Jurkevich Method Research Articles

Optical and γ-ray variability analysis of BL Lacertae object TXS 1902+556

ABSTRACT The variability data for the BL Lacertae object TXS 1902+556 in the optical and $\gamma$-ray wavebands were obtained from the 0.76-m Katzman Automatic Imaging Telescope and the Fermi Large Area Telescope (Fermi-LAT), covering periods of 14.4 and 14.7 yr, respectively. The variability properties were systematically analysed, with particular emphasis on the first comprehensive investigation of radiation variation in the optical waveband. Four well-established techniques were employed for this purpose: the Lomb–Scargle periodogram, REDFIT program, Jurkevich method, and discrete correlation function (DCF) approach. The optical waveband exhibits quasi-periodic oscillations (QPO) with a time-scale of $P_{\rm O}=276.8\pm 6.1$ d at a significance level $3.87\sigma$, while the $\gamma$-ray waveband does not exhibit any significant periodicity. However, it should be noted that the QPO time-scale is consistent with the Sun-gaps in the optical light curve within 2$\sigma$ uncertainties. The optical QPO behaviour is most likely attributed to the helical motion of the jet driven by the orbital motion in a supermassive black hole binary system. Moreover, we have provided an explanation for the absence of QPO in the $\gamma$-ray light curves. Furthermore, utilizing the DCF method, a weak correlation between the variability in the optical and $\gamma$-ray wavebands was observed, suggesting that the emission of TXS 1902+556 may be generated through a combination of synchrotron self-Compton (SSC) and external Compton (EC) processes, or a leptonic–hadronic hybrid process.

A radio quasi-periodic oscillation in the blazar PKS J2156−0037

Abstract The detection of quasi-periodic oscillations (QPOs) in blazar light curves is crucial for understanding their nature and fundamental physical processes. PKS J2156−0037 (z = 0.495), a blazar monitored by the Owens Valley Radio Observatory (OVRO) 40-m radio telescope, is the subject of this study. We searched for the presence of QPOs in the publicly available 15 GHz light curve of PKS J2156−0037, spanning 2008 January to 2020 January. We employed four well-established methods (the Jurkevich method, the generalized Lomb–Scargle periodogram, the weighted wavelet Z–transform, and the REDFIT method) that offer complementary strengths for robust periodicity detection. A consistent and statistically significant QPO signal was detected with a periodicity of around 611 d (at least 4.26σ local significance) and a global significance exceeding 99.83 per cent (or 2.92σ) based on Monte Carlo simulations with 105 simulated light curves (assuming underlying red noise processes). This is the first reported detection of such a variability feature in this object. The possible physical mechanisms responsible for radio QPOs in blazars are discussed briefly.

Optical Monitoring and Variability Analyses of the FSRQ 3C 454.3

Based on the database monitored by the 1.26 m National Astronomical Observatory–Guangzhou University Infrared/Optical Telescope, we studied the optical variabilities of FSRQ 3C454.3. The monitoring period was from 2016 October 17 to 2018 December 14, and there were 6701 observations covering the g, r, and i bands (2196 at the g band, 2214 at the r band, and 2291 at the i band). (1) The maximum variabilities were Δm g = 2.806 ± 0.124 mag at the g band; Δm r = 2.365 ± 0.160 mag at the r band; and Δm i = 3.126 ± 0.070 mag at the i band. (2) Among the gri intraday lightcurves, there are 172 portions of the data sets showing intraday variability (IDV). The distributions of IDV timescales (ΔT) can be profiled by a three-order Gaussian function, with the center values ΔT 1 = 17.18 minutes, ΔT 2 = 34.91 minutes, and ΔT 3 = 68.92 minutes. These results imply that the origin of IDVs is very complicated. (3) Based on the IDV timescales, we obtained the emission size R ≤ 7.17 × 1015 cm, fixed the broad-line region and modeled the spectral energy distributions. (4) We used the Jurkevich method, red-noise fitting, and the weighted wavelet Z-transform to analyze the long-term variabilities and obtained indications of a possible period of P = 2.92 ± 0.85 yr, and used the binary black hole system to explain this period. Based on the long-term period, we can estimate the time until merger of the binary black hole, t merge = 6.69 × 103 yr, and the luminosity of gravitational waves, L G = 1.56 × 1048 erg s−1.

