5 Analysis

Previous analyses, each devoted to a limited spectral domain, have attempted to interpret the SEDs of galaxies: Gavazzi et al. (2002a) for the continuum stellar radiation, Boselli et al. (1998, 2003 and in preparation) for the mid-IR emission, Popescu et al. (2002) for the FIR emission, and Niklas et al. (1997) for the radio emission. In this work, for the first time we analyze the SEDs as determined in the whole spectral range.

   

Table 9: Template dust extinction corrected SEDs.

$\lambda$ ($\mu$m)	Log $(F(\nu)/F(K))$
	S0a	Sa	Sab-Sb	Sbc-Sc	Scd-Sd	Im	BCD	$L_{\rm H}$<8.3	$8.3\leq L_{\rm H}<9$	$9\leq L_{\rm H}<9.8$	$9.8\leq L_{\rm H}<10.5$	$L_{\rm H}\geq 10.5$
0.20	-3.22(2)	-2.46(5)	-1.51(5)	-1.04(15)	-0.72(4)	-0.38(7)	-0.36(4)	- (1)	-0.37(11)	-0.87(9)	-1.22(12)	-1.62(10)
0.37	-1.25(5)	-0.96(10)	-0.92(7)	-0.59(16)	-0.47(6)	-0.26(15)	-0.32(9)	-0.12(3)	-0.28(21)	-0.58(17)	-0.88(15)	-1.06(16)
0.44	-0.78(6)	-0.42(11)	-0.45(7)	-0.26(22)	-0.16(6)	0.06(21)	-0.10(11)	0.11(4)	-0.03(27)	-0.21(21)	-0.40(19)	-0.53(18)
0.55	-0.48(6)	-0.21(11)	-0.25(7)	-0.13(22)	-0.07(6)	0.13(21)	-0.04(10)	0.23(3)	0.08(27)	-0.09(21)	-0.18(19)	-0.28(18)
1.25	0.06(5)	0.07(9)	0.05(6)	-0.02(7)	-(-)	0.19(6)	0.08(2)	0.22(2)	0.19(4)	0.09(3)	0.05(12)	0.06(16)
1.65	0.13(6)	0.13(10)	0.11(6)	0.13(14)	-(1)	0.15(7)	0.11(2)	0.21(2)	0.15(5)	0.14(7)	0.13(19)	0.12(16)
2.10	0.00(6)	0.00(11)	0.00(7)	0.00(22)	0.00(6)	0.00(35)	0.00(17)	0.00(20)	0.00(32)	0.00(22)	0.00(19)	0.00(18)
6.75	-0.95(5)	-0.96(9)	-0.46(7)	-0.14(21)	-0.37(5)	-0.19(14)	-0.57(11)	-0.15(4)	-0.35(18)	-0.34(18)	-0.16(18)	-0.61(17)
12	-(1)	-0.54(4)	-0.24(7)	0.26(13)	-(1)	-(1)	-(-)	- (-)	- (-)	- (1)	0.13(13)	-0.33(14)
15	-1.37(5)	-1.30(10)	-0.47(7)	-0.13(21)	-0.14(4)	0.06(9)	-0.48(7)	0.02(2)	-0.30(10)	-0.46(18)	-0.22(19)	-0.63(17)
25	-(1)	-(1)	-0.40(7)	0.46(13)	-(1)	-(1)	-(1)	- (-)	- (1)	0.72(3)	0.28(11)	-0.10(12)
60	-0.19(2)	0.19(7)	0.43(7)	1.14(17)	1.29(5)	1.44(6)	1.39(6)	- (-)	1.48(10)	1.18(14)	1.05(14)	0.43(15)
100	0.36(2)	1.01(6)	0.97(7)	1.63(17)	1.72(5)	1.78(7)	1.65(8)	2.00(3)	1.70(9)	1.67(14)	1.61(13)	0.97(15)
170	0.36(4)	1.15(5)	1.27(7)	1.78(11)	1.88(4)	1.89(10)	1.93(9)	2.05(4)	1.82(12)	1.83(15)	1.68(10)	1.15(11)
28000	-(1)	-(1)	-1.55(5)	-1.46(8)	-(-)	-(1)	-(-)	- (-)	- (-)	- (-)	-1.63(9)	-1.44(9)
63000	-2.46(2)	-2.09(2)	-1.57(5)	-1.08(11)	-(-)	-(1)	-(-)	- (-)	- (-)	- (1)	-1.21(9)	-1.40(12)
126000	-2.00(3)	-1.68(6)	-1.34(5)	-1.01(10)	-(1)	-(1)	-(1)	- (-)	- (-)	- (1)	-1.10(13)	-1.47(14)
210000	-(1)	-(1)	-1.31(5)	-0.81(10)	-0.72(2)	0.33(4)	-(1)	- (-)	0.51(3)	-0.72(3)	-0.95(11)	-1.06(10)

