The FMOS-COSMOS Survey of Star-forming Galaxies at z ∼ 1.6. VI. Redshift and Emission-line Catalog and Basic Properties of Star-forming Galaxies

Our main galaxy sample is based on the COSMOS photometric catalogs (Capak et al. 2007; Ilbert et al. 2010, 2013; McCracken et al. 2010, 2012) that include the UltraVISTA/VIRCam photometry. For observations after February 2015, we used the updated photometric catalog from Ilbert et al. (2015). For each galaxy in these catalogs, the global properties, such as photometric redshift, stellar mass, SFR, and level of extinction, are estimated from SED fits to the broad- and intermediate-band photometry using LePhare (Arnouts et al. 2002; Ilbert et al. 2006). We refer the reader to Ilbert et al. (2010, 2013, 2015) for further details. For the target selection, we computed the predicted flux of the Hα emission line from the intrinsic SFR and extinction estimated from our own SED fitting adopting a constant SFH (see Silverman et al. 2015b).

For the FMOS H-long spectroscopy, we preferentially selected galaxies that satisfy the criteria listed below.

• 1.  
  ${K}_{{\rm{S}}}\leqslant 23.5$, a magnitude limit on the UltraVISTA K_S-band photometry (auto magnitude).
• 2.  
  $1.46\leqslant {z}_{\mathrm{phot}}\leqslant 1.72$, a range for which Hα falls within the FMOS H-long spectral window.
• 3.  
  ${M}_{* }\geqslant {10}^{9.77}\,{M}_{\odot }$ (for a Chabrier IMF)
• 4.  
  Predicted total (not in-fiber) Hα flux ${F}_{{\rm{H}}\alpha }^{\mathrm{pred}}\geqslant 1\,\times {10}^{-16}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$.

We refer to those satisfying all of the above criteria as Primary objects. From the COSMOS photometric catalog, 3876 objects are identified as meeting the above criteria (the Primary-parent sample), and 1582 objects were observed in the H-long mode (the Primary-HL sample).

Figure 2 shows the SFR as a function of M_* for the Primary-parent sample (red contours) and the Primary-HL sample (blue circles). The observed objects trace the so-called main sequence (e.g., Noeske et al. 2007) of star-forming galaxies over two orders of magnitude in stellar mass. However, the limit on the predicted Hα flux removed a substantial fraction (60%) of potential targets selected only with the K_S and M_* criteria (shown by black dashed contours). In Figure 2, we indicate median SFRs in bins of M_* separately for the parent galaxies limited with and without the limit on the predicted Hα flux. It is shown that the limit on ${F}_{{\rm{H}}\alpha }^{\mathrm{pred}}$ results in the observed sample being biased $\sim 0.2\,\mathrm{dex}$ higher in the average SFR at all stellar masses. We found that the Primary-HL sample includes 70 objects detected by Chandra X-ray observations (see Section 3.3) by checking counterparts. These X-ray-detected objects are excluded for studies of the properties of a pure star-forming population.

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In addition to the Primary sample, the FMOS-COSMOS catalog contains a substantial number of star-forming galaxies at z ∼ 1.6 not satisfying all of the criteria described above. This is because the criteria were loosened down to M_* ≥ 10^9.57 M_⊙ and/or ${F}_{{\rm{H}}\alpha }^{\mathrm{pred}}\geqslant 4\times {10}^{-17}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$ for a part of the runs, and we also allocated a substantial number of fibers through the program to those at z ∼ 1.6 identified in the photometric catalog but not satisfying all of the criteria for the Primary objects. We refer to these objects observed in the H-long mode as the Secondary-HL sample, which contains 1242 objects. In Figure 3, we show the distributions of galaxy properties for both the Primary-HL and the Primary+Secondary-HL objects. The Secondary-HL sample includes objects with lower or higher z_phot and/or lower M_* outside the limits, while the majority are those with ${F}_{{\rm{H}}\alpha }^{\mathrm{pred}}$ lower than the threshold.

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In Figure 4, we show the Primary-HL and Secondary-HL objects in the (B − z) versus (z − K) diagram. These colors are based on the photometric measurements (Subaru B and z⁺⁺ and UltraVISTA K_S) given in the COSMOS2015 catalog (Laigle et al. 2016). It is demonstrated that the majority (95%) of the Primary+Secondary-HL sample match the so-called sBzK selection (Daddi et al. 2004).

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Herschel-PACS observations cover the COSMOS field at 100 and 160 μm down to 5σ detection limits of ∼8 and ∼17 mJy, respectively (Lutz et al. 2011). These limits correspond to an SFR of roughly 100 M_⊙ yr⁻¹ at z ∼ 1.6. We allocated fibers to these far-IR-luminous objects for particular studies of starburst and dust-rich galaxies (e.g., Kartaltepe et al. 2015; Puglisi et al. 2017) also in view of their follow-up with ALMA (Silverman et al. 2015a, 2018a, 2018b). The objects were selected by cross-matching between the Herschel-PACS Evolutionary Probe (PEP) survey catalog and the IRAC-selected catalog of Ilbert et al. (2010), and their stellar mass and SFR are derived from SED fits (further detailed in Rodighiero et al. 2011). For these objects, a higher priority with respect to fiber allocation had to be made, since these objects are rare and would not be sufficiently targeted otherwise.

Our parent sample of the PACS sources contains 231 objects in the range $1.44\leqslant {z}_{\mathrm{phot}}\leqslant 1.72$, and 116 objects were selected for FMOS H-long spectroscopy. We refer to these objects as the PACS-HL sample. Figure 2 shows the distribution of the Herschel-PACS sample in the M_*-versus-SFR plot. It is shown that these objects are limited to be above an SFR of $\sim 100\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$. Further analyses of this subsample are presented in companion papers (Puglisi et al. 2017; J. Kartaltepe et al. 2019, in preparation).

We have dedicated a fraction of FMOS fibers to obtaining spectra for optical/near-infrared counterparts to X-ray sources from the Chandra COSMOS Legacy survey (Elvis et al. 2009; Civano et al. 2016). The FMOS-COSMOS catalog includes 84 X-ray-selected objects intentionally targeted as compulsory. However, there are many X-ray sources other than those that have been targeted as star-forming galaxies (i.e., the Primary/Secondary-HL sample) or infrared galaxies. We thus performed position matching between the full FMOS-COSMOS catalog and the full Chandra COSMOS Legacy catalog.¹⁵ In total, we found an X-ray counterpart for 742 (including the intended 84 objects) of the FMOS extragalactic objects. Most of these X-ray-detected objects are probably AGN-hosting galaxies. These objects are not included in the analyses presented in the rest of this paper, but studies of these X-ray sources are presented in companion papers (Schulze et al. 2018; D. Kashino et al. 2019, in preparation).

We also allocated a substantial number of fibers to observing lower-redshift (0.7 ≲ z ≲ 1.1, where Hα falls in the J-long window) infrared galaxies selected from S-COSMOS Spitzer-MIPS observations (Sanders et al. 2007) and Herschel-PACS and SPIRE from the PEP (Lutz et al. 2011) and HerMES (Oliver et al. 2012) surveys, respectively. We used the photometric redshifts of Salvato et al. (2011, for X-ray-detected AGNs) and Ilbert et al. (2015) and for the source selection. We derived the total IR luminosity, calculated from the best-fit IR template using the SED fitting code LePhare and integrating from 8 to 1000 μm. These luminosities are in the range ${10}^{11}\lesssim {L}_{\mathrm{IR}}/{L}_{\odot }\lesssim {10}^{12.5}$, spanning the luminosity regime of luminous and ultraluminous infrared galaxies (LIRGs and ULIRGs; see review by Sanders & Mirabel 1996). Our parent sample includes 1818 objects in the range $0.66\leqslant {z}_{\mathrm{phot}}\leqslant 1.06$. Of these, we observed 344 in the J-long mode. Further analysis of this particular subsample will be presented in a future paper (J. Kartaltepe et al. 2019, in preparation).

The collected spectral data have been processed with the standard reduction pipeline, FIBRE-pac (Iwamuro et al. 2012), generating one- and two-dimensional (1D and 2D, respectively) spectra for each object. The relevant noise and squared-noise spectra are also provided by the pipeline. The noise level is estimated from the pixel variance between the observed frames. Examples of these spectra are shown in Silverman et al. (2015b; see Figure 10). We first visually inspected all 1D and 2D spectra to search for the presence of the emission lines using the graphical interface SpecPro¹⁶ (Masters & Capak 2011), and then we performed emission-line fitting to the 1D spectra as described in Section 4.2.

The FMOS spectrographs are equipped with a mask mirror to block the light at the wavelengths of bright OH airglow lines to avoid the saturation (Kimura et al. 2010). Thus, the OH mask effectively reduces the spectral coverage. The observed spectra are quite noisy at the wavelengths of the OH mask and unmasked sky lines. Correspondingly, the noise spectra show sudden increases in the noise level at these wavelengths. As described below, these wavelengths are removed for the emission-line fitting and continuum flux measurements (see Figures 11 and 14 of Silverman et al. 2015b).

The amount of wavelength coverage lost by the OH mask and residual sky lines should be taken into account to evaluate the success rate of the observations (see Section 5.1). To estimate the fraction of the lost coverage, we should keep in mind that the original IRS1 OH mask was replaced with a copy of the mask used in IRS2 in mid-2012. Thus, our first seven runs conducted in 2012 March were carried out with the old mask (see Table 1), while subsequent observations were conducted with the newer one. This change was intended to homogenize the performance between the two spectrographs and reduce the amount of wavelength coverage lost by the rather conservative mask originally implemented in IRS1. Furthermore, for a period of the H-long observations in 2012 March, the OH mask was misaligned in IRS2; thus, some additional pixels at OH-free wavelengths were masked out. This problem was fixed for the latter observations. In the H-long mode, the typical fraction of wavelength coverage lost by the OH mask and residual sky lines is ≈0.30, on average, throughout the project. In 2012 March, however, this fraction was elevated to 0.40 (IRS1) and 0.34 (IRS2) due to using the old mask mirror and the misalignment, respectively. In the J-long mode, the typical lost fraction is ≈0.27, being elevated to 0.35 (only IRS1) in a single run conducted in 2012 March.

Our procedure for emission-line fitting makes use of the IDL package mpfit (Markwardt 2009). Candidate emission lines were modeled with a Gaussian profile after subtracting the continuum. The Hα and [N ii] or Hβ and [O iii] lines were fit simultaneously while fixing the velocity widths to be the same and allowing no relative offset for the line centroids. The flux ratios of the doublets [N ii] λ6584/6548 and [O iii] λ5007/4959 were fixed to be 2.96 and 2.98, respectively (Storey & Zeippen 2000).

The spectral data processed with FIBRE-pac are given in units of μJy, which were converted into flux density per unit wavelength, i.e., $\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}\,{\mathring{\rm A} }^{-1}$, before fitting. The observed flux density ${F}_{\lambda ,i}$, where i denotes the pixel index, was fit with weights defined as the inverse of the squared-noise spectra output by the pipeline. The weights W_i were set to zero for the pixels impacted by the OH mask or sky residuals.

We assessed the quality of the fitting results based on the signal-to-noise ratio (S/N) calculated from the formal errors on the model parameters returned by the mpfitfun code. We emphasize that these S/Ns do not include the uncertainties on the absolute flux calibration described in later sections. In addition, we have also estimated the fraction of flux lost by bad pixels (i.e., pixels with W_i = 0). For all lines, we define the "bad-pixel loss" as the fraction of the contribution occupied by the bad pixels to the total integral of the Gaussian profile,

$$\begin{eqnarray}&&{f}_{\mathrm{badpix}}=\displaystyle \frac{{\displaystyle \sum }_{\left\{i| {W}_{i}=0\right\}}{P}_{i}}{{\displaystyle \sum }_{i}{P}_{i}},\end{eqnarray} \tag{ 1 }$$

where P_i is the flux density of the best-fit Gaussian profile at the ith pixel (not the observed spectrum). We disregard any tentative line detections if ${f}_{\mathrm{badpix}}\gt 0.7$.

The goodness of the line fits is given by the reduced χ² statistic, ${\chi }^{2}/\mathrm{dof}$, where dof is the degrees of freedom in the fits. Figure 5 shows the resultant ${\chi }^{2}/\mathrm{dof}$ values as a function of line strength (upper panel) and S/N (lower panel) separately for Hα+[N ii] in H-long and Hβ+[O iii] in J-long. The distribution of the reduced ${\chi }^{2}$ statistics clearly peaks at ${\chi }^{2}/\mathrm{dof}\simeq 1$, with no significant trends with either line strength or S/N.

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In relatively few cases, a prominent broad emission-line component was present, and we included a secondary broad component for Hα or Hβ. Furthermore, we also added a secondary narrow Hα+[N ii] (or Hβ+[O iii]) component with a centroid and width different from the primary component, when necessary (e.g., a case in which there is a prominent blueshifted component of the [O iii] line, possibly attributed to an outflow). Such exceptional handling was applied for only 5% of the whole sample (108 out of 1931 objects with a line detection). Most of these objects are X-ray-detected, and we postpone a detailed analysis of these objects to a future paper while focusing here on the basic properties of normal star-forming galaxies.

For nondetections of emission lines of interest, we estimate upper limits on their in-fiber fluxes if we have a spectroscopic redshift measurement from any other detected lines in the FMOS spectra and the spectral coverage for undetected lines. The S/N of an emission line depends not only on the flux and the typical noise level of the spectrum but also on the amount of loss due to bad pixels. These effects have been considered on a case-by-case basis by performing dedicated Monte Carlo simulations for each spectrum.

