The MOSDEF Survey: The Nature of Mid-infrared Excess Galaxies and a Comparison of IR and UV Star Formation Tracers at z ∼ 2

For the MOSDEF survey (Kriek et al. 2015) we obtained spectroscopic data from the MOSFIRE spectrograph (McLean et al. 2012) on the 10 m Keck I telescope. MOSFIRE provides spectroscopic data with wavelength coverage from 0.97 to 2.40 μm at moderate resolution (R = 3000–3650). We obtained spectra for sources in five extragalactic fields: AEGIS, COSMOS, GOODS-N, GOODS-S, and UDS. MOSDEF targets were selected from the deep H-band imaging provided by the CANDELS survey (Grogin et al. 2011; Koekemoer et al. 2011) in areas with overlapping coverage from the 3D-HST grism survey (Brammer et al. 2012; Momcheva et al. 2016). The targets were selected in three redshift intervals (1.37 <z < 1.70, 2.09 < z < 2.61, and 2.95 < z < 3.80) to ensure coverage of the strong rest-frame optical emission lines (i.e., [O ii], Hβ, [O iii], Hα, [N ii], [S ii]) in the Y, J, H, and K bands. AGNs were identified prior to targeting using X-ray imaging from Chandra and/or IR imaging from IRAC on the Spitzer telescope. AGNs were given higher targeting weights, as were brighter sources and sources with more secure prior redshift estimates, either photometric or spectroscopic. For the full details of the MOSDEF survey, see Kriek et al. (2015).

Our full sample using data from the first 3 yr of the MOSDEF survey includes 792 galaxies, 92 of which are identified as AGNs. For this study we limit our sample to sources at 1.4 < z < 2.61 to ensure that 24 μm observations from MIPS on Spitzer correspond to rest-frame ∼8 μm data. We further restrict our analysis to sources with significant 24 μm and UV detections, which limits our sample in this paper to 194 galaxies, 52 of which are AGNs (see Section 2.3).

Using the MOSDEF spectroscopy, we measure the flux of multiple rest-frame optical emission lines and use this to estimate the Balmer decrement (from Hα/Hβ) and to identify optical AGNs using the [O iii]/Hβ versus [N ii]/Hα BPT diagram. In this section we briefly describe the methods used by Reddy et al. (2015) and Azadi et al. (2017) to measure the flux of these emission lines.

For MOSDEF galaxies the Hβ, [O iii], Hα, and [N ii] emission line fluxes are estimated by fitting Gaussian functions as described in Reddy et al. (2015). We allow a linear fit to the continuum, a single Gaussian component for Hβ and [O iii], and a triple Gaussian function for [N ii] λ6550, Hα, and [N ii] λ6585 fit simultaneously. The spectra of each galaxy were perturbed 1000 times within the error spectra, and the dispersion of the perturbed lines was taken as an estimate of the error in the emission-line flux (Reddy et al. 2015).

To identify optical AGNs, we use the procedure described in Azadi et al. (2017). We use the MPFIT nonlinear least-squares fitting function in IDL (Markwardt 2009) and use the error spectra to determine the errors on the fit. We require the continuum around each emission line to be flat, and we require the same physical components (i.e., narrow line, broad line, outflow) to have the same FWHM and velocity offset, as determined from the line with the highest signal-to-noise ratio (S/N). The spacing between the [O iii] λ4960 and [O iii] λ5008 forbidden lines (as well as between the [N ii] λ6550 and [N ii] λ6585 lines) is fixed, and their flux ratios are set to be 1:3. We fit [O iii] λ5008 simultaneously with [O iii] λ4960, and Hα with [N ii] λ6550 and [N ii] λ6585, using four different models.

In model 1, all lines are fit with a narrow component with FWHM < 2000 km s⁻¹. In model 2, in addition to the narrow component, we allow for an underlying broad component for the Hβ and Hα lines with FWHM > 2000 km s⁻¹. In model 3, we fit each line with a narrow component and an additional component with FWHM < 2000 km s⁻¹ and a velocity offset relative to the narrow component; this represents an outflow component. In model 4, the narrow, outflow, and broad Hβ and Hα components are all fit. The fit from model 1, with only single narrow components, is considered to be the best fit for the sources unless the additional components improve the reduced χ² at the 99% confidence level. For more details on the AGN line-fitting procedure, see Section 2 in Azadi et al. (2017). We note that the fluxes of the narrow components of the Hβ and Hα lines are corrected for the underlying stellar absorption (for more details, see Reddy et al. 2015).

In the MOSDEF survey we use three methods to identify AGNs: X-ray imaging from Chandra, IRAC MIR imaging from Spitzer, and the BPT diagram using the MOSDEF spectral line measurements. Details of MOSDEF AGN identification using each method are described in Azadi et al. (2017); relevant details are repeated here.

X-ray AGNs were identified prior to MOSDEF targeting using Chandra observations with a depth of 4 Ms in GOODS-S, 2 Ms in GOODS-N, 800 ks in AEGIS, and 160 ks in the COSMOS field, corresponding to hard-band flux (${f}_{2\mbox{--}10\mathrm{keV}}$ [erg s⁻¹ cm⁻²]) limits of 1.6 × 10⁻¹⁶, 2.8 × 10⁻¹⁶, 5.0 × 10⁻¹⁶, and 1.8 × 10⁻¹⁵, respectively, in each field. X-ray catalogs were generated according to the method described by Laird et al. (2009), Nandra et al. (2015), and Aird et al. (2015). To identify the optical, NIR, and Spitzer IRAC counterparts of the X-ray sources, we use the likelihood ratio technique (e.g., Brusa et al. 2007; Laird et al. 2009; Aird et al. 2015), where the source with the highest likelihood ratio is selected as the best match for sources with multiple counterparts. We then matched the X-ray counterparts to the 3D-HST catalogs used for targeting in the MOSDEF survey. We estimate the rest-frame 2–10 keV X-ray luminosities based on the hard-band (2–7 keV) or the soft-band (0.5–2 keV) flux (when there is no detection for the hard band), assuming a simple power-law spectrum with Galactic absorption, photon index of Γ = 1.9, and the MOSDEF redshift.

Although X-ray imaging is reliable for AGN identification, it may fail to identify highly obscured and Compton-thick AGNs. IR imaging can recover some of these heavily obscured AGNs, as UV and optical photons from the central engine are absorbed by dust grains in the obscuring structure and reemitted at longer wavelengths. Several mid-IR AGN selection techniques have been proposed using IRAC (Fazio et al. 2004) data from the Spitzer telescope. In MOSDEF we use the Donley et al. (2012) criteria with some slight modifications. The Donley et al. (2012) criteria are

$$\begin{eqnarray}&&x={\mathrm{log}}_{10}\left(\displaystyle \frac{{f}_{5.8\mu {\rm{m}}}}{{f}_{3.6\mu {\rm{m}}}}\right),\quad y={\mathrm{log}}_{10}\left(\displaystyle \frac{{f}_{8.0\mu {\rm{m}}}}{{f}_{4.5\mu {\rm{m}}}}\right)\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&x\geqslant 0.08\,{\rm{and}}\,y\geqslant 0.15\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&y\geqslant (1.21\times x)-0.27\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&y\leqslant (1.21\times x)+0.27\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&{f}_{4.5\mu {\rm{m}}}\gt {f}_{3.6\mu {\rm{m}}}\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&{f}_{5.8\mu {\rm{m}}}\gt {f}_{4.5\mu {\rm{m}}}\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&{f}_{8.0\mu {\rm{m}}}\gt {f}_{5.8\mu {\rm{m}}}.\end{eqnarray} \tag{ 7 }$$

We require detections in all IRAC bands with S/N limits of 3, 3, 2.4, and 2.1, respectively, in channels 1–4 (Mendez et al. 2013). Our slight modifications are that we do not require the criteria listed in Equation (4) and we allow Equations (5)–(7) to hold within the 1σ errors on the IRAC photometry. The Donley et al. (2012) criteria are very pure, which allows for the creation of a sample without contamination from non-AGNs, but are also fairly restrictive. These slight modifications are made to include a handful of additional sources that are highly likely to be AGNs (for more details, see Azadi et al. 2017).

