THE zCOSMOS–SINFONI PROJECT. I. SAMPLE SELECTION AND NATURAL-SEEING OBSERVATIONS^*

The optical-to-IRAC photometric data reported in Tables 2 and 3 were used to perform SED fitting analysis to estimate galaxy stellar mass, SFR, dust extinction (A_V), and age (i.e., the time elapsed since the beginning of star formation). In a few cases the sources were blended in some of the IRAC bands (due to the poorer angular resolution compared to the other bands), and such IRAC data were excluded from the fit. We used the HyperZmass software, i.e., a modified version of the public HyperZ code (Bolzonella et al. 2000), which fits photometric data points with synthetic stellar population models, and picks the best-fit parameters by minimizing the χ² between observed and model fluxes. The stellar mass is obtained by integrating the SFR over the galaxy age, and correcting for the mass loss in the course of stellar evolution (∼40% for a galaxy of ∼1 Gyr and a Chabrier IMF; see Pozzetti et al. 2007). The best-fit results strongly depend on the assumptions concerning metallicity, initial mass function (IMF), stellar population models, extinction law, and SFH. In order to minimize the number of free parameters in this work we used only models built with solar metallicity, and adopted the Chabrier (2003) IMF. We fixed the redshift to the spectroscopic values, used the Calzetti et al. (2000) law to account for dust extinction, and the prescription of Madau (1995) to treat the Lyα forest flux decrement. The dust extinction parameter (i.e., A_V = E(B − V) × 4.05; cf. Calzetti et al. 2000) was allowed to range from A_V = 0 to A_V = 3 in steps of 0.1.

As recently discussed in Maraston et al. (2010, hereafter MA10), the assumption on the SFH is crucial to derive astrophysically plausible best-fit parameters, and should be chosen based on the expected properties of the galaxy sample. In particular, MA10 argued that models with constant SFR (CSFR), and the so-called τ-models characterized by an SFR exponentially decreasing with time as e^−t/τ, do not give a realistic representation of z ∼ 2 star-forming galaxies. When age is left as a free parameter both models lead to very low ages (≲ 0.1–0.3 Gyr), which would imply a formation redshift almost identical to the redshift at which the galaxies are observed. As extensively discussed in MA10, such unrealistically young ages are the consequence of the outshining effect by the most recently formed stellar populations, and should not be considered real. In an attempt to circumvent this difficulty, a lower limit (of ∼0.1 Gyr) is often imposed to the galaxy age, with the result that many (most) galaxies are found to cluster at such imposed minimum age. This is because in such fits the current SFR and A_V are dictated by the rest-frame UV part of the spectrum, but within the assumed SFH such an SFR would largely overproduce mass (then violating the near-IR flux constraints) if not for very short ages. Such unrealistically short ages suffice to demonstrate that the average past SFR must have been much lower than the current values, hence SFR (on average) must have been secularly increasing with time. Thus, the best-fit ages derived using either CSFR or τ-models should rather be interpreted as those of stars providing the bulk of the light in those bands for which the photometry is affected by the smallest errors (as it is built-in in the χ² procedure), i.e., in the optical, which corresponds to the rest-frame UV.

Moreover, "τ-models" automatically assume that all galaxies are caught at the minimum of their SFRs, while it appears more plausible that z ∼ 2 star-forming galaxies are close to their SFR peak, given that this is the cosmic epoch of maximum star formation activity and given the functional form of the SFR(M_⋆, t) relation (Renzini 2009; Peng et al. 2010; Bouché et al. 2010; MA10). Our zC-SINF sample includes by selection only star-forming galaxies at 1.4 < z < 2.5, with very young stars boosting the Hα emission line. We then adopted two different types of SFHs: (1) CSFR with an age lower limit of 0.1 Gyr, using stellar population models from both Maraston (2005) and Bruzual & Charlot (2003, hereafter MA05 and BC03, respectively) and (2) SFR exponentially increasing with time (SFR ∝e^+t/τ), i.e., the so-called inverted τ-models (inv-τ; cf. MA10), with fixed formation redshift (z_f ≃ 5, i.e., fixed ages, see Section 3.2.3), then using MA05 stellar population models. As MA05 templates (both CSFR and inv-τ) are built with the Kroupa (2001) or Salpeter (1955) IMF, we used the following relations to correct galaxy stellar masses, according to the adopted Chabrier (2003) IMF: log$(M_{\star,\rm Chabrier})= {\rm log}(M_{\star,\rm Kroupa})-0.04$ and ${\rm log}(M_{\star,\rm Chabrier})= {\rm log}(M_{\star,\rm Salpeter})-0.23$. The same corrections apply to log(SFR).

