KEPLER PHOTOMETRY OF FOUR RADIO-LOUD ACTIVE GALACTIC NUCLEI IN 2010–2012

Fluctuations emerging directly from the surfaces of ADs or from coronae above them can produce rest frame variations no faster than about t_var ≃ GM_BH/c³ or ≃ 8 minutes for M_BH = 10⁸ M_☉. The fastest real variations can provide a way of measuring the lower limits on masses of the SMBHs. Most X-ray and optical variability of the best studied cases, Seyfert galaxies and radio-quiet quasars, is "red noise," i.e., where the PSD arising from the Fourier transform of the light curve is characterized by P(f)∝f^α, with α < 0, below some break frequency, f_b; above f_b the PSD is usually dominated by measurement errors with a white noise character (α = 0) or perhaps by white noise with an astrophysical origin. The PSD can also yield the size of the largest emitting region if there is a flatter slope, often α ∼ −1 at low frequencies and ∼ − 2 at intermediate frequencies (e.g., Markowitz et al. 2003) before perhaps turning to ∼0 at the highest frequencies. Variations yielding red-noise can be produced if energy is released over a wide range of time-scales characteristic of different orbital periods and turbulent transport in ADs (e.g., Mangalam & Wiita 1993).

Recently, detections of QPOs in five AGN have been made, mostly in X-rays. The best case is that of the Narrow Line Seyfert 1 galaxy RE J1034+396 (Gierliński et al. 2008), where a period of a little more than 1 hr was detected. The presence of optical QPOs has been suggested for the high declination BL Lac object, S5 0716+714, for some time (e.g., Quirrenbach et al. 1991). A wavelet analysis of archival optical spectra of S5 0716+714 indicated the presence of five nights with QPOs present at ⩾0.99 probability, with central periods ranging between ≃ 25 and ≃ 73 minutes (Gupta et al. 2009). New observations of this same blazar led to an even stronger indication of an ∼15-minute QPO (Rani et al. 2010).

The simplest QPO model assumes that a single hot spot in the inner portion of the AD is responsible, and that radiation from this disk is directly detected, e.g., when an FSRQ is in a faint, quiescent state. Given a measured period, P (in seconds) one can estimate the SMBH mass M via

$$\begin{equation} \frac{M}{M_{\odot }} = {\frac{3.23 \times 10^4 P}{(r^{3/2} + a)(1+z)}}, \end{equation} \tag{ 1 }$$

where r is the hot spot distance in units of GM/c², a is the black hole (BH) spin-parameter, and z is the redshift (Gupta et al. 2009). The shortest periods are obtained for the innermost stable circular orbit, and the strongest radiation emerges near there. For low redshift objects, a 5 hr period, which would be very difficult to detect from ground-based observations, but rather easy for Kepler to find, corresponds to SMBH masses of 4.0 × 10⁷ and 2.5 × 10⁸ M_☉, for Schwarzschild and extreme Kerr BHs, respectively. In practical terms, we need to observe for many months to be sensitive to ADs surrounding billion-solar-mass BHs because any large hot spots in ADs are probably both rare and short-lived, lasting no more than dozens of orbits (∼2 weeks).

For core-dominated FSRQs, where the emission is almost certainly dominated by jets within several degrees to our line of sight, the radio–X-ray variability can result from changes in a variety of physical parameters: the synchrotron-emitting population of particles; the conditions under which they move; the orientation to line of sight; or the Doppler factor, δ ≡ [γ(1 − βcos θ)]⁻¹, with γ = (1 − V²/c²)^−1/2 the Lorentz factor, β = V/c the velocity of the shock through the jet, and θ the angle between the observer's line of sight and the jet axis. Major flares arise from new shocks passing through the jets (Marscher & Gear 1985), but smaller fluctuations could arise from turbulence behind those shocks (Marscher et al. 2008) or "mini-jets" (Giannios et al. 2009, 2010; Nalewajko et al. 2011). Alternatively, variations in the magnetic fields, changes in the ambient medium, and changes in the injected particle distribution can also cause variations in emitted light. The light travel time across the radiating region, modified by the Doppler factor, is the characteristic time scale. If these variable emissions arise from shocks in relativistic jets, as is expected to be the case for FSRQs in high states, then the observed t_var ≃ ΔR(δc)⁻¹ (Gopal-Krishna et al. 2003). Here ΔR is the physical size of the emitting region in its rest frame (roughly a jet diameter) and δ the Doppler factor. In this case, variability timescales can constrain the jet's δ (Jorstad et al. 2005). Constraints on the jet velocity and viewing angle can be particularly tight if other data, such as apparent superluminal motions of radio knots, where V_app = Vsin θ(1 − βcos θ)⁻¹, can be detected through very long baseline interferometry. Our four FSRQ targets are all Very Long Baseline Array (VLBA) calibrators with compact radio structures (e.g., [HB89] 1924+507=4C50.47, a member of the Caltech–Jodrell Bank flat-spectrum sample survey in Britzen et al. 2008).

