Weighted Wavelet Z-transform Research Articles

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.

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.

Two Quasi-periodic Oscillations in ESO 113-G010

In the narrow-line Seyfert galaxy (NLS1) ESO 113-G010, two quasi-periodic oscillation (QPO) signals are detected in the XMM-Newton data collected in 2005 November. The XMM-Newton telescope has an exposure longer than 100ks in the energy range of 0.3–10 keV. The data are analyzed using the Lomb-Scargle periodogram (LSP) and the weighted wavelet Z-transform (WWZ) methods. It is found that there are ∼2.24 hour and ∼4.09 hour QPOs in the observation with the confidence levels of 7.3σ and 4.8σ, respectively. The two QPO signals have a relationship of approximately 1:2 (1:1.83). The absence of QPO in another observation of the object suggests that it is a transient phenomenon. The relationship between the mass of the ESO 113-G010 central black hole (BH) MBH and its frequency fQPO satisfies the known logarithmic linear relation in highly accreting BH systems, from stellar-mass BHs to supermassive BHs. The energy spectrum analysis reveals that the source has a soft X-ray excess below 1 keV.

Blazar Mrk 501 shows rhythmic oscillations in its γ-ray emission

Quasi-periodic oscillations (QPO) originating from innermost regions of blazars can provide unique perspective of some of the burning issues in blazar studies including disk-jet connection, launch of relativistic jets from the central engine, and other extreme conditions near the fast rotating supermassive black holes. However, a number of hurdles associated with searching QPOs in blazars e.g., red-noise dominance, modest significance of the detection and periodic modulation lasting for only a couple of cycles, make it difficult to estimate the true significance of the detection. In this work, we report a $\sim$ 330-day QPO in the Fermi/LAT observations of the blazar Mrk 501 spanning nearly a decade. To establish consistency of the result, we adopted multiple approaches to the time series analysis and employed four widely known methods. Among these, Lomb-Scargle periodogram and weighted wavelet z-transform represent frequency domain based methods whereas epoch folding and z-transformed discrete auto-correlation function are time-domain based analysis. Power spectrum response method was followed to properly account for the red-noise, largely inherent in blazar light curves. Both local and global significance of the signal were found to be above 99\% over possible spurious detection. In the context where not many $\gamma$-ray QPOs have been reported to last more than 5 cycles, this might be one of the few instances where we witness a sub-year timescale $\gamma$-ray QPO persisting nearly 7 cycles. A number of possible scenarios linked with binary supermassive black hole, relativistic jets, and accretion disks can be invoked to explain the transient QPO.

Detection of a quasi-periodic oscillation in γ-ray light curve of the high redshift blazar B2 1520+31

We detected a possible quasi-periodic oscillation (QPO) of ~ 71 days in the 0.1 -- 300 GeV gamma-ray Fermi-LAT light curve of the high redshift flat spectrum radio quasar B2 1520+31. We identify and confirm that quasi-period by Lomb Scargle periodogram (LSP), and weighted wavelet z-transform (WWZ) analyses. Using this QPO period, and assuming it originates from accretion-disc fluctuations at the innermost stable circular orbit, we estimate the central supermassive black hole mass to range between ~ 5.4 * 10$^{9}$ M$_{\odot}$ for a non-rotating black hole and ~ 6.0 * 10$^{10}$ M$_{\odot}$ for a maximally rotating black hole. We briefly discuss other possible radio-loud active galactic nuclei emission models capable of producing a gamma-ray QPO of such a period in a blazar.

Possible ~1 hour quasi-periodic oscillation in narrow-line Seyfert 1 galaxy MCG–06–30–15

We found a possible ~1 h quasi-periodic oscillation (QPO) in a ~55 ks X-ray observation of the narrow-line Seyfert 1 galaxy MCG–06–30–15 made with the XMM-Newton EPIC/pn detector in the energy range 0.3–10 keV. We identify a total modulation of ~16% in the light curve and find a ≃3670 s quasi-period using Lomb-Scargle periodogram (LSP) and weighted wavelet Z-transform (WWZ) techniques. Our analyses of eight light curves of MCG–06–30–15, indicated the possible presence of an oscillation during one of them. The LSP indicates a statistically significant (≃3σ) QPO detection. A WWZ analysis shows that the signal at this possible roughly 3670 s period is present, and rather persistent, throughout the observation; however, a signal around 8735 s is more persistent. We briefly discuss models that can produce X-ray QPOs with such periods in narrow line Seyfert 1 galaxies, as both other claimed QPO detections in this class of AGN had very similar periods.