In Appendix A, Figure 20 (entirely published as online-only material) shows the best-fit SEDs that we have obtained with the three mentioned combinations of models and SFHs. The corresponding best-fit parameters are listed in Table 4. It is worth noticing that the best-fit SEDs obtained with different templates are very similar; those obtained with BC03+CSFR and MA05+CSFR models almost fully overlap each other. In the following subsections the SED best-fit parameters (in particular M* and SFR) obtained in the three cases are compared to each other, thus showing what kind of systematics may affect the quantities derived from SED fitting procedures applied to our z ∼ 2 galaxies.

The main difference between MA05+CSFR and BC03+CSFR models is that the BC03 population synthesis models do not include the contribution of the stars in the thermally pulsing asymptotic giant branch (TP-AGB) phase, which instead in MA05 models contribute a significant fraction of the luminosity (especially in the near-IR) for stellar population ages in the range between ∼0.2 and ∼2 Gyr. As a consequence, to compensate for the lack of this contribution, BC03+CSFR models tend to overestimate galaxy stellar masses and ages with respect to MA05+CSFR models for galaxies in which stellar population in this age range dominate (MA05; Maraston et al. 2006; Wuyts et al. 2007, etc.). Moreover, for ages in excess of ∼0.1 Gyr, MA05 models tend to have redder B − V colors with respect to the BC03 models, which is due to differences in the adopted stellar evolutionary tracks that affect also other evolutionary phases (e.g., different treatment of overshooting in the stellar interiors; see the top panel of MA05 Figure 27, and also the top-left panel of the Bruzual 2007 Figure 3). The redder colors of MA05 model spectra at a given stellar age require younger best-fit ages in order to reproduce the observed colors, and this drives the results toward lower stellar masses and higher SFRs.

This is illustrated in the left panels of Figures 2 and 3 comparing masses and SFRs obtained with the BC03+CSFR and MA05+CSFR models for the zC-SINF sample. Note that the ages derived with both MA05+CSFR and BC03+CSFR models are indeed very low for the majority of the zC-SINF galaxies, and tend to cluster to the artificially imposed minimum age (i.e., 0.1 Gyr, see the previous subsection and Table 4). These galaxies are shown as red filled circles in the left panels of Figures 2 and 3, and for them MA05+CSFR and BC03+CSFR models give consistent results. Instead, results differ for galaxies for which at least BC03+CSFR ages exceed 0.2 Gyr: MA05+CSFR masses are smaller and SFRs are higher, both by a factor of ∼1.5, compared to those obtained with BC03+CSFR models. These discrepancies can be ascribed to a combination of the two effects mentioned above, MA05 optical colors being redder than BC03 ones for ages older than ∼0.1 Gyr, and near-IR color being redder for ages older than ∼0.2 Gyr.

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An option for avoiding excessively young ages from the best-fit procedures is to fix the galaxy formation redshift (z_f, as the beginning of star formation) to some high value. The age then follows from the cosmic time difference between the formation redshift z_f and the redshift z_spec at which the galaxy is observed. Galaxies indeed abound at z > 2 (and even at z ≫ 2) and are the likely precursors of those we observe at z ∼ 2. This latter procedure was adopted in MA10 in conjunction with "inverted-τ" models, by fixing z_f ≃ 5 and τ > 0.3 Gyr, and the same recipe is used here, then comparing the results to those of CSFR models. The outcome is fairly insensitive to the precise value of z_f because most stars are formed in the last τ time interval in these inverted-τ models (MA10). In practice, since most of the galaxies in our sample are clustered at z ∼ 2–2.5, the assumption that star formation begins at z ≃ 5 implies galaxy ages in the range ∼1.1–2.1 Gyr. Clearly, the two objects at z ∼ 1.4 turn out to be older with ages ∼3 Gyr. The values of τ selected by the best-fit procedure range from ∼0.345 to 0.89 Gyr.

Stellar masses and SFRs derived assuming a constant SFR and those obtained from inverted-τ models (in both cases using MA05 stellar population models) are compared in the right panels of Figures 2 and 3. Stellar masses from inverted-τ models are on average ∼1.5 times higher than those obtained assuming a constant SFR, and the SFRs are ∼2 times lower. Therefore, specific SFRs (i.e., SFR/M_⋆) are on average a factor ∼3 lower when adopting inverted-τ models. As discussed in the previous section, and reported in Table 4, best-fit ages are typically very short with CSFR models. Since for such models M_⋆ = Age × SFR (apart from the mass return fraction) the best-fit procedure picks a higher SFR (and a higher A_V) in order to match the M_⋆-sensitive near-IR flux. In doing so, the "best" compromise is one in which M_⋆ is underestimated and SFR and A_V are overestimated, compared to the inverted-τ models, which instead are allowed to accumulate mass for typically a ∼10 times longer time.