Quasi-periodic Oscillation Analysis for the BL Lacertae Object 1823+568

We studied the optical band periodic variability of 1823+568 using the Jurkevich method, the Lomb–Scargle periodogram and the REDFIT38 software, and found evidence of quasi-periodic oscillation. An unprecedented variability with period days was identified by three different analysis methods. This quasi-periodic variability most likely results from nonballistic helical jet motion driven by the orbital motion in a binary black hole system. Considering the light-travel time effect, the real physical period is P d = 67.1 yr. Moreover, we estimated that the primary black hole mass is M ≃ 1.92 × 109 M ⊙ to 3.43 × 109 M ⊙.

Statistical Characteristics of Sunspot Umbra Oscillations in the Ca Bandtwo

A group of successive evolutionary images of a sunspot were observed on 4th March 2014 at the Ca II H (396.85nm) line by the telescope on board of the Hinode satellite. The calculated oscillation period of the sample point in the umbra is 149.75s by using the Jurkevich (JK) method. A proper averaged value of the intensity profile is selected as the steady background radiation, then the distribution of the extreme values of oscillations in the umbra is analyzed by a statistical method. The results show that the valley values follow a normal distribution, while the peak values satisfy a partial normal distribution. The distribution of these extreme values indicates that the 3min oscillation of the umbra may be caused by the propagation of a traveling wave with a period of about 5min in the umbra. The variation of light intensity caused by the traveling wave may be proportional to the square of the displacement of the traveling wave, resulting in a 3min period of the light intensity, which is one half of the period of traveling wave.

Optical monitoring of BL Lac object S5 0716+714 and FSRQ 3C 273 from 2000 to 2014

Using the 1.56m telescope at the Shanghai Observatory (ShAO), China, we monitored two sources, BL Lac object S5 0716+714 and Flat Spectrum Radio Quasar (FSRQ) 3C 273. For S5 0716+714, we report 4969 sets of CCD (Charge-coupled Device) photometrical optical observations (1369 for V band, 1861 for R band and 1739 for I band) in the monitoring time from Dec.4, 2000 to Apr.5, 2014. For 3C 273, we report 460 observations (138 for V band, 146 for R band and 176 for I band) in the monitoring time from Mar. 28, 2006 to Apr. 9, 2014. The observations provide us with a large amount of data to analyze the short-term and long-term optical variabilities. Based on the variable timescales, we can estimate the central black hole mass and the Doppler factor. An abundance of multi-band observations can help us to analyze the relations between the brightness and spectrum. We use Gaussian fitting to analyze the intra-day light curves and obtain the intra-day variability (IDV) timescales. We use the discrete correlation function (DCF) method and Jurkevich method to analyze the quasi-periodic variability. Based on the VRI observations, we use the linear fitting to analyze the relations between brightness and spectrum. The two sources both show IDV properties for S5 0716+714. The timescales are in the range from 17.3 minutes to 4.82 hours; for 3C273, the timescale is 35.6 minutes. Based on the periodic analysis methods, we find the periods P(V) = 24.24 days, P(R)=24.12 days, P(I)=24.82 days for S5 0716+714, and P = 12.99, 21.76 yr for 3C273. The two sources displayed the "bluer-when-brighter" spectral evolution properties. S5 0716+714 and 3C 273 are frequently studied objects. The violent optical variability and IDV may come from the jet. Gaussian fitting can be used to analyze IDVs. The relations between brightness (flux density) and spectrum are strongly influenced by the frequency.

The nearly periodic fluctuations of blazars in long-term X-ray light curves

By means of structure function method, we have analyzed 20 blazars observed by the Rossi X-Ray Timing Explorer (RXTE) to search for possible variability period. There are the year-like periodic values in 11 of these blazars. The year-like periodicities in AO 0235+164, Mrk 501, 3C 273 and PKS 1510-089 are also found by the discrete correlation function method, the Jurkevich method and the power spectrum method. AO 0235+164, Mrk 501 and 3C 273 have possible nearly periodic values of about 370 days, 630 days and 370 days, respectively. PKS 1510-089 has two nearly periodic components, about 230 and 330 days. The year-like periodicities could be explained in the framework of a binary black hole system. The turbulence behind a shock may also give rise to the year-like periodicities, dominated by the dominant eddies’ turnover times. Also, the year-like periodicities may be from the interplay of a shock with essentially helical structures wrapping around a relativistic jet.

