EDP Sciences
Free Access
Issue
A&A
Volume 544, August 2012
Article Number A80
Number of page(s) 57
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/201219008
Published online 01 August 2012

© ESO, 2012

1. Introduction

The dynamics of accretion around BHs should be similar for different masses, with characteristic size scales and hence timescales simply scaling with their mass (at a given accretion rate relative to the Eddington limit). Therefore, we expect to find similarities between the properties of luminous accretion flows around stellar mass BHs in X-ray binaries (BH-XRBs; MBH ~ 10 M) and supermassive black holes (SMBHs) in Active Galactic Nuclei (AGN; with MBH ~ 106−109 M). However, the details and reliability of the proposed scaling relations are currently not well understood (see Merloni et al. 2003; Körding et al. 2007; McHardy 2010, for a review).

X-ray variability – thought to originate in the innermost regions of the accretion flow – is an important aspect of the AGN-XRB connection (e.g. Uttley et al. 2002; Markowitz et al. 2003; Vaughan et al. 2003b, 2011; McHardy et al. 2006; McHardy 2010). Both AGN and BH-XRBs show “red noise” power spectra (or power spectral density, PSD) that decrease steeply at high frequencies (short timescales) as a power law, P(ν) ~ να (where ν is temporal frequency), typically with α ≈ 2. Below some characteristic frequency νb the PSDs flatten, and these bend frequencies scale approximately inversely with the BH mass from BH-XRBs to AGN. However, the PSDs of BH-XRBs depend on the “state” in which the system is observed. In the soft state the PSD is usually well described by a simple bending power-law, with a slope α > 2 above some bend frequency νb, and a slope of α ≈ 1 extending unbroken to much lower frequencies (Cui et al. 1997). In the hard state the PSDs are generally more complex, with additional bends and peaks at lower frequencies, and are usually modeled as a mixture of zero-centred Lorentzian components (see e.g. Remillard & McClintock 2006; Wilms et al. 2006). In addition there are transitional states that display a range of timing behavior. The accretion “states” of AGN are not clearly understood (Körding et al. 2006; Fender et al. 2006) but there is some evidence to support the idea that luminous, radio-quiet AGN represent supermassive analogues of BH-XRB in the “soft states” (Uttley et al. 2002; McHardy et al. 2004; Uttley & McHardy 2005; Vaughan et al. 2011).

One striking and common property of the X-ray variability of BH-XRBs is the prominent quasi-periodic oscillations (QPOs, see e.g. Remillard & McClintock 2006), which are seen as strong, narrow peaks in the PSDs. Until recently there were no robust claims of QPOs in AGN (see e.g. Vaughan & Uttley 2005). This changed when Gierliński et al. (2008) reported a QPO for the Narrow-line Seyfert 1 (NLSy1) RE J1034+396, which remains the only case to date for an AGN (see also Middleton et al. 2009; Vaughan 2010).

The main purpose for the present paper is to characterize the PSD of a large sample of AGN including a range of AGN subclasses. With this large sample we address some outstanding problems such as: what is the most common PSD shape for AGN? how does this compare to BH-XRBs? How does the PSD vary with AGN properties (BH mass, AGN subtype or luminosity)? Are there any other strong candidate of QPO among the AGN? We have made use of the extensive XMM-Newton archive to obtain a sample of 104 AGN with 209 observations of at least 40 ks. This is the largest sample of PSDs of AGN ever analyzed.

thumbnail Fig. 1

PSDs fits (continuous line) to Model A (left) and Model B (right) for the Mrk 335 data (ObsID 306870101) using the broad (0.2−10 keV) energy band. The dashed lines shows the two components of the model: constant Poisson noise and the source PSD model (power-law, left; bending power-law, right). The dot-dashed line shows the “global” 90% confidence limit use to flag QPO candidates. Appendix B shows the corresponding figures for the complete sample.

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2. The sample and the data

We have selected observations of AGN from the XMM-Newton public archives until February 2012. Note that this should include all the sources within the 2XMMi DR3 catalogue (Watson et al. 2009). The AGN are all identified in the catalogue of Quasars and AGN by Véron-Cetty & Véron (2010)1 with z  <  0.4. We have selected data according to the following inclusion criteria: (1) include one or more members of the AGN sample (search radius 9 arcmin from the centre of the FOV), and (2) observation duration T > 40 ks. The second criteria ensures a reasonable frequency range for the PSD estimation (the lowest observable frequency scales is 1/T). The final sample comprises 209 observations and 104 distinct AGN.

Table 1 gives details of the sample members and relevant XMM-Newton observations. The optical classification (Col. 3) is taken from Véron-Cetty & Véron (2010). Three objects (NGC 4636, NGC 4736, and NGC 6251) were re-classified into the LINER class according to González-Martín et al. (2009). The sample comprises 61 Type-1 AGN (3 QSOs, 54 Seyferts, and 4 LINERs), 21 Type-2 AGN (11 Seyferts and 10 LINERs), 15 NLSy1, and 7 BLLACs. Note that we consider S1i class in the catalogue (broad Paschen lines observed in the infrared) as Type-1 Seyfert and S1h (broad polarized Balmer lines detected) as Type-2 Seyferts. The redshifts given in Col. 4 (Table 1) were taken from the NASA/IPAC extragalactic database (NED2) using the redshift-independent distance when it was available. The cosmology assumed was H0 = 75 km s-1 Mpc-1. BH masses (MBH) and bolometric luminosity (Lbol) reported in the literature are shown in Cols. 5 and 6 together with the corresponding reference (Col. 7). We included the reverberation mapping estimate if available and the velocity dispersion estimate using the correlation reported by Tremaine et al. (2002) otherwise. The velocity dispersions are taken from HyperLeda database3.

3. Data reduction

XMM-Newton data were processed using the SAS (v10.0.2) and the most recent calibration files available. In this paper, only the EPIC pn data (Strüder et al. 2001) were analyzed; the pn data have a higher count rate and lower pile-up distortion than the MOS data (the effect of pile-up on PSD estimation is discussed by Tomsick et al. 2004).

