Lomb-Scargle Research Articles

Characteristic differences between IGS final and ray-traced tropospheric delays and their impact on precise point positioning and tropospheric delay estimates

The length of the convergence time in Precise Point Positioning (PPP) is a result of unmodeled errors. The tropospheric delay error is considered a major error source that affects the PPP solution accuracy and convergence time, especially in the height coordinates. Recent research showed that Numerical Weather Models (NWM)-based tropospheric correction models are superior to traditional empirical tropospheric models. We investigate the tropospheric delay difference between the ray-traced NWM and the final troposphere estimates from the International GNSS Service (IGS). Long time series of about 5 years of tropospheric delay are obtained from the European Centre for Medium-Range Weather Forecast and compared with the final IGS tropospheric delay time series for 30 globally distributed IGS stations. It is shown that the ray-traced tropospheric delay differences depend on time and experience seasonal variations with a non-zero mean. The mean is found to be 0.47 cm and the standard deviation is 1.40 cm. To model such differences, the least-squares spectral analysis approach is used to estimate the deterministic part of the tropospheric residuals (linear trend and periodic signals). The remaining tropospheric differences are estimated as a random walk process with 5 mm/√h random noise. To study the effect of the developed model on both station position and tropospheric delay estimate, we implement our model in GPS processing software, and the data from 15 IGS stations are processed. These stations are divided into two groups. The first group consists of nine IGS stations from the same network used to estimate the model, and their corresponding model values are extrapolated to the test epochs in 2018. However, the second group consists of six IGS stations, and their corresponding values are interpolated from the nearby stations. It is shown that the root means square error (RMSE) of station position in both groups can be improved by 5.68%, 0.76%, and 11.88% in Easting, Northing, and Up directions, respectively. In addition to the improvement in the RMSE of station positions, an improvement of 7.91% is obtained for total tropospheric delay estimates.

Variability of OB stars from TESS southern Sectors 1–13 and high-resolution IACOB and OWN spectroscopy

Context. The lack of high-precision long-term continuous photometric data for large samples of stars has impeded the large-scale exploration of pulsational variability in the OB star regime. As a result, the candidates for in-depth asteroseismic modelling have remained limited to a few dozen dwarfs. The TESS nominal space mission has surveyed the southern sky, including parts of the galactic plane, yielding continuous data across at least 27 d for hundreds of OB stars. Aims. We aim to couple TESS data in the southern sky with ground-based spectroscopy to study the variability in two dimensions, mass and evolution. We focus mainly on the presence of coherent pulsation modes that may or may not be present in the predicted theoretical instability domains and unravel all frequency behaviour in the amplitude spectra of the TESS data. Methods. We compose a sample of 98 OB-type stars observed by TESS in Sectors 1–13 and with available multi-epoch, high-resolution spectroscopy gathered by the IACOB and OWN surveys. We present the short-cadence 2 min light curves of dozens of OB-type stars, which have one or more spectra in the IACOB or OWN database. Based on these light curves and their Lomb–Scargle periodograms, we performed variability classification and frequency analysis. We placed the stars in the spectroscopic Hertzsprung–Russell diagram to interpret the variability in an evolutionary context. Results. We deduce the diverse origins of the mmag-level variability found in all of the 98 OB stars in the TESS data. We find among the sample several new variable stars, including three hybrid pulsators, three eclipsing binaries, high frequency modes in a Be star, and potential heat-driven pulsations in two Oe stars. Conclusions. We identify stars for which future asteroseismic modelling is possible, provided mode identification is achieved. By comparing the position of the variables to theoretical instability strips, we discuss the current shortcomings in non-adiabatic pulsation theory and the distribution of pulsators in the upper Hertzsprung–Russell diagram.

Comparing significance criteria for cyclic modulations in time series

General solutions are derived for least-squares fits of amplitude, phase shift and baseline shift of sinusoidal modulations to normally distributed time series. Four cases are compared: weighted and unweighted fit, with and without a baseline shift. Computer simulations have been performed of the statistical distribution of the amplitude resulting from fits to white noise. A normalised amplitude is defined which follows exactly a Rayleigh distribution, even for small, uneven-sampled data sets. Equations are provided for the width of the distribution and the cumulative probability function. A simple criterion for the statistical significance of the amplitude fitted to a time series is derived and compared for equivalence with the Lomb–Scargle criterion based on a power function.

