ORIGIN OF 12 μm EMISSION ACROSS GALAXY POPULATIONS FROM WISE AND SDSS SURVEYS

WISE has mapped the full sky in four bands centered at 3.4, 4.6, 12, and 22 μm, achieving 5σ point-source sensitivities better than 0.08, 0.11, 1, and 6 mJy, respectively. Every part of the sky has been observed typically around 10 times, except near the ecliptic poles where the coverage is much higher. Astrometric precision is better than 015 for high signal-to-noise (S/N) sources (Jarrett et al. 2011) and the angular resolution is 61, 64, 65, and 12'' for bands ranging from 3 μm to 22 μm.

This paper is based on data from the WISE Preliminary Release 1 (2011 April), which comprises an image atlas and a catalog of over 257 million sources from 57% of the sky. An object is included in this catalog if it: (1) is detected with S/N ⩾ 7 in at least one of the four bands, (2) is detected on at least five independent single-exposure images in at least one band, (3) has S/N ⩾ 3 in at least 40% of its single-exposure images in one or more bands, and (4) is not flagged as a spurious artifact in at least one band. We refer the reader to the WISE Preliminary Release Explanatory Supplement for further details⁷ (Cutri et al. 2011).

The SDSS (York et al. 2000; Stoughton et al. 2002) is a five-band photometric (ugriz bands) and spectroscopic survey that has mapped a quarter of the sky, providing photometry, spectra, and redshifts for about a million galaxies and quasars. The MPA–JHU catalog (Brinchmann et al. 2004, hereafter B04) is a value-added catalog based on data from the Seventh Data Release (DR7; Abazajian et al. 2009) of the SDSS.⁸ It consists of almost 10⁶ galaxies with spectra reprocessed by the MPA–JHU team, for which physical properties based on detailed emission line analysis are readily available. Here, we give a brief description of the catalog and the methodology employed to estimate SFRs. We refer the reader to the original papers for an in-depth discussion.

The MPA–JHU catalog classifies galaxies according to their emission lines, given the position they occupy in the BPT (Baldwin et al. 1981) diagram that plots the [O iii] λ5007/Hβ versus [N ii] λ6584/Hα flux ratios. This separates galaxies with different ionizing sources as they populate separate sequences on the BPT diagram. In most galaxies, normal star formation can account for the flux ratios. However, in some cases an extra source such as an AGN is required. In this paper, we follow this BPT classification to distinguish between: (1) SF galaxies (class SF and low S/N SF from B04), (2) AGNs (class AGN and low S/N LINER from B04), and (3) composite systems that present signatures of the two previous types (class C from B04). Note that broad-lined AGN-like quasars and Seyfert 1 galaxies are not included in the sample, as they were targeted by different criteria by the SDSS.

SFRs are derived by different prescriptions depending on the galaxy type. The methodology adopted by B04 is based on modeling emission lines using Bruzual & Charlot (1993) models along with the CLOUDY photoionization model (Ferland 1996) and spectral evolution models from S. Charlot & G. Bruzual (2008, in preparation) to subtract the stellar continuum. To correct lines for dust attenuation, MPA–JHU adopts the multicomponent dust model of Charlot & Fall (2000), where discrete dust clouds are assumed to have a finite lifetime and a realistic spatial distribution. This approach produces SFRs that take full advantage of all modeled emission lines. For AGNs and composite galaxies in the sample, SFRs were estimated by the relationship between the D₄₀₀₀ spectral index and the specific SFR (SFR/M_☉ or SSFR), as calibrated for SF galaxies (see Figure 11 in B04). These estimates have been corrected in the latest MPA–JHU DR7 release by using improved dust attenuations and improved aperture corrections for non-SF galaxies following the work by Salim et al. (2007). Gas-phase oxygen abundances, 12 + log (O/H), are available for SF galaxies as calculated by Tremonti et al. (2004). Throughout this paper we adopt the spectral line measurements as well as estimates of SFR, metallicity, and dust extinction given by the MPA–JHU catalog.

The SDSS pipeline calculates several kinds of magnitudes. In this work we have adopted modified Petrosian magnitudes for flux measurements, which capture a constant fraction of the total light independent of position and distance. When appropriate, we have also used model magnitudes (modelMag) as they provide the most reliable estimates of galaxy colors. Magnitudes are corrected for galactic reddening using the dust maps of Schlegel et al. (1998).

