JSTOR

1. INTRODUCTION

The nature of active galactic nuclei (AGNs) is an important and open question in astrophysics. Variability is one of the important observational characteristics of AGNs and the periodicity of outbursts in some AGNs is particularly interesting, because variability analysis is one of the powerful methods in understanding their central engines and energy production processes. Through the variability analysis, we can get much information on the physics mechanism of AGNs. The confirmed periodicity would help us locate the relevant physical parameters and would strongly limit the physical models in AGNs (Lainela et al. 1999).

The quasar 3C 279 identified by Sandage & Wyndham (1965) is an optically violent variable (OVV) quasar (Webb et al. 1990) at redshift z = 0.538. It is one of the closest of the EGRET-detected and the best-observed flat spectrum radio quasars (Kubo et al. 1998). 3C 279 shows extreme variability at almost all wavelengths (see Fan 1999; Hartman et al. 2001; Kniffen et al. 1993; Pian et al. 1999; Trimble & Aschwanden 1999; Xie et al. 1999, 2004). At optical wavelengths, it shows variability on different time scales, from intraday to years (Böttcher et al. 2007). A series of flares with △B = 3–4 mag were observed in the period before 1951 (Dai et al. 2001). Since then the object is less active (Dai et al. 2001). But Villata et al. (1997) observed a big outburst in 1988 with B = 12.13 mag. A median timescale variation of about 49 days with △R ∼ 0.91 mag was observed by Xie et al. (2004). Kartaltepe & Balonek (2007) analyzed the light curve of R band with the autocorrelation function and found that there are peaks at 550, 360, and 100 days. The optical light curve of 3C 279 suggests a tendency to repeat outbursts at about 7 yr intervals (Eachus & Liller 1975). Fan (1999) analyzed the periodicity of infrared variability with Jurkevich method and found a strong period about 7.1 ± 0.44 yr. In addition, a major near-millimeter flare was detected by Matsuo et al. (1989) for the first time. In general, the γ-ray emission of 3C 279 demonstrates the variability with a typical timescale of (Villata et al. 1997).

The quasar 3C 279 is the first object which was observed to exhibit the phenomenon of apparent superluminal motion (Whitney et al. 1971; Unwin et al. 1989). For the superluminal velocities, one possible interpretation is the effects of relativistic bulk motion in a jet which forms a small angle with the line of sight. Thus differences in velocities could be attributed to differences in these angles. The fact that changes in the position angle projected into the sky were observed suggested the existence of a precessing jet (Carrara et al. 1993). The presence of different apparent speeds and position angles in the jet of 3C 279 was confirmed by Wehrle et al. (2001). In addition, the precession jet in 3C 279 was investigated in detail by Abraham & Carrara (1998). Carrara et al. (1993) found there exists a relatively short precession period of about 30 yr by fitting the data of the jet component Cc, C3, and C4 (Cc is the Cotton’s component; C3 and C4 are given in Fig. 1 of Carrara et al. 1993).

Obviously, 3C 279 is an extremely active object and there may be a precession jet in 3C 279. The precession jet can be responsible for the variability. In order to investigate the variability and check the precession model, we collected the available radio, optical, and X-ray band observation data and analyze it using three different periodic analysis methods in this work.

2. OBSERVATION DATA AND VARIABILITY ANALYSIS OF THE LIGHT CURVES

We present the historical light curves of 3C 279 at 22 GHz, 37 GHz, optical R-band, and X-ray (2–10 keV) band compiled from the literature (Salonen et al. 1987; Teräsranta et al. 1992, Teräsranta et al. 1998, 2004, 2005; Shrader et al. 1994; Hartman et al. 1996; Xie et al. 1999, 2001; Katajainen et al. 2000; Dai et al. 2001; Villata et al. 1997; Kartaltepe & Balonek 2007; Chatterjee et al. 2008). The light curves are shown in Figure 1. In addition, we list the characteristics of the observation data in Table 1. From Figure 1 and Table 1, we can see that 3C 279 is a very active object, with a variability index of V_22 GHz = 0.69, V_37 GHz = 0.74, V_R = 0.96, and V_X = 0.91. The variability index defined by V = (F_max - F_min)/(F_max + F_min) is the relative flux change (Fan et al. 2002), where F_max is the maximal flux and F_min is the minimal flux. From Figure 1, we can also observe that there is regular variability and similar behavior in the light curve of radio, optical, and X-ray bands, which reveals the possibility of periodicity.

TABLE 1 Characteristics of the Light Curves of 3C 279 at Four Bands

Open New Window

(30 KB)

Fig. 1.— Light curves of 3C 279 at 22 GHz, 37 GHz, R band, and X-ray band.