Incidentally, it is worth noting that such a large difference in specific SFRs would have an impact on the comparison of the integral of the cosmic SFR density with the growth of cosmic stellar mass density (cf. Wilkins et al. 2008). Note that these systematic differences are much smaller for the few objects for which CSFR+MA05 models give ages older than 0.2 Gyr (open circles in Figures 2 and 3) compared to those for which CSFR+MA05 models give ages below 0.2 Gyr (red filled circles).

For the reason mentioned above and in Sections 3.2.1, we favor inverted-τ models for the description of our z ∼ 2 actively star-forming galaxies. However, in the following we keep reporting all three sets of SED-fitting results (CSFR with BC03 and MA05, and inv-τ with MA05) in order to better gauge the robustness (or the systematic uncertainties) of the results. We note in fact that the χ² procedure often gives formal error in M_⋆ or SFR which are just a few percent. Such exceedingly small formal errors clearly contrast with the much larger systematic differences noted above. Given the benchmark nature of these SINFONI galaxies, quoting the results for various assumed SFHs will also favor intercomparisons with future data sets.

We detected the Hα line emission for 25 of the 30 galaxies observed. For each detected target, we measured the global Hα flux, systemic redshift, and velocity dispersion from spatially integrated spectra in circular apertures centered on the centroid of the line emission determined from the line maps (extracted as described in Section 4.3.2). The aperture size was chosen to enclose the total flux estimated from a curve-of-growth analysis within the deepest part of the effective FoV. Typical aperture radii (r_ap) for our objects range from 075 to 15 and are reported in Table 5.

The Hα properties were derived using the code LINEFIT (developed by the SINS team and described by FS09 and Davies et al. 2011) assuming that a single Gaussian profile represents the intrinsic emission line profile of the source. In the fitting procedure, LINEFIT takes into account the instrumental spectral resolution by convolving a Gaussian profile with the spectral response function represented by empirical night sky line profiles (see Section 4.2). The resulting profile is fit to the observed spectrum by means of a minimization procedure that accounts for the noise spectrum of the data through Gaussian weighting, and the formal uncertainties of the best-fit parameters are derived from 100 Monte Carlo simulations. The noise spectrum is computed from the "sigma cube" associated with each data set (Section 4.2) and further accounts for deviations from Gaussian scaling with aperture size (due to, e.g., correlated noise) from an analysis of the effective noise properties of each data cube (see Section 5.2 and Appendix C of FS09 for details). A linear continuum component underneath Hα was simultaneously fit with the emission line profile; in most cases, however, the continuum is essentially undetected in our ∼1 hr integration SINFONI data.

The total Hα fluxes F(Hα) are given in Table 5, along with the vacuum redshifts z(Hα) and integrated velocity dispersions σ(Hα)_integrated corresponding to the central wavelength and width of the best-fit Gaussian profile. For undetected sources, the 3σ upper limits on the total Hα fluxes are reported. These upper limits were derived based on the noise spectrum for a fixed circular aperture of 1'' radius centered at the expected position of the source, assuming that the Hα redshift is equal to the redshift from the zCOSMOS optical spectroscopy and that the intrinsic line width is σ(Hα)_integrated = 130 km s⁻¹ (the average value for the detected sources). We emphasize that the velocity dispersions listed in Table 5 and quoted throughout this paper are corrected for the instrumental velocity broadening. We also note that, given the measurement procedure, the global σ(Hα)_integrated values in Table 5 include a contribution from internal velocity gradients (e.g., due to rotation), as they are obtained from the integrated spectra without any shift of individual pixels to the systemic velocity. The uncertainties from the absolute flux calibration are estimated to be ∼10% and those from the wavelength calibration, ≲ 5%. Together with uncertainties from the continuum placement and the choice of aperture for the measurements (see Section 4.3.3), we estimate that systematic uncertainties amount to 30% typically, and up to 50% for the objects with the lowest S/N.

Table 5 also lists the fractional contribution frac_BB(Hα) from the integrated Hα line flux to the total broadband flux density from the observed magnitude in K or H band (Table 3) for the targets at z > 2 or z < 2, respectively. The associated uncertainties reported in the table correspond to the formal measurement uncertainties of the Hα flux and broadband magnitudes. The combined systematic uncertainties (including those of the absolute flux calibration) are largely dominated by those of the SINFONI Hα data and are thus typically 30%, and up to 50% for the faintest objects.