We have cross-matched data from WISE and the MPA–JHU catalog to construct a galaxy sample covering an effective area of 2344 deg², or 29% of the DR7 (legacy) spectroscopic footprint. WISE sources were selected to have 12 μm fluxes above 1 mJy, also requiring objects to have clean photometry at 3.4, 4.6, and 12 μm. For MPA–JHU sources, we selected objects with de-reddened Petrosian magnitude r_petro < 17.7 and r-band surface brightness μ_r < 23 mag arcsec⁻². This selects a conservative version of the SDSS main galaxy sample (see Strauss et al. 2002). Using a matching radius of 3'' we find 96,217 WISE objects with single optical matches (40% of the SDSS sample in the intersection area) and 73 sources with two or more counterparts. The latter are mostly large extended sources or close interacting systems of two members. For the rest of this paper we will focus on the single IR–optical matches that constitute the vast majority (>99.9%) of the galaxy population. By using random catalogs generated over the effective area, the expected false detection fraction at 3'' is 0.05%.

Each region of the sky has been observed at least 10 times by WISE, with the number of observations increasing substantially toward the ecliptic poles. Within our effective area, the median coverage depth at 12 μm is about 13, varying typically between 10 and 20. At these levels, the average completeness of the sample is expected to be over 90%, as shown in the WISE Preliminary Release Explanatory Supplement (Section 6.6).

We derived stellar masses for all galaxies using the kcorrect algorithm (Blanton & Roweis 2007), which fits a linear combination of spectral templates to the flux measurements for each galaxy. These templates are based on a set of Bruzual & Charlot (2003) models that span a wide range of star formation histories, metallicities, and dust extinction. This algorithm yields stellar masses that differ by less than 0.1 dex on average from estimates using other methods (for example, the method based on fitting the 4000 Å break strength and Hδ absorption index proposed by Kauffmann et al. 2003b).

To derive rest-frame colors and monochromatic luminosities in the infrared we used the fitting code and templates⁹ of Assef et al. (2010), applied to our combined ugriz photometry plus WISE 3.4 μm, 4.6 μm, and 12 μm fluxes. Assef et al. (2010) present a set of low-resolution empirical spectral energy distribution (SED) templates for galaxies and AGNs spanning the wavelength range from 0.03 μm to 30 μm, constructed with data from the NOAO Deep Wide-field Survey Boötes field (Jannuzi et al. 2010) and the AGN and Galaxy Evolution Survey (C. Kochanek et al. 2011, in preparation). The code fits three galaxy SED templates that represent an old stellar population (elliptical), a continuously SF population (spiral), and a starburst component (irregular), plus an AGN SED template with variable reddening and intergalactic medium absorption. These templates have been successfully used to test the reliability of IRAC AGN selection and to predict the color–color distribution of WISE sources (Assef et al. 2010). We also use these templates to assess the relative contribution of AGNs to the energy budget.

Instead of trying to derive a new calibration of the SFR in the IR, we take the approach of comparing IR luminosities directly to optical dust-corrected SFRs. This makes our results largely independent of any particular SFR calibration. Note all optical SFRs used in this paper have been corrected for dust extinction.

We begin our analysis by exploring the general properties of the WISE 12 μm selected galaxy sample. The sample is composed of a mixture of 70% SF galaxies, 15% AGNs, 12% composite galaxies, and 3% galaxies lacking BPT classification due to the absence of detectable lines in the spectra (most lack Hα emission). The composition of the MPA–JHU optical sample is 44% SF, 12% AGNs, 6% composite, and 37% unclassifiable, which means that the 12 μm selection is highly efficient in recovering SF systems and avoids objects with weak or no emission lines. In terms of the total optical galaxy populations, 61% (SF), 53% (AGNs), and 76% (composite) of the SDSS galaxies have 12 μm flux densities above 1 mJy. In Figure 1 (top row) we plot the distribution of redshift, stellar mass, D₄₀₀₀ index, and rest-frame u−r color for SF galaxies, AGNs, and composite systems, as well as for the three classes all together. The majority of WISE–SDSS 12 μm sources are SF galaxies at 〈z〉 = 0.08 with stellar masses of ∼10^10.2 M_☉; these are typical values for the SF class. They clearly populate the blue peak of the galaxy bimodal distribution around (u − r)₀ = 1.6 and have inherently young stellar populations (D₄₀₀₀ ∼ 1.3, or ages of ∼0.5 Gyr). AGNs are, as expected, comparatively more massive (M* ∼ 10^10.7 M_☉), redder ((u − r)₀ ∼ 2.1), and older (∼1–6 Gyr), dominating the massive end of the 12 μm galaxy distribution. As a population, AGNs do not differ significantly (in terms of these properties) in comparison to the corresponding purely optical sample. Composite galaxies present intermediate properties between the SF and AGN samples. Note that the bulk of galaxies lacking BPT classification (due to weak or absent emission lines) is missed in our IR–optical sample. These objects primarily populate the red sequence of the galaxy distribution (e.g., Baldry et al. 2004), and hence are not expected to be prominent at 12 μm.