For each object with a measurement of spectroscopic redshift, we created N_sim = 500 spectra containing an artificial emission line with a Gaussian profile at a specific observed-frame wavelength of undetected lines based on the spectroscopic redshift. The line width was fixed to a typical FWHM of 300 $\mathrm{km}\,{{\rm{s}}}^{-1}$ (Section 6.1), and Gaussian noise was added to these artificial spectra based on the processed noise spectrum. In doing so, we mimicked the impact of the OH lines and the masks. We then performed a fitting procedure for these artificial spectra with various amplitudes in the same manner as the data and estimated the 2σ upper limit for each undetected line by linearly fitting the sets of simulated fluxes and the associated S/Ns.

In addition to the line fluxes, we also measured the average flux density within the spectral window for individual objects regardless of the presence or absence of a line detection. The average flux density $\left\langle {f}_{\nu }\right\rangle$ and the associated errors were derived by integrating the extracted 1D spectrum of each galaxy as follows:

$$\begin{eqnarray}&&\left\langle {f}_{\nu }\right\rangle =\displaystyle \frac{{\displaystyle \sum }_{i}{f}_{\nu ,i}{W}_{i}{R}_{i}}{{\displaystyle \sum }_{i}{W}_{i}{R}_{i}d\lambda },\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{\rm{\Delta }}\left\langle {f}_{\nu }\right\rangle =\displaystyle \frac{\sqrt{{\displaystyle \sum }_{i}{\left({N}_{\nu ,i}{W}_{i}{R}_{i}d\lambda \right)}^{2}}}{{\displaystyle \sum }_{i}{W}_{i}{R}_{i}d\lambda },\end{eqnarray} \tag{ 3 }$$

where $d\lambda =1.25\,\mathring{\rm A}$ is the wavelength pixel resolution, N_i is the associated noise spectrum, and R_i is a response curve.

Beside being used to estimate the equivalent widths of detected emission lines, these quantities can also allow for absolute flux calibration by comparing them with the ground-based H- or J-band photometry. For comparison, we use the fixed 3'' aperture magnitudes H(J)_MAG_APER3 from the UltraVISTA-DR2 survey (McCracken et al. 2012) provided in the COSMOS2015 catalog (Laigle et al. 2016), applying the recommended offset from the aperture to total magnitudes (see the Appendix of Laigle et al. 2016). For comparison with the reference photometry, we define R_i in the above equations based on the response curve of the VISTA/VIRCam H- or J-band filters,¹⁷ and flux densities were then converted to (AB) magnitudes. In the calculation of these equations, we did not exclude the detected emission lines because our primary purpose is to compare these to the ground-based broadband photometry, which, in principle, includes the emission-line fluxe.¹⁸ We disregard the measurements with S/N < 5 and also exclude objects whose A- and/or B-position spectrum (obtained through the ABAB telescope nodding) falls on the detector next to those of flux standard stars, since these spectra may be contaminated by leakage from the neighbor bright star spectrum. Finally, we successfully measured the flux density for 2456 objects observed in the H-long mode and 1700 objects observed in J-long.

In Figure 6, we compare the observed magnitudes H_AB from the FMOS H-long spectra with the UltraVISTA H-band magnitudes separately for the two spectrographs (IRS1 and IRS2) of FMOS. Here the observed values were computed from spectra produced by the standard reduction pipeline, and we refer to these as the "raw" magnitude. Data points from a single observing run (2013 December 28) are highlighted for reference. It is clear that there is a global offset of ∼1 mag in the observed magnitudes relative to the reference UltraVISTA magnitudes. This reflects the loss flux falling outside the fiber aperture. In addition, we can also see that an ∼0.5 mag systematic offset exists between the two spectrographs. This offset is due to the difference in the total efficiency of the two spectrographs. Prior to the aperture correction, we first corrected for this offset between IRS1 and IRS2, as follows:

$$\begin{eqnarray}&&{H}_{\mathrm{IRS}1}={H}_{\mathrm{IRS}1}^{\mathrm{raw}}+(\left\langle {\rm{\Delta }}{H}_{\mathrm{IRS}2}^{\mathrm{raw}}\right\rangle -\left\langle {\rm{\Delta }}{H}_{\mathrm{IRS}1}^{\mathrm{raw}}\right\rangle )/2,\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&{H}_{\mathrm{IRS}2}={H}_{\mathrm{IRS}2}^{\mathrm{raw}}-(\left\langle {\rm{\Delta }}{H}_{\mathrm{IRS}2}^{\mathrm{raw}}\right\rangle -\left\langle {\rm{\Delta }}{H}_{\mathrm{IRS}1}^{\mathrm{raw}}\right\rangle )/2,\end{eqnarray} \tag{ 5 }$$

where $\left\langle {\rm{\Delta }}{H}_{\mathrm{IRS}i}^{\mathrm{raw}}\right\rangle$ is the median offset of the observed magnitude relative to the reference magnitude. This correction has been done for each observing run independently. We did the same for the J-band observations as well.

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Figure 7 shows the observed magnitudes after correcting for the offset between IRS1 and IRS2. The magnitudes from the H-long (left panel) and J-long (right panel) spectra are shown as a function of S/Ns separately for each spectrograph. The correlations are in good agreement between the two spectrographs and between the spectral windows. The threshold S/N = 5 corresponds to ≈23.5 ABmag for both H and J.

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We emphasize that in the rest of the paper, as well as in our emission-line catalog, the correction for the differential throughput between the two IRSs is applied for all observed quantities, including emission-line fluxes, formal errors, and upper limits on the line fluxes. Therefore, catalog users do not need to care about this instrumental issue. Meanwhile, the fluxes in the catalog denote the in-fiber values; hence, the aperture correction should be applied using the correction factors given in the catalog, if necessary (see the next subsection for details).

As already mentioned, the emission-line and broadband fluxes measured from observed FMOS spectra arise only from the regions of each target falling within the 12 diameter aperture of the FMOS fibers. Therefore, it is necessary to correct for flux falling outside the fiber aperture to obtain the total emission-line flux of each galaxy. The amount of aperture loss depends on both the intrinsic size of each galaxy and the conditions of the observation, which include variable seeing size and fluctuations of the fiber positions (typically less than 02; Kimura et al. 2010). We define three methods for aperture correction.

First, the aperture correction can be determined by simply comparing the observed H (or J) flux density obtained by integrating the FMOS spectra to the reference broadband magnitude for individual objects. This method can be utilized for moderately luminous objects for which we have a good measurement of the integrated flux from the FMOS spectra (observed H_AB ≲ 22.5). This method cannot be applied for objects with poor continuum detection and suffering from flux leakage from bright objects.

Second, we can use the average offset of the observed magnitude relative to the reference magnitude for each observing run. This method can be applied to fainter objects and those with insecure continuum measurements (e.g., impacted by leakage from a bright star) for correcting the emission-line fluxes.

Lastly, we determine the aperture correction based on HR imaging data. In the COSMOS field, we can utilize images taken by the HST/ACS (Koekemoer et al. 2007; Massey et al. 2010) that almost entirely cover the FMOS field and offer a high spatial resolution. The advantage of this method is that we can determine the aperture correction object by object, taking into account their size properties and a specific seeing size of the observing night. Hereafter, we describe this third method in detail (see also Kashino et al. 2013; Silverman et al. 2015b).

For each galaxy, the aperture correction is determined from the HST/ACS I_F814W-band images (Koekemoer et al. 2007). In doing so, we implicitly assume that the difference between the on-sky spatial distributions of the rest-frame optical continuum (i.e., stellar radiation) and nebular emission is negligible under typical seeing conditions ($\gtrsim 0\buildrel{\prime\prime}\over{.} 5$ in FWHM). This assumption is reasonable for the majority of the galaxies in our sample, in particular, those at z > 1, whose typical size is <1''.

We performed photometry on the ACS images of the FMOS galaxies using SExtractor version 2.19.5 (Bertin & Arnouts 1996). The flux measurement was performed with a fixed aperture size at the positions of the best-matched objects in the COSMOS2015 catalog, if it exists, otherwise at the position of the fiber pointing. For the majority of the sample, we used the measurements in the 2'' diameter aperture (FLUX_APER2) but employed the 3'' aperture (FLUX_APER3) for a small fraction of the sample if the size of the object extends significantly beyond the 2'' aperture and, consequently, the ratio FLUX_APER3/FLUX_APER2 is ≳1.3.¹⁹. We visually inspected the ACS images to check for the presence of significant contamination by nearby objects, flagging such cases in the catalog.

Next, we smoothed the ACS images by convolving with a Gaussian point-spread function (PSF) for the effective seeing size. We then performed aperture photometry with SExtractor to measure the flux in the fixed FMOS fiber aperture FLUX_APER_FIB and computed the correction factor as ${c}_{\mathrm{aper}}$ = FLUX_APER2(3)/FLUX_APER_FIB. The size of the smoothing Gaussian kernel (i.e., the effective seeing size) was retroactively determined for each observing run to minimize the average offset relative to the reference UltraVISTA broadband magnitudes (McCracken et al. 2012) from Laigle et al. (2016; see Section 4.4). We note that the effective seeing sizes determined are in broad agreement with the actual seeing conditions during the observing runs (∼05–14 in FWHM) that were measured from the observed PSF of the guide stars. We note that the effective seeing size determined here includes the effect of the positioning errors of the FMOS fibers (≲02). The scatter in the flux measurement caused by fluctuations of the aperture positions of σ = 02 is ∼0.03 dex (for an object of an effective radius of 05 with an effective seeing of 07). Therefore, the effect of the fiber positioning errors should be negligible in the entire uncertainty of the flux measurements (see below).

Figure 8 shows the derived aperture correction factors as a function of the reference magnitude separately for the H and J bands. We excluded insecure estimates of aperture correction, which includes cases where the blending or contamination from other objects is significant. The aperture correction factors range from ∼1.2 to ∼4.5, and the median values are 2.1 and 2.5 for the H and J bands, respectively. This small offset between the two bands is due to the fact that seeing is worse for shorter wavelengths under the same condition. Note that the formal error on the correction factor that comes from the aperture photometry on the ACS image (e.g.,FLUXERR_APER2) is small (typically <5%), and thus the scatter seen in Figure 8 is real, reflecting both variations in the intrinsic sizes of galaxies and the seeing conditions of observing nights.

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Figure 9 shows offsets between the observed and reference magnitudes, before and after correcting for aperture losses, as a function of the reference magnitudes. The average magnitude offset is mitigated by applying the aperture correction. After aperture correction, we found the standard deviation of the magnitude offsets to be 0.42 (0.50) mag, after (before) taking into account the individual measurement errors in both $\left\langle {f}_{\nu }\right\rangle$ of the observed FMOS spectra and the reference magnitude. There is no significant difference between H and J. Note that this comparison also provides a sense of testing agreement between the first method of aperture correction estimation, described above, that relies on the direct comparison between the observed flux density on the FMOS spectra and the reference magnitude.

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In the catalog, we provide the best estimate of aperture correction for each of the galaxies, regardless of the presence or absence of a spectroscopic redshift measurement. For 67% of the sample observed in the H-long spectral window and 80% in J-long, the best aperture correction is based on the HST/ACS image described above. However, for the remaining objects, the estimates with this method are not robust due to blending, significant contamination from other sources, or any other troubles on the pixels of the ACS images. Otherwise, there is no ACS coverage for some of those falling outside the area (see Figure 1). For such cases, we provide as the best aperture correction an alternative estimate based on the second method that uses the average offset of all objects observed together in the same night. When applying the aperture correction from this second method for all objects, the agreement between the aperture-corrected observed flux density and the reference magnitude is slightly worse, with an estimated intrinsic scatter of ≈0.57 mag for both H- and J-long, than that based on the ACS image-based aperture correction.

In the following, we use these best estimates of aperture correction without being aware of which method is used. Throughout the paper, when any aperture-corrected values, such as total luminosity and SFRs, are shown, the error includes in quadrature a common factor of 1.5 (or 0.17 dex) in addition to the formal error on the observed emission-line flux to account for the intrinsic uncertainty of aperture correction. Lastly, we emphasize that the aperture correction is determined for all of the individual objects using the independent observations (i.e., HST/ACS and UltraVISTA photometry) and just average information of the FMOS observations (i.e., mean offset), but not relying on the individual FMOS measurements. This ensures that the uncertainty of aperture correction is independent of the individual FMOS measurements.

Out of the full sample, we obtained spectroscopic redshift measurements for 1931 objects. The determination of spectroscopic redshift is based on the detection of at least a single emission line, expected to be either Hα, [N ii], Hβ, or [O iii]. For our initial target selection, galaxies were selected based on the photometric redshift z_phot, so Hα+[N ii] and Hβ+[O iii] are expected in either the H-long or J-long spectral window. For the majority of the sample, we identified the detected line as Hα or [O iii] according to their z_phot. However, this is not the case for a small number of objects for which we found a clear combination of Hα+[N ii] or the [O iii] doublet (+Hβ) in a spectral window not expected from the z_phot. For objects observed in both the H and J bands, we checked whether their independent redshift measurements were consistent. If not, we reexamined the spectra to search for any features that could solve the discrepancy between the spectral windows. Otherwise, we disregarded line detections of lower S/N. For objects observed two or more times, we adopted a spectrum with the highest S/N of the line flux. For objects with consistent line detections in the two spectral windows (i.e., Hα+[N ii] in H-long and Hβ+[O iii] in J-long), we regarded a redshift estimate based on higher-S/N detection as the best estimate (z_best). There are also objects that were observed two or more times in the same spectral window. In particular, the repeat J-long observations have been carried out to build up exposure time to detect faint Hβ at higher S/N. In the catalog presented in this paper, however, we adopted a single observation with detections of the highest S/N, instead of stacking spectra taken on different observing runs.²¹

We assign a quality flag (zFlag) to each redshift measurement based on the number of detected lines and the associated S/N as follows (see Section 4.2 for details of the detection criteria).

• zFlag 0: No emission line detected.
• zFlag 1: Presence of a single emission line detected at 1.5 ≤ S/N < 3.
• zFlag 2: One emission line detected at 3 ≤ S/N < 5.
• zFlag 3: One emission line detected at S/N ≥ 5.
• zFlag 4: One emission line at S/N ≥ 5 and a second line at S/N ≥ 3 that confirms the redshift.