We extracted maps of the velocity-integrated Hα line flux, velocity (relative to the systemic velocity), and velocity dispersions for the zC-SINF sample in the same manner as described above for the integrated properties, but now applying the procedure to the spectrum of individual spaxels. Prior to the fitting, the data cubes were lightly smoothed with 3 pixel wide median filtering in both spatial and in the spectral dimensions, in order to improve the S/N. Because of the short ≈1 hr integration time for our pre-imaging SINFONI data, the kinematic maps for a large fraction of the sample are significantly affected by low S/N even after median-filtering, and hamper reliable extraction of the full two-dimensional information. Higher S/N as well as higher spatial resolution will be achieved for the subset of the sample followed-up with SINFONI+AO observations.

For the pre-imaging data sets, useful kinematic information can nevertheless be obtained from position–velocity (p–v) diagrams, as well as profiles of the velocities and velocity dispersions extracted along the major axis of the objects. For the p–v diagrams, we used a synthetic slit with a width of 6 pixels (075) in all cases, integrating the spectra along the direction perpendicular to the slit orientation. The slit was always positioned so as to pass through the centroid of the Hα emission based on the extracted line map. Whenever possible, the slit was aligned with the kinematic major axis identified from the velocity fields, and defined as the direction of steepest observed velocity gradient across the source. In those cases, the Hα kinematic major axis is generally consistent with the morphological major axis identified from the Hα line maps as well as the Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) I-band imaging. In the other cases (i.e., for data with too low S/N), the slit was aligned with the morphological major axis, and we verified with p–v diagrams extracted along several different position angles that larger velocity differences were not measured for different directions than along the morphological position angle. The maximum observed velocity difference, v_obs = v_max − v_min, was derived from the major axis velocity profile obtained from fits to spectra integrated in contiguous, 6 pixel wide apertures equally spaced along the major axis (with centers separated by 3 pixels). Significant velocity differences could be measured in 17 of the 25 detected sources from the pre-imaging no-AO data sets presented in this paper.

To estimate the Hα sizes of the detected zC-SINF objects, we determined the half-light radius based on the curve-of-growth analysis in circular apertures described in Section 4.3. The intrinsic sizes r_1/2(Hα) are corrected for the effective spatial resolution by subtracting in quadrature the PSF half-width at half-maximum (HWHM) appropriate for each data set. For one source (ZC415087), the observed half-light radius is smaller than the PSF HWHM; since the PSF was not observed simultaneously with the data, this could be attributed to variations in time of the seeing between the observations of the acquisition star used as PSF calibrator and the science target. For this galaxy, we adopted the observed size as the upper limit to the intrinsic size. The formal uncertainties of the r_1/2(Hα) were estimated as in FS09 (and turn out to be very similar as well), accounting for variations of ≈20% in the PSF FWHM between successive OBs and for deviations from axisymmetry of the PSF profiles (the median ellipticity of the PSFs associated with our data sets is ≈0.1); the resulting uncertainties on the r_1/2(Hα) measurements are typically ≈35% (median). These uncertainties do not account for other potentially important factors affecting size determinations, such as the dependence on the sensitivity of the data, the actual intrinsic surface distribution of the Hα emission, and the measurement method. We address these issues further in the following subsection.

The velocity-integrated Hα line maps and the position–velocity diagrams of all detected objects in the zC-SINF sample are shown in Appendix B, Figure 21 (entirely published as online-only material), along with the ACS I-band images and the source-integrated spectra around Hα. The maximum observed velocity difference measurements are given in Table 5.

In view of the relatively short integration times of about 1 hr for the zC-SINF pre-imaging SINFONI data sets, we examined the possible impact of surface brightness sensitivity on the derived total Hα fluxes and half-light radii. For the measurements presented in this work, we chose a curve-of-growth analysis in circular apertures for its simplicity, and because it does not rely on assumptions about the intrinsic spatial distribution of the line emission. This approach also allowed us to derive in a uniform and consistent manner size estimates for all detected objects, which span a significant range in apparent sizes and were observed under different seeing conditions.

We point out, however, that other methods would lead to more robust size estimates for the better resolved sources with higher S/N data, as discussed by N. Bouché et al. (2011, in preparation; see also FS09). For instance, the use of elliptical apertures to construct the curves of growth would be more appropriate for sources with elliptical isophotes, such as inclined disk-like systems. Our use of circular apertures gives r_1/2(Hα) values that are analogous to circularized half-light radii; the latter are by definition smaller than the actual half-light radius by a factor of $\sqrt{b/a}$, where b/a is the ratio of the projected size along the minor and major axes of the galaxy. In addition, and more importantly, the curves of growth are affected by the surface brightness sensitivity of the data. Estimating the impact on the total flux measurements is complicated by the a priori unknown details and extent of the intrinsic spatial distribution of the Hα line emission.

