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

Blazars are a class of radio-loud active galactic nucleis that aim their jets almost directly at Earth (Urry & Padovani 1995). Blazar emission extends from MHz radio frequencies to TeV gamma-ray energies. The multiwavelength radiations from blazars are dominated by the non-thermal radiations from their jets. Besides the two-bump spectral energy distribution, erratic variability at all wavelengths is the distinguished feature of blazars emission, which is an important tool for investigating physics of blazars.

Blazar variability is usually aperiodic. Accompanying the data of blazars increasing with technological advancements of astronomical telescopes, a few possible quasi-periodic variabilities of blazars with a broadband of timescales were reported (e.g., Urry 2011; Gupta 2014). Naturally, these findings are mainly in optical band because of the abundant optical data (e.g., Bai et al. 1998, 1999; Fan & Lin 2000; Xie et al. 2008; Li et al. 2009; King et al. 2013; Bhatta et al. 2016). Among them, the most persuasive case is OJ 287, whose optical quasi-periodic cycle is ∼12 years (Kidger et al. 1992; Valtonen et al. 2006). Zhang et al. (2014) reported a quasi-periodic variability of optical emission in PKS 2155-304 (redshift z = 0.116; Falomo et al. 1993) with a timescale of 317 ± 12 days.

Up to now, the Large Area Telescope on the Fermi Gamma-ray Space Telescope has been collecting data for more than 8 years, which enables the finding of quasi-periodic variability with timescales of a few years in gamma-ray flux (e.g., Ackermann et al. 2015; Sandrinelli et al. 2016a). Interestingly, Sandrinelli et al. (2014) confirmed the optical periodic variability of PKS 2155-304 by Zhang et al. (2014) with independent data, and furthermore, they found marginal evidence of its quasi-periodic variability with a period cycle of ∼619 days in gamma-ray flux, with the Fermi-LAT data in the interval 2008 August 6 (Modified Julian Day, MJD, 54684) to 2014 June 9 (56817 MJD). However, Sandrinelli et al. (2014) pointed out that their result is tentative due to the limited time interval.

In this paper, we present a detailed analysis of the Fermi-LAT light curves of PKS 2155-304 in the interval 2008 August 4 (54682.66 MJD) to 2016 October 26. Our results reveal a 4.9σ significance-level quasi-periodic variability in the gamma-ray flux of PKS 2155-304. The period cycle is ∼640 days, which is consistent with the finding of Sandrinelli et al. (2014). The paper is organized as follows: in Section 2we describe the LAT data analysis and show the main results, and in Section 3 we provide a summary and some discussion.

The Large Area Telescope (Atwood et al. 2009; Abdo et al. 2009) on board Fermi satellite is an electron–positron pair production telescope, and it is sensitive to gamma-ray photons from ∼20 MeV to ∼500 GeV (Atwood et al. 2009). It has a 2.4 sr field of view, a point-spread function ∼08, and an effective area of ∼8000 cm² at 1 GeV. This satellite operates in a continuous entire sky survey mode, every two ∼1.6 hr spacecraft orbits.

We use data from the observations from 2008 August 4 to 2016 October 26 (MJD: 54682.66-57687.59) with a circular region of interest (ROI) of 15^◦ radius centered on the position of PKS 2155-304. In the analysis, the new Pass 8 LAT database (Atwood et al. 2013) is used with keeping only the SOURCE class photon-like events (evclass = 128 and evtype = 3). We exclude events with zenith angles over 90^◦. The events from 100 MeV to 500 GeV are selected to improve the point-spread function, and to reduce diffuse emissions. Using Fermi ScienceTools gtmktime, we perform a selection to obtain high-quality data in the good time intervals with the expression (DATA_QUAL>0)&&(LAT_CONFIG==1). We adopt the instrumental response function "P8R2_SOURCE_V6." We use files gll_iem_v06.fit and iso_P8R2_SOURCE_V6_v06.txt to model the two background templates, including Galactic and extragalactic diffuse emissions. To reduce and analysis the database, we use the Fermi Science Tools version v10r0p5 package and follow the standard procedure as in the data analysis thread that is provided in the FermiScience Support Center.⁶

The binned maximum likelihood method is adopted to determine the spectral parameters and flux intensity. The events are extracted from a 20° × 20° square ROI centered on PKS 2155-304's coordinate with energy over 100 MeV. We bin the data 10 equal logarithmically spaced bins per decade in energy dimensionality, with a spatial pixel size of 01 × 01. For sources modeling, we fit all the photons with a model file. The model file is composed of all known 3FGL sources (Acero et al. 2015), derived from 4 years of survey data in the ROI; the two background diffuse emissions are included. The model file are generated with script from user contributions.⁷ In the model file, the spectral shapes of our target and other gamma-ray sources in the ROI are modeled by using the same models in 3FGL. The flux normalization and the spectral parameters of all sources within 5^◦ are set free; for the sources within 5°–10°, only flux normalization is set free; and the parameters of other sources located in ROI but beyond 10^◦ are fixed to the values in 3FGL catalog, except for setting free the normalization of significantly variable sources (i.e., Variability_Index exceeds the threshold of 72.44) in the ROI. The test statistic value (TS), defined as TS = −2ln (${{ \mathcal L }}_{0}/{{ \mathcal L }}_{1}$), is used to determine the source detection significance.

