NGC 1808

   
5 PAH and continuum emission: Relations to the ISM conditions and star-forming activity

The two most striking aspects seen in the spectra presented in Fig. 3 are their remarkable similarity in the ${\lambda = 5}$- $11~{\rm\mu m}$ regime dominated by PAH emission, and the spread in relative intensity of the longer wavelength emission attributed to VSGs. In this section, we focus on these two spectral components after discussing extinction effects at MIR wavelengths.

   
5.1 The effects of extinction at mid-infrared wavelengths

Interstellar extinction can significantly affect the MIR spectral energy distribution (SED) in obscured sources. In this regard, Rigopoulou et al. (1999) noted the gradual suppression of the PAH 8.6$~\mu$m feature in progressively obscured starbursts and ULIRGs. They further proposed that variations in the PAH 6.2$~\mu$m/7.7$~\mu$m ratio are dominated by extinction effects on the basis of the trend of decreasing ratio with increasing extinction observed in a subset of their sample for which reliable extinction determinations were available.

Another important consideration concerns the trough centered near 9.7$~\mu$m traditionally attributed to absorption by interstellar silicate dust grains. Recent studies have cast doubt on the reliability of extinction estimates based on the observed feature depth. Sturm et al. (2000) discussed this issue in detail based on SWS data of M 82 and NGC 253, from a comparison with the spectrum of the Galactic reflection nebula NGC 7023 and from considerations of the relative optical depths expected for silicate absorption near 9.7 and 18$~\mu$m. In particular, they showed that the M 82 SWS spectrum, including the dip at 9.7$~\mu$m, can be well reproduced by a combination of the NGC 7023 spectrum and a power law rising from 8.5$~\mu$m longwards without invoking large extinctions. More generally, the overall spectral invariance in the 5- $11~{\rm\mu m}$ region among a variety of Galactic and extragalactic sources which are known or expected to cover a large range in extinction seems to argue in favour of the 9.7$~\mu$m "absorption feature'' being predominantly due to the gap between the main PAH emission complexes (e.g. Helou et al. 2000).

These suggestions raise the important question of how such an interpretation can be reconciled with the large and variable extinction in M 82, NGC 253, and NGC 1808 determined by alternative methods based, for instance, on the relative intensities of H recombination lines. To address this issue, we explored quantitatively the effects of extinction at MIR wavelengths by applying a range of extinction to a representative template spectrum constructed in a similar way as Sturm et al. (2000). We added to a PDR component (from the ISOCAM data of NGC 7023) a power law $f_{\nu} \propto (\lambda - 8.5)^{\alpha}$ which represents well the VSG emission seen in our data. We adopted an index $\alpha = 1.5$and scaled the two components so as to obtain resulting spectra similar to that of M 82. For the purpose of illustrating the effects of different levels of extinction, the choice of these parameters is irrelevant.

We considered two representative geometries: a uniform foreground dust screen and a homogeneous mixture of dust and sources. For these models, the observed intensity $I({\lambda})$ of the emerging radiation is proportional to the total intrinsic intensity of the sources $I_{0}(\lambda)$ by the factors ${\rm e}^{-\tau_{\lambda}}$ and $(1 - {\rm e}^{-\tau_{\lambda}})/\tau_{\lambda}$, respectively, where $\tau_{\lambda}$ is the optical depth related to the extinction in magnitude via $A_{\lambda} = 1.086~\tau_{\lambda}$. We adopted the extinction law proposed by Draine (1989) and investigated the effects of deviations from this law in the 3- $10~{\rm\mu m}$ region as found towards the Galactic Center (Lutz 1999; hereafter simply "GC law''). Such deviations are consistent with the H recombination line spectrum observed with the SWS in M 82 (Förster Schreiber et al. 2001). We varied the level of extinction specified in visual magnitudes A_Vfor the mixed model in the range $A_{V}^{\rm MIX} = 0$- $700~{\rm mag}$. For a meaningful comparison, we varied A_V for uniform foreground obscuration in the range $A_{V}^{\rm UFS} = 0$- $50~{\rm mag}$, which results in the same attenuation at 10$~\mu$m as the range considered for the mixed model. We normalized each extincted model spectrum to the integrated flux between 6.0 and 6.6$~\mu$m, as for the spectra of Fig. 3.