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We then divide the sample into three subsamples of monochromatic infrared luminosity: faint (L_12 μm < 10^9.2 L_☉), intermediate (10^9.2 L_☉ < L_12 μm < 10¹⁰ L_☉), and bright (L_12 μm > 10¹⁰ L_☉) sources. There are no large biases with redshift, i.e., the different classes are sampled roughly without preference at all luminosities. Both SF galaxies and AGNs become more massive for higher IR luminosities and we have checked that this also holds in narrow redshift slices. As we will show below, this is due to the coupling between the IR and the optical emission. Interestingly, the 12 μm SF galaxies change by a factor of 0.8 dex in mass toward high 12 μm luminosities while keeping the same color and stellar content. The AGN population, while getting slightly more massive, becomes bluer and dominated by younger stars as IR luminosity increases. Figure 2 shows the redshift distribution of the rest-frame 12 μm luminosity for our sample. It can be seen that while high luminosity sources naturally lie at higher redshifts, the redshift distribution of the different classes is very similar, except at the lowest redshifts (z < 0.02) where very few AGNs/composite galaxies are observed.

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The absence of red-sequence galaxies in our sample is not surprising, but there is also a number of SF galaxies without IR emission due to our flux limit. Figure 3 shows the mass, redshift, and colors of SF galaxies with and without 12 μm emission, as well as for the entire SF optical sample. On average, SF galaxies not present in our sample have bluer colors, lie at lower redshifts, and have stellar masses around 10^9.3 M_☉, roughly an order of magnitude below the 12 μm SF galaxy sample. At this level, galaxies have very little dust mass, and hence cannot re-radiate much in the IR.

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The main result here is that WISE 12 μm selected galaxies are primarily typical blue-sequence (SF) galaxies. It is safe to assume that the majority of blue-sequence galaxies correspond to late morphological types (e.g., Strateva et al. 2001; Shimasaku et al. 2001; Baldry et al. 2004). AGNs and composite objects are also represented, belonging either to the red sequence or to a transitional regime among the two former classes. It is interesting that the detection efficiency is largest for composite systems, which was also found by Salim et al. (2009) for 24 μm sources that lie in the so-called green valley (e.g., Martin et al. 2007). This is a region located between the red and blue cloud sequences, best identified in the NUV–r color–magnitude diagram, where SF activity is being actively quenched and galaxies are thought to be in transitional stage in their migration from the blue to the red sequence.

Most galaxies in our sample are either normal luminosity IR galaxies (L_12 μm ∼ 10^9.2–10 L_☉; 60%), low luminosity IR galaxies (L_12 μm < 10^9.2 L_☉; 31%), or luminous infrared galaxies (LIRGs; L_12 μm ∼ 10^10–10.8 L_☉; 9%). However, ULIRGs are also present. There are 114 objects with L_12 μm > 10^10.8 L_☉ (roughly equivalent to L_TIR > 10¹² L_☉ using the conversion of Chary & Elbaz 2001), corresponding to a surface density of 0.049 deg⁻². This is comparable to the 0.041 deg⁻² surface density found by Hou et al. (2009). These ULIRGs naturally lie at higher redshift (〈z〉 = 0.2) and populate the massive end of the SF sequence above ∼10¹¹ M_☉. We reiterate that these results come from matching WISE to the relatively bright SDSS spectroscopic sample. WISE galaxy populations down to r ∼ 22.6 are analyzed in L. Yan et al. (2011, in preparation).