Improving the Lomb–Scargle Periodogram with the Thomson Multitaper

Abstract A common approach for characterizing the properties of time-series data that are evenly sampled in time is to estimate the power spectrum of the data using the periodogram. The periodogram as an estimator of the spectrum is (1) statistically inconsistent (i.e., its variance does not go to zero as infinite data are collected), (2) biased for finite samples, and (3) suffers from spectral leakage. In astronomy, time-series data are often unevenly sampled in time, and it is popular to use the Lomb–Scargle (LS) periodogram to estimate the spectrum. Unfortunately, from a statistical standpoint, the LS periodogram suffers from the same issues as the classical periodogram and has even worse spectral leakage. Here, we present an improvement on the LS periodogram by combining it with the Thomson multitaper approach. The multitaper spectral estimator is well established in the statistics and engineering literature for evenly sampled time series. It is attractive because it directly trades off bias and variance for frequency resolution, and is fast to compute: compared to an untapered spectral estimator, the multitaper adds no more than a couple of seconds for a time series with a million data points on a current desktop computer. Here, we describe an estimator that combines the multitaper with the LS periodogram. We show examples in which this new approach has improved properties compared to traditional approaches in the case of unevenly sampled time series. Finally, we demonstrate an application of the method to astronomy with an application to Kepler data.

Confirmed short periodic variability of subparsec supermassive binary black hole candidate Mrk 231

ABSTRACT Here we confirm the short periodic variability of a subparsec supermassive binary black hole (SMBBH) candidate Mrk 231 in the extended optical photometric data set collected by the Catalina Real-Time Transient Survey (CRTS) and All-Sky Automated Survey for Supernovae (ASAS-SN). Using the Lomb–Scargle periodogram and 2DHybrid method, we detected the significant periodicity of ∼1.1 yr beyond a damped random walk model in the CRTS+ASAS-SN optical data set. Mrk 231 has been previously proposed as an SMBBH candidate with a highly unequal mass ratio (q ∼ 0.03), very tight mutual separation of ∼590 au, and an orbital period of ∼1.2 yr. Hence, our result further supports, even though not prove, the intriguing hypothesis that SMBBHs with low mass ratios may be more common than close-equal mass SMBBHs. This result, however, was obtained from the contribution of the CRTS data with limited sampling cadence and photometric accuracy, and further monitoring of Mrk 231 is crucial to confirm the periodicity.

Methods detecting rhythmic gene expression are biologically relevant only for strong signal.

The nycthemeral transcriptome embodies all genes displaying a rhythmic variation of their mRNAs periodically every 24 hours, including but not restricted to circadian genes. In this study, we show that the nycthemeral rhythmicity at the gene expression level is biologically functional and that this functionality is more conserved between orthologous genes than between random genes. We used this conservation of the rhythmic expression to assess the ability of seven methods (ARSER, Lomb Scargle, RAIN, JTK, empirical-JTK, GeneCycle, and meta2d) to detect rhythmic signal in gene expression. We have contrasted them to a naive method, not based on rhythmic parameters. By taking into account the tissue-specificity of rhythmic gene expression and different species comparisons, we show that no method is strongly favored. The results show that these methods designed for rhythm detection, in addition to having quite similar performances, are consistent only among genes with a strong rhythm signal. Rhythmic genes defined with a standard p-value threshold of 0.01 for instance, could include genes whose rhythmicity is biologically irrelevant. Although these results were dependent on the datasets used and the evolutionary distance between the species compared, we call for caution about the results of studies reporting or using large sets of rhythmic genes. Furthermore, given the analysis of the behaviors of the methods on real and randomized data, we recommend using primarily ARS, empJTK, or GeneCycle, which verify expectations of a classical distribution of p-values. Experimental design should also take into account the circumstances under which the methods seem more efficient, such as giving priority to biological replicates over the number of time-points, or to the number of time-points over the quality of the technique (microarray vs RNAseq). GeneCycle, and to a lesser extent empirical-JTK, might be the most robust method when applied to weakly informative datasets. Finally, our analyzes suggest that rhythmic genes are mainly highly expressed genes.