Open New Window

In the following sections, we will use the following methods to analyze the data of 3C 279: the power-spectrum method, the discrete correlation function (DCF) method, and the Jurkevich method.

3. ANALYSIS METHOD AND PERIODICITY RESULTS

The power-spectrum method is a traditional method which can be applied to the periodicity analysis of unevenly sampled data. The power spectrum density was estimated by an algorithm (Lomb-Scargle periodogram) given by Lomb (1976) and Scargle (1982).

For a times series X(t_k) (k = 0,1…,N₀), the periodogram, as a function of frequency ω, is defined by where τ is defined by the equation and where ω = 2πν. Thus, the periodogram is a function of frequency ν.

Based on the definition of P_X(ω), if the signal X(t_k) is purely noise, the power in P_X(ω) would follow an exponential probability distribution. This exponential distribution provides a convenient estimate of the probability that a given peak is a true signal, or whether it is the result of randomly distributed noise. For a power level z, the false alarm probability is given by (see Scargle 1982; Press et al. 1994) where N is the number of frequencies searched for the maximum. According to Press et al. (1994), N is very nearly equal to the number of data points N₀ when the data points are approximately equally spaced and the estimate of N need not be very accurate. The error in the period is estimated by calculating the half width at half-maximum (HWHM) of the peak and the routine for the calculation was obtained from Numerical Recipes (Press et al. 1994).

The result of the power-spectrum method is shown in Figure 2. The a) panel of Figure 2 gives the results of 22 GHz, showing the peaks at P₁ = 134.2 ± 0.9, P₂ = 176.8 ± 1.7, P₃ = 243.9 ± 3.0, P₄ = 379.9 ± 6.7, P₅ = 686.7 ± 18.1, and P₆ = 776.3 ± 32.4 days, and this means that there are six possible periods in the light curve of 22 GHz. According to equation (3), the false-alarm probability for each of these results is smaller than 3%. For the results of P₁, P₃, P₄, P₅, and P₆, we note that there exists a simple relationship: P₃ ≈ 2P₁, P₄ ≈ 3P₁, P₅ ≈ 5P₁, and P₆ ≈ 6P₁. However, this simple relationship is not found between the result P₂ and P₁. From the b panel of Figure 2, we see that there are four significant peaks at P₁ = 136.6 ± 1.1, P₃ = 252.1 ± 3.7, P₄ = 372.9 ± 7.7, and P₆ = 813.7 ± 34.6 days, which implies that there are four possible periods in the light curve of 37 GHz. The false-alarm probability for each of these results is smaller than 1%. In addition, we can note that there is also a simple relationship: P₃ ≈ 2P₁, P₄ ≈ 3P₁, and P₆ ≈ 6P₁. One can see that the result of 37 GHz is in good agreement with the previous result based on the 22 GHz data. The c and d panel of Figure 2 gives the results of R band and X-ray band, respectively. From the c and d panel of Figure 2, we can see the timescales are P₁ = 125.1 ± 1.5, P₃ = 279.4 ± 18.8, P₅ = 626.5 ± 66.4 days for R band, and P₁ = 126.6 ± 1.5, P₃ = 288.1 ± 7.0, P₅ = 618.8 ± 22.3, P₆ = 759.5 ± 41.3 days for X-ray band. They are consistent with the results of 22 and 37 GHz. Referring to the foregoing analysis, we can observe that the period of P₁, P₃, P₄, P₅, and P₆ appear in almost every band. This means that they are possible periods in the light curve of 3C 279. However, it is interesting to note that the period of P₃, P₄, P₅, and P₆ are, respectively, about 2, 3, 5, and 6 times the period P₁. This makes it doubtful that the periods P₃, P₄, P₅, and P₆ are the astronomical multiple frequency of the period of P₁. Via the analysis above, we consider that the possible period of P = 130.6 ± 1.3 days (the average of four periods P₁ in the results of 22 GHz, 37 GHz, R band, and X-ray band) is indeed existent in the light curves of 3C 279. The period of P = 130.6 days is consistent with the peak at 100 days obtained by Kartaltepe & Balonek (2007) when they analyzed the entire 14 yr data set of 3C 279 at R band by using the autocorrelation function. In addition, it is interesting to note that the period of 7.1 yr (about 2592 days) for 3C 279 found by Fan (1999) is about 20 times the period 130.6 days. For the result of P₂ = 176.8 days, we find that it only appears in the results of 22 GHz and there is not the astronomical multiple frequency relationship with other results. So we consider that it is an unauthentic result and more observation is needed to confirm it.

(34 KB)

Fig. 2.— Result of power-spectrum method in 3C 279 at four different bands using the data shown in Fig. 1. (a)–(d) The results at 22 GHz, 37 GHz, R band, and X-ray band, respectively.