We now have a large sample of 12 μm selected galaxies that range from low-IR to ULIRG luminosities, for which high-quality optical spectra and dust-corrected optical SFRs are available. First, we examine the relation between L_12 μm and stellar mass. B04 have shown that, at least for SF systems, SFR and stellar mass are strongly correlated in the local universe. There is also evidence that this relationship evolves with redshift (Noeske et al. 2007, Daddi et al. 2007). Although it is expected that more massive galaxies are naturally more luminous, it is unclear whether more massive systems would have more dust emission in the mid-IR. Figure 4 shows the correlation between monochromatic 12 μm luminosity and stellar mass for our sample. The correlation is tight for SF systems over nearly three orders of magnitude in stellar mass (gray points, top panels). Several studies have found that the distributions of [O iii] emission line flux to the AGN continuum flux at X-ray, mid/far-IR, and radio wavelengths (i.e., where stellar emission and absorption by the torus are least significant) are very similar for both type I and type II AGNs (Mulchaey et al. 1994; Keel et al. 1994; Alonso-Herrero et al. 1997). Based on this, Kauffmann et al. (2003a) and Heckman et al. (2004) have shown that [O iii] flux is a reliable estimator of AGN activity. Following these works, we split the AGN sample by [O iii] luminosity. We see that strong AGNs ($L_{[{\rm O\,\mathsc{iii}}]}>10^{7}\,L_{\odot }$) have IR luminosities considerably larger than weak AGNs ($L_{[{\rm O\,\mathsc{iii}}]}<10^{7}\,L_{\odot }$), following approximately the same relationship with mass as SF systems. Weak AGNs, instead, lie well below that correlation and show a larger scatter. We note that the contribution by SF regions to the [O iii] flux is <7% (Kauffmann et al. 2003a).

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In the right bottom panel of Figure 4, we compare the ages of stars in all subsamples as derived from the D₄₀₀₀ spectral index. SF galaxies have the youngest stellar populations, peaking at ∼0.5 Gyr, followed by considerably older composite galaxies (∼1.5–2 Gyr). Strong AGNs, which dominate the massive end, have intermediate stellar populations (∼1.5 Gyr) that are closer to SF/composite systems than to weak AGNs (see Figure 1). In contrast, weak AGNs tend to be hosted by early-type galaxies with significantly older stars (∼3 Gyr), as found also by Kauffmann et al. (2003a) after comparing AGN host sizes, surface densities, and concentration ratios with those of normal early-type galaxies. This highlights the importance that young/old stars have in powering the 12 μm emission. For AGNs of roughly similar stellar mass, only when younger stars begin to dominate (and the active nuclei becomes more powerful) is the IR emission comparable to actively SF systems. Qualitatively, the same result holds if we use the dust-corrected r-band absolute magnitude instead of stellar mass.

Since galaxies of different ages have very different IR output, an interesting question to address is how the 12 μm luminosity budget depends upon the age of the stellar populations. Figure 5 shows the cumulative fraction of the integrated 12 μm luminosity produced in galaxies of a given age. In SF galaxies, ∼80% of the total IR luminosity is produced by galaxies younger than 0.6 Gyr. Composite galaxies and strong AGNs reach the same fraction at ages of 1.5 Gyr and 2 Gyr, respectively. In weak AGNs, instead, most of the mid-IR emission is produced within a range of ∼1–3 Gyr. This inventory of 12 μm luminosity in the local universe shows where the bulk of the IR emission resides, shifting from stellar populations of a few hundred Myr in actively SF galaxies to a few Gyr in galaxies hosting weak AGNs. Thus, it underlines again the important role that young/old stars have in powering 12 μm emission. As we will see later in Section 3.6, this also supports the idea that transition galaxies (i.e., composite/strong AGNs) form a smooth sequence that joins highly active galaxies with quiescent galaxies.