A leading model for any jet-based quasi-periodic variations is the intersection of an outward propagating shock with a helical structure within the jet (Rani et al. 2009). Even small deviations in the viewing direction result in significant changes in flux. The period of a QPO and its stability between events in a given source is a mode discriminator. Helical structures in a jet are relatively long-lived, so that QPOs associated with them should have similar periods during successive events. But if QPOs involve turbulent cells behind the shock in the jet (Marscher et al. 2008; Rani et al. 2009), short-lived dominant eddies are expected to give rise to different periods.

Dramatic variability is a defining characteristic of blazars; however, the duty cycles of activity are still not fully characterized, since the number of objects subject to sustained monitoring from the ground is not large. FSRQs vary on timescales of minutes to decades, with the most variable (e.g., 3C 279) ranging 2 mag from their average level and up to 5 mag above their low quiescent level (Kartaltepe & Balonek 2007). Microvariability, at the level of 0.03 mag over the course of a night (typically 6 hr) is quite common, with duty cycles around 50% for blazars (Gopal-Krishna et al. 2011; Carini et al. 2007; Goyal et al. 2012, and references therein). When the smallest variations detectable from the ground, at about 0.01 mag per night, are included, the blazar duty cycle rises to ∼80%. The duty cycle for similar small variations from normal radio loud (steep spectrum) quasars, for which jets are present, but not strongly Doppler boosted, is closer to 20% (e.g., Sagar et al. 2004; Stalin et al. 2004; Ramírez et al. 2009), which might be expected. More surprisingly, radio-quiet QSOs show a similar duty cycle to radio-loud quasars, indicative of variability arising from ADs or perhaps from jets that are present only on nuclear scales (e.g., Gopal-Krishna et al. 2003; Ramírez et al. 2009). For one example, CTA 102 is a well studied, but otherwise typical, highly polarized bright (V ∼ 15) blazar. Osterman Meyer et al. (2009) found variations as large as 0.1 mag in 15 minutes, with typical slopes of 0.01 mag hr⁻¹.

Structure function (SF) analysis is used to characterize the variability timescale and infer the physical scales when the Doppler factor and orientation to our line of sight are also measured. Bachev et al. (2012) monitored the short term optical variability of 13 highly variable blazars (not a complete sample) over the course of 5 yr. They found surprisingly low variability: several objects varied slowly and smoothly at rates of up to ∼0.1 mag hr⁻¹, but many displayed no short term variability. They quote only a ∼2% chance of observing variability of more than 0.1 mag hr⁻¹ during their observations.

The Kepler focal plane has 21 modules each with two 2200 × 1024 pixel CCDs for astronomical observation and four CCDs for fine guidance. The images are out of focus to improve sensitivity to periodic signals for extrasolar planet detection around bright stars. Thus the signal from even a point source is spread over several 298 pixels. The signals from pixels in an aperture whose size is a function of anticipated magnitude are sent down by the Kepler spacecraft (Bryson et al. 2010). For faint targets such as our AGN (V magnitudes 17.8–18.6), the signal is several hundred electrons per second, a far different regime for instrumental response (and artifacts) than for the bright stars (V < 10) searched for extrasolar planets. We observed all of our targets in long cadence (LC) 30-minute mode, yielding ∼4500 samples each quarter per target. In addition, we observed our targets in short cadence (SC) 1-minute mode for a single quarter each year (∼125,000 samples). Object B falls on dead CCD module 3 for one quarter of each year (Q8 and Q12 during Cycles 2 and 3), so we have only six quarters of data for it. In LC mode for Object D at V = 18.4 in the Kepler Input Catalog (KIC), the measured per-cadence noise level (1σ) was 0.9%. In SC mode, the per-cadence noise level at V = 18.4 was 3.4%. A record of the observations is given in Table 2.

