Probing Star Formation in Galaxies at z ≈ 1 via a Giant Metrewave Radio Telescope Stacking Analysis

Our sample contains 3698 blue star-forming galaxies with M_B ≤ −21, a median redshift z_med = 1.1, and a median stellar mass M_⋆ = 10^10.3 M_⊙. Figure 2(A) shows the median-stacked image of these galaxies: an unresolved source, detected at ≈17σ significance with L_1.4GHz = (4.13 ± 0.24) × 10²² W Hz⁻¹, is clearly visible. Figure 2(B) shows the image obtained from stacking locations offset by 100'' from the DEEP2 galaxies; this shows no evidence of either emission or systematic effects.

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To obtain the total SFR from the 1.4 GHz luminosity, we adopt the calibration of Yun et al. (2001),

$$\begin{eqnarray}&&\mathrm{SFR}({M}_{\odot }\,{\mathrm{yr}}^{-1})=(5.9\pm 1.8)\times {10}^{-22}\,{L}_{1.4\mathrm{GHz}}({\rm{W}}\,{\mathrm{Hz}}^{-1}),\end{eqnarray} \tag{ 1 }$$

which assumes a Salpeter IMF, with masses in the range (0.1–100) M_⊙. The ≈30% uncertainty in this relation arises primarily from estimates of the local SFR density (Yun et al. 2001); this systematic uncertainty has not been included in our error estimates below. Using our measured rest-frame 1.4 GHz luminosity in Equation (1) yields a median SFR of SFR_RADIO = (24.4 ± 1.4) M_⊙ yr⁻¹ for the 3698 galaxies of our sample.

The fact that the stacked radio emission is unresolved implies a transverse size ≲8 kpc at z_med = 1.1. Note that any uncorrected phase errors arising from the ionosphere would increase the observed spatial extent of the radio emission. Star formation in the DEEP2 galaxies thus appears to typically arise from the central regions, of size ≪8 kpc.

We examined the dependence of the SFR and the specific star formation rate (sSFR, defined as the SFR per unit stellar mass) on redshift by dividing the sample into six uniformly spaced redshift bins covering z ≈ 0.7–1.45, and carrying out the median stacking independently for the galaxies in each bin. For the sSFR, the stacking was carried out in the ratio L_{1.4 GHz}/M_⋆ for each galaxy, so as to not introduce errors from averaging in the stellar mass. Figures 3(A) and (B) show, respectively, the median SFR and the median sSFR of each subsample plotted against the median redshift of its bin. We find that both the SFR and the sSFR decrease with decreasing redshift, with SFR $\propto \,{(1+z)}^{1.98\pm 0.50}$ and sSFR $\propto \,{(1+z)}^{3.94\pm 0.57}$ over 0.7 ≲ z ≲ 1.45. This is consistent with earlier studies, mostly based on optical SFR indicators, which have obtained sSFR ∝ (1 + z)^β with β ≈ 2.8–3.8 for 0 < z ≲ 2.5 (e.g., Karim et al. 2011; Fumagalli et al. 2014; Ilbert et al. 2015; Tasca et al. 2015). We note that median SFR of our galaxies increases less steeply with redshift than the median sSFR because the median stellar mass of the sample decreases with increasing redshift (see also Sklias et al. 2017, for Herschel-detected galaxies at 1.2 < z < 4).

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To study the SFR evolution of galaxies with similar stellar mass, we chose subsamples of the DEEP2 galaxies in two different mass ranges, 10.3 < log[M_⋆/M_⊙] < 10.7 and log[M_⋆/M_⊙] > 10.7. The mass ranges were chosen to ensure that the median stellar mass of each subsample is approximately equal in each redshift bin. Figures 4(A) and (B) show the redshift evolution of SFR and sSFR, respectively, for galaxies in the above mass ranges. We find that the SFR increases with redshift as SFR ∝ (1 + z)^1.83±0.53 and SFR ∝ (1 + z )^3.53±0.72 for, respectively, the lower-mass (10.3 < log[M_⋆/M_⊙] < 10.7) and higher-mass (log[M_⋆/M_⊙] > 10.7) subsamples, while the sSFR increases ∝(1 + z)^2.02±0.42 (low-mass subsample) and ∝(1 + z)^3.49±0.94 (high-mass subsample). We thus find only marginal (≈2σ significance) evidence that the SFR increases more steeply with redshift for the higher-mass subsample in our data. Indeed, excluding the last redshift bin from our fits reduces the statistical significance of the difference in the exponents of the two subsamples further, to ≈1σ significance. We thus find no statistically significant evidence of a difference in the redshift evolution of the SFR for low-mass and high-mass galaxies, with stellar masses log[M_⋆/M_⊙] > 10.3 in the redshift range 0.7 ≲ z ≲ 1.45.

