AVERAGE INFRARED GALAXY SPECTRA FROM SPITZER FLUX-LIMITED SAMPLES

In the point source catalog of the FLS (Fadda et al. 2006), there are 38 sources with f_ν(24 μm) > 10 mJy. Of these, 13 are bright galactic stars. The remaining 25 sources have been observed with the IRS: 19 are in our program 40038, four in archival program 20128 (P.I.: G. Lagache), one in archival program 20083 (P.I.: M. Lacy), and one in archival program 40539 (P.I.: G. Helou). Characteristics and observational details of these 25 sources are given in Table 1.

Spitzer spectroscopic observations were made with the IRS¹ Short Low module in orders 1 and 2 (SL1 and SL2) and with the Long Low module in orders 1 and 2 (LL1 and LL2), described in Houck et al. (2004). These give low-resolution spectral coverage from ∼5 μm to ∼35 μm.

For our new observations, sources were placed on the slit by using the IRS peakup mode with the blue camera (13.5 μm< λ< 18.7 μm). All images when the source was in one of the two nod positions on each slit were coadded to obtain the image of the source spectrum. The background which was subtracted was determined from coadded background images that added both nod positions having the source in the other slit (i.e., both nods on the LL1 slit when the source is in the LL2 slit produce LL1 images of background only). The difference between coadded source images minus coadded background images was used for the spectral extraction, giving two independent extractions of the spectrum for each order. These independent spectra were compared to reject any highly outlying pixels in either spectrum, and a final mean spectrum was produced.

The extraction of one-dimensional spectra from the two-dimensional images was done with the SMART analysis package (Higdon et al. 2004), beginning with the Basic Calibrated Data products, version 15, of the Spitzer flux calibration pipeline. Final spectra were boxcar-smoothed to the approximate resolution of the different IRS modules (0.2 μm for SL1 and SL2, 0.3 μm for LL2, and 0.4 μm for LL1).

Spectra for all FLS sources in Table 1 are illustrated among the spectra in Figures 1–4. Spectra for FLS starbursts are in Figure 1 and are truncated at 20 μm in the rest frame because of the absence of any significant features in the low-resolution spectra beyond that wavelength; most Bootes starburst spectra were illustrated in Houck et al. (2007). Spectra for Bootes and FLS AGN in Table 3 are illustrated in Figures 2–4.

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Measured spectral parameters for all starbursts with IRS spectra from FLS and Bootes are summarized in Tables 2 and 3, and spectral parameters for all AGNs are in Tables 4 and 5. For purposes of classifying sources as starburst or AGNs for inclusion in the tables and figures, sources with strong polycyclic aromatic hydrocarbon (PAH) features are defined as starbursts, and sources with silicate absorption or emission features are defined as AGNs. While such classifications could be further quantified, and while there are certainly composite sources, the systematic differences between spectra defined by this simple classification are obvious when comparing the starbursts in Figure 1 with the AGNs in Figures 2–4.

All of the sources from the Bootes and FLS samples which are characterized primarily by PAH emission are listed in Tables 2 and 3. These tables give measured fluxes and equivalent widths (EW) for PAH emission features and for the [Ne iii] 15.56 μm emission line; continuum flux densities at 5.5 μm and 15 μm are also given. Equivalent widths and fluxes are given for the 6.2 μm and 11.3 μm features; these are measured within SMART as single Gaussians on top of a linear continuum, using the continuum baseline between 5.5 μm and 6.9 μm for the 6.2 μm feature, between 10.4 μm and 12.2 μm for the 11.3 μm feature, and between 14.9 μm and 16.2 μm for the 15.6 μm feature. As discussed by Houck et al. (2007) and by Weedman and Houck (2008), the stronger 7.7 μm feature is measured only by the flux density at the peak of the feature, which is a combination of feature strength and continuum strength, because of the large uncertainty in separating the underlying continuum from the PAH feature. Most values for the Bootes sources in Tables 2 and 3 are reproduced from Houck et al. (2007). Results for all FLS sources and for archival Bootes sources in program 20113 (P.I.: H. Dole) derive from our new spectral extractions.

The continuum strength which we choose for comparing source luminosities is measured by the flux density at rest frame 15 μm. This wavelength is chosen because it falls between PAH features in starbursts, and between silicate absorption or emission features in AGNs. As a result, it accurately represents the continuum of the underlying dust emission. Continuum fluxes, redshifts, and resulting continuum luminosities νL_ν (15 μm) for all PAH sources are given in Table 3. This table also includes a continuum measure at 5.5 μm, although for PAH sources some of this "continuum" may arise from broad wings of PAH emission.