Time intervals of quiescent particle background were determined through an algorithm that maximizes the signal-to-noise ratio of the net source spectrum by applying different constant count rate threshold on time series of single-event, E > 10 keV events, from the full field-of-view (Piconcelli et al. 2004).

The AGN sky coordinates were retrieved from NED4 and source counts in each case were accumulated from a circular aperture of radius 40 arcsec5). The background events were selected from a source-free circular region on the same CCD chip as the source. We selected only single and double pixel events (i.e. PATTERN =  = 0−4). Bad pixels and events too close to the edges of the CCD chip were rejected (using the standard FLAG =  = 0 inclusion criterion).

Source and background light curves were extracted (using evselect) in 100 s time bins, in three energy ranges: 0.5−10 keV (total band, T), 0.5−2 keV (soft band, S), and 2−10 keV (hard band, H). These were screened for high background and flaring activity (see González-Martín et al. 2011, for a detailed explanation of the procedure). High background periods at the beginning and/or end of an observation were removed. Where short periods of high background occurred in the middle of observations we excised the bad data and used the expected values derived by a linear interpolation of the neighbor data points to replace the missing data. This replacement is only done when less than 5 consecutive points need to be interpolated. For longer periods, the lightcurve is truncated selecting the largest consecutive period. Note that drop outs are less than 1% of the duration of the light-curve in all the observations presented here. Only light curves with remaining good durations longer than 40 ks were considered for further analysis. The net exposure times are listed in Col. 9 of Table 1. We also extracted the EPIC-pn spectra, with response matrix and auxiliary files generated using rmfgen and arfgen, respectively.

4. Data analysis

4.1. Hard band 2–10 keV luminosity estimates

The 2−10 keV luminosity was estimate by fitting the 2−10 keV spectrum using an absorbed power-law model (using xspec version 12.6.9q). For the Galactic absorption we used the hydrogen column density (NH) estimates from the HI maps of Dickey & Lockman (1990). Additional absorption was also considered to account for the curvature of the spectrum of some AGN. The free parameters in the model were the intrinsic NH, spectral index, and the power-law normalization. We did not attempt a more detailed spectral analysis, as we required only reasonable estimates of the X-ray luminosity. This method was already used by Ho et al. (2001) to estimate the luminosity in sources with low signal-to-noise data. The resulting 2−10 keV luminosities are given in Col. 10 of Table 1.

We have compared these luminosities with those for the same objects reported by González-Martín et al. (2009); Panessa et al. (2006); O’Neill et al. (2005, and references therein). LLAGN (i.e. Type-2 Seyferts and LINERs) show a very good agreement while Type-1 Seyferts, QSOs, and NLSy1 show the highest discrepancies, as expected due to the high long-term variability. NLSy1 show strong soft excesses interpreted as optically thick material seen in reflection (Crummy et al. 2006) or optically thin material seen in absorption (Gierliński & Done 2004). This soft-excess shows long-term variability (see Boller et al. 1996, and references therein).

4.2. Power spectrum estimation

The PSD gives the distribution of variability power (amplitude squared) as a function of the temporal frequency. The standard method for estimating the PSD is by calculating the periodogram (Priestley 1981; Percival & Walden 1993; Vaughan et al. 2003a). Figure 1 shows the periodogram for Mrk 335. All the periodograms of the sample are shown in the electronic edition of the paper. We use the “(rms/mean)2” normalisation throughout (see Vaughan et al. 2003a, and references therein).

The periodogram data were fitted using the maximum likelihood method discussed in Vaughan (2010, hereinafter V10) and Barret & Vaughan (2012). For a given parametric model P(ν;θ), the best-fitting model parameters, θ, were found by maximizing the likelihood function, which in practice was done by minimizing the following fit statistic (1)This is (twice) the minus log-likelihood, where Ij and Pj are the observed periodogram and the model spectral density at Fourier frequency νj, respectively. Confidence intervals on each model parameter were estimated by finding the set of parameter values for which ΔS = S(θ) − Smin ≤ 1.0, this corresponds to 68.3% intervals (this closely parallels the ΔC method discussed by Cash 1979). See also Vaughan et al. (2005).

Following the previous work on the PSDs of AGN we used two models:

  • Model A: simple power law plus constant (denoted H0 by V10). (2)The model has three parameters: N, the power law normalization; α, the spectral index; C, an additive constant to account for Poisson noise.

  • Model B: a bending power law plus constant (denoted H1 by V10). (3)The free parameters for this model are: the normalization N, the spectral index above the bend α, the bend frequency νb, and the constant C.

These XMM-Newton data are relatively insensitive to the exact low frequency index, and we assume the typical value of 1 found from long-term X-ray monitoring studies (e.g. Uttley et al. 2002; Markowitz et al. 2003; McHardy et al. 2004, 2006). The lowest frequencies available with these XMM-Newton data are  ~0.7−2.5 × 10-5 Hz (set by the minimum and maximum duration of continuous observations, 40 and  ~130 ks respectively). The typical high frequency bend for a low mass Seyfert galaxy occurs at around νb ~ few   10-4 Hz, which implies only  ~10−40 Fourier frequencies below νb, usually insufficient to obtain a precisely constrained power law index.

Temporally close observations of the same objects were analyzed together to better constrain the final parameters (the periodograms were fitted simultaneously with all parameters except C tried between the datasets). Note that we consider as temporally close observations those coming from the same observing run according to the first 6 digits of the ObsID. The resulting parameters are shown in Tables 2 and 3.