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We note, in passing, that the DEEP2 galaxy sample is not complete in stellar mass. As such, it is possible that massive dusty galaxies with high SFRs have been excluded from our stellar mass subsamples due to dust obscuration. This effect is likely to vary with redshift as the observed optical bands translate to shorter rest-frame UV wavelengths at higher redshifts, with correspondingly higher dust extinction effects. Any dependence of the mass completeness of the sample on redshift, if present in our sample, is likely to affect our results.

Next, we studied the dependence of the SFR on M_⋆ by stacking galaxy subsamples binned by stellar mass. Figure 5(A) shows the median SFR of each subsample plotted against its median M_⋆: a tight correlation between SFR and M_⋆ (usually referred to as the "main sequence"; e.g., Noeske et al. 2007) is clear in the figure, with SFR $=\,(13.4\pm 1.8)\times {[{M}_{\star }/({10}^{10}{M}_{\odot })]}^{(0.73\pm 0.09)}$ M_⊙ yr⁻¹. Our main-sequence power-law index of $\alpha \approx 0.73\pm 0.09$ is in good agreement with earlier studies at similar redshifts (z ≈ 0.5–2.5), which have typically obtained $\alpha \approx 0.6\mbox{--}0.9$ (e.g., Elbaz et al. 2007; Noeske et al. 2007; Santini et al. 2009; Pannella et al. 2015).

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Whitaker et al. (2014) studied the main-sequence relation for mass-complete samples at different redshift intervals in the range 0.5 < z < 2.5, finding evidence for a flattening of the slope of the main sequence at high stellar masses in all redshift bins. Our main-sequence relation at ${z}_{\mathrm{med}}=1.1$ is in good agreement with the relation obtained by Whitaker et al. (2014) at z ≈ 1.25. However, our sensitivity is too low to confirm the presence of a changing slope in the main sequence.

We examined the evolution of the main sequence with redshift by dividing the full sample into two redshift bins (0.7 < z < 1.0 and 1.0 < z < 1.45), and then independently applying the median stacking procedure to six stellar mass bins within each redshift bin. Figure 5(B) shows the median SFR plotted against the median M_⋆ for galaxies in the high-z and low-z subsamples, indicated by filled squares and circles, respectively. We obtained SFR = (10.7 ± 2.3) × [M_⋆/(10¹⁰ M_⊙)]^(0.70±0.15) M_⊙ yr⁻¹ for the low-z subsample (z_med ≈ 0.85) and SFR = (17.3 ± 2.1) ×[M_⋆/(10¹⁰ M_⊙)]^(0.77±0.09) M_⊙ yr⁻¹ for the high-z subsample (z_med ≈ 1.20). We thus find only weak (≈2σ significance) evidence that the normalization of the main sequence increases with increasing redshift, by a factor of ≈1.6 between z ≈ 0.85 and z ≈ 1.2. Similar results have been obtained in earlier studies, albeit mostly using either optical SFR indicators (e.g., Noeske et al. 2007), or galaxy samples with photometric redshifts (e.g., Santini et al. 2009; Pannella et al. 2015). However, we find no evidence that the slope of the main sequence evolves with redshift, over 0.7 ≲z ≲ 1.45, contrary to the expected decline in slope with time expected in cosmic downsizing scenarios (Cowie et al. 1996), due to the shifting of star formation activity from more-massive to less massive galaxies with time (see also Santini et al. 2009; Pannella et al. 2015).

Our main-sequence relation at z ≈ 1.25 is consistent within the errors with the relation obtained by Whitaker et al. (2014) at the same redshift. However, our relation at z ≈ 0.85 is significantly above that of Whitaker et al. (2014) at z ≈ 0.75. This is consistent with a decline in the normalization of the main sequence with decreasing redshift (e.g., Elbaz et al. 2007), as the two low-z subsamples have different redshift distributions, 0.5 < z <1.0 for Whitaker et al. (2014) and 0.7 < z < 1.0 for this work.

