063$ . The relationships of both spectral indices and colour with respect to brightness indicate a mild BWB trend throughout the observation period, both intraday and long-term. We also performed a periodicity search using the weighted wavelet Z-transform and Lomb–Scargle methods. A recurrent optical emission pattern with a quasi-periodicity of $\sim$ 340 days is detected in the combined V- and R-band light curves. The observational results indicate that the blazar 1E 1458.8+2249 has a complex variability, while emphasising the need for future observations to unravel its underlying mechanisms.

Catching profound optical flares in blazars

ABSTRACT Flaring episodes in blazars represent one of the most violent processes observed in extra-galactic objects. Studies of such events shed light on the energetics of the physical processes occurring in the innermost regions of blazars, which cannot otherwise be resolved by any current instruments. In this work, we present some of the largest and most rapid flares captured in the optical band in the blazars 3C 279, OJ 49, S4 0954+658, TXS 1156+295, and PG 1553+113. The source flux was observed to increase by nearly ten times within a time-scale of a few weeks. We applied several methods of time series analysis and symmetry analysis. Moreover, we also performed searches for periodicity in the light curves of 3C 279, OJ 49 and PG 1553+113 using the Lomb–Scargle method and found plausible indications of quasi-periodic oscillations (QPOs). In particular, the 33- and 22-day periods found in 3C 279, i.e. a 3:2 ratio, are intriguing. These violent events might originate from magnetohydrodynamical instabilities near the base of the jets, triggered by processes modulated by the magnetic field of the accretion disc. We present a qualitative treatment as the possible explanation for the observed large amplitude flux changes in both the source-intrinsic and source-extrinsic scenarios.

Rieger-type cycles on the solar-like star KIC 2852336

Context. A Rieger-type periodicity of 150–180 days (six to seven times the solar rotation period) has been observed in the Sun’s magnetic activity and is probably connected with the internal dynamo layer. Observations of Rieger cycles in other solar-like stars may give us information about the dynamo action throughout stellar evolution. Aims. We aim to use the Sun as a star analogue to find Rieger cycles on other solar-like stars using Kepler data. Methods. We analyse the light curve of the Sun-like star KIC 2852336 (with a rotation period of 9.5 days) using wavelet and generalised Lomb-Scargle methods to find periodicities over rotation and Rieger timescales. Results. Besides the rotation period of 9.5 days, the power spectrum shows a pronounced peak at a period of 61 days (about six times the stellar rotation period) and a less pronounced peak at 40–44 days. These two periods may correspond to Rieger-type cycles and can be explained by the harmonics of magneto-Rossby waves in the stellar dynamo layer. The observed periods and theoretical properties of magneto-Rossby waves lead to the estimation of the dynamo magnetic field strength of 40 kG inside the star. Conclusions. Rieger-type cycles can be used to probe the dynamo magnetic field in solar-type stars at different phases of evolution. Comparing the rotation period and estimated dynamo field strength of the star KIC 2852336 with the corresponding solar values, we conclude that the ratio Ω/BD, where Ω is the angular velocity and BD is the dynamo magnetic field, is the same for the star and the Sun. Therefore, the ratio can be conserved during stellar evolution, which is consistent with earlier observations that younger stars are more active.

Large-amplitude periodic outbursts and long-period variables in the VVV VIRAC2-β data base

ABSTRACT The VISTA Variables in the Via Lactea (VVV) survey obtained near-infrared photometry towards the Galactic bulge and the southern disc plane for a decade (2010–2019). We designed a modified Lomb–Scargle method to search for large-amplitude ($\Delta K_{s, 2-98{{\ \rm per\ cent}}}$ > 1.5 mag) mid to long-term periodic variables (P> 10 d) in the 2nd version of VVV Infrared Astrometric Catalogue (VIRAC2-β). In total, 1520 periodic sources were discovered, including 59 candidate periodic outbursting young stellar objects (YSOs), based on the unique morphology of the phase-folded light curves, proximity to Galactic H ii regions and mid-infrared colours. Five sources are spectroscopically confirmed as accreting YSOs. Both fast-rise/slow-decay and slow-rise/fast-decay periodic outbursts were found, but fast-rise/slow-decay outbursts predominate at the highest amplitudes. The multiwavelength colour variations are consistent with a variable mass accretion process, as opposed to variable extinction. The cycles are likely to be caused by dynamical perturbations from stellar or planetary companions within the circumstellar disc. An additional search for periodic variability amongst YSO candidates in published Spitzer-based catalogues yielded a further 71 candidate periodic accretors, mostly with lower amplitudes. These resemble cases of pulsed accretion but with unusually long periods and greater regularity. The majority of other long-period variables are pulsating dusty Miras with smooth and symmetric light curves. We find that some Miras have redder W3 − W4 colours than previously thought, most likely due to their surface chemical compositions.