Note: the values in parenthesis give the total number of objects in each Hubble type and wavelength bin that were combined to form the templates.

5.1 The template SED

The template SEDs in bins of morphological type and luminosity are obtained as median combinations of the normalized (to the K band) SEDs. We used only the detected values and imposed that at least 2 photometric points were available. The resulting extinction corrected template SEDs in different classes of morphological type and luminosity are shown in Figs. 3a and c respectively. The observed (dust attenuated) SEDs of M 82 and Arp220 (from Elbaz et al. 2002), are given for comparison in Figs. 3b and 3d. The median values of $F(\lambda)/F(K)$ for the templates in the 18 bands considered in this work are given in Table 9, while the fitting models in the visible (corrected and uncorrected for dust extinction) and in the FIR are given in Tables 10, 11 and 12 respectively. The values in parenthesis in Table 9 give the total number of objects in each Hubble type and wavelength bin that were combined to form the templates.

Figure 3: The extinction corrected a) and dust attenuated b) template SEDs in bins of morphological type and luminosity ( c),  d)). The dust attenuated SEDs of M 82 (continuum black line) and Arp 220 (dotted black line) are also given for comparison.

By analyzing Fig. 3 we can observe that: a) the relative contribution to the SED of the young stellar component, emitting in the UV, and of the relatively cold dust emitting at $\sim$60-200 $\mu$m increases from early to late-type spirals and/or from high-mass to low-mass objects; b) the 60 to 100 $\mu$m flux density ratio increases with the total FIR emission, indicating a general increase of the big grains dust temperature from massive Sa to low-luminosity Scd-Im-BCD and, to a much higher degree, in starburst galaxies. c) optically selected spirals have UV to near-IR SEDs similar to those of sturburst galaxies such as M 82 or Arp 220, despite the fact that these extreme objects have dust attenuations several order of magnitudes higher than normal galaxies, $A({\rm UV})\sim 1$ for optically selected spirals vs. $A({\rm UV})\sim 3.5$ for M 82 (Buat et al. 2002) and $A({\rm UV})\geq 100$ for Arp 220 (Haas et al. 2001). At the same time the far-IR emission of optically-selected, normal galaxies is more than a factor of 10-100 less important than in sturbust galaxies.

It is thus extremely dangerous to use the SEDs of starburst galaxies such as M 82 and Arp 220 as templates of normal late-type galaxies at high redshift, as often done, since these objects may not be representative of the mean late-type galaxy population even at earlier epochs, when star formation was expected to be more active.

5.2 The stellar contribution to the mid-IR emission

The Bruzual & Charlot models fitted to the data trace the stellar emission from 1000 Å  to 10 $\mu$m, and can thus be used to estimate the stellar contribution to the emission of our target galaxies at 6.75 $\mu$m. The ratio of the total flux (dust plus star) to the stellar flux at 6.75 $\mu$m, [F_6.75(d+s)/F_6.75(s)], determined for all galaxies detected at 6.75 $\mu$m, and with available visible or near-IR photometry, is given in Table 8, while the median value for each morphological class in Table 13.

