A DISTINCTIVE DISK–JET COUPLING IN THE SEYFERT-1 ACTIVE GALACTIC NUCLEUS NGC 4051

The Advanced CCD Image Spectrometer (ACIS) on the Chandra X-ray telescope was used to collect eight observations of NGC 4051 between 2009 January 1 (MJD 54848.2) and 2009 July 31 (MJD 55043.1). We list these observations of approximately 10 ks exposures in Table 1. X-ray observations are subject to photon pile-up. Photon pile-up is when multiple low-energy photons arrive at the same CCD pixel in a single frame and register identically to one higher energy photon. It reduces the number of soft, i.e., low energy photons that are detected while increasing the hard, i.e., high energy photon counts which can mislead analysis by making the spectrum appear harder than it actually is. To avoid photon pile-up, we used the mode with the minimal integration time, i.e., the continuous clocking mode, with integration times of only 2.85 ms. Such a fast integration time helps to prevent against multiple photons being counted as one higher energy photon, but does so at the expense of one spatial dimension. The resulting image is 1 × 1024 pixels with a resolution <1'' and an effective field of view of 83 × 83, with spatial resolution in only one dimension.

We used HEASOFT version 6.7, FTOOLS version 6.7, XSPEC version 12.5.1, CALDB version 4.1, and CIAO version 4.1 in the data reduction and analysis of these images. The CIAO psextract routine was used to extract a spectrum and background for a point source as well as the companion auxiliary response functions and response matrix functions. To do so, we used a circular extraction region of diameter 2'' centered at 1203096, +44°31'525, while another 2'' diameter circular extraction region was used approximately 20'' off-source for the background. This aperture size ensured encapsulation of the source, assuming it was a point source and not elongated, but not so large as to include effects from the background.

We analyzed X-ray data between the energy range of 0.5 and 10.0 keV with a minimum of 10 counts per bin. A power-law component modeling the continuum was initially fit to the data. To check for pile-up in our source before further modeling was attempted, we also used an annulus with inner radius of 09 and outer radius of 17 to obtain an additional spectrum from each observation using psextract. Again, requiring a minimum of 10 counts per bin, we fit power-law models to the annular spectra for comparison. If pile-up was present, the spectra from the annuli would be softer than those extracted from the central region. In general, we found that the two spectra were equivalent, within errors, suggesting that any pile-up is minimal in all observations.

A description of the line-of-sight absorption is as follows and was included in all modeling. The Galactic absorption was modeled as an effective H column density of 1.15 × 10²⁰ cm⁻² (Kalberla et al. 2005) using phabs. Two absorption edges typical to Seyfert AGN (Reynolds 1997) at K-shell rest energies of O vii and O viii of 0.739 and 0.871 keV, respectively, were modeled using zedge. These three rest-frame values were frozen, while individual normalizations were allowed to vary.

Figure 1 shows a sample spectrum fit with a simple power-law model. This attempt at fitting the data resulted in a poor fit for all spectra and in particular the spectrum presented in Figure 1 had a χ²/ν of 1770/366. By looking at the ratio of the data to the model, one can see the obvious excess at low energies typical of Seyfert galaxies (Reynolds 1997). To better characterize the source flux, a disk blackbody component was added shown in Figure 2. Typically, it is thought that this soft excess is not the result of a thermal blackbody component, but of an atomic process that is not trivial to model (e.g., Gierlinski & Done 2004; Crummy et al. 2006). Figure 3 plots the temperature and flux from the putative disk component. We find that the temperature does not vary with flux, suggesting that it is not a blackbody thermal component. However, the addition of the disk blackbody does produce a formally better fit.

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In Figure 2, we not only include a power-law component and a disk blackbody, but also an unresolved Gaussian that models a narrow Fe Kα line and a broad Fe Kα line. The fit is improved to χ²/ν = 368.3/353. It should be noted that the Fe Kα lines are not detected at more than the 2σ level of confidence, except in the last two exposures. However, they were included in the modeling for completeness (see Table 2). In Seyferts and AGN, Fe K-shell emission due to fluorescence and recombination is the most prominent of the X-ray emission lines (e.g., Miller 2007). The shape and broadening of the Fe Kα line, initially modeled by Fabian et al. (1989) for a zero-spin Schwarzschild black hole and by Laor (1991) for a maximally spinning black hole, are dependent on the spin of the black hole, the inner and outer radii of the emitting region, the inclination angle of the disk and the efficiency of the disk emissivity. With this in mind, we modeled the broad Fe Kα line with the XSPEC model laor that produces an emission line from an accretion disk and includes general relativistic effects (Laor 1991). Keeping the emissivity as a function of radius (∝R⁻³), the outer radius fixed at 400 $\textit{GM}\;c^{-2}$, and the inclination fixed at 30°, we let the inner radius vary.

