Two Repeated Transient Quasiperiodic Oscillations in the γ-Ray Emission from the Blazar 3C 279

In this work, we report for the first time two repeated transient quasiperiodic oscillations (QPOs) in the γ-ray light curve of the TeV blazar 3C 279. We search for the periodicity in the light curve and estimate its confidence level using the weighted wavelet Z-transform, the Lomb–Scargle periodogram, and the REDFIT techniques. The main results are as follows: (1) a QPO of ∼33 days (>2.5σ) is found during the flare of 117 days (MJD 55008–55125) from 2009 June to November. Interestingly, the same QPO (∼39 days) reappeared in the flaring duration from MJD 59430 to 59585, with the confidence level of >4σ. (2) Another transient QPO of ∼91 days with a significance of >3.8σ is found during a period with 455 days (MJD 58430–58985) from 2019 February to 2020 May. Under the premise of considering the QPOs reported in the literature, the QPO of ∼40 days is repeated three times and the QPO of ∼91 days is repeated twice. We discuss several physical models explaining the QPOs of this blazar. Our study may suggest that the two QPOs originate from the twin jets of the binary black holes at the center of 3C 279. The repeated occurrence of QPOs of a similar scale strongly supports the geometric scenario of a blob spiraling within the jet. Furthermore, the hypothesis of a sheath in the jet may also be a potential explanation for the repetitive γ-ray flare patterns observed in the light curve.


