HARMONIC QPOs AND THICK ACCRETION DISK OSCILLATIONS IN THE BL LACERTAE OBJECT AO

Transcription

1 The Astrophysical Journal, 650:749Y762, 2006 October 20 # The American Astronomical Society. All rights reserved. Printed in U.S.A. HARMONIC QPOs AND THICK ACCRETION DISK OSCILLATIONS IN THE BL LACERTAE OBJECT AO F. K. Liu, G. Zhao, and Xue-Bing Wu Department of Astronomy, Peking University, Beijing, China; fkliu@bac.pku.edu.cn, wuxb@bac.pku.edu.cn Received 2006 April 24; accepted 2006 June 26 ABSTRACT Periodic outbursts are observed in many active galactic nuclei (AGNs) and are usually explained with a supermassive black hole binary (SMBHB) scenario. However, multiple periods are observed in some AGNs and cannot be explained in this way. Here we analyze the periodicity of the radio light curves of AO at multiple frequencies and report the discovery of six quasi-periodic oscillations (QPOs) in the integer frequency ratio 1:2:3:4:5:6, of which the second, with period P 2 = yr, is the strongest. We fit the radio light curves and show that the initial phases of the six QPOs have differences of 0 or relative to each other. We suggest a harmonic relationship among the QPOs. The centroid frequency, relative strength, harmonic relationship, and relative initial phases of the QPOs are independent of radio frequency. The harmonic QPOs are likely due to quasi-periodic injection of plasma from an oscillating accretion disk into the jet. We estimate a supermassive black hole mass of M BH ( ) ; 10 8 M and an accretion rate ṁ With knowledge of the accretion disk, this implies that the inner region of the AO accretion disk is a radiatively inefficient accretion flow. The oscillatory accretion is due to p-mode oscillations of the thick disk, probably excited by a SMBHB. Theoretical predictions for the fundamental oscillation frequency and the harmonics show good consistency with the observations. Harmonic QPOs would disappear if the thick disk became geometrically thin as the result of an increase in accretion rate. We discuss the observations of AO in the context of the SMBHBYthick disk oscillation scenario. Subject headinggs: accretion, accretion disks BL Lacertae objects: individual (AO ) galaxies: active galaxies: interactions hydrodynamics radio continuum: galaxies 1. INTRODUCTION Blazars, consisting of BL Lacertae objects and flat-spectrum radio quasars, are a subclass of active galactic nuclei (AGNs) whose relativistic jets are nearly aligned with the line of sight, and which show extreme variability at radio through optical and X-ray to highenergy -ray wavelengths (Antonucci 1993; Urry & Padovani 1995; Wagner & Witzel 1995; Ulrich et al. 1997). Long-term multiwavelength monitoring has shown that the variability of blazars is very complex, with large-amplitude changes on timescales ranging from tens of minutes, hours, and days to months and years at all wavelengths. The outbursts with timescales on the order of years or longer in some blazars are periodic (Sillanpää etal. 1988; Liu et al. 1995b; Liu et al. 1997; Raiteri et al. 2001; Qian & Tao 2004) and of particular interest, as they might be connected to the presence of a supermassive black hole binary (SMBHB) at the center (Sillanpää et al. 1988; Liu & Wu 2002; Qian & Tao 2004; Ostorero et al. 2004), whose ultimate coalescence would generate an outburst of gravitational wave radiation ( Thorne & Braginskii 1976) and be the main target of a future space gravitational wave detector, the Laser Interferometer Space Antenna (LISA) ( Merritt & Milosavljević 2005). SMBHBs in galactic nuclei are expected within the hierarchical galaxy formation model in the cold dark matter cosmology ( Kauffmann & Haehnelt 2000), in which present-day galaxies are the products of frequent minor mergers. Active SMBHBs and final coalescence have been suggested to be the physical origin of the peculiar radio morphologies in some AGNs (for a recent review, see Komossa 2003), for example, the helical morphology of radio jets ( Begelman et al. 1980), the interruption and recurrence of activity in double-double radio galaxies ( Liu et al. 2003), the X-shaped feature of winged radio sources ( Merritt & Ekers 2002; Liu 2004), and the orbital motion of radio cores (e.g., Sudou et al ). Since being discovered in the BL Lac object OJ 287 (Sillanpää et al. 1988), the periodic optical outbursts of blazars have been ascribed to the orbital motion of a SMBHB (Sillanpää et al. 1988; Abraham & Romero 1999; Valtaoja et al. 2000; Liu & Wu 2002; Rieger 2004; Lobanov & Roland 2005). However, it is unclear how SMBHBs in AGNs trigger the observed periodic outbursts if present. Scenarios proposed in the literature include (1) direct impact of the secondary black hole against a standard thin accretion disk (e.g., Lehto & Valtonen 1996) or an inefficient accretion flow, for example, an advection-dominated accretion flow ( Liu & Wu 2002), (2) rotating helical jets due to the orbital motion of the SMBHB (Katz 1997; Villata et al. 1998; Ostorero et al. 2004; Rieger 2004), and (3) periodic changes in jet orientation introduced by the Lens-Thirring precession of a warped disk (Abraham & Romero 1999; Lobanov & Roland 2005). Although the detailed physical mechanisms in these models are different, all suggest a common feature with a single period in the light curves. One more complication in the investigation of the periodicity of blazars arises from observations of low-frequency X-ray quasiperiodic oscillations (QPOs) in black hole X-ray binaries (Hasinger et al. 1986; van der Klis 1989; Strohmayer et al. 1996) and possibly in Sgr A* at the Galactic center (Török 2005), which are believed to be due to oscillations of the disk. Black hole X-ray binaries, so-called microquasars, are a physical analog to AGNs and are powered through accretion by stellar-mass black holes, of about 10 M. As the variation timescale of an accretion disk around a black hole is proportional to the mass of the black hole and the formation of a jet is coupled with the accretion disk (Gallo et al. 2003; Fender & Belloni 2004; Fender et al. 2004), the lowfrequency QPOs (with typical frequency 1 Hz) in microquasars correspond to a period on the order of years or longer in a blazar system with black hole mass larger than 10 8 M. Disk oscillations may cause a periodic change in accretion and the QPOs in an