2.1. Production of Light Curves

We produce the light curves of PKS 2155-304 through two methods: the maximum likelihood optimization and the exposure-weighted aperture photometry (Corbet et al. 2007; Kerr 2011).

In the method of maximum likelihood optimization, the light curves are obtained by dividing the data into separate equal time bins on 10 day timescales. We perform the unbinned maximum likelihood fitting technique for each time bin. In this case, we use the same parameters of sources as the best-fitting model file, but frozen in the parameters of spectrum shape, as described in Ackermann et al. (2015). Compared with the binned analysis, the events are selected in a circle ROI of 15° centered on the position of PKS 2155-304, and the length of timescale is 10 days for each time bin. The light curve is presented in Figure 1 (upper panel). For testing the impact of difference of time-length on the power, we also obtain the monthly light curve using the same method (see the upper panel of Figure 2).

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In the method of exposure-weighted aperture photometry, the probabilities of every photon in the ROI are calculated with the Fermi tools gtsrcprob. Then we sum the probabilities (rather than the number of photons) within 3° radius centered on the position of target using 2.5 days time bin. And each time-bin count is weighted by its relative exposure. The light curve is presented in Figure 3 (upper panel).

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2.2. Searching for Quasi-periodic Variability

2.2.1. Analyses on Gamma-Ray Data

We use two methods to search for the quasi-periodic signal: Lomb-Scargle Periodogram (LSP; Lomb 1976; Scarle 1982) and Weighted Wavelet Z-transform (WWZ; Foster 1996). The corresponding LSP and time-averaged WWZ powers are shown in the right lower panel in Figures 1–3. The 2D plane contour plot of the WWZ power spectrum (scalogram) using a Morlet mother function (filled color contour) is also shown in Figures 1–3 (left lower panel). All the powers show a clear peak at ∼640 days. The uncertainty of the period cycle is evaluated with the half width at half maximum of the Gaussian fitting, centered at the maximum power. Both analyses on the LSP and WWZ powers give a period of 1.74 ± 0.13 year. We have tested the impact of different time bins on the position of the peak power, and found that the impact is negligible.

In low-frequency the fluctuations of power are enhanced because of random noise, especially for the length of period cycle comparable to the whole light curves. The artificial peak sometimes misidentified as a signal. The significance of a signal in low-frequency is difficult to estimate. For obtaining the robust significance, we simulate light curves based on the obtained power spectral density (PSD) and the probability density function of observed variation. The final stimulated light curves therefore have full statistical and variability properties of the gamma-ray flux. In order to determine the best-fit PSD, we model the power with a power-law function: $P(f)=A\,{f}^{-\alpha }+c$, where α is the power-law index and c marks the Poisson noise level. The details of the method are provided in Emmanoulopoulos et al. (2013) and Bhatta et al. (2016). We simulate 10⁶ light curves with the method and evaluate the significance of the signal. The red solid line, green dashed–dotted line, and blue dashed line in Figures 1–3 represent the 5σ, 4σ, and 3σ confidence level, respectively.

We fold the gamma-ray photons by using a phase-resolved likelihood analysis method with a 636.7 day period. The folded light curves with phase zero corresponding to MJD 54682.66 are shown in Figure 4. We fit the phase-resolved light curves with a constant-flux, and derive the reduced ${\chi }_{\mathrm{red}}^{2}=767.5/14$. Therefore we can claim a significant variability of the phase-resolved light curves. Furthermore this result confirms the signal again. Clearly, the amplitude of gamma-ray flux varies with phase.

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2.2.2. Analyses on X-ray Data

As far as we know, there is no study on the long term X-ray quasi-period variability of PKS 2155-304 (see Lachowicz et al. 2009 for a study on the short term X-ray quasi-period variability). Therefore, using the same techniques, we analyze long term (2005 November 17 to 2016 October 25) X-ray (0.3–10 keV) light curves of PKS 2155-304 from Swift-XRT (Stroh & Falcone 2013).⁸ The results are shown in Figure 5. No significant signal is found in the LSP power spectrum.

