Detection of a high-confidence quasi-periodic oscillation in radio light curve of the high redshift FSRQ PKS J0805-0111
Guo-Wei Ren, Hao-Jing Zhang, Xiong Zhang, Nan Ding, Xing Yang, Fu-Ting Li, Pei-Lin Yan, Xiao-Lin Xu
aa r X i v : . [ a s t r o - ph . H E ] S e p Research in Astronomy and Astrophysics manuscript no.(L A TEX: ms2019-0352.tex; printed on October 1, 2020; 0:36)
Detection of a high-confidence quasi-periodic oscillation in radio lightcurve of the high redshift FSRQ PKS J0805-0111
Guo-Wei Ren , , Hao-Jing Zhang , Xiong Zhang , Nan Ding , Xing Yang , Fu-Ting Li , Pei-LinYan and Xiao-Lin Xu College of Physics and Electronics, Yunnan Normal University, Kunming 650500, P. R. China; [email protected] Department of Astronomy, Xiamen University, Xiamen 361005, P. R. China; School of Physical Science and Technology, Kunming University, Kunming 650214, P. R. China;
Received 20xx month day; accepted 20xx month day
Abstract
In this work, we have searched quasi-periodic oscillations (QPOs) in the 15 GHzlight curve of the FSRQ PKS J0805-0111 monitored by the Owens Valley Radio Observatory(OVRO) 40 m telescope during the period from January 9,2008 to May 9,2019, using theweighted wavelet Z-transform (WWZ) and the Lomb-Scargle Periodogram (LSP) techniques.This is the first time to search for periodic radio signal in the FSRQ PKS J0805-0111 bythese two methods. All two methods consistently reveal a repeating signal with a periodicityof 3.38 ± > . × cm. Key words: active galactic nuclei: flat spectrum radio quasar: individual: PKS J0805-0111 -galaxies: jets - method: time series analysis
Active galactic nuclei (AGNs) are very energetic extragalactic sources and they are generally powered byaccreting supermassive black holes (SMBHs) with masses of − M ⊙ in the centers of the galax-ies (Gupta et al. 2019; Esposito et al. 2015). Blazars represent an extreme subclass of radio-loud AGNs Guo-Wei Ren et al. with their relativistic jets aligned very closely to observers’ line of sight, and they are characterized bylarge amplitude, rapid and violent variability across the entire electromagnetic spectrum, high and variablepolarization at radio and optical energies, with non-thermal continuum emission ranging from radio to high-energy -rays, and superluminal jet speeds (Urry & Padovani 1995; Angel & Stockman 1980; Xiong et al.2017). Blazars are often subclassified into two categories according to the observed features: BL Lacertaeobjects (BL Lac) and flat spectrum radio quasars (FSRQs). BL Lac have featureless optical spectra withweak or no emission lines, possibly due to the emission being dominated by the jet, while FSRQ have a flatradio spectrum with a spectral index α . and broad quasar-like emission lines in the optical spectra.The blazars’ emission is dominated by relativistic jets, and the beaming effect boost the relativistic jets(Sandrinelli et al. 2016). The blazars’ broadband spectral energy distributions (SEDs) have an obviouslydouble-peaked structure. These two peaks have different physical origins: The low-energy peak at the IR-optical-UV band is considered to be caused by the synchrotron emission of relativistic electrons, and thehigh-energy peak at the GeV-TeV gamma-ray band is explained by the inverse Compton (IC) scattering(Xiong et al. 2017; B¨ottcher 2007; Dermer 1995).Blazars’ light curves generally display a series of features, especially aperiodic or quasi-periodic vari-ability in a wide range of temporal frequencies-equivalently. Blazars show signatures of QPOs in the multi-frequency blazar light curves, including radio, optical, X-ray and γ -ray, have been found (Bhatta 2018). TheQPOs on different timescales, from decades down to a few minutes (Gupta 2018; Bhatta 2017; Bhatta et al.2016). Research on QPO of blazars is one of the most active fields of extragalactic astronomy, and providesan important way to explore the radiation mechanism in blazars (Li et al. 2018). According to the time spansof the variability, the characteristic timescales of variabilities can be broadly divided into three classes, viz.,intraday variability (IDV) or micro-variability, which is defined as having timescales ranging