Figure 10 presents our simulations. The plots outline the distinct behaviours for the two geometries considered with increasing A_V. They especially emphasize the fact that for the mixed model, differential extinction effects over the spectrum rapidly reach an asymptotic regime where large variations in A_V become less and less perceptible as A_V increases. In addition, except for the most extreme cases ( $A_{V} > 20~{\rm mag}$), the choice of dust and source geometry has little impact. This is because the absolute levels of extinction are fairly small and the wavelength dependence of extinction is relatively weak; the wavelength range covered is thus too limited to probe appreciably different optical depths which could allow the discrimination between different dust and sources distributions.

For the Draine extinction law, the effects are largest between 8 and 13$~\mu$m. Our models illustrate well how the PAH 8.6 and 11.3$~\mu$m features are substantially suppressed as extinction increases, indicating that their ratio with the PAH features at 6.2 and 7.7$~\mu$m can be much affected by obscuration. Moreover, for a continuum level defined over the limited 8- $13~{\rm\mu m}$ interval, relatively small optical depths would be inferred even if the extinction is in fact large. Assuming the GC law at 3- $10~{\rm\mu m}$ results in a remarkably different behaviour. The extinction effects are significantly smaller in the 8- $13~{\rm\mu m}$region and the suppression of the PAH 8.6 and 11.3$~\mu$m features is much less important. The largest effects are observed in the relative level between the short and long wavelength regions. This is a consequence of the much flatter GC law between 3 and 10$~\mu$m.

Our simulations indicate that dust obscuration adds a significant degree of degeneracy in the interpretation of the observed MIR emission, complicating the determination of intrinsic properties. Depending on the extinction law used, the shape of the PAH 8.6 and 11.3$~\mu$m features as well as their flux ratio with the PAH 6.2 and 7.7$~\mu$m features vary considerably. Therefore, extinction estimates based on diagnostics involving the PAH 8.6 or 11.3$~\mu$m feature may be strongly biased by the choice of extinction law. Furthermore, part of the spread in intensity observed in the long-wavelength continuum relative to the shorter wavelength emission could be attributed to varying extinction levels (see Fig. 3 and Sect. 5.2 below).

The interpretation of the 9.7$~\mu$m trough as largely due to the gap between the flanking PAH complexes appears to hold over a wide range of extinction, especially for the GC extinction law. The near-invariance of the 5- $11~{\rm\mu m}$ spectrum is therefore not inconsistent with large and/or variable obscuration among and within galaxies. We illustrate this with the case of M 82, for which a mixed model with $A_{V} = 52~{\rm mag}$ best reproduces the observed H recombination lines from radio to optical wavelengths while the best-fit uniform foreground screen extinction of $A_{V} = 5~{\rm mag}$ provides a much poorer fit (Förster Schreiber et al. 2001). We applied these two extinction models to the same template as for the simulations described above. The resulting spectra are plotted along with the observed spectrum of M 82 in the bottom panels of Fig. 10. We did not attempt to fine-tune the models by formal fitting. Given the uncertainties on the exact nature of the emitting particles, specific assumptions on model parameters are not well constrained and a simple empirical approach is sufficient for our purposes. The comparison shows that strictly from the point of view of the 5- $16~{\rm\mu m}$range, both extinction models reproduce equally well the observed SED of M 82, thus demonstrating that a high extinction cannot be excluded from the overall shape of the MIR spectrum alone.

We wish to emphasize that we do not dismiss the possibility of silicate absorption around 9.7$~\mu$m in general but merely want to point out the difficulties involved in the interpretation of the observed feature. The SEDs of moderately to highly obscured sources including ULIRGs often exhibit a strong dip near 9.7$~\mu$m together with suppressed PAH 8.6 and 11.3$~\mu$m features relative to those at 6.2 and 7.7$~\mu$m, consistent with the presence of silicate grains (e.g. Dudley & Wynn-Williams 1997; Dudley 1999; Laurent et al. 2000; Le Floc'h et al. 2002). Given the near invariance of the PAH spectrum in a wide range of environments, it should be possible to define an indicator measuring the differential extinction between the 9.7$~\mu$m region and adjacent less affected intervals that quantifies the absolute extinction. One must however be aware of the importance of sufficient wavelength coverage and resolution to assess properly the impact of the PAH complexes which can make the silicate absorption look artificially deep, of the dependence of the inferred A_Von the assumed extinction law and spectral intervals used to measure the feature depth, and of the limited sensitivity of this diagnostic leading to rather large uncertainties in the derived A_V. The upcoming launch of SIRTF in 2003 will provide 5- $40~{\rm\mu m}$spectroscopy with an increase in sensitivity by two orders of magnitude and will help us address this issue by enabling a better sampling of the continuum emission as well as both the 9.7 and 18$~\mu$m silicate bands.

