The large color gradients found in galaxies with 2.2 µm excesses imply that the source of the excess is located primarily within the nucleus. In the following discussion we shall assume that the galaxian flux can be decomposed into a nuclear source with an infrared excess, and an extended source with normal galaxy colors. For these fiducial colors we adopt 3.3, 0.74, 0.20, 0.16, and 0.12 for V - K, J - H, H - K, CO and H2O, respectively, which are appropriate values for all but very late-type galaxies (Table 9). We shall first briefly discuss the various non-stellar effects to be compared with the data. Note that the color of the different emission mechanisms to be considered were calculated by adopting the flux calibration of Wilson et (1972) for JHK, and the flux calibration of Johnson (1966a) for U and V. For the CO and H2O indices, it was assumed that at the effective wavelengths of the narrow band filters given in Table 2, Lyr could be represented by a 10000 K black body.
a) Dust Absorption
For purely absorbing (zero albedo) dust, completely external to the emitting source, we have
For dust that is uniformly mixed with the emitting source,
In both eq. (1) and (2) is the optical depth of the dust and I0 is the intensity of the emitting source if no dust were present. For we adopt the Van de Hulst reddening curve (Johnson 1968), which is essentially the same reddening curve discussed by Whitford (1956). Note that for small values of , the reddenings given by eqs. (1) and (2) are similar. Observational evidence for reddening from "well-mixed" dust has been presented by Leibowitz (1973) in galactic planetary nebulae, by O'Connell (1970) in the galaxy NGC 3034 (M82), and by Turnrose (1976) in the galaxy NGC 2903.
b) Dust Emission
For emission by dust grains, we have
The dust is expected to be a combination,of graphite and silicates, with emissivity 1 / x, and 0 x 3 (Werner and Salpeter 1969, Aannestad 1975). We assumed x = 2, as for a uniform conducting sphere of radius a, with a << (Van de Hulst 1946).
c) Gaseous Emission
For optically thin free-free emission, we have simply
Thermal emission from gas, as in a typical H II region, includes free-free, free-bound, bound-bound, and two photon processes. We have assumed Te = 8000 K, and calculated the gaseous JHK colors from the formulae in Willner, Becklin, and Visvinathan (1972). The V - K color was calculated using the absolute magnitude calibration in Huchra (1977b) appropriate for Huchra's standard line ratio set, composed of mean line ratios in LMC H II regions and Orion. The U - V color was also adopted from Huchra (1977b). The CO and H2O indices appropriate for an H II region were estimated by interpolation of the broad-band gaseous flux dependence. The adopted final colors are given in Table 13.
It is well known that gaseous excitation conditions differ between the nuclear and outer regions of spiral galaxies (Morgan and Osterbrock 1969; Spinrad and Peimbert 1975). The purely infrared colors, being mostly unaffected by line emission, are largely insensitive to excitation changes (Willner et al. 1972). However, 70% of the gaseous V flux is contributed by line emission , while-only 30% is from the continuum (Huchra 1977b), and the same is not true for the UVK colors. Nevertheless, the colors in Table 13 will not differ by more than 30% for reasonable excitation variations (Huchra 1977b) and are thus of sufficient accuracy for the purposes of this discussion. Note that the gaseous H - K color is considerably redder, while the gaseous J - H color is considerably bluer, than typical galaxy JHK colors.
d) Non-Thermal Emission
For a pure non-thermal spectrum, we adopt
In a color-color diagram, the locus of different n values is then a straight line.
The different non-stellar effects discussed above are illustrated in Figures 24 and 25, where various colors are plotted against H - K, our primary indicator of a galaxian 2.2 µm excess. (The V - H rather than V - K color is plotted in Figure 25c to avoid false correlation with H - K.) Also shown are the multiaperture data from Tables 3 and 5 for galaxies with a 2.2 µm excess, for the anomalously colored galaxy NGC 5253, and for the two Sb galaxies with largest inclination angle, NGC 4565 and 5746. Morphologically, the 12 galaxies in the 2.2 µm excess sample include 6 spirals (NGC 253, 891, 3079, 3628, 4631, and 5907) with large inclination angle, 3 objects (NGC 2146, 3034, and 5128) of a distinctly peculiar morphological character, and three comparatively normal looking galaxies (NGC 1068, 1365, and 6946). The relatively normal colors of such galaxies as NGC 520, 2976, 4490, and 5195 suggest that morphological peculiarities alone do not lead to a large 2.2 µm excess.