IRS redshifts in Table 3 are determined from PAH emission features, assuming rest wavelengths of 6.2 μm, 7.7 μm, 8.6 μm, and 11.3 μm. For the 29 sources also having optical redshifts from spectra in the Sloan Digital Sky Survey (SDSS; Gunn et al. 1998), the average difference in z between IRS and optical redshifts is 0.0013. The SDSS optical classifications all agree with the IRS starburst classification for the sources in Table 3, except for 3 sources noted which are optically classified as Seyfert 2 and one as a narrow-line AGN.

Spectra of PAH sources displayed in Figures 1 and in Figures 7–11 are normalized by the peak flux density at 7.7 μm. This is chosen because f_ν(7.7 μm) is a well-defined parameter for comparing with PAH sources at high redshift, where f_ν(7.7 μm) is the brightest observed portion of the rest-frame spectrum and strongly influences the MIPS flux densities observed for faint sources (Weedman and Houck 2008). To provide a measure of spectral slope and of dispersion among spectral shapes, the ratios of continuum flux density at rest frame 24 μm and 15 μm to the peak flux density f_ν(7.7 μm) are also given in Table 3.

Figures 2 and 3 show the 16 sources from Bootes and FLS with silicate emission, and Figure 4 shows the eight sources with silicate absorption. Spectral parameters for these silicate sources, which we classify as AGNs, are listed in Tables 4 and 5. The AGN classifications from the IRS spectra are consistent with the optical SDSS classifications (noted in Table 5) when optical spectra are available (16 of the 24 sources). IRS redshifts for the silicate sources in Table 5 are not as accurate as for the PAH sources in Table 3, because fewer narrow spectral features are available for measure. Only eight silicate sources have confident redshifts from both IRS and SDSS, and the average difference in z for these is 0.0088.

Because of the weakness of PAH features in these sources, we list in Table 4 measures (usually upper limits) only for the 6.2 μm feature, and also give measures or limits for the [Ne iii] 15.56 μm emission line. Table 4 also includes optical depth τ_si as a measure of depth for the 9.7 μm silicate absorption feature. This is defined as τ_si = ln[f_ν(cont)/f_ν(abs)], for f_ν(abs) measured at the wavelength of maximum depth for absorption and f_ν(cont) being an unabsorbed continuum at the same wavelength, extrapolated from either side of the absorption feature as in Spoon et al. (2007). Strength of silicate emission features is not measured because of uncertainty in defining the underlying continuum.

The continuum flux density and luminosity at 15 μm rest-frame wavelength are given for the AGN sources in Table 5, as well as continuum flux density at 5.5 μm. For the AGN sources, which do not have strong 7.7 μm PAH emission, spectra are normalized using the continuum at 8 μm rest frame. This wavelength is chosen because it defines a localized spectral peak of the continuum for sources with strong silicate absorption; this peak arises because of absorption features redward and blueward of the peak. The values of f_ν(8 μm) are given in Table 5, along with the ratios of continuum flux densities at 15 μm and 24 μm to the f_ν(8 μm).

Of the 24 AGNs in Table 4, 17 have redshifts from SDSS, and three additional sources without SDSS redshifts have firm IRS redshifts from well-defined spectral features (strong silicate absorption or atomic emission lines). The IRS spectra in Figures 2–4 confirm the SDSS redshifts for 8 sources; source AGN23 has an IRS spectrum that indicates z∼ 1.1 compared to the SDSS redshift of 0.35. This source is shown in Figure 2 using the IRS redshift, but because of the redshift ambiguity is not used in the average spectra discussed below.

Sources AGN3, AGN5, AGN9 and AGN17 do not have SDSS redshifts and do not have strong silicate absorption or atomic emission features that enable a confident IRS redshift. Of these four, sources AGN5, AGN9, and AGN17 are shown in Figures 2–4 at the estimated IRS redshift. These estimates derive from comparisons to other spectra of known redshift by seeking the best match for rest-frame spectra of these three sources. Because of the uncertainty in z, however, sources AGN5, AGN9, and AGN17 are not used in deriving our average spectra.

Source AGN3 is particularly interesting. Brown et al. (2006) present a redshift distribution of all type 1 QSOs in the Bootes survey field with f_ν(24 μm) > 1 mJy having optical redshifts determined from the AGNs and Galaxy Evolution Survey (AGES, Cool et al. 2006). Although individual AGES redshifts are not published, the distribution of redshifts and 24 μm fluxes in Figure 8 of Brown et al. show that a type 1 QSO is present in Bootes having f_ν(24 μm) > 10 mJy and z = 2.4. This source must be in our 10 mJy Bootes sample because sources were chosen from the same survey, but it is not among the sources with either SDSS redshifts or firm IRS redshifts.