Figure 4 shows the relationship between [F_6.75(d+s)/F_6.75(s)] and the morphological type. The stellar contribution to the total mid-IR emission of galaxies strongly depends on the morphological type. In early-types ($\leq$S0a), the emission at 6.75 $\mu$m is completely dominated by the photosphere of the cold stellar population (see Table 13). The average stellar contribution to the 6.75 $\mu$m emission of spiral galaxies is always important, ranging from $\sim$80% in Sa to $\sim$20% to Sc and Im. In BCD the stellar emission contributes on average at $\sim$50%. Given the low detection rate in irregular galaxies (Im and BCD), their average [F_6.75(d+s)/F_6.75(s)] ratios might be biased towards objects whose stellar contribution to the mid-IR emission is important, the only ones with detectable 6.75 $\mu$m flux. The decrease of the dust emission observed in BCD and Im galaxies, however, could be due either to their low metallicity, or to the destruction of the carriers of the UIB expected in high UV radiation fields (Boselli et al. 1998). We do not see any strong relationship between the [F_6.75(d+s)/F_6.75(s)]ratio and the total K band luminosity or concentration index parameter. However all galaxies with $C_{31}\rm (K)> 4$ have their mid-IR emission at 6.75 $\mu$m dominated by stars. Among the ISOCAM resolved galaxies, these objects have also a C₃₁(6.75 $\mu$m) index >4 (Boselli et al. 2003), suggesting that the spatial distribution of the stellar component dominating the mid-IR emission is similar to that emitting in the near-IR.

In the assumption that the stars dominating the emission at $\sim$7 $\mu$m have a spatial distribution similar to those emitting in the near-IR, we can re-scale our K band images (Boselli et al. 1997) using Table 8 and subtract them from the ISOCAM LW2 images of Boselli et al. (2003) to obtain images of the pure dust emission at 6.75 $\mu$m. We apply this correction, as an exercize to the Sab galaxy VCC 1727 (Fig. 5). The ISOCAM LW2 image at 6.75 $\mu$m shows a very pronunced nucleus, a clumpy, ring-like structure and a smoothed, diffuse external region. The emitting dust, on the contrary, is mostly located along the ring-like structure. Most of the nuclear and part of the diffuse emission in the 6.75 $\mu$m image is stellar.

The determination of the stellar contribution to the 12 and 15 $\mu$m emission of galaxies cannot be easely quantified since the Bruzual & Charlot models are limited to the spectral domain $\lambda$ $\leq$ 10 $\mu$m. The extrapolation of our fit (Fig. 2) indicates that the stellar contribution can be important at 15 $\mu$m, even though less than at 6.75 $\mu$m.

This result has to be taken in serious consideration when mid-IR deep surveys are used to estimate the star formation activity of galaxies at high z, where rest-frame mid-IR fluxes might be dominated by the stellar emission.

 

 

Table 13: The average stellar contribution to the 6.75 $\mu$m emission for different morphological classes.

Type	$\log[F_{6.75}(d+s)/F_{6.75}(s)]$
S0a	$-0.17 \pm 0.13$
Sa-Sab	$0.08 \pm 0.33$
Sb-Sbc	$0.39 \pm 0.18$
Sc	$0.76 \pm 0.29$
Scd-Sd	$0.50 \pm 0.30$
Sm-Im	$0.60 \pm 0.37$
BCD	$0.27 \pm 0.31$

5.3 The dust emission

As extensively discussed in Sect. 3.1, in a given galaxy the energy emitted by the various stellar populations and absorbed by dust must equal the total energy radiated in the mid- and far-IR domain. However $A({\rm UV})$ was estimated in Sect. 3.1 just from FIR, which is a combination of the 60 and 100 $\mu$m fluxes, not from the integral of the dust emission as determined on the SEDs. It remains to be checked whether the global extinction A( $\rm 1000~ \AA <\lambda< 10~\mu$m), which depends on the adopted geometrical model and on the choice of the galactic extinction law, is consistent with the observed mid- and far-IR emission.