Introduction
Blazars belong to a subgroup of active galactic nuclei (AGNs), with relativistic jets almost aligned with Earth.Typically, blazars are classed into BL Lacertae objects and flat-spectrum radio quasars (FSRQ) based on the width of the emission line in their spectrum.Moreover, blazars exhibit highly distinctive radiation traits, capable of emitting across all the electromagnetic (EM) spectrum, from radio waves to highenergy γ-rays (Urry & Padovani 1995), and flux variabilities on various timescales.This provides sufficient conditions for the study of flux variability.The variability of light curves provides important information for revealing the nature of blazars.In general, blazars emit radiation in the complete EM spectrum depicting extremely irregular and erratic variability behaviors in their flux.However, as the level of observation continues to improve, an increasing number of possible periodic variations have been discovered in the light curves of blazars (e.g., Sandrinelli et al. 2016;Chen et al. 2022;Das et al. 2023;Gong et al. 2023;Ren et al. 2023), such as quasiperiodic oscillations (QPOs).QPOs will help us to understand the mechanism in the innermost regions of blazars.There are many types of QPOs, from the day-like to the year-like timescales, and different types have different physical mechanisms.Sarkar et al. (2020) and Roy et al. (2022) reported the day-like QPO, and they believed that the magnetic reconnection event in the jet may be the cause of this kind of QPO.For the month-like QPO, there are several possible physical mechanisms, for example the motion of the relativistic blob in the helical jet (Zhou et al. 2018) and the kink instability in the relativistic jet (Dong et al. 2020).To date, many physical explanations have been proposed for the year-like QPO.The most famous of these is the binary supermassive black hole (SMBH), and the most famous binary SMBH system is OJ 287 (Komossa et al. 2023).OJ 287 has an orbital period of 12.062 yr and is decaying at a rate of 36 days per century (Valtonen et al. 2018).
The FSRQ 3C 279 whose redshift is 0.538 is known for its rapid variations in brightness.3C 279 is not only the first detected apparent superluminal velocity quasar (Whitney et al. 1971), but also the first detected FSRQ emitting high-energy γray (Hartman et al. 1992).Early high-energy γ-ray telescopes could not detect 3C 279, and it was not until 1991 that 3C 279 was detected by the Energetic Gamma Ray Experiment Telescope as a high-energy phenomenon with an energy range from 30 MeV to over 5 GeV (Hartman et al. 1992).Since the Fermi satellite's operation (Atwood et al. 2009), 3C 279 has also been continuously reported to exhibit high-energy and even very high-energy behavior (e.g., Morozova et al. 2011;Roustazadeh & Böttcher 2012;Adams et al. 2022).Oke (1967) reported that the brightness of 3C 279 changed by 0.25 mag in 24 hr, and compared to 1966, the visual magnitude has changed by ∼2 mag.Interestingly, during 2001-2002, the optical R band actually changed by more than 0.5 mag in 24 hr (Kartaltepe & Balonek 2007).There are many similar reports (e.g., Ackermann et al. 2015;Prince 2020;Rajput et al. 2020) on the variability of 3C 279, which indicates that this source has very strong variability.Furthermore, the multiple-wavelength temporal correlation and variable behavior of 3C 279 has been widely studied.Hartman et al. (2001) conducted a correlation analysis on the light curves of 3C 279 in 1999 January-February and 2000 January-March in the optical, X-ray, and γ-ray, and found that the three are not consistent patterns.Zhang et al. (2021) conducted a correlation analysis on optical, X-ray, and gamma-ray light curves under the long timescale.The research results indicate a strong correlation between X-ray and γ-ray light curves, whereas their correlation with the optical band appears to be weaker.
Meanwhile, Zhang et al. (2021) also mentioned that 3C 279 exhibits a 5.6 yr QPO in the 32 yr long optical R-band light curve.This is not the first time that 3C 279 has been reported to have a QPO.As early as 1999, Fan (1999) reported that 3C 279 had a QPO of 7.1 ± 0.44 yr in the K band, and they speculated that this was caused by the instability of a slim accretion disk.The year-like QPO of 3C 279 is reported by Sandrinelli et al. (2016).Ren et al. (2023) reported two QPOs (101 and 40 days) in the γ-ray light curve during MJD 57700-58400 through continuous wavelet transform.They also estimated the confidence of these two QPOs by simulating light curve's power spectral density (PSD) and probability density function, indicating that both QPOs are reliable.
It is common for different types of QPOs to exist in a single source.Gong et al. (2023) searched for the QPO behavior of S4 0954 + 658 in the γ-ray light curve.It turns out that S4 0954 + 658 has two QPOs (66 and 210 days), which are caused by a plasma blob moving helically inside the jet.Another typical source with multiple QPOs is S5 0716 + 714.Hong et al. (2018) reported that this source was detected in the optical I band with a QPO of about 50 minutes; Chen et al. (2022) found a QPO of 31.2 days in the γ-ray light curve of this source.Then, Li et al. (2023) discovered a QPO of 960 days.The physical scenario corresponding to each QPO may be different.
In addition, "repeated patterns" have also been studied in 3C 279 (see Section 3 for details).We analyzed 10 out of the 35 bright sources mentioned in literature (Ren et al. 2023; these 10 sources have multiple QPOs).Here, we focus on discussing 3C 279 because we found QPOs in its repeating patterns.Aiming to search for the repeated QPO signals of blazar 3C 279 in the γ-ray band based on the 15 yr data provided by Fermi Large Area Telescope (Fermi-LAT).In Section 2 of this paper, we discuss the analysis procedures for the γ-ray light curve and the results obtained through various methods in searching for periodic signals.In Section 3, we discuss the plausible physical scenarios for the repetitive occurrence of these two types of transient QPOs.