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We now explore the relationship between infrared luminosity and optical, dust-corrected SFR. Figure 6 shows L_12 μm versus SFR_opt, color coded by the D₄₀₀₀ spectral index. As discussed by Kauffmann et al. (2003b), the D₄₀₀₀ index is a good indicator of the mean age of the stellar population in a galaxy. The dashed line indicates the reference relation of Kennicutt (1998), as given by Chary & Elbaz (2001) in terms of 12 μm luminosity, to convert IR luminosity into "instantaneous" SFR. It was derived from simple theoretical models of stellar populations with ages 10–100 Myr without considering factors like metallicity or more complex star formation histories. While this makes it strictly valid only for young starbursts, the Kennicutt relation is quite often applied to the more general population of SF galaxies. Figure 6 shows that the IR emission from SF galaxies (left panel) correlates fairly well with SFR_opt. The correlation is tighter for high SFRs, becoming broader and slightly asymmetric for low SFRs. A least-squares fit to the SF sample is given by

$$\begin{eqnarray} &&\log L^{\rm SF}_{\rm 12\,\mu m}=(0.987\,\pm\, 0.002)\log {\rm SFR}_{\rm opt}+(8.962\,\pm\, 0.003).\nonumber\\ \end{eqnarray} \tag{ 1 }$$

This expression is close to the Chary & Elbaz (2001) relation at high SFRs, which is not surprising given that relation was calibrated using the IRAS Bright Galaxy Sample (Soifer et al. 1987), i.e., luminous galaxies with L_12 μm > 10⁹ L_☉. The small differences are likely attributable to luminosity/redshift selection effects and the slight differences between ISO and WISE 12 μm filters. More importantly, the agreement is quite good considering the different origin (FIR versus optical emission lines) of the SFRs. Relative to the Chary & Elbaz (2001) conversion, L_12 μm is comparatively suppressed by a factor >1.6 for SFR_opt below ∼0.1 M_☉ yr⁻¹. This is likely because low SFR systems have very low stellar masses (<10⁹ M_☉), and therefore become more transparent due to the increasing fraction of stellar light that escapes unabsorbed by dust. We note, however, that the spatial distribution of dust in H ii regions and/or molecular clouds could also have influence (e.g., Leisawitz & Hauser 1988). In addition, we have repeated the test for the bluest galaxies in the SF galaxy class, obtaining no significant differences. This suggests that other effects like metallicity could also be relevant.

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For AGNs, the coupling between optical SFR and IR luminosity follows a different relationship (right panel of Figure 6). Most AGNs lie in a broader distribution above the instantaneous conversion of Kennicutt, particularly those with SFR_opt below ∼1 M_☉ yr⁻¹. For a fixed SFR, the IR emission is higher by a factor of several relative to SF galaxies, suggesting that L_12 μm is not driven by the current SF for most AGNs. Weak AGNs are predominantely associated with massive, early-type galaxies increasingly dominated by old stars at low SFRs (∼0.1 M_☉ yr⁻¹). Given their red optical colors, it is unlikely that recent SF could be responsible for their IR emission. More likely, dust grains heated due to older stars or an AGN are driving this emission. Note, however, that in Section 3.8 we will show that the contribution of AGNs at 12 μm is of minor importance for most AGNs, except perhaps for most powerful ones. Only strong AGNs, which are dominated by intermediate-to-young stellar populations, tend to occupy a region similar to SF galaxies in Figure 6. They show a clear "excess" in L_12 μm at SFR_opt ∼0.5 M_☉ yr⁻¹ that gradually decreases when stars get younger toward higher SFRs. This shows that the age of stars in an AGN is an important factor in determining the origin of the 12 μm emission. An expression fitting AGNs (weak and strong) is given by

$$\begin{eqnarray} &&\log L^{\rm AGN}_{\rm 12\,\mu m}=(0.582\,\pm\, 0.004)\log {\rm SFR}_{\rm opt}+(9.477\,\pm\, 0.002).\nonumber\\ \end{eqnarray} \tag{ 2 }$$