The γ-Ray and Optical Variability Analysis of the BL Lac Object 3FGL J0449.4−4350

We have assembled the historical light curves of the BL Lac Object 3FGL J0449.4−4350 at optical and γ-ray bands, the time spanning about 10 yr, analyzed the periodic variability of the light curves by using four different methods (Lomb–Scargle periodogram, REDFIT38, Jurkevich and DACF). We detected a marginally possible quasi-periodic oscillation of ∼450 days. Assuming it originates from the helical motion jet in a supermassive binary black hole system undergoing major merger, we estimate the primary black hole mass M ∼ 7.7 × 109 M⊙. To explore the origin of the γ-ray, we investigated the optical-γ-ray correlations using discrete correlation function method, and found that the correlation between the two bands is very significant. This strong correlation tends to imply lepton self-synchro-Compton model to produce the γ-ray.

The Nature of γ-Ray Variability in Blazars

Abstract We present an in-depth and systematic variability study of a sample of 20 powerful blazars, including 12 BL Lacs and 8 flat-spectrum radio quasars, applying various analysis tools such as flux distribution, symmetry analysis, and time-series analysis on the decade-long Fermi/LAT observations. The results show that blazars with steeper γ-ray spectral indexes are found to be more variable, and the γ-ray flux distribution closely resembles a log-normal probability distribution function. The statistical variability properties of the sources as studied by power spectral density analysis are consistent with flicker noise (P(ν) ∝ 1/ν)—an indication of long-memory processes at work. Statistical analysis of the distribution of flux rise and decay rates in the light curves of the sources, aimed at distinguishing between particle acceleration and energy-dissipation timescales, counterintuitively suggests that both kinds of rates follow a similar distribution and the derived mean variability timescales are on the order of a few weeks. The corresponding emission region size is used to constrain the location of γ-ray production sites in the sources to be a few parsecs. Additionally, using Lomb–Scargle periodogram and weighted wavelet z-transform methods and extensive Monte Carlo simulations, we detected year-timescale quasi-periodic oscillations in the sources S5 0716+714, Mrk 421, ON +325, PKS 1424−418, and PKS 2155−304. The detection significance was computed taking proper account of the red noise and other artifacts inherent in the observations. We explain the results in light of current blazar models with relativistic shocks propagating down the jet viewed close to the line of sight.

Searching for Quasiperiodic Modulations in γ-Ray Active Galactic Nuclei

Abstract We perform a systematic search of quasiperiodic variabilities in γ-ray active galactic nuclei in the third Fermi Large Area Telescope source catalog (3FGL). We employ two techniques, Lomb–Scargle Periodogram and Weighted Wavelet Z-transform, to obtain power spectra of γ-ray light curves covering from 2008 August to 2016 December. The results show that besides several objects that have been reported in previous works, an additional source, the flat spectrum radio quasars PKS 0601-70 has a possible quasiperiodic variability of 450 days in its γ-ray light curves with the significance of >3σ. The physical implications of our findings are discussed.

Loose Ends for the Exomoon Candidate Host Kepler-1625b

Abstract The claim of an exomoon candidate in the Kepler-1625b system has generated substantial discussion regarding possible alternative explanations for the purported signal. In this work, we examine these possibilities in detail. First, the effect of more flexible trend models is explored, and we show that sufficiently flexible models are capable of attenuating the signal—although this is an expected byproduct of invoking such models. We also explore trend models using x- and y-centroid positions, and show that there is no data-driven impetus to adopt such models over temporal ones. We quantify the probability that the 500 ppm moon-like dip could be caused by a Neptune-sized transiting planet to be <0.75%. We show that neither autocorrelation, Gaussian processes, nor a Lomb–Scargle periodogram are able to recover a stellar rotation period, demonstrating that K1625 is a quiet star with periodic behavior <200 ppm. Through injection and recovery tests, we find that the star does not exhibit a tendency to introduce false-positive dip-like features above that of pure Gaussian noise. Finally, we address a recent reanalysis by Kreidberg et al. and show that the difference in conclusions is not from differing systematics models but rather the reduction itself. We show that their reduction exhibits, in comparison to the original analysis: (i) slightly higher intraorbit and post-fit residual scatter, (ii) ≃900 ppm larger flux offset at the visit change, (iii) ≃2 times larger y-centroid variations, and (iv) ≃3.5 times stronger flux-centroid correlation coefficient. These points could be explained by larger systematics in their reduction, potentially impacting their conclusions.

