5 The nature of the 4 $\mu$m continuum

We first discuss the nature of the 4 $\mu$m continuum, as inferred from our observations. Because of the filter cutoff, $L^\prime$ misses the 3.3 $\mu$m aromatic emission feature (e.g., Moorwood & Salinari 1983; Moorwood 1986), and thus should be a measure of the AFE-free continuum. As mentioned in Sect. 2.2, the K-L color is a sensitive diagnostic of the fraction of hot dust contained in the observing aperture. The 4 $\mu$m continuum of most of the galaxies we observed is consistent with stellar photospheres together with moderate dust extinction. As expected, the best cases for pure stellar K-L colors are the ellipticals which have median K-L = 0.21. Within the 14 $^{\prime\prime}$ observing aperture, we find no evidence for circumstellar dust in the ellipticals, since their NIR colors are inconsistent with dust emission at any temperature.

In roughly a third of our sample, the K-L color ($\ga$1) signifies a flat or rising 4 $\mu$m continuum. Even a small fraction (5%) of hot (600 K) dust can cause this inflection, and is very likely the cause of the large variance in the 3-5 $\mu$m continua, as noted by Helou et al. (2000). Because of the characteristics of the $L^\prime$ filter, we conclude that the red K-L color must represent a continuum property, rather than short-wavelength AFEs. Such a continuum is typically accompanied by a lower F_6.75/F₁₅ ratio (see Fig. 2), due either to AFE suppression or to an F₁₅ excess (or both). Either way, we are observing a significant fraction of hot dust in the central regions of these galaxies, with physical conditions that favor red K-L, namely strong 0 and high pressure.

   
5.1 Physical conditions in star forming regions with hot dust

Malhotra et al. (2001) describe a physical picture in which the infrared line emission arises in a PDR which surrounds an expanding H  II region. They suggest that the ISO diagnostics are probing the typical distance from an OB star or cluster to the PDR gas, rather than the global rate of star formation. Our new 4 $\mu$m data are consistent with this picture. Red K-L tends to be associated with an intense UV radiation field 0. The trend shown in Fig. 5 suggests that rising 4 $\mu$m continua are observed when UV radiation field $G_0 \ga 10^{3.5}$. It is easy to show that such an intense 0 must be found within a few tens of pc from the ionizing star cluster. Assuming the FUV luminosity of a single star to be 10³⁹ erg s^-1 (!), and with a star cluster consisting of 100 OB stars, the typical distance for G₀= 10^3.5 is 10 pc. In the same conditions, at a distance of 100 pc we would need 10 000 massive stars, more than all but those in the most luminous Super Star Clusters (SSCs: e.g., Calzetti et al. 1997; Turner et al. 2000). With the lower FUV luminosity from lower-mass stars, the distance to maintain the intense 0 would be even smaller. Hence, it is likely that red K-L is probing a region within a few tens of pcs from star clusters containing a few hundred OB stars. Such sizes are more than a hundred times smaller than the projected size of our observing aperture at the median distance of the sample (see Sect. 2).

Hot dust as measured by high-resolution 10-12 $\mu$m images of infrared-luminous starbursts also tends to be compact, and compact nuclear starbursts generally dominate their starburst activity (Soifer et al. 2001). Typical MIR sizes in the Soifer et al. sample range from <125 pc to $\sim$1 kpc; however these may be partly overestimated since the spatial resolution for the nearest galaxy in their study (NGC 3690) is 210 pc arcsec^-1 which procured mostly upper limits (<125 pc) for the size of the emitting regions.

The hot dust that gives rise to red K-L must be heated by massive stars, and according to the PDR models, tends to be found in high-pressure environments and, from the above discussion, in close proximity of the H  II region. This intense environment suppresses AFE emission, probably because of the strong UV radiation field, as proposed by earlier work (e.g., Normand et al. 1995). In the framework of an expanding H  II region surrounded by a PDR, such conditions are likely to obtain in young H  II regions, still embedded within their natal molecular cloud, which have not yet had time to break through the cloud surface. At first glance then, K-L appears to be a measure of age: hot dust is found preferentially in young H  II regions.

Nevertheless, the attribution of the rising 4 $\mu$m continuum to youth has some problems. Some very young systems have "normal'' photospheric+extinction K-L colors: the two brightest star clusters in NGC 1569 contain Wolf-Rayet (W-R) stars and their age has been estimated at <5 Myr (Origlia et al. 2001). We measure for NGC 1569 K-L=0.7, consistent with stellar photospheres + extinction, not with hot dust. Haro 2 (not in this sample) also contains W-R stars (Vacca & Conti 1992), and as such must be younger than 5 Myr, but K-L=0.5 (Thuan 1983). Thus, young systems are not necessarily associated with red K-L and hot dust.