Finally, in order to compare to the fundamental plane of accretion onto black holes as described by Gültekin et al. (2009a), just the power-law component within the energy range of 2–10 keV was used to compute the total flux associated with each observation. This component contributes to more than 95% of the total flux in the 2–10 keV range, with the broad Fe Kα line contributing 2%–5% of the total flux. We plot this light curve in Figure 4, and list the results for each spectrum in Table 1. The continuum flux varies by almost a factor of three, which can be attributed to fluctuations in the mass accretion rate.

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A combination of the Very Large Array (VLA) and Extended Very Large Array (EVLA) antennas was used to observe NGC 4051 six times between 2008 December 31 (MJD 54831.3) and 2009 July 31 (MJD 55043.1). These observations were approximately 1 hr integrations centered at 8.4 GHz with a bandwidth of 50 MHz in two channels with two polarizations. We chose this frequency to ensure that the self-absorption of the synchrotron emission was not a problem. Exposure dates and times are listed in Table 3. During each observation, the antennas switched from on source, located at 1^h203^m1^s +44°31'8'' to a phase calibrator located at 12^h21^m4^s +44°11'4'' every 3.33 s. 3C 286 was used as the flux calibrator with 3.33 s of integration at the end of each observation. During the seven months spanning the observations, the VLA/EVLA evolved from its A configuration, which has its longest baseline of 36.4 km, to its C configuration with a maximum baseline of only 3.4 km. This significantly changed the resolution of the resulting images, and steps were taken to ensure a consistent comparison among the six observations. The resolution during each configuration is listed in Table 3.

The Common Astronomy Software Applications (CASA) package, version 3.0.0, developed by the National Radio Astronomy Observatory (NRAO), was used to reduce the radio observations. The routine setjy was used to set 3C 286 as the flux calibrator, while the routine gaincal set the gain calibration incorporating both the phase calibrator source located at 12^h21^m4^s +44°1'4'' and 3C 286 as references. Either antenna VA06, VA08, VA10, or VA12 was used as the reference antenna for these calibrations. Antennas that were off or showed discontinuities that were not characteristic of the overall data in either phase or amplitude were excluded, resulting in only one or two EVLA antennas per data set. The CLEAN algorithm was then run to create an image, using a threshold of 0.1 mJy as well as Briggs weighting and robust parameter of 0.5. Briggs weighting provides a smooth transition between natural and uniform visibility weighting and is characterized by a robust parameter where 2.0 is approximately natural weighting and −2.0 is approximately uniform (Briggs 1995). No self-calibration was done because the source was too faint, which is consistent with methods described by Giroletti & Panessa (2009), who also observed NGC 4051 at 8.4 GHz. Figure 5 shows an example of the type of images that were produced.

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After the CLEAN algorithm was run, the flux density was measured using CASA's imfit, which fit Gaussian curves to the peak intensities. Because of the four different configurations, we were only able to resolve structures in the A configuration, as seen in Figure 5, which afforded the best resolution. In order to make a fair comparison between all the measurements, the Gaussian fits were restricted to an area of approximately 8'' × 6'' ensuring the inclusion of all the structures present in the images. Fortunately, as seen in the work done by Giroletti & Panessa (2009), there does not appear to be any extensive large-scale diffuse emission that would be resolved out in higher resolution configurations. If this were the case, the flux would decrease with higher resolution, when in fact Table 3 demonstrates that the flux in the B configuration, a higher resolution, is higher than in the flux in the C configuration, a lower resolution. This strongly suggests that the radio variability observed between the B and C configurations is intrinsic, not instrumental. However, it is unclear if the diffuse emission has been resolved out in the A configuration. For this reason, we quote our results with and without the A array measurements. The measurements are listed in Table 3 and the light curve is shown in Figure 6. The errors in these measurements also include a systematic error of 3% of the total flux, added in quadrature, to account for the calibration errors. These measurements, including the integral flux densities as well as the peak flux densities, do vary by a factor of three, which is comparable to the X-ray variations. In order to compare to Gültekin et al. (2009a), we scaled the fluxes as F_ν ∝ ν^−0.5 from 8.4 GHz to 5 GHz as Ho (2002) did.