Fermi-LAT Data
Fermi-LAT5 is an imaging, wide-field-of-view, high-energy γ-ray telescope covering the energy range from below 20 MeV to over 300 GeV.In 3 hr, Fermi-LAT can make a complete observation of every point in the sky.In order to obtain a suitable light curve, we downloaded LAT events in the mission elapsed time (MET) 239557417-702000005 (∼14.5 yr) from the Fermi PASS 8 database.In the energy range from 100 MeV to 300 GeV, we selected the "SOURCE" class (evclass = 128, evtype = 3) registered events from a 15°circular region of interest centered on the source location (R.A.=194°.042, decl.=−5°.789).A 90°zenith angle was set to avoid interference from photons around the Earth.Standard filters "( DATA_QUAL > 0) &&( LAT_CONFIG = 1)" were used to select a good time interval and high-quality data.The input XML model file contains two components: Galactic (gll_iem_v07) and isotropic extragalactic (iso_P8R3_SOURCE_V3_v1.txt).The processed file contains time, flux, flux error and test statistic (TS) value.3C 279 is a bright source, so we choose flux with TS greater than 25.
We visually identified sinusoidal-like periodic variations and fitted them using a simple sine function.Ultimately, we observed pronounced periodic variations in three time intervals for 3C 279, as depicted in Figure 1.Finally, We obtained a light curve (5 day bin and 3 day bin) with TS 25 (5σ), as shown in Figures 1, 2, and 3.The QPOs previously published in 3C 279, which are of short-term type, and the QPOs reported in this study are shown in Table 1.