Figure 7: Top panel: Log of the far-infrared-to-blue flux ratio FIR/B vs. K-L. FIR/B was taken from Dale et al. (2000), with FIR calculated according to the canonical dependence on F60 and F100 (Lonsdale Persson & Helou 1987). Bottom panel: Log  $L_{\rm FIR}/{\rm area}$ versus K-L. $L_{\rm FIR}$ is the far-infrared luminosity and the area is the one of the ellipse with axes of the size reported in NED; $L_{\rm FIR}/{\rm area}$ is in erg s-1 kpc-2. Galaxies with corrected $H-K\leq 0.35$ are shown as open circles, and H-K > 0.35 as filled ones. The vertical dotted line separates the "active'' and "passive'' regimes ( $K-L\protect\ga 1$).

It also might be that K-L is a diluted version of the flux ratio FIR/B, since variations in FIR/B, or star-formation activity, might be translated into variations of the hot-dust versus stellar fraction in our observing aperture. We investigate this in the top panel of Fig. 7, where we have plotted Log(FIR/B) vs. K-L. There is no correlation between these two quantities, although the galaxy with the highest value of FIR/B is associated with the reddest K-L (IRAS 23365+3604). It is thus difficult to interpret K-L as an indicator of generic star formation, since the hot dust traced by K-L appears to be independent of the cooler grains traced by FIR.

   
5.2 "Active'' and "passive'' star formation

We therefore propose an alternative explanation, namely two "extreme'' distinct modes of star formation. Recent models have shown that dust heating and molecular hydrogen production are more efficient in dense ($\ga$500 cm^-3), compact ($\la$100 pc) environments (Hirashita et al. 2002). Moreover, in low-metallicity BCDs, the size of the brightest star-forming complex and its ionized gas density are very well correlated, with the densest regions being also the most compact (Hunt et al. 2002). In this same BCD sample, size and density are independent of age, since ages derived from recombination line equivalent widths are all $\la$5 Myr. The correlations in the KP sample studied here seem to suggest a similar "dichotomy'' since a strong UV radiation field, compact size, and pressure are associated with hot dust. The most compact dense regions in the BCD study by Hunt et al. (2002) were interpreted by them as indicative of "active'' star formation, characterized by an intense physical environment harboring several hundreds/thousands of massive stars, and capable of efficiently heating dust. At a comparable star-formation rate, the less dense, less compact H  II regions, termed "passive'' by Hunt et al. (2002), are not able to heat dust efficiently because of the more diluted radiation field (Hirashita et al. 2002). We would argue that a rising 4 $\mu$m continuum is yet another signature of "active'' star formation. A falling 4 $\mu$m continuum would be a sign of "passive'' star formation, since the physical conditions are not able to produce a measurable fraction ($\ga$5%) of hot dust; these more diffuse regions tend to have lower pressures, a less intense radiation field, and prominent AFEs in the MIR spectrum.

It might be argued that the two extremes are simply a measure of the star-formation rate (SFR). We have attempted to test this hypothesis by plotting the far-infrared luminosity per unit area $L_{\rm FIR}/{\rm area}$ against K-L, since $L_{\rm FIR}$ is frequently used to measure SFRs (e.g., Thronson & Telesco 1986). The bottom panel of Fig. 7 shows that the two quantities are not significantly correlated, nor is K-L correlated with $L_{\rm FIR}$, that is without normalizing by the area (not shown). We already said that, although aperture effects may be important because of the large IRAS apertures, the top panel of the same figure shows no correlation between K-L and the $L_{\rm FIR}$ normalized to the B band, nor with F₆₀/F₁₀₀ (Sect. 3.1), yet another star formation indicator of common use. It appears, therefore, that the difference between the two extremes is of qualitative rather than quantitative origin.

It should be emphasized that "active'' and "passive'' star formation as we are defining them are local concepts: in a single galaxy, different regions may be characterized by either mode. In our Galaxy AFEs are notably diminished in H  II regions (Cesarsky et al. 1998), and the MIR continuum tends to be stronger in denser structures (Abergel et al. 2002). M 82 is an another example, since where the infrared continuum peaks, there are few if any AFEs, but at the H  II region-molecular cloud interface, the AFEs dominate (Normand et al. 1995). On galactic scales, there is also evidence that AFEs are diminished as the intensity of star formation increases (Förster Schreiber et al. 2002). With our ground-based data, we are investigating the properties of the dominant mode of star formation in the observing aperture, weighted by the brightness of the components. At longer wavelengths, higher spatial resolution is necessary to separate the two modes because in large apertures (e.g., IRAS, ISO), the cooler "standard'' ISM virtually overwhelms any hot dust emission.