2 750 LIU, ZHAO, & WU Vol. 650 X-ray black hole binary system ( Rezzolla et al. 2003a), which could lead to periodic jet emission due to jet-disk coupling. To understand the physical origin of periodic outbursts, it is essential to investigate in detail their structure in both light curves and the power density spectrum, and the dependence of the periodicity on observational wavelength. For example, the discovery of double peaks in the periodic optical outbursts of the BL Lac object OJ 287 (Sillanpää et al. 1996) led to a second version of the SMBHB model (Lehto & Valtonen 1996), while the investigation of the relation between the optical outburst structure and the radio variations led to a third (Valtaoja et al. 2000; Liu & Wu 2002). It is generally believed that the short-term variability of blazars is nonperiodic (e.g., Wagner & Witzel 1995; Ulrich et al. 1997), but the short-term periodic brightness flickering may have been found to be superposed on long-term periodic variations in some blazars, for example, OJ 287 (Wu et al. 2006) and 3C 66A (Lainela et al. 1999). In order to place more constraints on models for the periodic outbursts in AGNs, recently we started a program to investigate the relationships between periodic major outbursts and minor events and the long- and shortterm periodicities of a large sample of AGNs (G. Zhao, F. K. Liu, & X.-B. Wu 2006, in preparation). Here we report the finding of multiple QPOs with frequencies in the harmonic resonant relationship 1:2:3:...in the BL Lac object AO This object, with redshift z = 0.94, is one of the most violently variable objects, and the periodicity of its outbursts in the optical and radio bands has been widely investigated and reported in the literature (e.g., Webb & Smith 1989; Webb et al. 2000; Roy et al. 2000; Raiteri et al. 2001, 2005). Roy et al. (2000) analyzed data from the University of Michigan Radio Astronomy Observatory at frequencies of 4.8, 8.0, and 14.5 GHz from 1975 to 1999 and discovered a period of 5.8 yr at 8.0 and 14.5 GHz, which is consistent with observations of a period of 5.7 yr in the optical ( Raiteri et al. 2001, 2005). Ostorero et al. (2004) interpreted the long-term periodicity of the major outbursts with a helical jet model and associated the minor events with rotation of nonperiodic inhomogeneities. However, the radio outbursts are double peaked, and the burst peaks do not appear as regularly as the predicted period ( Raiteri et al. 2001, 2005), implying that the substructure of the outburst is complex. On the other hand, multiple short periods although at a much less significant level of signal-to-noise ratio and with poor identification of central frequency have been claimed in the literature. Webb & Smith (1989) first identified three peaks with periods of 2.79, 1.58, and 1.29 yr in the Fourier power spectrum of the optical light curves. Subsequent observations marginally confirmed the periods, with 2.7 and 1.2 yr in the optical (Webb et al. 2000) and with 1.8, 2.8, and 3.7 yr in radio wave bands using the discrete correlation function ( DCF) analysis method ( Raiteri et al. 2001). Our work is based on the three radio databases of the University of Michigan Radio Astronomy Observatory ( UMRAO), the National Radio Astronomy Observatory ( NRAO), and the Metsähovi Radio Observatory. In x 2, we start the investigation by analyzing the consistency of the UMRAO and NRAO databases, comparing the best-sampled observations at 8.0 GHz from UMRAO and those at 8.2 GHz from NRAO and then merging the observational data at these two frequencies. The results of the periodicity analysis for the combined light curves at 8 GHz and identification of the harmonic QPOs are given in x 3. In x 4, we investigate the dependence of QPO properties on radio frequency. After estimating the mass of the central supermassive black hole (SMBH) and the accretion rate in x 5.1, we analytically discuss the p-mode oscillation of the thick disk in x 5.2. A SMBHBYdisk oscillation scenario for multiple harmonic QPOs Fig. 1. Correlation of the observations from UMRAO at 8.0 GHz ( y-axis) and from NRAO at 8.2 GHz (x-axis). The data are 10 dayyaveraged, and the solid line is a least-squares fit. is suggested and discussed in x 6. Our discussion and conclusions are given in x 7. We assume a flat cosmology with H 0 = 75 km s 1 Mpc 1, = 0, and q 0 = 0.5 throughout, leading to a source distance d 4.4 Gpc. 2. DATABASES AND THEIR CONSISTENCY UMRAO has been monitoring AO at 4.8, 8.0, and 14.5 GHz for about three decades (Aller et al. 1985, 1999), while NRAO s database contains observational data at 2.5 and 8.2 GHz spanning about 20 years (Fiedler et al. 1987; Waltman et al. 1991; Lazio et al. 2001). At frequencies of 22 and 37 GHz, the Metsähovi Radio Observatory started collecting flux data in 1980 ( Teräsranta et al. 1998, 2004). As the central frequencies of 8.0 and 8.2 GHz are almost the same and light curves at these two frequencies are the best sampled in both the UMRAO and NRAO databases, here we investigate the consistency of the observations and construct a combined light curve based on the data from both databases. The UMRAO observations span about 25 years with