from minutesto a few hours, short-term timescale variability (STV), which has timescales of days to weeks, even months,and long-term timescale variability (LTV) of a few months to years (Gupta et al. 2016; Xiong et al. 2017;Li et al. 2018). The discovery of QPO in the light curve variability could have deep consequences on theglobal understanding of the sources, constituting a fundamental building block of models (Sandrinelli et al.2016). It is need more long-term observations to search for periodic variations in many timescales.The blazar PKS J0805-0111 (RA=08h 05m 12.9s, Dec= -01d 11m 37s; and Z = 1.388) was identi-fied as a FSRQ, this source has been detected by many currently available instruments, it is cataloged byFermi/LAT as 3FGL J0805.2-0112 (Acero et al. 2015), its optical (R-band) brightness was recorded to be17.87 magnitudes (Healey et al. 2008). Since 2008, PKS J0805-0111 has been monitored in the 15GHzradio band by the 40 m telescope of the OVRO (Richards et al. 2011).In this paper, we analyze the long term ( 11.3 years) observations of FSRQ PKS J0805-0111 and reportour discovery of a high confidence QPO of the 15 GHz radio flux variability. In section 2, we describe the15 GHz radio observations. In section 3, We present time series analysis of the light curve using the WWZand the LSP, we test these two methods with astronomical analogue signals, besides, we also elaborateon the false alarm probability and the Monte Carlo simulation technique which is used to compute thestatistical significance of the detected periodicity. In section 4, we discuss three scenarios to explain the igh-confidence radio QPO in FSRQ PKS J0805-0111 3 QPO behavior of FSRQ PKS J0805-0111, and estimate the distance between the primary black hole andthe secondary black hole; Our conclusions be summarized in section 5.
OVRO announced 15GHz radio band observation data from a source FSRQ PKS J0805-0111 observedwith a 40-meter telescope from January 9, 2008, to May 9, 2019, for a total of 4138 days ( ∼ V A = q ( A max − A min ) − σ (1)Where A max , A min and σ represent the maximum value, minimum value, and average value of themagnitude errors in the radio observation data, respectively. Similarly, we can calculate the fractional vari-ance FV with a mean flux of h F i with S variance, and (cid:10) σ err (cid:11) is the mean error squared, as stated in theformula given in Vaughan et al. (2003): F var = s S − h σ err ih F i (2)The error of fractional variability can be estimated as stated in the formula given in Aleksi´c et al. (2015): σ F var = vuut F var + s N h e err i h F i + 4 N h σ err ih F i F var − F var (3)In this case, we can get V A = 0 . , F var = 0 . ± . through the above formula, which shows thatthere is a modest change in this source during this time. Figure 1 shows the light curve of PKS J0805-0111,and the blue curve is a sinusoidal fitting curve, which is plotted to help to indicate the modulation in thelight curve, as can be seen from Figure 1, there is a clear outbreak activity in this source, and four distinctpeaks can be clearly seen, from the light curve, we can visually see that this source has a QPO between1100 days and 1300 days. The 15 GHz radio band light curve of FSRQ PKS J0805-0111, for observations taken from January 9,2008to May 9, 2019 is plotted in Figure. 1. A visual inspection indicated a possible a QPO in the observationsmade during the whole observations.We carried out QPO search analysis using two methods of long time-series analysis: WWZ and LSP.We discussed the methods, analysis and the results in detail below.
Guo-Wei Ren et al.
MJD (day) -0.10 0.1 0.2 0.3 0.4 F l u x D en s i t y ( Jy ) Fig. 1: Long-term light curve of FSRQ PKS J0805-0111 at 15 GHz in January 9,2008 to May 9, 2019(MJD 54474 to 58612) obtained from OVRO, the data integration times is 4138 days ( ∼ y x Fig. 2: Graph of cosine function analog periodic signals.
WWZ period
Time period power WWZ power
Fig. 3: Periodic analysis of the cosine function by the WWZ transform. igh-confidence radio QPO in FSRQ PKS J0805-0111 5
Power time
Fig. 4: Periodic analysis of the cosine function by the LSP method. y x Fig. 5: random noise.