We also use the BPT diagram to identify optical AGNs. To measure the [N ii]/Hα and [O iii]/Hβ line ratios, we use the line-fitting procedure described in Section 2.2. We exclude any sources that require a significant broad component for either of the Hβ or Hα lines since broad emission lines can dominate over the host galaxy in the broadband photometry and affect the stellar-mass measurements. As shown in Coil et al. (2015) and Azadi et al. (2017), we consider sources above the Meléndez et al. (2014) line to be optical AGNs in our sample, as this line provides a reliable AGN sample for MOSDEF sources when compared to X-ray and IR AGNs in our sample.

We estimate stellar masses in MOSDEF using SED fitting of the multiwavelength photometry from 3D-HST (Skelton et al. 2014) and our spectroscopic redshift measurements. We use the FAST stellar population fitting code (Kriek et al. 2009), with a Chabrier (2003) stellar IMF, Conroy et al. (2009) Flexible Stellar Population Synthesis (FSPS) models, the Calzetti et al. (2000) dust reddening curve, and a fixed solar metallicity, with delayed exponentially declining star formation histories (SFHs).

Radiation from AGNs may contribute to the observed SED, particularly at UV and MIR wavelengths, which could impact our derived stellar masses of their host galaxies. We previously tested fitting the potential contribution from AGNs to the SED using additional power-law contributions to the photometry at UV and MIR wavelengths (Azadi et al. 2017). The FAST code can be run with or without the template error function (which accounts for wavelength-dependent mismatch between the observed photometry and the templates; e.g., Kriek et al. 2009), and as shown in Azadi et al. (2017), the stellar masses that we obtain for MOSDEF AGNs by running FAST without the template error function and subtracting power-law components for the AGN light are consistent with those estimated using the template error function (and not subtracting additional AGN components). Therefore, in this study we use results from FAST with the template error function.

In this study we restrict our analysis to galaxies with 3σ Spitzer/MIPS 24 μm detections. We use 24 μm data from the Far-Infrared Deep Extragalactic Legacy (FIDEL) Survey (Dickinson & FIDEL Team 2007). We use the measurements of Shivaei et al. (2017) for the 24 μm flux densities. In brief, Shivaei et al. (also see Reddy et al. 2010) use higher spatial resolution data from IRAC to determine the location of each object. Around each object a subimage is constructed and a point-spread function (PSF) is fit simultaneously to all sources, including the object of interest, and a covariance matrix is used to determine the robustness of each fit. The background flux is estimated by fitting the PSF to random positions at least 1 FWHM away from the object, and the standard deviation of those fluxes is taken as the noise.

As noted above, we limit our sample to galaxies and AGNs with 1.4 < z < 2.61 to ensure that their 24 μm flux densities cover the rest-frame ∼8 μm luminosity (${L}_{8}=\nu {L}_{\nu }[8\,\mu {\rm{m}}]$). In our analysis we use various luminosity-dependent template sets (e.g., Chary & Elbaz 2001; Dale & Helou 2002; Rieke et al. 2009) to extrapolate the total IR luminosity (${L}_{\mathrm{IR}}$) from the observed 24 μm band; we describe these templates and the procedure to estimate ${L}_{\mathrm{IR}}$ fully in Section 3.2.1 below. We estimate the rest-frame 8 μm luminosity, ${L}_{8}$, based on the same template. The values of ${L}_{8}$ estimated in this manner do not depend significantly on which template set is used; results using the Chary & Elbaz, Dale & Helou, or Rieke et al. template sets are consistent with each other.

As we discuss below in Section 3, including FIR data plays an important role in accurately estimating the bolometric IR luminosity, which allows us to more cleanly select galaxies where the IR emission is substantially elevated relative to the dust-corrected UV. In part of our analysis below (see Section 3.2.3) we include the Herschel/PACS 100 and 160 μm data available in the AEGIS, COSMOS, and GOODS fields (Oliver et al. 2010; Elbaz et al. 2011; Magnelli et al. 2013). The number of MOSDEF galaxies with robust PACS 100 and 160 μm detections is 63 and 58, respectively (40 galaxies have detections at both wavelengths). To measure the 100 and 160 μm flux densities, we use the prescription described above for 24 μm flux densities. We note that the majority of the MOSDEF galaxies do not have a robust detection at 24 μm or FIR wavelengths. While this study is limited to sources with significant 24 μm detection, the ${L}_{\mathrm{IR}}$ from Shivaei et al. (2017) used in Section 3.2.3 is estimated using stacks of the MIPS and Herschel images.

Studying a sample of BzK-selected galaxies at $z\sim 2$, Daddi et al. (2007a) report the existence of a population of so-called "MIR-excess" galaxies for which the total IR luminosity as estimated from the MIPS 24 μm flux densities shows an excess relative to that expected from other SFR tracers. Specifically, they identify MIR-excess sources as galaxies satisfying the following criterion:

$$\begin{eqnarray}&&\mathrm{log}\left(\displaystyle \frac{{\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}}}{{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}}\right)\gt 0.5,\end{eqnarray} \tag{ 8 }$$

where ${\mathrm{SFR}}_{\mathrm{IR}}$ is the SFR estimated from the MIPS 24 μm flux density, ${\mathrm{SFR}}_{\mathrm{UV}}$ is the SFR estimated from the UV data, and ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ is the SFR estimated from the UV data corrected for dust extinction.

The empirical threshold of 0.5 dex is chosen by Daddi et al. (2007a) assuming that the intrinsic scatter in this ratio is symmetric to first order. In their study, Daddi et al. (2007a) use the luminosity-dependent Chary & Elbaz (2001) templates to convert observed 24 μm flux to ${L}_{\mathrm{IR}}$. They correct ${\mathrm{SFR}}_{\mathrm{UV}}$ for dust reddening using the relation between the color excess and $B-z$ color from Daddi et al. (2004), which is derived using a Calzetti et al. (2000) attenuation law. Daddi et al. (2007a) find that ∼25% of their BzK-selected galaxies at $z\sim 2$ show such an excess at MIR wavelengths (after removing the X-ray-detected AGNs from their sample) and emphasize that the existence of this population is independent of the templates used for estimating the bolometric IR luminosity.

As noted above, in this paper we aim to investigate how the templates used for estimating ${L}_{\mathrm{IR}}$ and the choice of the dust correction methods used for estimating ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ (which may depend on the adopted SFH as shown below) affect the identification of MIR-excess galaxies.

In this section we describe various methods used in this study for estimating ${L}_{\mathrm{IR}}$ and for correcting ${\mathrm{SFR}}_{\mathrm{UV}}$ for dust extinction. We implement these methods in Section 3.3 in order to identify MIR-excess galaxies in our sample.

3.2.1. Estimating the Total IR Luminosity from Luminosity-dependent Templates

The first sets of templates adopted in our analysis are luminosity-dependent templates from Chary & Elbaz (2001), Dale & Helou (2002), and Rieke et al. (2009) that estimate ${L}_{\mathrm{IR}}$ from a single 24 μm band observation. We describe each of these template sets in this section.

