The Dusty Heart of NGC 4151 Revealed by λ ∼ 1–40 μm Reverberation Mapping and Variability: A Challenge to Current Clumpy Torus Models

In some references, the author name "Oknyansky" has been transliterated as "Oknyanskij." We have adopted "Oknyansky" throughout the main text of the paper but used "Oknyanskij" in the reference list when necessary so the citation can be readily found in the Astrophysics Data System.

We transformed the V photometry in Koshida et al. (2014) to B, based on colors from the other programs.

The errors on the nuclear B-band flux have been estimated by detrending (linearly) the dependence of B − V versus 0.5 × (B + V), evaluating the scatter after detrending, and then correcting for the galaxy flux within the measurement aperture from Doroshenko et al. (1998). These steps are important because (1) the true errors in measuring the galaxy are likely to be significantly larger than the nominal photometric internal errors, particularly in the face of atmospheric seeing and its variations from night to night (e.g., Peterson et al. 1995), and (2) although large measurement apertures significantly reduce the seeing issues, they also dilute the nuclear flux with that from the galaxy, and the resulting net error in the nuclear flux needs to reflect this effect. The resulting errors (corrected to an aperture of 6'') range from ∼5% for the SAI photometry when the nucleus is bright to ∼8% for the photometry of Shomshekova et al. (2019). Given the amplitude of the variations in nuclear B-band output, these errors are not a significant issue in our analysis.

http://maxi.riken.jp/mxondem/index.html

Although supernova 2018aoq was discovered on 2018 April 1 (JD:2458208), 73'' from the NGC 4151 nucleus (see http://www.rochesterastronomy.org/sn2018/sn2018aoq.html), we do not see its influences in the X-ray light curves, possibly due to it being relatively faint compared to the AGN.

Due to the lack of constraints at shorter wavelengths and the strong contamination from the accretion disk variability, the temperature of this component cannot be accurately determined. We adopt an upper value of 2200 K.

Small variations similar to those found by Schnülle et al. (2015) are not ruled out by this simple analysis.

https://github.com/legolason/PyIICCF/

We arbitrarily increased the fitting weights of the J, H, and K data at JD 2452700–2452900 by a factor of 5 to mitigate the fitting bias of the AMP parameter due to the relatively short duration and resulting modest sampling of the high-flux epochs. This adjustment did not significantly change the best-fit values of other parameters.

Because the K-band variability includes two time lags, the lag from this single-lag model is systematically larger than the shorter lag (and smaller than the longer lag) reported in Section 3.2.4 and Table 6.

The second reference only gives L-band photometry, which we correct to the K band by multiplying the flux density by 0.506, derived from the SAI photometry when the source was of similar brightness.

To confirm this variability, we have carried out a χ² test (e.g., de Diego 2010) of the N-band data points. For a number of measurements with the flux f_i and uncertainty σ_i , the χ² is defined as

$$\begin{eqnarray}&&{\chi }^{2}=\displaystyle \sum _{i}\displaystyle \frac{{\left({f}_{i}-\bar{f}\right)}^{2}}{{\left({\sigma }_{i}\right)}^{2}},\end{eqnarray} \tag{ 6 }$$

where $\bar{f}$ is the average value of all the measurements. From the χ² distribution, a p-value can be computed to describe the significance of the measurements randomly selected from a normal Gaussian distribution, i.e., the AGN is not variable. Because there is no evidence for variations on a yearly timescale, we combined measurements in the same year as described in Appendix B. We then obtained the χ² (for 18 degrees of freedom, dof = 18) for the N-band measurements to be 283.5 with a p-value of ∼10⁻⁵⁰. Even if we arbitrarily increase all flux uncertainties by a factor of 3, we still have a p-value of 0.007, too small for the flux variation to be due to random measurement errors. Thus, the N-band variations over decadal timescales are undoubtedly real.

We adopted the PSF photometry from the SEIP source catalog, which is measured based on a mosaic image from two sets of observations made in 2007 May 30 and 2008 June 23. We took the median JD of these two dates.

This measurement is based on aperture photometry, which could underestimate the source flux.

The original paper adopted a distance of 14 Mpc for NGC 4151 and reported the size to be (2.0 ± 0.4) pc.

The original paper assumed NGC 4151 is at a distance of 13.3 Mpc and reported a size of $3.3({\sin }^{-1}\theta )$ pc.

We have converted the optical-to-IR relative flux density variation amplitude AMP (see Equation (4)) into the optical-to-IR relative luminosity variation amplitude and denoted it by AMP (ν F_ν ) or f_{B, DRW}. This parameter describes the amount of dust emission that responds to the optical variations.

The T ∼ 2100 K temperature of the hottest dust component is higher than the typical value of ∼1800 K assumed for the dust sublimation of graphite (e.g., Barvainis 1987; Mor et al. 2009). However, the higher temperature may be a result of stochastic heating of transient very small graphite particles as discussed in the next section. Alternatively, this temperature may result because the dust sublimation zone is likely adjacent to the gas in AGN broad-line regions (Baskin & Laor 2018).