In order to test the reliability of WWZ and LSP method, we used the analog periodic signal as the astro-nomical observation data for verification. In this paper, we tested the accuracy of the two research methodsby the cosine function y = cos π with a period of π as shown in Figure 2 , the test results of these twomethods are: Figure 3 shows the periodic analysis results of the cosine function by the WWZ method, andthe periodic analysis results of the sinusoidal function by the LSP method is shown in Figure 4.In order to further determine the reliability of the WWZ and LSP methods in analyzing observations,the random noise data are we added to the periodic signal data of the cosine function simulation, and thesetwo methods are tested again. The specific process is calculated by the Python program, and the test resultsare as follows: Figure 5 shows random noise, the superimposed graph of random noise and cosine function Guo-Wei Ren et al. y x Fig. 6: Superimposed graph of random noise and cosine function. period
Time0.000 18.45 36.90 55.35 73.80WWZ period power A WWZ power
Fig. 7: Periodic analysis of the random noise and sinusoidal function by the WWZ method.is shown in Figure 6, Figure 7 and Figure 8 shows the results of periodic analysis for the cosine functionwith random noise added by the WWZ and LSP method, respectively.The results show that the standard cosine simulation data and the cosine simulation data with randomnoise was analyzed by WWZ and LSP methods, which is the same as T ≈ . , this proves that using thesetwo methods for periodic research is reliable. Wavelet analysis simultaneously decomposing data into time and frequency domains to estimate and de-termine the significance of a period (Gupta et al. 2019). However, we using wavelet analysis to processnon-equal interval data in practice, the interpolation method was used to reduce the impact of the astronom-ical observation signals are affected by the observation season, the weather, and the phase of the moon, butthis has a great influence on the authenticity of the data. igh-confidence radio QPO in FSRQ PKS J0805-0111 7
Power time
Fig. 8: Periodic analysis of the random noise and sinusoidal function by the LSP method.
WWZ period(days)
Time(MJD)
WWZ power
Fig. 9: WWZ of the light curve presented in Figure 9. The left panel shows the distribution of color-scaledWWZ power (with red most intense and blue lowest) in the time-period plane; the right panel shows thetime-averaged WWZ power (solid blue curve) as a function of period showing a distinct peak stands outaround the timescale of ± days; the black dashed lines indicate the thresholds of FAP fixed at σ (99 . , the blue dashed lines indicate the thresholds of FAP fixed at σ (99 . .We calculated the WWZ power for a given time and frequency by the WWZ method (King et al. 2013;Bhatta et al. 2016; Bhatta 2017; Gupta et al. 2019). It is defined by Foster (1996), he points that, theanalysis result can be significantly improved, and the period can be obtained more accurately, if the wavelettransform is regarded as the projection of the vector. Lomb-Scargle Periodogram (Foster 1996) is used widely to determine if QPOs are present in the observa-tions, it is a popular method of time series analysis (Bhatta et al. 2016; Bhatta 2017, 2018). The method is a
Guo-Wei Ren et al.
Power(Arbitrary unit)
Period(day)
Periodogram 95% cont. 99% cont. 99.7% cont.
Fig. 10: The results of the LSP analysis for the period search, showing a distinct peak stands out around thetimescale of ± days. The dashed red, black and green curves represent the , and . significance levels, respectively, from MC simulations.discrete Fourier transform (DFT)-based periodic extraction algorithm. The LSP’s basic principle is that us-ing a series of trigonometric functions by the least-squares method linear combination y = acosωt + bsinωt to fit the time series, and the characteristics of signal are converted from the time domain to the frequencydomain on this basis (Scargle 1982). For the non-uniform sampling time series x ( t i ) , i = 1 , , · · · , N ,the power spectrum is defined as: P LS ( f ) = 12 N × nP Ni =1 x ( t i ) cos [2 πf ( t i − τ )] o P Ni =1 cos [2 πf ( t i − τ )] + nP Ni =1 x ( t i ) sin [2 πf ( t i − τ )] o P Ni =1 sin [2 πf ( t i − τ )] (4)The parameter f and τ represent the test and the time offset, respectively, which can be obtained by thefollowing formula. tan (2 πf τ ) = P Ni =1 sin πf t i P Ni =1 cos πf t i (5) In this paper, we analyze the 15 GHz radio observations of the source FSRQ PKS J0805-0111 announcedby OVRO used the WWZ and LSP method, we found that the QPO of this source is about 3.38 years.In order to search for QPOs of the source FSRQ PKS J0805-0111, we analyzed the 15 GHz flux densityvariations by the WWZ method at first, which is one of the most common time series analysis methods.the WWZ transform of FSRQ PKS J0805-0111 light