Astron. Astrophys. 344, 779-786 (1999)

3. Results and analysis

The entire LWS spectrum from m, for both the on and off-source positions, is shown in Fig. 1. No significant emission is detected in the off-position, in agreement with the COBE non-detection of CII(158 µm) at such high galactic latitudes (Bennett et al. 1994). The spectral scan at the off-source position shows greater noise, due to the shorter integration time, than the on-source spectrum. However the off-source observation still achieved its objective, which was to demonstrate that the local ISM does not contaminate the FIR spectrum of NGC 4414.

Fig. 1. ISO LWS spectrum of NGC 4414 (top and middle ) and off position (bottom ) with all detectors averaged. Middle panel shows two-temperature dust emission (69 K and 24.5 K) scaled to 25 µm and 245GHz continuum observations as solid line over spectrum. We show the flux density of NGC 4414 both in Jy and in Watts/cm2/µm to aid the comparison with other data.

As a check of the flux calibration, we calculated the continuum flux through the IRAS 60 and 100 µm passbands. The LWS "60 µm" and "100 µm" fluxes are 31.5 Jy and 76 Jy respectively, and are within 10% of the IRAS Addscan flux densities, 31.5 Jy and 70 Jy (Young et al. 1989). We do not consider the difference in ISO LWS and IRAS calibration at 100 µm to be significant. There remain small differences, particularly at m, in the relative calibration of the individual LWS detectors. However these are minor calibration uncertainties and as such do not affect the conclusions of this paper. Odenwald et al. (1998) compared galaxy fluxes determined by IRAS and through COBE DIRBE observations and found, as we here for ISO LWS, that while the m flux was about equal to the IRAS flux, the 100 µm IRAS fluxes were lower (by up to 20-30% compared to DIRBE). The favorable comparison to these data and the excellent fit to grey-body thermal dust emission curves (next section) suggests that the fluxes presented here are calibrated to better than about 15%.

3.1. Dust continuum emission

While necessarily an oversimplification, even for a galactic disk, we model the FIR spectral energy distribution with thermal emission from a cool and warm dust component and a single emissivity law. The ISO LWS grating-scan provides full spectral coverage of the FIR regime, and consequently a much greater constraint on the temperature of the dust emission than the previous IRAS 25 µm, 60 µm and 100 µm flux densities.

We assume that the warm component produces the IRAS 25 µm emission and that the cool component generates the flux detected in Paper II. The resolved mm-continuum emission contributes in an 80" aperture (LWS beam FWHM) centered on the galaxy nucleus. The total IRAS addscan 25 µm flux density is . To model the dust emission, we take , where , which is a continuous function leaving a "standard" (i.e. ) emissivity at longer wavelengths and is very similar to the wavelength dependence derived by Draine & Lee (1984).

The dust temperatures of the two component model which yield the continuum emission shown in Fig. 1 (middle panel) are 69 and 24.5 K. The cool dust temperature is substantially warmer than the we assumed for the cool component in Paper II, although LWS only observes the warmer inner galactic disk of NGC 4414. A lower dust temperature of may well be appropriate for the outer disk (cf. Sect. 3.4).

Assuming a grain cross-section of per H-nucleus (e.g. Krügel & Chini 1994; Pollack et al. 1994), we calculate gas masses of and (including Helium) within the LWS beam. This cross-section is a factor 1.45 greater than that of Draine & Lee (1984). It should be noted that cooler material (), which does not contribute significantly to IRAS fluxes, is present at larger radii so this is not the total gas mass of NGC 4414 (cf. Sect. 3.4).

The gas mass we derived from our HI, ¹²CO, and ¹³CO observations (Paper II) was about within the LWS beam, using a mean value of about derived from comparison between ¹²CO(1-0) and the ¹²CO(2-1), ¹³CO(1-0), ¹³CO(2-1), and 1.2 mm continuum. If this mass were correct, then the average grain cross-section within the LWS beam would be less than that derived by Draine & Lee. It is more likely that in 1997 we overestimated the gas mass because (1) at the time no temperature information was available and we assumed and (2) we used the average of the ¹³CO column densities provided by the ¹³CO(1-0) and ¹³CO(2-1) measurements - the ¹³CO(2-1) is probably a better estimate. If we adopt the gas mass of for the central of NGC 4414, the average CO-H₂ conversion factor is about .