To gauge the impact of surface brightness sensitivity on the total line fluxes, we used data of the SINS Hα sample with a range of integration times from typically a few hours up to 10 hr per object. The curve-of-growth analysis for the 40 SINS objects with integrations longer than 1 hr (with mean and median of 4 hr) was repeated after adjusting the surface brightness limits of each data set to the equivalent limits for 1 hr integration time. More specifically, we determined the average S/N per pixel at the radius r_ap at which the curve of growth converges, based on the data with full integration time T_int, and used to compute the total Hα flux. To mimic the shallower surface brightness limits for 1 hr integrations, we scaled the above average S/N per pixel by $1 / \sqrt{T_{\rm int}}$ appropriate in the background-limited regime and identified the new r_ap for 1 hr as the radius at which the S/N per pixel corresponds to the scaled value. From the curve of growth and total flux measured within this new radius, we re-calculated the r_1/2(Hα). This is clearly a simplistic approach, but we verified for a few objects that consistent results would be obtained if we had used cubes combining only a subset of the exposures amounting to 1 hr integration time to estimate the r_1/2(Hα) in shallower data.

The results indicate that the total flux derived from the shallower data is on average ∼10% lower than for a typical integration time of 4 hr, albeit with significant scatter. Unsurprisingly, the median differences tend to increase for data sets with higher integrations, up to ∼30% for 7–10 hr. The scatter also increases, probably as a result of the diverse source morphologies. This exercise further indicates that the half-light radii could be underestimated by comparable amounts of ∼10%–30%. This simple analysis thus suggests that while undoubtedly present, surface brightness limitations in our zC-SINF pre-imaging data do not appear to lead to substantial (i.e., by factors of two or more) underestimates of the total Hα fluxes or sizes of the targets, at the very least in a comparative sense with the deeper SINS Hα sample. The longer integrations of the AO-assisted SINFONI observations planned for the second part of our program is expected to provide better constraints, in particular on the Hα sizes.

One of the main advantages of our zC-SINF sample is the availability of both Hα IFS and multiwavelength photometric information. This allows us to compare the derived Hα properties with those estimated from the broadband photometry. In particular, in the following sections we compare the SFRs from the Hα intrinsic luminosities with those obtained from the SED fits and from the UV rest-frame luminosity.

In Figures 9, 10, and 11, we plot L⁰(Hα) and L⁰⁰(Hα), derived in the previous section, as a function of the SFR estimated by fitting the galaxy SEDs with BC03+CSFR, MA05+CSFR, and MA05+inv-τ templates, respectively (SFR_SED). From these figures, it is evident that for the zC-SINF sample (red filled circles) the slope of the best-fit SFR_SED–L(Hα) relation better agrees with the one-to-one relation derived from Equation (2) (black dashed line) when Hα luminosities are corrected for dust extinction with $A_{V, {\rm H}\,{\mathsc{ii}}}$ (Equation (1)) instead of A_{V, SED}. This statement remains true also taking into account the relatively small fraction of Hα flux missed by these 1 hr integration time SINFONI data (i.e., ∼10%–30%), see Section 5.1. Our results show that this is the case regardless of the stellar population models adopted or the SFH assumed. This result is in agreement with the finding by FS09 for the SINS targets (overplotted as open squares in Figure 9 for comparison), and in contrast to the conclusions by Erb et al. (2006b) and Reddy et al. (2010). As already mentioned in Section 5.1, these other studies of z ∼ 2 galaxies claimed that in their sample Hα regions are as extincted as the stellar UV continuum, and no further correction is needed for L(Hα).

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Reddy et al. (2010) suggested that this discrepancy could be due to the lower stellar masses and SFRs of their sample with respect to the bulk of the SINS sample, and that it is possible that the nebular reddening may on average be larger for galaxies that are forming stars at a higher rate. This lower reddening for lower mass galaxies may be related to these galaxies naturally having lower metallicities. Alternatively, it could also be due to the presence of a more important older and, on average, less attenuated stellar population (e.g., Epinat et al. 2009). Our results are consistent with this explanation, as our zC-SINF sample includes only objects comparable to those with the highest masses and Hα luminosities (hence SFRs) of the SINS sample. From Figure 9, it appears that the SINS objects (open squares) with lower SFRs and masses do not necessarily need a larger dust extinction correction to match the L(Hα)–SFR_SED relation (dashed line), as instead needed for the most massive and active SINS galaxies.