The energy of the stellar light absorbed by dust is equal to the difference between the integrals of the stellar SEDs (i.e. the Bruzual & Charlot models) prior and after the extinction correction. This should equal the energy radiated in the FIR:

$$\int\limits_{20\rm ~\mu m}^{2000\rm ~\mu m} F(\lambda){\rm d}... ...000\rm ~\AA}^{10\rm ~\mu m} F_{\rm obs}(\lambda){\rm d}\lambda$$ (8)

where the integral on the left is performed under the two modified black-body functions fitted to the data between 20 and 2000 $\mu$m (far-IR). The integrals on the right are performed under the Bruzual & Charlot models prior and after the extinction correction. We disregard the dust emission in the range 5-20 $\mu$m due to the lack of model fitting in the mid-IR domain, whose energy contribution to the total should however be small.

To illustrate our method we give in Fig. 6 the SED of the galaxy VCC 1554. The energy of the stellar light absorbed by dust is marked by the shaded region shortward of 10 $\mu$m, the energy re-emitted in the FIR by the shaded region between 20 and 2000 $\mu$m.

Figure 4: The relationship between the total flux (dust plus stars) to the stellar flux at 6.75 $\mu$m, [F6.75(d+s)/F6.75(s)], and the morphological type.

Figure 5: The gray-level images of the Sab galaxy VCC 1727 at 6.75 $\mu$m: a) the observed images (dust+star), b) the stellar image (scaled from the K band image), c) the image of the dust emission, corrected for stellar contribution (dust). The three images are displayed with the same cuts and on the same scale (6.45 $\times$ 6.45 arcmin).

Figure 6: The SED of the galaxy VCC 1554. The energy of the stellar light absorbed by dust is indicated by the shaded region in between the Bruzual & Charlot extinction corrected model (light green continuum line) and the observed one (emeralde green continuum line) in the wavelength range 0.1-10 $\mu$m. The energy re-emitted by dust in the FIR is shown by the violet shaded region in the wavelength range 20-2000 $\mu$m. The photometric data are shown by blue dots, the optical spectrum is given in red.

Figure 7: The relationship between the total energy emitted in the far-IR and that emitted by stars and absorbed by dust in the range between 1000 Å and 10 $\mu$m (see Eq. (8)). The continuum line is the one to one relation, while the dashed line is the bysector fit. Filled symbols are galaxies whose extinction has been determined directly using the observed FIR/UV ratio, empty symbols are objects without far-IR and/or UV data, whose extinction has been determined using the average A(UV) for their morphological type class.

Figure 7 shows the relationship between the total energy emitted in the far-IR and that emitted by stars and absorbed by dust in the range between 1000 Å and 10 $\mu$m (Eq. (8)). The median value of the ratio between the energy absorbed by dust and that emitted in the far-IR is 1.27 for the entire sample, 1.03 for those objects whose extinction has been determined directly using the observed FIR/UV ratio, as illustrated in Fig. 8.

The almost linear relation between the absorbed star light and the energy emitted by dust, combined with their ratio close to one, leads us to conclude that the prescription given in Sect. 3.1 to correct stellar SEDs is sufficiently accurate for optically-selected spiral galaxies, even for objects without UV and far-IR data.

The ratio between the energy absorbed by dust and that emitted in the far-IR shows however a weak residual trend with morphological type (Fig. 9) and luminosity (Fig. 10): it is significantely larger than unity in early-type, massive galaxies.

Figure 8: The distribution of the ratio between the energy absorbed by dust and that emitted in the far-IR for the entire sample a), for galaxies whose extinction has been determined using the observed FIR/UV ratio b), and for those objects without far-IR and/or UV data whose extinction has been determined using the average value of A(UV) for their morphological class c).