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.

Stellar rotation periods from K2 Campaigns 0–18

Context. Rotation period measurements of stars observed with the Kepler mission have revealed a lack of stars at intermediate rotation periods, accompanied by a decrease of photometric variability. Whether this so-called dearth region is a peculiarity of stars in the Kepler field, or reflects a general manifestation of stellar magnetic activity, is still under debate. The K2 mission has the potential to unravel this mystery by measuring stellar rotation and photometric variability along different fields in the sky. Aims. Our goal is to measure stellar rotation periods and photometric variabilities for tens of thousands of K2 stars, located in different fields along the ecliptic plane, to shed light on the relation between stellar rotation and photometric variability. Methods. We use Lomb–Scargle periodograms, auto-correlation and wavelet functions to determine consistent rotation periods. Stellar brightness variability is assessed by computing the variability range, Rvar, from the light curve. We further apply Gaussian mixture models to search for bimodality in the rotation period distribution. Results. Combining measurements from all K2 campaigns, we detect rotation periods in 29 860 stars. The reliability of these periods was estimated from stars observed more than once. We find that 75–90% of the stars show period deviation smaller than 20% between different campaigns, depending on the peak height threshold in the periodograms. For effective temperatures below 6000 K, the variability range shows a local minimum at different periods, consistent with an isochrone age of ∼750 Myr. Additionally, the rotation period distribution shows evidence for bimodality, although the dearth region in the K2 data is less pronounced compared to the Kepler field. The period at the dip of the bimodal distribution shows good agreement with the period at the local variability minimum. Conclusions. We conclude that the rotation period bimodality is present in different fields of the sky, and is hence a general manifestation of stellar magnetic activity. The reduced variability in the dearth region is interpreted as a cancelation between dark spots and bright faculae. Our results strongly advocate that the role of faculae has been underestimated so far, suggesting a more complex dependence of the brightness variability on the rotation period.

A Computational Error and Restricted Use of Time-series Analyses Underlie the Failure to Replicate period-Dependent Song Rhythms in Drosophila.

From 1980 to 1991, Kyriacou, Hall, and collaborators (K&H) reported that the Drosophila melanogaster courtship song has a 1-min cycle in the length of mean interpulse intervals (IPIs) that is modulated by circadian rhythm period mutations. In 2014, Stern failed to replicate these results using a fully automated method for detecting song pulses. Manual annotation of Stern's song records exposed a ~50% error rate in detection of IPIs, but the corrected data revealed period-dependent IPI cycles using a variety of statistical methods. In 2017, Stern et al. dismissed the sine/cosine method originally used by K&H to detect significant cycles, claiming that randomized songs showed as many significant values as real data using cosinor analysis. We first identify a simple mathematical error in Stern et al.'s cosinor implementation that invalidates their critique of the method. Stern et al. also concluded that although the manually corrected wild-type and perL mutant songs show similar periods to those observed by K&H, each song is usually not significantly rhythmic by the Lomb-Scargle (L-S) periodogram, so any genotypic effect simply reflects "noise." Here, we observe that L-S is extremely conservative compared with 3 other time-series analyses in assessing the significance of rhythmicity, both for conventional locomotor activity data collected in equally spaced time bins and for unequally spaced song records. Using randomization of locomotor and song data to generate confidence limits for L-S instead of the theoretically derived values, we find that L-S is now consistent with the other methods in determining significant rhythmicity in locomotor and song records and that it confirms period-dependent song cycles. We conclude that Stern and colleagues' failure to identify song cycles stems from the limitations of automated methods in accurately reflecting song parameters, combined with the use of an overly stringent method to discriminate rhythmicity in courtship songs.