Recent work by Salim et al. (2009) compared NUV/optical SFRs with L_TIR calibrated from 24 μm fluxes for red- and green-sequence objects at z ∼ 0.7 (corresponding to rest-frame 14 μm, close to the WISE 12 μm band). They find large excess IR emission for a given SFR, attributed mainly to older stellar populations, and to a lesser extent to an AGN. We find broadly consistent results, but for 12 μm selected AGN sources with optical SFRs. Kelson & Holden (2010) have suggested that thermally pulsating asymptotic giant branch (TP-AGB) carbon stars with ages of 0.2–1.5 Gyr (corresponding to D₄₀₀₀ ∼1.2–1.5) can also contribute significantly to the mid-IR flux. As seen in Section 3.3, this does not seem to be important for our much older, weak AGNs, and perhaps marginally relevant in strong AGNs that have typical stellar ages slightly above the upper 1.5 Gyr limit. The case of SF galaxies is interesting because most of the 12 μm luminosity seems to originate from galaxies in the ∼0.3–0.6 Gyr age range and this luminosity correlates relatively well with the optical SFR. While the age ranges seems to overlap, it is difficult to prove whether TP-AGB dominate the emission or not. Further SED decomposition and modeling of stellar populations is required to find the fraction of mid-IR luminosity powered by TP-AGB stars, a task that is potentially complicated by metallicity effects and uncertainties in the ensemble colors of such stars. However, the general picture is consistent with previous results (Salim et al. 2009; Kelson & Holden 2010) that find evidence for the mid-IR being sensitive to star formation over relatively long (>1.5 Gyr) timescales.

Finally, we consider composite systems, which present considerable SF activity along with spectral signatures of an AGN (middle panel of Figure 6). By definition, these objects have up to 40% (see B04) of their Hα emission coming from a non-stellar origin, though the fraction is <15% for most galaxies. With masses, ages, and optical colors intermediate between the SF and AGN sequences, composite galaxies closely follow the Kennicutt relation, except at the low SFR end where older stars once again begin to dominate. A least-squares fit for composite galaxies has a slope intermediate between AGNs and SF galaxies, and is given by

$$\begin{eqnarray} &&\log L^{\rm comp}_{\rm 12\,\mu m}=(0.671\,\pm\, 0.003)\log {\rm SFR}_{\rm opt}+(9.249\,\pm\, 0.002).\nonumber\\ \end{eqnarray} \tag{ 3 }$$

We note that the optical SFRs utilized here, while not ideal, are probably the best estimates publicly available for such a large and diverse population of galaxies in the local universe. Other methodologies that use more sophisticated dust corrections and employ H₂, FIR, or radio data could provide more accurate values, but are difficult to apply across the entire sample and data are not always available (see Saintonge et al. 2011 for a calibration of SFR based on H₂ masses). This is particularly relevant for SFRs in AGNs, which can present large >0.5 dex formal errors (see Figure 14 of Brinchmann et al. 2004). We have verified that the SDSS SFRs in our sample are in broad agreement with UV-based SFRs derived by Salim et al. (2007) (S. Salim 2011, private communication), with an average offset/scatter of 0.055/0.387 for the total sample (0.013/0.334 for strong AGNs and 0.242/0.567 for weak AGNs).

WISE is less sensitive at 22 μm than at 12 μm, but a significant fraction of our sample (∼30%) has measured 22 μm fluxes above 5 mJy (note we find no 22 μm galaxies without 12 μm detection). Similar to the 12 μm sample, this 22 μm subsample is a mixture comprised of 65% SF galaxies, 14% AGNs, and 19% composite systems. However, the fraction of strong AGNs is 38%, compared to 16% for 12 μm sources. As 22 μm is closer to the dust emission peak and is not affected by polycyclic aromatic hydrocarbon (PAH) emission features, it is interesting to compare with the 12 μm galaxies of our previous analysis. Figure 6 shows the linear fits for the 22 μm subsample (triangle markers). These relations are very similar to the 12 μm fits (solid line for SF galaxies, square markers for AGNs, and composite galaxies) supporting the independence of our results on the particularities of a single mid-IR band.

Given the strong correlations between optical or IR light and stellar mass, a more interesting metric for comparison is the SSFR or SFR/M_☉, that measures the current relative to past SFR needed to buildup the stellar mass of the galaxy. The SSFR traces the star formation efficiency and its inverse defines the timescale for galaxy formation or the time the galaxy required to buildup its current mass. Higher values of SSFR are indicative of a larger fraction of stars being formed recently. While ideally we would use gas mass or total mass instead of stellar mass for the normalization, such masses are not easily measured.