The likelihood ratio test (LRT) was used to select between the two models. The simpler model (A) is preferred in the absence of a strong preference for the more complex model (B). For reasons explained by Protassov et al. (2002) and Freeman et al. (1999) the LRT is not well calibrated when when the null values of the additional parameter of the more complex model are not well defined, as is the case here (e.g. the null value for the bend frequency in Model B is not well defined in this sense). An accurate calibration of this test using posterior predictive checks can be computationally expensive (see V10), so in this case we used the standard LRT with a p < 0.01 significance threshold as a crude but simple check for the presence of a bend in the PSD. The simulation results of V10 suggest that this criterion is conservative in the sence that the number of false positives is fewer than expected. Where a bend is detected (i.e. Model B selected) we parametrized the PSD amplitude at the bend frequency as Apsd = νb × P(νb) = N/2 (following Papadakis 2004), where N is the normalisation (Eq. (3)), i.e. the peak in ν × P(ν) space.

The Poisson noise level, C, was usually considered a free parameter. The expected Poisson noise level was calculated assuming the standard formula (e.g. Uttley et al. 2002; Vaughan et al. 2003a) and this value was used in cases where the parameter C was poorly constrained in the periodogram fitting (these observations are indicated by an asterisk in Tables 2 and 3).

As a crude but simple check for the presence of highly coherent oscillations (strictly or quasi-periodic) we identify the largest data/model outlier from each periodogram. This was then compared to the distribution expected for periodogram data to give a p-value. Candidate QPOs were flagged when a p < 0.01 criterion was met (after correcting for the number of frequencies in the periodogram). A similar test was applied to the periodogram data after smoothing using a three-point top-hat filter, i.e. testing the running mean of each triplet of adjacent points. This test improves sensitivity to QPOs that are broader than the frequency resolution of the data. These p-values are not correctly calibrated, for reasons explained in Vaughan (2010), but such tests proved to be extremely efficient as a crude indicator of potentially interesting data.

There are two main types of bias that may effect Fourier-based power spectral analysis, “aliasing” and “leakage” (see Priestley 1981; Percival & Walden 1993; Deeter & Boynton 1982; Uttley et al. 2002). Aliasing is negligible for the present data, which are contiguously sampled. Leakage may however cause intrinsically steep power spectra (power law indices α ≳ 2) to show slopes close to α = 2. This point is discussed further in Sect. 5.7.

5. Results

5.1. Variability of the sample

We considered an observation variable if there was an excess above the constant value expected from the Poisson noise in the periodogram. We report the detection of variability in Col. 11 of Table 1 as: (T) for the total 0.5−10 keV, (S) for the soft 0.5−2 keV, and (H) for the hard 2−10 keV energy bands; (N) indicates no variability detected in any band.

Seventy five out of the 104 AGN (72%) showed variability in at least in one of the three bands tested. Among them, 56 showed significant variability in the total band, while three varied only in the hard band (NGC 985, 2E 0414+0057, and NGC 4258). Twenty nine of the 104 AGN (28%) did not show significant variability in any of the three bands tested. These sources are: 12 of the 14 LINERs; 2 of the 11 Type-2 Seyferts; 12 of 54 Type-1 Seyferts; 2 of the 3 QSOs; and 1 of the 7 BL Lacs. All the NLSy1s and 78% of the Type-1 Seyferts were variable, but most of LINERs are not variable. Finally, five sources were variable only in some of the observations (namely, OJ +287, NGC 2992, PG 1116+215, Mrk 279, Mrk 205, 3C 273, X Com, and RBS 1399). The lack of detected variations in these cases can be attributed to the limited quality of the data.

5.2. Model selection

Among the variable sources, we have been unable to constrain the parameters of Model A in six sources, and an additional nine have unconstrained values in a subset of the observations and/or energy bands (marked as ♣ in Tables 2 and 3). This is due to the low number of bins in the PSD above the Poisson noise (e.g. see Fig. 1 of NGC 4151, ObdID = 112830201, for the total energy band in the electronic edition).

Model B is selected over Model A (using the LRT) in 17 AGN (44 observations, see Table 3). However, MS 22549-3712 and Mrk 586 gave very poorly constrained parameters for Model B. We consider these two sources as tentative detections of a bending PSD. Moreover, we have found a break in PKS 0558-504 far from that reported by Papadakis et al. (2010). However, our bend is more likely a bump on the PSD or a broad QPO as claimed by Papadakis et al. (2010). All the objects for which Model B was selected are Type-1 AGN but the Circinus galaxy.

5.3. QPO detection

The test for highly periodic oscillations found no candidates besides KUG 1031+398 (better known as RE J1034+396). A QPO of a νb = 2.6    ×    10-4 Hz was previously detected in this source by Gierliński et al. (2008). The apparent significance of the QPO is lower than that reported by Gierliński et al. (2008), for reasons discussed by V10.

A QPO candidate was previously reported for 3C 273 by Espaillat et al. (2008) using a wavelet technique to analyze 19 observations of 10 AGN obtained with XMM-Newton. For 3C 273 they used four XMM-Newton observations, all of them included in our analysis. We found no indication of a QPO from these data. Another case of QPO reported in the literature is the blazar PKS 2155-304. Lachowicz et al. (2009) reported a 4.6 h QPO in the 0.3−10 keV data (from ObsID 158961401). We have analyzed 8 observations of this source, including this one; none showed indications of a QPO. Gaur et al. (2010) analyzed all the XMM-Newton archival data of this source and reported a possible QPO in only one observation. This observation is included in our analysis and the hint of the QPO around 1.7    ×    10-4 Hz can be seen in our PSD (see Fig. 1, in the electronic edition), consistent with their findings. However, the strength of this fluctuation above the continuum is not strong enough to suggest a QPO detection.

thumbnail Fig. 2

Histograms of power-law slopes for Model A (black-filled histogram) and Model B (blue-dashed histogram). Top, middle, and bottom panels show the histograms for the total, soft, and hard bands, respectively. The dashed-lines show the mean value for each distribution.

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5.4. Slopes

The mean and standard deviation of the power law indices using Model A (for observation where Model B is not selected) was α = 2.01    ±    0.01 for the total energy band (α = 2.06    ±    0.01 and α = 1.77    ±    0.01 for the soft and hard bands, respectively). Figure 2 (black filled histogram) shows the distribution of this parameter for the three energy bands6. The distributions are statistically indistinguishable according to the K-S test.