However, we again note that the DEEP2 galaxies are selected to have $R\lt 24.1$, i.e., they are selected at rest-frame wavelengths of ≈2700–3800 Å, and that the sample is not mass complete. Massive dusty galaxies with high SFRs are likely to have been excluded due to their high extinction. Our "color" selection also excludes some of these galaxies as these are likely to be red in color. This might affect our results by flattening the slope of the main sequence. The effect is likely to be stronger for higher-redshift galaxies, as these are selected at rest-frame UV wavelengths, <3000 Å, where the extinction effects are larger. This could cause our inferred main-sequence slopes to appear flatter, especially in the high-z subsample.

The SFRs of high-z star-forming galaxies, such as the DEEP2 galaxies of our sample, are usually estimated from optical or near-IR imaging or spectroscopy, based on SFR tracers such as the rest-frame UV continuum luminosity or the [O ii]λ3727 or Hα line luminosity. However, the measured luminosities in these SFR tracers are reduced from their intrinsic values due to extinction by dust in the interstellar medium of the target galaxy. The use of such tracers hence usually underestimates the SFR in high-z galaxies. A variety of prescriptions are available in the literature to correct for the dust attenuation (e.g., Salim et al. 2007; Hao et al. 2011), but their accuracy is unknown, as dust extinction effects are likely to depend on the physical properties of the galaxies (e.g., stellar mass, color, metallicity, etc). In the case of the DEEP2 galaxy sample, we have estimated the median total SFR (i.e., both unobscured and obscured) from the rest-frame 1.4 GHz radio continuum, which is unaffected by dust extinction. In this section, we estimate the SFRs of different subsamples of the DEEP2 galaxies from a set of optical/UV tracers that are commonly used for high-z galaxies (the near-ultraviolet (NUV) continuum luminosity, the rest-frame U-band continuum luminosity, and the [O ii]λ3727 line luminosity). We then compare these median SFR estimates to the radio-derived median SFRs to infer the correction for dust extinction that should be applied to the SFR inferred from each tracer for similar populations of star-forming galaxies, as a function of color, stellar mass, and redshift. The SFR correction factor will be referred to as the dust extinction correction factor , defined as

$$\begin{eqnarray}&&{\epsilon }_{{\rm{X}}}\equiv {\mathrm{SFR}}_{\mathrm{RADIO}}/{\mathrm{SFR}}_{{\rm{X}}},\end{eqnarray} \tag{ 2 }$$

where X corresponds to the SFR tracer in question (i.e., the NUV continuum luminosity, the U-band continuum luminosity, the [O ii]λ3727 line luminosity, etc.), and ${\epsilon }_{X}\geqslant 1$.

The [O ii]λ3727 line luminosity is a popular SFR tracer in high-z galaxies, especially for objects at z ≈ 0.7–2.5, for which the Hα line is redshifted to near-IR wavelengths. In the case of the DEEP2 galaxies of our sample, reliable [Oii]λ3727 line luminosities are available for galaxies at 0.8 < z < 1.4, and one can hence immediately infer the SFR for these galaxies from this tracer, using standard calibrations (e.g., Kennicutt 1998). Following Weiner et al. (2007), we assume a line ratio [O ii]λ3727/H_α = 0.69, appropriate for high-redshift galaxies. We then apply the calibration (valid for a Salpeter IMF; Kennicutt 1998)

$$\begin{eqnarray}&&[{\mathrm{SFR}}_{{\rm{O}}{\rm{II}}}/{M}_{\odot }\,{\mathrm{yr}}^{-1}]=7.9\times {10}^{-42}[{L}_{{\rm{H}}\alpha }/\mathrm{erg}\,{{\rm{s}}}^{-1}],\end{eqnarray} \tag{ 3 }$$

to obtain a median SFR of SFR_{O ii} = 12.5 M_⊙ yr⁻¹. Combining this with our median radio SFR estimate yields a median dust extinction correction factor of _{O ii} ≈ 2.0 for the [O ii]λ3727 SFR estimator. We emphasize that this correction factor is applicable for main-sequence, star-forming galaxies with M_B ≤ −21.