The criteria have been slightly modified from those used in Silverman et al. (2015b; where Flag = 4 if a second line is detected at S/N ≥ 1.5). Note that objects with zFlag = 1 are not used for scientific analyses in the rest of the paper.

In Table 4, we summarize the numbers of observed galaxies and the redshift measurements with the corresponding quality flags. In the second through fourth rows, the numbers of galaxies observed in each spectral band are reported, while the numbers of galaxies observed in two or three bands are reported in the last four rows. Table 5 summarizes the number of galaxies with detections of each of four emission lines.

In the top panel of Figure 10, we display the distribution of all galaxies with a spectroscopic redshift measurement split by the quality flag. There are three redshift ranges, corresponding to possible combinations of the detected emission lines and the spectral ranges, as summarized in Table 5. In the middle panel, we compare the distribution of the FMOS-COSMOS galaxies to the redshift distribution from the VUDS observations (Le Fèvre et al. 2015). It is clear that our FMOS survey constructed a complementary spectroscopic sample that fills the redshift gap seen in the recent deep optical spectroscopic survey. In the bottom panel of Figure 10, we show objects for which Hα is detected in the H-long band with the positions of OH airglow lines. The wavelengths of the OH lines are converted into redshifts based on the wavelength of the Hα emission line as ${z}_{\mathrm{OH}}={\lambda }_{\mathrm{OH}}/6564.6\mathring{\rm A} -1$. It is clear that the number of successful detections of Hα is suppressed near the bright OH airglow lines, shown by gray stripes. This is because pixels at these wavelengths are lost due to high noise caused by the OH mask and residual sky lines. The fraction of lost pixels achieves approximately 30% of the spectral coverage of the H-long band. Note that this fraction is slightly increased for observations in 2012 March (see Section 4.1). This reduces the success rate of the line detection.

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Based on the full sample, we have a 37% (1931/5247) overall success rate for acquiring a spectroscopic redshift with a quality flag $z\mathrm{Flag}\geqslant 1$, including all galaxies observed in any of the FMOS spectral windows. We note that, given that only ∼70% of the H-long band is available for line detection due to the OH masks, the effective success rate can be evaluated to be ∼37/0.7 = 53%. The full catalog, however, contains various galaxy populations selected by different criteria, and many galaxies may satisfy criteria for different selections; i.e., the subsamples overlap each other. In later subsections, we thus focus our attention separately on each of the specific subsamples of galaxies as described in Section 3. In Table 6, we summarize the successful redshift measurements for each subsample.

The Primary-HL sample includes galaxies selected from the COSMOS photometric catalog, as described in Section 3.1. For these objects, our line identification assumed that the strongest line detected in the H-long band is the Hα emission line, although, for some cases, only the [N ii] line was measured, and Hα was disregarded due to significant contamination on Hα. For other cases with no detections in the H-long window, the strongest line detection in the J-long spectra was assumed to be the [O iii] λ5007 line. We observed 1582 galaxies that satisfy the criteria given in Section 3.1 in the H-long mode and successfully obtained redshift measurements with zFlag ≥ 1 for 749 (47%) of them. The measured redshifts are in the range 1.36 ≤ z_spec ≤ 1.74. Focusing on the detection of the Hα line in the H-long mode, we successfully detected it for 712 (643) at ≥1.5σ (≥3σ). We note that the remaining 37 objects include [N ii] detections in the H-long mode and Hβ and/or [O iii] detections in the J-long mode. In addition to the Primary objects, we also observed another 1242 star-forming galaxies at z ∼ 1.6 that do not match all of the criteria for the Primary target (the Secondary-HL sample; see Section 3.1). In Table 6, we summarize the number of redshift measurements for the Primary-HL and Secondary-HL samples, as well as for the subset after removing the X-ray-detected objects.

In Figure 11, we compare the spectroscopic redshifts with the photometric redshifts used for the target selection from the photometric catalogs (Ilbert et al. 2013, 2015) for the Primary-HL sample. For those with zFlag ≥ 2 (i.e., ≥3σ), the median and standard deviation σ_std of $({z}_{\mathrm{phot}}-{z}_{\mathrm{spec}})/(1+{z}_{\mathrm{spec}})$ are −0.0099 (−0.0064) and 0.028 (0.024), respectively, after (before) taking into account the effects of limiting the range of photometric redshifts ($1.46\leqslant {z}_{\mathrm{phot}}\leqslant 1.72$). To account for the edge effects, we adopted a number of sets of the median offset and ${\sigma }_{\mathrm{std}}$ to simulate the photometric redshift for each z_spec measurement, then determined the plausible values of the intrinsic median and σ_std that could reproduce the observed median offset and σ_std of $({z}_{\mathrm{phot}}-{z}_{\mathrm{spec}})/(1+{z}_{\mathrm{spec}})$ after applying the limit of 1.46 ≤ z_phot ≤ 1.72.

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The PACS-HL sample include 116 objects in the range 1.44 ≤ z_phot ≤ 1.72 detected in the Herschel-PACS observations (Section 3.2). We successfully measured spectroscopic redshifts for 56 (43%) objects with zFlag ≥ 1, including 32 (28%) secure measurements (zFlag = 4). These measurements include 43 (3, 2) detections of Hα (≥3σ) in the H-long (H-short, J-long) band, as well as a single higher-z object with a possible detection of the [O iii] doublet in the H-long band (z_spec = 2.26).

In the J-long band, we observed 344 lower-redshift galaxies selected from the infrared data (see Section 3.4) and succeeded in measuring a spectroscopic redshift with zFlag ≥ 1 for 188 objects (55%). We detected the Hα emission line at S/N ≥ 1.5 (≥3.0) for 172 (169) objects. We note that six objects have a detection of Hβ+[O iii] in the J-long and are thus not within the lower-redshift window.

We observed a total of 742 objects detected in the X-ray from the Chandra COSMOS Legacy survey (Elvis et al. 2009; Civano et al. 2016). Of these, 385 and 533 objects were observed in the H-long and J-long modes, respectively, while 177 were observed with both of these. We obtained a redshift measurement for 281 (263) objects with zFlag ≥ 1 (≥2). The entire sample of X-ray objects includes 75 lower-redshift (0.72 ≤ z_spec ≤ 1.1) objects with a detection of Hα+[N ii] in the J-long band and 29 (1) higher-redshift (2.1 ≤ z_spec ≤ 2.6) objects with a detection of Hβ+[O iii] in the H-long (H-short). The remaining majority of the sample are those at intermediate-redshift range with detections of Hα+[N ii] in the H-long band and/or Hβ+[O iii] in the J-long band.

In Figure 12, we plot the observed in-fiber Hα flux F_Hα (corrected for neither dust extinction nor aperture loss) as a function of associated S/N for each galaxy in our sample, split by the spectral window. As naturally expected, there is a correlation between F_Hα and S/N but with large scatter in F_Hα at fixed S/N. This is mainly due to the presence of "bad pixels" impacted by OH masks and residual sky emission (see Section 4.2). The figure indicates that, in the H-long band, the best sensitivity achieves ${F}_{{\rm{H}}\alpha }\sim {10}^{-17}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$ at S/N = 3, while the average is $\sim 3\times {10}^{-17}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$.

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In Figure 13, we show the correlation between ${F}_{{\rm{H}}\alpha }$ (corrected for aperture but not for dust) and the FWHM of the Hα line in velocity units for galaxies with an Hα detection (≥3.0σ) in the H-long band ($1.43\leqslant {z}_{\mathrm{spec}}\leqslant 1.74$). The emission-line widths are not deconvolved for the instrumental velocity resolution ($\approx 45\,\mathrm{km}\,{{\rm{s}}}^{-1}$ at $z\sim 1.6$). Although there is a weak correlation between these quantities, the line width becomes nearly constant at ${F}_{{\rm{H}}\alpha }\gtrsim 1\times {10}^{-16}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$. The central 90th percentile of the observed FWHM is 108–537 $\mathrm{km}\,{{\rm{s}}}^{-1}$, with a median at 247 $\mathrm{km}\,{{\rm{s}}}^{-1}$. Limiting to those with ${F}_{{\rm{H}}\alpha }\geqslant 1\times {10}^{-16}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$, the median is 292 $\mathrm{km}\,{{\rm{s}}}^{-1}$.

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In Figure 14, we show the rest-frame equivalent width (EW₀) of the Hα emission line as a function of aperture-corrected continuum flux density $\left\langle {f}_{\lambda ,\mathrm{con}}\right\rangle$ averaged across the H-long spectral window. The continuum flux density was computed with Equation (2), excluding the emission-line components. The equivalent widths were not corrected for differential extinction between the stellar continuum and nebular emission. The 759 objects shown here are limited to a detection of Hα at ≥3σ in H-long and a secure measurement of the continuum level (≥5σ). The observed ${\mathrm{EW}}_{0}({\rm{H}}\alpha )$ ranges from ≈10 to $300\,\mathring{\rm A}$, with a median $\left\langle {\mathrm{EW}}_{0}({\rm{H}}\alpha )\right\rangle =71.7\,\mathring{\rm A}$. The sample shows a clear negative correlation between $\left\langle {f}_{\lambda ,\mathrm{con}}\right\rangle$ and ${\mathrm{EW}}_{0}({\rm{H}}\alpha )$. The continuum and Hα flux reflect, respectively, M_* and SFR. Thus, this correlation may be shaped by the fact that specific SFR ($\mathrm{sSFR}=\mathrm{SFR}/{M}_{* }$) decreases, on average, with M_*.

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In Figure 15, we plot the observed Hα luminosity, L_Hα (corrected for aperture loss but not for dust extinction), as a function of redshift separately in the two redshift ranges that correspond to where Hα is detected (J-long or H-long/short). The observed L_Hα is a weak function of redshift, increasing toward higher redshift, as shown by the linear regression that is derived in each range. This trend is almost negligible compared to the range spanned by the sample (${\rm{\Delta }}z\approx 0.4$ each). For objects with an Hα detection (≥3σ) in the H-long spectral window, the central 90th percentile of L_Hα is ${10}^{41.7}\mbox{--}{10}^{42.7}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ with a median $\left\langle {L}_{{\rm{H}}\alpha }\right\rangle ={10}^{42.25}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$.

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The sulfur emission lines [S ii] λλ6717, 6731 fall in the H-long (J-long) spectral window, together with Hα at 1.43 < z < 1.68 (0.70 < z < 1.00). For those with a detection of Hα and/or [N ii], we fit the [S ii] lines at the fixed spectroscopic redshift determined from Hα+[N ii], as described in Kashino et al. (2017b).

We successfully detected the [S ii] lines for a substantial fraction of the sample. Table 7 summarizes the detections of the [S ii] lines. In total, we detected [S ii] λ6717 and [S ii] λ6731 at ≥3σ for 146 and 111 objects, respectively, with 55 with both detections at ≥3σ (see the top row in Table 7). Limiting those to have an Hα detection (>3σ) in H-long, we detected [S ii] λ6717 for 84, [S ii] λ6731 for 54, and both for 22 objects (all at ≥3σ). In Figure 16, we show the observed fluxes of [S ii] λ6717 and [S ii] λ6731 as a function of observed Hα flux, corrected for neither dust nor aperture loss. The observed flux of the single [S ii] line is, on average, ≈1/5 times the observed Hα flux, ranging from F_{[S ii]} ≈ 4 × 10⁻¹⁸ to $8\times {10}^{-17}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$.

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To evaluate the accuracy of our redshift measurements, we compared spectroscopic redshifts measured from Hα+[N ii] detected in the H-long spectra and those measured from Hβ+[O iii] in the J-long spectra. In the top panel of Figure 17, we show the distribution of $({z}_{H}-{z}_{J})/(1+{z}_{\mathrm{best}})$ for 350 galaxies with independent line detections (≥3σ) in both H-long and J-long. Of these, 172 objects have detections both at ≥5σ. Here the best estimate of redshift z_best is based on a detection with a higher S/N between the two spectral windows. The standard deviation σ_std of ${dz}/(1+z)$ is 3.3 × 10⁻⁴ for objects with ≥3σ detection (${\sigma }_{\mathrm{std}}=2.2\times {10}^{-4}$ for ≥5σ), with a negligibly small median offset (2.6 × 10⁻⁵). The estimated redshift accuracy ${\sigma }_{\mathrm{std}}/\sqrt{2}$ is thus $\approx 70\,\mathrm{km}\,{{\rm{s}}}^{-1}$.

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An alternative check of redshift accuracy can be done using objects that have been observed two or more times in the same spectral band on different nights. For these objects, we have selected the best spectrum to construct the line measurement catalog. However, the "secondary" measurements can be used to evaluate the "primary" ones. In the lower panel of Figure 17, we show the distribution of the difference between the primary (z_prim) and the second-best (${z}_{2\mathrm{nd}}$) redshift measurements, separately for measurements obtained in H-long (29 objects) and J-long (113). Objects are limited to those with ≥3σ detection in the primary and secondary spectra. The standard deviation σ_std of $({z}_{2\mathrm{nd}}-{z}_{\mathrm{prim}})/(1+{z}_{\mathrm{best}})$, reported in the figure for both H-long (${\sigma }_{\mathrm{std}}=3.5\times {10}^{-4}$) and J-long (${\sigma }_{\mathrm{std}}=3.3\times {10}^{-4}$) observations, is similar to that estimated by comparing the H-long and J-long measurements.