Chary & Elbaz (2001) construct their templates using data from ISO, IRAS, and SCUBA for local galaxies to create 105 templates covering 0.1–1000 μm.⁹ The ${L}_{\mathrm{IR}}$ (8–1000 μm) is determined using the Sanders & Mirabel (1996) relation. These templates span a range of ${L}_{\mathrm{IR}}$ of 10⁸–10¹³ ${L}_{\odot }$, from normal galaxies to luminous and ultraluminous IR galaxies (LIRGs: 10¹¹ ${L}_{\odot }$ ≤ ${L}_{\mathrm{IR}}$ ≤ 10¹² ${L}_{\odot }$; ULIRGs: ${L}_{\mathrm{IR}}$ ≥ 10¹² ${L}_{\odot }$). The templates are luminosity dependent: a single template describing the IR emission is specified for a given luminosity.

To estimate ${L}_{\mathrm{IR}}$ using the Chary & Elbaz templates, we first shift the templates to the redshift of each source and then convolve them with the MIPS 24 μm response curve. From the 105 templates, we consider the one that at 24 μm returns the closest value to the observed flux as the best template and adopt the luminosity corresponding to that template from Chary & Elbaz (2001) as the total IR luminosity. We convert ${L}_{\mathrm{IR}}$ to ${\mathrm{SFR}}_{\mathrm{IR}}$ using the relationship given in Kennicutt (1998), converted to a Chabrier (2003) IMF. Thus,

$$\begin{eqnarray}&&{\mathrm{SFR}}_{\mathrm{IR}}[{M}_{\odot }\,{\mathrm{yr}}^{-1}]=2.8\times {10}^{-44}\times {L}_{\mathrm{IR}(8\mbox{--}1000\mu {\rm{m}})}[\mathrm{erg}\,{{\rm{s}}}^{-1}].\end{eqnarray} \tag{ 9 }$$

The semi-empirical templates of Dale & Helou (2002) are constructed using data from ISO, IRAS, and SCUBA for 69 local galaxies with ${L}_{\mathrm{IR}(8\mbox{--}1000\mu {\rm{m}})}\lt {10}^{11}\,{L}_{\odot }$. Dale & Helou (2002) develop a theoretical model with three components for the emission from small and large dust grains, as well as PAH molecules (see also Dale et al. 2001). In their model the mass of each dust grain has a power-law distribution as a function of intensity with a slope of α, and different templates are constructed based on variations of α from 1 to 2.5. We use Dale & Helou (2002) templates with the empirical calibration of Marcillac et al. (2006) to scale each template (for a given α) to a specific total ${L}_{\mathrm{IR}}$ (see Equation (1) in Marcillac et al. 2006; see also Papovich et al. 2007; Reddy et al. 2012). We integrate these templates to estimate the total ${L}_{\mathrm{IR}}$ and find the template that provides the best match to the observed 24 μm flux in a similar fashion to that described above for the Chary & Elbaz (2001) templates. We convert ${L}_{\mathrm{IR}}$ to ${\mathrm{SFR}}_{\mathrm{IR}}$ using Equation (9).

Rieke et al. (2009) consider a sample of 11 local LIRGs and ULIRGs with Spitzer/IRS spectra and additional photometric data from optical to radio wavelengths. Rieke et al. (2009) calculate the IR luminosity for each of their galaxies using the Sanders et al. (2003) calibration and combine the SED of the galaxies with similar luminosities to build a set of average templates with ${L}_{\mathrm{IR}(5\mbox{--}1000\mu {\rm{m}})}$ between 10^9.75 and 10¹³ ${L}_{\odot }$. We estimate ${\mathrm{SFR}}_{\mathrm{IR}}$ directly from the 24 μm flux densities using Equation (14) in Rieke et al. (2009). We note that Rieke et al. (2009) assume a Rieke et al. (1993) IMF, which, according to the author, has a similar behavior to the Chabrier IMF assumed throughout this paper.

3.2.2. Estimating the Total IR Luminosity from Luminosity-independent Conversions

3.2.3. Estimating the Total IR Luminosity from Luminosity-independent, Mass-dependent Conversions

3.2.4. Correcting ${\mathrm{SFR}}_{\mathrm{UV}}$ for Dust Absorption

In this section we describe how the ${\mathrm{SFR}}_{\mathrm{UV}}$ is estimated in our work and describe the four methods used to correct ${\mathrm{SFR}}_{\mathrm{UV}}$ for dust extinction. To estimate ${\mathrm{SFR}}_{\mathrm{UV}}$ (uncorrected for dust extinction), we fit the SEDs of our sources using the 3D-HST photometric catalogs and measure the UV flux (at a rest-frame wavelength of 1600 Å) from the best-fit stellar population model (for more details, see Reddy et al. 2015). We convert the estimated luminosity to ${\mathrm{SFR}}_{\mathrm{UV}}$ using the Kennicutt (1998) relation adjusted to a Chabrier (2003) IMF:

$$\begin{eqnarray}&&{\mathrm{SFR}}_{\mathrm{UV}}[{M}_{\odot }\,{\mathrm{yr}}^{-1}]=7.7\times {10}^{-29}\times {L}_{\nu (1600\mathring{\rm A} )}[\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{Hz}}^{-1}].\end{eqnarray} \tag{ 10 }$$

The dust-corrected ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ is given by ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}\,={10}^{0.4{A}_{\mathrm{UV}}}\times {\mathrm{SFR}}_{\mathrm{UV}}$, where A_UV is the UV extinction. To estimate ${A}_{\mathrm{UV}}$, we either use the color excess, $E(B-V)$, from SED fitting assuming A_λ = K(λ) $E(B-V)$, where K is the attenuation curve, or use the UV continuum slope. We also investigate the effect of changing the assumed dust attenuation law and the assumed SFH in the SED modeling. For the dust attenuation we compare the widely used Calzetti et al. (2000) law with the more recent attenuation curve derived by Reddy et al. (2015) using data from the first 2 yr of the MOSDEF survey. For the SFH, we investigate two models: (i) a delayed exponentially declining SFH, and (ii) a constant SFH. We investigate the effect of the adopted dust attenuation law and SFH on the UV extinction correction and consequently on our estimates of ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ and the fraction of MIR-excess sources that are identified.

In our first method for correcting ${\mathrm{SFR}}_{\mathrm{UV}}$, we measure $E(B-V)$ by fitting the SEDs using the FAST code (Kriek et al. 2009) with a Chabrier (2003) IMF, Conroy et al. (2009) FSPS models, a delayed exponentially declining SFH with τ varying from 100 Myr to 1 Gyr, and the Calzetti et al. (2000) reddening curve and assuming a fixed solar metallicity. In the second method we fit the SEDs with all of the same input parameters, except we use the Reddy et al. (2015) attenuation curve.

In the third method, we use the UV spectral slope, β, to estimate the dust correction and derive ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ for each galaxy in our sample. Rather than measuring the slope directly from the photometry, we measure the slope from the fits to the SEDs (we discuss this choice in Section 4.1). The input parameters in the SED fitting remain the same as in the row above. To measure the UV slopes, we follow the prescription of Calzetti et al. (1994) and use several continuum windows spanning 1250–2600 Å to avoid the stellar absorption features at these wavelengths. We then find the average relation between A_UV, as recovered from the full SED fits to each of our galaxies, and the observed value of β:

$$\begin{eqnarray}&&{A}_{\mathrm{UV}}=1.99\beta +4.13.\end{eqnarray} \tag{ 11 }$$

Finally, we recalculate A_UV for each individual galaxy based on the measured β and the average relationship given in Equation (11) above.