The standard Kepler pipeline data have the day-to-week-scale drifts removed because the pipeline is optimized for extrasolar planet detection, which also removes real astrophysical brightness variations of the same timescales. Therefore, we used pre-pipeline data, "SAP FLUX," in our analysis. This was also the approach taken by Mushotzky et al. (2011) and Carini & Ryle (2012) in their analyses of Kepler data for brighter AGN. This choice means that some of the long term variations that are seen in the data are instrumental and not intrinsic to the source, but we can also be confident that we are not discarding any of the short term data trends that are intrinsic to the source. We removed the largest contribution of this effect on the PSDs we computed by performing end-matching (discussed below) on each quarter (for LC data) or each month (for SC data).

We note that there is no precise way to translate the observed signal in electrons/second to optical magnitude because this was not a mission design feature; Kepler was designed to measure very precise changes in relative brightness, not very precise absolute brightness. The light curves formed by Kepler long term data are affected at the few percent level by differential velocity aberration which originates in the motion of the spacecraft in its annual orbit around the sun. As the spacecraft moves, it keeps a constant field of view in the constellation Cygnus, and the angle formed by its velocity is constantly changing. This causes a target's point spread function to move with respect to the detector array, and because a limited number of optimal aperture ("postage stamp") pixels is downloaded, each quarter's light curve would have a characteristic rising or falling slope or a concave or convex shape, superposed on other effects such as thermal drift. The finite number of pixels used for photometry is also responsible to the steps seen between quarters; after a spacecraft roll, an object falls on a different CCD and in a different location with respect to the pixel array. Five of the 16 CCDs that our four AGN land on each year are affected by an unstable amplifier electronics problem which causes a quasi-periodic signal to move across the CCDs (see Kolodziejczak et al. 2010 for technical details). This Moiré effect, so-called because of its resemblance to a Moiré pattern, affects faint sources more than bright sources because it is additive, not multiplicative. At the time of writing, no models had been developed to remove the effect from faint source signals. Affected CCDs and modules are listed in Table 13 of the Kepler Instrument Handbook; see also their Figure 24 (Kepler Project 2009a), and for module number identification, see Figure 2-1 of the Kepler Archive Manual (Kepler Project 2009b). These "Moiré patterns" look like ripples with timescales of days, and are visible in data from some quarters, as listed in Table 2. The vast majority (80%) of our data are of excellent quality and are not affected by this problem.

We show light curves for all four AGN in Figure 1. The time axis is given in Barycentric Julian Date (BJD), the standard Kepler time unit which is referenced to the solar system barycenter; it differs from the more familiar (heliocentric) Julian Date by ±4 s (the recently discovered absolute timing error in the FITS headers (M. Still, Kepler Blog of 2012 December 12⁵) has no effect on our studies). The repeated annual patterns of differential velocity aberration are the clearest features, producing long term smooth variations.

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We found a ∼7% rise in the flux of CGRaBS J1918+4937 (Object C) during Q10 which lasted about 5 or 6 days around BJD = 2455755 (Figure 2). We confirmed that there was no plausible contamination source, e.g., a nearby star that might have flared and been incorporated into the pixels included in its photometry. This variation shares no characteristics with known artifacts, hence, we conclude that it is real. Object C also showed three consecutive fluctuations of ∼3% amplitude during a span of about 25 days during Q9. Other variations in Object C during Q7 and Q11 might be real, but because there was some Moiré effect present in those quarters, we cannot make that attribution. Object A (MG4 J192325+4754) showed several significant flares of ∼4%–6% size over a period of 10 days in Q12. This quarter is one of the two for that AGN that should not have been affected at all by Moiré problems but this quarter was affected by solar coronal mass ejections (Kepler Project 2012); however, the interval in question was well away from those disruptions and also well away from the monthly gaps and glitches. Neither Object B nor D showed any short-term variability of any type during any quarter.

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No fast astrophysical flares (shorter than a few hours) were detected in any of our targets. Our search method was as follows. Two of us independently searched the SC and LC light curve data for flares. We used the Pyke task Keppixseries (Still & Barclay 2012) to examine the data in each target's pixel; then we used topcat⁶ (Taylor 2005) to find the flag values for anomalously high data points, identified in the Kepler Archive Handbook, Table 2-3. Both the two significant (defined at 4–6 consecutive high points each) flares turned out to be instrumental and not astrophysical. The problems were flagged in the FITS files as "coarse pointing" but were actually probably "argabrightening" (Jenkins et al. 2010) and were not recognized as such by the pipeline software. During Q12, strong solar coronal mass ejections caused spacecraft coarse pointing problems that were manifested as many anomalously high data points along with several anomalously low readings (Kepler Project 2012).