QPO Signal Analysis and Results
To study the periodicity of 3C 279 in the γ-ray light curve, three methods are commonly used to analyze the QPO signal: the weighted wavelet Z-transform (WWZ), the Lomb-Scargle periodogram (LSP), and REDFIT.The LSP method is used in the field of astronomy because it can deal with irregularly sampled data (VanderPlas 2018).The LSP method converts the data set into the frequency domain, uses the least-squares method to fit a series of linear combinations of trigonometric functions, and the power spectrum of the light curve quantifies the contribution of each frequency to the total signal (Lomb 1976;Scargle 1982;VanderPlas 2018).At this point, the importance of the peak needs to be quantified.Here we use false-alarm probability (FAP) to evaluate the confidence level of the peak (Horne & Baliunas 1986).The meaning represented by the value of FAP is the probability of generating a peak of similar magnitude to the original data set in a data set without signal.In other words, the value of (1−FAP) represents the probability that the peak is not caused by noise.According to the literature, FAP , where N is the number of independent frequencies in the frequency range (i.e., trial factor).The topic of independent frequency estimation is not yet fully resolved, and some methods have been proposed in the literature to address this issue (Horne & Baliunas 1986;Jetsu & Pelt 1999;Zechmeister & Kürster 2009;Olspert et al. 2018;VanderPlas 2018) days) (where 10 days is close to the data collection pace, i.e., 5 days, "x" is half the total length of the data, and δf is the frequency resolution, determined by the total length of the data.).By using the above method, we calculate that the N corresponding to EP1,EP2,and EP3 are 29,17,and 31,respectively.Based on the fact that the width of any peak in the periodogram actually reflects the length of the monitoring, when the QPO is significantly larger than the intrinsic width, the uncertainty of the Gaussian fit may be related to the actual uncertainty of the period.Therefore, we fit the peaks with Gaussian functions and indicate the uncertainty of the peaks using the full width at half maximum (FWHM).The LSP calculation result of the light curve in the EP3 is shown in the panel (b) of the Figure 2 where the green dotted line represents  the FAP = 0.01%.It is obvious that there is a peak that represents the QPO of 38.8 ± 3.1 days higher than 4σ.Similarly, the panel (b) of Figure 3 indicates the confidence level of the peak (32.4 ± 3.9) is higher than 2.5σ for light curve in the EP1.For the light curve of in the EP2, the LSP calculation result is shown in the panel (b) of Figure 4.The orange dotted line in Figure 4 shows the FAP = 0.01%, and the confidence level of the peak (91 ± 6.5 days) is higher than 4σ.
The WWZ (Foster 1996) method converts the data into time domain and frequency domain, and convolutes the light curve with the kernel related to time and frequency (Sarkar et al. 2021).The WWZ map is given by , 1 and the f, the complex conjugate of the f * , is as follows: where the τ is the time shift and ω is the frequency.Assuming there are underlying periodic signals in the data set, WWZ will provide the size and time range of the possible periodic characteristics.Moreover, the power value of WWZ will decrease as the periodic signal weakens.We used the WWZ method to analyze the γ-ray light curve of 3C 279, and obtained the power spectrum color scale diagrams of three time epoch.Therefore, in the panel (c) of Figure 2 it is strongly illustrated that there is a 39.4 ± 2.8 days QPO in the EP3.The WWZ power spectrum of the light curve in the EP1 is shown in the panel (c) of Figure 3 that indicates the existence of a QPO for 33 ± 2.1 days; In addition, in the panel (c) of Figure 4 it is  strongly illustrated that there is a 91 ± 6.5 days QPO in the EP2.The third method, named REDFIT, is based on LSP and is used to estimate confidence level by assuming red noise as autoregressive of the first order.Since the emission of AGNs is usually autoregressive, it is allowed to use a first-order autoregressive (AR1) process to evaluate the red-noise spectrum.At the same time, in the process of AR1, we can also detect the credibility of time-series flux peaks in the background of red noise.We utilized the "REDFIT3.8e"6algorithm to estimate the frequency spectrum of the light curve, with a parameter selection of n50 = 0 and a window choice of Welch.As shown in the panel (a) of Figure 4, there is a peak (91.8 ± 9.2 days) that exceeds the 99% confidence level (it is worth noting that the highest confidence level provided by the algorithm is 99%).Similarly, the right panel and left panel in Figure 5 indicate the confidence level of the peak (40 ± 4.9 days and 34.8 ± 6.6 days) is higher than 99%.
The QPOs in light curves may not be generated by the true source.For instance, the statistical characteristics of a large number of light curves suggest that AGNs exhibit red-noiselike behavior that could give rise to spurious QPOs, meaning that QPOs could simply be a red-noise signal.Additionally, the instability of light-curve sampling (such as weather and seasonal changes) can also generate false QPOs.Therefore, we must perform a confidence level test on the obtained QPO signal.We determine the significance of periodic signals through simulating light curves.The specific steps are as follows: first, we ensure that the generated light curves are  1) spectrum.The blue dashed line, green dashed line, and purple dashed line represent confidence curves at 90%, 95%, and 99%, respectively.Panel (b): the power spectrum of the light curve in EP2.The black solid line is the power spectrum, and the red, blue, green, purple, and orange dashed lines indicate the confidence level of 95% (2.5σ), 99.7% (3σ), 99.98% (3.8σ), 99.99% (4σ), and FAP =0.01%(4σ), respectively.Panel (c): WWZ map of the light curve in EP2.Panel (d): the black solid line shows the time-averaged WWZ.The green, blue, purple, and red dashed lines represent the confidence level of 95% (2.5σ), 99.7% (3σ), 99.98% (3.8σ), and 99.99%(4σ).contaminated by red noise at the same level as the original data.Then, we calculate the PSD of each light curve.Finally, significance curves are calculated by counting the PSD data points at each frequency (Emmanoulopoulos et al. 2013;Zhang & Wang 2022).We model the PSD of the light curves and compared to a pure power law, a smooth bending power law can more reasonably model the red-noise PSD (González-Martín & Vaughan 2012; Chen et al. 2022).The form of the smooth bending power law can be expressed as where the model parameters A, α, f bend , β, and C are the normalization, low-frequency slope, bend frequency, highfrequency slope, and Poisson noise, respectively (Emmanoulopoulos et al. 2013).We use the maximum likelihood estimation method to obtain the corresponding PSD parameters, as shown in Table 2. Based on the above model, we can simulate a large number of artificial light curves, and obtain the PSD for each artificial light curve through the aforementioned LSP periodic analysis.Finally, we simulated 10 4 artificial light curves using the "DELightcurveSimulation"7 Python code.To obtain the significance curves, we calculated the PSD for each artificial light curve and the results are as follows: (1) the peak of the spectrum of light curve in EP1 is greater than the 99% (2.5σ).
(2) the peak of the spectrum of light curve in the EP3 is greater than the 99.99% (4σ) confidence level (panels (b) and (d) in Figure 2).(3) the light curve in the EP2, the peak of the spectrum of both WWZ and LSP (panels (d) and (b) in Figure 4) is greater than the 99.98% (3.8σ) confidence level.
Therefore, in the light curve of 3C 279, the ∼39 and ∼91 days QPOs have a high confidence level.