We note that our derivation of the average relationship between A_UV and β given in Equation (11) depends on the assumed dust attenuation law and SFH. Our final method for measuring ${A}_{\mathrm{UV}}$ is using the relation between A_UV and β from Reddy et al. (2015):

$$\begin{eqnarray}&&{A}_{\mathrm{UV}}=1.84\beta +4.48.\end{eqnarray} \tag{ 12 }$$

Reddy et al. (2015) obtain this relation using the same method described above for Equation (11), but instead of a delayed exponentially declining SFH they assume a constant SFH with a fixed age of 100 Myr when performing the initial SED fitting. Under this assumption, a higher amount of dust is required to turn an intrinsically blue SED into a given observed SED, while with a slowly declining SFR both populations of old and newly formed stars exist. This mix of stellar population can match an observed SED without requiring as much dust (e.g., Schaerer et al. 2013). Additionally, we note that assuming a constant SFH with an age that is allowed to vary over a range similar to the e-folding time in our delayed-τ model (100 Myr–1 Gyr) results in a similar ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ to that in our third method.

Another approach for estimating the UV continuum reddening is using the nebular reddening. In general, it has been shown that the visual extinction of nebular lines is greater than the reddening of the UV–optical continuum, as the ionizing radiation originates from regions close to the dusty molecular clouds (e.g., Calzetti et al. 1994; Calzetti et al. 2000). We additionally tested correcting the UV emission for dust absorption and estimating the ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ and $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ using the ratio of the Balmer emission lines (Hα/Hβ) and the relation between the nebular and stellar $E(B-V)$ from Reddy et al. (2015, Equations (10) and (13)). While we find that the fraction of MIR-excess galaxies identified with this ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ is relatively low, this correction method results in substantial scatter in $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ compared to the other methods discussed above. This scatter is due to both the relatively low S/N in the observed Hβ flux measurements and the large scatter around the average relation between nebular and stellar reddening (Reddy et al. 2015).

Figures 1–4 illustrate the $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ as a function of redshift for galaxies in the MOSDEF sample, where the ${\mathrm{SFR}}_{\mathrm{IR}}$ in each column is estimated using the templates described in Sections 3.2.1–3.2.3, and ${\mathrm{SFR}}_{\mathrm{UV}}$ is corrected for extinction using different methods described in Section 3.2.4. In these figures we present the median $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ and the percentage of galaxies identified as MIR excess in each panel, with errors estimated from bootstrap resampling. A median ratio close to 1 indicates a good agreement between ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ and ${\mathrm{SFR}}_{\mathrm{UV}}$ +${\mathrm{SFR}}_{\mathrm{IR}}$ for that combination of methods. We note that in some galaxies $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ may legitimately be higher than 1, but we do not expect this ratio to be substantially greater than 1 for the bulk of the population. AGNs are included in Figures 1–4; we discuss the impact of AGNs on the MIR-excess population in Section 3.5.

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We note that each of the methods used to calculate the SFR has uncertainties and caveats (e.g., the effect of the adopted SFH on the UV attenuation estimation, or the uncertainty on the UV continuum slope measurements in optically thick galaxies). We discuss these issues further in Section 4.

Overall, Figures 1 and 2 indicate that the percentage of 24 μm detected galaxies classified as MIR-excess galaxies can vary widely, from 20% to 78%, depending on the templates used to estimate ${L}_{\mathrm{IR}}$ and the ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ estimation. In the first two rows of Figure 1 the percentage of MIR-excess galaxies drops owing to a variation from the Calzetti et al. attenuation curve to that of Reddy et al. As discussed in Reddy et al. (2015), the overall shape of these attenuation curves is similar, but the normalization of Calzetti et al. is higher. The Reddy et al. curve thus results in slightly higher $E(B-V)$ in the red galaxies, which explains the lower percentage of MIR excess and median $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ in the second row of Figure 1. While the numbers do not change significantly from row 2 to row 3 in Figure 1, when we adopt a constant SFH in Figure 2, we find a significantly lower fraction of MIR-excess galaxies. However, the median ratio is closer to 1, indicating that using a constant SFH may result in a larger dust correction when estimating ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$.

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As mentioned above, when the ratio of $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ is close to unity, the SFRs are in better agreement with each other, although each of the SFR tracers has uncertainties (see Section 4, which may result in a scatter around $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ ∼ 1). The median $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ with the methods shown in Figure 1 varies from 2.8 to 11.0. These high values are due primarily to an overestimation of ${L}_{\mathrm{IR}}$ found when applying local templates at high redshifts, as we discussed in Sections 3.2.2 and 3.2.3.

We note that, using the Chary & Elbaz (2001) templates and the Calzetti et al. (2000) attenuation curve, Daddi et al. (2007b) find that ∼20%–30% of BzK-selected $z\sim 2$ galaxies are MIR excess, while we find a much higher fraction of MOSDEF galaxies (61%) with the same prescription. In Section 4 we discuss how various effects result in such a substantial difference in the incidence found in these studies.

In Figure 3 we use luminosity-independent conversions from Elbaz et al. (2011) and Wuyts et al. (2008) for estimating ${L}_{\mathrm{IR}}$. In the left column we use a universal ratio of ${L}_{\mathrm{IR}}$/${L}_{8}$ = 4.9 from Elbaz et al. (2011), and in the right column we use the conversion factors from Wuyts et al. (2008) for MIPS 24 μm fluxes at the redshift of each of our galaxies. Comparing Figures 3 and 1 indicates that using the Elbaz et al. (2011) method results in a substantial decrease in both the median $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ and the fraction of MIR-excess galaxies compared to the Chary & Elbaz (2001) method. However, given the errors, we do not find any significant differences between the numbers resulting from the Wuyts et al. (2008) and the Dale & Helou (2002) methods. Overall, we find that a luminosity-independent conversion such as the Elbaz et al. (2011) universal ratio leads to better agreement between ${\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}}$ and ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ at z ∼ 2.

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In Figure 4 we use $\langle {L}_{\mathrm{IR}}\rangle /\langle {L}_{7.7}\rangle$ given in bins of stellar mass in Shivaei et al. (2017), combined with ${L}_{7.7}$/${L}_{8}$ = 1.25, to estimate ${L}_{\mathrm{IR}}$ for individual galaxies considered in this study. The median $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ ratio indicates an improvement compared to the results shown in the left panel of Figure 1, which uses the same template set but where ${L}_{\mathrm{IR}}$ was estimated directly from the 24 μm data using the luminosity-dependent template from Chary & Elbaz (2001). The percentage of MIR-excess galaxies is substantially lower in Figure 4 as well.

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Overall, the results using the stellar-mass-dependent method of Shivaei et al. (2017, see Figure 4) and the luminosity-independent method of Elbaz et al. (2011, see first column of Figure 3) are consistent with each other. These methods, combined with the ${\mathrm{SFR}}_{\mathrm{UV}}$ extinction correction based on the relation between ${A}_{\mathrm{UV}}$ and β (estimated from the best fit to the SED assuming a delayed exponentially declining SFH model, as shown in the third rows of Figures 3 and 4), lead to $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ close to unity and identification of 22%–32% of our galaxies as MIR excess. We emphasize again that while the similar UV correction method shown in the fourth rows of Figures 3 and 4 (which is derived assuming a constant SFH) leads to a much lower fraction of MIR-excess galaxies, a larger dust correction for estimating ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ may be required.

We further test the methodology of Shivaei et al. (2017) with the Dale & Helou (2002) and Rieke et al. (2009) templates (instead of the Chary & Elbaz 2001 templates) and estimate the average ${L}_{8}$ and ${L}_{\mathrm{IR}}$ values in bins of stellar mass. We show $\langle {L}_{\mathrm{IR}}\rangle /\langle {L}_{8}\rangle$ in bins of stellar mass in Figure 5 and list the values in Table 1. The $\langle {L}_{\mathrm{IR}}\rangle /\langle {L}_{8}\rangle$ ratios estimated using these various templates are consistent with each other. While the three sets of templates used for estimating $\langle {L}_{\mathrm{IR}}\rangle /\langle {L}_{8}\rangle$ in Table 1 are luminosity dependent, we assume that these ratios are luminosity independent and can thus be used to estimate ${L}_{\mathrm{IR}}$ directly for a $z\sim 2$ galaxy with a 24 μm detection, whether or not it is detected with Herschel. Figure 5 also illustrates that the stellar-mass-dependent conversions of Shivaei et al. (2017) are consistent with the single, luminosity-independent conversion factor assumed by Elbaz et al. (2011) for high stellar mass sources ($\mathrm{log}\,{M}_{* }/{M}_{\odot }\gt 10$). Shivaei et al. (2017) find that a larger correction factor is required for lower stellar mass sources, which results in the identification of a larger population of MIR-excess galaxies (32%) with their ${\mathrm{SFR}}_{\mathrm{IR}}$ estimation compared to the Elbaz et al. method (22%). We explore the effect of stellar mass in identification of MIR-excess galaxies further in the next section.