Radio and γ-Ray Variability in the BL Lac PKS 0219−164: Detection of Quasi-periodic Oscillations in the Radio Light Curve

Abstract In this work, we explore the long-term variability properties of the blazar PKS 0219−164 in the radio and the γ-ray regime, utilizing the OVRO 15 GHz and the Fermi/LAT observations from the period 2008–2017. We found that γ-ray emission is more variable than the radio emission implying that γ-ray emission possibly originated in more compact regions while the radio emission represented continuum emission from the large-scale jets. Also, in the γ-ray, the source exhibited spectral variability, characterized by the softer-when-brighter trend, a less frequently observed feature in the high-energy emission by BL Lacs. In radio, using Lomb–Scargle periodogram and weighted wavelet z-transform, we detected a strong signal of quasi-periodic oscillation (QPO) with a periodicity of 270 ± 26 days with possible harmonics of 550 ± 42 and 1150 ± 157 day periods. At a time when detections of QPOs in blazars are still under debate, the observed QPO with high statistical significance (∼97%–99% global significance over underlying red-noise processes) and persistent over nearly 10 oscillations could make one of the strongest cases for the detection of QPOs in blazar light curves. We discuss various blazar models that might lead to the γ-ray and radio variability, QPO, and the achromatic behavior seen in the high-energy emission from the source.

A γ-ray Quasi-periodic Modulation in the Blazar PKS 0301–243?

Abstract We report a nominally high-confidence γ-ray quasi-periodic modulation in the blazar PKS 0301–243. For this target, we analyze its Fermi-LAT Pass 8 data from 2008 August to 2017 May. Two techniques, i.e., maximum likelihood optimization and exposure-weighted aperture photometry, are used to build the γ-ray light curves. Then, both the Lomb–Scargle periodogram and the weighted wavelet Z-transform are applied to the light curves to search for period signals. A quasi-periodicity with a period of 2.1 ± 0.3 yr appears at the significance level of , although it should be noted that this putative quasi-period variability is seen in a data set that is barely four times longer. We speculate that this γ-ray quasi-periodic modulation may be evidence of a binary supermassive black hole.

Search for Exoplanets around Northern Circumpolar Stars. II. The Detection of Radial Velocity Variations in M Giant Stars HD 36384, HD 52030, and HD 208742

Abstract We present the detection of long-period RV variations in HD 36384, HD 52030, and HD 208742 by using the high-resolution, fiber-fed Bohyunsan Observatory Echelle Spectrograph (BOES) for the precise radial velocity (RV) survey of about 200 northern circumpolar stars. Analyses of RV data, chromospheric activity indicators, and bisector variations spanning about five years suggest that the RV variations are compatible with planet or brown dwarf companions in Keplerian motion. However, HD 36384 shows photometric variations with a period very close to that of RV variations as well as amplitude variations in the weighted wavelet Z-transform (WWZ) analysis, which argues that the RV variations in HD 36384 are from the stellar pulsations. Assuming that the companion hypothesis is correct, HD 52030 hosts a companion with minimum mass 13.3 M Jup orbiting in 484 days at a distance of 1.2 au. HD 208742 hosts a companion of 14.0 M Jup at 1.5 au with a period of 602 days. All stars are located at the asymptotic giant branch (AGB) stage on the H–R diagram after undergoing the helium flash and leaving the giant clump.With stellar radii of 53.0 R ⊙ and 57.2 R ⊙ for HD 52030 and HD 208742, respectively, these stars may be the largest yet, in terms of stellar radius, found to host substellar companions. However, given possible RV amplitude variations and the fact that these are highly evolved stars, the planet hypothesis is not yet certain.

Least-Squares Wavelet Analysis of Unequally Spaced and Non-stationary Time Series and Its Applications

Least-squares spectral analysis, an alternative to the classical Fourier transform, is a method of analyzing unequally spaced and non-stationary time series in their first and second statistical moments. However, when a time series has components with low or high amplitude and frequency variability over time, it is not appropriate to use either the least-squares spectral analysis or Fourier transform. On the other hand, the classical short-time Fourier transform and the continuous wavelet transform do not consider the covariance matrix associated with a time series nor do they consider trends or datum shifts. Moreover, they are not defined for unequally spaced time series. A new method of analyzing time series, namely, the least-squares wavelet analysis is introduced, which is a natural extension of the least-squares spectral analysis. This method decomposes a time series to the time–frequency domain and obtains its spectrogram. In addition, the probability distribution function of the spectrogram is derived that identifies statistically significant peaks. The least-squares wavelet analysis can analyze any non-stationary and unequally spaced time series with components of low or high amplitude and frequency variability, including datum shifts, trends, and constituents of known forms, by taking into account the covariance matrix associated with the time series. The outstanding performance of the proposed method on synthetic time series and a very long baseline interferometry series is demonstrated, and the results are compared with the weighted wavelet Z-transform.