The mean value of the slope α when Model B model is preferred is α = 3.08    ±    0.04 for the total energy band (α = 3.03    ±    0.01 and α = 3.15    ±    0.08 for the soft and hard energy bands, respectively). These slopes are significantly steeper than those found from the Model A fit, i.e. where no PSD bend was detected. Figure 2 (blue-dashed filled histogram) shows the distributions of slopes when Model B is preferred.

5.5. Frequency bend

We have found PSD bends for 17 AGN. Figure 3 shows the histograms of frequency bends. Note that the weighted mean value is reported when more than one observation is available for the same object. The resulting mean values are log    (νbr) = −3.47    ±    0.10 for the total band (results for the soft and hard bands were almost identical).

Table 3 shows the PSD model parameters for the objects where Model B was selected. Of these, seven have not been previously reported in the literature: ESO 113-G10, Mrk 586, 1H0707-495, ESO 434-G40, Circinus, NGC 6860, and MS 22549-3712 (although Mrk 586 and MS 22549-3712 are weak detections, see Sect. 5.2). Table 4 summarise the PSD information for the source bend detections in the present analysis together with a compilation of 17 AGN with PSD bend frequencies from the literature. We have examined the XMM-Newton data for all of them. This extend of the list of AGN with detected PSD bends to 24 objects (or 22 if we exclude Mrk 586 and MS 22549-3712). Appendix A gives a short description of the published bends together with a comparison with our results.

thumbnail Fig. 3

Histograms of the bend frequency for Model B. Top, middle, and bottom panels show the histograms for the total, soft, and hard bands, respectively. The dashed-lines show the mean value for each distribution.

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5.6. PSD bend amplitude

Papadakis (2004) found that the PSD amplitude at the bend frequency, in terms of ν × P(ν), was roughly constant over a sample of AGN, at Apsd ~ 0.017, based on an analysis of normalized excess variances. Table 4 (Col. 11) shows Apsd calculated from the estimated Model B parameters where a bend was detected. Although the mean value is A = 0.009    ±    0.011, roughly consistent with the Papadakis (2004) result, this is dominated by three AGN with high Apsd values, namely 1H 0707-495, NGC 4051, and NGC 4395 (excluding PKS 0558-504 since it might not be a bend, see Sect. 5.2). These three sources are NLSy1s with low BH masses, which may indicate Apsd is not constant over all AGN but depends on MBH and/or source type.

5.7. Leakage distortion

A fraction of the power below and above the observed frequency range can “leak” into the observed bandpass due to the side-lobes of the Fejer kernel (see Priestley 1981; Percival & Walden 1993). This is the problem of spectral leakage, discussed by Deeter & Boynton (1982), Uttley et al. (2002) and Vaughan et al. (2003b). If the power spectrum is steep (e.g. α ≳ 2) at or below the lowest observed frequency (ν1 = 1/T) this can lead to a significant distortion of the periodogram, as demonstrated by Uttley et al. (2002). However, the effect of leakage will be to reduce the sensitivity to bends, and QPOs, and bias the slope toward α = 2, not to introduce spurious PSD features. Indeed, the detection of a bend to a flatter slope (α ≲ 2) at low frequencies is an indication that leakage cannot be significant. Some of the data sets for which the best-fitting model is a single power law (Model A) with slope α ≈ 2 are possibly be affected by leakage, for example NGC 3516 and NGC 4151 which are known to show bends to flatter slopes at frequencies lower than those covered by the XMM-Newton observations (Markowitz et al. 2003).

Fougere (1985) discussed methods to recover accurate power spectral indicies in the presence of strong leakge. The simplest method that is reasonable effective at reducing leakage bias is “end matching”, removing a linear trend from the time series such that the first and last data points have equal values. We have used this technique for those sources best fitted to Model A for the 0.2−10 keV band. We recovered Model A as the preferred fit in all cases except IGR J21277+5656 (, ). A longer observation is needed to confirm the presence of the bend in this source. Moreover, after applying end-matching we are unable to constrain the parameters for Fairall 9. (The time series of this time series is essentially a linear trend, no short timescale variability remains after end matching.)

Figure 4 compares the slope estimates with and without end matching. Only PKS 1547+79 shows a lower slope after the end-matching. However, the light-curve before end matching shows only a (roughly) linear trend; after end-matching no significant variability remains. The indices obtained after the end matching are on average higher than those obtained without end matching – the mean index is  ⟨ α ⟩  = 2.29    ±    0.01 – but still significantly lower than the mean high frequency index of those sources with detected power spectral bends.

thumbnail Fig. 4

Slopes obtained for Model A best-fit using the “end-matching” routine versus those obtained without using “end-matching”. The dashed histograms are the normalized histograms for each distribution. The dashed line represents the one-to-one correlation and dot-dashed lines are the mean values for each distribution.

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6. Discussion

6.1. Summary of results

We have presented an analysis of the high frequency power density spectra (PSD) of a sample of 104 AGN observed with XMM-Newton. These PSDs span up to  ≈3 orders of magnitude in frequency, ranging from minutes to over days. Our main results can be summarized as follows:

  • Variability: 72 per cent of the sample showed significant variability in at least one of the three energy bands tested. Moreover, most of LINERs in our sample do not vary (12 out of the 14 LINERs).

  • PSD shape: The PSDs of the majority of the variable AGN could be described by a single power-law (i.e. Model A) with a mean slope of α ≈ 2. In 17 sources – all Type-1 Seyferts (many are NLSy1s) but the Circinus galaxy – we found a strong preference for the bending power-law model (i.e. Model B). For this subset, the slope above the bend frequency is steep, α ~ 3.0, above a bend frequency typically around νb ~ 3.4 × 10-4 Hz. Spectral leakage, which can bias the slope estimates in some cases, does not appear to explain discrepancy between the slopes found for Model A and B.

  • QPO detection: None of the sources analyzed in our sample show a QPO, with the exception of KUG 1031+398 (RE J1034 + 396), discussed extensively in the literature.