relatively sparse data sampling (0.1 data points per day), while those from NRAO cover a shorter time of about 15 years with relatively dense data sampling (0.5 data points per day). To remove the effects of intraday variability (Romero et al. 1997) and of noise due to uneven sampling, we compose two quasi-simultaneous observational light curves by averaging the observational data with a 10 day time interval, which is much shorter than the variability timescale (on the order of months) of major outbursts but gives, respectively, about one and five observations in each bin at 8.0 and 8.2 GHz to smooth the intraday random variations. The results are shown in Figure 1. The standard error in the figure is the statistical error. A least-squares fit gives, with a correlation coefficient r = 0.989, F 8:0 ¼ ( 0:017 0:014) þ (1:072 0:006)F 8:2 ; where F 8:0 and F 8:2 are the radio fluxes at 8.0 GHz (UMRAO) and at 8.2 GHz (NRAO), respectively. The results show that the observations from UMRAO and NRAO are consistent with each other with a linear relation but the slope is not exactly unity. So we merged the observational data at 8.0 and at 8.2 GHz to obtain a combined light curve by converting NRAO s observations using the fitted relation (eq. [1]). The combined radio light curve at ð1þ

3 No. 2, 2006 HARMONIC QPOs IN AO Fig. 2. Power spectrum of the combined radio light curve at 8 GHz. The fitted centroid periods of QPOs are indicated. The dashed and dash-dotted lines are the 1 and 3 significance levels, respectively. 8 GHz is given in Figure 7 below, which shows that the combined light curve fully covers several major outbursts in detail although the combined data do not cover a significantly longer time. In the following sections, we give results of the periodicity analysis and discussion based on the combined light curve at 8 GHz. In order to show how efficiently and to what extent the combination of two databases can improve the results, we also analyze the radio light curves at 8.0 and 8.2 GHz separately. 3. MULTIPLE QPOs IN THE COMBINED 8 GHz LIGHT CURVE We analyze the periodicity of the combined light curve at 8 GHz by computing the Fourier power spectrum with a Lomb normalized periodogram ( Lomb 1976; Scargle 1982), which is designed to properly treat unevenly sampled data. The power spectrum is shown in Figure 2. There are several very prominent peaks in the power spectrum with very high signal-to-noise ratios. We identify a peak with a QPO if (1) it is at least 5 times higher than the nearby background noise, (2) it has a Gaussian profile, and (3) it is also detected with other period analysis methods, for example, the Jurkevich Vm 2 method (Jurkevich 1971) or the z-transform discrete correlation function technique (Alexander 1997), or (4) it correlates with other QPOs, for example, having a harmonic relationship. Before discussing the results from the combined light curve, we first investigate the effect of the combination of the two databases. We analyze, respectively, with the Lomb method, the light curves at 8.0 GHz from UMRAO and at 8.2 GHz from NRAO; the power spectra are given in Figure 3. All the peaks in Figure 3 are present in Figure 2, and the combination of the two databases can be seen to significantly improve the signal-to-noise ratio of the power spectrum, which in the combined light curve is unprecedentedly high. This is because the radio light curve at 8.0 GHz has relatively sparse data points and misses the structural information of the major bursts, while the observations at 8.2 GHz span a shorter time interval and give only broad peaks in the power spectrum with small coherence quality factors. The second effect one can read from Figures 2 and 3 is that although most of the peaks in the power spectrum of the combined radio light curve can be found in the power spectra of the radio light curves at 8.0 and 8.2 GHz, the central frequency of each peak is significantly different. A prominent peak at 8.50 yr in the periodogram of the radio light curve at 8.0 GHz is absent in both the power spectra of the combined radio light curve and the light curve at 8.2 GHz. Therefore, it is probably spurious because of the low signal-to-noise ratio, due to the incomplete coverage of major outbursts in the sparsely sampled light curve at 8.0 GHz and to the loss of the burst structure information. To solve this problem, much more intensive observations are need. The peaks in Figure 2 are Gaussian, although some of them overlap with each other. Therefore, we fitted each peak profile with a Gaussian function or, if necessary, fitted several peak profiles together with Gaussian functions. The fit results are given in Table 1. Columns (1) and (2) give the observational radio frequency obs and the averaged periods of the fundamental QPO and their standard errors. We discuss the definition of the fundamental QPO and how to calculate the average period below. The centroid frequency and the standard error of each peak are given in column (3) and indicated in Figure 2. The fit goodness 2 is presented in column (7). The standard error is that of the fitted Gaussian function and is considered to contain all the effects, including random variations in the exact quasi-periodic oscillation, the large and changing width of the outburst structure, the poor coverage of some outbursts, random variations in intensity, and in particular the intrinsic coherence of variability. To quantify the coherence of the variabilities, we calculate the quality factor Q = /HWHM and give it in column (6), where HWHM is the half-width at half-maximum of a peak. The quality factor Q in Table 1 increases with QPO frequency and Fig. 3. Same as Fig. 2, but for the UMRAO (left) and NRAO (right) light curves analyzed separately.