The secondary measurements can also be used to evaluate the accuracy of emission-line flux measurements. In Figure 18, we compare the primary and secondary measurements of the Hα flux in the H-long window (upper panel; 24 objects) and in the Hβ (middle panel; 58 objects) and [O iii] λ5007 fluxes (lower panel; 109 objects) in the J-long window. Because the two measurements are based on spectra taken under different seeing conditions, the aperture correction needs to be applied for comparison. We remind readers that the aperture correction is evaluated once for each object and observing night. It is shown that the primary and secondary measurements are in good agreement, as well as that aperture correction improves their agreement, as shown by histograms in the inset panels. We found the intrinsic scatter of these correlations to be 0.19, 0.21, and 0.19 dex for Hα, Hβ, and [O iii], respectively, after taking into account the effects of the individual formal errors of the observed fluxes. These intrinsic scatters should be attributed to the uncertainties of the aperture corrections and, indeed, similar to the estimates made in Section 4.5 (see Figure 9).

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Some of our FMOS-COSMOS targets were observed in the MOSFIRE Deep Evolution Field (MOSDEF) survey (Kriek et al. 2015). The latest public MOSDEF catalog, released on 2018 March 11, contains 616 objects in the COSMOS field. Cross-matching with the FMOS catalog, we found 45 sources included in both catalogs, and of these, 15 objects have redshift measurements in both surveys.

Among the matching objects, all 11 FMOS measurements with zFlag = 4 and a single zFlag = 3 agree with the MOSDEF measurements, which all have a quality flag (Z_MOSFIRE_ZQUAL) of 7 (based on multiple emission lines at S/N ≥ 2). The three inconsistent measurements are as follows. An object (z_FMOS = 1.515 with zFlag = 3) has an [O iii] detection at >5σ, with a possible consistent detection of Hα, in the FMOS spectra, while the MOSDEF measurement is z = 2.101 with a flag of 7. The photometric redshift z_phot = 1.674 (Laigle et al. 2016) prefers the FMOS measurement. For the remaining two (FMOS/MOSDEF measurements (flags) are ${z}_{\mathrm{FMOS}/\mathrm{MOSDEF}}\,=1.581/2.555$ (2/6) and ${z}_{\mathrm{FMOS}/\mathrm{MOSDEF}}=1.584/2.100$ (1/7), respectively), the detections of Hα on the FMOS spectra are not robust, both being significantly affected by the OH mask. The photometric redshift prefers z_MOSDEF for the former (${z}_{\mathrm{phot}}\,=2.612$) and z_FMOS for the latter (${z}_{\mathrm{phot}}=1.458$). We note that there are moderately bright OH lines at 1.5088, 1.5518, and 2.0339 μm, which would perfectly conspire to emulate Hβ [O iii] λ5007 and Hα at z = 2.099. The two z_MOSDEF = 2.10 measurements may be affected by this circumstance.

The redshift range of the MOSDEF survey is 1 ≲ z ≲ 3.5 but has a higher sampling rate at 2 < z < 2.6. Therefore, it is not straightforward to estimate the failure rate in our survey, which could be overestimated. The small sample size of the matching objects also makes it difficult. However, we could conclude that, for objects with zFlag = 3 and 4, the failure rate should be below 10% (1/13 = 7.7%).

For these 12 consistent measurements, we found the median offset and standard deviation of $({z}_{\mathrm{FMOS}}-{z}_{\mathrm{MOSDEF}})/(1+{z}_{\mathrm{MOSDEF}})$ to be $-1.63\times {10}^{-5}$ ($4.9\,\mathrm{km}\,{{\rm{s}}}^{-1}$) and $2.57\,\times {10}^{-4}$ ($77\,\mathrm{km}\,{{\rm{s}}}^{-1}$). This indicates that there is no significant systematic offset in the wavelength calibration of the FMOS survey relative to the MOSDEF survey.

A part of the CANDELS-COSMOS field (Grogin et al. 2011; Koekemoer et al. 2011) is covered by the 3D-HST survey (Brammer et al. 2012), which is a slitless spectroscopic survey using the HST/WFC3 G141 grism to obtain near-infrared spectra from 1.10 to $1.65\,\mu {\rm{m}}$. This configuration yields detections of Hα and [O iii] lines for those matched to the FMOS catalog. For redshift and flux comparisons with our measurements, we employed the public "linematched" catalogs (ver. 4.1.5) for the COSMOS field (Momcheva et al. 2016), in which the spectra extracted from the grism images were matched to photometric targets (Skelton et al. 2014).²² Cross-matching the 3D-HST and FMOS catalogs, we found 78 objects that have redshift measurements from both surveys. We divided these objects into two classes according to the quality flags in the 3D-HST catalog (flag1 and flag2). The "good" class contains 67 objects with both flag1 = 0 and flag2 = 0, while the remaining 11 objects are classified in the "warning" class.

In Figure 19, we compare our FMOS redshift measurements to those from 3D-HST for the 78 matching sources. The colors indicate the quality flags of the FMOS measurements (see Section 5.1), and the symbols correspond to the quality classes of the 3D-HST measurements as defined above. In the inset, we show the distribution of $({z}_{\mathrm{FMOS}}-{z}_{3\mathrm{DHST}})/(1+{z}_{3\mathrm{DHST}})$ for all objects along the diagonal one-to-one line (gray histogram) for the subsample with FMOS $z\mathrm{Flag}\geqslant 3$ and in the 3D-HST "good" class (red histogram). We find that an average offset of ${dz}/(1+z)=0.0009$ and a standard deviation of ${\sigma }_{\mathrm{std}}\,=0.0029$ (0.0022 for the "good" sample) after 3σ clipping, which corresponds to $870\,\mathrm{km}\,{{\rm{s}}}^{-1}$, is consistent with the typical accuracy of the redshift determination in 3D-HST (Momcheva et al. 2016).

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We further examine the possible line misidentification for the 10 cases where two spectroscopic redshifts are inconsistent (labeled in Figure 19). Of these objects, we found that the FMOS z_spec is quite robust for three zFlag = 4 objects (IDs 247, 659, and 4179) and one zFlag = 3 object (ID 4447). A single zFlag = 3 object (ID 2710; z_spec = 0.815) has a clear detection of a single line. If this line is [S iii] λ9531 in reality, the corresponding redshift agrees with that from 3D-HST. For the other five objects, our FMOS measurements are not fully robust, including a single zFlag = 4 object (ID 1862), while four of these are flagged as "warning" in 3D-HST. We thus would conclude that the possibility of line misidentification (including fake detections) is equal to or less than 6/67 = 9%, even down to zFlag ≥ 2. A similar estimate of the possibility (≲10%) has been obtained from a comparison with the zCOSMOS-Deep survey (Lilly et al. 2007) for matching objects (see Silverman et al. 2015b).

Next, we compare our flux measurements to those in 3D-HST for the matching sample. In contrast to fiber spectroscopy, slitless grism spectroscopy is less affected by aperture losses and therefore offers an opportunity to check our measurements with aperture correction. Objects used for this comparison are limited to have a detection of Hα or [O iii] at ≥3σ in both FMOS and 3D-HST and a consistent redshift estimation ($| {dz}| /(1+z)\leqslant 0.01$). In the top panel of Figure 20, we compare Hα fluxes measured from FMOS (corrected for aperture loss) with those from 3D-HST for 28 objects. Here the Hα fluxes from 3D-HST include the contribution from [N ii] λλ6548, 6584 because these lines are blended with Hα due to the low spectral resolution (R ∼ 100). Therefore, we also show the total fluxes of Hα and [N ii] λλ6548, 6584 for the FMOS measurements (orange circles). Eight of the 28 objects have no detection of [N ii]. Even with no inclusion of [N ii], good agreement is seen between the measurements of both programs, with a median offset of −0.09 dex and an rms scatter of 0.23 dex. As naturally expected, the inclusion of [N ii] lines further improves the agreement, resulting in an offset of 0.02 dex and a scatter of 0.17 dex.

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The bottom panel of Figure 20 shows the comparisons of observed Hβ and [O iii] fluxes. We show the total fluxes of [O iii] λλ4959, 5007 for the FMOS measurements because 3D-HST does not resolve the [O iii] doublet. Similar to Hα, there is good agreement between flux measurements for these lines with little average offset (<0.1 dex) and small scatter (<0.2 dex).

The agreement of our flux measurements with the slitless measurements from 3D-HST indicates the success of our absolute flux calibration including aperture correction. The scatter found in the comparisons (∼0.2 dex) is equivalent to that found in comparisons using repeat observation (Section 7.2), as well as to the typical uncertainty in the aperture correction (Section 4.5).

In this section, we focus our attention on the star-forming population at z ∼ 1.6, in particular, with a detection of Hα at ≥3σ. Therefore, we limit this discussion to those that were observed in the H-long band. We exclude X-ray objects identified in the Chandra COSMOS Legacy catalog (see Section 3.3).

We first construct a broad sample from COSMOS2015, named Broad-L16, to be sufficiently deep relative to the FMOS sample. We limit the sample to be flagged as a galaxy (TYPE = 0), being within the strictly defined 2 deg² COSMOS field (FLAG_COSMOS = 1), inside the UltraVISTA field (FLAG_HJMCC = 0), inside the good area (not masked area) of the optical broadband data (FLAG_PETER = 0), and inside the FMOS area covered by all of the pawprints (see Figure 1). As a consequence, the effective area used for this evaluation is 1.35 deg², after removing the masked regions.²³ For details of these flags, we refer the reader to Laigle et al. (2016).

We further impose a limit on the photometric redshift $1.3\leqslant {z}_{\mathrm{phot}}\leqslant 1.9$ and the UltraVISTA K_S-band magnitude ${K}_{{\rm{S}}}\leqslant 24.0$, where we use the 3'' aperture magnitude (KS_MAG_APER3). This limiting magnitude corresponds to the 3σ limit in the UltraVISTA deep layer and ≥5σ for the ultradeep layer. Finally, we find 39,435 galaxies satisfying these criteria. We then performed the position matching between the H-long sample and the COSMOS2015 catalog with a maximum position error of 10, yielding the matched sample that consists of 2878 objects (Broad-L16 ∩  FMOS HL).²⁴ The fraction with respect to the Broad-L16 sample is 7.3%, and we detected Hα at ≥3σ for 1014 of these; thus, the success rate is 35% (1014/2878).

Next, we imposed additional limits on the Broad-L16 sample while simultaneously trying to keep the sampling rate as high as possible and not lose Hα-detected objects. For this purpose, we use the stellar mass and SFR estimates from SED fitting given in the COSMOS2015 catalog. We computed predicted Hα fluxes as follows:

$$\begin{eqnarray}&&{F}_{{\rm{H}}\alpha }^{\mathrm{pred}}=\displaystyle \frac{1}{4\pi {d}_{{\rm{L}}}{({z}_{\mathrm{phot}})}^{2}}\displaystyle \frac{\mathrm{SFR}/({M}_{\odot }\,{\mathrm{yr}}^{-1})}{4.6\times {10}^{-42}}\times {10}^{-0.4{A}_{{\rm{H}}\alpha }}.\end{eqnarray} \tag{ 6 }$$

This is the modified version of Equation (2) of Kennicutt (1998) for the use of a Chabrier (2003) IMF. Dust extinction is taken into account with ${A}_{{\rm{H}}\alpha }={k}_{{\rm{H}}\alpha }E(B-V)/{f}_{\mathrm{neb}}$, where ${k}_{{\rm{H}}\alpha }=2.54$ is the wavelength dependence of extinction (Cardelli et al. 1989). The extinction $E(B-V)$ is taken from the COSMOS2015 catalog²⁵ and is multiplied by a factor of 1/f_neb = 1/0.5 to account for enhancement of extinction toward nebular lines (see Section 9.3).²⁶ Finally, we define the Selected-L16 sample by imposing the criteria ${K}_{{\rm{S}}}\leqslant 23.0$, $1.43\leqslant {z}_{\mathrm{phot}}\leqslant 1.74$, $\mathrm{log}{M}_{* }/{M}_{\odot }\geqslant 9.6$, and the predicted Hα flux ${F}_{{\rm{H}}\alpha }^{\mathrm{pred}}\geqslant 1\times {10}^{-16}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$, in addition to the criteria on the Broad-L16 sample. As a consequence, the Selected-L16 sample includes 3714 objects.

Cross-matching the Selected-L16 sample with the FMOS H-long sample, we find 1209 objects, and 628 of these have a successful detection of Hα (≥3σ) in the H-long spectra. Thus, the sampling rate is 33% (1209/3714), and the success rate is 52% (628/1209). It is worth noting that the rate of failure detection can be reasonably explained: if the redshift distribution is uniform, approximately 20% of those within $1.43\,\leqslant {z}_{\mathrm{phot}}\leqslant 1.74$ may fall outside the redshift range covered by the H-long window for their uncertainty on the photometric redshift ($\delta {z}_{\mathrm{phot}}\approx 0.06;$ see below). Moreover, ≈35% of the potential objects may be lost due to severe contamination by OH skylines (see Figure 10). In Table 8, we summarize the selection and the sizes of the samples defined in this section. We note that it is not guaranteed that all objects in the Selected-L16 sample were included in the input sample for the fiber allocation software.