Figure 24. The J - H color is plotted against H - K for the galaxies with a 2.2 µm excess, using the data from Table 3. Also shown is the anomalously colored galaxy NGC 5253. Using fiducial colors of J - H = 0.74 and H - K = 0.20, various non-stellar effects have been illustrated and are denoted as follows: A - reddening from a dust screen, labelled by optical depth at V, V. B - reddening from dust completely mixed with the stars, labelled by V. C - dust emission with emissivity 1 / 2 and temperature T = 600 K; labelled by the fractional contribution of the dust to the 2.2 µm light. The arrow points to the position the tick mark labelled 0.6 would have for dust with grey body emissivity. D - same as C, but for dust with T = 1000 K. E - the effect of increasing the contribution from free-free emission with Te = 20000 K to the 2.2 µm light. F - the effect of increasing the contribution from "H II region" emission with Te = 8000 K to the 2.2 µm light. G - a pure power law spectrum labelled by n, where I . See text for further details.
Figure 25. - a) and b) The CO and H2O indices are plotted against H - K color for galaxies with a 2.2 µm excess, using the data in Table 3. Using fiducial values of CO index = 0.16, H2O index = 0.12, and H - K = 0.20, the non-stellar effects illustrated are: A - reddening from a dust screen. C - dust emission, with T = 600 K. D - dust emission, with T = 1000 K. The tick marks and arrows have the same meaning as in Figure 24. c) The H - K color is plotted against V - H for the galaxies with a 2.2 µm excess using the data in Tables 3 and 4. Also shown is the anomalously colored galaxy NGC 5253, and two Sb galaxies of large inclination angle, NGC 4565 and 5746. Because the H - K and V - K colors for NGC 5746 are referred to different apertures, the point plotted for this galaxy is only a limit, in the sense suggested by the arrow. Using fiducial values of H - K = 0.2 and V - H = 3.1, the various non-stellar effects illustrated are: A - reddening from a dust screen. B - reddening from dust well-mixed with the stars. C - dust emission with T = 600 K. D - dust emission with T = 1000 K. F - H II region emission. The tick marks and arrows have the same meaning as in Figure 24.
It appears from Figures 24 and 25 that the Van de Hulst reddening curve does not adequately fit the color excesses. There are several ways to account for the discrepancies:
First, the Van de Hulst curve may simply not apply in external galaxies. However, no physically plausible reddening curve could reproduce the color residuals in at least two galaxies, NGC 1068 and 1365. Furthermore, color residuals in the two highly inclined spirals NGC 4565 and 5746, with V - H excesses comparable to those in most of the 2.2 µm excess objects, are well matched by the Van de Hulst curve. The bulge-to-disc ratio in these two galaxies are larger than in the other objects, and so in this respect are better fit by the simple dust screen model.
A second possibility is that the assumed fiducial colors are inappropriate. However, the intrinsic colors which would produce agreement, J - H 0.6 and V - H 1.0, are far too blue.
A third possibility is that as the wavelength is decreased, the flux is weighted more and more by unobscured stars, while as the wavelength is increased, the flux is weighted more and more by regions that are visually optically thick. Under these circumstances, the value of AV calculated for a given color residual will increase as the baseline shifts redward - which is precisely the effect observed. For instance, the color residuals E(V - H), E(J - H), and E(H - K) for the group of galaxies NGC 253, 5907, and 6946 lead to AV values of ~ 1, 2, and 3, respectively. Simple numerical models indicate that for small values of central source reddening (AV 3), E(V - H) / E(J - H) E(V - H) / E(H - K) 2, while much larger values of central source reddening (AV ~ 10) are required to produce E(H - K) / E(J - H) 1.5. It thus seems likely that this effect plays a role in Figure 25c, but not in Figure 24.