Discussion and Conclusions
We collected and processed the γ-ray light curve of the blazar 3C 279 provided by Fermi-LAT during MET 239557417-702000005 (∼14.5 yr).The results indicate that there is a similar QPO (∼33 and ∼39 days) during two flare periods, and after one strong flare, there is also an other QPO (∼91 days).Confidence test results showed that the QPO at ∼91 days exceeded a confidence level of 3.8σ, the QPO at ∼39 days exceeded a confidence level of 4σ, and the confidence level for the QPO at ∼33 days was approximately 2.5σ.
Fermi-LAT provided potential spurious QPOs8 (among which are ∼30 and ∼91 days signals) in the light curve and identifies possible causes for their generation.The Moon is a bright γ-ray source and its orbital period is 27.32 days.If the line of sight is close to the Moon during observations, γ-ray emitted from the Moon could potentially contaminate the light curve, leading to the presence of month-like periodicity in the  Note.In which, we use the R-squared value to characterize the goodness of fit.
obtained data.If the month-like periodicity were caused by the Moon, it should be persistent rather than transient.Additionally, we collected spectral indices for three periods, as shown in Figure 6.As stated by Wang & Jiang (2024), the variation in spectral indices reflects the activity of the source; thus we believe the light curve is generated by the source, rather than being caused by lunar effects.Furthermore, with regards to the ∼91 days QPO, Fermi-LAT has stressed that it arises from certain positions used for aperture photometry and located close to bright sources.The data considered in this work were obtained through likelihood analysis, and therefore do not exhibit the aforementioned situations.In addition, random processes can also produce pseudoperiods, but these false periods usually occur less than three cycles.When it reaches four cycles, it may be a potential signal; when it reaches five cycles, the signal is considered unlikely to be produced by a random process (Vaughan et al. 2016).Although the QPOs found during both flares were of four cycles, a QPO with similar value and four cycles has already appeared once in this source (QPO: 40 ± 8 days).Within the error range, we consider the three QPOs (40 ± 8, 33 ± 2.1, and 39 ± 2.8 days) are the same transient QPO.Therefore, this type of QPO appears three times in the entire light curve and this signal is highly likely to be a genuine physical signal.At the same time, the other QPO with a value of 91 days and five cycles, it is reasonable to consider them as genuine physical signals.
Next, based on the assumption that QPOs originate from central activities, we will discuss several possible mechanisms.One physical mechanism for generating QPO is the binary SMBH.When the secondary black hole periodically crosses the accretion disk of the primary black hole, it manifests as periodic variations in the light curve.Due to the presence of a secondary black hole, the variation in the relative motion speed of the material in the jet with respect to the observer can also lead to the generation of QPOs (O'Neill et al. 2022).The Lense-Thirring precession of accretion disks also cause the QPO signal.Furthermore, the P-mode oscillation of the accretion disk triggers quasiperiodic outbursts of the jet, generating a series of proportionate QPOs (see Liu et al. 2006;Wang et al. 2014).The mechanisms listed above can all explain long-term QPOs quite well.However, the repeated QPOs reported in this paper are short-timescale.As mentioned earlier, the set of two repeated QPOs with a period of several dozen days is a specific phenomenon that is found for the first time.It is no longer suitable and accurate to explicate with the models of a single QPO or the parsec-scale binary SMBH with a stable period of few hundred days.Building upon existing physical models (such as the binary black hole model, the sheathed jet hypothesis, and the helical motion of blobs within the jet), we consider a model that can simultaneously account for the repetitive occurrence of both sets of QPOs.
First of all, the GeV γ-ray radiation is triggered through the inverse Compton scattering (IC) between keV X-ray and relativistic electrons, where prolific high-energy photons of keV X-ray inherit a large fraction of energy from the relativistic electrons.The high-energy photons propagate along the jet and are eventually observed by us.We assume that γ-ray QPO originates from the jet, and the repetition of γ-ray QPO is related to the properties of the jet.If the research object is a binary black hole and each black hole making up the binary black hole system has a jet, then the entire system can produce two sets of reproducible QPOs.For the subject of this study, Qian et al. (2019) previously reported that the nucleus of 3C 279 is likely a binary black hole, with each black hole having a jet.At the same time, Dmytriiev et al. (2023) proposed that the high-energy radiation from 3C 279 is consistent with the lepton model of IC scattering.Here, for the physical properties of the jet, we consider two physical structures.