Table 8.  Summary of the Sampling and Success Rates

Sample	Selection	Ngalaxies	Fraction
Broad-L16	In the FMOS field (1.35 deg2)
	And TYPE = 0 (flagged as a galaxy)
	And FLAG_COSMOS = 1
	And $\mathrm{FLAG}\_\mathrm{HJMCC}=0$
	And $\mathrm{FLAG}\_\mathrm{PETER}=0$
	And ${K}_{{\rm{S}}}\leqslant 24.0$ and $1.3\leqslant {z}_{\mathrm{phot}}\leqslant 1.9$	39,435
$\cap$ FMOS HL	And observed in the H-long	2878	7.3% (2878/39,435)
$\cap$ FMOS HL + Hα	And Hα detection (3σ) in the H-long	1014	35.2% (1014/2878)
Selected-L16	Criteria for Broad-L16
	And ${K}_{{\rm{S}}}\leqslant 23.0$ and $1.43\leqslant {z}_{\mathrm{phot}}\leqslant 1.74$
	And $\mathrm{log}{M}_{* }/{M}_{\odot }\geqslant 9.6$
	And ${F}_{{\rm{H}}\alpha }^{\mathrm{pred}}\geqslant 1\times {10}^{-16}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$	3714
$\cap$ FMOS HL	And observed in the H-long	1209	32.6% (1209/3714)
$\cap$ FMOS HL + Hα	And Hα detection (3σ) in the H-long	628	51.9% (628/1209)

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We investigate possible biases in the FMOS sample as functions of the properties of galaxies. In Figure 22, we show the distribution of the SED-based quantities (z_phot, K_S, M_*, SFR, and ${F}_{{\rm{H}}\alpha }^{\mathrm{pred}}$ from left to right) for galaxies matched in the Broad-L16 sample. As shown in the top panels of Figure 22, the sampling rates of both the observed and Hα-detected sample depend on these quantities. We note that the nonuniform sampling in terms of z_phot is trivial because we preferentially selected galaxies within a narrower range of z_phot ($1.46\leqslant {z}_{\mathrm{phot}}\leqslant 1.72$), within which the sampling is nearly uniform. In the middle panel in each column, we show the success rate, which is the fraction of the Hα-detected objects relative to the observed objects at a given x-axis value. It is also clear that the success rate depends significantly on these galaxy properties, e.g., as shown by the trends with ${K}_{{\rm{S}}}$ and ${F}_{{\rm{H}}\alpha }^{\mathrm{pred}}$.

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Next, we show the Selected-L16 sample in the same manner in Figure 23. At first glance, the distribution of the observed/Hα-detected FMOS objects is more similar to that of the parent sample. Correspondingly, it is also clear that the sampling rate is now more uniform against any quantity of these than those of the Broad-L16 sample shown in Figure 22. However, the sampling rate still varies substantially as a function of some of these galactic properties. In particular, the sampling rate increases rapidly around $\mathrm{log}{M}_{* }/{M}_{\odot }\approx {10}^{10.5}$. Given a tight correlation between M_* and K_S magnitude, this trend with M_* corresponds to the decrease in the sampling rate with increasing K_S. This is partially because the latter part of our observations was especially dedicated to increasing the sampling rate of most massive galaxies. However, the success rate shows no significant trend as a function of M_* and K_S-band magnitude. As opposed to M_* (or K_S), not only the sampling rate but also the success rate appears to increase as ${F}_{{\rm{H}}\alpha }^{\mathrm{pred}}$ increases (right panels). This is naturally expected because stronger lines are more easily detected. From these results, we conclude that the spectroscopic sample (even after applying the criteria defined in this section) is biased toward massive galaxies and having higher ${F}_{{\rm{H}}\alpha }^{\mathrm{pred}}$.

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To quantify these trends, we show in Figure 24 the cumulative sampling and success rates as a function of M_* (upper panel) and predicted Hα flux (lower panel). The cumulative sampling rate is defined as the fraction of observed and/or Hα-detected galaxies above a given M_* or ${F}_{{\rm{H}}\alpha }^{\mathrm{pred}}$ with respect to the Selected-L16 sample but without the limit on the quantity corresponding to the x-axis. The cumulative success rate is defined in the same manner between the Hα-detected and observed galaxy samples. In the upper panel, it is shown that the cumulative sampling rate of the observed galaxies (∩ FMOS HL; red line) increases at ${M}_{* }\geqslant {10}^{10}\,{M}_{\odot }$ and reaches a level of ≈60% (≈35%) at ${M}_{* }={10}^{10.7}\,{M}_{\odot }$. The cumulative sampling rate of the Hα-detected subsample (green line) shows a similar trend, increasing monotonically with M_* from 17% at the lower M_* limit to 35% at ${10}^{11}\,{M}_{\odot }$. In contrast, the cumulative success rate (purple line) is nearly uniform across the entire M_* range. In the lower panel of Figure 24, the cumulative sampling rate for the Hα-detected subsample (green line) increases from ∼10% at ${F}_{{\rm{H}}\alpha }^{\mathrm{pred}}\lt {10}^{-16}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$ to 35%. The cumulative success rate (purple line) also increases slowly from 40% to 70% as the threshold ${F}_{{\rm{H}}\alpha }^{\mathrm{pred}}$ increases.

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We compare our spectroscopic measurements with those based on the SED fits from COSMOS2015. In Figure 25, we compare the spectroscopic redshifts with the photometric redshifts. Limiting those in the Selected-L16 sample (red circles and red histogram), we find that the median and the standard deviation of $({z}_{\mathrm{phot}}-{z}_{\mathrm{spec}})/(1+{z}_{\mathrm{spec}})$ are −0.0112 (−0.0086) and 0.0264 (0.0237), respectively, after (before) taking into account the effect of limiting the range of photometric redshifts ($1.43\leqslant {z}_{\mathrm{phot}}\leqslant 1.74$). The level of the uncertainties in the photometric redshifts is very similar to that in the older version (Ilbert et al. 2013), as described in Section 5.2. Because there is only a little systematic offset in our z_spec measurements in comparison with the MOSDEF and 3D-HST surveys (Section 7), the median offset between z_spec and z_phot, which is significant compared to the scatter, should be regarded as the systematic uncertainty in the photometric redshifts.

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Next, in Figure 26, we compare the observed Hα fluxes to the predicted Hα fluxes. The observed fluxes are converted to the total fluxes by applying the aperture correction (see Section 4.5). Note that the observed fluxes are not corrected for extinction, while the predicted fluxes include the reduction due to extinction. It is shown that the observed fluxes are in broad agreement with the predicted values. Limiting those in the Selected-L16 sample (red circles), we found a small systematic offset of $\mathrm{log}{F}_{{\rm{H}}\alpha }^{\mathrm{obs}}/{F}_{{\rm{H}}\alpha }^{\mathrm{pred}}=-0.16\,\mathrm{dex}$ (median). This offset may be attributed to the application of inaccurate dust extinction. We revisit the dust extinction by using the new estimates of galaxy properties with spectroscopic redshifts in Section 9.3.

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For FMOS galaxies with a spectroscopic redshift based on an emission-line detection, we rederived the stellar masses based on SED fitting using LePhare (Arnouts et al. 2002; Ilbert et al. 2006). The stellar mass is defined as the total mass contained in stars at the considered age without the mass returned to the ISM. Our procedure follows the same method as in Ilbert et al. (2015) and Laigle et al. (2016); i.e., our estimation is consistent with the COSMOS2015 catalog. The SED library contains synthetic spectra generated using the population synthesis model of Bruzual & Charlot (2003), assuming a Chabrier (2003) IMF. We considered 12 models combining the exponentially declining SFH (${e}^{-t/\tau }$ with $\tau /\mathrm{Gyr}=\left\{{\rm{0.1:30}}\right\}$) and delayed SFH (${{te}}^{-t/\tau }$ with $\tau =1$ and 3 Gyr) with two metallicities (solar and half solar) applied. We considered two attenuation laws, including the Calzetti et al. (2000) law and a curve $k{(\lambda )=3.1(\lambda /5500\mathring{\rm A} )}^{-0.9}$, with $E(B-V)$ being allowed to take values as high as 0.7.

For the SED fitting, we used photometry from the COSMOS2015 catalog measured with 30 broad-, intermediate-, and narrowband filters from GALEX NUV to Spitzer/IRAC ch2 (4.5 μm), as listed in Table 3 of Laigle et al. (2016). Note that IRAC ch3 and ch4 were excluded, since the photometry in these bands may be affected by the PAH emissions, which are not modeled in our templates. For CFHT, Subaru, and UltraVISTA photometry, we used measurements in 3'' aperture fluxes and applied the offsets provided in the catalog to convert them to the total fluxes.

In Figure 27, we show the histograms of the resulting ${\chi }^{2}/{N}_{\mathrm{band}}$ values (where N_band is the number of bandpasses that were used for fitting) for the best-fit SEDs separately for non-X-ray and X-ray-detected sources (see Section 3.3). It is shown that the ${\chi }^{2}/{N}_{\mathrm{band}}$ values are concentrated around ${\chi }^{2}/{N}_{\mathrm{band}}=1$ for non-X-ray star-forming galaxies, which indicates that the fitting has reasonably succeeded for the majority of the sample. In contrast, the fitting may be unreasonable for many of the X-ray sources, as indicated by their ${\chi }^{2}/{N}_{\mathrm{band}}$ distribution, which is widely spread out to ${\chi }^{2}/{N}_{\mathrm{band}}\sim 100$. The main reason for such lower goodness-of-fit is the additional emission from an AGN at the rest-frame UV and near-to-mid-IR wavelengths. The derivation of SED properties for X-ray sources, accounting for the AGN emission component, is postponed to a future companion paper (D. Kashino et al. 2019, in preparation). Throughout the paper, we disregard the LePhare estimates for all X-ray-detected sources and those with ${\chi }^{2}/{N}_{\mathrm{band}}\geqslant 6$.

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We estimated the total SFR of our sample galaxies directly from the UV continuum luminosity in order to compare with those estimated from Hα luminosity. Dust extinction is accounted for based on the slope ${\beta }_{\mathrm{UV}}$ of the rest-frame UV continuum spectrum (e.g., Meurer et al. 1999). The UV slope ${\beta }_{\mathrm{UV}}$ is defined as ${f}_{\lambda }\propto {\lambda }^{{\beta }_{\mathrm{UV}}}$. We measured the rest-frame FUV (1600 Å) flux density and β_UV by fitting a power-law function to the broad- and intermediate-band fluxes within $1200\,\mathring{\rm A} \,\leqslant {\lambda }_{\mathrm{eff}}/(1+z)\leqslant 2600\,\mathring{\rm A}$, where λ_eff is the effective wavelength of the corresponding filters. The slope β_UV is converted to the FUV extinction, A₁₆₀₀, as well as to the reddening value, ${E}_{\mathrm{star}}(B-V)$, with the following relations from Calzetti et al. (2000):

$$\begin{eqnarray}&&{A}_{1600}=4.85+2.31\,{\beta }_{\mathrm{UV}},\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&{E}_{\mathrm{star}}(B-V)={A}_{1600}/{k}_{1600},\end{eqnarray} \tag{ 8 }$$

where k₁₆₀₀ = 10.0. We set the lower and upper limits to be ${E}_{\mathrm{star}}(B-V)=0$ and 0.8, respectively. The extinction-corrected UV luminosity, L₁₆₀₀, is then converted to SFR using a relation from Daddi et al. (2004),

$$\begin{eqnarray}&&{\mathrm{SFR}}_{\mathrm{UV}}({M}_{\odot }\,{\mathrm{yr}}^{-1})=\displaystyle \frac{{L}_{1600}(\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{Hz}}^{-1})}{1.7\times 8.85\times {10}^{27}},\end{eqnarray} \tag{ 9 }$$

where a factor of 1/1.7 is applied to convert from a Salpeter (1955) IMF to a Chabrier (2003) IMF. We disregard the measurements with poor constraints of either the UV luminosity (<5σ) or the UV slope $\sigma ({\beta }_{\mathrm{UV}})\gt 0.5$ (only 6% of the sample of Hα-detected (≥3σ) galaxies).

In the upper panel of Figure 28, we show the distributions of the estimates of M_* and UV-based SFR for the entire FMOS sample, removing those with a resultant $\chi /{N}_{\mathrm{band}}^{2}\geqslant 6$ and X-ray objects. Objects are shown in the figure separated into three redshift ranges, as labeled. In the lower panel of Figure 28, we show the reddening ${E}_{\mathrm{star}}(B-V)$, estimated from β_UV, as a function of M_* for the same objects shown in the upper panel. It is clear that the average and scatter in ${E}_{\mathrm{star}}(B-V)$ increase with increasing M_*.

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Next, we compute the intrinsic SFR from the observed Hα flux, applying a correction for aperture loss and dust extinction, through Equation (6). It is known that the extinction of the nebular emission is enhanced, on average, relative to the extinction toward the stellar component, which is expressed with a factor f_neb as ${E}_{\mathrm{neb}}(B-V)={E}_{\mathrm{star}}(B-V)/{f}_{\mathrm{neb}}$. In the local universe, a factor ${f}_{\mathrm{neb}}=0.44$, derived by Calzetti et al. (2000), has been widely applied, whereas observations at higher redshifts have measured larger values (∼0.5–1; e.g., Kashino et al. 2013; Price et al. 2014). There remain large uncertainties in the constraints on the f_neb factor because these results may depend on the method used to determine the level of extinction and the extinction laws applied. In the remainder of the paper, we adopt the Cardelli et al. (1989; R_V = 3.1) and Calzetti et al. (2000; R_V = 4.05) extinction laws, respectively, for the nebular and stellar extinction, following the analysis in the original work of Calzetti et al. (2000), where they used a similar law by Fitzpatrick (1999) for the nebular emission.

We here determine the f_neb by comparing the SFRs estimated from the observed Hα and UV luminosities, both uncorrected for dust extinction, as in Kashino et al. (2013). For this investigation, we limit our sample to 702 galaxies having Hα detection (≥5σ) and estimates of M_*, SFR_UV, and E_star(B − V) (see Section 9). We excluded all X-ray-detected objects and possible AGNs flagged by the emission-line width of $\geqslant 1000\,\mathrm{km}\,{{\rm{s}}}^{-1}$ and/or their emission-line ratios of [O iii] λ5007/Hβ and [N ii] λ6584/Hα (see Kashino et al. 2017b for details).