We constructed PSDs for all the LC data, then fitted slopes to the low-frequency and high-frequency portions of those PSDs. We computed PSDs with a discrete Fourier transform using Period04 (Lenz & Breger 2005), both for the original simple aperture photometry (SAP) count rates and our "corrected" data, which underwent the following processing steps that fixed bad data points and would also allow us to use a fast Fourier transform on the light curves (see Figures 3 and 4). First, monthly "glitches" were removed. These instrumental effects from the temporary changes in CCD sensitivities, produced by the temperature changes resulting from reorientation of the spacecraft required to send back data each month, were often at the level of 2%–5% of the flux. We modeled them as exponential decays, with amplitudes and time constants as free parameters and then subtracted (or added) the corrections needed to produced smooth post-glitch curves. The typical decay time was 0.8–1.5 days. Second, the gaps produced by the monthly data downloads, along with the occasional other gaps in the data (usually just a few dozen isolated points per quarter, occasionally two to five contiguous points) were filled in by fitting third order polynomials to the data on either side of the gaps and then adding noise derived from the local standard deviation. In the case of Q12 data, which was affected by coronal mass ejections, these additional gaps lasted up to 4 days. Third, single point outliers more than 4σ from the local mean were removed and replaced with points generated from that local mean with a random dispersion based on that σ value. Finally, in order to minimize errors in the PSD produced by the low-frequency instrumental drifts discussed above and to take into account the fact that we do not have an infinitely long data train, we "end-matched" each light curve (e.g., Fougere 1985; Mushotzky et al. 2011), removing a linear trend so that the last several points were at the same level as the first several points in each quarter.

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The PSD slope is determined from equally weighted points in the PSD. The PSD is not uniformly populated with data; there is far more data at the high-frequency end than the low-frequency end. The slopes at the high-frequency end are invariably consistent with 0, or white noise, and our fits were done so as to force the high-frequency PSD to a zero slope. Then the low-end PSD slope was found via a least squares procedure computed starting at the lowest-frequency points until that slope started to flatten dramatically, which was indicative of the location of the break frequency. The results are summarized in Table 3, which includes results for the original SAP data, end-matched SAP, corrected SAP and corrected-end-matched SAP. The slopes based on original SAP counts are usually between −1.5 and −2.0, but vary somewhat from quarter to quarter for the same source and from source to source, with Object D usually having a shallower slope than the other three. The corrected data yielded very similar slopes to those of the original data, though they were usually slightly steeper. It is very difficult to estimate the actual errors in the PSDs (see Vaughan et al. 2003), but the quarter-to-quarter differences between slopes of the same object are usually characterized by standard deviations of 0.1–0.2, so the uncertainties involved in the computations should be no larger than this, since there is probably some degree of intrinsic variation between quarters.

The slopes found using end-matched SAP data are almost always shallower than those using the pure SAP counts, which is expected since some of the long term drift, which yields power at the lowest frequencies, is removed with end-matching. They are usually between −1.2 and −1.9. In general, if the true PSD has large contributions from frequencies below the observed range (i.e., less than the inverse of the length of the data train, which is 3 months for us) then this "red-noise leak" adds power with spectral index −2 when computing the PSD, e.g., Uttley et al. (2002). Note that if the intrinsic PSDs are actually steeper than −2.0, then low-frequency power is even more dominant. It was shown by Fougere (1985) that under these circumstances ignoring end-matching tends to drive the estimated slopes toward around −2.0, with the effect greatest for the steepest slopes; however, incorporating end-matching provides much closer estimates of the actual slopes fed into simulations. The fact that end-matching applied to the Kepler data typically slightly flattens the slopes indicates that the intrinsic slopes were not steeper than −2.0. We show typical examples in Figure 5.

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We also fitted the SC data and give, in Table 4, the results for the original SAP data, the corrected SAP data and the corrected, end-matched SAP data; however, the last two values were always the same to at least two significant figures. For each quarter for each source, the break frequencies in the SC data turned out to be essentially the same as in the LC data, which reinforces our confidence in the fitting.