Next, the observed B-band magnitudes of our 3698 target galaxies are available from the DEEP2 survey. Since the sample galaxies lie in the redshift range 0.7 ≲ z ≲ 1.45, the observed-frame B-band corresponds to rest-frame emission wavelengths 180–260 nm, i.e., at NUV wavelengths. About 90% of the NUV continuum emission of a galaxy is provided by young stars (of ages below 200 Myr; Kennicutt & Evans 2012). The rest-frame 230 nm NUV luminosity of a galaxy can hence be used to infer its SFR (e.g., Hao et al. 2011; Murphy et al. 2011; Kennicutt & Evans 2012), via the relation (applicable for a Kroupa IMF; Kroupa & Weidner 2003)

$$\begin{eqnarray}&&\mathrm{log}\ \left(\displaystyle \frac{{\mathrm{SFR}}_{\mathrm{NUV}}}{{M}_{\odot }\,{\mathrm{yr}}^{-1}}\right)=\mathrm{log}\ \left(\displaystyle \frac{\nu {L}_{\nu }}{\mathrm{erg}\,{{\rm{s}}}^{-1}}\right)-43.17.\end{eqnarray} \tag{ 4 }$$

Assuming that this calibration applies to the rest-frame wavelength range of 180–260 nm (note that the calibration is in $\nu \times {L}_{\nu }$ and hence the above assumption is good to first order), we apply it to the observed-frame B-band luminosities, to obtain a median SFR (after adding 0.15 dex to shift to a Salpeter IMF) of SFR_NUV = 5.2 M_⊙ yr⁻¹. Comparing our median radio SFR with this median NUV SFR then yields _NUV ≈ 4.7, for star-forming galaxies with M_B ≤ −21.

The DEEP2 survey also provides the rest-frame U-band (λ ≈ 3600 Å) absolute magnitude of our target galaxies (Newman et al. 2013). The rest-frame U-band continuum luminosity can be used to estimate the SFR following the prescription of Hopkins et al. (2003),

$$\begin{eqnarray}&&\mathrm{log}\ \left(\displaystyle \frac{{\mathrm{SFR}}_{{\rm{U}}}}{{M}_{\odot }\,{\mathrm{yr}}^{-1}}\right)=1.186\times \mathrm{log}\left(\displaystyle \frac{{L}_{{\rm{U}}}}{1.81\times {10}^{21}\,{\rm{W}}\,{\mathrm{Hz}}^{-1}}\right),\end{eqnarray} \tag{ 5 }$$

which assumes a Salpeter IMF. This yields a median SFR of SFR_U = 9.6 M_⊙ yr⁻¹. Combining this U-band median SFR estimate with our median radio SFR then yields a dust extinction correction factor of _U ≈ 2.5 for the U-band SFR, again for star-forming galaxies with M_B ≤ −21.

We thus find that the largest dust extinction correction factor is needed for the NUV 230 nm continuum luminosity, with _NUV ≈ 4.7; the dust correction factors are similar for the rest-frame U-band continuum luminosity (_U ≈ 2.5) and for the [O ii]λ3727 line luminosity (_{O ii} ≈ 2.0).

We also examined the dependence of the dust extinction correction factor for the NUV-, U-band-, and O ii-based SFR estimators on redshift, absolute B-band magnitude, color, and stellar mass. To examine the dependence of _X on absolute B-band magnitude, we compared the dust extinction correction factors for galaxies with M_B ≤ −20 with the above estimates of _X for M_B ≤ −21. To do this, we restricted to the redshift range 0.7 < z < 1.0, for which the DEEP2 sample is complete down to M_B ≤ −20 (Newman et al. 2013). Including all DEEP2 galaxies with M_B ≤ −20 and restricting the redshift range to 0.7 < z < 1.0, we obtained dust extinction correction factors of _NUV ≈ 3.9, _U ≈ 2.5, and _{O ii} ≈ 1.6. In the same redshift range, for M_B ≤ −21, we obtain _NUV ≈ 5.0, _U ≈ 2.4, and _{O ii} ≈ 2.2. The dust extinction correction factor thus appears to be systematically larger for brighter galaxies, except for the calibration based on the U-band luminosity.