Assuming that the appropriate dust correction equalizes the UV- and Hα-based SFRs, the dust-uncorrected ratio ${\mathrm{SFR}}_{{\rm{H}}\alpha }^{\mathrm{uncorr}}/{\mathrm{SFR}}_{\mathrm{UV}}^{\mathrm{uncorr}}$ is expressed as a function of ${E}_{\mathrm{star}}(B-V)$ with a parameter f_neb as follows:

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{log}\left(\displaystyle \frac{{\mathrm{SFR}}_{{\rm{H}}\alpha }^{\mathrm{uncorr}}}{{\mathrm{SFR}}_{\mathrm{UV}}^{\mathrm{uncorr}}}\right) & = & -0.4{E}_{\mathrm{star}}(B-V)\\ & & \quad \times \ \left(\displaystyle \frac{{k}_{{\rm{H}}\alpha }}{{f}_{\mathrm{neb}}}-{k}_{1600}\right),\end{array}\end{eqnarray} \tag{ 10 }$$

where k₁₆₀₀ = 10.0 (Calzetti et al. 2000) and ${k}_{{\rm{H}}\alpha }=2.54$ (Cardelli et al. 1989). The observed Hα flux is converted to SFR${}_{{\rm{H}}\alpha }^{\mathrm{uncorr}}$ following Equation (6) without the extinction term, and aperture correction is applied. The values of ${E}_{\mathrm{star}}(B-V)$ were estimated from the UV slope ${\beta }_{\mathrm{UV}}$ using the Calzetti et al. (2000) law (Section 9.2).

In Figure 29, we plot the ratio ${\mathrm{SFR}}_{{\rm{H}}\alpha }^{\mathrm{uncorr}}/{\mathrm{SFR}}_{\mathrm{UV}}^{\mathrm{uncorr}}$ as a function of ${E}_{\mathrm{star}}(B-V)$. There is a clear correlation between the SFR ratio and reddening. It is apparent that more than half the data points fall above the line with the conventional value ${f}_{\mathrm{neb}}=0.44$ for local galaxies. We found that the best fit of Equation (10) yields a value of ${f}_{\mathrm{neb}}=0.53\pm 0.01$, with a scatter of 0.15 dex after accounting for the individual errors. Using the Calzetti et al. (2000) curve for both stellar and nebular reddening (i.e., replacing ${k}_{{\rm{H}}\alpha }$ with 3.33) results in a higher value (${f}_{\mathrm{neb}}=0.69$), which is in agreement with Kashino et al. (2013), where we did so.

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Lastly, we compare in Figure 30 the different SFR indicators: the rest-frame UV, Hα, and those obtained from the SED fitting (i.e., the same procedure with LePhare as for the stellar mass). Because the f_neb factor is adjusted so that the Hα-based SFR matches the UV-based SFR, on average, these two SFRs show good agreement. In contrast, we find a systematic offset (median 0.4 dex) in comparison with the SFR through the SED fitting. Similarly, some bias (∼0.25 dex) was found by Ilbert et al. (2015) from a comparison with SFR from IR+UV flux.

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In Figure 31, we show 907 galaxies with an Hα detection (≥3σ) in the H-long spectral window. Of them, 702 galaxies have an Hα detection at ≥5σ (cyan circles). Observed Hα fluxes are corrected for dust extinction by using ${A}_{{\rm{H}}\alpha }\,=2.54{E}_{\mathrm{star}}(B-V)/0.53$ (see Section 9.3). Vertical error bars include in quadrature the individual formal errors on the flux measurements (i.e., errors from line fitting) and a common uncertainty of 0.17 dex for aperture correction (see Section 4.5), as well as individual measurement errors on ${E}_{\mathrm{star}}(B-V)$, while not including any systematic uncertainty in the extinction law. The average detection limit is estimated by assuming the 3σ detection limit of Hα flux of $6\times {10}^{-18}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$ (see Figure 12) and taking into account the M_*-dependent aperture correction and dust extinction. The detection limit increases with M_*, mainly because the level of extinction increases on average with M_* (see the lower panel of Figure 28). The observed data points are well above this line across the whole M_* range, indicating that the observed distribution of SFR at fixed M_* is less biased by the detection limit.

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The correlation between M_* and SFR is evident. The Spearman's rank correlation coefficient is ρ = 0.52 for all objects with ${\rm{S}}/{\rm{N}}({\rm{H}}\alpha )\geqslant 3.0$ shown here. To illustrate the behavior of the observed sequence more clearly, we separated the data points into bins of M_* from 10^9.4 to 10^11.4 M_⊙ with a constant interval of 0.2 dex. In Figure 31, we indicate the median values and the central 68th percentiles in each bin. These median points indicate possible bending of the main sequence, as reported by several authors (e.g., Whitaker et al. 2014; Lee et al. 2015; Schreiber et al. 2015).

We parameterize the observed M_*–SFR relation. In doing so, we exclude the objects below 10^9.5 M_⊙ and use the individual points, taking into account errors on both log M_* and log SFR. We first employ a power-law function to fit the data as follows:

$$\begin{eqnarray}&&\mathrm{log}\ \mathrm{SFR}/({M}_{\odot }\,{\mathrm{yr}}^{-1})=\alpha +\beta \mathrm{log}\left[\displaystyle \frac{{M}_{* }}{{10}^{10}{M}_{\odot }}\right].\end{eqnarray} \tag{ 11 }$$

We fit to two subsamples: one contains all 876 galaxies above ${M}_{* }\geqslant {10}^{9.5}\,{M}_{* }$, and the other is limited to 609 objects in the range ${10}^{9.5}\leqslant {M}_{* }/{M}_{\odot }\leqslant {10}^{10.5}$ to avoid the effect of the possible bending. We summarize the results in Table 9 and indicate the best-fit relations in Figure 31. The best-fit relation for the former (${M}_{* }\geqslant {10}^{9.5}\,{M}_{* }$) has a slope of β = 0.500 ± 0.017, which is shallower than the slope of β = 0.755 ± 0.035 for the latter subsample limited to ${10}^{9.6}\leqslant {M}_{* }/{M}_{\odot }\leqslant {10}^{10.5}$. Hence, it is obvious that the shallower slope is caused by the massive population.

Table 9.  Best-fit Parameters for the M_*–SFR Relation

Parameters	N	Parameters			χ2 (χ2/dof)a
Power law (Equation (11))		α	β
M*/M⊙ ≥ 109.5	876	1.285 ± 0.008	0.500 ± 0.017		2261 (2.59)
109.5 ≤ M* / M⊙ ≤ 1010.5	609	1.290 ± 0.009	0.755 ± 0.035		1187 (1.95)
Broken power law (Equation (12))		alow	ahigh	b
M*/M⊙ ≥ 109.5	876	0.844 ± 0.055	0.292 ± 0.037	1.476 ± 0.016	2200 (2.52)
Asymptotic function (Equation (13))		${{ \mathcal S }}_{0}$	$\mathrm{log}{{ \mathcal M }}_{0}$	γ
M*/M⊙ ≥ 109.5	876	1.74 ± 0.033	10.205 ± 0.068	1.17 ± 0.10	2206 (2.53)

Note.

^aThe χ² statistics are computed including errors on both log SFR and log M_*. The dof is N − n_p, where n_p is the number of parameters.

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We next account for the bending feature of the M_*–SFR relation at ${M}_{* }\sim {10}^{10.5}\,{M}_{\odot }$. We employ two functional forms, a broken power law and an asymptotic function, proposed by Whitaker et al. (2014) and Lee et al. (2015), respectively. The broken power law is parameterized as

$$\begin{eqnarray}&&\mathrm{log}\ \mathrm{SFR}/({M}_{\odot }\,{\mathrm{yr}}^{-1})=a\left(\mathrm{log}{M}_{* }/{M}_{\odot }-10.2\right)+b,\end{eqnarray} \tag{ 12 }$$

where the value of a is different above (a_high) and below (a_low) the characteristic mass of $\mathrm{log}{M}_{* }/{M}_{\odot }=10.2$. The characteristic mass is fixed following the original paper (Whitaker et al. 2014), though the best-fit value is $\mathrm{log}{M}_{* }/{M}_{\odot }=10.31\pm 0.04$ if we allow it to vary. The asymptotic function is defined as

$$\begin{eqnarray}&&\mathrm{log}\ \mathrm{SFR}/({M}_{\odot }\,{\mathrm{yr}}^{-1})={{ \mathcal S }}_{0}+\mathrm{log}\left[1+{\left(\displaystyle \frac{{M}_{* }}{{{ \mathcal M }}_{0}}\right)}^{-\gamma }\right],\end{eqnarray} \tag{ 13 }$$

where ${{ \mathcal S }}_{0}$ is the asymptotic value of the $\mathrm{log}\ \mathrm{SFR}$ at high M_*, ${{ \mathcal M }}_{0}$ is the characteristic mass for turnover, and γ is a low-mass slope.

Table 9 gives the results of fits to the individual objects with ${M}_{\ast }\geqslant {10}^{9.5}\,{M}_{\odot }$. With the asymptotic relation, the characteristic mass for turnover is constrained to be $\mathrm{log}{{ \mathcal M }}_{0}/{M}_{\odot }=10.205\,\pm 0.068$, which is fully consistent with the fixed characteristic mass ($\mathrm{log}{M}_{* }/{M}_{\odot }=10.2$) of the broken power-law fit, as well as the result of Lee et al. (2015), as discussed below. In Figure 31, we show the best fits with the broken power law and asymptotic function. The two functional forms yield almost identical M_*–SFR relations across the M_* range probed, which both well fit the median SFRs.

The tight constraint on the turnover characteristic mass ${{ \mathcal M }}_{0}$, as well as the significant difference detected between a_low and a_high, indicate the presence of bending of the sequence at ${M}_{* }\approx {10}^{10.2}$. This is also supported by the fact that, compared with the simple power law, the resultant χ² is reduced by ${\rm{\Delta }}{\chi }^{2}\approx 60$ by invoking the bending feature (Table 9). Meanwhile, there is no significant difference between the fits with the broken power law and the asymptotic function.

In Figure 32, we compare our results with the M_*–SFR relations from the literature. The power-law fit to the limited M_* range ($9.5\leqslant \mathrm{log}{M}_{* }/{M}_{\odot }\leqslant 10.5$) is fully consistent with our previous result (Kashino et al. 2013) and the parameterization from a compilation across a wide redshift range derived by Speagle et al. (2014). On the other hand, fit to the entire M_* range ($\mathrm{log}{M}_{* }/{M}_{\odot }\geqslant 9.5$) yields a shallower slope. The difference with Kashino et al. (2013) may be attributed to the increased weight of the massive population and their different sample selection. The broken power-law fit to the FMOS data yields a shallower high-mass slope (a_high = 0.29) than the result from Whitaker et al. (2014; a_high = 0.62 for a sample at 1.5 < z < 2.0). In contrast, the best fit with the asymptotic function (Equation (13)) is in good agreement with the result with the same parameterization by Lee et al. (2015) at $\left\langle z\right\rangle =1.19$, with a similar characteristic mass $\mathrm{log}{{ \mathcal M }}_{0}(=10.31)$ for the turnover. Lee et al. (2015) also found a high-mass power-law slope of 0.27 for ${M}_{* }\gt {10}^{10}\,{M}_{\odot }$, which is rather similar to our ${a}_{\mathrm{high}}(=0.29)$. The steeper high-mass slope found by Whitaker et al. (2014) may be attributed, at least partially, to the fact that the authors derived the total SFR using IR luminosity estimated from Spitzer/MIPS 24 μm flux with a luminosity-independent conversion. Lee et al. (2015) showed that total SFRs estimated in this way are overestimated at $\mathrm{log}\ \mathrm{SFR}/({M}_{\odot }\,{\mathrm{yr}}^{-1})\gtrsim 2$. This effect is thus more important at high masses and would artificially make the high-mass slope steeper.

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In Figure 31, the observed scatter in SFR${}_{{\rm{H}}\alpha }$ appears to increase with M_*. We estimate the intrinsic scatters of the M_*–SFR relation as a function of M_*. For this purpose, we define the offset from the best-fit M_*–SFR relation at fixed M_* as $\mathrm{log}\ \mathrm{sSFR}/\left\langle \mathrm{sSFR}\right\rangle$ and divide the sample into four bins of M_*: log M_*/M_⊙ = [9.4:9.9], [9.9:10.4], [10.4:10.7], and [10.7:11.5]. Here we use the best fit with the asymptotic function (Equation (13)), but the use of another fit (i.e., simple or broken power-law fit for ${M}_{* }\geqslant {10}^{9.5}\,{M}_{\odot }$) does not change the conclusions.

Figure 33 shows the distributions of $\mathrm{log}\ \mathrm{sSFR}/\left\langle \mathrm{sSFR}\right\rangle$ for the entire sample and in the four M_* bins. These distributions are well fit with a lognormal profile (solid blue lines). The standard deviations of these lognormal profiles (σ_gaus) and the values directly computed from the sample after 3σ clipping (σ_std) are indicated in each panel, which agree with each other.

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The intrinsic scatter is then estimated from σ_std by accounting for the individual uncertainties on log M_* and log SFR. The individual errors were obtained by summing in quadrature the statistical uncertainties on the individual Hα-based SFR (the formal errors), log M_*, and a common 0.17 dex for aperture correction. The uncertainty on log M_* was included by multiplying it by the slope of the relation at a given M_*. Systematic uncertainties and the error on f_neb = 0.53 were not included. We also deconvolved the effect of the time evolution of the average sSFR across 1.43 ≤ z ≤ 1.74 (≈0.04 dex) by using the actual redshift distribution of the sample. We adopted the scaling relation $\mathrm{sSFR}\propto {(1+z)}^{3.14}$ from Ilbert et al. (2015).

We found the intrinsic scatter to be 0.24 dex for the entire sample and found it to increase with M_* from 0.19 to 0.37 dex in the four bins shown in Figure 33. The intrinsic scatter in $\mathrm{sSFR}/\left\langle \mathrm{sSFR}\right\rangle$ found at low-to-intermediate masses is in good agreement with previous constraints of the width of the main sequence (≈0.2 dex; e.g., Salmi et al. 2012; Speagle et al. 2014). Noeske et al. (2007) obtained an observed value of 0.35 dex and put an upper limit of <0.30 dex on the intrinsic scatter. It is also argued that the scatter around the main sequence is nearly redshift-independent across a wide redshift range ($0\leqslant z\lesssim 4$; e.g., Speagle et al. 2014; Ilbert et al. 2015; Schreiber et al. 2015). Ilbert et al. (2015) parameterized the sSFR function in the M_* bins with a lognormal function convolved with the measurement uncertainties and found the intrinsic scatter to be ≈0.28–0.46 dex, increasing with M_*. The M_* dependence they found is qualitatively consistent with our result, while the scatter they found is larger than our findings at all masses.