Figure 10: Extinction effects at MIR wavelengths. The top panels show the extinction law from Draine (1989), and the modifications to this law at $\lambda \leq 10~{\rm \mu m}$appropriate for the Galactic Center line of sight (Lutz 1999). The middle panels show the variations of the SED of a template spectrum affected by various levels of extinction, for different dust and source geometries and extinction laws, as labeled in each plot. The template combines the spectrum of the Galactic PDR NGC 7023 and a power-law spectrum (shown individually in the bottom panels by the dashed and dotted lines, respectively). "UFS'' and "MIX'' stand for uniform foreground screen and mixed model. The grey shading outlines the range of variations for $A_{V}^{\rm UFS} = 0$- $50~{\rm mag}$ and $A_{V}^{\rm MIX} = 0$- $700~{\rm mag}$. The various curves show the results for selected extinction levels, corresponding to similar attenuation factors at $10~{\rm\mu m}$ between the two extinction models (labeled in each plot). The bottom panels show non-formal fits (grey solid line) to the spectrum of the starburst core of M 82 (black solid line), using the template PDR + power-law spectrum, attenuated by the best-fit extinction for each geometry assuming the GC extinction law and derived from radio to optical H recombination line measurements (see Sect. 5.1). All spectra are normalized to the total flux between 6.0 and $6.6~{\rm\mu m}$, except for the power-law.

   
5.2 The ${\lambda \geq 11~\mu m}$ continuum emission

The $\lambda \ga 11~{\rm\mu m}$ continuum emission in our data exhibits a large spread in intensity relative to the shorter wavelength emission. Similar variations have been seen in normal spirals and starburst galaxies observed with ISO instruments and, based on evidence provided by Galactic sources, are generally interpreted in terms of the relative contribution of H II regions to the MIR emission (e.g. Laurent et al. 2000; Roussel et al. 2001a; Dale et al. 2001). A close link between the 15$~\mu$m/7$~\mu$m colour as measured through the ISOCAM broad-band LW3 and LW2 filters ( $\lambda = 12$- $15~{\rm\mu m}$ and $\rm 5$- $8.5~{\rm\mu m}$, respectively) and the IRAS 25$~\mu$m/12$~\mu$m colour has been emphasized by Dale et al. (2001) and Roussel et al. (2001a).

In order to assess quantitatively the relationship between the long-wavelength continuum properties and the H II regions, we investigated the relationship between the 15$~\mu$m narrow-band continuum and the [Ar II] 6.99$~\mu$m line emission. The [Ar II] 6.99$~\mu$m is the most direct probe of H II regions and the least contaminated by PAH emission available from our ISOCAM data sets. The [][]Ar ionization potential of 15.8 eV is close to that of H (13.6 eV). Argon being a noble element, it is, like neon, not expected to be significantly depleted onto dust grains; while the argon gas-phase abundance may increase with time as a result of star formation activity and differ among galaxies, it is not likely to vary significantly over scales of $\sim$100- $1000~{\rm pc}$ as covered by the starburst regions in our sample. For the relatively low nebular excitation in all three sources (Fig. 4; see also Sturm et al. 2000; Förster Schreiber et al. 2001), argon is mostly singly-ionized so that the [Ar II] 6.99$~\mu$m emission should trace the H II regions in much the same way as H recombination lines and its luminosity, scale with the radiation field intensity of the young stars. In addition, since the gas-phase abundances of the galaxies are solar within a factor of a few (e.g. Webster & Smith 1983; Forbes et al. 1992; Förster Schreiber et al. 2001), the proportionality factor should be roughly similar.

