DISCOVERY OF POLARIZATION REVERBERATION IN NGC 4151

During the period 1997–2003 NGC 4151 declined from the end of a high state and passed through a low minimum level of activity (Lyuty 2006). There is some evidence for a slow long-term change in the degree of polarization over the seven-year period. This is most obvious if we compare years where the mean U-band continuum level was approximately the same. As can be seen from Figure 1, the polarized flux around MJD 2400 is more than a factor of two lower than that around MJD 1300 when the total fluxes are comparable. Similarly, the polarized flux is also lower around MJD 2750 compared with MJD 1200. This change in the percentage polarization after the photometric minimum around MJD 2000 suggests a possible reduction on a dynamical timescale in the number of scatterers after the low state. Another possible explanation, strongly favored by other observations (see Gaskell 2010, 2011 for extensive discussion), is that the continuum variability could be non-axisymmetric and the anisotropy could be varying from year to year. Unfortunately, we did not have good polarimetric coverage in the year of the photometric minimum.

In order to search for polarization reverberation on short timescales, we have removed the long-term trends by subtracting fourth-order polynomials (shown in Figure 1) from the total flux and polarized flux time series. The two time series were cross-correlated using the interpolation method of Gaskell & Sparke (1986). Details of the method are given in Gaskell & Peterson (1987). We show the resulting cross-correlation function (CCF) for the entire data set in Figure 2.

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The centroid of the CCF calculated from the first moments above 0.7 times the peak correlation gives a lag of 8 days. In Table 1, we also give the considerably less certain lags from the centroids of the CCFs for the individual observing seasons. The median of the lags for the individual years is consistent with the lag from the whole of the seven observing seasons. The differences in lags in Table 1 are not statistically significant, but if the variability is non-axisymmetric (Gaskell 2010, 2011), future better observations could show that real variations in the polarization lags vary from year to year.

As is well known (Gaskell & Peterson 1987), the distribution of errors in the peaks in CCFs is non-Gaussian with a tail extending to high errors. This can be seen in the simulations of Maoz & Netzer (1989), White & Peterson (1994), and Peterson et al. (1998). We estimated the error in the lag of the polarized flux in three different ways. First, we used the formula of Gaskell & Peterson (1987). This gave an error of ±3.5 days for the lag derived from the whole data set. We also performed Monte Carlo simulations where we added noise to the observations equal to the observational errors. This gave an error in the lag of ±2.5 days. Finally, where possible we calculated the lags for the individual years as described above. They are again the first moment lags calculated above 0.7 of the peak in the CCF. These lags are shown in Table 1 with the approximate errors from the Gaskell & Peterson (1987) formula. As can be seen, even though the errors are substantially larger because of the small number of observations, the median lag for the individual years (8.5 days) is close to the lag we obtained from all years. The median of the absolute values of the differences of the individual lags for each year from the lag for all years is 1.5 days. These three separate error estimates suggest that the error in the lag for the whole sample is of the order of ±3 days.

For the period 1990–1998, Oknyanskij et al. (1999) find a delay of 35 ± 8 days for the K band relative to the U band. This includes the peak of activity at the start of our polarimetric monitoring. For the low state during our monitoring, Minezaki et al. (2004) find a similar delay of 48 ± 2.5 days, and by the end of our observations Swain et al. (2003) constrained the radial extension of the K-band emitting region to 0.04 pc, which also corresponds to a time lag of ∼48 days. Kishimoto et al. (2009) found an identical K-band size in 2009. Note that Swain et al. (2003) believed that the K-band emission comes from the outer accretion disk while Kishimoto et al. (2007, 2009) attribute it to the inner boundary of the torus. The difference in both interpretations may lie in the assumed dust sublimation radius. If one assumes a grain-size distribution favoring larger grains, the dust can survive at a relatively close distance of 0.04 pc from the central source. Indications that dust grains in AGNs tend to be larger than in standard Milky Way dust are found from examining quasar reddening curves (Gaskell et al. 2004).

Oknyanskij (1993) did determine a K-band lag during the low state of NGC 4151 in the 1970s of 18 ± 6 days which is marginally consistent with the polarization reverberation delay we measure, but as Oknyanskij et al. (2006) point out, their observations and those of Minezaki et al. (2004) show that, as would be expected, the high state of NGC 4151 at the start of our polarimetric monitoring destroyed the dust close to the black hole, and the K-band observations show that the dust had still not reappeared at smaller radii within several years of the high state.