Errors in the dust and gas masses vary linearly with the grain cross-section, which is unlikely to be wrong by more than a factor averaged over large area () given the mixture of conditions present. The temperature uncertainties are strongly dominated by the emissivity law. We fit Hildebrand's (1983) discontinuous emissivity law and find a "cool" dust temperature of 30.5 K. A emissivity-law, where , and a cool dust temperature of 27.5 K fits as long as the frequency dependence of the dust emissivity steepens to for wavelengths m in order to fit the 1.2 mm data point.

For the same cross-section, these different temperatures, 30.5 K and 27.5 K, yield gas masses a factor 3 and 2, respectively, lower than the cold component (24.5 K) included in the model shown in Fig. 1. In all cases, the warm component is less than 1% of the mass.

A large data set consistently points to a ratio of order for the inner disk of this normal galaxy. The or Hildebrand emissivities would yield still lower values which are very difficult to reconcile with our ¹²CO and ¹³CO observations ( close to ). The complete LWS scan provides strong constraints on the dust temperature. The other crucial dust measurement, however, is our earlier 1.2 mm map which allows us to exclude a massive cool component, undetectable by the LWS, in the inner disk. If the total uncertainty in the 1.2 mm measurement is up to 30%, then, if the inner disk 1.2 mm flux density were raised by 30%, a cool component could then be present which would raise the gas mass to . We estimate the neutral gas mass of the inner disk of NGC 4414 to be in the range , yielding the above factor. These data suggest that the mass of the molecular ring in the Milky Way may be overestimated as well.

3.2. Spectral line emission

The OI(63 µm), NII(122 µm), and CII(158 µm) lines are obviously well detected in Fig. 1. The rest-frame wavelengths, line fluxes and luminosities are given in Table 2. The OIII(88 µm) line is visible in both detectors 4 and 5 and the flux given in Table 2 is the average with the uncertainty reflecting the difference. The OI(146 µm) line may be detected at a very low level which is given in Table 2 as well. In Figs. 2 and 3 we show the individual spectra of these lines after subtracting our two-component model to the dust continuum. No unexpected strong lines are present in the spectrum.

Fig. 2. ISO LWS spectrum of NGC 4414 with model of dust continuum subtracted.

Fig. 3. Individual lines in ISO LWS spectrum of NGC 4414 with model of dust continuum subtracted, which is why the base of the line is not always at zero. At some wavelengths two detectors overlap; the thickness of the black area indicates the difference between the two datasets. The last panel shows the region covering the undetected OIII(52) and NIII(57) lines.

Table 2. Lines detected in NGC 4414; wavelengths are laboratory rest wavelengths. Uncertainties are intended to include calibration and rms noise.

Where does the line emission come from? No consensus is reached for the Galaxy - PDRs (Tielens & Hollenbach 1985a - hereafter TH85a), the cold neutral medium (CNM; Bennett et al. (1994), the extended low-density warm ionized medium (ELDWIM; Heiles 1994), and perhaps even HII regions (Gry et al. 1992) have been cited as major sources for the CII line emission. It must be stressed that the three reliable line fluxes (CII, NII, and OI) and one other detection (OIII) are absolutely not sufficient to derive the physical conditions over the several kpc² of the ISO beam. The present observations nonetheless provide substantial and currently unique information about the global emission of a spiral disk which is not available for the Milky Way, where data for many individual galactic sources are available. In the following, the CNM refers to atomic and molecular clouds and their edges and by ELDWIM we mean the diffuse ionized gas of all sorts. All neutral clouds have surfaces and are surrounded by ionized gas so it appears inevitable that neutral clouds have some photodissociated gas. Furthermore, we now know that the clumpy nature of clouds creates pockets of photo-dissociated gas deep into molecular and atomic clouds (e.g. Boissé 1990) and this material belongs to the CNM. PDR, as used here, refers to a region exposed to a strong UV field generated locally in conjunction with an HII region (Fig. 1 in TH85a) such as in Orion (Tielens & Hollenbach 1985b).