Figure 11 presents the 15$~\mu$m continuum versus [Ar II] 6.99$~\mu$m luminosities for our galaxies, normalized to unit projected surface area ( $\Sigma_{\rm 15~\mu m}$ and $\Sigma_{\rm [Ar~II]}$). The data are shown for the selected regions as well as for the individual resolution elements enclosed within the radii defining the outer limit of the disk regions in M 82 and NGC 253. Resolution elements with measurements at <$3\sigma$ were excluded. The data points follow a well defined distribution, with a remarkable overlap for the different galaxies. Least-squares fitting to the resolution elements' data accounting for the individual formal uncertainties yields the relation

$$\log(\Sigma_{\rm 15~\mu m}) = 1.01~\log(\Sigma_{\rm [Ar~II]}) + 0.807,$$ (1)

with dispersion around the fit of 0.203 dex. The extinction paths in the diagram of Fig. 11 are nearly parallel to the locus formed by the data points; however, implausibly large differential extinctions would be required in order to account entirely for the observed distribution.

The essentially linear proportionality we find between $\Sigma_{\rm 15~\mu m}$ and $\Sigma_{\rm [Ar~II]}$indicates that the 15$~\mu$m emission provides a good quantitative indicator of the star-forming activity in starburst environments, to within uncertainties determined by the dispersion of the data and by extinction (a factor of 2.5 for an $A_{V} = 50~{\rm mag}$assuming purely foreground extinction). Roussel et al. (2001b) reached a similar conclusion for more quiescent spiral disks where the 12- $15~{\rm\mu m}$ emission scales linearly with the H$\alpha$line flux. Part of the scatter in Fig. 11 may result from variations in the physical conditions and exact composition of the gas and dust within and between the galaxies. More important factors, however, are variations in relative spatial distribution of the emission and possibly of the excitation state of the gas.

The observed relationship holds remarkably well in view of the differences in morphology of the 15$~\mu$m continuum and [Ar II] 6.99$~\mu$m line emission as seen in Figs. 5-7, and 9. The correlation extends however over two to three orders of magnitude, much larger than the dispersion of a factor of 1.6. Undoubtedly, the relative spatial variations between both tracers contribute significantly to the scatter. Within the starburst cores of M 82 and NGC 253, where the steeply rising SEDs at $\lambda \ga 11~{\rm\mu m}$ are dominated by VSG emission, the differences may be attributed to different ranges in exciting photon energies for VSGs and [Ar II] 6.99$~\mu$m line as well as to extinction effects (Sect. 4). For NGC 1808, the spatial distributions differ probably because a different dust/particles population produces the flat long-wavelength continuum (Sect. 4). Nevertheless, the data for NGC 1808 and for the disk regions of M 82 and NGC 253, characterized by flat $\ga$ $11~{\rm\mu m}$ SEDs, are well described by Eq. (1).

Variations of the excitation state of the photoionized nebulae may influence the $\Sigma_{\rm 15~\mu m}$ versus $\Sigma_{\rm [Ar~II]}$ relationship as well. In particular, the [Ar III] 8.99$~\mu$m line is fairly strong in the ISO-SWS spectrum of M 82 (Fig. 4) but the [Ar III] 8.99$~\mu$m/[Ar II] 6.99$~\mu$m ratio of 0.18 (0.26 after extinction correction) is low and abundance estimates indicate that $\sim$$25\%$ only of the argon is doubly ionized (Förster Schreiber et al. 2001). As emphasized in Sect. 4, the spatial distributions of various MIR fine-structure lines and Br$\alpha$ are similar and suggest a roughly constant excitation state of the H II regions across M 82 (Achtermann & Lacy 1995). This is further confirmed by the nearly uniform He I 2.06$~\mu$m/Br$\gamma$ ratio in the central $260 \times 160~{\rm pc}$ which corresponds closely to the excitation derived from the SWS [Ne III] 15.56$~\mu$m/[Ne II] 12.81$~\mu$m, [Ar III] 8.99$~\mu$m/[Ar II] 6.99$~\mu$m, and [S IV] 10.5$~\mu$m/[S III] 18.7$~\mu$m ratios within larger apertures up to $430 \times 225~{\rm pc}$(Förster Schreiber et al. 2001). Similar arguments are more difficult for NGC 253 and NGC 1808 because of the lack of relevant data. However, the [Ar III] 8.99$~\mu$m/[Ar II] 6.99$~\mu$m $\approx 0.03$measured from the SWS spectrum of NGC 253 is substantially lower than for M 82, as is the [Ne III] 15.56$~\mu$m/[Ne II] 12.81$~\mu$m ratio (0.06 compared to 0.18; Thornley et al. 2000; see also Giveon et al. 2002 for the relationship between these two MIR line ratios). For NGC 1808, we can only note from the ISOCAM spectra (Fig. 3) that the weakness of the 15.7$~\mu$m feature and the non-detection of [Ar III] 8.99$~\mu$m indicate low excitation supporting that argon mostly is singly ionized. Summarizing, the excitation state of the gas might cause for M 82 a general but small offset to the left in the relationship of Fig. 11 compared to the other galaxies because of the larger fraction of ${\rm Ar^{++}}$ while spatial variations are not likely to introduce scatter larger than this offset. These effects are expected to be smaller for both NGC 253 and NGC 1808.