Ilbert et al. (2015) argued that, as a caveat, the dynamical range of sSFR covered by the data may be not enough large in many cases to correctly estimate the width of the main sequence. Indeed, in our case, the criterion on the predicted Hα flux in the preselection of the spectroscopic targets reduces the sampling rate, especially of a population with low M_* and SFR (see Section 3.1). Figure 2 shows that this selection bias exists across the whole M_* range, while being mitigated more or less at ${M}_{* }\gtrsim {10}^{10.7}\,{M}_{\odot }$. Establishing the main sequence based on Hα at high redshifts may require further unbiased deep spectroscopic surveys with high multiplicity, which will finally be achieved by upcoming projects and instruments, such as the Multi-Object Optical and Near-infrared Spectrograph (MOONS).

For the following exercises, we selected galaxies in a similar way to Kashino et al. (2017b), as follows. The sample is limited to having a detection of Hα at ≥3σ in the H-long band and a stellar mass estimate (see Section 9). Any objects, either detected in the X-ray or with the FWHM of Hα greater than $1000\,\mathrm{km}\,{{\rm{s}}}^{-1}$, are removed from the sample. Furthermore, we removed a fraction of the individual galaxies as possible AGNs by using their observed emission-line ratios, Hα/[N ii], and [O iii]/Hβ. We excluded objects that are located above the theoretical "maximum starburst" line derived by Kewley et al. (2001) or have a line ratio of log [N ii] λ6584/Hα ≥ −0.1 or log [O iii] λ5007/Hβ ≥ 0.9.

Finally, we have 907 galaxies, which are referred to as Sample-H. Of these, there are 648 galaxies that have both a redshift in the range $1.43\leqslant {z}_{\mathrm{spec}}\leqslant 1.67$ and J-long coverage, which are referred to as Sample-HJ. For Sample-HJ, the upper limit of the redshift range is slightly decreased to ensure that all of the key emission lines, including [S ii] λλ6717, 6731, fall within the wavelength ranges of the FMOS H-long and J-long windows. In Table 10, we summarize the number of galaxies and line detections in each subsample. We group the galaxies by the S/N of their emission-line detections: high quality (HQ) if S/N ≥ 5 for Hα and S/N ≥ 3 for other lines, and low quality (LQ) if 3 ≤ S/N < 5 for Hα and 1.5 ≤ S/N < 3 for other lines. The typical range of the stellar mass is $\mathrm{log}{M}_{* }/{M}_{\odot }\approx 9.46\mbox{--}11.17$ (the central 95th percentiles). Note that the sizes of Sample-H and Sample-HJ increase by 265 and 365, respectively, relative to the corresponding samples in Kashino et al. (2017b).

Table 10.  Summary of Emission-line Detections for the Samples Used in Section 11 ^a

Samples	Sample-Hb	Sample-HJc
zspec range	$1.43\leqslant z\leqslant 1.74$	$1.43\leqslant z\leqslant 1.67$
Median zspec	1.579	1.557
Hα	907 (702)	648 (506)
[N  ii]	551 (347)	419 (272)
[S  ii]	72 (19)	62 (17)
Hβ	⋯	203 (136)
[O  iii ]	⋯	242 (220)
${\rm{H}}\alpha +\left[{\rm{N}}\,{\rm{II}}\right]$ d	551 (325)	419 (254)
Hα + [S  ii]	72 (18)	62 (16)
[O  iii] + Hβ	⋯	170 (114)
${\rm{H}}\alpha +\left[{\rm{N}}\,{\rm{ii}}\right]+\left[{\rm{O}}\,{\rm{iii}}\right]+{\rm{H}}\beta$	⋯	118 (59)
${\rm{H}}\alpha +\left[{\rm{S}}\,{\rm{ii}}\right]+\left[{\rm{O}}\,{\rm{iii}}\right]+{\rm{H}}\beta$	⋯	19 (6)

Notes.

^aThe threshold S/N is 3 for Hα and 1.5 for other lines. In parentheses, the numbers of detections with higher S/N (≥5 for Hα and ≥3 for other lines) are listed. ^bSample-H consists of 907 galaxies with Hα (≥3σ). ^cSample-HJ consists of 648 galaxies with both Hα (≥3σ) and the additional J-long coverage. ^dThe numbers of galaxies with multiple emission-line detections are listed in the 8th–12th rows.

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Both individual and stacked measurements were corrected for the Balmer absorption for the Hβ line as a function of M_* and SFR by using a relation as follows (Kashino & Inoue 2018):

$$\begin{eqnarray}&&\displaystyle \frac{{F}_{{\rm{H}}\beta }^{\mathrm{int}}-{F}_{{\rm{H}}\beta }^{\mathrm{obs}}}{{F}_{{\rm{H}}\beta }^{\mathrm{int}}}=\displaystyle \frac{1}{2}\left[\mathrm{erf}\left(-0.626\left(x+0.248\right)\right)+1\right],\end{eqnarray} \tag{ 14 }$$

where

$$\begin{eqnarray}&&x=\mathrm{log}\ \mathrm{SFR}/({M}_{\odot }\,{\mathrm{yr}}^{-1})-1.32\left(\mathrm{log}\ {M}_{* }/{M}_{\odot }-10\right).\end{eqnarray} \tag{ 15 }$$

For this equation, we used M_* from SED fitting and SFR_UV (Section 9) and substituted the median values in each bin for stacked measurements. Although the Hα fluxes were not corrected for the Balmer absorption following our previous study (Kashino et al. 2017b), the effects (≲3%) do not alter the conclusions.

For comparison, we extracted a sample of local galaxies from the SDSS. The stellar mass and SFR from the MPA-JHU catalog (Kauffmann et al. 2003b; Brinchmann et al. 2004; Salim et al. 2007) are converted to a Chabrier IMF to match our sample. We divided the galaxies into two categories—star-forming and AGN—by using the Kauffmann et al. (2003a) classification line in the BPT diagram and excluded AGNs from the sample for the following analysis. The SDSS comparison sample consists of 80,003 star-forming galaxies in the range 0.04 ≤ z ≤ 0.10. To illustrate the average relation between line ratios and stellar masses of local star-forming galaxies, we split the sample into bins of M_* in the range 10^8.6 ≤ M_* ≤ 10^11.2 with a bin size of 0.2 dex and computed the pseudo-stacked line ratios from the mean line fluxes in each bin (see Kashino et al. 2017b). We refer the reader to Kashino et al. (2017b) for a full description of the sample construction of local galaxies.

Figure 34 shows FMOS galaxies in the N2-BPT diagram, in comparison with the SDSS galaxies and average locations of samples at higher redshifts from the literature (Shapley et al. 2015; Strom et al. 2017). The distribution of the SDSS galaxies is represented by the red contour that encloses 95% of the sample.

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As we originally reported in Kashino et al. (2017b), star-forming galaxies at z ∼ 1.6 in the FMOS sample are located, on average, offset from the sequence of the SDSS galaxies. The N2-BPT locus of our FMOS galaxies can be described empirically using a simple functional form. We fit the individual galaxies with detection of all four lines (N = 118; S/N ≥ 3.0 for Hα and ≥1.5 for others). The best-fit curve for the locus of the FMOS galaxies (green line in Figure 34) takes the form of

$$\begin{eqnarray}\begin{array}{r}\begin{array}{rcl}{\rm{l}}{\rm{o}}{\rm{g}}\left([{\rm{O}}\,{\rm{iii}}]/{\rm{H}}\beta \right) & = & \displaystyle \frac{0.61}{{\rm{l}}{\rm{o}}{\rm{g}}([{\rm{N}}\,{\rm{ii}}]/{\rm{H}}\alpha )-(0.13\pm 0.03)},\\ & & \,+\,(1.09\pm 0.04)\end{array}\end{array}\end{eqnarray} \tag{ 16 }$$

where the coefficient is fixed to 0.61 (Kewley et al. 2001). Here we accounted for the errors on both line ratios simultaneously.

The offset is further clearly seen by comparing the stacked line ratios between the FMOS (blue circles) and SDSS (yellow squares) samples. The FMOS stacked points are located along the upper envelope of the red contour and in agreement with the best-fit curve to the individual galaxies.

Figure 35 shows the S2-BPT diagram that replaces the x-axis of the N2-BPT diagram with the [S ii]/Hα ratio. While the [S ii] lines are not detected for the majority of the individual galaxies, it is evident that the stacked measurements certainly differ from the average locus of the local galaxies. The data points of the high-M_* bins are located near the left-hand envelope of the red contour that encloses 95% of the SDSS sample.

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We previously reported the possible offset of the high-z galaxies toward the left-hand side of the diagram, i.e., lower [S ii]/Hα at fixed [O iii]/Hβ, and we regarded this offset as a key observational feature to support our hypothesis that an increase in the ionization parameter is the primary origin of the evolution of the observed emission-line ratios (see Figure 12 of Kashino et al. 2017b). Our larger sample in this paper confirmed the offset toward a lower [S ii]/Hα ratio at log [O iii]/Hβ ∼ 0 in higher M_* bins (M_* ≳ 10^10.3 M_⊙).

In Figure 36, we show the [O iii] λ5007/Hβ ratio as a function of M_* for both FMOS Sample-HJ and the local SDSS sample. This is known as the mass–excitation (MEx) diagram (Juneau et al. 2011). It is clear that the FMOS galaxies occupy a region distinct from the local galaxies, well above the upper envelope of the red contour enclosing 95% of the local sample. Across the entire M_* range probed, the line ratio increases at fixed M_* by ≈0.5 dex, from z ∼ 0.1 to 1.6. Similar to the SDSS sample, the FMOS galaxies exhibit an inverse correlation between [O iii]/Hβ and M_*. We derived a linear fit to the locus of the FMOS galaxies while limiting to 170 galaxies in Sample-HJ having both Hβ and [O iii] detections (≥1.5σ). The best-fit relation (solid green line in Figure 36) is given as

$$\begin{eqnarray}&&\mathrm{log}([{\rm{O}}\,{\rm{III}}]/{\rm{H}}\beta )=0.23-0.54\times \left[\mathrm{log}{M}_{* }/{M}_{\odot }-10\right].\end{eqnarray} \tag{ 17 }$$

The stacked measurements in five M_* bins are in good agreement with the best-fit relation. With respect to the best-fit linear relation, the intrinsic scatter is found to be ${\sigma }_{\mathrm{int}}=0.17$ (only for objects with both detections) after accounting for the individual measurements errors on log M_* and log[O iii]/Hβ.

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For comparison, we show the best-fit linear relation to the KBSS-MOSFIRE samples at z ∼ 2.3 (Strom et al. 2017), indicating a further increase in the emission-line ratio at fixed M_*. The best-fit relation to the higher-redshift sample has a shallower slope (−0.29) than the FMOS sample at z ∼ 1.6 due to higher ratios at high M_*. Turning to the SDSS sample, the stacked points show a further steeper slope at lower masses. Fitting to those at M_* ≤ 10¹⁰ M_⊙, we find the slope to be −0.72. The gradual change of the slope indicates that the [O iii]/Hβ ratio evolves with redshift in a mass-dependent way: the more massive the systems are, the faster the [O iii]/Hβ decreases with redshift.

In Figure 36, we overplot the empirically calibrated division line between AGNs and star-forming (or composite) galaxies at z ∼ 0.1 (solid black line; Juneau et al. 2014). It is clear that the majority of the FMOS galaxies are located above this classification line. For comparison to the star-forming population, Figure 36 shows X-ray AGNs at z ∼ 1.6 from the full FMOS catalog. For these X-ray-detected objects, we estimated stellar masses using the SED3FIT package (Berta et al. 2013) based on the MAGPHYS software (da Cunha et al. 2008), including the emission from an AGN torus (a full analysis of the SEDs of X-ray sources is presented in D. Kashino et al. 2019, in preparation). These objects tend to have even higher [O iii]/Hβ ratios than the star-forming population at fixed M_*, while roughly one-third of them are virtually mixed with the star-forming population. We found that shifting the division line in the MEx diagram by Δlog M_* = + 0.5 dex yields a reasonable classification between the star-forming galaxies and X-ray sources (dashed black line in Figure 36). This is in agreement with the luminosity-dependent offset modeled by Juneau et al. (2014; see Appendix B) for the threshold luminosity of the FMOS sample, which is ${L}_{{\rm{H}}\alpha }^{\mathrm{thresh}}\approx {10}^{41.5}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ (see Figure 15). Coil et al. (2015) found that a shift of +0.75 dex in M_* is required to purely distinguish AGNs from star-forming galaxies at z ∼ 2.3 using the MOSDEF survey (Kriek et al. 2015), while recently, Strom et al. (2017) argued that an even larger shift (∼1 dex) is needed for the KBSS-MOSFIRE sample.

In Figure 37, we show the observed [N ii] λ6584/Hα ratios as a function of M_* for the FMOS Sample-H and the local SDSS sample. We plot 557 galaxies with both Hα and [N ii] detections, divided into two groups: HQ objects (N = 325; cyan circles) if S/N(Hα) ≥ 5 and S/N([N ii]) ≥ 3 and LQ objects (N = 226; gray circles) if S/N(Hα) ≥ 3 and S/N([N ii]) ≥ 1.5. For others, the upper limits are shown by downward arrows. The region occupied by the FMOS galaxies is largely overlapped with the locus of the SDSS sample, while a number of objects have a lower [N ii]/Hα ratio than the lower envelope of the red contour enclosing 95% of the SDSS sample. The stacked measurements (large blue circles), however, are clearly off from the average locus of the SDSS galaxies. The amount of the offset is a strong function of M_*, from ≥0.5 dex at M_* ∼ 10^9.7 M_⊙ to <0.1 dex at the massive end (${M}_{* }\geqslant {10}^{11}\,{M}_{\odot }$).