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Table 1.  Average Bolometric Correction Factor, $\langle {L}_{\mathrm{IR}}\rangle /\langle {L}_{8}\rangle$, Determined when Stacked Herschel Data Are Included, Using the Methodology of Shivaei et al. (2017)

$\langle {L}_{\mathrm{IR}}\rangle /\langle {L}_{8}\rangle$	Chary & Elbaz (2001)	Dale & Helou (2002)	Rieke et al. (2009)
$9.6\lt \mathrm{log}\left(\displaystyle \frac{{M}_{* }}{{M}_{\odot }}\right)\lt 10.0$	13.9 ± 3.1	12.5 ± 2.5	15.6 ± 3.9
$10.0\lt \mathrm{log}\left(\displaystyle \frac{{M}_{* }}{{M}_{\odot }}\right)\lt 10.6$	5.21 ±  0.43	4.63 ± 0.34	5.21 ±  0.43
$10.6\lt \mathrm{log}\left(\displaystyle \frac{{M}_{* }}{{M}_{\odot }}\right)\lt 11.6$	6.25 ± 0.31	4.81 ± 0.18	4.31 ± 0.15

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In this section, we examine how the incidence of MIR excess varies with the stellar mass of the galaxies. In the top panels of Figure 6 we plot $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ versus stellar mass for the Daddi et al. (2007b) prescription (left panels) and for our preferred method (right panels), where the stellar masses are derived from SED fitting as discussed in Section 2.4. The correlation coefficients (cc) and their corresponding significance (p) are shown in each panel. We use the r-correlate routine in IDL, which calculates the Spearman's rank correlation coefficient and the significance of its deviation from zero. In the bottom panels we plot the fraction of MIR-excess galaxies as a function of stellar mass in intervals of ${\rm{\Delta }}\mathrm{log}({M}_{* }/{M}_{\odot })=0.5$ dex. We calculate the errors assuming a binomial distribution using the Bayesian method of Cameron (2011).

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The relation between $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ and stellar mass varies from a statistically significant negative trend in the right panel to a statistically significant positive trend in the left panel. It is possible that neither of these trends reflects an intrinsic, underlying correlation, and instead they may be the result of observational selection biases and inaccurate ${L}_{\mathrm{IR}}$ estimates. Figure 6 shows that there is a selection bias in the lowest-mass bin, where we are unable to detect galaxies with low $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$. This selection bias, combined with an overestimation of ${L}_{\mathrm{IR}}$ in more massive galaxies with Chary & Elbaz (2001) templates, leads to an observed positive correlation in the left panel. In the right panel, for massive galaxies we have a more reliable estimate of ${L}_{\mathrm{IR}}$ and therefore find an overall negative trend due to the selection bias at the low-mass end. If we limit our analysis to the four middle stellar-mass bins where the majority of our sources are, we still find a significant difference between the fraction of MIR-excess galaxies in the two panels.

Investigating the relation between ${\mathrm{SFR}}_{\mathrm{IR}}$ and ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ with stellar mass in these two methods can help resolve this discrepancy. The method used by Daddi et al. (2007b) overestimates ${L}_{\mathrm{IR}}$ in moderately massive to massive galaxies compared to our preferred method. There is also a large scatter between ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ and stellar mass using the Daddi et al. (2007b) prescription with the Calzetti et al. (2000) attenuation curve, compared to our preferred methodology with the Reddy et al. (2015) attenuation curve. A combination of these two trends results in the observed differences in the middle stellar-mass bins in Figure 4.

We note that Daddi et al. (2007b) find that MIR-excess sources are preferentially identified in galaxies with large stellar masses and find that the fraction of MIR-excess galaxies increases with increasing stellar mass. While using the same methodology, we also find a significant positive correlation, and as argued above, this could occur as a result of selection biases and ${L}_{\mathrm{IR}}$ overestimation.

Overall, we find that the relation between $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ and stellar mass, as well as the fraction of MIR-excess galaxies in bins of stellar mass, strongly depends on the templates and reddening corrections used. Observational selection biases, inaccurate ${L}_{\mathrm{IR}}$ estimation, and variations in the reddening correction used can lead to the discrepancies between the trends shown in Figure 6.

Several studies have proposed that the observed MIR-excess occurs in galaxies owing to an underlying AGN contribution (e.g., Daddi et al. 2007b; Alexander et al. 2011). Daddi et al. (2007a), after excluding the X-ray-detected AGNs, find that 20%–30% of the $z\sim 2$ galaxies (BzK-selected star-forming galaxies with K < 20.5) are MIR excess and argue that the existence of this population reflects the presence of an underlying obscured AGN population. Generally, AGNs can provide a substantial contribution to the observed MIR emission, though the MIR colors (i.e., IRAC colors) are distinguishable from star-forming galaxies (e.g., Alonso-Herrero et al. 2006; Donley et al. 2012). Here we address the question of whether AGNs may substantially contribute to and perhaps even be the main source of the MIR-excess phenomenon.

While the analysis by Daddi et al. (2007b) was limited to X-ray-selected AGNs, in the MOSDEF survey we benefit from having a sample of AGNs identified at different wavelengths. As discussed in Section 2.3, in addition to X-ray- and IR-detected AGNs, we can use optical BPT selection, which can recover AGNs that might be missed by X-ray and IR imaging (Azadi et al. 2017).

In Figures 1–4 we presented 24 different methods for the identification of MIR-excess galaxies, based on different combinations of methods to correct the UV emission for dust and extrapolate from the observed 24 μm flux to estimate the total IR luminosity. As discussed above, the combination of the dust correction estimated from the UV spectral slope and the Shivaei et al. (2017) method (the luminosity-independent, mass-dependent, $\langle {L}_{\mathrm{IR}}\rangle /\langle {L}_{8}\rangle$ derived using Herschel stacks) results in ${\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}}$ and ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ being consistent for the bulk of the galaxies and is therefore the preferred methodology in this paper. The prescription used by Daddi et al. (2007b) corresponds to using the color excess from the SED fits with the Calzetti et al. reddening curve and the Chary & Elbaz (2001) luminosity-dependent IR templates. We compare our preferred methodology and the Daddi et al. (2007b) prescription in Figure 7 and find the fraction of sources that are identified as X-ray, IR, or optical AGNs above and below the MIR-excess threshold. With the Daddi et al. (2007b) prescription in the top panel of Figure 7 we find a higher percentage of X-ray, IR, and/or optical AGNs at 2σ–3σ in the MIR-excess region. With our preferred method in the bottom panel, we find that none of the three AGN identification techniques result in AGNs being more prevalent in the MIR-excess region. However, the median $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ ratio of 4.9 found with the Daddi et al. (2007b) prescription indicates that the higher incidence of AGNs in MIR-excess galaxies is due to the faulty estimation of the total SFR, and with the more reliable estimates in the bottom panel of this figure we no longer find any evidence for a significantly higher prevalence of AGNs in MIR-excess galaxies.