Theil Entropy as a Non-Lineal Analysis for Spectral Inequality of Physiological Oscillations.

Theil entropy is a statistical measure used in economics to quantify income inequalities. However, it can be applied to any data distribution including biological signals. In this work, we applied different spectral methods on heart rate variability signals and cellular calcium oscillations previously to Theil entropy analysis. The behavior of Theil entropy and its decomposable property was investigated using exponents in the range of [−1, 2], on the spectrum of synthetic and physiological signals. Our results suggest that the best spectral decomposition method to analyze the spectral inequality of physiological oscillations is the Lomb–Scargle method, followed by Theil entropy analysis. Moreover, our results showed that the exponents that provide more information to describe the spectral inequality in the tested signals were zero, one, and two. It was also observed that the intra-band component is the one that contributes the most to total inequality for the studied oscillations. More in detail, we found that in the state of mental stress, the inequality determined by the Theil entropy analysis of heart rate increases with respect to the resting state. Likewise, the same analytical approach shows that cellular calcium oscillations present on developing interneurons display greater inequality distribution when inhibition of a neurotransmitter system is in place. In conclusion, we propose that Theil entropy is useful for analyzing spectral inequality and to explore its origin in physiological signals.

Temperature Analysis of Flaring (AR 11283) and Non-flaring (AR 12194) Coronal Loops

Here, we study the temperature structure of flaring and non-flaring coronal loops, using extracted loops from images taken in six extreme ultraviolet channels recorded by Atmospheric Imaging Assembly/Solar Dynamics Observatory. We use data for loops of an X2.1-class-flaring active region (AR 11283) during 22:10 UT until 23:00 UT, on 2011 September 6; and a non-flaring active region (AR 12194) during 08:00:00 UT until 09:00:00 UT on 2014 October 26. By using the spatially synthesized Gaussian differential emission measure (DEM) forward-fitting method, we calculate the peak temperatures for each strip of the loops. We apply the Lomb–Scargle method to compute the oscillation periods for the temperature series of each strip. The periods of the temperature oscillations for the flaring loops ranged from 7 to 28.4 minutes. These temperature oscillations show very close behavior to the slow-mode oscillation. We observe that the temperature oscillations in the flaring loops started at least around 10 minutes before the transverse oscillations and continue for a long time duration even after the transverse oscillations ended. The temperature amplitudes increased during the flaring time (20 minutes) in the flaring loops. The periods of the temperatures obtained for the non-flaring loops ranged from 8.5 to 30 minutes, but their significances are less (below 0.5) in comparison with the flaring ones (near to one). Hence the detected temperature periods for the non-flaring loops’ strips are less probable in comparison with the flaring ones, and maybe they are just fluctuations. Based on our confined observations, it seems that the flaring loops’ periods show more diversity and their temperatures have wider ranges of variation than the non-flaring ones. More accurate commentary in this respect requires more extensive statistical research and broader observations.

Four-Channel Interference of Dual-Antenna GNSS Reflectometry and Water Level Observation

The signals at higher elevation angles could be received by a left-handed circularly polarized (LHCP) antenna because LHCP components dominate the reflected signals at higher elevation angles. This letter explores a four-channel interference method of dual-antenna global navigation satellite system (GNSS) reflectometry capable and its application in retrieving the water level. Compared to single-antenna observation using a oscillating signal-to-noise ratio (SNR), due to the capability of receiving the reflected signals at high elevation angles, the proposed method has higher temporal resolution. The criterion based on the effective value of the time series is proposed to evaluate the quality of oscillating carrier phase difference. The Lomb–Scargle method and cosine fitting are used to estimate the oscillated frequency of carrier phase difference. Through normalizing cosine oscillation and time scale by the GNSS signal amplitude and wavelength, the time-series from multisatellites could be combined to retrieve the height. At last, the experiment is conducted to demonstrate the proposed method, and the results show that when the criterion threshold is under 0.2, the centimeter-level precision of the retrieved height could be achieved. Two-satellite observation combining satellite pseudorandom noise (PRN) 15 and 24 could decrease the time span of the observation to 320 s from 480 s for only using single satellite, and the root mean square error (RMSE) reduces to 6.2 cm from 9.5 and 18.9 cm of the satellite PRN 15 and 24.