The final possibility we shall consider is that one of the emission mechanisms discussed above is occurring. Now the colors in Table 13 rule out any significant contribution from H II region emission. For instance, using the data for NGC 253 as an example, if the measured JHK colors are a combination o,f a normal stellar component (U - V ~ 1., V - K ~ 3.3) and an H II region contributing about 20% of the 2.2 µm flux, all reddened by AV = 2, the resulting U - V color should be ~ 0.5, as opposed to the observed value of 1.5. Similar problems occur in trying to fit the other color residuals. Furthermore, even in the bluest Markarians, galaxies which are optically the most dominated by gaseous emission, the contribution to the V flux by such emission is no more than 30% (Huchra 1977b), which amounts to only a 1% contribution at 2.2 µm.
The presence of a dust emission component can well. account for the displacement of the points in both Figures 24 and 25, and seems an especially appealing explanation for the color residuals in three galaxies - NGC 1068, 1365, and 5253. Published 3.5 µm, 5 µm, 10 µm, and 20 µm photometry is available for some of the galaxies measured in this paper (e.g. Rieke and Low 1972; Kleinmann and Wright 1974; Becklin et al. 1971; Becklin, Fomalont, and Neugebauer 1973; Glass 1973, 1976; Penston et al. 1974), including six of the galaxies in Figure 24 - NGC 253, 1068, 3034, 5128, 5253, and 6946. In fact the first five of these objects are among the brightest 10 µm extragalactic sources known, so there is clearly some correlation between H - K color excess and 10 µm emission. If the infrared radiation is in fact due to dust, the 2 - 10 µm spectra can generally not be fit by a single blackbody temperature, implying instead a dust shell with a range of temperatures, in analogy with galactic H II regions (cf. Becklin and Wynn-Williams 1974). Now the dust temperatures implied by the JHK excesses are in the range 600 - 1000 K, but because of uncertainties in AV, unambiguous color temperatures cannot be formed. The K - L (3.5 µm) color would be very useful in this respect, but the available data is mostly at much smaller aperture sizes and much lower statistical accuracy than are the observations in this paper. Nevertheless, in all cases published K - L colors for the galaxies in Figure 24 indicate the presence of non-stellar emission, at least at L. Extrapolated to the aperture sizes in this paper, available K - L colors do provide a lower limit of ~ 600 K to the temperature of any dust component that is emitting as much as 10% at 2.2 µm. There is no physical problem in forming such a warm dust component, since relevant condensation temperatures are > 1000 K (Gilman 1969).
If we assume a value of 1 for a / Q (the ratio of grain mass times grain radius to grain absorption efficiency), the required warm dust masses seem physically plausible. Taking NGC 1068 as an example, with AV = 0 the JHK color residuals can be fit with a dust component having T ~ 700 K and contributing 30% of the 2.2 µm flux in a 27" beam. At a distance modulus of 31.29 (Sandage and Tammann 1975), this leads to a mass of ~ 2 × 103 M, compared to a dust mass of ~ 5 × 104 M estimated by Rees et al. (1969) on the basis of the 2 - 20 µm spectrum, and a mass of 1 × 108 M for a 30 K dust component estimated on the basis of the submillimeter spectrum by Hildebrand et al. (1977). For NGC 5253, with AV = 0, the K - K color residual can be fit by a 10% contribution from 700 K dust to the 34" 2.2 µm measurement, which at a distance modulus of 29.49 (Sandage and Tammann 1975) leads to a dust mass of ~ 10 M. Warm dust mass estimates for the other galaxies are ambiguous because of previously mentioned uncertainties in AV, but appear to be mostly in the range 10 - 100 M.
Three Seyfert galaxies were measured in this study - NGC 1068, 1566, and 6814. The measured J - H colors for all three are normal, while the measured H - K color advances from normal in NGC 1566, to somewhat red in 6814, to very red in 1068. Our results are thus consistent with the work of Penston et al. (1974), who in a study of 11 Seyferts also found a range of H - K colors from normal to very red, with NGC 1068 having the largest excess of all.
Because the CO and H2O indices are so affected by reddening (Figures 25a, b), it is difficult to recover any useful information about possible differences in the stellar luminosity function between galaxies with a 2.2 µm excess and "normal" galaxies. However, the case of NGC 3034 seems noteworthy: relative to the other 2.2 µm excess objects with the reddest JHK colors, both the CO and H2O indices are very large, which suggests that above normal numbers of late-type giants and/or supergiants are present. O'Connell (1970), in an optical study of the stellar content in this galaxy, reached a similar conclusion.