Leaf phenology amplitude derived from MODIS NDVI and EVI: Maps of leaf phenology synchrony for Meso‐ and South America

AbstractThe leaf phenology (i.e. the seasonality of leaf amount and leaf demography) of ecosystems can be characterized through the use of Earth observation data using a variety of different approaches. The most common approach is to derive time series of vegetation indices (VIs) which are related to the temporal evolution of FPAR, LAI and GPP or alternatively used to derive phenology metrics that quantify the growing season. The product presented here shows a map of average ‘amplitude’ (i.e. maximum minus minimum) of annual cycles observed in MODIS‐derived NDVI and EVI from 2000 to 2013 for Meso‐ and South America. It is a robust determination of the amplitude of annual cycles of vegetation greenness derived from a Lomb–Scargle spectral analysis of unevenly spaced data. VI time series pre‐processing was used to eliminate measurement outliers, and the outputs of the spectral analysis were screened for statistically significant annual signals. Amplitude maps provide an indication of net ecosystem phenology since the satellite observations integrate the greenness variations across the plant individuals within each pixel. The average amplitude values can be interpreted as indicating the degree to which the leaf life cycles of individual plants and species are synchronized. Areas without statistically significant annual variations in greenness may still consist of individuals that show a well‐defined annual leaf phenology. In such cases, the timing of the phenology events will vary strongly within the year between individuals. Alternatively, such areas may consist mainly of plants with leaf turnover strategies that maintain a constant canopy of leaves of different ages. Comparison with in situ observations confirms our interpretation of the average amplitude measure. VI amplitude interpreted as leaf life cycle synchrony can support model evaluation by informing on the likely leaf turn over rates and seasonal variation in ecosystem leaf age distribution.

Determination of time-varying periodicities in unequally spaced time series of OH* temperatures using a moving Lomb–Scargle periodogram and a fast calculation of the false alarm probabilities

Abstract. We present an approach to analyse time series with unequal spacing. The approach enables the identification of significant periodic fluctuations and the derivation of time-resolved periods and amplitudes of these fluctuations. It is based on the classical Lomb–Scargle periodogram (LSP), a method that can handle unequally spaced time series. Here, we additionally use the idea of a moving window. The significance of the results is analysed with the typically used false alarm probability (FAP). We derived the dependencies of the FAP levels on different parameters that either can be changed manually (length of the analysed time interval, frequency range) or that change naturally (number of data gaps). By means of these dependencies, we found a fast and easy way to calculate FAP levels for different configurations of these parameters without the need for a large number of simulations. The general performance of the approach is tested with different artificially generated time series and the results are very promising. Finally, we present results for nightly mean OH* temperatures that have been observed from Wuppertal (51∘ N, 7∘ E; Germany).

Generalized Lomb\u2013Scargle analysis of mathrm {^{36}Cl} decay rate measurements at PTB and BNL

Recently Pomme et al. (Solar Phys 292:162, 2017) did an analysis of {^{36}hbox {Cl}} radioactive decay data from measurements at the Physikalisch-Technische Bundesanstalt (PTB), in order to verify the claims by Sturrock and collaborators of an influence on beta-decay rates measured at Brookhaven National Lab (BNL) due to the rotation-induced modulation of the solar neutrino flux. Their analysis excluded any sinusoidal modulations in the frequency range from 0.2 to 20/year. We carry out an independent analysis of the same PTB and BNL data, using the generalized Lomb–Scargle periodogram to look for any statistically significant peaks in the range from 0 to 14 per year, and by evaluating the significance of every peak using multiple methods. Our results for the PTB data are in agreement with those by Pomme et al. For BNL data, we do find peaks at some of the same frequencies as Sturrock et al., but the significance is much lower. All our analysis codes and datasets have been made publicly available.

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.