Open New Window

In order to investigate the reliability of these results, we also adopted the discrete correlation function (DCF) method to analyze the periodicity information of 3C 279 in the light curve of radio, optical, and X-ray band. The DCF method, described in detail by Edelson & Krolik (1988), is intended to calculate the correlation coefficient of two data sets as a function of the time shift between them. The method can be used to analyze the correlation of two variable temporal series with a time lag and can also be used to search for periodicity of a unique temporal data set. If there is a period, T_pe, in the light curve, the DCF should exhibit a maximum value at time delay τ = 0 and τ = T_pe. Namely, it will show a peak at the lags τ = 0 and τ = T_pe.

In order to determine the values of the DCF of each pair of data (a_i,b_j), we first calculate the set of unbinned discrete correlations (UDCF) of all measured pairs (a_i,b_j) where and are the average of the data sets, and σ_a and σ_b are the corresponding standard deviations. Each pair of data can be associated with the pairwise lag △t_ij = t_j - t_i. The time bins can be measured directly through the useful function DCF(τ). The UDCF_ij values are averaged over M, where M is the number of pairs for which τ - △τ/2 ≤ △t_ij < τ + △τ/2 and τ is the time lag. Then, the standard error for each time lag τ is

The resulting DCF is shown in Figure 3, from which we can see that the timescales T_pe, estimated from peaks in the DCF, are 138, 217, 272, and 525 days for the 22 GHz data sets; 138, 252, 381, and 818 days for the 37 GHz data sets; 152, 362, 853, and 1240 days for the optical R-band data sets and 120, 381, 520, 636, 785, 899, 1121, and 1230 days for the X-ray data sets. These results are consistent with the results obtained by the power-spectrum method. Taking into account the astronomical multiple frequency relationship, the result of the DCF method is about 137 days (the average of four periods of about 130 days in the result of the DCF method), which is in good agreement with the previous result of 130.6 days based on the power-spectrum method. For the result of 217 days, one can also see that it only appears in the results of 22 GHz and there is not the astronomical multiple frequency relationship with other results. So it must be ruled out and more observation is needed to confirm it.

(39 KB)

Fig. 3.— Result of the discrete correlation function (DCF) method in 3C 279 at four different bands using the data shown in Fig. 1.

Open New Window

For comparing and further investigating the reliability of these results, we also adopted the Jurkevich method (Jurkevich 1971) to analyze the database of 3C 279. The Jurkevich method is based on the expected mean square deviation and the unequally spaced observations in astronomy observation. It tests a series of trial periods around which the data are folded. All data are divided into m groups according to their phases around each group (bin). The statistical parameters of lth group are given by with x_i and m_l the individual observation and the number of observations in the lth group, respectively. Then the sum of the squared deviations in m groups is computed by If a trial period equals to a true one, would have reached its minimum.

For Jurkevich method, Kidger et al. (1992) introduced an f-test and the parameter f can be calculated where is the normalized value. In the normalized plot, a value corresponding to f = 0 implies there is no periodicity at all. The best period can be found from the plot. In general, if f≥0.5, it implies there is a significant periodicity in the sample; if f ≤ 0.25, it usually indicates that the periodicity, if genuine, is a weak one. For f ≤ 0.25, a further test is needed with the relationship between the depth of minimum and the noise in the “flat” section of the curve close to the adopted period. If the absolute value of the relative change of the minimum to the “flat” section is larger than 10 times the standard error of this “flat” section, the periodicity in the data can also be considered significant. The result of the Jurkevich method is shown in Figure 4. From Figure 4, one can note that there are several obvious minimum values of at the period 134, 267, 380, and 772 days for the 22 GHz data sets; 137, 275, 374, and 825 days for the 37 GHz data sets; 126, 267, and 491 days for the R-band datasets; and 126, 251, and 763 days for the X-ray data sets, respectively. Taking into account the astronomical multiple frequency relationship, the result of the Jurkevich method is about 130.7 days (the average of four periods of about 130 days in the result of the Jurkevich method). Although the parameter f corresponding to the period of 130.7 days is smaller than 0.25 for all bands, the depth of the result is significant compared with the “flat” section. In addition, the results are consistent with those results obtained with the power-spectrum method and the DCF method. From the foregoing analysis, we are sure that there exists a real period about P = 130.6 ± 1.3 days in the light of 3C 279.

(34 KB)

Fig. 4.— Normalized Jurkevich test result for the period search in 3C 279 at four different bands using the data shown in Fig. 1.