In star-forming galaxies, the rest-frame UV luminosity over the spectral range of 1500–2800 Å is dominated by the contribution of young (OB) stars, and does not suffer much contamination by the older stellar population. Hence, the L_ν luminosity over this wavelength range, corrected for dust extinction, scales linearly with the SFR and can be used as an efficient SFR indicator. Based on synthetic stellar population models, different calibrations have been obtained to convert UV luminosity to SFR, depending on the reference wavelength used, templates, and IMF (see Kennicutt 1998, and reference therein). In this work, we used the relation relative to 1500 Å, and adjusted for BC03 models (following Daddi et al. 2004, Equation (5)), and for the Chabrier IMF (as in Section 3.2.1):

$$\begin{equation} {\rm log}({\rm SFR}_{\rm UV})= {\rm log}(L_{1500})-27.95-0.23, \end{equation} \tag{ 3 }$$

where SFR_UV is in unit of (M_☉ yr⁻¹), and L₁₅₀₀, in (erg s⁻¹ Hz⁻¹), is the intrinsic luminosity already corrected for dust extinction. As for galaxies at 1.4 ≲ z ≲ 2.5 the λ = 1500 Å flux is redshifted in the B-band (which actually samples the 1250–1800 Å rest frame), we used the B-band magnitudes and the spectroscopic redshift information to derive the observed 1500 Å luminosities. The intrinsic 1500 Å luminosity, entering Equation (3), was obtained by multiplying this observed luminosity by the factor $10^{0.4\,A_{1500}}$, where A₁₅₀₀ is the extinction parameter at λ = 1500 Å. We computed A₁₅₀₀ from the (B − z) colors according to the relation

$$\begin{equation} A_{1500}=2.5\,(B-z+0.1), \end{equation} \tag{ 4 }$$

derived from Daddi et al. (2004, Equation (4)) (i.e., E(B − V)_UV = 0.25 (B − z + 0.1) and A₁₅₀₀ = 10 E(B − V)_UV; cf. Daddi et al. 2007), which provides an approximate estimate for the extinction of star-forming BzK-selected galaxies at z ∼ 2.

In Figures 12 and 13 we compare the extinction parameter E(B − V)_UV, derived from the (B − z) color, and the SFR from the UV rest-frame luminosities (both reported in Table 6) with those estimated by fitting the galaxy SED with MA05+CSFR, BC03+CSFR, and MA05+inv-τ models. From these figures it appears that SED fits and UV-derived values of E(B − V) and SFR correlate quite tightly, with some small offset, ≲ 0.05 in E(B − V) and ≲ 0.2 dex in SFR. We note that in Daddi et al. (2004) the relations used to derive both the E(B − V) parameter, and the SFR_UV were calibrated using BC03+CSFR models. This could be the cause of the slight offset in the SFR_UV −SFR(MA05+CSFR) and SFR_UV −SFR(MA05+inv-τ) relations observed in the left and right panels of Figure 13. However, the SFRs derived with different stellar population models and SFHs agree within ∼0.2 dex with the SFR_UV, and notice that the trend is opposite for CSFR and inverted-τ models, which give systematically lower SFR.

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Figure 14 is similar to Figures 9–11, but shows the L⁰(Hα) and L⁰⁰(Hα) as a function of the SFR_UV, derived from Equation (3), rather than from the SED fit. As expected, this figure confirms that for our zC-SINF sample the H ii regions appear to be obscured by roughly twice as much compared to the stars. It is worth noticing that the L⁰(Hα) and L⁰⁰(Hα) shown in this figure were obtained by using the extinction parameters derived from the (B − z) colors instead of the ones derived from the SEDs. This was done to minimize the systematic effects related to different methods to measure the extinction. In fact, we verified that by correcting L_obs(Hα) with A_{V, SED}, obtained using BC03+CSFR models, in Figure 14 we would obtain a different slope (0.72 instead of 1.04) of the best-fit L(Hα)–SFR_UV relation for the zC-SINF objects, and a slightly larger scatter.

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For the 25 Hα-detected objects we computed the rest-frame Hα equivalent width (EW(Hα)) as the ratio of the Hα line integrated flux to the flux density (expressed per unit wavelength) of the stellar continuum. The latter quantity was derived from H and K broadband magnitudes for objects at z < 2 and z > 2, respectively, then corrected for the Hα line fractional contribution (i.e., frac_BB(Hα) in Table 5). Note that for most of the objects frac_BB(Hα) <10%, while only for two galaxies it reaches 20%–40% (i.e., ZC410041 and ZC411737). The resulting EW(Hα)s are reported in Table 6, where for the Hα undetections we list equivalent width upper limits. As for frac_BB(Hα) (see Section 4.3), the uncertainties listed for EW(Hα) in the table correspond to the formal measurement uncertainties while the systematic uncertainties, dominated by those of the SINFONI data, are typically 30% and up to 50% for the faintest sources. While the Hα line integrated flux gives an estimate of the current SFR (as only stars with masses >10 M_☉ and age <20 Myr contribute significantly to the ionizing flux), EW(Hα) probes the relative importance of the youngest most massive stars relative to the bulk of the stellar population, which is responsible for the continuum emission at the same Hα wavelength. Therefore, EW(Hα) is a stellar age indicator, being sensitive to the ratio of current over past (average) SFR.