Blazars can be "bluer when brighter" or "redder when brighter," e.g., Raiteri et al. (2008) and Palma et al. (2011). Accordingly, we obtained optical and near-infrared photometry from CCD observations of our targets at the Palomar Observatory 60 inch telescope in 2010 September, November, and December, during Kepler Q7. We used Sloan g'r'i'z' filters to evaluate the overall spectral shape within the very broad Kepler bandpass (Kepler's CCDs, which have no filters, are sensitive to visual wavelengths between from 4200–9000 Å). Data on the target AGN and five to six nearby comparison stars in each field were reduced with the aperture photometry tasks in IRAF. Data were calibrated using the stellar magnitudes in the KIC (Brown et al. 2011). Dereddening was applied using values from the NASA Extragalactic Database (NED). Results are given in Table 5. Objects A and B have nearly power-law spectra consistent with nonthermal emission, with α = 1.5 and 2.9, respectively for S∝ν^−α). For comparison, blazar 3C 454.3, observed on 2010 November 23 in the course of another Palomar program, had a spectral index α = 2.0. In contrast, Object C has a nearly flat spectrum (bluer than the other three objects) consistent with a blue continuum spectrum showing a single emission line, Mg ii at 2798 Å (Healey et al. 2008; FITS spectrum provided by M. S. Shaw 2013, private communication). In Object C, therefore, the optical emission could have a significant contribution from thermal Big Blue Bump emission, but disentangling the relative contributions of nonthermal and thermal emission requires high quality spectrophotometry which is beyond the scope of this paper. Object D has a spectrum peaked at the i' band, but the large uncertainty at the z' band is sufficient to encompass a power law similar to those seen in Objects A and B.

5.4.1. Upper Limits on Variability

5.4.2. Morphology

In 30 quarters of data, the strongest flare we saw was an excursion of ∼7% amplitude in Object C during Q10, and lasting about 5 days. Object A also showed several significant flares of ∼4%–6% size over a period of 10 days in Q12. Object C showed three excursions of ∼3% in Q9. Objects B and D showed no days-scale variability during any quarter. The flares could be caused by magnetic reconnection events or random fluctuations within the jets or by brightening in the AD. No microvariability on timescales of minutes to hours was detected, possibly because the SC noise levels of 2%–3.4% were too high; ground-based observations show that levels of 0.01–0.03 mag (∼1%–3%) are common in blazars, but rare in other classes of AGN, as reviewed in our Introduction.

We did not detect any astrophysical QPOs, which was unsurprising given the rarity of such events. Given the very long, consistent, light curves produced by Kepler, we greatly improved the chance of finding QPOs, if they were to be present on timescales of tens of minutes to weeks and sufficiently strong. We quantified our sensitivity to sine waves injected at a range of frequencies and amplitudes: in a blind study where one of us added such signals to real data another of us discovered that he could detect them in the PSDs at a level of ∼3% of the original amplitude for 18th magnitude targets, but could not do so for periodic signals at 1% amplitude.

The comparative smoothness of the Kepler light curves within each quarter is consistent with the finding by Bauer et al. (2009) that only 35% of blazars showed V > 0.4 mag of variation over 3.5 yr, as observed with intermittent sampling during the Palomar Quest survey. Over the six and two–three decades between the Palomar Observatory Sky Surveys and the Kepler observations, Objects A, B, and D showed no change in brightness within ±0.2 mag while Object C showed no change within about ±0.1 mag from the time of the Mt. Hopkins CCD observations for the KIC (2003–2006) to the Kepler observations. The objects were therefore in similar activity states during those observations, consequently, the comparison does not tell us whether the objects were in low or high activity states. Longer term optical variability of quasars has traditionally involved frequent monitoring of a modest number of objects from individual observatories; those observations indicate that essentially all quasars do vary substantially over decades, and changes over a year or two are expected (e.g., Pica et al. 1988; Hawkins 2002). Averages of such monitoring can yield statistical measures of quasar variability through the use of SFs (e.g., Hughes et al. 1992; Collier & Peterson 2001). Such monitoring, however, can be biased in favor of "interesting" objects, with those known to be variable being covered more frequently and some "uninteresting" objects can be dropped from the programs in favor of newly discovered variable objects. With the advent of massive sky surveys that revisit patches of the sky, such as the Sloan Digital Sky Survey (SDSS; York et al. 2000), a new approach has become possible: one can compute average variability estimates for tens of thousands of quasars divided into substantial bins by their redshifts, luminosities, and other properties (e.g., Vanden Berk et al. 2004; de Vries et al. 2005). Recently, SF analyses of quasar variability using SDSS and the Palomar Sky Survey have led to estimates of quasar variability and a damped random walk model that seems to explain its main properties (MacLeod et al. 2010, 2012; Ruan et al. 2012). One conclusion of that work particularly relevant to our study is that radio-loud quasars are slightly more variable than radio-quiet ones. Specifically, the average SF_inf, a measure of the strength of variability, was around 0.26 mag (in g') for the whole sample while the average for the radio-loud sample was 0.34 mag (MacLeod et al. 2010), where the redshifts in both categories were quite similar. Our densely sampled Kepler data on four AGN complement those programs with baselines of years that looked at very large numbers of objects much less frequently.