6.2. Scaling relations

Several papers have demonstrated a strong, approximately linear correlation between the PSD bend timescale (Tb = 1/νb) and the black hole mass (e.g. Uttley et al. 2002; Markowitz et al. 2003; Vaughan et al. 2005), as expected from simple scaling arguments (Shakura & Sunyaev 1976; Fender et al. 2006). The simplest relation between timescale and fundamental AGN properties that we might consider is (4)where A and C are coefficients, and we expect A ≈ 1 for a linear mass-timescale relation. McHardy et al. (2006) presented an extension of this model allowing for dependence of Tb on both MBH and bolometric luminosity Lbol: (5)Table 4 gives values of log    (νb) for objects in which we find strong evidence for a bending power law PSD. From these we derive Tb (in units of days). This table also includes values for MBH and Lbol taken from the literature and the values of log    (fb), MBH, and Lbol compiled exclusively from previous literature. Together, these present the largest compilation of characteristic timescales for AGN to date. Note that the BH masses are derived by several different methods, but we have used estimates from reverberation mapping campaigns where these are available.

We fitted models following Eqs. (4) and (5) to data from the 22 AGN in Table 4. We have used the Tb values from our analysis when available and those from the literature otherwise, except for PKS 558-504 for which we have used the value reported in the literature7. The models were fitted by simple linear regression8 (i.e. unweighted least squares) on the log transformed variables, with Tb in units of days, Lbol in units of 1044 erg s-1, and MBH in units of 106 M, as in McHardy et al. (2006).

thumbnail Fig. 5

Observed bend timescale versus the BH mass. The continuous line is the best-fitting following Eq. (4). The dashed lines illustrate the  ± 1 dex region around this model. Circles represent NLSy1s, squares represent Type-1 Seyferts, and the small green star is the Type-2 Seyfert. The open symbols are data-points reported in the literature and filled symbols are the data-points reported here. The Cygnus X-1 data are shown as a red big star. A dotted line is used to link multiple frequency bends for the same object.

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Fitting Eq. (4) gave parameter estimates A = 1.09    ±    0.21 and C = −1.70    ±    0.29, leaving a sum squared error (SSE) of 11.14 (for 19 degrees of freedom, d.o.f.). The data and best-fitting regression line are shown in Fig. 5. Fitting Eq. (5) gave parameter estimates A = 1.34    ±    0.36, B = −0.24    ±    0.28, and C = −1.88    ±    0.36, leaving a sum squared error (SSE) of 10.69 (for 18 d.o.f.). The parameter governing the luminosity dependence, B, is consistent with zero (p = 0.38 for 18 d.o.f.). Figure 6 compares the bend timescale predicted by this relation (based on the observed MBH and Lbol) to the observed Tb values (compare with Fig. 2 of McHardy et al. 2006). Figure 7 shows the residuals (as a ratio of observed to model Tb) against Lbol/LEdd for the two different models.

In order to test the reliability of these parameters we have used the “bootstrap” method (Efron & Tibshirani 1993). We generated N = 104 simulated datasets, each comprising 22 “observations” (of Tb, MBH, Lbol) generated by drawing an AGN at random (with replacement) from the real data. This provides a simple alternative assessment of the parameter confidence intervals. The 68.3 per cent confidence intervals on the parameters are: A =  [1.02,1.66] , B =  [−0.52, −0.046]  and C =  [−2.12, −1.65] . The boostrap confidence intervals are slightly narrower than the standard regression intervals.

In order to test how well these scaling relations work over the full range of black hole masses we also show representatives values for the BH-XRB Cygnus X-1 (red star in the figures)9. The Cygnus X-1 points were not included in the fitting, yet are clearly consistent with an extrapolation to much lower MBH, strongly supporting the reliability of such relations over the full range of MBH. Indeed, fitting the two models including the Cygnus X-1 data resulted in parameter estimates consistent with those given above.

thumbnail Fig. 6

Observed bend timescale against the predicted value based on the best-fitting model following Eq. (5). Symbols are the same as explained in Fig. 5.

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thumbnail Fig. 7

Ratio between the observed and predicted Tb values against Eddington rate (Lbol/LEdd) using Eq. (4) (top) and Eq. (5) (bottom). The continuous line shown in the top panel corresponds to the linear fit of the data. Symbols are the same as explained in Fig. 5.

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The main difference compared with the results obtained by McHardy et al. (2006) is a weak dependence of Tb on Lbol in the present analysis. This remains the case when the fitting is repeated with or without the Cygnus X-1 data (B = −0.27    ±    0.27), using a lower mass estimate for NGC 439510, or using a weighted least squares regression (i.e. making use of the confidence intervals on Tb). However, if we use smaller black-hole masses for NGC 4395 ((log    (MBH) = 4.5, see Vaughan et al. 2005; Uttley & McHardy 2005) and NGC 5506 (log    (MBH) = 6.5, see McHardy et al. 2006), and NGC 6860 is removed11, the dependence with the Lbol found by McHardy et al. (2006) is recovered (B = −0.70    ±    0.30, p = 0.01). Thus, this weak dependence on Lbol could be due to either the fact that our sample is more complete sample (more objects and new estimates from the old bends) or due to uncertainties on the BH mass and/or Lbol estimates. A bigger sample with better estimates on the BH mass and Lbol is need to check the dependence on Lbol.

thumbnail Fig. 8

Observed characteristic timescale versus the FWHM of Hβ expressed in km   s-1. Symbols are the same as explained in Fig. 5.

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6.2.1. BLR versus variability

McHardy et al. (2006) also presented strong correlation between Tb and the width of the (permitted) optical lines, V, specifically Hβ. We have compiled optical line widths for the objects in Tables 3 and 4 based on the available literature. For most sources we have used as V the full width at half maximum (FWHM) of the Hβ line, the exceptions are NGC 5506 and ESO 434-G40, which are both heavily obscured and for which we have used the FWHM of the Paβ line. Figure 8 shows the resulting timescale-FWHM relation. The linear correlation coefficient is r = 0.692 (highly significant; p = 5.0    ×    10-4). Simple linear regression of log (Tb) on log    (V) was used to fit a relation of the form (6)The best-fitting parameter values were D = 2.9 ± 0.7 and E = −10.2 ± 2.3, leaving a sum squared error (SSE) of 13.47 (for 19 degrees of freedom, dof). This relation is again slightly flatter than the D = 4.2 found by McHardy et al. (2006). The 68.3 per cent confidence intervals on these parameters calculated by the bootstrap method are D =  [2.2,3.5]  and E =  [−12.3, −7.9] .