Multiband Variability Analysis of 3C 454.3 and Implications for the Center Structure

We have analyzed the light curves of 3C 454.3 at the infrared, optical, soft X-ray (0.3–10 keV), and γ-ray (0.1–300 GeV) waveband, and found the evidence of quasi-periodicity. The light curves show that 3C 454.3 is a strongly active object. A period signal of P = 210.8 ± 12.1 days is confirmed by two methods consistently: the Lomb-Scargle periodogram and the Jurkevich method. The variations of the infrared, optical, soft X-ray, and γ-ray are well correlated, which suggests that these seven band emissions originate from the same population of electrons in the jet. The multifrequency variations in the emission fluxes of 3C 454.3 may be caused by the nonballistic helical motion of emitting components in the jet, which has the precession and the helical magnetic field. Moreover, these provide some evidence for the existence of a supermassive binary black hole (SMBBH) system in the center of 3C 454.3.

Long-term optical and radio variability of BL Lacertae

Well-sampled optical and radio light curves of BL Lacertae in B,V,R,I bands and 4.8, 8.0, 14.5GHz from 1968 to 2014 were presented in this paper. A possible 1.26±0.05yr period in optical bands and a 7.50±0.15yr period in radio bands were detected based on discrete correlation function, structure function as well as Jurkevich method. Correlations among different bands were also analyzed and no reliable time delay was found between optical bands. Very weak correlations were detected between V band and radio bands. However, in radio bands the variation at low frequency lagged that at high frequency obviously. The spectrum of BL Lacertae turned mildly bluer when the object turned brighter, and stronger bluer-when-brighter trends were found for short flares. A scenario including a precessing helical jet and periodic shocks was put forward to interpret the variation characteristics of BL Lacertae.

Light Curve Periodic Variability of Cyg X-1 using Jurkevich Method

The Jurkevich method is a useful method to explore periodicity in the unevenly sampled observational data. In this work, we adopted the method to the light curve of Cyg X-1 from 1996 to 2012, and found that there is an interesting period of 370 days, which appears in both low/hard and high/soft states. That period may be correlated with black hole physics and accretion disk geometry.

Optical monitoring of the Seyfert galaxy NGC 4151 and possible periodicities in its historical light curve

We report B, V and R band CCD photometry of the Seyfert galaxy NGC 4151 obtained with the 1.0 m telescope at Weihai Observatory of Shandong University and the 1.56 m telescope at Shanghai Astronomical Observatory from 2005 December to 2013 February. Combining all available data from literature, we have constructed a historical light curve from 1910 to 2013 to study the periodicity of the source using three different methods (the Jurkevich method, the Lomb-Scargle periodogram method and the Discrete Correlation Function method). We find possible periods of P1 = 4 ± 0.1, P2 = 7.5 ± 0.3 and P3 = 15.9 ± 0.3 yr.

Optical quasi-periodic oscillation and color behavior of blazar PKS 2155–304

PKS 2155–304 is a well studied BL Lac object in the southern sky. The historical optical data during different periods have been collected and compiled. Light curves spanning 35 yr have been constructed. The R-band light curve has been analyzed by means of three methods: the epoch folding method, the Jurkevich method and the discrete correlation function method. It is derived that there is an evident periodic component of 317 d (i.e. 0.87 yr) superposed on a long-term trend with large-amplitude variation in the light curve. The variability of this source is accompanied by a slight color variation, and the brightness and color index are correlated with each other. On a long-term time scale, PKS 2155–304 exhibits a tendency of bluer-when-brighter, which means the spectrum becomes flatter when the source brightens.

The Long-term Light Variation of BL Lac Object 1ES 1959+650

According to the data of optical observations of the Tuorla Observatory in Finland, using the power spectrum method, DCF (Discrete Correlation Function) method, and Jurkevich method, respectively, we analyzed the periodicity of the long-term light variation of the BL Lac object 1ES 1959+650, and obtained its light period to be P =1.4±0.3 yr. Assuming that the origin of the periodicity is concerned with the accretion disk, we obtained the region where the instability of this source occurs being R =9.65 Rg, here Rg represents the Schwarzschild radius.