curve was computed for the minimum and maximumfrequencies of f min = 1 / , and f max = 1 / , respectively. The results are shown in Figure 9, The mostsignificant spectral power peak yielded by WWZ, and we further estimate its significance level by testingthe false alarm probability (FAP) of the null hypothesis. The probability that P N ( ω ) = P LS ( ω ) /σ willbe between some positive z and z + dz is e − z . If we scan some N i independent frequencies, the probability igh-confidence radio QPO in FSRQ PKS J0805-0111 9 that none give values larger than z is (1 − e − z ) N i : p ( > z ) ≡ − (1 − e − z ) N i is FAP(Ciaramella et al.2004). The smaller the false alarm probability, the higher degree of the significance for the peak.We analyzed the 11.3 years long OVRO light curve of FSRQ PKS J0805-0111, the results are as follows:It is showing a distinct peak stands out around the timescale of ± days with a single-trial FAPsignificance of . × − , which represents a very strong periodicity in the associated periodic signal.We estimated the period uncertainty by calculating the σ (99 . and σ (99 . confidence intervalon the observed period, by the FAP method.We performed the LSP analysis of the entire light curve in order to further confirm the presence of theabove QPO by the different method.We performed LSP method on the observations, the LSP method of FSRQ PKS J0805+0111 light curvewas computed for the minimum and maximum frequencies of f min = 1 / , and f max = 1 / , respec-tively. What needs to be emphasized is that the estimate of the total number of periodogram frequencies n ,it is critical to the evaluation of the periodogram. In this work, we evaluate the total number of periodogramfrequencies using N eval = n T f max (6)Since the observations we get are not equally spaced, spurious peaks may be generated, which makesit difficult to estimate the confidence of the peak height in the power spectrum. So, we should considerthis effect in this case. The red noise process may be product the periodic variability of blazars, and thered noise was modeled as an approximately power low Power spectral density (PSD): P ∝ f − α + C . Wemolding the wavelength variability as red noise with a power law index α to assessed the confidence of ourfindings. We then performed a Monte Carlo simulation technique (Timmer & Koenig 1995) for determiningthe significance of the periods, a large number of (typically 20000) light curves were simulated for everyspectral slope α values. We obtaining the α index by fitted the spectrum of the periodogram with power law.Using even sampling interval to simulated the 10000 light curves, and computed their LSP. Figure 10 givesthe results, showing a distinct peak stands out around the timescale of ± days. The local , and . MC simulations contours are represented by the dashed red, black and the green curves,respectively.
Generally, some periodic or quasi-periodic behavior were displayed in the light curves of blazars, studyingthese periodic or quasi-periodic behavior is an important method to investigate the nature of the physicalmechanisms within the emission regions. However, many researchers have been reported the QPOs of a fewblazars at different wavelengths on diverse timescales, they can be approximately divided into three classes,viz., intra-day variability, short-term timescale variability, and long-term timescale variability. Studies onQPOs could provide novel insights into a number of blazar aspects, some physical models has been reportedby many researchers, e.g., binary SMBH AGN system (Lehto & Valtonen 1996; Valtaoja et al. 2000; Fanet al. 2007), helical structure in inner jets (Conway & Murphy 1993), precessing accretion disk model (Katz 1997), the thermal instability of thin disks scenario. The observed periodic flux modulations could beexplained by a number of models.In this paper, we have attempted to detect the possible periodicity of the FSRQ PKS J0805-0111 in theradio 15 GHz light curve using the OVRO observations acquired during the period from January 9,2008to May 9, 2019 (MJD 54474 to 58612). The period of 15 GHz radio band is ± days by WWZanalysis, the confidence interval on the observed period is more than σ (99 . , by the FAP method; theperiod of 15 GHz radio band by LSP analysis is ± days, the significance level is more than . ,from MC simulations. It can be concluded that the QPO of FSRQ PKS J0805-0111 is . ± . years( > . confidence level).Although it is not well understood for the physical mechanism in blazars on long-term timescales, somepossible interpretations, such as, 1) the thermal instability of thin disks scenario; 2) the spiral jet scenario;3) the binary supermassive black hole scenario, have been applied to explain the long-term periodic vari-ability.In the scenario of thermal instability of thin disks, the cyclic periodic outburst leaded by the thermalinstability of thin disk. The uncertainty