For galaxies with constant SFR over their lifetime, the equivalent width should be in inverse proportion to the galaxy stellar age, according to a power law, as the stellar continuum steadily increases with time, while the Hα flux remains almost the same (see also van Dokkum et al. 2004). In fact, some authors suggested to derive constraints on galaxy SFHs by studying EW(Hα) as a function of the age (e.g., FS09; Erb et al. 2006b; see also Kriek et al. 2011). However, ages estimated from SED fitting strongly depend on the shape of the assumed SFH, and should be considered with some caution, also due to the parameter degeneracy affecting the best-fit choice (cf. Bolzonella et al. 2000). In fact, as discussed in Section 3.2, for our actively star-forming galaxies at z ∼ 2, when using constant SFR models, ages are underestimated due to the dominant contribution of the youngest stellar population to the stellar light, and cluster around the imposed age lower limit. On the other hand, ages estimated with inverted-τ models seem to be more realistic for these targets, but they are imposed by the choice of the formation redshift, z_f.

Hence, we examined the equivalent width of our zC-SINF sample as a function of the (z − H) color, i.e., a quantity tightly related to galaxy age, sampling the rest-frame 4000 Å break for galaxies at z = 1.4–2.5, and independent of the stellar population models employed (Figure 15). However, as the (z − H) color depends also on the dust extinction parameter, we had to take into account the (z − H) color variation, as a function of both age and of E(B − V). The MA05 synthetic stellar population models with constant SFR, indicate that the (z − H) color is nearly constant in the redshift interval 1.4 ≲ z ≲ 2.5 at a given age, and E(B − V). In Figure 15 we consider both the case of the same dust attenuation for H ii regions and stellar continuum (EW(Hα), left panel), and the case of extra attenuation, according to Equation (1) from Calzetti et al. (2000) (EW₀₀(Hα), right panel, cf. Section 5.1). For comparison, we show the region occupied by synthetic stellar population models with constant SFR, solar metallicity, and five different values of dust extinction (E(B − V) = 0.0, 0.15, 0.2, 0.3, 0.4, chosen to include all values derived for the target galaxies). All the curves show the EW(Hα) and (z − H) color evolution in the age range 0.1–1.5 Gyr, and in steps of 0.1 Gyr (marked by small dots on the curves). The rest-frame EW(Hα) of a template at a given age and E(B − V) was computed as the ratio of the Hα flux, derived from the model SFR via the Kennicutt (1998) conversion, to the r-band flux density of the template, assuming CSFR. For consistency, the Kennicutt (1998) conversion was corrected, as in Equation (2), for the Chabrier IMF, and the BC03 for the Chabrier IMF were used for the r-band continuum and the z − H colors.

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If one assumes that stellar continuum and nebular regions are equally extincted by dust, the equivalent width does not depend on dust attenuation. In fact, in the left panel of Figure 15, at a given age, and for increasing values of E(B − V), the model curves have redder colors, but the same EW(Hα) values. However, under this assumption, we do not find a good agreement between data points and synthetic galaxy models. The measured EW(Hα) tends to lie below the model curves with E(B − V) > 0, in regions that would correspond to unphysical ages older than that of the universe at z ∼ 2, and null (i.e., black curve) or negative color excesses. On the other hand, if one assumes extra dust attenuation for nebular regions with respect to the stars ($A_{V,{\rm H\,\mathsc{ii}}}=A_{V}/0.44$; right panel of Figure 15) all the model curves tighten on a locus that forms an extension of the unreddened curve, and at a given age, EW₀₀(Hα) exponentially decreases (as $10^{-0.33\ A_V(1/0.44 -1)}\sim 10^{-1.7 E(B-V)}$) for increasing values of E(B − V). From Figure 15 it is evident that, although with a large scatter, for zC-SINF galaxies the case of extra dust attenuation better matches with the model predictions. So, these results confirm what we found in the previous sections by comparing Hα luminosity with SFR from SED fitting. That is, for our sample Hα seems to be more extincted than the UV stellar continuum, in agreement with the prescription of Calzetti et al. (2000). The fact that a substantial fraction of the data points in the right panel of Figure 15 show larger equivalent width than the model curves suggests that some of our galaxies could have sub-solar metallicities, which would produce higher equivalent widths (higher Hα luminosity) for a given SFR, age, and E(B − V) (cf. Erb et al. 2006b).