Figure 7 shows the SSFR as a function of 12 μm luminosity for the different galaxy classes. The nearly flat correlation for SF galaxies means that no matter the IR output, the amount of star formation per unit mass remains relatively constant. SF galaxies display a weak dependence with L_12 μm that gets narrower toward higher luminosities. As noted before, a possible origin for such residual SSFR could be due to a metallicity gradient. Calzetti et al. (2007) studied individual SF regions of fixed aperture in nearby galaxies with known Paα surface density and found that low metallicity galaxies have a small deficit in 24 μm emission compared to high metallicity galaxies. Relaño et al. (2007) confirmed that while 24 μm luminosity is a good metallicity-independent tracer for the SFR of individual H ii regions, the metallicity effect should be taken into account when analyzing SFRs integrated over the whole galaxy. We test qualitatively for a metallicity effect by calculating the SFR per unit mass per unit metallicity, where the metallicity is given by the 12 + log (O/H) gas-phase oxygen abundance derived from optical nebular emission lines. The SF population displays an almost perfectly flat relationship over almost four orders of magnitude in L_12 μm, such that independent of IR output, a galaxy of given mass and metal content converts gas into stars at a nearly constant rate. We note that these metallicities represent the current metal abundance rather than the luminosity-weighted average of past stellar populations. They also do not suffer from complications due to α-element enhancement or age uncertainties, characteristic of methods relying on absorption-line indices. Bond et al. (2012) arrive at a similar conclusion regarding a constant SSFR in nearby galaxies using Herschel 250 μm and WISE 3.4 μm data.

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Compared to SF galaxies, AGNs have SSFRs lower by a factor of ∼10, mainly because of their higher stellar masses. However, strong AGNs lie much closer to the SF sequence than weak AGNs. The former are hosted by high stellar mass galaxies, but also have young stellar populations that drive up the SFR at high L_12 μm. Weak AGNs do not have this boost in SFR and hence have lower SSFRs. Once again, composite systems populate a region intermediate between SF galaxies and strong AGNs. Previous studies (e.g., Brinchmann et al. 2004; Salim et al. 2007) have shown the relationship between the SFR and M*, identifying two different sequences: galaxies on an SF sequence and galaxies with little or no detectable SF. While the general result is that the SSFR of massive, red galaxies is lower at 0 < z < 3, the exact dependence of SSFR on mass is still a matter of debate, particularly in view of recent results that trace the evolution at higher redshift (e.g., Noeske et al. 2007; Dunne et al. 2009; but see the discussion by Rodighiero et al. 2010). In our sample of SF galaxies we find that the dependence of L_12 μm on M* is such that the efficiency by which gas is transformed into stars is nearly independent of the IR emission reprocessed by the dust. In strong AGNs the star formation activity is "suppressed" moderately, but considerably more in the case of weak AGNs. This suggests a sequence where a strong AGN phase is a continuation of the SF sequence at high stellar mass, that gradually turns AGNs into a population with weakened SF activity and lower L_12 μm, dominated by older and redder stars.

Based on optical data, Kauffmann et al. (2003a) found that strong AGN hosts are indeed populated by relatively young stars, suggesting many of them could be post-starburst systems with extended star formation. With UV data, Salim et al. (2007) showed there is a close connection between massive SF galaxies and strong AGNs. Using IR data, we find that the smooth sequence of galaxies from Figures 6 and 7 supports the hypothesis of strong AGNs being the continuation at the massive end of the normal SF sequence. An interesting question is whether the mid-IR luminosity in powerful AGNs is driven by "normal" ongoing SF, or by hot dust left over after the last episode of SF. Further investigation is required to fully understand this matter.

Recent work on resolved nearby galaxies has shown a definite correlation between IR color and luminosity. Y. Shi et al. (2011, in preparation) found that for a variety of sources ranging from ULIRGs to blue compact dwarf galaxies, the flux ratio f_24 μm/f_5.8 μm traces the SSFR and also correlates with the compactness of SF regions. While ideally we would like to know the SFR surface density, we first explore the relation between SSFR and 4.6–12 μm galaxy color, as shown in Figure 8. Galaxies from the main SF sequence (blue contours) correlate strongly with IR color, with strong AGNs (black contours) continuing the trend at bluer colors. Weak AGNs extend (red contours) that relationship remarkably well toward the low star formation end, albeit with higher dispersion and a slightly steeper slope. Hence, for the same increase in SSFR, AGNs experience a smaller variation in IR color than typical SF objects. This is probably due to the combination of a metallicity effect and the different stellar populations that regulate the IR emission budget. In any case, this suggests that the higher the SSFR, the more prominent the 12 μm IR emission becomes relative to 4.6 μm, where the latter is expected to strongly correlate with stellar mass. This shows that the 4.6–12 μm color serves well as a rough first-order indicator of star formation activity over three orders of magnitude in SFR. A simple expression fitting all galaxies is given by

$$\begin{eqnarray} &&\log {\rm SSFR}=(0.775\pm 0.002)(W2-W3)_{0}-(12.561\pm 0.006).\nonumber\\ \end{eqnarray} \tag{ 4 }$$