In the first structure, we consider that blobs within the jet undergo a helical motion.If different parts of the helical jet are at different angles to our line of sight, even if the radiation intensity of the jet remains unchanged, the effective radiation intensity in the line-of-sight direction will vary with the angle, causing flux variations to be observed (Zhou et al. 2018).Therefore, the periodic changes in the light curve that we observe are likely due to periodic changes in the viewing angle.The viewing angle(θ obs ) can be expressed as where f the is elevation angle of the blob's helical trajectory, ψ is the angle between the line of sight and the central axis of the jet, and P obs is the observed period in the light curve.
The relativistic effect and the Lorentz enhancement ) effect cause P obs to be much smaller than P rf .So the relationship between the P obs and the actual physical period (P rf ) is expressed as The value of f is between 0°and 5°.According to the classic value of blazar, we choose f = 2°, ψ = 5°, and the value of Γ is 15 (Jorstad et al. 2004).Therefore, we can calculate that in the EP1, EP2, and EP3, the real periods corresponding to the observed periods are 12. 99, 38.14, and 16.35 yr.In the improved model, the blob moves helically in the curved jet, at this time the angle ψ will no longer be a constant value, but time-dependent ψ(t) (Sarkar et al. 2021;Roy et al. 2022).In our QPO timescale, fluctuations in ψ have almost negligible effect on the value.However, due to the difference in inclination, this will cause a sudden increase (or decrease) in the flux.This may also explain the increased flux of the light curve of 3C 279 in the first cycle of EP1, the first cycle of EP2, and the second cycle of EP3.
In the second structure, we consider that there is the sheath layer within the jet.According to Marscher et al. (2010), as the radiation feature moving within the fast core of the jet traverses 8. DCFs of the light curves between EP1, Ren, and EP3.The specific light-curve pair is labeled in the upper-right corner of each plot.
the almost stationary ring-shaped condensation system in the slow layer of the jet, the resulting photon field exhibits a highly relativistic acceleration in the moving reference frame.Thus, with each such passage, photons undergo effective IC scattering.Consequently, when this ring system persists, one can observe very similar γ-ray flares occurring years apart.The model also predicts the recurring appearance of similar lightcurve patterns within the long-term light curve.Blinov et al. (2021) first reported the sustained pattern of γ-ray flares with EVPA rotations in the emissions of the blazar 3C 279.Within these recurring light-curve appearances, the light curve from the period 55002-55134 was rereported by Novikova et al. (2023), who found that within this time span, the γ-ray light curve of the blazar 3C 279 exhibited a total of four occurrences of similar pattern.
As shown in Figure 7, the three segments of the light curve ("EP1," "Ren," and "EP3") exhibit strong similarities.We used the discrete correlation function (DCF) to calculate the correlation between these light curves, and the results are presented in Figure 8.The results of the DCF calculation indicate a strong correlation among the three segments of the light curve.Thus, we consider the physical mechanisms underlying the three segments of light curves to be consistent.In other words, the three segments are the same repeated pattern.Figure 9 yields consistent conclusions with the above.
In the literature (see, e.g., Marscher et al. 2010;Jorstad et al. 2013;Blinov et al. 2021;Novikova et al. 2023) discussing the repetitive patterns in γ-ray light curves, the repeated patterns in light curves lack "periodicity," i.e., the repeated segments of light curves without QPO.Although each repeated pattern in our study corresponds to a light curve with QPO, it does not preclude us from using the model of a sheath in the jet to explain the repetition of these light curves.If the repetitive patterns in this study are also governed by this model, it suggests that there are still some unknown details within this structure causing periodic variations in the energy of scattered electrons.It is also possible that the number of seed photons involved in the IC scattering exhibits periodic changes.Regardless of which aspect is at play, this holds significant research value.
Both of the abovementioned structures can give rise to the repetitive occurrence of QPOs, but they cannot account for two different timescales of QPOs.Therefore, we propose that the two QPOs observed in this study originate from the two jets of the binary black holes, and the repetitive occurrence of each type of QPO may be related to the geometric structures within the jets.In addition, these QPOs (repetitive pattern) should be verified by long-term, high-tempo, high-quality, quasi-simultaneous multiwavelength observations.