6.3. PSD shapes

For the ten objects with well-constrained Model B parameters, the high frequency slope is steep (α ≈ 3). Such steep high frequency PSDs have been reported in the literature (e.g. Mrk 335 and Mrk 766 by Arévalo et al. 2008; Vaughan & Fabian 2003, respectively, see our Table 4 for details), but with little explicit discussion of this point.

There seems to be no fundamental physical requirement for the PSD slope to be steeper than α = 2 at high frequencies (see footnote 7 of Vaughan et al. 2011). Indeed, α ≈ 2 seems to be the norm for BH-XRBs in “hard” states in the  ~5−50 Hz regime, above which there may be further steeping (Nowak et al. 1999; Revnivtsev et al. 2000). The “soft” states may show steeper PSDs (Revnivtsev et al. 2000; McHardy et al. 2004), and so the steep high frequency PSDs observed from these AGN may support the argument that AGN are supermassive analogues of soft state BH-XRBs. There are alternative explanations that must be considered, however. These include the fact that the AGN PSDs presented here are based on XMM-Newton data with a relatively soft X-ray response, while the BH-XRB results are based on observations at harder X-rays with RXTE, and therefore the known energy dependence of the high frequency slope (Nowak et al. 1999; Vaughan et al. 2003b; McHardy et al. 2004) may explain the apparently steeper slopes in AGN. (We have relatively little information about the PSDs of BH-XRBs at  ~1 keV. See Uttley et al. 2011, for a rare example based on a bright “hard” state observation.) Another possibility is that the steeper slopes are the result of a selection effect and are not representative of the larger population of bright AGN. The PSD bend is easier to detect when the high frequency slope is steep, and when the bend is at relatively low frequency. We cannot exclude the possibility that only a subset of AGN show such steep slopes but these are the ones for which the PSD bend, and hence high frequency slope, is easiest to constrain.

The majority of the sample did not show evidence of a bend (i.e. insufficient evidence to select Model B over Model A in a LRT). The mean value of the PSD index for these objects was α ≈ 2. The simplest interpretation is that these generally more massive objects have lower νb, and hence we see only the high frequency part of the PSD. This slope is α ≈ 2.3 when the leakage distortion is reduced using end matching, but this remains flatter than the high frequency slope for objects that do show evidence for a PSD bend. It remains possible that a more rigorous method to account for the leakage bias (e.g. the methodology described by Uttley et al. 2002) could recover steeper slopes. But this could also result from a selection effect. If AGN show a wide range of high frequency PSD slopes, e.g. α ~ 2−4 above the bend frequency, then those with flatter slopes will be more difficult to detect, as the change in slope (from the low frequency index of 1) is less pronounced.

In order to study whether we detect all the expected bends, we have computed the predicted characteristic time scale Tb for sample members with MBH estimates (70 out of the 104), assuming bolometric luminosity of Lbol = 30 × L2−10 (estimated as explained in Sect. 4.1). The PSD bend timescales is predicted to be within the observed frequency range for only 17 sources. Of these we do indeed detect bends in 13. The exceptions are 1H 419-577, NGC 4593, IRAS 13224-3809, and NGC 7314. However, note that if we use the relation found by McHardy et al. (2006) IRAS 13224-3809 and NGC 7314 are not expected to show a bend in our frequency range. For the rest of the sample members the predicted Tb value places it outside of the observed PSD bandpass. Moreover, all the non-variable sources have an expected bend well above the range analyzed here.

6.4. Lack of QPOs

We find no strong evidence for highly coherent oscillations (QPOs) beyond the well known example of KUG 1031+398. Some authors have pointed to the extremely soft spectrum of this source as an explanation of why this source appears to be unique in showing a QPO. In fact, even for this source the QPO appears to be transient (Middleton et al. 2009, 2011). Less coherent oscillations, i.e. QPOs with a broader features in the PSD, are common to BH-XRBs, especially in harder spectral states, but are difficult to detect in the majority of the currently available data, as discussed by Vaughan & Uttley (2005) and Vaughan et al. (2011).

Appendix A: PSD breaks/bends in the literature

Here we give a short summary of previously reported PSD frequency bends/breaks together and a comparison with our results. Table 4 shows the parameter values discussed here. It should be noted that the XMM-Newton data discussed in the present paper are sensitive to bends only in the frequency range from  ≳ 10-4 to  ~few  ×    10-3.

  • Mrk 335: The 0.2−10 keV band PSD of Mrk 335 was reported by Arévalo et al. (2008) using the same data-set used here. Our results are consistent with theirs.

  • NGC 3227: Uttley & McHardy (2005) analyzed the 2−10 keV band PSD of NGC 3227 using RXTE data and reported a break at 2.6    ×    10-5 Hz, a factor  ~9 lower than our result. Kelly et al. (2011) analysed the RXTE and XMM-Newton data using a different method for power spectrum estimation, and obtained a bend frequency of  ~3.7    ×    10-5 Hz. Some of the discrepancy between these results and ours may be due to the different energy bands and responses used in the different the analyses, i.e. 2−10 keV RXTE data used by Uttley & McHardy (2005) compared to 0.2−10 keV XMM-Newton data used here, although it seems unlikely this can account for all the difference.

  • KUG 1031+398: V10 presented an analysis of the KUG 1031+398 data using essentially the same method as in the present analysis. The two sets of results are fully consistent with each other.