MONOS: Multiplicity Of Northern O-type Spectroscopic systems

Context. Massive stars are a key element for understanding the chemical and dynamical evolution of galaxies. Stellar evolution is conditioned by many factors: Rotation, mass loss, and interaction with other objects are the most important ones for massive stars. During the first evolutionary stages of stars with initial masses (i.e., MZAMS) in the MZAMS ∼ 18–70 M⊙ range, they are of spectral type O. Given that stars in this mass range spend roughly 90% of their lifetime as O-type stars, establishing the multiplicity frequency and binary properties of O-type stars is crucial for many fields of modern astrophysics. Aims. The aim of the MONOS project is to collect information to study northern Galactic O-type spectroscopic binaries. In this second paper, we tackle the study of the 35 single-line spectroscopic binary (SB1) systems identified in the previous paper of the series, analyze our data, and review the literature on the orbits of the systems. Methods. We have measured ∼4500 radial velocities for a selection of diagnostic lines for the ∼700 spectra of the studied systems in our database, for which we have used two different methods: a Gaussian fit for several lines per object and cross-correlation with synthetic spectra computed with the FASTWIND stellar atmospheric code. We have also explored the photometric data delivered by the TESS mission to analyze the light curve (LC) of the systems, extracting 31 of them. We have explored the possible periods with the Lomb-Scargle method and, whenever possible, calculated the orbital solutions using the SBOP and GBART codes. For those systems in which an improved solution was possible, we merged our radial velocities with those in the literature and calculated a combined solution. Results. As a result of this work, of the 35 SB1 systems identified in our first paper we have confirmed 21 systems as SB1 with good orbits, discarded the binary nature of six stars (9 Sge, HD 192 281, HDE 229 232 AB, 68 Cyg, HD 108, and α Cam), and left six stars as inconclusive due to a lack of data. The remaining two stars are 15 Mon Aa, which has been classified as SB2, and Cyg OB2-22 C, for which we find evidence that it is most likely a triple system where the O star is orbiting an eclipsing SB1. We have also recalculated 20 new orbital solutions, including the first spectroscopic orbital solution for V747 Cep. For Cyg OB2-22 C, we have obtained new ephemerides but no new orbit.

The effect of principal component analysis in the diagnosis of congestive heart failure via heart rate variability analysis.

In this study, we investigated the effect of principal component analysis (PCA) in congestive heart failure (CHF) diagnosis using various machine learning algorithms from 5-min HRV data. The extracted 59 heart rate variability (HRV) features consist of statistical time-domain measures, frequency-domain measures (power spectral density estimations from Fourier transform and Lomb-Scargle methods), time-frequency HRV measures (Wavelet transform), and nonlinear HRV measures (Poincare plot, symbolic dynamics, detrended fluctuation analysis, and sample entropy). All these HRV features are the classifiers' inputs. We repeated the study ten times using the first one to the first 10 principal components from PCA instead of all HRV features. Nine different classifiers, namely logistic regression, Naive Bayes, k-nearest neighbors, decision tree, AdaBoost, support vector machines, stochastic gradient descent, random forest, and artificial neuronal network (multilayer perceptron) are examined. The proposed study results in the 100% accuracy, 100% specificity, and 100% sensitivity after utilizing PCA (with the first eight principal components) using the Random Forest classifier where the maximum classifier performances are the 86% accuracy, 79% specificity, and 86% sensitivity before PCA. In conclusion, PCA is beneficial in the diagnosis of patients with CHF. In addition, we experienced the online Python-based visual machine learning tool, Orange, which can implement well-known machine learning algorithms.