The relationship between the 15$~\mu$m continuum and star formation intensity is supported by the analysis of a larger sample including spiral and starburst galaxies that will be presented in a forthcoming paper (Förster Schreiber, Roussel, & Sauvage, in preparation). In this paper, based on the previous work of Roussel et al. (2001b) for spiral disks, we find that the 15$~\mu$m continuum as well as the 7$~\mu$m PAH-dominated emission correlate well with the star formation rate over nearly 7 orders of magnitude, with the interesting distinction of two regimes that correspond to quiescent star formation in disks and more intense activity in circumnuclear regions and starbursts.

   
5.3 The ${\lambda = 5}$-${11}~\mu$m emission

The near invariance of the 5- $11~{\rm\mu m}$ spectrum seen in our data of M 82, NGC 253, and NGC 1808 has been noted in a number of other studies of different types of galaxies powered mainly by star formation, as well as in a variety of Galactic sources (see Tielens et al. 1999 for a review; see also e.g. Boulanger et al. 1998a; Helou et al. 2000; Uchida et al. 2000). This indicates that the PAHs are very stable under a wide range of physical conditions despite their small sizes (typically $\sim$100 atoms) and is taken as direct observational evidence for the stochastic nature of the emission processes involved. Furthermore, if different types of PAHs coexist, the near constancy in the 5- $11~{\rm\mu m}$ region suggests that their relative abundances vary little. Finally, it has consequences on the interpretation of and extinction measurements from the 9.7$~\mu$m silicate absorption feature because of the intrinsic gap between the main 6- $9~{\rm\mu m}$ and 11- $13~{\rm\mu m}$ PAH complexes (Sect. 5.1).

Variations of the relative intensities of the PAH features do exist, however. We focus on the PAH 6.2$~\mu$m/7.7$~\mu$m and PAH 8.6$~\mu$m/11.3$~\mu$m ratios, maps of which were presented for M 82 and NGC 253 in Sect. 3.2. Of particular interest is also the enhancement of the PAH 11.3$~\mu$m relative to the other features in NGC 1808 compared to M 82 and NGC 253, evident in Fig. 3. The variations of PAH ratios in our sample are comparable to those observed within and between Galactic sources of similar types (e.g. Cesarsky et al. 1996a; Boulanger et al. 1998a; Lu 1998; Crété et al. 1999; Uchida et al. 2000), along the disk of the spiral galaxy NGC 891 (Mattila et al. 1999), and among a sample of 15 starbursts and ULIRGs (Rigopoulou et al. 1999). A detailed discussion of PAH ratios is beyond the scope of this paper, but we briefly mention possible interpretations of the variations seen in our data in the light of some recent theoretical and empirical work.