We further note that the bulk of star formation associated with starbursts is not necessarily of the "active'' type. AFEs are always detected in galaxy nuclei with H  II-region spectra (Roche et al. 1991); indeed these features dominate the integrated spectra of prototypical starbursts such as M 82 and NGC 253 (Sturm et al. 2000). They are also used to distinguish star formation from nuclear activity as the mechanism powering ultra-luminous infrared galaxies (ULIRGs, Genzel et al. 1998). This apparent "paradox'' can be understood through the association of AFEs with the cool dust phase of the PDR (Haas et al. 2002). The hot dust we measure with K-L is heated by the intense 0 close to the H  II region, and without high-resolution ($\la$100 pc) measurements, the copious emission from the diffuse cooler dust and AFEs in the PDRs dominates the observed flux.

We have found evidence for hot dust in roughly 1/3 of the KP galaxies observed. It is not clear, however, whether the properties of these "active'' star-forming galaxies are "extreme'' compared to other examples of nuclear starbursts. An upper limit to the bolometric surface brightness of these objects can be deduced from the estimates given in Sect. 5.1: if we have a nuclear star cluster containing 100-1000 massive stars concentrated in a region of 10-100 pc in diameter, the bolometric surface brightness would be roughly $\la$ $10^{11}{-}10^{12}~L_\odot$ kpc^-2. This coincides approximately with the maximum mean surface brightness in the sample of low- and high-redshift starbursts of (Meurer et al. 1997). However, our estimate refers to the nuclear star clusters, not to the mean surface brightness over the observing aperture as in Meurer et al. As star clusters go, those we have detected with K-L are not extraordinary, since they are several times less bright than the resolved UV clusters described by Meurer et al. (1995).

What we have called the "active'' mode is characterized by the formation of compact star-forming complexes within a high-pressure environment in an intense 0. High pressure is also implicated in the strong galactic winds common in starbursts (Heckman et al. 1990). Such conditions also favor the formation of dusty SSCs (Bekki & Couch 2001), which are frequently found in merging galaxies (e.g., the Antennae: Whitmore et al. 1995; NGC 1741: Johnson et al. 1999), ULIRGs (Scoville et al. 2000; Shioya et al. 2001), and nuclear starbursts (e.g., M 82: Gallagher & Smith 1999; NGC 253: Keto et al. 1999; NGC 4214: Leitherer et al. 1996). Although somewhat uncertain, the nuclear star clusters inferred from our data have properties similar to SSCs, which could be yet another signature of "active'' star formation.

5.3 Speculations for high-redshift studies

The physical environment of the "active'' mode, especially high pressure, results naturally from interactions or mergers (Bekki & Couch 2001). Interestingly, interactions and mergers also produce red K-L (Joseph et al. 1984). According to the Cold Dark Matter hierarchical clustering scenario of galaxy formation, the frequency and intensity of interactions are expected to increase with redshift, and semi-analytic recipes for galaxy formation based on "collisional starbursts'' are successful at reproducing SFRs, colors, morphology, and mass trends with redshift (Somerville et al. 2001). Presently, the bulk of star formation in galaxies, including starburst galaxies and ULIRGs, takes place in the "passive'' regime. But, due to the higher probability of strong tidal stresses and mergers, this situation may have been reversed in the past with the "active'' regime being the preferred way to form stars at high redshift.

In this context, it is puzzling that we maintain that ULIRGs host passive star formation, although most if not all of them are mergers. The most plausible explanation of this paradox involves spatial resolution and the relative dominance of the "passive'' ISM in ULIRGs (see Sect. 5.2). Given the large contribution from their cool ISM, the emission in ULIRGs integrated over large spatial scales appears passive. Even though "active'' star formation must be occurring, it can be revealed only on small spatial scales, or by its hot dust. A case in point is the ULIRG in our sample, IRAS 23365+3604. This galaxy hosts several young ($\leq$10 Myr) star clusters (Surace et al. 2000), but is classified optically as a LINER (Veilleux et al. 1995). The LINER classification is probably not caused by an AGN, but rather by shocks generated in galactic superwinds (Lutz et al. 1999). We classify this object as "active'' because of its extremely red K-L, but its ISO spectrum contains prominent AFEs (Tran et al. 2001). Young star clusters probably heat the dust responsible for the red K-L, while the ISO aperture encompasses the entire galactic disk (see Surace et al. 2000). Hence, IRAS 23365+3604 appears both active and passive: active because of its red K-L, and passive because of the overwhelming disk ISM.

Including the effects of active star formation in models of galaxy evolution (e.g., Granato et al. 2000) would not be straightforward. Nevertheless, when star formation occurs on spatial scales $\la$100 pc (see Sect. 5.1), the intense radiation field, high pressure, and diminished AFEs should be taken into account. Indeed, suppressed AFEs coupled with the hot dust revealed by our photometry substantially alter the infrared spectrum of star-forming galaxies. This may be especially important in hierarchical merger models because of the supposed link between "active'' star formation and interactions.