Possible Quasi-periodic Modulation in the z = 1.1 Gamma-Ray Blazar PKS 0426–380

Abstract We search for γ-ray and optical periodic modulations in distant flat-spectrum radio quasar (FSRQ) PKS 0426–380 (the redshift z = 1.1). Using two techniques (i.e., the maximum likelihood optimization and the exposure-weighted aperture photometry), we obtain γ-ray light curves from Fermi-LAT Pass 8 data covering from 2008 August to 2016 December. We then analyze the light curves with the Lomb–Scargle periodogram and the weighted wavelet Z-transform. A γ-ray quasi-periodicity with a period of 3.35 ± 0.68 yr is found at the significance level of . The optical–UV flux covering from 2005 August to 2013 April provided by the ASI Science Data Center is also analyzed, but no significant quasi-periodicity is found. It should be pointed out that the result of the optical–UV data could be tentative because of the incompleteness of the data. Further long-term multiwavelength monitoring of this FSRQ is needed to confirm its quasi-periodicity.

Revisiting Quasi-periodic Modulation in γ-Ray Blazar PKS 2155-304 with Fermi Pass 8 Data

Abstract We examine the gamma-ray quasi-periodic variability of PKS 2155-304 with the latest publicly available Fermi-LAT Pass 8 data, which covers the years from 2008 August to 2016 October. We produce the light curves in two ways: the exposure-weighted aperture photometry and the maximum likelihood optimization. The light curves are then analyzed by using Lomb-Scargle Periodogram (LSP) and Weighted Wavelet Z-transform, and the results reveal a significant quasi-periodicity with a period of 1.74 ± 0.13 years and a significance of ∼4.9σ. The constraint of multifrequencies quasi-periodic variabilities on blazar emission model is discussed.

Periodicity Analysis of X-ray Light Curves of SS 433

SS 433 is sofar the unique X-ray binary that has the simultaneously detected orbital period, super-orbital period, and nutation period, as well as a bidirectional spiral jet. The study on its X-ray light variability is helpful for understanding the dynamic process of the system, and the correlations between the different wavebands. In this paper, two time-series analysis techniques, i.e., the Lomb-Scargle periodogram and weighted wavelet Z-transform, are employed to search for the periods in the Swift/BAT (Burst Alert Telescope) (15–50 keV) and RXTE/ASM (Rose X-ray Timing Explorer/All Sky Monitor) (1.5–3, 3– 4, and 5–12 keV) light curves of SS 433, and the Monte Carlo simulation is performed for the obtained periodical components. For the 15–50 keV energy band, five significant periodical components are detected, which are P1(∼6.29 d), P2 (∼6.54 d), P3 (∼13.08 d), P4 (∼81.50 d), and P5 (∼162.30 d). For the 3–5 and 5–12 keV energy bands, the periodical components P3 (∼13 d) and P5 (∼162 d) are detected in both energy bands. However, for the 1.5–3 keV energy band, no significant periodic signal is detected. P5 is the strongest periodic signal in the power spectrum for all the energy bands of 3–5, 5–12, and 15–50 keV, and it is consistent with the previous result obtained from the study of optical light curves. Furthermore, in combination with the radio spiral jet of SS 433, it is suggested that the X-ray and optical variability of P5 (∼162 d) is probably related to the precession of its relativistic jet. The high correlation between the X-ray and optical light curves may also imply that the X-ray and optical radiations are of the same physical origin. P3 shows a good agreement with the orbital period (∼13.07 d) obtained by the previous study, and P2 and P4 are respectively the high-frequency harmonics of P3 and P5. P1 is detected only in the power spectrum of the 15–50 keV energy band, and it is consistent with the nutation period of the system. As the energy of energy band decreases (from hard X-ray to soft X-ray), the number of detected periods becomes gradually less, this result verifies that the radiation in the high-energy band (hard X-ray) comes primarily from the jet, and the radiation in the low-energy band (soft X-ray) may be dominated by the medium around the binary system. The multiple X-ray periods obtained from the present study have provided a reliable basis for the further analysis of the multi-band data of SS 433, and the study on the dynamical mechanism of the system.