Overall, there is good observational evidence that the inner radius of the torus did not change significantly during our monitoring that finished in 2003 May. Koshida et al. (2009) report that the inner boundary of the torus moved in after 2003, but when Pott et al. (2010) and Kishimoto et al. (2011) took new interferometry data, the radius of the K-band emission region was again at ∼0.04 pc from the center. The K-band emission comes from the hottest dust, and lags given by the cross-correlation method are biased toward material at the smallest radii (Gaskell & Sparke 1986) so the K-band lag is giving the inner radius of the dust torus. From the Oknyanskij et al. (1999) and Minezaki et al. (2004) measurements, we can conclude the inner radius of the dusty torus during our polarimetric monitoring was ∼40 lt-day. This strongly rules out dust scattering being the cause of the polarization reverberation we detect.

We modeled dust scattering off a variety of optically thick torus geometries. We considered cylindrical tori and tori with elliptical cross sections. In all cases, we set the inner radii to be 40 lt-day as indicated by the IR reverberation mapping. Various opening and viewing angles were modeled. The resulting first moment delays in the polarized flux were ∼43 days (i.e., slightly greater than the inner radius), and varied only by 10%–15% with changing geometries and viewing angles. These modeled lags are clearly inconsistent with the ∼8 days lag we find from the observations. So long as the torus was not too thin (i.e., the half-opening angle is not >53°), the polarization of the dust model averaged over the lag was perpendicular to the radio axis for all the type-1 viewing angles, which is inconsistent with the observed P.A. We thus believe that scattering from the torus is not the cause of the lag in the polarized flux. For more extensive discussion of the effect of the geometry and viewing angle on the degree and direction of polarization, see Goosmann & Gaskell (2007).

Scattering off a polar distribution of electrons (Giannuzzo & Salvati 1993) also produces the wrong polarization angle, but a flattened electron distribution produces polarization parallel to the radio axis (see discussion in Goosmann & Gaskell 2007). We therefore used STOKES to model the polarization lag from cylindrical electron-scattering disks. We found that for disks which were optically thick to electron scattering, the lag was equal to the inner radius. Thus, if the electron-scattering region is optically thick in NGC 4151, it has an inner radius of ∼8 lt-day.

The geometry of the scattering region is similar to that of a broad-line region (BLR; see a review by Gaskell 2009a). Furthermore, the lag we find is comparable to the size of the BLR of NGC 4151. Gaskell & Sparke (1986) obtained a size of 5 ± 2 lt-day for the radius of the C iv emitting region of the BLR in NGC 4151 during 1978–1980. Metzroth et al. (2006) obtained radii of 3.4 ± 1.3 days for 1988 and 3.3 ± 0.9 days for 1991. They also obtained identical radii for He ii. Gaskell & Sparke (1986) estimated the size of the region emitting Hβ and Hγ to be ∼6 lt-day during 1980–1981. More recent observations by Bentz et al. (2006) give 6.6 ± 1 lt-day for 2005. Note again that the responsivity-weighted radii given by reverberation mapping are biased toward the inner radii of the emitting region.

While our observed polarization lag is in good agreement with the observed radii of the C iv and Hβ emission in NGC 4151, the observed inner radius for a given line reflects the radial variation of ionization and there is almost certainly BLR gas inside that radius. If the gas density of the electron-scattering region in our STOKES models is somewhat lower than a canonical BLR density (i.e., 10⁸ cm⁻³ rather than 10¹⁰ cm⁻³), then the model is no longer optically thick, the mean free path to electron scattering becomes significant, and we find that the lag is greater than the inner radius of our hypothetical disk. For example, a disk with a density of 10⁸ cm⁻³ would give a mean free path of ∼6 lt-day. It is therefore possible to reproduce the observed polarization lag without having to have an artificial hole in the middle of the distribution of electrons.

Interestingly, the radius we obtain for the electron-scattering disk (i.e., toward the outer edge of the BLR) is in good agreement with the location deduced quite independently by Smith et al. (2005) from modeling the change in polarization with velocity across the profiles of broad emission lines. Nevertheless, it is more intuitive to assume a continuous accretion flow from the torus down to the supermassive black hole.