A luminous type 1 QSO should show strong silicate emission (Hao et al. 2005). Of the three Bootes sources in Table 4 without firm SDSS or IRS redshifts, source 3 is the only source whose IRS spectrum is consistent with a strong silicate emission source at z = 2.4. As seen in Figure 3, the rest-frame spectrum of this source shows an increasing continuum at ∼ 10 μm that is just as expected for the onset of a strong 9.7 μm silicate emission feature. We note also in Figure 3 the close similarity of the rest-frame spectrum of source AGN3 to that of source AGN21, a type 1 QSO with a known SDSS redshift and the most luminous source in our 10 mJy sample, as discussed below. The MIPS flux of source AGN3 (Houck et al. 2007) of 10.3 mJy is also in agreement with the flux of 10.5 mJy plotted by Brown et al. (2006). We conclude, therefore, that source AGN3 is the QSO at z = 2.4 identified by Brown et al. (2006), and we include this source in our average spectra.

Each source in Tables 2–5 is individually interesting, and many comparisons could be made among various properties, because extensive multiwavelength data already exist for most of these objects. For the present, we are not undertaking such an overall multiwavelength analysis except for noting in Tables 3 and 5 the general agreement between optical and IRS spectral classifications. The primary result we discuss here is the relation between mid-infrared luminosity and the infrared spectral characteristics. This result is crucial to understanding the nature of sources which are seen in surveys of the mid-infrared sky, and in using these surveys to determine evolutionary characteristics of starbursts and AGNs.

This 10 mJy sample clearly shows that the most luminous sources are those with AGN characteristics (silicate features) rather than starburst characteristics (PAH features). In Figure 5, the redshifts and 24 μm fluxes are compared for sources with and without measurable PAH features. It is seen that, while the flux distributions are similar, the redshifts are generally much higher for the AGNs, implying greater luminosities.

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This result is made clear in Figure 6 where luminosity distributions are shown. Luminosities are compared using rest-frame νL_ν(15 μm) in ergs s⁻¹. (Log νL_ν(15 μm)(L_☉) = log νL_ν(15 μm)(ergs s⁻¹) - 33.59.) As mentioned previously, a wavelength of 15 μm is used for comparison of intrinsic luminosities because the 15 μm continuum is a pure dust continuum, without contamination by PAH or emission line spectral features and is between the 10 μm and 17 μm silicate features. Being an intermediate mid-infrared wavelength, it is not as dominated by luminosity from the hot dust associated with AGN or the cool dust associated with a starburst as would be a shorter or longer wavelength.

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In Figure 6, luminosities νL_ν(15 μm) are compared to the EW of the 6.2 μm PAH feature. This figure shows our most important results. It shows the dramatic range in dust continuum luminosities that is covered by the sample, a factor of 2.5 × 10⁴ in luminosity, a range that encompasses virtually all extragalactic sources observed so far with Spitzer, regardless of the selection criterion. The faintest source is source SB11 in Tables 2 and 3, a blue compact dwarf in Bootes with log νL_ν (15 μm) = 41.85 (ergs s⁻¹); the most luminous sources are sources AGN11 and AGN21 in Tables 4 and 5, with AGN11 being an absorbed silicate source and AGN21 an emission silicate source, with log νL_ν (15 μm) = 46.2. (Source AGN3 in Table 5, the QSO at z = 2.4 discussed in Section 2.3, does not have a measurement of νL_ν (15 μm) because the observed rest-frame spectrum does not extend to 15 μm. It certainly is among the sources with log νL_ν(15 μm) > 45.0 (ergs s⁻¹) so is included in the average for this luminosity bin discussed below in Section 3.2.)

Figure 6 shows a well-defined gap in the distribution of PAH strength at 0.4 μm< EW(6.2 μm) < 0.5 μm. 21 of the 60 sources show EW(6.2 μm) > 0.47 μm, and the remaining sources all have EW(6.2 μm) < 0.37 μm. We also note that the "pure" starbursts in Brandl et al. (2006) show a lower limit for EW(6.2 μm) at about this value; 21 of 22 Brandl et al. starbursts have EW(6.2 μm) > 0.4 μm. We interpret these empirical results for both our 10 mJy sample and the Brandl et al. sample to mean that sources with EW(6.2 μm) > 0.4 μm are pure starbursts. Sources in which the strength of the PAH feature is diluted by additional mid-infrared continuum arising from an AGN would show EW(6.2 μm) < 0.4 μm, and we consider such sources as composite starburst+AGN. Sources with the smallest values of EW(6.2 μm) are dominated by the AGN component. These interpretations lead to the classifications shown in Figure 6.