4 752 LIU, ZHAO, & WU Vol. 650 TABLE 1 Harmonic QPOs in the Radio Light Curves at 4.8, 8, 14.5, 22, and 37 GHz Analyzed with the Lomb Power Spectrum Method obs (GHz) (1) P s (yr) (2) (10 3 day 1 ) (3) rms (%) (4) P (yr) (5) Q (6) 2 (7) N (8) / s (9) ID (10) 0 (;) (11) Combined Light Curve Individual Light Curves (5) ( 0.41) (5) ( 0.29) (5) (0.36) correlates with the repetitions of a QPO in the combined radio light curve, which is calculated as N = T,whereT 26.3 yr is the total observation time for the combined data sample. A strong correlation between the quality factor Q and the repetition number N is evident from Figure 4, implying that the value of the coherence factor Q and the quality of QPOs are limited by the duration of the monitoring program. Therefore, to understand the intrinsic coherence of a QPO, we have to monitor the object for a much longer time. In the Lomb periodogram of the combined 8 GHz light curve, we identify six QPOs, with frequencies (periods) 1 = ; 10 3 day 1 (P 1 = yr), 2 = ; 10 3 day 1 (P 2 = 5.45 yr), 3 =0.7568; 10 3 day 1 (P 3 =3.62yr), 4 =0.9691; 10 3 day 1 (P 4 = 2.83 yr), 5 = ; 10 3 day 1 (P 5 = 2.15 yr), and 6 =1.511; 10 3 day 1 (P 6 = 1.81 yr). The periods of the QPOs and their standard errors are given in column (5) of Table 1. To estimate the relative contribution of each QPO signal to the total flux variation, we compute the relative percentage root mean square (rms) and give the results in column (4). The results show that the QPO with period P =5.45yristhe strongest, with rms 10%, although the other QPOs are also significant. We identify the frequency of the strongest QPO with the fundamental, with frequency s. In order to confirm the detection of multiple QPOs, we next apply the least-variance analysis introduced by Jurkevich (1971) Fig. 4. Quality factor Q vs. repetition number N of QPOs in the combined radio light curves. The correlation of Q and N implies that the Q-value is limited by the time the object is monitored and that much longer observations are needed to place stringent constraints on the intrinsic coherence of QPOs.

5 No. 2, 2006 HARMONIC QPOs IN AO Fig. 5. Normalized Jurkevich periodicity analysis results for the combined radio light curve at 8 GHz. The minima corresponding to periods 1.78, 3.46, 5.34, 7.90, and yr are prominent. A period is strong if f > 0.25, with f = (1 V 2 m )/V 2 m. and the z-transform discrete correlation function ( ZDCF) technique (Alexander 1997) to the combined 8 GHz light curve. The Jurkevich method has been successfully developed to search for periods in the optical light curves of some blazars (e.g., Kidger et al. 1992; Liu et al. 1995b, 1997). The method is based on the expected mean square deviation and specifically designed for unevenly sampled data sets. It tests a run of trial periods. A light curve is first folded on a trial period, and the variance Vm 2 is computed first for each phase bin and then over a whole period. For a false trial, Vm 2 is almost constant, but for a true one it reaches a minimum. Instead of the normalized Vm 2 itself, a parameter f = (1 Vm 2)/V m 2 is usually introduced to describe the significance of a period in a light curve (Kidger et al. 1992; Liu et al. 1995b). It is suggested that f > 0.25 implies a strong period. A more general description and a robust test of the method has been given by Liu et al. (1997). The results of the analysis with the Jurkevich Vm 2 method are given in Figure 5. In the V m 2 plot, with very high signal-to-noise ratio, there are several very prominent broad minima at the trial periods 1.78, 3.46, 5.34, 7.90, 11.60, and yr. The last period may not be real, because it is very long and the data sample covers it fewer than two times. Among all six QPOs detected with the Lomb power spectrum method, strong QPOs of period P 1, P 2, P 3, and P 6 with rms larger than 7% are clearly detected by the Vm 2 method, although the central frequencies of the periods shift toward to the lower end and cannot be determined accurately because of high noise. Weak QPOs 4 and 5, with rms P6%, are insignificant in the normalized Vm 2 plot and are nearly drowned out by noise. In Figure 5, a period P = 7.90 yr is significant but not present in the Lomb periodogram shown in Figure 2. One possibility is that the QPO at P 1 = yr with low quality factor Q in the Lomb periodogram may consist of several QPOs (e.g., those periods P = 7.90, 11.60, and yr in the normalized Vm 2 plot) and cannot be resolved because of the very low quality factor Q. However, it is more likely that the 7.90 yr period in Figure 5 does not represent a real QPO but is just a spurious period at the position of 2 and 4 times the two strong QPOs with P 3 =3.62yrandP 6 = 1.81 yr, respectively. Or, the period P = 7.90 yr could just be the result of an incorrect identification of noise. We also analyzed the combined radio light curve with the ZDCF technique (Alexander 1997), which is designed to properly treat unevenly sampled data sets. The discrete self-correlation Fig. 6. Periodicity analysis results with the ZDCF method. The results are consistent with those from the Jurkevich Vm 2 method, and the two weakest QPOs in the Lomb periodogram are missing. function has been successfully used to search for periods in the light curves of AO (e.g., Raiteri et al. 2001), and ZDCF is basically the same as DCF. The self-zdcf function of the combined radio light curve at 8 GHz is shown in Figure 6. In self- ZDCF, a local maximum implies a period. In the figure, all the maxima have very broad profiles and the period is difficult to determine accurately. Because our purpose is to confirm the periodicity results obtained with the Lomb power spectrum method and the Jurkevich method, we do not try to compute periods from ZDCF accurately but simply estimate a period at peak. The five identified QPOs have periods of 11.34, 7.39, 5.53, 3.33, and 1.88 yr. The periodicity analysis results with the ZDCF and Jurkevich methods are consistent with each other within the estimated errors but not fully consistent with the results from the Lomb power spectrum method. Like the Jurkevich method, ZDCF does