The NII emission comes from ionized gas, unlike the CII (the ionization potential of carbon is lower than that of hydrogen so the carbon can be ionized while the H remains largely neutral - this is not the case for oxygen or nitrogen). The OI 63 and 145 µm lines are respectively from levels 228 and 326 K above the ground state and require high densities to be excited. The IR line cooling of HII regions is dominated by the OIII 52 and 88 µm lines except for the lowest effective stellar temperatures (Rubin 1985). CII is not a major coolant of such HII regions. The IR line cooling in standard PDRs and PDR/HII regions is dominated by OI (63 µm) followed by the CII and OI 145 µm lines (TH85a,b; Hermann et al. 1997) with , an order of magnitude lower than in galaxies (e.g. Stacey et al. 1991).

Let us start with OI. OI emission is from neutral gas but combines with C or O to form CO or O₂ when shielding is sufficient (Fig. 1 of TH85a). The OI 63 and 145 µm lines come from PDRs and the observed intensity ratio OI is in agreement with a wide range of parameters for the TH85a PDRs. In Orion and in the young Planetary Nebula NGC 7027 I(OI 63)/(CII 158) and OI 145 µm is somewhat weaker (factor ) than CII (TH85b; Hermann et al. 1997; Liu et al. 1996), close to the standard model in TH85a. We may reasonably attribute 3-10% of the CII emission in NGC 4414 to classical PDR/HII regions.

The OIII emission comes from classical HII regions but not from the ELDWIM. The OIII (88 µm) line is typically stronger than the NII emission from HII regions so while some of the NII flux comes from HII regions, most of the NII is from the ELDWIM. This is the case in the Galaxy (Bennett et al. 1994; Heiles 1994) where both the NII 122 µm and 205 µm lines were detected (Wright et al. 1991). The Galactic OIII emission has not been measured.

The density, or distribution of densities, of the diffuse ionized gas is unknown but is certainly below the critical density for the NII lines. This means that the emission per NII ion varies directly with the unknown volume density. From the Galactic CII/NII(205) intensity ratio, Heiles (1994) argues that the ELDWIM could be the major source of CII emission but stresses that large uncertainties, including uncertainties in collisional cross-sections (Heiles 1994; Osterbrock 1989), are present. In the low density limit, and assuming that all of the NII emission comes from the ELDWIM, the ELDWIM could account for all of the CII emission detected in NGC 4414, just as in the Galaxy. This shows that the ELDWIM may well be an important contributor but also that the low-density limit is probably not appropriate. The CII/NII ratio decreases as the density of the ELDWIM increases. Two factors, however, suggest that the CNM is an important, and probably the most important, source of CII emission. Firstly, the cooling rates estimated for the CNM (Wolfire et al. 1995; Boulanger et al. 1996) provide for 20 - 80% of the CII emission from NGC 4414. Secondly, CII emission clearly increases with star formation activity (e.g. Crawford et al. 1985), although imperfectly, whereas LWS spectra of galaxies show that NII emission is weak in starbursts. Were the CII and NII coming from the same gas (the ELDWIM), then actively star-forming galaxies with strong CII emission like NGC 4038/9, Circinus, NGC 5713, and Arp 299 would not have such weak (or undetected) NII 122 µm lines (see next section). Nonetheless, Heiles' point is well taken - the ELDWIM contribution to the CII flux could equal that of the CNM.

Considering only the flux in the IRAS 60 and 100 µm bands, the ratio is 0.0055 in NGC 4414, which places it in the normal range for spiral galaxies (Stacey et al. 1991; Malhotra et al. 1997). Integrating over the entire spectrum, , as in the Galaxy (Wright et al. 1991). Similarly, the CII/CO(1-0) luminosity ratio is about 1600 within the LWS beam, close to the average value for the non-starburst galaxies in Stacey et al. (1991).

3.3. Comparison of NGC 4414 with other galaxies

LWS spectra have been presented for the following galaxies - NGC 4038/8, Circinus, Arp 299, Arp 220, and NGC 5713 observed with ISO LWS and NGC 253 and NGC 3256 observed by Carral et al. (1994) with the KAO. A more heterogeneous set of observations of these lines is also available for the central area of M 82 (Lord et al. 1996b).