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We note that while in Figure 7 we illustrate only 2 of the 24 methods of SFR estimation discussed in this paper, we perform a similar analysis for all the other methods as well. Of the other 22 combinations of methods investigated for SFR estimation, none result in a significantly higher fraction (at even the 2σ level) of AGNs among MIR-excess galaxies than in MIR-normal galaxies.

X-ray detection is a well-known, reliable method for robust AGN identification (e.g., Mendez et al. 2013; Azadi et al. 2017); however, it fails to identify highly absorbed AGNs with hydrogen column densities of ${N}_{{\rm{H}}}\gt 1.5\times {10}^{24}$ cm⁻² (e.g., Della Ceca et al. 2008; Comastri et al. 2011). Studies predict that 10%–50% of AGNs are Compton thick (e.g., Akylas & Georgantopoulos 2009; Alexander et al. 2011; Lanzuisi et al. 2015). The absorbed and reprocessed radiation from these AGNs buried in dust may contribute to the observed MIR radiation in galaxies.

To examine whether the excess observed at MIR wavelengths in our galaxies occurs as a result of obscured AGN activity, we exclude the X-ray-detected AGNs from our sample and then stack the X-ray photons from the remaining sources. In this section we investigate the hardness ratio (H–S/H+S), where H and S are the net count rates in the hard (rest-frame 2–10 keV) and soft (rest-frame 0.5–2 keV) X-ray bands, respectively, and are calculated for both the MIR-excess and MIR-normal galaxies. The hardness ratio is a tracer of the X-ray spectrum shape and the amount of obscuration. A positive hardness ratio indicates sources with a hard X-ray spectrum, indicating obscured AGNs, while a negative hardness ratio indicates sources with a softer spectrum, unobscured AGNs or the X-ray emission from star-forming galaxies. To estimate H and S, we use the number of counts measured within an aperture with a radius corresponding to 70% of the enclosed energy fraction for the PSF at each galaxy position, while the background is determined from background maps based on smoothing of local counts.

In Figure 8 we present the hardness ratio for the MIR-excess (purple) and MIR-normal (gray) galaxies using the Daddi et al. (2007b) method (left) and our preferred method (right). The errors on the hardness ratios are calculated using bootstrap resampling. We find a relatively harder signal in MIR-normal galaxies compared to the MIR-excess population (at the 2σ level with our preferred method). The negative hardness ratios indicate that a soft X-ray signal dominates in MIR-excess galaxies. When we consider all the other combinations of methods as discussed above, in none of them does the hardness ratio of MIR-excess galaxies reflect an underlying hard spectrum that could be due to an AGN. Finding a harder spectrum in MIR-normal galaxies compared to MIR-excess galaxies is at odds with the findings of Daddi et al. (2007b).

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We also calculate the average X-ray luminosities for the MIR-normal and MIR-excess galaxies based on our X-ray stacking in the hard X-ray band. When using our preferred method to identify MIR-excess galaxies, we measure an average rest-frame 2–10 keV X-ray luminosity of $\mathrm{log}({L}_{2\mbox{--}10\mathrm{keV}}/\mathrm{erg}\,{{\rm{s}}}^{-1})=42.7\pm 0.10$ for the MIR-normal galaxies. This luminosity is higher than the expected X-ray emission due to star formation processes: $\mathrm{log}({L}_{\mathrm{SF}}/\mathrm{erg}\,{{\rm{s}}}^{-1})\approx 42$ for z ∼ 2.1 star-forming galaxies with stellar masses ∼10^10.5 M_⊙, typical for our sample (see Lehmer et al. 2016; Aird et al. 2017).

For the MIR-excess galaxies we find a slightly lower average luminosity, $\mathrm{log}({L}_{2\mbox{--}10\mathrm{keV}}/\mathrm{erg}\,{{\rm{s}}}^{-1})=42.5\pm 0.12$. We note that while the luminosities of both of these populations are consistent with a star formation origin, the slightly higher ${L}_{(2\mbox{--}10\mathrm{keV})}$ in both MIR-excess and MIR-normal galaxies compared to the main sequence of star formation (for a similar stellar mass and redshift regime) could be due to some contribution from X-ray-undetected AGNs in this sample, as might be expected. The slightly lower ${L}_{{\rm{X}}}$ in MIR-excess galaxies compared to the MIR-normal galaxies may be due to the slightly lower masses of MIR-excess galaxies ($1.7\times {10}^{10}\,{M}_{\odot })$ compared to the MIR-normal galaxies ($2.9\times {10}^{10}\,{M}_{\odot }$).

Using the Daddi et al. (2007b) prescription, we find $\mathrm{log}({L}_{2\mbox{--}10\mathrm{keV}}/\mathrm{erg}\,{{\rm{s}}}^{-1})=42.5\pm 0.14$ for the MIR-normal galaxies and $\mathrm{log}({L}_{2\mbox{--}10\mathrm{keV}}/\mathrm{erg}\,{{\rm{s}}}^{-1})=42.6\pm 0.10$ for MIR-excess galaxies. The luminosities and the hardness ratios of the MIR-normal and MIR-excess galaxies identified with the Daddi et al. (2007b) method are both consistent with a star formation origin. The hard spectrum of the MIR-excess galaxy sample originally identified by Daddi et al. (2007b) is probably due to a few undetected X-ray AGNs, which would be detected with deeper X-ray surveys (see also Alexander et al. 2011; Rangel et al. 2013).

We showed in the section above that there is not a higher fraction of detected AGNs above the MIR-excess threshold than below it with our preferred method. Here we find that a stacking analysis of our X-ray-undetected sample does not indicate a harder spectrum in MIR-excess galaxies than in MIR-normal galaxies, which shows that AGNs do not contribute substantially to the MIR radiation in our MIR-excess sample.

In MOSDEF we benefit from having spectroscopic measurements for a statistically large sample of galaxies at z ∼ 2. Therefore, we can also estimate the SFR based on the Hα emission line (hereafter ${\mathrm{SFR}}_{{\rm{H}}\alpha }$) and investigate whether MIR-excess galaxies have elevated ${\mathrm{SFR}}_{{\rm{H}}\alpha }$ compared to the MIR-normal galaxies.

In Figure 9 we illustrate $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ versus ${\mathrm{SFR}}_{{\rm{H}}\alpha }$/${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ for the galaxies and AGNs in our sample. For this analysis we limit our sample to the sources with significant (>3σ) Hα and Hβ detections, which decreases our sample size to 114 sources. ${\mathrm{SFR}}_{{\rm{H}}\alpha }$ is calculated from the luminosity of the Hα line using the relation given by Kennicutt (1998) and is corrected for attenuation using the Balmer decrement (Hα/Hβ). Similar to the plots shown above, AGNs are included in this analysis and are shown in orange, although the AGNs may contribute to the Hα emission. The horizontal dotted line is the threshold of $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ ∼ 3.2 defined by Daddi et al. (2007b) for MIR-excess identification. The vertical dotted line shows the equivalent threshold on ${\mathrm{SFR}}_{{\rm{H}}\alpha }$/${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ ∼ 3.2, identifying sources that exhibit an excess in Hα emission (relative to the dust-corrected UV continuum emission).

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In both the Daddi et al. (2007b) prescription (left) and our preferred methodology (right) we find a positive trend between $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ and ${\mathrm{SFR}}_{{\rm{H}}\alpha }$/${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$. In both panels the majority of the MIR-normal galaxies also have ${\mathrm{SFR}}_{{\rm{H}}\alpha }$/${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ less than the vertical threshold, and only a very few of the MIR-normal galaxies are beyond this limit. The majority of MIR-excess galaxies identified with our prescription are below the vertical limit in the right panel, while with the Daddi et al. (2007b) prescription in the left panel almost half of them are above the vertical limit. However, as discussed above, such a high $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ using the Daddi et al. (2007b) prescription is due to an overestimation of the total IR luminosity. We also note that almost 40% of the MIR-excess sources that are beyond the vertical limit are AGNs in both panels and are expected to have elevated Hα emission.