Figures 16–18 show the distributions of Hα properties of the zC-SINF sample (red filled circles). The integrated velocity dispersions σ(Hα)_integrated and the half-light radii r_1/2(Hα) are plotted as a function of the total observed fluxes F(Hα), of the luminosities L(Hα) (uncorrected for dust extinction), and of the stellar masses M_⋆. Stellar masses are from BC03+CSFR models and Chabrier IMF, to allow a better comparison with other IFS samples using these assumptions (see below). We also indicate in the figures the typical sensitivity limits in terms of size and velocity width. These limits were determined following exactly the same procedure as described in FS09. In brief, we determined the average S/N per spatial resolution element within the half-light radius for each galaxy based on the Hα maps. We then calculated the necessary increase in half-light radius for the S/N per resolution element to drop below S/N = 3, keeping the total Hα flux and integrated line width fixed. These derived sizes correspond to the actual surface brightness sensitivity of each data set. The average limit in terms of r_1/2(Hα) as a function of F(Hα) was obtained by taking the running median through the individual limits (and similarly as a function of L(Hα) and M_⋆). The average limits in terms of σ(Hα)_integrated were computed in a similar manner, calculating the line width at which the S/N per spectral resolution element drops below S/N = 3 at fixed F(Hα) and r_1/2(Hα). Because the limits show significant scatter among the objects, and some of the sources have an average S/N per resolution element somewhat below 3, some of the individual measurements lie above the dashed lines in Figures 16–18, which represent typical sensitivity limits.

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The zC-SINF data are compared with the global Hα properties of other galaxy samples in the range 1.4 ≲ z ≲ 2.5 also observed with integral field spectrographs, taken from the SINS survey with SINFONI (FS09, open squares) and the sample observed with OSIRIS at the Keck II telescope by Law et al. (2009, hereafter L09; green filled triangles). The targets for all three studies were drawn from parent samples at z ∼ 2 selected with photometric criteria designed to identify massive star-forming galaxies, and are subject to similar biases introduced by the need for an accurate optical spectroscopic redshift and a sufficiently bright Hα emission. Although we include the results from L09, one should keep in mind that all targets of this sample were observed with the aid of AO and this may introduce differences in the derived Hα properties (see below). The median properties for these three samples (obtained by considering only the Hα detected objects) are shown in Table 7. The comparisons show that the zC-SINF and SINS samples span nearly the same ranges in integrated Hα flux, velocity width, and half-light radius. They also overlap largely in terms of total Hα luminosity and stellar mass. Instead, although the L09 sample covers roughly the same range in Hα flux and luminosity, and in stellar mass, the integrated velocity widths and half-light radii are systematically and significantly smaller, by factors of approximately two for the ensemble of objects, as well as for a given Hα flux/luminosity or a given stellar mass. As discussed by FS09 and L09, these differences could arise from distinct population properties, in particular, more compact sizes. We emphasize that no selection based on sizes was applied for our zC-SINF sample and for the majority of the SINS sample. The differences could also be partly due to a combination of the higher resolution and poorer surface brightness sensitivity for the AO-assisted OSIRIS data. Indeed, this is quite likely the case, given that smaller sizes for the given stellar mass would have implied higher velocities, which instead are lower (see Figure 18). This argues for the outer, high-velocity but low surface brightness regions having been lost. Moreover, the very similar M_⋆ distributions between the zC-SINF and L09 samples suggest that if the differences in sizes and velocity dispersions are attributed to intrinsic galaxy properties, stellar mass may not be the most important parameter driving these differences.

The new zC-SINF data follow a similar trend of increasing integrated Hα velocity dispersion with increasing Hα flux, Hα luminosity, and stellar mass as seen among the SINS and OSIRIS sample galaxies. Likewise, the Hα half-light radii tend to be larger for brighter and more massive sources, although the scatter is more significant. As discussed by FS09, the upper envelope of the distributions of σ(Hα)_integrated and r_1/2(Hα) versus F(Hα), L(Hα), and M_⋆ likely results from observational biases. More specifically, for SINFONI seeing-limited observations, the detection limits for 1 hr integration lies just above the locus of the measurements, implying that the zC-SINF sample may be missing the most extended sources and/or those with broadest velocity widths at a given Hα flux/luminosity or stellar mass. However, such a bias cannot explain the lack of sources with small velocity dispersion at high Hα fluxes/luminosities and stellar masses seen in Figures 16, 17, and 18, which could be the consequence of a real, physical σ(Hα)_integrated–M_⋆ relation. This issue, already pointed out by FS09 for the SINS sample, may not be surprising given that both kinematic components that provide the total dynamical support of galaxies (random motions and rotational/orbital motions) contribute to the measured σ(Hα)_integrated, which thus probes the full gravitational potential of the galaxies. Besides being due to inclination effects, the scatter in the σ(Hα)_integrated–M_⋆ diagram may possibly reflect variations in the gas and dark matter mass fraction among the sources.