BGLS-based method of estimating the rotational periods of asteroids

As the asteroid rotational period is important to the study of the properties of asteroids (e.g., super-fast rotators have structures owing an internal cohesion (rather than being rubble piles bounded by gravity only) so as not to fly apart), constructing an effective and fast method used to search the period attracts much researchers’ attention. Recently, the Bayesian generalized Lomb–Scargle (BGLS) periodogram was developed to improve the convergence efficiency of the Lomb–Scargle method. However, the result of BGLS varies with the frequency range and cannot meet the two minimum/maximum requirements for a complete rotation of the asteroid. We propose a robust BGLS-based method that efficiently determines rotational periods. The proposed method employs a polynomial series to fit folded light curves with potential periods, initially calculated using the BGLS periodogram, and adopts a merit function to estimate and refine best-fit periods. We estimate the rotational periods of 30 asteroids applying the new method to light curves from the Palomar Transient Factory. Results confirm the effectiveness of the BGLS-based method in deriving rotational periods from ground-based observations of asteroids. Further application of the BGLS-based method to sparse light curves, such as Gaia data, is discussed.

Possible Periodic Activity in the Short Bursts of SGR 1806-20: Connection to Fast Radio Bursts

Abstract Magnetars are highly magnetized neutron stars that are characterized by recurrent emission of short-duration bursts in soft gamma-rays/hard X-rays. Recently, FRB 200428 was found to be associated with an X-ray burst from a Galactic magnetar. Two fast radio bursts show mysterious periodic activity. However, it is unclear whether magnetar X-ray bursts are periodic phenomena. In this paper, we investigate the activity period of SGR 1806-20. More than 3000 short bursts observed by different telescopes are collected, including the observations of RXTE, HETE-2, ICE, and Konus. We consider the observation windows and divide the data into two subsamples to alleviate the effect of uneven sampling. The epoch-folding and Lomb–Scargle methods are used to derive the period of the short bursts. We find a possible period of about 398.20 ± 25.45 days, but other peaks exist in the periodograms. If the period is real, the connection between short bursts of magnetars and fast radio bursts should be investigated extensively.

Orbital variability of the optical linear polarization of the γ-ray binary LS I +61° 303 and new constraints on the orbital parameters

We studied the variability of the linear polarization and brightness of the γ-ray binary LS I +61° 303. High-precision BVR photopolarimetric observations were carried out with the Dipol-2 polarimeter on the 2.2 m remotely controlled UH88 telescope at Mauna Kea Observatory and the 60 cm Tohoku telescope at Haleakala bservatory (Hawaii) over 140 nights in 2016−2019. We also determined the degree and angle of the interstellar polarization toward LS I +61° 303 using two out of four nearby field stars that have Gaia’s parallaxes. After subtracting the interstellar polarization, we determined the position angle of the intrinsic polarization θ ≃ 11°, which can either be associated with the projection of the Be star’s decretion disk axis on the plane of sky, or can differ from it by 90°. Using the Lomb-Scargle method, we performed timing analyses and period searches of our polarimetric and photometric data. We found statistically significant periodic variability of the normalized Stokes parameters q and u in all passbands. The most significant period of variability, PPol = 13.244 ± 0.012 d, is equal to one half of the orbital period Porb = 26.496 d. The fits of the polarization variability curves with Fourier series show a dominant contribution from the second harmonic which is typical for binary systems with circular orbits and nearly symmetric distribution of light scattering material with respect to the orbital plane. The continuous change of polarization with the orbital phase implies co-planarity of the orbit of the compact object and the Be star’s decretion disk. Using a model of Thomson scattering by a cloud that orbits the Be star, we obtained constraints on the orbital parameters, including a small eccentricity e < 0.2 and periastron phase of ϕp ≈ 0.6, which coincides with the peaks in the radio, X-ray, and TeV emission. These constraints are independent of the assumption about the orientation of the decretion disk plane on the sky. We also extensively discuss the apparent inconsistency with the previous measurements of the orbital parameters from radial velocities. By folding the photometry data acquired during a three-year time span with the orbital period, we found a linear phase shift of the moments of the brightness maximum, confirming the possible existence of superorbital variability.