not detect the two weak periods at P 4 = 2.83 yr and P 5 = 2.15 yr obtained with Lomb s method. This might be due to the broad profiles of the strong 1.88 and 3.33 yr periods in the ZDCF or to the weakness of the two periods, so that the two weak QPOs are absent in the ZDCF. The conclusions from the three different analysis methods are that the strong QPOs with periods 12.02, 5.45, 3.62, and 1.81 yr are detected with unprecedentedly high signal-to-noise ratio in the combined 8 GHz radio light curve. Two weak QPOs with P = 2.83 yr and P = 2.15 yr are detected by the Lomb power spectrum method but are not detected by the other two methods, because of their weakness. They will be confirmed with a periodicity investigation of radio light curves at multiple frequencies in x HARMONIC RELATIONSHIP AND DEPENDENCE OF QPOs ON RADIO FREQUENCY 4.1. Harmonic Relationship of QPOs The ratio of centroid frequency to fundamental frequency, f = / s, of the six QPOs is given in column (9) of Table 1. We do not compute the error for the ratio, as the standard errors of the frequencies given in column (3) are limited by the time coverage of the data sample. The ratios f of the six QPOs can be given by the simple relation f = I/2 with I =1,2,3,4,5,6;that is, all six QPOs are in the harmonic relation 1 : 2 : 3 : 4 : 5 : 6 = 1:2:3:4:5:6. The identifications are given in column (10) of Table 1. With these identifications, we calculate the averaged P fundamental frequency s and the standard error s as s = s (j / j )/N

6 754 LIU, ZHAO, & WU Vol. 650 Fig. 7. Radio light curves of AO The observation frequencies are indicated at upper right. The solid lines are the result of fitting with six QPOs, and the dotted lines are the result of fitting with the fundamental QPO, of period P s. The results clearly show that in addition to the fundamental QPO the other five harmonics significantly contribute to the variations of the radio light curves. and 1/ s = P ( j/ j )/2N with j =2,..., 6, where N is the total number of QPOs used in the calculation. In this computation, we do not take into account the QPO with the lowest frequency, 1 (the longest period, P 1 = yr), because of its low quality factor, Q = The averaged frequency of the fundamental QPO is s =( ) ; 10 3 day 1 (period P s = yr). Using the least-squares method, we fitted the combined 8 GHz radio light curve both with the fundamental QPO alone ( 2 = ) and with the six detected QPOs ( 2 = ), and the results are given in Figure 7. The figure shows that the fundamental QPO alone cannot satisfactorily reproduce the radio light curve, while the fit with six QPOs can reproduce it very well until about the year This implies that the contributions from the harmonic QPOs are significant, and the subpeaks of the outbursts are not random but have the same physical origin as the major outbursts. The differences of the initial phases of the six QPO harmonics relative to the fundamental are listed in the last column of Table 1. The results show that QPOs 1, 2, 3, 5, and 6 almost have the same initial phase, with 0 0, while 0 for the fourth QPO, 4. The initial phase differences 0 of the first and the fifth QPOs deviate from zero because of the large fit uncertainties, due to the low quality factor Q for the first harmonic and to the weakness (rms = 4.70%) of the fifth harmonic, respectively. The relative initial phases of the QPOs

7 No. 2, 2006 HARMONIC QPOs IN AO Fig. 8. Same as Fig. 2, but for the radio light curves at 4.8 GHz (top left), 14.5 GHz (top right), 22 GHz (bottom left), and 37 GHz (bottom right). The radio data at 4.8 and 14.5 GHz are from UMRAO, and those at 22 and 37 GHz are from Metsähovi Radio Observatory. are consistent with the suggestion of a harmonic relationship among them Frequency Dependence of Harmonic QPOs In this subsection, we present QPO analyses with the radio light curves at 4.8, 14.5, 22, and 37 GHz and investigate the dependence of the harmonic QPOs on radio frequency. Since our purpose is to investigate the QPOs and their frequency dependence, we give only results from the Lomb power spectrum method. The radio data at 4.8 and 14.5 GHz from UMRAO and at 22 and 37 GHz from Metsähovi are plotted in Figure 7. The results of the periodicity analysis are given in Figure 8. Figure 8 shows that the Lomb periodograms of the radio light curves at these four radio frequencies are very noisy, and their signal-to-noise ratios are significantly lower than that of the combined radio light curve at 8 GHz. Among the six QPOs obtained at 8 GHz, the five strongest are detected in the radio light curves at all the radio frequencies, while the weakest QPO, with period P 5 = 2.15 yr and rms = 4.70%, at 8 GHz is significantly detected only at 14.5 GHz, at which frequency the radio light curve is relatively well sampled. At 4.8, 22, and 37 GHz, the weakest QPO is absent from the Lomb power spectra, probably because of poor sampling and the missing of information on the minor events. As at 8 GHz, the peak with a period at P 7yr obtained with both the Jurkevich Vm 2 and the ZDCF methods is not present in the Lomb periodograms at any of the radio frequencies in Figure 8. Table 1 lists the Gaussian-fitted centroid frequency, fit goodness 2, relative strength rms, quality factor Q, the ratio of the frequencies of the harmonics and the fundamental QPOs, and the averaged fundamental period P s. Again, the QPOs clearly have a harmonic relationship, and the identification of the harmonic number is given in column (10). Like what we did for the combined 8 GHz light curve, with the leastsquares method we also fitted the radio light curves at 4.8, 14.5, 22, and 37 GHz both with the fundamental QPO s alone and with the six QPOs together. The fitted light curves are given in Figure 7, and the differences of the initial phases of the harmonic and fundamental QPOs are listed in column (11) of Table 1. From the fit results in Table 1, the differences in initial phase of the six QPOs at the four radio frequencies are consistent with the results obtained at 8 GHz: five QPOs, 1, 2, 3, 5, and 6, have almost the same initial phase but are about different from the fourth one. The results strongly support the identification of the six QPOs and the harmonic relationship. The dependence of QPO centroid frequency on the observational radio frequencies is given in Figure 9, which shows that the QPO frequencies are independent of the radio frequency and that the ratios of the frequencies of the harmonic QPOs at the four radio wave bands to the fundamental, with s = ; 10 3 day 1 at 8 GHz, are also independent of the radio frequency, implying that the QPO centroid frequencies and the harmonic relationship are not determined by different radio emission