  • NGC 3516: Markowitz et al. (2003) reported the 2−10 keV PSD of NGC 3516 using RXTE data. They found a high-frequency break at log (νb) = −5.7    ±    0.4 (slopes of 1 and 2 below and above the frequency break, respectively). These are outside the frequency range available to the XMM-Newton data. As expected we find no strong evidence for a bend within the frequency bandpass considered here, and the Model A slope is consistent with the high frequency slope of Markowitz et al. (2003).

  • NGC 3783: the power spectrum of this objects has been discussed by Markowitz et al. (2003), Markowitz (2005), Summons et al. (2007), Arévalo et al. (2009) and Kelly et al. (2011) using combinations of RXTE and XMM-Newton data. These papers report a single bend in the PSD at  ~6.2    ×    10-6 Hz, outside the frequency bandpass available to the XMM-Newton data. The power spectral slopes reported here are slightly flatter than those reported by Markowitz (2005).

  • NGC 4051: the PSD of NGC 4051 has discussed by McHardy et al. (2004), Miller et al. (2010) and Vaughan et al. (2011). McHardy et al. (2004) used RXTE and XMM-Newton data and found a frequency bend at log (νb) ~ −3.1, albeit with a large uncertainty. Vaughan et al. (2011) analysed a series of XMM-Newton observations, finding broadly similar results but a slightly lower bend frequency (log    (νb) ~ −3.7). Here we report a PSD bend at log (νb) ~ −3.5, consistent with those reported by with other analyses.

  • NGC 4151: Markowitz et al. (2003) discussed the 2−10 keV PSD of NGC 4151 using RXTE data, and reported a break frequency (using a broken power law model) of  ~10-6 Hz, outside of the frequency bandpass available to the XMM-Newton data. The single power-law model (Model A) applied to the XMM-Newton data gave a best-fitting slope (2.1) identical to the high frequency slope reported by Markowitz et al. (2003).

  • Mrk 766: The PSD of Mrk 766 was studied by Vaughan & Fabian (2003), Markowitz et al. (2007) and Kelly et al. (2011). The main parameters (bend frequency and high frequency slope) are broadly compatible with our findings. The bend frequency reported by Markowitz et al. (2007) is slightly higher, but we assumed a low frequency slope of 1 whereas they fitted for this parameter and found a slightly steeper slope.

  • NGC 4395: Vaughan et al. (2005) report on the PSD using XMM-Newton data, and their results are completely consistent with those presented here (their fitting method differs from that used presently). Shih et al. (2003) previously used ASCA data to study the PSD of NGC 4395, finding a PSD break at log    (νb) = −3.5 (with slopes of α ~ 1 and α ~ 1.8 at low and high frequencies, respectively). However, the PSD reported by Shih et al. (2003) lacked data in the frequency range log    (ν) =  [−4,−3.4] , which hampered accurate estimation of the frequency break.

  • Fairall 9: Markowitz et al. (2003) and Kelly et al. (2011) discuss the PSD of this source using RXTE data. The former paper reports an upper limit on the bend frequency of log    (νb) ~ −6.4, and the latter paper gives an estimate of log    (νb) ≈ −5.6, outside of the frequency bandpass available to the XMM-Newton data; as expected given these results we find no strong evidence for a bend in the present analysis. The single power-law fit (i.e. Model A) shows a slope consistent with the previous high frequency slope estimates.

  • MCG − 06 − 30 − 15: Vaughan et al. (2003b) and McHardy et al. (2005) have reported on the PSD of this source. In the present paper we report and bend frequency higher than that reported by Vaughan et al. (2003b). However, they used a sharply broken power law while here we use a bending power law model, which means the frequency parameter is not strictly the same. McHardy et al. (2005) analysed together the RXTE and XMM-Newton data and found a good fit using the bending power law model. Their estimated bend frequency is a factor  ≈3 lower than that reported in the present paper. This may in part be due to the use of different energy bands between the analyses (e.g. 4−10 keV for RXTE and 0.2−10 keV XMM-Newton).

  • IC 4329A: Markowitz (2009) reported the 3−10 keV band PSD. They fitted the PSD to a broken power law with a break at log (νb) ~ −5.6, outside of the frequency bandpass avilable to the XMM-Newton data. They report a high frequency slope consistent with the slope using with Model A in the present study.

  • NGC 5506: Uttley & McHardy (2005) and Kelly et al. (2011) reported on the PSD of NGC 5506 using RXTE data. The PSD bend frequency estimated in the present analysis is a factor  ≈3 higher. This may in part be due to the use of different energy bands between the analyses (e.g. 2−10 keV for RXTE and 0.2−10 keV XMM-Newton).

  • NGC 5548: Markowitz et al. (2003) and Kelly et al. (2011) report on the PSD of NGC 5548. They found a break/bend frequency at log    (νb) ~ −6.1, far outside the the frequency bandpass avilable to the XMM-Newton data; as expected given these results we find no strong evidence for a bend in the present analysis. The single power-law fit (i.e. Model A) shows a slope consistent with the previous high frequency slope estimates.

  • Ark 564: The PSD of this source has been discussed by Pounds et al. (2001) and Markowitz et al. (2003) using RXTE data, Papadakis et al. (2002) using ASCA data, and McHardy et al. (2007) and Kelly et al. (2011) using combinations of these datasets. The bend frequency estimate reported in the present paper is a factor  ~6 lower than that reported by McHardy et al. (2007), but consistent with that from Kelly et al. (2011). However, as discussed by McHardy et al. (2007) the PSD of this source may be more complicated than the simple bending power law model assumes.

  • PKS 0558-504: Papadakis et al. (2010) combined XMM-Newton and RXTE data to estimate a PSD bend frequency of log    (νb) ≈ −5.2, outside the the frequency bandpass avilable to the XMM-Newton data. The apparent detection of a PSD bend, as reported in Table 3 is therefore quite unexpected. However, Papadakis et al. (2010) found evidence for a bump (perhaps a broad QPO) in the PSD at frequencies consistent with our bend. Thus, our bend detection is plausibly a misidentification caused by the more complicated PSD shape.