A Catalog of Short Period Spectroscopic and Eclipsing Binaries Identified from the LAMOST and PTF Surveys

Binaries play key roles in determining stellar parameters and exploring stellar evolution models. We build a catalog of 88 eclipsing binaries with spectroscopic information, taking advantage of observations from both the Large Sky Area Multi-Object fiber Spectroscopic Telescope (LAMOST) and the Palomar Transient Factory (PTF) surveys. A software pipeline is constructed to identify binary candidates by examining their light curves. The orbital periods of binaries are derived from the Lomb-Scargle method. The key distinguishing features of eclipsing binaries are recognized by a new filter \textit{Flat Test}. We classify the eclipsing binaries by applying Fourier analysis on the light curves. Among all the binary stars, 13 binaries are identified as eclipsing binaries for the first time. The catalog contains information: position, primary eclipsing magnitude and time, eclipsing depth, the number of photometry and radial velocity observations, largest radial velocity difference, binary type, the effective temperature of observable star $T_{\rm eff}$, and surface gravity of observable star log \emph{g}. The false-positive probability is calculated by using both a Monte Carlo simulation and real data from the SDSS Stripe 82 Standard Catalog. The binaries in the catalog are mostly with a period of less than one day. The period distribution shows a 0.22-day cut-off which is consistent with the low probability of an eclipsing binary rotating with such a period.

How far can we trust published TESS periods?

Possible inaccuracies in the determination of periods from short-term time series caused by disregard of the real course of light curves and instrumental trends are documented on the example of the period analysis of simulated TESS-like light curve by notorious Lomb-Scargle method.

Binary star detection in the open cluster King 1 field

A rarely studied open cluster, King 1 is observed using the 1.3-m telescope equipped with a 2k × 4k CCD at Vainu Bappu Observatory, India. We analyze the photometric data obtained from CCD observations in both B and V bands. Out of 132 detected stars in the open cluster King 1 field, we have identified four stellar variables, and two among them are reported as newly detected binary systems. The parallax values from Gaia DR2 suggest that the open cluster King 1 is in the background of these two detected binary systems, falling along the same line of sight, giving rise to different parallax values. Periodogram analysis was carried out using Phase Dispersion Minimization (PDM) and the Lomb-Scargle (LS) method for all the detected variables. PHysics Of Eclipsing BinariEs (PHOEBE) is extensively employed to model various stellar parameters of both the detected binary systems. Based on the modeling results obtained from this work, one of the binary systems is reported for the first time as an Eclipsing Detached (ED) and the other as an Eclipsing Contact (EC) binary of W-type W UMa.

Improved GPT2w (IGPT2w) model for site specific zenith tropospheric delay estimation in China

Despite being a systematic error source in global navigation satellite system (GNSS) positioning and navigation, tropospheric delay is a key parameter in GNSS meteorology. Therefore, deriving a zenith tropospheric delay (ZTD) value as accurately as possible from an empirical model without using auxiliary data is a prerequisite for the high-precision application of GNSS positioning and navigation. To reach the goal above, this paper proposes an improved model to estimate the ZTD based on the Global Pressure and Temperature 2 wet (GPT2w) model, which is called the improved GPT2w (IGPT2w) model. The GPT2w-derived ZTD is first calculated as the initial value of the IGPT2w model, and the time series of ZTD residual can thus be obtained between the GNSS- and GPT2w-derived ZTDs over GNSS stations. Analysis of the long time series variation of ZTD residuals using the multichannel singular spectrum analysis method reveals evident periodic signals. The Lomb–Scargle method is then used to determine the specific values of these periodic signals, and different periods are identified at various GNSS stations. Therefore, a ZTD residual model that considers annual, semi-annual, and seasonal periods is established. The IGPT2w model, in which the ZTD value is obtained by combining the estimated ZTD residual and the GPT2w-derived ZTD, can be acquired. A total of 188 GNSS stations in China throughout 2015 to 2017 are selected to validate the IGPT2w model. In the model, the GNSS-derived ZTD is obtained using the GAMIT/GLOBK software, and the accuracy is validated using radiosonde data with root mean square and bias of 1.9 and 0.1 cm, respectively, at 33 collocated stations in China. Statistical results reveal that the accuracy of the IGPT2w-derived ZTD is improved by 13.7% compared with that of the GPT2w-derived ZTD when the GNSS-derived ZTD is regarded as the reference. Such result indicates that the proposed IGPT2w model outperforms the GPT2w model in China.