Variability in Irradiance and Photometric Indices During the Last Two Solar Cycles

The Total Solar Irradiance (TSI) primarily varies on an 11-year time scale and is governed by features such as sunspots and associated decay products such as plage and faculae. These short-lived physical features can also modulate the solar irradiance at intermediate and short temporal scales. Here we investigate the periodic variations, at solar-surface-rotation time scales, of photometric indices derived from images obtained at the San Fernando Observatory (SFO), and we compare them to the properties of the contemporaneous TSI as measured by the Total Irradiance Monitor (TIM) onboard the SOlar Radiation and Climate Experiment (SORCE) spacecraft. Both the daily ground- and space-based data, which span from early 2003 to late 2018, present missing pixels. We use an autoregressive gap-filling method to construct continuous time series to be analyzed via Fourier and wavelet spectral techniques. Lomb–Scargle periodograms, which can handle time series with missing data, are used for comparison. Both the Fourier spectral power and the periodograms yield compatible results with statistically significant periodicities in the range 25 – 35 days. All of the time series have maximum power at 27 days. Significant secondary periods are found at 29 – 30 days and 34 – 35 days. Wavelet analyses of the full time series show that the photometric index resulting from the red-continuum photometric sum $[\Sigma _{\mathrm{{r}}}]$ and the TSI exhibit common high power at surface-solar-rotation scales during the active part of the solar cycle. The phase relation at the surface-solar-rotation scales is not definite. During the solar minimum interval between Solar Cycles (SCs) 23 and 24, variations in the TSI are found to be related to variations both in the photometric index $\Sigma _{\mathrm{{K}}}$, calculated from Ca ii K-line photometric sums and in the magnetic flux in the solar activity latitudinal band (as found in previous work). This suggests that the TSI changes during the minimum are caused by the reduced line-blanketing effect of diffused magnetic field.

Quasi-periodic behaviour in the optical and γ-ray light curves of blazars 3C 66A and B2 1633+38

ABSTRACT We report on quasi-periodic variability found in two blazars included in the Steward Observatory Blazar Monitoring data sample: the BL Lac object 3C 66A and the Flat Spectrum Radio Quasar B2 1633+38. We collect optical photometric and polarimetric data in V and R bands of these sources from different observatories: St. Petersburg University, Crimean Astrophysical Observatory, WEBT–GASP, Catalina Real-Time Transient Survey, Steward Observatory, STELLA Robotic Observatory, and Katzman Automatic Imaging Telescope. In addition, an analysis of the γ-ray light curves from Fermi–LAT is included. Three methods are used to search for any periodic behaviour in the data: the Z-transform Discrete Correlation Function, the Lomb–Scargle periodogram and the Weighted Wavelet Z-transform. We find pieces of evidence of possible quasi-periodic variability in the optical photometric data of both sources with periods of ∼3 yr for 3C 66A and ∼1.9 yr for B2 1633+38, with significances between 3σ and 5σ. Only B2 1633+38 shows evidence of this behaviour in the optical polarized data set at a confidence level of 2σ–4σ. This is the first reported evidence of quasi-periodic behaviour in the optical light curve of B2 1633+38. Also, a hint of quasi-periodic behaviour is found in the γ-ray light curve of B2 1633+38 with a confidence level ≥2σ, while no periodicity is observed for 3C 66A in this energy range. We propose different jet emission models that could explain the quasi-periodic variability and the differences found between these two sources.

Optical Variability Modeling of Newly Identified Blazar Candidates behind Magellanic Clouds

Abstract We present an optical variability study of 44 newly identified blazar candidates behind the Magellanic Clouds, including 27 flat spectrum radio quasars (FSRQs) and 17 BL Lacertae objects (BL Lacs). All objects in the sample possess high photometric accuracy and irregularly sampled optical light curves (LCs) in I filter from the long-term monitoring conducted by the Optical Gravitational Lensing Experiment. We investigated the variability properties to look for blazar-like characteristics and to analyze the long-term behavior. We analyzed the LCs with the Lomb–Scargle periodogram to construct power spectral densities (PSDs), found breaks for several objects, and linked them with accretion disk properties. In this way we constrained the black hole (BH) masses of 18 FSRQs to lie within the range , assuming a wide range of possible BH spins. By estimating the bolometric luminosities, we applied the fundamental plane of active galactic nuclei variability as an independent estimate, resulting in , with a mean error of 0.3. Many of the objects have very steep PSDs, with high-frequency spectral index in the range 3–7. An alternative attempt to classify the LCs was made using the Hurst exponent, H, and the plane. Two FSRQs and four BL Lacs yielded H > 0.5, indicating presence of long-term memory in the underlying process governing the variability. Additionally, two FSRQs with exceptional PSDs stand out as well in the plane.