All of these galaxies are more actively forming stars than NGC 4414. In the strong starbursts NGC 4038/9 and Arp 299, the strong lines are OIII 52, 88 µm, OI 63 µm, and CII 158 µm and the NII line is not detected. In the milder starbursts NGC 5713 and Circinus, CII is the strongest line followed by OI 63 µm and OIII 88 µm but NII is weak. The KAO observations of NGC 253 and NGC 3256 seem to place both galaxies in an intermediate case - equally strong CII and OI 63 µm and detected OIII but no NII observations were made. The spectrum of Arp 220 is dominated by absorption lines, presumably due to the small warm optically thick nucleus (Downes et al. 1993). The line strengths in the center of M 82 fit into the strong starburst class above. The NII lines are detected in M 82 but the NII (122/205) line ratio ( as opposed to in the Galaxy) suggests that the emission is from HII regions rather than the ELDWIM.

The observations described above fit into the framework where the high UV field and abundant molecular gas in starburst galaxies creates more dense PDR and HII regions. There is no evidence for a decrease in NII luminosity in starbursts because the NII 122 µm luminosity of NGC 4414 (or the Galaxy), if placed at the distance of NGC 5713, NGC 4038/9, or Arp 299, would not be detected in those spectra. While the NII/CII intensity ratio appears to decrease with increasing levels of star formation, the current observational uncertainties are such that this is not a strong limit to the fraction of CII emission coming from the same (ELDWIM) gas as the NII (see preceding section).

It is worth noting that published line fluxes are not available for Arp 299 or Circinus, NII was not observed in NGC 253 and NGC 3256, and the calibration of some of the lines in NGC 5713 is subject to caution (Lord et al. 1996a). The NGC 4414 data presented here are a unique data set.

3.4. A template for the emission of a galactic disk

The goal of this work is to provide a high-quality template for the global emission of the ISM of a galactic disk. We present the 10 GHz-10 THz (3 cm to 30 µm) spectrum of NGC 4414 in Fig. 4 along with a likely decomposition into physical processes. All data are for the entire disk except the LWS spectral lines but the emission at LWS wavelengths in the outer disk is probably very low. The cm-wave part is a fit to points in Duric et al. (1988) and Niklas et al. (1995). The mm-wave data are from Papers I and II and the FIR from this paper. Spectral lines have been averaged over a line width of . The cool (24.5 K) and warm (69 K) dust spectra are from the LWS spectrum in Fig. 1. The CI, H₂O, and high-J CO lines (indicated by vertical dashed lines) and the submm continuum have not yet been observed.

Fig. 4. Global radio - far-infrared spectrum of NGC 4414 including breakdown into emission processes. The CI, H2O, and high-J CO lines (indicated by vertical dashed lines) have not yet been observed.

We dispose of the following data for the thermal dust continuum: IRAS wideband 100, 60, and 25 µm whole-galaxy fluxes; ISO LWS spectrum covering the central ; and a map at 1.2 mm with a resolution of . A coherent picture can be obtained from these data. (a) The IRAS and LWS flux densities agree, showing that ISO detected all of the cool/warm dust in NGC 4414 - i.e. the dust contributing to the IRAS measurements ( K) is within the ISO LWS beam. (b) The 1.2 mm flux within the LWS beam is accounted for naturally by our fits to the LWS spectrum (24.5 and 69 K curves in Fig. 4) so no dust cooler than 24 K is required to fit the 1.2 mm flux within the LWS beam. (c) Substantial 1.2 mm flux is detected outside the ISO LWS beam yet the agreement between the ISO and IRAS flux densities at 100 and 60 µm shows that this outer disk material does not contribute measurably to the IRAS fluxes - the source of the emission is cold dust ( K), represented by the 15 K dust curve in Fig. 4. The temperature of the cold dust is not well constrained - detected at 1.2 mm but not at 100 µ by IRAS - but 15 K is a very plausible temperature.

What does the cold dust curve signify? Even at the longest wavelengths of the LWS, the emission from this component is 10% that of the warmer dust and such fluxes are within calibration uncertainties. Yet the gas mass associated with this cold component is about the same as that of the warmer (24.5 K) dust and perhaps even slightly greater because the metallicity is probably lower in the outer disk so a lower dust emissivity would be appropriate. This massive component is not present in the LWS beam because the 24.5 K dust provides all the flux observed within the ISO LWS beam at 1.2mm.

Fig. 4 may provide the best image to date of what the spectrum of the molecular ring of our Galaxy would look like if observed from another galaxy.

© European Southern Observatory (ESO) 1999

Online publication: March 29, 1999
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