Open New Window

4. DISCUSSION AND CONCLUSIONS

We investigated the periodicity of the light curve of 3C 279 at four different bands with three kinds of period analysis techniques and obtained a certain result. The result shows that there is a outburst period of P = 130.6 ± 1.3 days present in the light curve of 3C 279 at radio, optical, and X-ray band. The result is in good agreement with the peak at 100 days obtained by Kartaltepe & Balonek (2007) when they analyzed the entire 14 yr data set of 3C 279 by using the autocorrelation function. In addition, it is of interest to note that the period of 7.1 yr (about 2592 days) for 3C 279 obtained by Fan (1999) is about 20 times the period 130.6 days.

The unified model of AGNs is based on the accreting black hole system (Urry & Padovani 1995). This model can provide the best explanation for the enormous energy output. In this model there is a supermassive black hole in the center of the host galaxy and an accretion disk surrounding the black hole. For blazar type sources, most of the observed flux is usually dominated by nonthermal emission from their relativistic jets (Rieger 2004). The periodic variability of blazar may be associated with helical trajectories in extragalactic radio jet by differential Doppler boosting effects, and for nonballistic helical motion, the observed period may be much smaller than the real physical driving period because of light-travel time effects (Rieger 2004). Rieger (2004) discussed three possible periodic driving mechanisms for the origin of helical jet paths: (1) nonballistic helical motion driven by the orbital motion in a binary black hole system (BBHS), which is usually constrained to periods of P≥10 days; (2) ballistic or nonballistic helical jet paths driven by jet precession, which can well be responsible for periodicity on a timescale P_obs≥1 yr; and (3) nonballistic helical motion due to internal jet rotation, which may account for observed periods P ≤ 10 days. For the 130.6 day period in 3C 279, one possible explanation is the orbital-driven (nonballistic) helical motion jet model (Rieger 2004) which provides a geometrical interpretation of the blazar emission variability. According to the helical jet model, the period of the variability is caused by the changing of viewing angle: we see the source is brighter when the viewing angle is smaller and fainter when the viewing angle is larger (see Gower & Hutchings 1984; Li et al. 2006; Villata & Raiteri 1999; Ulrich et al. 1997).

For nonballistic helical motion, Rieger (2004) found that the observed period P_obs is generally significantly shortened relative to the real physical driving period P_d. For blazar type sources, the observed period is given by (see Rieger 2004, 2005) where z is the redshift and γ_b is the bulk Lorentz factor. Then, in the observation frames, the (physical) precessional periods P_p is For blazar type sources, the bulk Lorentz factor is γ_b ≃ (5 - 15) (Rieger 2004). Abraham & Carrara (1998) obtained the bulk motion of the jet in 3C 279 from the position angles, velocities and epoch of formation of the superluminal features in the radio jet. According to Homan et al. (2003) and Piner et al. (2003), there exists evidence for nonballistic helical motion of the jet in 3C 279. For 3C 279, the bulk Lorentz factor is γ_b = 9.1 (Abraham & Carrara 1998). Based on the equation (12) and our result P = 130.6 days, the precession period of nonballistic helical motion of the jet in 3C 279 is P_p ≃ 29.6 yr which is completely consistent with the precession period about 30 yr obtained by Carrara et al. (1993). So the variability period about 130.6 ± 1.3 days in 3C 279 is caused most likely by the orbital-driven (nonballistic) helical motion of the jet.

3C 279 is one of the typical superluminal radio sources (Cotton et al. 1979; Shields 1999). Wehrle et al. (2001) measured the apparent speeds for six superluminal components and found apparent speeds ranging from 4.8c to 7.5c. The superluminal velocities could be caused by the effects of relativistic bulk motions in a jet which forms a small angle with the line of sight, and differences in velocities may be due to differences in these angles. Abraham & Carrara (1998) particularly discussed a precessing jet model for 3C 279 and attempted to interpret the different apparent speeds and position angles of the older VLBI components with the model. In addition, the model successfully predicted the general trend of the projected position angle swing for 3C 279 (Jorstad et al. 2004). The evidence for the existence of precession jet in 3C 279 also comes from the observation of VLBA, VLBI, and VLA for the apparent speed, the skewing in position angle, and the bending trajectory of jet components (see Homan et al. 2003; Abraham & Carrara 1998; Jorstad et al. 2004; Piner et al. 2000; Cotton et al. 1979; de Pater & Perley 1983; Wehrle et al. 2001). Additionally, our results reveal there is a precession period on a timescale P_p ≃ 29.6 yr in 3C 279, which is completely consistent with the precession period of jet of about 30 yr obtained by Carrara et al. (1993), which suggests there exists a precessing jet in 3C 279.

We are grateful to anonymous referees for their constructive suggestions and valuable remarks to improve the manuscript. This work is supported by the National Natural Science Foundation of China (10878013) and the Natural Science Foundation of Yunnan Province (2006A0049M & 2007A230M).