Figure 11: Relationship between MIR tracers of H  II regions in M 82, NGC 253, and NGC 1808. The diagram shows the variations of the $15~{\rm\mu m}$ continuum luminosity as a function of the [Ar  II] $6.99~{\rm \mu m}$ line luminosity normalized per unit projected area. Data are plotted for selected regions (open symbols labeled "F'' for the ISOCAM field of view, "D'' for the disk regions, "C'' for the starburst core, and "P'' for the MIR peak). The filled circles and crosses show the values for individual resolution elements for M 82 and NGC 253, respectively, within radii of $30^{\prime \prime }$ and $15^{\prime \prime }$ (outer disk annulus; Table 2); measurements at <$3\sigma$ are excluded (4 points for M 82, 11 for NGC 253). Typical formal uncertainties are indicated by the error bar at the bottom left and are smaller than the symbol sizes; they are 5% for $\Sigma_{\rm 15~\mu m}$ and 10% for $\Sigma_{\rm [Ar~II]}$ (the median and average differ by <$1.5\%$). The straight line is a least-squares fit to the resolution elements' data accounting for the individual uncertainties. The effects of extinction are shown in the right part of the plot for a uniform foreground screen and a mixed model ("UFS'' and "MIX''), for the extinction law of Draine (1989, "D89'') and with modifications at 3- $10~{\rm\mu m}$ as found towards the Galactic Center (Lutz 1999, "GC''). Selected values of extinction in visual magnitudes AV are labeled.

Since the emission mechanism is stochastic in nature, PAH ratios are not directly related to the SED of the incident radiation (e.g. Boulanger et al. 1998a; Uchida et al. 2000). On the other hand, they may carry indirect information since PAHs exposed to hard and intense radiation fields can be ionized, lose H atoms, or be photodissociated (e.g. Léger et al. 1989; Allamandola et al. 1989; Schutte et al. 1993; Allamandola et al. 1999; Hudgins & Allamandola 1999). In particular, the PAH 8.6$~\mu$m/11.3$~\mu$m is believed to trace the fraction of singly ionized to neutral PAHs, presumably driven by the strength of the radiation field from the OB stars (see references above, and Joblin et al. 1996). Draine & Li (2001) presented a thorough calculation of the expected PAH spectrum as a function of various parameters including PAH size, charging conditions, and starlight intensity. Their results indicate that the PAH 6.2$~\mu$m/7.7$~\mu$m depends primarily on PAH size while the PAH 11.3$~\mu$m/7.7$~\mu$m is mainly sensitive to the fraction of ionized versus neutral PAHs and only modestly to PAH size. The effects of radiation field become noticeable only at high intensities ($\ga$10⁵ the average local Galactic far-UV flux in Habing units) and for large PAHs with $\ga$10² carbon atoms. Mattila et al. (1999) suggested that PAH 6.2$~\mu$m/7.7$~\mu$m variations may be due to differences in average temperature of the PAHs during their temperature spikes, related to PAH size or mean exciting UV photon energies. Alternatively, they could be attributed to broadening of the 7.7$~\mu$m feature at low radiation field energy densities (Uchida et al. 2000); this would reduce the PAH 7.7$~\mu$m flux and increase the continuum level within our fixed bandpasses. In addition to intrinsic variations, extinction can significantly alter the shape and relative intensities of the PAH features as shown in Sect. 5.1.

Of our sample galaxies, M 82 offers the most interesting case for interpretation. The overall bilobal structure in the maps of PAH ratios and CO gas distribution (Fig. 8) might result from the different composition and physical processes that the emitting PAHs undergo when exposed to the varying conditions across M 82, from the starburst core to the more quiescent disk via the transition regions marked by the molecular gas ring. The maxima in PAH 8.6$~\mu$m/11.3$~\mu$m ratio lie at smaller radii than the minima in PAH 6.2$~\mu$m/7.7$~\mu$m ratio, possibly indicating a higher degree of PAH ionization within the most intense starburst sites at the inner edge of the molecular ring; this is particularly striking southwest of the nucleus where the peak PAH 8.6$~\mu$m/11.3$~\mu$m coincides very well with the location of the most prominent H II region complexes (Sect. 3.2.1). The variations of PAH 6.2$~\mu$m/7.7$~\mu$m ratio could reflect differences in the PAH size distribution, combined with extinction effects, where larger PAHs can better form and survive in denser, more shielded environments associated with molecular gas concentrations. In NGC 253, the peak PAH 8.6$~\mu$m/11.3$~\mu$m ratio at the nucleus where the starburst is mainly occurring could also be due to a larger fraction of ionized PAHs. Finally, the enhanced PAH 11.3$~\mu$m feature in NGC 1808 compared to M 82 and NGC 253 could be explained by a more neutral mixture of PAHs and a more diffuse radiation field.