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To analytically describe the average M_*-versus-[N ii]/Hα relation, we used a functional form originally proposed by Zahid et al. (2014a) to parameterize the mass–metallicity relation,

$$\begin{eqnarray}&&{N}_{2}({M}_{* })={{ \mathcal R }}_{0}-\mathrm{log}\left[1-\exp \left({\left[\displaystyle \frac{{M}_{* }}{{{ \mathcal M }}_{0}}\right]}^{\gamma }\right)\right],\end{eqnarray} \tag{ 18 }$$

where N₂ denotes ${\rm{log}}\,[{\rm{N}}\,{\rm{II}}]\lambda 6584/{\rm{H}}\alpha$, ${{ \mathcal R }}_{0}$ is the asymptotic value of the line ratio in log scale at the high-mass end, ${{ \mathcal M }}_{0}$ is the characteristic mass at which the line ratio begins to saturate, and γ is the low-mass end slope. The best fit to the stacked line ratios of the FMOS Sample-H takes ${{ \mathcal R }}_{0}=-0.42\pm 0.04$, $\mathrm{log}{{ \mathcal M }}_{0}/{M}_{\odot }=10.16\pm 0.09$, and γ = 0.90 ± 0.14. The best-fit relation well traces the FMOS stacked points. For the local SDSS sample, we obtained the best-fit parameters of ${{ \mathcal R }}_{0}\,=-0.39$, $\mathrm{log}{{ \mathcal M }}_{0}/{M}_{\odot }=9.50$, and γ = 0.66 with the same procedure.

Supposing that the [N ii]/Hα ratio is sensitive to the gas-phase metallicity, the behavior of the stacked points, as well as the best-fit relation, support with higher confidence our past statement that the majority of massive (M_* ≳ 10^10.6 M_⊙) galaxies are already chemically mature at z ∼ 1.6 as much as local galaxies with the same stellar masses (Zahid et al. 2014b; Kashino et al. 2017b). In Figure 37, we also indicate the estimated intrinsic scatter of the FMOS sample around the average best-fit M_*-versus-[N ii]/Hα relation (green dashed lines). Though the derivation of the scatter is described in detail in the next subsection, the sequence is tight for almost the entire M_* range, except the lowest M_*, where the constraint is poor due to the small number of detections. It is seen that the amount of redshift evolution of the average [N ii]/Hα is comparable to twice the intrinsic scatter at M_* ∼ 10¹⁰ M_⊙.

Comparing to the local SDSS sample, it seems that the FMOS galaxies show a larger scatter in the [N ii]/Hα ratio at a given M_*. To estimate the intrinsic scatter in the line ratio, we define Δlog [N ii]/Hα as the offset of the [N ii]/Hα ratios with respect to ${N}_{2}({M}_{* })$, i.e., the best-fit M_*–[N ii]/Hα relation at a given M_*.

In Figure 38, we show the distribution of the Δlog [N ii]/Hα for objects with both Hα and [N ii] detections in different ranges of M_*, as labeled in each panel. The distribution of upper limits for the [N ii]-undetected objects is also shown in each panel. The upper left panel is for almost the entire stellar mass range ${10}^{9.2}\leqslant {M}_{* }/{M}_{\odot }\leqslant {10}^{11.5}$, while the other three panels are for the partial mass bins (log M_*/M_⊙ = [9.2:10.0], [10.0:10.6], and [10.6:11.5]). It is clear that the distributions of the Δlog [N ii]/Hα values of the Hα+[N ii]-detected objects are skewed toward higher values because the objects with both detections are biased toward having a higher [N ii]/Hα ratio with respect to the best-fit M_*–[N ii]/Hα relation, as seen in Figure 37.

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To estimate the true distribution and scatter, we first assumed that the line ratios of all galaxies follow a zero-mean normal distribution with respect to the best-fit M_*–[N ii]/Hα relation. We then estimated the intrinsic scatter in each M_* bin including upper limits. We computed the likelihood ${ \mathcal L }({\sigma }_{\mathrm{int}})$ for grids of σ_int as follows,

$$\begin{eqnarray}&&{ \mathcal L }({\sigma }_{\mathrm{int}})\propto \displaystyle \prod _{\mathrm{dec}}F({x}_{i},{\tilde{\sigma }}_{i})\displaystyle \prod _{\sup }(1-S({c}_{i},{\tilde{\sigma }}_{i})),\end{eqnarray} \tag{ 19 }$$

where x_i and c_i are the detection values and upper limits of Δlog [N ii]/Hα, respectively. The probability functions F and S are a zero-mean normal distribution function and a zero-mean normal survival function, respectively. The standard deviation ${\tilde{\sigma }}_{i}$ is computed for each object by summing in quadrature the uncertainties on log [N ii]/Hα, log M_*, and the intrinsic scatter σ_int. The uncertainties on log M_* were included by multiplying them by the slope of the best-fit M_*–[N ii]/Hα relation at a given M_*.

For the subsamples shown in Figure 38, we obtained a tight constraint on the intrinsic scatter σ_int, as indicated in each panel. We found σ_int = 0.14 ± 0.01 for the entire M_* range and the largest value (σ_int = 0.24 ± 0.02) in the lowest-M_* bin. In the figure, we overplot the normal distribution function (red curves) with a standard deviation convolved with the median error $\left\langle \delta \right\rangle$ (including the M_* uncertainties) in each bin (i.e., $\sigma =\sqrt{{\sigma }_{\mathrm{int}}^{2}+{\left\langle \delta \right\rangle }^{2}}$). These model distribution functions well trace the high-value tail of the histograms of the detected log [N ii]/Hα values, while there are no upper limits beyond the low-value tail of the model functions. This indicates that our estimates of σ_int are robust.

For further investigation of the trend of the intrinsic scatter and comparison with the SDSS galaxies, we repeated the likelihood analysis with narrower overlap binning. In the upper panel of Figure 39, we show the estimated σ_int as a function of M_* with the individual Δlog [N ii]/Hα values, in comparison with the SDSS sample. For the FMOS and SDSS samples, Δlog [N ii]/Hα are computed separately with their own best-fit relation. For the local galaxies, we show the stacked ratios normalized to the best-fit relation and the central 68th percentiles in the M_* bins (black dashed lines). Note that the increase in the scatter due to the individual measurement errors on [N ii]/Hα is negligible (≲5%) for the SDSS sample. It is clear that the intrinsic scatter of the FMOS galaxies increases with decreasing M_*, while being almost constant σ_int ≈ 0.1 at M_* ≳ 10^10.3 M_⊙. A similar trend is seen in the SDSS sample, although the intrinsic scatter of the local sample is smaller than that of the FMOS sample at fixed M_*.

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Next, we compare the scatters at fixed N₂(M_*) values, which are taken from the best-fit M_*–[N ii]/Hα relations for the FMOS and SDSS samples, respectively (lower panel in Figure 39). Now the trends of the intrinsic scatter are in rather good agreement between the local and FMOS samples, though the scatter of the FMOS sample is about twice the SDSS sample at the highest N₂(M_*). With respect to this, a caveat is that the local star-forming galaxies are limited to those below the Kauffmann et al. (2003a) division line in the BPT diagram, which is more strict than the maximum starburst limit adopted for the FMOS galaxies, and hence may effectively reduce the scatter, especially at high masses, where the line ratio is nearly saturated.

Comparing the two panels, it seems that the scatter in [N ii]/Hα is more directly related to N₂(M_*) rather than M_* itself, and thus σ_int varies more continuously with N₂ across its whole range. We thus parameterized σ_int as a function of N₂ by a second-order polynomial,

$$\begin{eqnarray}&&{\sigma }_{\mathrm{int}}=0.299+0.807{N}_{2}{({M}_{* })+0.856{N}_{2}({M}_{* })}^{2},\end{eqnarray} \tag{ 20 }$$

which is shown in the lower panel of Figure 39. We used this fit to indicate the estimated intrinsic scatter around the average M_*-versus-[N ii]/Hα relation in Figure 37.

The [N ii]/Hα ratio is known to reflect the gas-phase metallicity of the galaxy (e.g., Pettini & Pagel 2004), though it is also affected by other ISM conditions, such as the ionization parameter, the shape of ionizing spectra (e.g., Kewley et al. 2013), and the intrinsic ratio of N/O (Masters et al. 2014). Therefore, interpreting the scatter in [N ii]/Hα as a result of only variation in metallicity may lead to inaccurate insights. However, our result likely indicates that there is not a large difference in the amount of metallicity variation at fixed average metallicity between the local SDSS and z ∼ 1.6 FMOS samples. We note that the physical time across the redshift range of the FMOS sample (1.43 ≤ z ≤ 1.74; 0.69 Gyr) is similar to that of the local sample (0.04 ≤ z ≤ 0.10; 0.76 Gyr). Therefore, the effects of the time evolution of metallicity within the redshift ranges of the two samples should be small.

In Figure 40, we show the correlation between the Hα and [O iii] λ5007 fluxes after correcting for dust extinction and aperture loss. Extinction correction is applied by assuming the Cardelli et al. (1989) extinction law with f_neb = 0.53 (Section 9.3). Limiting the Hα+[O iii]-emitter sample, a strong correlation and good agreement exist between these quantities. We found the Spearman's rank correlation coefficient to be ρ = 0.63, excluding the null hypothesis of no correlation. The scatter of log [O iii]/Hα is found to be 0.28 dex with a small median offset of log [O iii]/Hα = −0.004.

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The [O iii]/Hα ratio is expected to depend on stellar mass because metallicity and dust extinction increase, on average, with M_*. In Figure 41, we show the dust-corrected (aperture as well) [O iii]/Hα ratio as a function of M_* for the subsamples. Limiting to the Hα+[O iii] emitters, it is clear that the line ratio decreases with increasing M_*, and that at high M_* (≳10^10.5 M_⊙), the majority of the Hα-detected objects have no significant detection of the [O iii] line. We note that the extinction-corrected [O iii]/Hα ratio has essentially the same information as the [O iii]/Hβ ratio (i.e., Figure 36).

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The lack of [O iii] detection at high M_* indicates possible biases that exist between the Hα- and [O iii]-selected populations. The [O iii] flux decreases more rapidly with increasing metallicity and the level of dust extinction; thus, the [O iii]/Hα ratio depends significantly on these properties. To indicate biases between the Hα- and [O iii]-emitter subsamples, we separate the objects into different M_* bins and compute the fraction of objects with [O iii] detection in each bin. We then compare the distribution of the observed Hα and [O iii] fluxes between the subsamples in each bin. In Figure 42, we show the distribution of the aperture-corrected Hα fluxes (not corrected for dust) for the Hα- and Hα+[O iii]-emitter samples in four bins of stellar mass (log M_*/M_⊙ < 9.9, 9.9 ≤ log M_*/M_⊙ < 10.3, $10.3\,\leqslant \mathrm{log}{M}_{* }/{M}_{\odot }\lt 10.7$, and log M_*/M_⊙ ≥ 10.7). For the Hα+[O iii]-emitter sample, we also plot the distribution of observed [O iii] fluxes. In each panel, we give the number of objects in the Hα- and Hα+[O iii]-emitter samples, as well as the median values of the observed Hα and [O iii] fluxes in log scale in units of ${10}^{-17}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$.

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In the lowest-M_* bin (upper left panel in Figure 42), we detected the [O iii] line (≥3σ) for more than half (55%) the Hα-emitter sample. The median Hα fluxes of the Hα- and Hα+[O iii]-emitter samples are similar to each other. At higher M_* bins, however, the fraction of Hα+[O iii] emitters is lower: 39%, 27%, and 9% in the second, third, and fourth bins, respectively. It is also clear that a difference becomes apparent between the median Hα fluxes of the Hα- and Hα+[O iii]-emitter samples: the Hα+[O iii] emitters are biased toward higher Hα flux.

For further insights, we separate the sample into bins of the level of extinction ${E}_{\mathrm{star}}(B-V)$ estimated from the UV slope (see Section 9.2). In Figure 43, we show the distribution of observed fluxes in four E_star(B − V) bins ($0\leqslant \mathrm{log}{E}_{\mathrm{star}}(B-V)\lt 0.16$, $0.16\leqslant {E}_{\mathrm{star}}(B-V)\lt 0.23$, $0.23\leqslant {E}_{\mathrm{star}}(B-V)\lt 0.35$, and ${E}_{\mathrm{star}}(B-V)\geqslant 0.35$). It is evident that, similar to the trend with M_*, the fraction of Hα+[O iii] emitters decreases with increasing extinction value, from 53% in the lowest bin to 9% in the highest bin.

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Our results clearly indicate that the [O iii] emission line traces more preferentially lower M_* galaxies and/or objects less obscured by dust. We note that there is a strong correlation between M_* and ${E}_{\mathrm{star}}(B-V)$ (Figure 28). In less massive galaxies, the higher [O iii] fluxes are associated with lower metallicities. We thus conclude that the use of [O iii] for the FMOS-COSMOS sample comes with biases toward lower M_*, lower metallicity, and/or less obscured populations than those traced by Hα at the same flux limit. Even so, the [O iii] emission line is a powerful tool for galaxy surveys at high redshifts, since low-mass and low-metallicity galaxies may be a dominant population in the early universe.

Note that the [O iii]- and [O iii]-single-emitter samples are not purely selected by the [O iii] line because we included the criterion on the predicted Hα flux in the preselection of the spectroscopic targets to achieve a high success rate of detecting Hα. Indeed, the majority of the [O iii]-emitter sample has a detection of Hα; thus, there are a small number of [O iii] single emitters in our FMOS catalog. We do not see any significant trends in either the Hα-detection fraction or the average [O iii] flux of the Hα+[O iii] emitters relative to the [O iii] emitters.