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Inspection of the image produced in the A configuration reveals evidence of jet production. As shown in Figure 5, three structures are present: a central source and two extended lobes. The central radio lobe is likely associated with the black hole, while the northwest and southeast lobes may be associated with the endpoints of the outflows in this system. The alignment and varying brightness between the three lobes suggest that this is a jet structure where the jet is partially projected into our line of sight, placing the northwest lobe closer and less obscured than the southeast lobe. We also note that these lobes are not seen in the point-spread function of the antennas and are therefore not artifacts of the clean algorithm. Observations by Christopoulou et al. (1997), Giroletti & Panessa (2009), and Kukula et al. (1995) note similar structures as well as the potential evidence for jet production.

These measurements by themselves can give insights into the physical processes that occur in an AGN, but through a comparison of the X-ray and radio luminosities we can explore how accretion is coupled to jet production. To quantify any correlation between the X-ray and radio fluxes, we calculated Spearman's rank coefficient (ρ). This ρ describes how well a data set exhibits a monotonic behavior between two variables; ρ < 0 corresponds to variables that are anti-correlated. We find a ρ of −0.66, with a probability of only 0.16 of zero correlation.

Figure 7 plots the X-ray versus radio luminosities. We assumed a distance of 10.0 Mpc derived from the redshift, z = 0.002336 (Peterson et al. 2004), and cosmological parameter H_° = 70 km s⁻¹ Mpc to obtain these luminosities. Figure 7 also includes the least-squares fit of a first-order polynomial to the data points, described by the following relation:

$$\begin{equation} \log L_{\rm radio} = (-0.72 \pm 0.04) \log L_{\rm X\hbox{-}ray} + (64 \pm 2). \end{equation} \tag{ 1 }$$

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To test the robustness of the anti-correlation, we used an F-test to compare the results of the first-order polynomial given above to fits with a zeroth-order polynomial as well as the fundamental plane relation of L_radio ∝ L^0.64_X-ray. At an 81% confidence level, we were able to rule out the flat model. However, at a 96% confidence level, our model excludes the fundamental plane relation. We also looked at the correlation between the data points excluding the A configuration, in the case that this array resolved out a substantial amount of flux. We found that the correlation was still inversely proportional, described as,

$$\begin{equation} \log L_\mathrm{radio} = (-0.12 \pm 0.05) \log L_\mathrm{X\hbox{-}ray} + (40 \pm 2). \end{equation} \tag{ 2 }$$

Using the same F-test, our second model may be consistent with being flat, for it only excludes a flat distribution at the 60% confidence level. However, the positive fundamental plane relation is again excluded, this time at a 98% confidence level.

To place the data from NGC 4051 in context, we plotted our data and best-fit line against the data and the best-fit line described in Gültekin et al. (2009a) in Figure 8. The best-fit line found by Gültekin et al. (2009a) is described as follows:

$$\begin{eqnarray} \log L_{\rm radio} &=& (0.67 \pm 0.12) \log L_{\rm X\hbox{-}ray}\nonumber\\ &&+ (0.78 \pm 0.27) \log M_{{\rm BH}} + (4.80 \pm 0.24).\qquad \end{eqnarray} \tag{ 3 }$$

One should notice that our data are not described by the positive correlation of L_radio ∝ L^0.67_X-ray denoted by the solid line, but instead by the dashed line and the dotted line described by L_radio ∝ L^−0.72_X-ray and L_radio ∝ L^{−0.12±0.05}_X-ray, respectively. In fact, our relation differs from this relation by 11.6σ, while including the A configuration, and 6.5σ, while not including it, when dividing the difference between the power laws by the larger of the two errors. The fundamental plane is known to have a large scatter, and NGC 4051 lies close to the plane. This exercise, however, makes clear how different the X-ray and radio coupling in NGC 4051 appears to be.

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Finally, we attempted to quantify whether or not there is a significant time delay between fluctuations in the X-ray and radio luminosities, which can be seen in Figures 4 and 6, respectively. We used a discrete cross-correlation function (DCCF) as described by Edelson & Krolik (1988) to quantify this delay. The sparse and uneven sampling of the six observations poses a natural limitation on the results of this analysis. This led us to linearly interpolate the data within the seven month period with uniform spacing. The time steps between interpolated points were 17 days, corresponding to the shortest time between observations. White & Peterson (1994) and Gaskell & Peterson (1987) describe similar techniques for interpolating and cross-correlating data in their respective variability studies of AGNs. The results, shown in Figure 9, place the minimum of the DCCF of −0.48 ±0.1 at −2.5 ± 5.3 days, suggesting that X-ray dips are leading the radio flares.

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