8 756 LIU, ZHAO, & WU Vol. 650 Fig. 9. Dependence of QPO frequencies on radio frequency. The horizontal dashed lines with small integer numbers N = 1, 2, 3, 4, 5, and 6 indicate the expected ratio of frequencies of the QPOs and the basic QPO with the lowest frequency (calculated based on the fundamental QPO frequency s at 8 GHz). The centroid frequencies and the harmonic relationship of the QPOs are independent of the observational radio frequency. regions in the relativistic jet. However, this independence does not mean that one could detect all the harmonic components of the QPOs at all wave bands. To answer this question, we investigated the dependence of relative amplitude rms on radio frequency. Figure 10 shows that the relative amplitude rms of all the QPOs is a function of radio frequency and that the third QPO has the strongest dependence. However, this conclusion is very sensitive to the periodicity analysis of the radio light curve at 37 GHz, which is poorly sampled. Therefore, the decrease of QPO amplitudes may be due to a loss of information on high-frequency QPOs in the poorly sampled radio light curves. To eliminate the effect of the incomplete coverage of outburst structures on the analysis, we calculate the ratio of the rms of the harmonics and rms ( s )ofthe fundamental QPO. The results are given in the bottom panel of Figure 10; rms/rms ( s ) for the first, fourth, and sixth components of the harmonic QPOs is nearly independent of frequency, while for the third harmonics the ratio decreases with radio frequency. Again, the conclusion is sensitive to the period analysis results for the 37 GHz light curve. If the results at 37 GHz are not considered, the QPO harmonics are nearly independent of radio frequency. The results suggest that if one were to detect the fundamental QPO, of period P s = 5.46 yr, in a well-sampled light curve at high frequency for example, in the optical wave bands one would simultaneously detect the other QPOs with periods P yr, P yr, and P yr. But, the QPO with period P 3 = 3.6 yr might not be observable in the optical wave band. Although this conclusion needs to be tested with many more observations at 37 GHz, our results suggest that the properties of QPOs would be independent of radio frequency and not be determined by the physical processes in the radio emission regions of the jet. 5. CENTRAL BLACK HOLE MASS AND THICK DISK OSCILLATIONS Raiteri et al. (2001) reported the detection of a P = yr period in the optical and radio light curves of AO Ostorero et al. (2004) interpreted this with a helical jet model, in which the quasi-periodic radio-optical light curve and the spectral energy distributions are caused by the varying orientation of a helical, inhomogeneous, nonthermally emitting jet, probably due to the orbital motion of the primary black hole in a binary Fig. 10. Percentage amplitude rms of QPO harmonics as a function of radio frequency (top) and the amplitude rms relative to that of the fundamental QPO (the second harmonic) vs. radio frequency (bottom). The solid lines are the fitted results using the least-squares method. system. In the helical jet model, the minor burst events are taken as nonperiodic flux fluctuations due to random plasma instabilities. However, our periodicity analyses show that the major outbursts and the minor burst events are the products of combinations of six harmonic QPOs, which suggests quasi-periodic radio emission from relativistic jets and a physical origin for the harmonic QPOs independent of the radio emission regions in the jet. The multiplicity, the harmonic relationship, the zero differences of initial phases, and the independence of relative rms on radio frequency imply that the harmonic QPOs in the radio light curves of AO are most likely due to a quasi-periodic injection of plasma from the accretion disk into the relativistic jet. Because of the coupling between jet and disk (Fender & Belloni 2004), such a quasi-periodic plasma injection implies a quasi-periodic oscillation of accretion around the SMBH. Both thin and thick accretion disks can oscillate quasiperiodically, but only the oscillation of a thick disk can be global and trigger such quasi-periodic accretion with harmonic frequencies. Rezzolla et al. (2003a) and Zanotti et al. (2003) found that the accretion rate of a torus or thick disk of finite radial extent is quasi-periodic because of the global p-mode oscillation, which could be excited by a global perturbation (Rezzolla et al. 2003b; Zanotti et al. 2003) or a local, periodic, strong agent (Rubio- Herra & Lee 2005a, 2005b). Such a torus or thick disk of finite