Figure 1 .
Figure 1.Top panel: the γ-ray light curve of 3C 279 with 5 day bin (TS 25) in about 14 yr.In this graph, the gray region represents QPO with a period of 40 days, labeled as EP1 (MJD 55008-55125) and EP3 (MJD 59430-59585) respectively.The purple region represents a QPO with a period of 91 days, labeled as EP2 (MJD 58530-58985).The blue region indicates that Ren et al. (2023) discovered two QPOs in this area, with periods of 40 and 101 days, respectively.Bottom panel: enlargement of EP2 in top image.The blue dotted line, the red dotted line, and the red arrow represent the mean value of the flux, the fitting result of the sine function, and the position of each peak, respectively.

Figure 2 .
Figure 2. Panel (a): the light curve of 3C 279 with 5 day bin (TS 25) in the EP3.The blue dotted line, red dotted line, and red arrow represent the average flux value, the fitting result of the sine function, and the position of each peak, respectively.Panel (b): the power spectrum of the light curve in panel (a).The black solid line is the power spectrum, and the red dash, the blue dash, and the green dashed lines indicate the confidence level of 99.7% (3σ), 99.99% (4σ), and FAP = 0.01% (4σ), respectively.Panel (c): WWZ map of the light curve in panel (a).Panel (d): the red solid line shows the time-averaged WWZ.The blue dashed and green dashed lines represent the confidence level of 99.99% (4σ) and 99.7% (3σ).

Figure 3 .
Figure 3. Panel (a): the light curve of 3C 279 with 3 day bin in the EP1.The blue dotted line, red dotted line, and red arrow represent the average flux value, the fitting result of the sine function, and the position of each peak, respectively.Panel (b): the power spectrum of the light curve in panel (a).The black solid line is the power spectrum, and the red dash, the blue dash and the green dash lines indicate the confidence level of 95%, 99%, and FAP = 1%, respectively.Panel (c): WWZ map of the light curve in panel (a).Panel (d): the black solid line shows the time-averaged WWZ.The red dash and green dash lines represent the confidence level of 95% and 99%.

Figure 5 .
Figure5.Results of the periodicity analysis by REDFIT for light curve in the EP1 (left) and EP3 (right).The black solid line is power spectrum of γ-ray light curve in this interval.Dotted lines from bottom to top represent the theoretical red-noise spectrum (red dashed line), the confidence level of 90% (blue dashed line), 95% (green dashed line), and 99% (purple dashed line).

6.
The spectral index α of EP1, EP2, and EP3 over time is shown in the figure.The blue dots and red dashed line represent the spectral index values and the average value, respectively.

Figure 7 .
Figure 7. From top to bottom are the light curves of EP1, Ren, and EP3 respectively.In this context, we refer to Ren et al. (2023) and have selected the light curve in the γ-ray band for MJD 58095-58291 as Ren.

Table 1
QPO Behavior in Blazar 3C 279 (Published and This Work)

Table 2
The Best Parameters of the Fitting of the PSD