of disk causes the related outburst of the jet because of there is acertain degree of the link between jet and disk. Random light variations could produced by thermal insta-bility of thin disks in jets with stochastic red noise characteristics, this process is stochastic (Li et al. 2017).Thence, this scenario be responsible for long-term QPO is hard.In the spiral jet scenario, the relativistic beaming effect lead to the QPO behavior of blazars, the changeof relativistic beaming effect cause the arises of the obvious flux variations because of the different parts ofsuch a helical jet pass closest to the line of sight, even though the emission from the jet have no intrinsicvariations. Furthermore, the viewing angle to the helical motion changes periodically when the emissionblob of the jet moves to us, thereby resulting in QPOs (Zhou et al. 2018). However, it needs to note that,low-frequency radio emission such as 15 GHz is less affected by the beaming effect, due to it is generallyconsidered to be dominated by the extended jet structure of the jet (Fan & Wu 2018).Consequently, we are more promising that the QPO behavior in the FSRQ PKS J0805-0111 may causedby the binary supermassive black hole model, which possibly can explain presence of year-like long-termtimescale variability in AGN (Komossa 2006). A SMBH system would led to a wiggling or precessing jetbecause of the orbital motion or rotation, i.e., there is a precession motion of a relativistic jet in an orbitdue to the gravitational torque induced by the non-coplanar secondary black hole in the primary accretiondisc, which produce the observed long-term timescale variabilities ranging from a few to tens of years (Katz1997; Caproni et al. 2013).If we assume that the long-term light variations of blazars are caused by the binary supermassive blackhole model, and the distance between the primary black hole and the secondary black hole can be calcu-lated.For the binary black hole mass ratio, Qian et al. discussed the secondary black hole and primary blackhole is about 1 (Qian et al. 2007), and Caproni and Abraham think this ratio is about 0.78 (Caproni &Abraham 2004). In this case, we calculated that the average of these two values is 0.89, and we use thisvalue as the ratio of the secondary black hole mass and the primary black hole mass. In addition, we obtain293 black hole mass of the typical blazars (Shen et al. 2011; Shaw et al. 2012; Liu et al. 2006; Wang et al.2004; Chai et al. 2012; Sbarrato et al. 2012; Zhou & Cao 2009; Zhang et al. 2012; Xie et al. 1991, 2004), igh-confidence radio QPO in FSRQ PKS J0805-0111 11 and we calculate the average value of these blazars’ black hole mass is ¯ M = 10 . M J . We assume thatthis is the primary black hole mass, and we take a binary black hole mass ratio of 0.89, therefore, secondaryblack hole mass can be calculated as m = 0 .
89 ¯ M = 0 . × . M J . The relevant parameters of thebinary black hole model according to the orbit period can calculated.In this case, we take P obs = 3 . years, M = 10 . M J , m = 0 . × . M J , according to Kepler’slaw: (cid:18) P obs z (cid:19) = 4 π a G ( M + m ) , (7)where Z , a and G represent the red shift, the distance between the primary black hole and the secondaryblack hole and universal gravitational constant, thus we can calculate the distance between the primaryblack hole and the secondary black hole is a ∼ . × cm. In this paper, we have searched QPOs in the 15 GHz light curve of the FSRQ PKS J0805-0111 monitoredby the OVRO 40 m telescope during the period from January 9,2008 to May 9,2019. Our main results areas follows:(1)We have found a quasi-periodic signal with a period of . ± . years ( > . confidence level)in the 15 GHz radio light curve of the FSRQ PKS J0805-0111 by the WWZ and the LSP method. This isthe first time that the quasi-periodic signal has been detected in this source.(2)In the scenario where the precession of the binary supermassive black holes cause the radio quasi-periodic variability, the distance between the primary black hole and the secondary black hole is about . × cm.This source could be a good binary supermassive black hole candidate. We will further monitor theoptical variability of the source in the optical band to further verify whether there is the precession ofbinary supermassive black holes. Acknowledgements
This work is supported by the National Nature Science Foundation of China(11663009), and the High-Energy Astrophysics Science and Technology Innovation Team of YunnanHigher School. This work is supported by the National Nature Science Foundation of China (11663009),and the High-Energy Astrophysics Science and Technology Innovation Team of Yunnan Higher School.This research has made use of data from the OVRO 40-m monitoring program (Fan & Wu 2018) which issupported in part by NASA grants NNX08AW31G, NNX11A043G, and NNX14AQ89G and NSF grantsAST-0808050 and AST-1109911.