9 No. 2, 2006 HARMONIC QPOs IN AO radial extent could be an optically thin and geometrically thick radiatively inefficient accretion flow ( RIAF) or an advectiondominated accretion flow (ADAF) between a central supermassive black hole and an outer-truncated, geometrically thin disk. It is clear now that such a configuration should be present in a black hole accretion system if the dimensionless accretion rate ṁ Ṁ/Ṁ Edd is lower than a critical value ṁ cr 0.02 (see, e.g., Meyer & Meyer-Hofmeister 1994; Narayan & Yi 1995; Narayan 2002; Esin et al. 1997; Meyer et al. 2000; Meyer-Hofmeister et al. 2005), where Ṁ Edd = L Edd /0.1c 2 is the Eddington accretion rate relative to the Eddington luminosity L Edd 1.26 ; [M/(10 8 M )] ergs s 1. Because the p-mode oscillation frequency of a thick accretion disk is determined by the disk s radial extent, defined with the dimensionless accretion rate, we now estimate the mass M BH of central black hole and then the dimensionless accretion rate ṁ of AO Black Hole Mass and Accretion Rate As there is no valid estimate of the black hole mass of AO in the literature, we estimate it and the accretion rate in this subsection, before we investigate the physical origin of the QPOs. Because of the high redshift (z = 0.94) and the very bright central nucleus, it is impossible to resolve the host galaxy of AO even with the Hubble Space Telescope and to infer the black hole mass using the tight relation between black hole mass and the properties of the galaxy bulge (e.g., stellar velocity dispersion ). However, we can estimate the mass using some recently suggested relations between emission-line properties and central black hole mass in AGNs. Reverberation mapping studies reveal an empirical relation between the size of the broad emission line region (BLR) and the optical continuum luminosity at rest-frame : 0:690:05 R BLR klk (5100 8) ¼ (2:23 0:21) 10 lt-days ergs s 1 (Kaspi et al. 2005). Together with the FWHM of the H emission line, which is a measurement of the characteristic velocity of broad emission line clouds, one can estimate the central black hole mass of an AGN with the relation M BH ¼ 1:936 ; 10 5 RBLR 1 lt-day 2 FWHM(H) 10 3 km s 1 M (Peterson et al. 2004). The environment of AO is rather complex because of the presence of several intervening foreground galaxies within a few arcseconds. Great efforts have been taken to study the emission-line features of this object with spectroscopic observations. Using the 3 m Shane Telescope at Lick Observatory, Cohen et al. (1987) identified emission lines of Mg ii,[nev], and [O ii] at the source redshift. With the 4 m William Herschel Telescope, Nilsson et al. (1996) detected not only the [Ne v] and [O ii] lines, but also prominent H and H hydrogen emission lines at the same redshift. Nilsson et al. determined the FWHM and flux (in the observer s frame) of H (4102 8) to be km s 1 and 3.9 ; ergs s 1 cm 2, and those of H (4340 8) to be km s 1 and 9.7 ; ergs s 1 cm 2, respectively. The equivalent widths of the H and H lines are 2.6 and (all quantities are given in the rest frame unless noted). With the assumption of a power-law optical continuum (F / ), we can estimate the flux at 5100 Å from the flux ð2þ ð3þ in the bluer band. However, deriving an accurate value of the spectral index is not a simple task for AO , because of its strong variation (Smith et al. 1987). A visual inspection of Figure 1 of Cohen et al. (1987) reveals that at (observer s frame), the continuum flux density is about 0.5 ; ergs s 1 cm 2 8 1, while at it is about 1.1 ; ergs s 1 cm From these flux values we can derive = 3.54, which is in fair agreement with the value of 3.6 corresponding to a faint state of the source reported in Figure 7 of Raiteri et al. (2001). However, when one takes into account the absorption by the intervening system at z = 0.524, this value is nearly halved. This can be inferred from the intrinsic (dereddened) hb Ri =1.72derived by Raiteri et al. (2005), which, when considering the amount of extra absorption tabulated in their Table 5, gives hi =1.75. We note that this -value implies a relatively flat shape in the optical band of the flux density versus wavelength plot (F k / k 2 ), which is also consistent with the dereddened spectrum shown in Figure 7 of Junkkarinen et al. (2004). Adopting = 1.75, from the observed flux at (rest-frame ) in Figure 1 of Cohen et al. (1987), we calculate the flux density at rest-frame to be 7.5 ; ergs s 1 cm 2 8 1, while from the continuum flux at estimated from the H line flux and equivalent width in Nilsson et al. (1996) we calculate the flux density at rest-frame to be 5.3 ; ergs s 1 cm From the average of these two estimates, we obtain the monochromatic luminosity at with kl k (5100 8) = 7.48 ; ergs s 1. From equation (2), we estimate the BLR size as R BLR = lt-days. Because of the lack of a detection of H for AO in the literature, we try to estimate its FWHM from the observations of other hydrogen Balmer lines. As the observed H line is probably contaminated by [O iii] k4363, we make the estimate with H line data. From the observations of 50 quasars in the Large Bright Quasar Survey (LBQS) given by Forster et al. (2001), we derive an empirical relation between the FWHM values of the H and H lines with the OLS bisector method ( Isobe et al. 1990): FWHM(H) ¼ 415:6 348:8 þ (1:07 0:15) FWHM(H): From the observations of the FWHM of the H line, we have FWHM(H) km s 1 for AO From equation (3), we estimate the central black hole mass in AO to be M BH ( ) ; 10 9 M. However, AO is a blazar-type object, and its optical continuum luminosity is generally dominated by the beamed synchrotron emission from a relativistic jet rather than by the emission from an accretion disk. The southern intervening galaxy with z =0.524 may also partly contribute to the optical continuum luminosity (Nilsson et al. 1996). Therefore, the black hole mass estimated with the optical continuum luminosity is an overestimate and can be taken only as an upper limit. To avoid such an overestimation of black hole mass, Wu et al. (2004) argued that the emission-line luminosity is probably a better tracer of the ionizing continuum luminosity of blazars, and they proposed a new empirical relation between the BLR size and the H emission-line luminosity: log R BLR (lt-days) ¼1:381 0:080 þ (0:684 0:106) log L H ergs s 1 ð4þ : ð5þ