For starbursts with EW(6.2 μm)> 0.4 μm, the median log νL_ν (15 μm) = 43.1. For composite sources with 0.1 μm< EW(6.2 μm)< 0.4 μm, the median log νL_ν (15 μm) = 44.0. For AGN sources with EW(6.2 μm)< 0.1 μm, the median log νL_ν (15 μm) = 45.0.

The change in the nature of mid-infrared spectra as a function of luminosity is also clearly shown in average spectra binned with luminosity. We consider four bins of luminosity: log νL_ν(15 μm) > 45.0 (ergs s⁻¹), 45.0 > log νL_ν(15 μm) > 44.0, 44.0 > log νL_ν(15 μm) > 43.0, and 43.0 > log νL_ν(15 μm) > 42.0. The normalized average spectra within these bins are shown in Figure 7 and tabulated in Table 6. The most important conclusion from Figure 7 is the progressive increase in PAH strength as luminosity νL_ν(15 μm) decreases.

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While these average spectra can be used as empirical spectral templates for different luminosities, the dispersion among spectra illustrates the uncertainties which arise when adopting a specific template. To allow an estimate of this dispersion within a luminosity bin, Figures 8–11 show the continuum flux densities at 15 μm and 24 μm relative to the normalizing peak at 7.7 μm (starbursts) or 8 μm (AGNs) for all of the individual sources which enter an average. The figures also show the most extreme sources in each bin.

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All sources do not cover all rest-frame wavelengths because of varying redshifts; for example, only three of the most luminous sources are at sufficiently low redshift to allow a measure of rest frame f_ν(24 μm). Average spectra are determined within different wavelength ranges using only the sources whose rest-frame spectra include those wavelength ranges.

We use the classification "starburst galaxies," or "starbursts," to mean galaxies whose spectra and luminosity are dominated by the consequences of on-going star formation. A fundamental measurement of importance for starbursts is the measure of star formation rate (SFR). Mid-infrared spectra of starbursts such as those in Figure 1 contain data for three indicators that give independent measures of SFR. These are the luminosity of the PAH emission features (e.g. Förster Schreiber et al. 2004; Brandl et al. 2006; Houck et al. 2007), the luminosity of the dust continuum (e.g. Kennicutt 1998; Calzetti et al. 2007), and the luminosity of the Neon emission lines (Ho and Keto 2007). These three indicators measure in different ways the luminosity arising from the young stars of the starburst. The PAH emission is excited by photons penetrating the photodissociation region (PDR) at the boundary between the H ii region and the surrounding molecular cloud; the dust continuum arises from dust intermixed in the H ii region and heated by the stars; and the emission lines arise within the H ii region from ionizing photons arising in the young stars.

If the geometry of the star-forming environment, the spectral distribution of stellar radiation, the temperature distribution and nature of the dust, and the gas to dust ratio were the same for all starbursts, any one of these parameters should give the same result for SFR. Of course, all starbursts are not the same among these many characteristics, so different indicators of SFR give different results depending on these characteristics. Although we do not attempt here an evaluation of the relative merits of various estimates of SFR, we can use the data for our 10 mJy sample of starbursts to estimate the dispersion that arises among these three different methods for measuring SFR.

For this comparison, we utilize the 7.7 μm PAH feature, the [Ne iii] 15.56 μm feature, and the strength of the dust continuum at 24 μm. The flux νf_ν(7.7 μm) at the peak of the PAH feature measures the luminosity in the photodissociation region, the flux of the Neon line measures the ionizing luminosity within the H ii region, and the flux density of the continuum measures the emission from warm dust. The measures used for comparison are given in Tables 2 and 3 and illustrated in Figures 12 and 13. Parameters are compared to EW(6.2 μm) which determines if a source spectrum arises strictly from a starburst without AGN contamination, as discussed in Section 3.1.

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In Figure 12, the distribution of the ratio νf_ν(7.7 μm) to f([Ne iii]) is shown for the sources in Tables 2 and 3 with PAH features. This is a measure of luminosity arising in the PDR compared to that arising in the H ii region. Including the limits which are shown, there is a weak trend in Figure 12 for PAH EW to increase as the ratio of PAH to [Ne iii] increases. This trend is as expected if the weak PAH sources contain an AGN contribution to the [Ne iii] luminosity. The comparison of SFRs is intended to apply only for sources which are pure starbursts, without an AGN contribution. These pure starbursts are taken as defined in Figure 6, based on a criterion that EW(6.2 μm) > 0.4 μm.