Overall, Figure 9 shows that MIR-excess galaxies in MOSDEF do not necessarily have high ${\mathrm{SFR}}_{{\rm{H}}\alpha }$/${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ values. Therefore, while the elevated ${\mathrm{SFR}}_{\mathrm{IR}}$ in ∼30% of the galaxies in our sample may be due to legitimately higher ${\mathrm{SFR}}_{\mathrm{IR}}$ than other SFR tracers, it may also be the result of an overestimation of ${\mathrm{SFR}}_{\mathrm{IR}}$.

In Section 3 (Figures 1–4), we examine various methods for the reddening correction of the UV photometry: using the color excess estimated directly from SED fitting with the Calzetti et al. (2000) and Reddy et al. (2015) attenuation curves, and using the average relationship between reddening and UV continuum slope assuming either a delayed-τ or constant SFH model for the underlying stellar population. Our results show that the different methods for estimating the reddening correction result in substantial changes to the fraction of MIR-excess galaxies identified (for a given set of IR templates).

Using the attenuation curve of Reddy et al. (2015) results in a decrease in $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ and the fraction of MIR-excess, compared to using the widely adopted Calzetti et al. (2000) attenuation curve. The magnitude of the decrease depends on the ${L}_{\mathrm{IR}}$ templates used. As discussed in Reddy et al. (2015), the overall shapes of the Calzetti et al. and Reddy et al. attenuation curves are identical at short wavelengths, but the Reddy et al. curve has a lower normalization. The substantially redder $E(B-V)$ (${\rm{\Delta }}E(B-V)$ ∼ 0.1) of Reddy et al.¹⁰ results in a higher UV correction factor compared to Calzetti et al. and hence a lower fraction of MIR-excess galaxies.

We find that using the UV spectral slope for the reddening correction, along with robust estimates of ${L}_{\mathrm{IR}}$, results in a median $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ ratio close to unity, illustrating a consistency between the ${\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}}$ and ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ measurements. Using the UV slope also results in the lowest percentage of MIR-excess galaxies (12%–74% depending on the ${L}_{\mathrm{IR}}$ estimation and the adopted SFH).

The UV slope used in this analysis is measured by fitting a power law to the SED fit (${\beta }_{\mathrm{SED}}$) at 1200–2600 Å assuming a delayed-τ SFH model (see Section 3.2.4). However, it is also common to estimate the UV slope by fitting a power law directly to the photometric data (${\beta }_{\mathrm{phot}}$) at these wavelengths (e.g., Reddy et al. 2015; Shivaei et al. 2015b). We find for the MOSDEF sample that using ${\beta }_{\mathrm{phot}}$ instead of ${\beta }_{\mathrm{SED}}$ increases the fraction of MIR-excess galaxies from 32% ± 3% to 50% ± 3% and the median $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ to 3.2 (using Shivaei et al. 2017, ${L}_{\mathrm{IR}}$ estimates). In Figure 10 we plot ${\beta }_{\mathrm{phot}}$ versus ${\beta }_{\mathrm{SED}}$ and find that while the values roughly scatter around the 1:1 line, the best-fit line is ${\beta }_{\mathrm{SED}}=0.8{\beta }_{\mathrm{phot}}+0.1$. This results in a larger extinction correction factor (${10}^{0.4{A}_{\mathrm{UV}}}$, assuming Equation (11)) using ${\beta }_{\mathrm{SED}}$, and consequently a smaller fraction of MIR-excess galaxies are identified using ${\beta }_{\mathrm{SED}}$ instead of ${\beta }_{\mathrm{phot}}$.

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The error bars in Figure 10 demonstrate the large uncertainty in the ${\beta }_{\mathrm{phot}}$ measurements, due to the relatively large errors on the UV photometric data, particularly in red galaxies that are faint at UV and optical wavelengths. Despite the large errors, ${\beta }_{\mathrm{phot}}$ provides an estimation of the slope independent of any assumption about the stellar population, while ${\beta }_{\mathrm{SED}}$ relies on the models adopted in the SED fitting. However, this can be a disadvantage in galaxies that have redder slopes owing to an older stellar population rather than dust obscuration. We note that while the errors on ${\beta }_{\mathrm{SED}}$ are not calculated here, they are expected to be smaller than the errors on ${\beta }_{\mathrm{phot}}$, as they are estimated using many more photometric data points.

Overall, we find that ${\beta }_{\mathrm{SED}}$ provides a good estimate of ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ when comparing ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ with ${\mathrm{SFR}}_{\mathrm{UV}}$ +${\mathrm{SFR}}_{\mathrm{IR}}$, and the commonly used ${\beta }_{\mathrm{phot}}$ may underestimate the reddening correction factor, as it results in a substantially higher fraction of MIR-excess galaxies and average $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$. Fitting a power law to the SED to estimate the UV spectral slope may be more reliable than fitting to the photometry directly, due to the larger uncertainties in the UV photometric data.

In this study we considered the use of six different templates/correction factors to estimate the total ${L}_{\mathrm{IR}}$ for the MOSDEF galaxies from the observed 24 μm flux. We find that extrapolating from the observed 24 μm data using templates based on local galaxies results in an overestimation of ${L}_{\mathrm{IR}}$ (see also Reddy et al. 2012) and consequently overestimates the fraction of MIR-excess galaxies. Our results using the methodologies of Elbaz et al. (2011) and Shivaei et al. (2017), considering luminosity-independent corrections that were calibrated using stacks of the FIR data, leads to a more accurate estimation of ${L}_{\mathrm{IR}}$ (as also seen in Santini et al. 2009; Elbaz et al. 2010, 2011; Nordon et al. 2010; Rodighiero et al. 2010, among others). Using the methods of Elbaz et al. (2011) and Shivaei et al. (2017) (along with the UV spectral slope), we identify 22% ± 3% and 32% ± 3% of our galaxies, respectively, as MIR-excess galaxies; these fractions are lower than those obtained using other IR templates. The advantage of Shivaei et al. (2017) is that it takes into account the dependence of $\langle {L}_{\mathrm{IR}}\rangle /\langle {L}_{8}\rangle$ on stellar mass. As illustrated in Figure 5, the ratios using the Shivaei et al. (2017) method (with the template sets of Chary & Elbaz 2001; Dale & Helou 2002; or Rieke et al. 2009) are generally consistent with ${L}_{\mathrm{IR}}$/${L}_{8}$ from Elbaz et al. (2011) and are discrepant only in our lowest stellar-mass bin of ${M}_{* }\lt {10}^{10}\,{M}_{\odot }$.

Using a robust ${L}_{\mathrm{IR}}$ estimation and the UV slope for the reddening correction, we find that ∼30% of the galaxies in our sample are MIR excess. Our analysis in Sections 3.5 and 3.6 does not provide any evidence for substantial AGN contribution in MIR-excess galaxies compared to the MIR-normal galaxies. Therefore, the excess MIR radiation detected in ∼30% of our sources is likely due to other phenomena contributing to MIR radiation. The observed 24 μm band at $z\sim 2$ also includes line emission from PAH molecules at rest-frame wavelengths of 5–12 μm. Therefore, the incidence of MIR excess may be due to PAH features in normal star-forming galaxies entering the infrared bands (see also Nordon et al. 2010; Lutz et al. 2011; Nordon et al. 2012).