10 758 LIU, ZHAO, & WU Vol. 650 Because no detection of H emission has been reported for AO in the literature, we estimate the luminosity from the observations of H and H line fluxes. Zheng (1988) studied the variations of the Balmer decrements of several quasars. From his Tables 2 and 3, we obtain averaged flux ratios 5 and 2.4 of H to H and H to H, respectively. From the observations of emission lines by Nilsson et al. (1996), we obtain the rest-frame H luminosity for AO as L H 1.68 ; ergs s 1 from the observed flux of the H emission line. The estimated H luminosity from the observed H flux is about 15% higher, which might be a result of contamination from [O iii] k4363. From equation (5) and the H luminosity estimated from the H emissionline flux, we calculate the BLR size as R BLR = lt-days, which is much smaller than that estimated from the optical continuum luminosity. With the estimated BLR size and H FWHM value, from equation (3) we estimate the black hole mass of AO to be M BH = ( ) ; 10 8 M, which is much smaller than the value obtained with the optical continuum luminosity method. McLure & Dunlop (2004) suggested estimating the black hole mass of AGNs from the UV continuum luminosity and the FWHM of the Mg ii emission line with an empirical relation (with cosmological parameters H 0 =70kms 1 Mpc 1, m = 0.3, and = 0.7; the distance of AO is 6.1 Gpc in this case): 0:62 2 kl3000 M BH ¼ 3:2 8 FWHM(Mg ii) ergs s 1 1kms 1 M : ð6þ For AO , the Mg ii emission line is observed to have an FWHM of 3100 km s 1 and a flux of 1.24 ; ergs cm 2 s 1 (Cohen et al. 1987). The equivalent width and the continuum flux are and 0.8 ; ergs cm 2 s 1 8 1, respectively. Using the observations of the Mg ii emission line and the continuum, we derive a rest-frame continuum luminosity at of kl = 7.37 ; ergs s 1 (using the same cosmological parameters as in McLure & Dunlop 2004). From equation (6), we obtain a black hole mass M BH = 4.42 ; 10 8 M, which is approximately the same as the estimate obtained with the luminosity of the H emission line. However, as with the optical continuum luminosity, the UV continuum luminosity of AO is also contributed by the jet emission and probably by the intervening galaxy. On the other hand, a recent study by Junkkarinen et al. (2004) indicated that the UV continuum of AO is heavily absorbed by the Galaxy and the intervening material at z = 0.524, which implies that the dereddened UV continuum is much larger than that observed (see their Fig. 7). Therefore, the UV continuum luminosity of AO suffers large uncertainties, and the estimated black hole mass derived with it may be unreliable and will be considered only as a reference. It has been found that there is a tight correlation between black hole mass and bulge velocity dispersion for nearby galaxies (Gebhardt et al. 2000; Merritt & Ferrarese 2001; Tremaine et al. 2002), which can be expressed as MBH log ¼ 8:13 0:06 1 M þ (4:02 0:32) log 200 km s 1 ð7þ (Tremaine et al. 2002). AGNs seem to follow the same correlation as nearby galaxies (Ferrarese et al. 2001; Onken et al. 2004). On the other hand, there is also a tight correlation between the central velocity dispersion of the galactic bulge and the FWHM of the [O iii] emission line in AGNs, with FWHM([O iii])/2.35 (Nelson & Whittle 1995). This suggests that black hole mass could be roughly estimated from the observed FWHM values of narrow forbidden lines in AGNs. For AO , both Cohen et al. (1987) and Nilsson et al. (1996) have detected narrow forbidden lines at redshift z = Cohen et al. estimated the FWHM values of [Ne v] k3426 and [O ii] k3727 as 600 and 200 km s 1, respectively. Nilsson et al. obtained FWHM values for [Ne v] k3346, [Ne v] k3426, and [O ii] k3727 of , , and km s 1, respectively. From the emission-line data on quasars in the LBQS (Forster et al. 2001), we know that the average FWHM value of [O iii] k5007 is comparable to those of [O ii] k3727 and other narrow forbidden lines. Therefore, we roughly take 600 km s 1 as the FWHM of [O iii] k5007. Using FWHM([O iii])/2.35, we derive a value of the central velocity dispersion = 255 km s 1. From equation (7), we estimate the black hole mass of AO to be M BH ( ) ; 10 8 M, which is consistent with the value obtained using the H luminosity. We have adopted four different kinds of method to derive the SMBH mass in AO Except for the optical continuum luminosity method, which apparently overestimates the SMBH mass, the other three methods give the SMBH mass in a range from 3 ; 10 8 to 6 ; 10 8 M, with typical uncertainties of a factor of a few. In the following discussion, we take the averaged mass M BH = ( ) ; 10 8 M for the central black hole of AO However, we must keep in mind that the value is derived either with the indirectly estimated H and [O iii] k5007 emission-line properties or with the UV continuum luminosity, which suffers serious contamination from the jet, southern intervening galaxy, and extra absorptions. In order to obtain a more reliable black hole mass, further studies are absolutely needed in order to accurately determine the emission-line and continuum properties of AO Wang et al. (2004) calculated a broad-line region luminosity L BLR 4.1 ; ergs s 1 for AO (adjusted to fit the cosmological parameters used here). If we adopt a typical covering factor C 0.1 for the broad emission line region (Netzer 1990), the bolometric or the ionizing luminosity is L bol = L ion L BLR /C 4.1 ; ergs s 1. From the estimated bolometric luminosity and black hole mass, we obtain the dimensionless accretion rate, ṁ 7 ; 10 3 (/0.1) 1 of AO , where is the conversion efficiency of matter to energy Thick Accretion Disk p-mode Oscillations and Physical Origin of Multiple QPOs The estimated dimensionless accretion rate of AO is about half as large as the critical accretion rate ṁ cr 0.02 in the accretion disk evaporation model ( Meyer et al. 2000; Liu et al. 2002), and much less than the ṁ cr 0.05 under the strong ADAF principle (Narayan & Yi 1995; Abramowicz et al. 1995), implying that the central region of the accretion disk in AO is an ADAF (or RIAF) and the outer region of the accretion disk is a truncated standard thin disk. There is no consensus in the literature about how to determine the transition radius R tr between inner thick ADAF and outer thin standard disk. Three kinds of methods based on different physical processes have been proposed: disk evaporation ( Meyer & Meyer-Hofmeister 1994; Liu et al. 1995a; Meyer et al. 2000; Liu et al. 2002; Różańska & Czerny 2000), the absence of a strong ADAF solution (Narayan & Yi 1995; Abramowicz et al. 1995), and disk instability of the inner, radiation pressureydominated region with energy transfer outward (Honma 1996; Kato & Nakamura 1998; Lu et al. 2004). The three methods generally give very different estimates of the