The results of our PSD analyses are shown in Table 3 (LC data) and Table 4 (SC data). As discussed in Section 5.3, possible systematic errors in slopes are minimized by the corrections for (post-monthly download) thermal drift and end-matching (last column of Table 3). The power-spectra for our quasars are dominated by red noise at lower frequencies and white noise at higher frequencies. We interpret the bulk of the red noise as intrinsic to the quasars; the white noise is instrumental. We find mean slopes between −1.2 and −1.8 for the red-noise portion of the PSDs for our four AGN. These slopes varied from quasar to quasar and, to a somewhat lesser extent, from quarter to quarter for the same object. Object D displayed the flattest slopes on the whole, while those for Object B were somewhat steeper but distinctly shallower than Objects A and C. Object B, tentatively classed as a Seyfert 1.5 galaxy, is the object in which our Palomar imaging detected the faint host galaxy surrounding the bright central point source, hence, the Kepler-detected optical emission had a small extra contribution from the host galaxy which could damp down any variation and flatten the resulting PSD. Among our four objects, there was no trend for PSD slopes to vary with redshift. The observed PSD slopes are consistent with those of turbulence in shocks in a relativistic jet or in an AD (Marscher & Travis 1991; Mangalam & Wiita 1993). Models of relativistic turbulence which may apply to our quasars are being developed in the context of gamma ray bursts (Zrake & MacFadyen 2013) and references therein.

Kepler measurements of the brighter Seyfert galaxies analyzed by Mushotzky et al. (2011) have substantially steeper slopes (between −2.6 and −3.3) for the PSDs of their four Seyferts; they also employed end-matching. Their objects were all substantially brighter than our targets (by factors of about 1.5–15) and so they could easily detect smaller fractional variations of 0.1%–1%. Given that our objects are at much greater distances, and therefore substantially more powerful, despite their lower fluxes, there might be some physical reason for the discrepancy. Their results of very steep PSD slopes were surprising, because long term X-ray measurements of other Seyferts yielded PSD slopes that are almost always shallower than −2.0 (e.g., Edelson & Nandra 1999; Markowitz et al. 2003; Markowitz 2009; Lachowicz et al. 2009). Further, for the brightest of one of these Seyferts, II ZW 229.015, for which Mushotzky et al. (2011) found slopes between −2.96 and −3.31, a reanalysis by a different method, coupled with ground-based observations yielded a best-fit shallower slope around −2.83 (Carini & Ryle 2012). Our independent analysis of data for that object following the correction and end-matching procedures used in this paper produced slopes consistent with −2.2. We note that Mushotzky et al. (2011) remark that "PSD analyses are notoriously susceptible to analytical systematics (see, e.g., Vaughan et al. (2003))." Users of PSDs are on firmer ground when comparing "apples to apples," that is, PSDs for different objects are internally consistent when computed by each group's analysis techniques, but PSDs generated by different groups' analysis techniques are much more difficult to compare.

The break frequencies at which the red noise and white noise contributions are equal were between ∼10^−4.2 Hz and 10^−4.7 Hz, corresponding to 0.2–0.6 days. Increasing the instrumental noise raises the white noise "floor" in the PSD diagrams, shifting the intersection of red noise and white noise to longer timescales (to the left in our figures). Kepler measurements of the brighter Seyfert galaxies analyzed by Mushotzky et al. (2011), which have smaller fractional noise, also have break frequencies of about 0.25 days.

We are currently acquiring additional LC data on each target. In future work, we will apply principal component analysis and cotrending basis vectors to the LC data to separate out common instrumental long term trends (such as differential velocity aberration and thermal drift, not Moiré effects) in the data. These techniques may allow us to patch together individual quarters, forming light curves two or more years long for three targets and several three-quarter light curves for the remaining target that falls on a dead CCD during one quarter each year. Our goal is to detect lower break frequencies in the PSDs to find the largest physical scale as was done for II Zw 229.015 by Carini & Ryle (2012) who used ground-based data to bridge quarterly amplitude jumps in their Kepler light curves.