If the galaxy is known to host an AGN, then the more accurate expression is

$$\begin{eqnarray} &&\log {\rm SSFR}=(0.840\pm 0.008)(W2-W3)_{0}-(12.991\pm 0.020).\nonumber\\ \end{eqnarray} \tag{ 5 }$$

These results show that there is a tight link between stellar mass, current SFR, and IR color in SF galaxies, which emphasizes the role of the dominant stellar population in regulating star formation.

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In the previous sections we noted that the emission from the AGN could have a significant effect on the IR emission, and potentially bias the luminosities of the AGN galaxy class. This could be particularly important for low SFR galaxies. We test for this effect by estimating the contribution of the AGN to the total energy budget for sources classified from the BPT diagram as either an AGN or as an SF galaxy. To do so, we analyze the fraction of the 12 μm luminosity contributed by each of the four templates used in the SED fitting process to our optical+IR photometry, paying particular attention to the AGN component. Figure 9 shows the median fraction of 12 μm luminosity contributed by each template, for objects classified as SF galaxies. The majority of the power is split among the irregular (Im), spiral (Sbc), and elliptical (E) templates, though the AGN contribution becomes significant for the most luminous sources, above 10^10.8 L_☉. This implies that the AGN has a negligible influence in SF galaxies. Figure 10 shows these fractions for weak and strong AGN galaxy classes. The elliptical component is now more prominent in weak AGNs of low luminosity, which is not unexpected. In general, the AGN component is now more important but is still far from contributing significantly below 10^10.8 L_☉. In most weak AGNs (∼80%), the AGN contribution to the 12 μm luminosity is below 40%. About ∼70% of strong AGNs show similar low AGN contributions at 12 μm. We note that in Figure 10 we used WISE aperture photometry for extended, nearby sources and profile-fitting magnitudes for unresolved galaxies with χ² < 3 (see Section 4.5 of WISE Preliminary Release Explanatory Supplement for further details). Although the differences are small, aperture photometry improves the quality of the SED fit of low luminosity galaxies, as it captures the more extended flux of objects at low redshifts.

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Note that in both cases, SF galaxies and AGNs, the emission is dominated by the spiral (Sbc) component, which has a relatively high mid-IR SED. This is because the template, originally constructed from Coleman et al. (1980) and extended into the UV and IR with Bruzual & Charlot (2003) synthesis models, also considers emission in the mid-IR from dust and PAHs. These are added by ad hoc linear combinations of appropriate parts of NGC 4429 and M82 SEDs obtained by Devriendt et al. (1999). Figure 11 shows the SED fit for AGNs with luminosities of $L_{[{\rm O\,\mathsc{iii}}]}\sim 10^6\, L_\odot$ and $L_{[{\rm O\,\mathsc{iii}}]}\sim 10^7\, L_\odot$. In each case we plot the object with the median χ², i.e., the typical fit for sources of those luminosities. The nine photometric bands are well fitted by the model in most cases. For AGNs with $L_{[{\rm O\,\mathsc{iii}}]}>10^{7.5}\, L_\odot$ we find the SED fit is reasonably good (although in general with higher χ²) except at the 22 μm band. We believe this is caused by the limitation of the algorithm (not the templates themselves) to properly fit highly reddened AGNs fainter than their hosts, as it is designed to punish the excessive use of reddening on the AGN when few relevant data points are used. Modifying the algorithm slightly to remove this behavior, we are able to obtain fits with better χ² values for these objects assigning much higher AGN fractions and reddening values, yet the lack of farther IR data to determine the origin of the 22 μm excess makes these numbers also uncertain. Therefore, while these results do not definitely rule out that the central AGN could have a considerable effect in some extreme sources (e.g., the very strong AGN), it certainly shows that they are not relevant for most of the galaxy populations analyzed in this paper.

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