Figure 6(A) shows the dependence of _X on redshift for the three SFR tracers. We find no evidence that the dust extinction correction factor varies with redshift over 0.7 < z < 1.45, for galaxies with M_B ≤ −21. Figures 6(B) and (C) plot _X against galaxy color and stellar mass, respectively, for the three SFR tracers. _X is seen to increase with both increasing color (i.e., from bluer to redder galaxies) and increasing stellar mass for all three estimators, with a strong dependence on color and stellar mass for the NUV luminosity and the [O ii]λ3727 line luminosity, and a weaker dependence for the rest-frame U-band luminosity. This is unsurprising for the NUV emission, given that dust attenuation is most effective at shorter wavelengths. The [O ii]λ3727 line emission suffers relatively little dust extinction in bluer and less massive galaxies, but is strongly affected by attenuation effects in redder and more-massive galaxies, making it a good tracer of the total SFR for blue galaxies with M_⋆ ≤ 10^10.4 M_⊙, but a less reliable tracer for more-massive galaxies.

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Finally, the dust extinction correction factor for the SFR estimate from the rest-frame U-band luminosity shows a relatively weak dependence on color and stellar mass, with _U varying by less than a factor of ≈2 over our color and stellar mass range. Furthermore, we find no evidence that _U varies with redshift (over 0.7 < z < 1.45) or B-band absolute magnitude (comparing galaxies with M_B ≤ −20 with those with M_B ≤ −21, in the same redshift range). After applying an average dust extinction correction factor of _U ≈ 2.5, the rest-frame U-band luminosity thus appears to yield a reasonable tracer of the total SFR for blue, star-forming, main-sequence galaxies at z ≈ 0.7–1.5.

We emphasize that the U-band luminosity of a galaxy is only likely to be a good tracer of the SFR for galaxies dominated by young stellar populations (e.g., Cram et al. 1998; Hopkins et al. 2003). Moreover, the U-band luminosity is known to depend on both the evolutionary timescale and the star formation history (e.g., Bell 2003; Hopkins et al. 2003), yielding a nonlinear relation between the SFR and the U-band luminosity (Hopkins et al. 2003). Specifically, the U-band luminosity may be contaminated by emission from older stellar populations, especially in low-luminosity galaxies. As such, caution should be used when inferring the SFR from the rest-frame U-band luminosity. Despite these caveats, the fact that the dust extinction correction factor for the SFR estimate from the U-band luminosity does not vary significantly with color, stellar mass, B-band absolute magnitude, or redshift for the subsample of DEEP2 galaxies with M_B ≤ −21, indicates that the rest-frame U-band luminosity may be an interesting tracer of the SFR in similar galaxies at z ≈ 1.

In the local universe, nebular emission lines have been shown to suffer more extinction, by a factor of ≈1.7, than the stellar continuum at the same wavelength in a wide range of galaxy types (e.g., Fanelli et al. 1988; Calzetti et al. 1994; Mayya & Prabhu 1996; Calzetti 1997; Sullivan et al. 2001; Cid Fernandes et al. 2005; Wild et al. 2011). This differential extinction has been shown to depend on galaxy properties such as the SFR, the sSFR, the inclination, etc. (e.g., Sullivan et al. 2001; Cid Fernandes et al. 2005; Wild et al. 2011; Battisti et al. 2016, 2017). A two-component dust model, including a diffuse, optically thin component arising from the galactic interstellar medium and a dense, optically thick component in the "birth-clouds" of actively star-forming regions, has been proposed to explain the excess attenuation suffered by the nebular emission (Calzetti et al. 1994; Charlot & Fall 2000). Nebular emission is expected to arise from ionized gas located close to young, hot, ionizing stars within the dense birth-clouds (i.e., is spatially associated with the optically thick dust component), while stellar emission arises from stars both in such regions and throughout the disk; this is expected to be the reason for the higher extinction affecting the nebular emission.

