6. Colors, dust temperature and mass of dust
Following Barvainis (1987), we assume the emissivity of the grains to depend on wavelength as and we use a simple model of optically thick grey-body dust emission: .
In the general situation of an AGN, the grain temperature varies strongly with distance to the central engine, following a power law (Barvainis 1987): K, where is the UV luminosity in units of ergs s-1 and r the radial distance in parsecs.
6.1. Color gradients in the near-infrared
6.1.1. Colors of the core
Owing to our limitation in spatial resolution in the M band (FWHM = 0.33"), we can measure at best the [L-M] and [K-L] colors of the core through an 0.6" diameter diaphragm centered on the near-infrared emission peak. We find [L-M] = 1.6 0.4 and [K-L] = 1.8 0.2. It must be noticed however that the contribution of stellar light in the K band (Thatte et al. 1997) has not been removed at this stage and that the observed [K-L] color does not relate only to the dust emission.
6.1.2. Colors of the extended structure
As for the colors of the sources forming the extended structures, and again because of different spatial resolutions in the K, L and M bands, we have considered the mean colors in a ring which extends from r = 0.3" to r = 0.5". This ring does include the emitting regions forming the extended structures along the two directions P.A. 100o and NS, at 3.5 and 4.8µm, but excludes in part the secondary peaks which delineate the extended structures at 2.2µm. Therefore, at 2.2µm, the ring includes more of the diffuse contribution possibly related with the stellar core analyzed by Thatte et al. (1997). The colors found for the ring, representative of a mean 0.4" radius, are [L-M] = 1.6 0.4 and [K-L] = 2.8 0.2.
6.2. Dust temperature
The advantage of interpreting the [L-M] color is that the L and M band flux contributions are known to arise almost entirely from the dust component. Within the limitation in spatial resolution from the M band data set, we do not detect any [L-M] color gradient within the central 1" region of NGC 1068 .
Under the simple assumption of optically thick grey-body emission from the dust component, the observed [L-M] color corresponds to a grain temperature 480 K. The foreground extinction to the core has been calculated by several authors (Bailey et al. 1988; Bridger et al. 1994; Efstathiou et al. 1995; Young et al. 1995; Veilleux et al. 1997; Glass 1997; Thatte et al. 1997; Rouan et al. 1998) and an estimate of 30 mag is retained. Applying a correction for such an extinction, we deduce an intrinsic color [L-M] = 0.8 0.4 and 700 K. The absolute luminosity of the AGN in NGC 1068 - assumed here to be the unique heating source of the dust grains in the AGN environment - can be approached only indirectly and is still quite uncertain. From the analysis by Pier et al. (1994) who have examined various methods for deriving the absolute luminosity of the AGN in NGC 1068 and summarize the current knowledge on this question, we deduce = 4 1044 erg s-1. However it should be noted that this figure has been obtained assuming a reflected light fraction frefl 0.01, while the consideration of ionized gas in regions further out inside the ionization cone (ENLR) leads to a value frefl 0.001 (Bland-Hawthorn et al. 1991). Then a value as high as = 4 1045 erg s-1 should be envisaged as well. In addition, most of these estimates have been derived without taking into account the fraction of UV-optical flux which provides the dust grains heating: already the K magnitude of the innermost core (FWHM = 0.12"), 9.3, corresponds to an energy output of 8 erg s-1. It might be important to consider the energy radiated in the near- to mid-infrared bands for the evaluation of . In conclusion, the figures currently available for in NGC 1068 might be lower limits.
Still, under the simple model of optically thick grey-body dust emission, reaching 480 K at r = 28 pc requires = 8 erg s-1, a value roughly consistent with the highest figure given above for in NGC 1068 . This figure goes up to = 6.5 erg s-1 if the grain temperature is of 700 K at r = 28 pc (extinction-corrected estimate), pushing NGC 1068 to the limit between AGN and quasars. This question certainly deserves further attention and above all the consideration of a more elaborated model of the dust region, with regard to its geometry and heating. This is beyond the scope of the current paper and will be discussed in the future.
The [K-L] color in the extended structures can be contaminated by some stellar contribution in the 2.2µm band. From grains at 480 K, which are the dominant contributors, we expect a [K-L]dust color of 4.0. Given the observed [K-L] value, we deduce that the percentage of the flux at 2.2µm which arises from the dust component (with at most 480 K) is 30%. For this estimate, we have not considered any correction for extinction.
How can the lack of [L-M] color gradient between the 0.6" diameter core and the extended structures be explained? Given the unresolved and intense core emission at 2.2µm (FWHM = 0.12" from Rouan et al. 1998) it can be inferred that the hottest dust grains are extremely confined and located at a radius less than 4 pc. With = 8 1045 erg s-1, they would be present only up to r = 1.1 pc. Hence, there must exist a very steep dust temperature gradient close to the central heating source. Such a few parsec scale corresponds to a resolution which is well beyond that accessible at 3.5 & 4.8µm. In fact, the L and M emission we are measuring in an 0.6" diameter core is already strongly dominated by the warm grains. Because of this suspected steep temperature gradient, the procedure applied previously to derive the stellar contribution in the 0.3" to 0.5" radius ring cannot be used in the core.
6.3. Mass of the hot dust
The mass of dust associated with the near-infrared emission can be estimated only in a rough way, as it depends on the (unknown) grain composition and grain size distribution. Assuming graphite grains and following Barvainis (1987), the infrared spectral luminosity of an individual graphite grain is given by: where a is the grain radius, is the absorption efficiency of the grains, and is the Planck function for a grain temperature . Following Barvainis (1987), we take a=0.05µm and in the near-infrared, , leading to =0.058 (for the K band).
Because no [L-M] color gradient is detected towards the 0.6" diameter core, we consider the simple case of 2 populations of dust grains in that region, hot grains at T = 1500 K and warm grains at T = 500 K, matching the extreme values in that region. Solving the equation for the three bands available, K, L and M, one derives 2 1045 and 9 1047, for the number of grains at 1500 K and 500 K respectively, in the 0.6" diameter core. This indicates that there are 450 times more warm dust grains than hot dust grains in the 0.6" diameter core. The warm dust grains dominate the [L-M] color. With a grain density =2.26 g cm-3, the mass of warm dust grains is found to be M(warm dust) 0.5 . This mass is above that of hot dust grains detected in two Seyfert 1 nuclei: 0.05 in the case of NGC 7469 (Marco & Alloin 1998) and 0.02 in the case of Fairall 9 (Clavel et al. 1989). This result supports the fact that only a small fraction of the dust present in the torus is heated close to its sublimation temperature.
© European Southern Observatory (ESO) 2000
Online publication: December 17, 1999