While studies predict that 5%–20% of the bolometric IR radiation is from PAH molecules (e.g., Smith et al. 2007; Shipley et al. 2016), the strength of radiation from PAH molecules varies with galaxy stellar mass, metallicity, and/or star formation activity (e.g., Engelbracht et al. 2006; Smith et al. 2007; Shipley et al. 2016; Shivaei et al. 2017). Shivaei et al. (2017), after including PAH features in their templates and determining calibrations from Herschel data, find that the PAH radiation at 7.7 μm depends on the age and stellar mass of galaxies and is lower in young galaxies with ages ≲500 Myr, as well as galaxies with ${M}_{* }\lt {10}^{10}\,{M}_{\odot }$. Our analysis in the right panel of Figure 6 indicates that at ${M}_{* }\lesssim {10}^{10}\,{M}_{\odot }$ we identify many MIR-excess galaxies. This high incidence of MIR excess in low-mass galaxies could be due to a selection effect: given that our sample is selected based on 24 μm observations, if a galaxy has strong PAH features, it is more likely to be detected at 24 μm and to be included in our sample. While according to Shivaei et al. (2017) in lower-mass galaxies, for a given ${L}_{\mathrm{IR}}$, PAH emission is suppressed, there could also be an increased scatter in the strength of PAH emission in individual galaxies at lower mass. Such an increased scatter could result in a higher fraction of MIR-excess galaxies at M_* ≲ 10¹⁰ M_☉.

Indeed, the scatter in the relative strength of PAH emission to ${L}_{\mathrm{IR}}$ is lower in moderate-mass galaxies with M_* > 10¹⁰ M_☉ (Shivaei et al. 2017). If we limit our analysis to galaxies with M_* > 10¹⁰ M_☉, where we likely do not have stellar-mass selection biases in our sample, the fraction of MIR-excess galaxies decreases to 24% ± 2%. However, given that ${\mathrm{SFR}}_{{\rm{H}}\alpha }$ is not elevated in the MIR-excess galaxies in our sample, the intrinsic fraction of MIR-excess may be even lower than 24%.

Our multiwavelength AGN and X-ray stacking analysis shows that it is unlikely for either detected or undetected AGNs to contribute substantially to the MIR excess observed in our MIR-excess galaxies. Following a similar prescription to that of Daddi et al. (2007b) for SFR estimations, we find that X-ray AGNs are more prevalent in the MIR-excess region at the 2σ level and that IR and optical AGNs show the same behavior as well (despite the fact that, unlike Daddi et al. (2007b), our sample is not BzK selected). However, when using more robust estimates of SFRs, we do not find a higher incidence of AGNs in the MIR-excess region; therefore, the higher prevalence of detected AGNs in MIR-excess sources using the methodology of Daddi et al. (2007b) primarily occurs as a result of inaccurate SFR estimates.

More recently, using similar methodologies to those of Daddi et al. (2007b), Rangel et al. (2013) find that at $z\sim 2$ the fraction of X-ray-detected AGNs above the MIR-excess threshold is three times higher than below the threshold. However, they argue that this is due to a strong correlation between $({\mathrm{SFR}}_{\mathrm{IR}}+{\mathrm{SFR}}_{\mathrm{UV}})/{\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ and ${L}_{\mathrm{IR}}$ and show that the fraction of X-ray-detected AGNs above and below the MIR-excess threshold is very similar if considered in narrow bins of ${L}_{\mathrm{IR}}$.

Our stacking analysis in Figure 8 shows that the hardness ratio of X-ray-undetected MIR-excess and MIR-normal galaxies does not vary depending on the methods used to estimate SFRs. Unlike in Daddi et al. (2007b), in almost all of our combinations of methods we find a harder X-ray spectrum for MIR-normal galaxies than for the MIR-excess population, indicating, if anything, a higher incidence of AGNs in the normal galaxies than the MIR-excess population. With our preferred methodology (right column of Figure 8) we find that the MIR-excess galaxies have a soft X-ray spectrum with a hardness ratio of −0.16 ± 0.14 and an average X-ray luminosity of ∼10⁴² erg s⁻¹ in both the soft and hard X-ray bands, consistent with a minimal AGN contribution and the bulk of the X-ray emission from the MIR-excess galaxies being associated with star formation.

Using deep X-ray data in the CDFN and CDFS fields, Rangel et al. (2013) stack the X-ray-undetected sources and find hardness ratios of −0.50 ± 0.12 and −0.45 ± 0.15, respectively, above and below the MIR-excess threshold. Neither of these hardness ratios indicates the presence of underlying obscured AGN activity. By limiting their sample to the same depth (1 Ms) as Daddi et al. (2007b), Rangel et al. (2013) find a harder spectrum with a hardness ratio of −0.16 ± 0.16 for MIR-excess galaxies and argue that the relatively harder spectrum in Daddi et al. (2007b) is due to a few undetected X-ray AGNs in that sample that are detected with the deeper X-ray data. These findings indicate that some of the sources identified as MIR excess in the Daddi et al. (2007b) sample are indeed obscured AGNs, but this does not show that an MIR excess occurs generally owing to a contribution from AGNs.

While the Daddi et al. (2007b) and Rangel et al. (2013) samples utilize the CDFS and CDFN fields (see also Alexander et al. 2011), MOSDEF spans a larger number of fields, which have different X-ray depths. To investigate the effect of X-ray depth, we estimate the hardness ratio of the X-ray-undetected sample in each of our fields above and below the MIR-excess threshold, using our preferred method for SFR estimates. We do not find a harder spectrum in MIR-excess stacks compared to the MIR-normal galaxies in any of these fields. Overall, our stacking analysis does not indicate a hard X-ray spectrum or a strong AGN contribution to MIR-excess galaxies.

In this study using our preferred methodology we identify 32% ± 3% of the MOSDEF sample as MIR-excess galaxies. As discussed in Section 4.2, once the stellar-mass selection biases are taken into account, this fraction decreases to 24% ± 2%. While these fractions are similar to the fraction of MIR-excess galaxies (∼20%–30%) identified by Daddi et al. (2007b) in their BzK-selected sample at a similar redshift and a similar stellar-mass regime, as discussed extensively above, the overestimation of ${L}_{\mathrm{IR}}$ in the Daddi et al. (2007b) analysis is likely to play an important role in their identification of MIR-excess galaxies. Using a similar approach to Daddi et al. (2007b) (in column 1, row 1 of Figure 1), we identify 61% ± 3% of our sources as MIR-excess galaxies.

We note additional minor differences in our approaches: here we use the color excess estimated from SED fitting with the Calzetti et al. (2000) attenuation curve for the reddening correction in our estimate of ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$, whereas Daddi et al. (2007b) use the relation between $E(B-V)$ and $B-z$ color from Daddi et al. (2004) assuming the Calzetti et al. (2000) attenuation curve. In addition, the Daddi et al. (2007b) sample is BzK selected, and different galaxy selections could lead to differences in the MIR-excess fraction. With a similar ${L}_{\mathrm{IR}}$ estimation to that of Daddi et al., using our UV spectral slope method instead of the Calzetti et al. attenuation curve results in a significant decrease in the MIR-excess fraction in Figure 1. Therefore, the identification of a large population of MIR-excess galaxies when reproducing the Daddi et al. (2007b) method appears to be due to underestimating the dust-corrected ${\mathrm{SFR}}_{\mathrm{UV},\mathrm{corr}}$ combined with an overestimate of ${\mathrm{SFR}}_{\mathrm{IR}}$ due to the use of locally calibrated, luminosity-dependent IR templates.

With a more careful estimation of the SFRs, and after correcting for stellar-mass selection biases, in this work we find that 24% of our $z\sim 2$ galaxies are MIR excess. This incidence is primarily due to enhanced PAH emission at z ∼ 2 in moderate-mass galaxies, rather than obscured AGN activity. PAH emission may also affect the incidence of MIR excess in the Daddi et al. sample, but the inaccurate SFR estimation is likely to play a dominant role in their analysis.