While it is clear that nebular emission is significantly more extincted than the stellar continuum in local star-forming galaxies, the situation is much more unclear at high redshifts. For example, similar extinction factors have been obtained for nebular line and stellar continuum emission in UV-selected galaxies at z ≈ 2 (e.g., Erb et al. 2006; Reddy et al. 2010) and in far-IR-selected main-sequence galaxies at z ≈ 0.79–1.5 (Puglisi et al. 2016), while higher extinction of the nebular emission (similar to or even larger than that in the local universe) has been obtained in samples of optical- and near-IR-selected galaxies at z ≈ 1–2 (e.g., Förster Schreiber et al. 2009; Kashino et al. 2013; Wuyts et al. 2013; Price et al. 2014). Pannella et al. (2015) also found evidence for redshift evolution in the differential extinction of nebular and stellar emission in their sample of sBzK galaxies, with similar extinction factors at high redshifts (out to z ≈ 3) and higher extinction of the nebular emission (albeit by a lower factor, ≈1.3, than that seen in the local universe) at z ≈ 1. Finally, given that it is possible that the results may depend on galaxy type, we note that Price et al. (2014) obtained a higher attenuation (by a factor of ≈1.8) for the nebular emission in a sample of 163 main-sequence star-forming galaxies at z ≈ 1.36–1.5.

In the previous section, we estimated the dust extinction factors in the DEEP2 galaxies for three UV/optical SFR indicators, the nebular [O ii] λ3727 line, and the stellar NUV (≈230 nm) and U-band (≈360 nm) continua. Here, we compare the extinction of nebular emission with that of stellar emission in the DEEP2 galaxies; for this, we use the SFR estimate from the U-band continuum, as its wavelength (≈3600 Å) is very similar to that of the [O ii] λ3727 line. The dust extinction factor $\epsilon (\lambda )$ is the ratio of the intrinsic luminosity F_int(λ) to the observed luminosity F_obs(λ), and is hence related to the color excess [E(B − V)] and the reddening curve [k(λ)] by (e.g., Calzetti et al. 2000)

$$\begin{eqnarray}&&\epsilon (\lambda )=\displaystyle \frac{{F}_{\mathrm{int}}(\lambda )}{{F}_{\mathrm{obs}}(\lambda )}\equiv {10}^{0.4.E(B-V).k(\lambda )}.\end{eqnarray} \tag{ 6 }$$

The ratio of the logarithms of the dust extinction factors for the [O ii] λ3727 line emission and the U-band continuum is then

$$\begin{eqnarray}\begin{array}{rcl}{E}_{{\rm{O}}{\rm{II}}/{\rm{U}}} & = & \displaystyle \frac{\mathrm{log}({\epsilon }_{{\rm{O}}{\rm{II}}})}{\mathrm{log}({\epsilon }_{{\rm{U}}})}\equiv \displaystyle \frac{{E}_{\mathrm{gas}}({\text{}}B-V).k(373\,{\rm{nm}})}{{E}_{\mathrm{star}}({\text{}}B-V).k(360\,\mathrm{nm})}\\ & \approx & \displaystyle \frac{{\text{}}{E}_{\mathrm{gas}}({\text{}}B-V)}{{\text{}}{E}_{\mathrm{star}}({\text{}}B-V)},\end{array}\end{eqnarray} \tag{ 7 }$$

where we have assumed k(λ = 373 nm) ≈ k(λ = 360 nm). We obtain E_{O ii/U} ≈ E_gas(B−V)/E_star(B−V) = (0.76 ± 0.04) for the DEEP2 galaxies with M_B ≤ −21, over 0.7 < z < 1.4. The fact that E_{O ii/U} < 1 in our sample indicates that the nebular emission in the DEEP2 galaxies suffers less extinction than the stellar continuum at a similar wavelength. This is very different from the situation in nearby galaxies (where the ratio is ≈1.7) and is also qualitatively different from the results obtained in earlier studies of high-z galaxies, which found either higher extinction of the nebular emission (e.g., Price et al. 2014) or comparable extinctions for the nebular and stellar emission (e.g., Förster Schreiber et al. 2009; Puglisi et al. 2016).

We emphasize that our earlier caveat that the measured rest-frame U-band continuum luminosity might contain contributions from old stars does not affect the above conclusion. Contamination of the U-band continuum by emission from old stars would imply that our U-band SFR estimate is an upper limit, i.e., that our estimate of the dust extinction factor for the U-band stellar continuum is a lower limit. This then implies that our estimate of E_{O ii/U} is an upper limit to the true value. In other words, the possibility of contributions from an old stellar population to the U-band luminosity can only reduce the inferred value of E_{O ii/U}, and hence does not affect our conclusion that the nebular emission in the DEEP2 galaxies of our sample suffers less extinction than the stellar emission.