  • NGC 7469: The 2−10 keV PSD of NGC 7479 was discussed by Markowitz (2010) using RXTE and XMM-Newton data. The found a bend outside the frequency bandpass available to the XMM-Newton data. As expected based on this, we find no evidence for a bend using the XMM-Newton data alone. The high frequency slope reported by Markowitz (2010) is consistent with our slope using the single power-law model (α = 1.8    ±    0.2).

Appendix B: Catalogue of PSDs

thumbnail Fig. B.1

PSDs best fits for the 0.2−10 keV band.

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4

The NASA/IPAC Extragalactic Database (NED): http://ned.ipac.caltech.edu/

5

This includes approximately 90 per cent of the PSF for an on-axis source with the EPIC pn instrument.

6

Where more than one observation was available for the same object we computed the weighted mean. This was calculated only in the case of multiple distinct observations; when multiple observations occurred close in time the periodogram data were fitted simultaneously (see Sect. 4.2).

7

Our bend in PKS 558-504 could the result of a bump (or broad QPO) already reported by Papadakis et al. (2010).

8

There are several reasons for not weighting the data according to the uncertainties on Tb. Firstly, the high frequency bend in X-ray binaries is not stationary but varies in frequency by a factor of  ~few, it is therefore plausible that the estimates of Tb may not represent the “true” long-run average values if AGN power spectral are similarly non-stationary on very long timescales. Secondly, the MBH and Lbol estimates are also subject to significant statistical and systematic errors that are difficult to quantify. These represent additional sources of variance in the data not accounted for by the confidence limits on Tb.

9

We used the black hole mass of MBH = 15    ±    1   M recently presented by Orosz et al. (2011). For the bolometric luminosity and characteristic time scale we took the average of several estimates of the PSD bend frequency from Axelsson et al. (2006) and bolometric flux from Wilms et al. (2006) (using the data from their Model 5, Table 1 – see McHardy et al. (2006) for justification of this choice of model). The observations were chosen to be those with simultaneous bend frequency and bolometric flux estimates. The luminosity Lbol was derived assuming a distance of D = 1.86    ±    0.12 kpc (Reid et al. 2011). The final bolometric luminosity and frequency bend are Lbol = 2.26    ±    0.73    ×    1037 erg s-1 and νb = 13.2    ±    6.0 Hz, respectively.

10

NGC 4395 is the object in our sample with the most “leverage” on the regression model. It could have a lower black hole mass as discussed by Vaughan et al. (2005) and Uttley & McHardy (2005) than the reverberation mapping mass of Peterson et al. (2005).

11

We tried to remove NGC 6860 because it is one of the drop-outs in our correlation.

Acknowledgments

This research has made use of the NASA Astrophysics Data System Bibliographic Services, and the NASA/IPAC Extragalactic Data base (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This paper is based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and the USA (NASA). O.G.M. acknoledges to the C5D00070-2006 grant of the MICINN for the finantial support. O.G.M. thanks Dr. Iossif Papadakis for his help understanding variability processes in AGN and the interpretation of the results of the present study.

References

Online material

Table 1

Sample main observational properties.

Table 2

Parameters of the fit of to Model A.

Table 3

Parameters of the PSD fits to Model B.

Table 4

Compilation of frequency breaks reported here and in the literature.

All Tables

Table 1

Sample main observational properties.

Table 2

Parameters of the fit of to Model A.

Table 3

Parameters of the PSD fits to Model B.

Table 4

Compilation of frequency breaks reported here and in the literature.

All Figures

thumbnail Fig. 1

PSDs fits (continuous line) to Model A (left) and Model B (right) for the Mrk 335 data (ObsID 306870101) using the broad (0.2−10 keV) energy band. The dashed lines shows the two components of the model: constant Poisson noise and the source PSD model (power-law, left; bending power-law, right). The dot-dashed line shows the “global” 90% confidence limit use to flag QPO candidates. Appendix B shows the corresponding figures for the complete sample.

Open with DEXTER
In the text
thumbnail Fig. 2

Histograms of power-law slopes for Model A (black-filled histogram) and Model B (blue-dashed histogram). Top, middle, and bottom panels show the histograms for the total, soft, and hard bands, respectively. The dashed-lines show the mean value for each distribution.

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In the text
thumbnail Fig. 3

Histograms of the bend frequency for Model B. Top, middle, and bottom panels show the histograms for the total, soft, and hard bands, respectively. The dashed-lines show the mean value for each distribution.

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In the text
thumbnail Fig. 4

Slopes obtained for Model A best-fit using the “end-matching” routine versus those obtained without using “end-matching”. The dashed histograms are the normalized histograms for each distribution. The dashed line represents the one-to-one correlation and dot-dashed lines are the mean values for each distribution.

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In the text
thumbnail Fig. 5

Observed bend timescale versus the BH mass. The continuous line is the best-fitting following Eq. (4). The dashed lines illustrate the  ± 1 dex region around this model. Circles represent NLSy1s, squares represent Type-1 Seyferts, and the small green star is the Type-2 Seyfert. The open symbols are data-points reported in the literature and filled symbols are the data-points reported here. The Cygnus X-1 data are shown as a red big star. A dotted line is used to link multiple frequency bends for the same object.

Open with DEXTER
In the text
thumbnail Fig. 6

Observed bend timescale against the predicted value based on the best-fitting model following Eq. (5). Symbols are the same as explained in Fig. 5.

Open with DEXTER
In the text
thumbnail Fig. 7

Ratio between the observed and predicted Tb values against Eddington rate (Lbol/LEdd) using Eq. (4) (top) and Eq. (5) (bottom). The continuous line shown in the top panel corresponds to the linear fit of the data. Symbols are the same as explained in Fig. 5.

Open with DEXTER
In the text
thumbnail Fig. 8

Observed characteristic timescale versus the FWHM of Hβ expressed in km   s-1. Symbols are the same as explained in Fig. 5.

Open with DEXTER
In the text
thumbnail Fig. B.1

PSDs best fits for the 0.2−10 keV band.

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In the text

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