The optical periodic analysis of BL Lac object AO 0235+164

BL Lac object AO 0235+164 is a well-known object. We collect a large number of effective observation in B, V, R and I band from historical literatures. The possible periods are analyzed by means of discrete correlation function (DCF) method, structure function (SF) method and Jurkevich (J-K) method. The results show that there are possible periodic variations of 2.63–2.66 years in B band, 2.79–2.84 years in V band, 2.57–2.87 years in R band, 2.62–2.88 years in I band, respectively.

Optical variability of Mrk 421

We observed Mrk 421 in V and R band using the 1.0 m telescope at Weihai Observatory of Shandong University since 2009 April to 2012 May. The available historical data in B and V band were also assembled for constructing light curves. The brightness of Mrk 421 ranges from 11.40 to 16.14 in the B band light curve, and from 11.38 to 14.56 in the V band. Analyses with the Jurkevich method and the structure function method showed a possible period of about 1.36 years for its long periodic variability. This period could be explained by a close binary black hole system (BBHS) model with a primary black hole mass of 1.70×108 M ⊙ and a secondary ∼(0.49–2.9)×107 M ⊙. We showed the color variability of Mrk 421, a bluer when brighter behavior during its lower state. Analyses of spectral index variations show that only a host galaxy contribution is not sufficient to explain the spectral index variations in Mrk 421, and some intrinsic mechanism is needed.

Long-term Periodicity Analysis of Polarization Variation for Radio Sources

We use the database of University of Michigan Radio Astronomy Observatory (UMRAO) at three radio bands (4.8, 8 and 14.5 GHz) to analyse the long-term polarization variation in search of the possible periodicity. Using the power spectral analysis method (PSA), the Jurkevich method and the discrete correlation function (DCF) method, we find that there are 16 sources lying in periodicity. The results show the astrophysically meaningful periodicity covering 2.1 years to 16.2 years at 4.8 GHz, 2.8 years to 16.3 years at 8 GHz, and 1.8 years to 16.6 years at 14.5 GHz.

Methods for the Quasi-Periodic Variability Analysis in Blazars

In this work, four methods are introduced to analyse the unevenly sampled data. The four methods are power spectral density, auto-correlation function, structure function and Jurkevich method. Some interesting mathematical links are derived amongst the four methods. These links show that the four methods have the same performance. For the Jurkevich method, the effect of the width of bins is apparent. If the width is half the time scale, the method has better performance.

Long term periodicity analysis of the spectral index of 2251+158

We analyze the radio spectral index of blazars from the University of Michigan Radio Astronomy Observatory database, and find that there exists quasi-periodic activity in 2251+158. The long-term periodicity analysis is accomplished by three methods, which are the Jurkevich method (Jurkevich), the discrete correlation function (DCF), and the Periodogram method (P). The results show that 2251+158 has two strong periodicities, which are P1 = 6.3 ± 1.1 yr and P2 = 3.8 ± 1.2 yr.

Long-term variation time scales in OJ 287

The light curve data from 1894 to 2008 are compiled for the BL Lacertae object OJ 287 from the available literature. Periodicity analysis methods (the Discrete Correlation Function-DCF, the Jurkevich method, the power spectral (Fourier) analysis, and the CLEANest method) are performed to search for possible periodicites in the light curve of OJ 287. Significance levels are given for the possible periods. The analysis results confirm the existence of the 12.2±0.6 yr time scale and show a hint of a ∼53 yr time scale. The 12.2±0.6 yr period is used as the orbital period to investigate the supermassive binary black hole system parameters.

PERIODICITY ANALYSIS OF THE SPECTRAL INDEX IN 3C 273 AND 3C 446

In this work, we used the preliminary data of University of Michigan Radio Astronomy Observatory (UMRAO) for the spectral index calculation for two blazars, 3C 273 (1226+023) and 3C 446 (2223-052), and found that the spectral indices are variable. Therefore, we used three methods (Jurkevich method (J), the discrete correlation analysis (D), and the Periodogram method (P)) to investigate the period in the spectral index variation curves. The results show that 3C 273 has a quasi-period of 8.8 ± 1.3 yr , and 3C 446 has a period of 5.8 ± 1.2 yr .