For these pure starbursts, the median and dispersion in the PAH to [Ne iii] ratio in Figure 12 are log [νf_ν(7.7 μm)/f([Ne iii])] = 2.8 ± 0.3. This result indicates that we should expect a dispersion by a factor of ± 2.0 between SFR estimates from PAH compared to those from [Ne iii], even for pure starbursts.

In Figure 13, the distribution of the ratio f_ν(24 μm) to f_ν(7.7 μm) is shown for the sources in Tables 2 and 3 with PAH features. This is a measure of luminosity arising from warm dust within both the H ii region and PDR compared to luminosity arising in the PDR. There is a weak trend for this ratio to change with EW(6.2 μm). This trend is expected, simply because EW(6.2 μm) is also a measure of PAH strength compared to the continuum. For the pure starbursts with EW(6.2 μm) > 0.4 μm, the median and dispersion of the ratio are log[f_ν(24 μm)/f_ν(7.7 μm)] = 0.3 ± 0.3; the dispersion is the same as for the dispersion in PAH to [Ne iii]. This result indicates that either PAH measures or dust continuum measures would give the same value for SFR to within a factor of 2.

This analysis considers only the empirical scatter among the three mid-infrared parameters which can be used for SFR measures, but it does not explain the sources of this scatter. Given the many assumptions which enter the transformation from an observed spectral parameter to a SFR, the utility of our empirical result is primarily to conclude that it is possible to estimate the SFR to a factor of ∼ 2 using several indicators within a mid-infrared spectrum, but more detailed assumptions regarding the nature of the starburst would be necessary to improve such estimates.

Average spectra are important for adopting spectral templates as a function of luminosity for use in modeling source counts (e.g. Chary et al. 2004; Lagache et al. 2004; Le Floc'h et al. 2005; Caputi et al. 2007). Such modeling is the fundamental source of conclusions regarding the evolution of extragalactic infrared sources, and different assumptions regarding templates give different answers. A utility of the average spectra in Figures 7 through 11 and Table 6 is that these comprise an empirically derived set of templates and dispersions among the templates which arise directly from a flux-limited sample of sources selected only as infrared sources. These templates can be used with assumptions for luminosity functions and evolution of sources to predict source counts at mid-infrared wavelengths, although we do not at present undertake such predictions.

For now, we use the four average spectra and corresponding luminosities only to illustrate the observed MIPS f_ν(24 μm) which would arise at different redshifts from the templates for the various luminosity bins shown in Figures 7 through 11. The determination of MIPS f_ν(24 μm) is made using the synthetic photometry tool in SMART and relating flux to luminosity with a cosmology having H₀ = 71  km s^-1 Mpc⁻¹, Ω_M = 0.27 and Ω_Λ = 0.73. Results are in Figure 14.

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A particularly important implication of the results in Figure 14 is that the sources at the highest redshifts which are detected in MIPS surveys with f_ν(24 μm) ≳ 1 mJy should only be the luminous AGN without strong PAH features, sources like those in Figure 11 having log νL_ν(15 μm) > 45.0. For sources in this luminosity bin, the observed MIPS f_ν(24 μm) remains above 1 mJy to a redshift of 3. By contrast, sources in luminosity bins whose average spectra show strong PAH features (log νL_ν(15 μm) < 44.0) would drop to f_ν(24 μm) < 0.1 mJy for z > 1.

In fact, however, this prediction is proven incorrect by the large numbers of PAH-dominated sources at z∼ 2 and f_ν(24 μm) ≳ 1 mJy which have been discovered by Spitzer (e.g. Yan et al. 2007; Farrah et al. 2008; Pope et al. 2008). Explaining such sources requires luminosity evolution for starbursts such that PAH dominated spectra can be found in sources with log νL_ν(15 μm) > 45.0. By considering only the most luminous starbursts discovered so far using a PAH luminosity indicator, this evolution has been quantified to scale as (1 + z)^2.5 for the most luminous starbursts (Weedman and Houck 2008). Applying evolution by this factor would raise the curve for log νL_ν (15 μm) = 44.0 in Figure 14 to fluxes more than a factor of 10 brighter than shown and would indeed predict PAH sources to be found at z∼ 2 with f_ν(24 μm) ∼ 1 mJy.

This result is illustrated in Figure 14 by taking the most extreme spectra in Figure 10 for 44.0 < log νL_ν(15 μm) < 45.0 and assigning luminosities log νL_ν(15 μm) = 45.0 to spectra with those extreme shapes. The lower spectrum, having strong PAH features, would reach f_ν(24 μm) = 1 mJy at z = 2 using luminosity log νL_ν(15 μm) = 45.0, although the actual luminosity of this source is log νL_ν(15 μm) = 44.3.