DETECTION OF POSSIBLE QUASI-PERIODIC OSCILLATIONS IN THE LONG-TERM OPTICAL LIGHT CURVE OF THE BL LAC OBJECT OJ 287

ABSTRACT The detection of periodicity in the broadband non-thermal emission of blazars has so far been proven to be elusive. However, there are a number of scenarios that could lead to quasi-periodic variations in blazar light curves. For example, an orbital or thermal/viscous period of accreting matter around central supermassive black holes could, in principle, be imprinted in the multi-wavelength emission of small-scale blazar jets, carrying such crucial information about plasma conditions within the jet launching regions. In this paper, we present the results of our time series analysis of the ∼9.2 yr long, and exceptionally well-sampled, optical light curve of the BL Lac object OJ 287. The study primarily used the data from our own observations performed at the Mt. Suhora and Kraków Observatories in Poland, and at the Athens Observatory in Greece. Additionally, SMARTS observations were used to fill some of the gaps in the data. The Lomb–Scargle periodogram and the weighted wavelet Z-transform methods were employed to search for possible quasi-periodic oscillations in the resulting optical light curve of the source. Both methods consistently yielded a possible quasi-periodic signal around the periods of ∼400 and ∼800 days, the former with a significance (over the underlying colored noise) of . A number of likely explanations for this are discussed, with preference given to a modulation of the jet production efficiency by highly magnetized accretion disks. This supports previous findings and the interpretation reported recently in the literature for OJ 287 and other blazar sources.

Vartools: A program for analyzing astronomical time-series data

Abstract This paper describes the Vartools program, which is an open-source command-line utility, written in C, for analyzing astronomical time-series data, especially light curves. The program provides a general-purpose set of tools for processing light curves including signal identification, filtering, light curve manipulation, time conversions, and modeling and simulating light curves. Some of the routines implemented include the Generalized Lomb–Scargle periodogram, the Box-Least Squares transit search routine, the Analysis of Variance periodogram, the Discrete Fourier Transform including the CLEAN algorithm, the Weighted Wavelet Z-Transform, light curve arithmetic, linear and non-linear optimization of analytic functions including support for Markov Chain Monte Carlo analyses with non-trivial covariances, characterizing and/or simulating time-correlated noise, and the TFA and SYSREM filtering algorithms, among others. A mechanism is also provided for incorporating a user’s own compiled processing routines into the program. Vartools is designed especially for batch processing of light curves, including built-in support for parallel processing, making it useful for large time-domain surveys such as searches for transiting planets. Several examples are provided to illustrate the use of the program.

Temporal evolution of long-timescale periodicities in ULX NGC 5408 X-1

Context. NGC 5408 X-1 is one of the few ultraluminous X-ray sources with an extensive monitoring program in X-rays (a temporal baseline of 4.2 yr), making it one of the most suitable candidates to study the long-timescale quasi-periodic oscillations (QPOs). Aims. Previous timing analysis of the Swift data of NGC 5408 X-1 led to detection of multiple periodicities ranging from 2.6 d to 230 d. In this paper, we focus on the statistical significance and the temporal evolution of these periodicities. Methods. A time-series analysis technique in the time-frequency domain, the weighted wavelet Z-transform (WWZ), was employed to identify the periodicities and trace their variations with time. Results. Three periodic components were detected from the WWZ periodogram, corresponding to periods of 2.65$\pm$0.01 d, 115.4$\pm$14.4 d and 189.1$\pm$15.2 d. All three have statistical significance higher than 99.74%. The 2.65-d periodicity is quite stable in the majority of the light curve. The 115-d periodicity is the most prominent but appears variable. The 189-d periodicity is persistent across the whole time coverage. It shows a steadily decreasing trend from the beginning (193 d period) to the end (181 d period). Conclusions. The long-timescale periodicities in NGC 5408 X-1 are most likely of super-orbital origin, and are probably associated with the precession of a warped accretion disc. The disc may have been broken into two distinct planes with different precessing periods, i.e. the 189-d and 115-d periodicities corresponding to the outer and inner disc, respectively.