This increase could be due to an underestimate of the far-IR emission of massive, early-type galaxies, that could exist if we missed a colder dust component in quiescent objects with low UV interstellar radiation field.

We remind that the extinction values derived using this prescription are significantly smaller than those obtained using the Calzetti's law, which is probably more accurate for starburst galaxies (see Gavazzi et al. 2002a and Buat et al. 2002 for a detailed discussion on this issue).

5.4 The radio emission

For 25 galaxies detected at more than one frequency in the centimetric domain, we derive the slope of the radio continuum spectrum by a simple linear fit to the data. Excluding galaxies VCC 857, 1110 and 1450 showing large inconsistencies in the radio continuum flux densities and 8 additional objects with signs of nuclear activity (LINER, Seyfert, see Table 2) we obtain an average spectral slope $\alpha=0.76 \pm 0.27$, consistent with the canonical synchrotron slope $\alpha=0.8$ found by Niklas et al. (1997) by carefully separating the contribution of the thermal from the synchrotron emission (see Table 8).

5.5 The bolometric luminosity of optically-selected, late-type galaxies

By integrating the fit models in the stellar and FIR domain, we calculate the (observed) bolometric luminosity of our target galaxies:

$$L_{\rm Bol} = \int\limits_{1000~\rm\AA}^{10~\rm\mu m} F_{\rm ... ...imits_{20~\rm\mu m}^{2000~\rm\mu m} F(\lambda){\rm d}\lambda .$$ (9)

As before, we disregard the contribution of UIB and of the very small grains in the 5-50 $\mu$m range, thus this esitimate gives a lower limits to the total bolometric luminosity.

Figure 9: The ratio between the energy absorbed by dust and that emitted in the far-IR as a function of the morphological type. Symbols as in Fig. 7.

Figure 10: The ratio between the energy absorbed by dust and that emitted in the far-IR as a function of the H band luminosity. Symbols as in Fig. 7.

Figure 11: The relationship of the ratio of the total uncorrected stellar luminosity (from the Bruzual & Charlot model) to the total FIR luminosity versus the bolometric luminosity of the target galaxies. Symbols are as in Fig. 7.

Figure 11 shows that the bolometric luminosity of optically-selected late-type galaxies in the range 10⁸ $\leq$ $L_{\rm bol}$ $\leq$ 10 $^{11}~ L_\odot$, is dominated by the stellar emission. The median value of the ratio between the energy emitted by stars in the 1000 Å- 10 $\mu$m range and by dust in the Far-IR is 4.0, significantly higher than $f_B/f_{\rm FIR} \sim 1.6$ found by Soifer et al. (1987) who determined the stellar emission from the B band luminosity alone. No relation is observed between the stellar to FIR ratio and the bolometric luminosity, except for an higher dispersion at high luminosity.

Figure 12 shows that the far-IR to bolometric luminosity ratio increases from early Sa spirals ( $L_{\rm FIR}/L_{\rm bol} \leq 0.1$) to Sc-Sd galaxies ( $L_{\rm FIR}/L_{\rm bol} \sim 0.2{-}0.4$), consistently with Popescu & Tuffs (2002). BCDs have $L_{\rm FIR}/L_{\rm bol} \sim 0.2$. The apparent discrepancy with Popescu & Tuffs (2002) who occasionaly observed $L_{\rm FIR}/L_{\rm bol} > 0.5$in BCDs is probably due to a systematic difference in determining the stellar contribution to the bolometric luminosity in the two works. We trust our values being based on a robust estimate of the stellar contribution to the bolometric luminosity consequent to a complete and homogeneous spectro-photometric dataset extending from the UV to the near-IR that we have fitted with Bruzual & Charlot population synthesis models.

Figure 12: The relationship between the far-IR to bolometric luminosity ratio and the morphological type. Symbols are as in Fig. 7.