The relative intensity of PAH and continuum emission can also hold information on the physical environment within astronomical sources. In particular, the ratio of the peak intensity of the PAH 7.7$~\mu$m to the underlying continuum, hereafter PAH 7.7$~\mu$m L/C ratio, has been shown to constitute a powerful discriminator between star formation activity or an AGN as the main source of the bulk of infrared luminosity (Rigopoulou et al. 1999; see also Genzel et al. 1998; Laurent et al. 2000; Tran et al. 2001). Starburst-dominated objects are characterized by ratios $\ga$1 while AGN-dominated ones have ratios $\la$1. We compared measurements of the PAH 7.7$~\mu$m L/C ratio from our data of M 82, NGC 253, and NGC 1808 with those obtained by Rigopoulou et al. (1999) for a large sample including starbursts, AGNs, and ULIRGs. Our motivation was to assess how much this indicator depends on the source luminosity at the faint end and compare the spread in global ratios among different galaxies with the spatial variations within individual galaxies.

Figure 12 shows the PAH 7.7$~\mu$m L/C ratio versus peak PAH 7.7$~\mu$m luminosity for selected regions of our galaxies, for individual resolution elements of M 82 and NGC 253 (within the radii defining the outer limit of the disk regions in Table 2), and for the Rigopoulou et al. (1999) sample. We measured the PAH 7.7$~\mu$m peak intensity and underlying continuum according to the definitions of Rigopoulou et al. We note that with these definitions, the continuum might be underestimated in highly obscured sources as a result of extinction affecting notably the 11$~\mu$m region (as also discussed by Laurent et al. 2000). We chose the PAH 7.7$~\mu$m peak luminosity as other characteristic property, taken as an approximate indicator of the total infrared luminosity. Although the PAH to infrared luminosity ratio can vary by up to factors of several in different environments (Rigopoulou et al. 1999), our assumption has little consequences on the interpretation of Fig. 12 since the data span a range in luminosity extending over more than six orders of magnitude.

Our data of M 82, NGC 253, and NGC 1808 extend very well the trend defined by the global properties of pure starburst galaxies and ULIRGs, populating the PAH 7.7$~\mu$m L/C $\ga 1$ region down to luminosities about an order of magnitude lower. The ratios in all three galaxies lie well above the starburst-AGN separation at a ratio of unity and form a tighter distribution. The average and $1\sigma$ dispersion for the individual resolution elements in M 82 and NGC 253 are $5.0 \pm 0.9$ compared to $3.7~ \pm~ 2.5$ for the pure starbursts of Rigopoulou et al. and $2.8~ \pm~ 1.0$for their ULIRGs (excluding those with ratios $\leq$1 or with only limits on the measurements). It is also interesting to note that the starburst trend holds for regions on spatial scales ranging from $\approx$ $60~{\rm pc}$for the smallest individual regions in NGC 253 up to several kiloparsecs for the largest starbursts and ULIRGs (see the near-infrared images of Rigopoulou et al. 1999).

Figure 12: Diagnostic diagram for dominant starburst versus AGN activity. The data for selected regions in M 82, NGC 253, and NGC 1808 as well as individual resolution elements for M 82 and NGC 253 (large labeled and small unlabeled filled symbols, respectively; see inset) are compared to the global properties for the samples of starburst galaxies, AGNs, and ULIRGs of Rigopoulou et al. (1999; open circles, crosses, and stars). For M 82 and NGC 253, resolution elements within radii of $30^{\prime \prime }$ and $15^{\prime \prime }$ (outer disk annulus; Table 2) are plotted, and typical formal uncertainties are indicated by the error bar at the top left: <$1\%$ for $L_{\rm Peak~PAH~7.7\mu m}$ and 4% for PAH 7.7$~\mu$m L/C ratio (uncertainties are comparable to or smaller than the symbol sizes; average and median values differ by <$1\%$).

NGC 1808