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In this paper, we analyzed the Fermi-LAT data of PKS 2155-304 from 2008 to 2016. Our results reveal a quasi-periodic variability in gamma-ray flux with a period cycle of 1.74 ± 0.13 years and a significance of 4.9σ, confirming the finding of Sandrinelli et al. (2014) with much higher significance.

We also analyzed the long term X-ray light curve obtained from the observations of Swift-XRT (Stroh & Falcone 2013). However, no significant quasi-periodic variability is found, which may be due to insufficient statistics.

Ackermann et al. (2015) reported marginal evidence for quasi-periodic modulation in gamma-ray flux of PG 1553+113, which is correlated with the oscillations observed in radio and optical fluxes. For PKS 2155-304, Zhang et al. (2014) found its quasi-periodic variability with a quasi-period ${T}_{1}\sim 317$ days in optical flux. This periodicity was confirmed in Sandrinelli et al. (2014) by their data on VRIJHK photometries. Moreover, Sandrinelli et al. (2014) revealed a possible quasi-periodic variability of $2\times {T}_{1}$ in gamma-ray flux of PKS 2155-304, with 6 year Fermi-LAT data. Sandrinelli et al. (2016b) found marginal evidence (∼3σ) of quasi-periodic variability with a period cycle ${T}_{2}\sim 280$ days in Fermi gamma-ray light curve of PKS 0537-441 during a high state extending from 2008 August 10 to 2011 August 27; however, they found no signal of quasi-period variability in the entire duration of the Fermi-LAT light curve 2008–2015. Sandrinelli et al. (2016b) also found evidence of quasi-periodic variability with a period cycle $\tfrac{1}{2}\times {T}_{2}$ in optical flux of PKS 0537-441. However, the optical and gamma-ray quasi-periodic modulations in PG 1553+113 have the same period.

So far, three blazars (PG 1553+113, PKS 2155-304, and PKS 0537-441) have been reported as having quasi-periodic variability in gamma-ray fluxes with the significance of ≥3σ (Sandrinelli et al. 2014, 2016b; Ackermann et al. 2015). Among them, the significance of ∼1.74 years period gamma-ray cycle for PKS 2155-304 presented in this paper is the highest. The three blazars are high-synchrotron-peaked BL Lac objects (HBLs), whose synchrotron peak frequency is greater than 10¹⁵ Hz (Abdo et al. 2010). HBLs usually have hard gamma-ray spectra (i.e., the photon spectral index ${{\rm{\Gamma }}}_{\gamma }\lt 2$; Acero et al. 2015). The mass of super massive black hole (SMBH) in HBLs is $\sim {10}^{8}\ {M}_{\odot }$ (e.g., Woo et al. 2005). HBLs are thought to possess a lower accretion rate (e.g., Ghisellini & Tavecchio 2008). On the side of emission mechanism, the optical-X-ray emission of HBL is the synchrotron radiation from high-energy electrons in the jet, and the gamma-ray emission is likely produced by a synchrotron-self Compton process.

The mechanism causing the quasi-periodic variabilities in blazars is poorly understood (Ackermann et al. 2015), which should be related to the relativistic jet itself (e.g., jet precession) or to the process feeding the jet (pulsational accretion flow instabilities). Ackermann et al. (2015) have outlined three kinds of models for explaining the quasi-periodic variabilities in HBLs: (i) pulsational accretion flow instabilities, with such instabilities possibly inducing a quasi-periodic injection of plasma into jet, which could then produce quasi-periodic variabilities in jet emissions; (ii) jet precession/rotation, or helical structure, with Doppler factors changing periodically; (iii) binary SMBH system, with a total mass of $\sim {10}^{8}\ {M}_{\odot }$ and a milliparsec separation. Based on the current observations, one cannot determine the physical scenario for the quasi-periodic variabilities in PKS 2155-304. However, on the other side, with the assumption that the jet optical-gamma-ray emissions are produced in the same region, the previously listed three models predict the same period for optical flux and gamma-ray flux. If the optical and gamma-ray quasi-periodic modulations in PKS 2155-304 are real, the different optical and gamma-ray periods in PKS 2155-304 could challenge the most popular one-zone emission model. We would like to suggest that multifrequencies periodic modulations in blazars may put extra constraint on blazar emission models.

We thank the referee for the very helpful suggestions that have significantly improved our manuscript. We acknowledge financial support from the 973 Program of China under grant 2013CB837000, the National Natural Science Foundation of China (No. 11573060), the Key Laboratory of Astroparticle Physics of Yunnan Province (No. 2016DG006), the Strategic Priority Research Program, and the Emergence of Cosmological Structure of the Chinese Academy of Sciences, Grant No. XDB09000000. The work of D.H.Y. is supported by CAS "Light of West China" Program.