References
Acero, F., Ackermann, M., Ajello, M., et al. 2015, ApJS, 218, 23 2Aleksi´c, J., Ansoldi, S., Antonelli, L. A., et al. 2015, A&A, 576, A126 3Angel, J. R. P., & Stockman, H. S. 1980, ARA&A, 18, 321 2Bhatta, G. 2017, ApJ, 847, 7 2, 7
Bhatta, G. 2018, Galaxies, 6, 136 2, 7Bhatta, G., Zola, S., Stawarz, Ł., et al. 2016, ApJ, 832, 47 2, 7B¨ottcher, M. 2007, Ap&SS, 309, 95 2Caproni, A., & Abraham, Z. 2004, ApJ, 602, 625 10Caproni, A., Abraham, Z., & Monteiro, H. 2013, MNRAS, 428, 280 10Chai, B., Cao, X., & Gu, M. 2012, ApJ, 759, 114 10Ciaramella, A., Bongardo, C., Aller, H. D., et al. 2004, A&A, 419, 485 9Conway, J. E., & Murphy, D. W. 1993, ApJ, 411, 89 9Dermer, C. D. 1995, ApJ, 446, L63 2Esposito, V., Walter, R., Jean, P., et al. 2015, A&A, 576, A122 1Fan, J. H., Liu, Y., Yuan, Y. H., et al. 2007, A&A, 462, 547 9Fan, X.-L., & Wu, Q. 2018, ApJ, 869, 133 10, 11Foster, G. 1996, AJ, 112, 1709 7Gupta, A. 2018, Galaxies, 6, 1 2Gupta, A. C., Tripathi, A., Wiita, P. J., et al. 2019, MNRAS, 484, 5785 1, 6, 7Gupta, A. C., Agarwal, A., Bhagwan, J., et al. 2016, MNRAS, 458, 1127 2Healey, S. E., Romani, R. W., Cotter, G., et al. 2008, ApJS, 175, 97 2Heidt, J., & Wagner, S. J. 1996, A&A, 305, 42 3Katz, J. I. 1997, ApJ, 478, 527 10King, O. G., Hovatta, T., Max-Moerbeck, W., et al. 2013, MNRAS, 436, L114 7Komossa, S. 2006, Mem. Soc. Astron. Italiana, 77, 733 10Lehto, H. J., & Valtonen, M. J. 1996, ApJ, 460, 207 9Li, X.-P., Luo, Y.-H., Yang, H.-Y., et al. 2017, ApJ, 847, 8 10Li, X.-P., Luo, Y.-H., Yang, H.-Y., et al. 2018, Ap&SS, 363, 169 2Liu, Y., Jiang, D. R., & Gu, M. F. 2006, ApJ, 637, 669 10Qian, S.-J., Kudryavtseva, N. A., Britzen, S., et al. 2007, ChJAA (Chin. J. Astron. Astrophys.), 7, 364 10Richards, J. L., Max-Moerbeck, W., Pavlidou, V., et al. 2011, ApJS, 194, 29 2Sandrinelli, A., Covino, S., Dotti, M., & Treves, A. 2016, AJ, 151, 54 2Sbarrato, T., Ghisellini, G., Maraschi, L., & Colpi, M. 2012, MNRAS, 421, 1764 10Scargle, J. D. 1982, ApJ, 263, 835 8Shaw, M. S., Romani, R. W., Cotter, G., et al. 2012, ApJ, 748, 49 10Shen, Y., Richards, G. T., Strauss, M. A., et al. 2011, ApJS, 194, 45 10Timmer, J., & Koenig, M. 1995, A&A, 300, 707 9Urry, C. M., & Padovani, P. 1995, PASP, 107, 803 2Valtaoja, E., Ter¨asranta, H., Tornikoski, M., et al. 2000, ApJ, 531, 744 9Vaughan, S., Edelson, R., Warwick, R. S., & Uttley, P. 2003, MNRAS, 345, 1271 3Wang, J.-M., Luo, B., & Ho, L. C. 2004, ApJ, 615, L9 10Xie, G. Z., Liu, F. K., Liu, B. F., et al. 1991, A&A, 249, 65 10Xie, G. Z., Zhou, S. B., & Liang, E. W. 2004, AJ, 127, 53 10 igh-confidence radio QPO in FSRQ PKS J0805-0111 13igh-confidence radio QPO in FSRQ PKS J0805-0111 13