Evolution of the complicated decaying branch of the very long outburst in XTE J1701-462

I analyze the evolution of the features which occurred on the timescale of weeks in the very long (∼600d) X-ray outburst of the neutron star low-mass X-ray binary XTE J1701-462. I used RXTE/ASM (1.5–12keV) and Swift/BAT (15–50keV) observations for a time-series analysis of the long-term variations. I utilized the means (usually one-day) of intensity I to increase the signal-to-noise ratio. I applied weighted wavelet Z-transform to investigate the cyclic modulation of I. Using the combined data from both satellites, I also calculated the hardness ratio HR=I(15–50keV)/I(1.5–12keV) and investigated its evolution throughout the outburst. Despite the largely different profiles of the light curves in the ASM and the BAT bands especially in the first fourth of the outburst, the profiles of the measures of their scatter (the σresASM and the σresBAT curves) display mutual similarities. Both the σresASM and σresBAT curves achieved their maxima in the primary peak of the light curve which was present only in the ASM band. The formation of the quasi-periodic variations occurred and their approximate cycle-length PC was decided already in the surrounding of this peak when the bolometric luminosity was close to or even exceeding the Eddington limit. The modulation with PC is present in some time segments only in the ASM band, while the intensity variations are always chaotic in the BAT band. Using the results of spectroscopy of Lin et al., I suggests that only multicolor disk, dominant in the ASM band, was involved in this cycle. The existence of this cycle did not depend on the exact type of the Z, so it was independent of the exact conditions in the inner disk region. The length of PC displayed a large and gradual increase from ∼16 to ∼26days with the progress of the outburst. Using models of Foulkes et al., I interpret these variations as a superorbital cycle, caused by tilting and warping of the irradiated disk.

Periodic radio variabilities of the blazar 1156+295: harmonic oscillations

(Quasi)-periodic oscillations of the radio luminosity of a typical blazar 1156+295 were analysed to investigate the dynamic processes associated with the central engine of the active galactic nucleus. Three numerical techniques, the Lomb-Scargle periodogram, the Weighted Wavelet Z-transform and the improved Phase Dispersion Minimization, were used to search for candidate periodicities in the radio light curves of 1156+295 at 14.5, 8.0 and 4.8 GHz. The results of these methods are consistent with the detection of four periodic components with characteristic periods of similar to 1.7 (P-4), similar to 2.4 (P-3), similar to 3.4 (P-2) and similar to 7.5 yr (P-1), which suggest a harmonic relationship in frequency of 4: 3: 2: 1 with f(1) as the fundamental frequency. Except for the fact that P-1 persistently shows in the whole time span, the three others appear intermittent and are only prominent during certain time ranges. The second harmonic mode (P-2) is most powerful at all three observing frequency bands. The multiplicity and harmonic relation of the periodicities in 1156+295 reconfirms that global p-mode oscillations of the accretion disc are coupled to the jet. The oscillation of the disc is likely driven by Kelvin-Helmholtz instabilities in the inner edge of the accretion disc.

Periodic radio variabilities in NRAO 530: a jet–disc connection?

Time series analysis techniques, Lomb-Scargle periodogram and weighted wavelet Z-transform, have been employed to search for year-time-scale periodicities from the radio light curves of a typical blazar NRAO 530. The periodicity analysis using the two methods show consistent results: two strong and persistent periods of similar to 10 and similar to 6 yr are prominent at all three wavelengths; three other weaker periodicities with shorter time-scales (similar to 5, similar to 3.5 and similar to 3 yr) were also seen; in addition, the 14.5-GHz WWZ power spectrum revealed a similar to 2-yr periodic component during the time interval 1983-1990. Statistical significance analysis suggests that these periodicities might result from physically periodic process. The characteristic frequencies of these periodicities seem to have a harmonic relationship, and the fundamental frequency, i.e. the first-order harmonic, is about 0.05 yr(-1) (P-0 = 20 yr). But the fundamental frequency was not pronounced. The multiplicity and apparent harmonic relationship of the periodicities could be interpreted by the global p-mode oscillation of the accretion disc, if the jet and disc are coupled. In this scenario, the periodic fluctuations in the accretion rate consequently lead to the observed periodic variabilities of the radio luminosity.

Confirming the 115.5-day periodicity in the X-ray light curve of ULX NGC 5408 X-1

The Swift/XRT light curve of the ultraluminous X-ray source NGC 5408 X-1 was re-analyzed with two new numerical approaches, the Weighted Wavelet Z-transform and CLEANest, and the results are different from previous studies. Both techniques detected a prominent periodicity with a time scale of 115.5 ± 1.5 days, in excellent agreement with the detection of the same periodicity first reported by Strohmayer. Monte Carlo simulations were employed to test the statisitical confidence of the 115.5-day periodicity, yielding a statistical significance of > 99.98% (or > 3.8σ). The robust detection of the 115.5-day quasi-periodic oscillations, if they are due to the orbital motion of the binary, would infer a mass of a few thousand M☉ for the central black hole, implying there is an intermediate-mass black hole in NGC 5408 X-1.