The three panels of Figure 7 plot the ratio E_{O ii/U} ≈ E_gas(B−V)/E_star(B−V) as a function of color, stellar mass, and redshift. The right and middle panels of the figure show that higher values of E_{O ii/U} are obtained in redder and more-massive galaxies: nebular emission in redder and more-massive galaxies thus appears to suffer larger extinction (relative to the stellar continuum) than similar emission in bluer and less massive galaxies (see also Puglisi et al. 2016). Furthermore, the [O ii] λ3727 emission in the reddest and most massive galaxies shows significantly larger extinction than the U-band stellar continuum. Both of these are consistent with a scenario in which larger amounts of the second dust component (assuming a two-component dust model similar to that of Charlot & Fall 2000) are present in the actively star-forming regions in dusty, massive galaxies, and that this second dust component is less prevalent or absent in blue galaxies.

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Figure 7(C) shows that the ratio E_{O ii/U} increases with decreasing redshift in the DEEP2 galaxies, over $1.4\gtrsim z\gtrsim 0.7$. The dashed straight line shows the best linear fit to the data; we obtain E_{O ii/U} = (1.51 ± 0.24) − (0.61 ± 0.30) × z. Using this relation to extrapolate to lower redshifts, we obtain E_{O ii/U} ≈ E_gas(B−V)/E_star(B−V) = (1.51 ± 0.24) at z = 0. Interestingly, this is consistent with the estimates of the excess extinction (a factor of ≈1.7) suffered by nebular emission in local star-forming galaxies (e.g., Calzetti et al. 1994, 2000; Cid Fernandes et al. 2005). In the context of the two-component dust model, this suggests that the optically thick dust component steadily builds up in actively star-forming regions of main-sequence galaxies, causing a steady increase in the excess attenuation suffered by the nebular emission relative to the stellar continuum.

To address the possibility that the U-band continuum luminosity might not be a good tracer of the SFR, we have also carried out the analysis via a different approach, using the dust extinction factor estimated from the NUV 230 nm continuum luminosity. To estimate the dust extinction factor for the stellar continuum at 373 nm (i.e., at the wavelength of the O ii λ3727 line), we need to know the extinction curve of the DEEP2 galaxies. Since this is not known, we use a range of local extinction curves [k(λ)], for the Milky Way (Cardelli et al. 1989), Large and Small Magellanic Clouds (LMC and SMC, respectively; Gordon et al. 2003), and local starburst galaxies (Calzetti et al. 1994). These yield E_{O ii/373nm} ≈ E_gas(B−V)/E_star(B−V) = (0.63–0.93), with the lowest and highest values for the extinction curves of the local starbursts and the SMC, respectively. Note that our result based on using the U-band luminosity as an SFR indicator lies in the middle of these estimates. We also continue to find that the ratio E_{O ii/373nm} increases with decreasing redshift, over $1.4\gtrsim z\gtrsim 0.7$. Extrapolating to lower redshifts for each assumed reddening curve, we obtain E_{O ii/373nm} ≈ 1.3–1.9 at z = 0 (again with the lowest and highest values for the extinction curves of local starbursts and the SMC, respectively), broadly consistent with estimates of the excess extinction suffered by nebular emission in local galaxies. We thus find no evidence that our conclusions might be affected by our use of the U-band continuum luminosity as an SFR indicator.

The timescale on which neutral gas is depleted by star formation, and its dependence on redshift, stellar mass, etc., is a subject of much interest in studies of galaxy evolution (e.g., Schiminovich et al. 2010; Saintonge et al. 2011, 2013; Tacconi et al. 2013; Genzel et al. 2015; Schinnerer et al. 2016). If star formation activity is to be maintained in a galaxy beyond its gas depletion timescale, the gas content must be replenished, probably by accretion of gas from the intergalactic medium. Most studies of the gas depletion timescale in high-z, star-forming galaxies have focussed on the molecular gas, due to the difficulty in estimating atomic gas masses in galaxies at z ≳ 0.25, where it is very difficult to detect the weak H i 21 cm emission line. Molecular emission studies of star-forming galaxies have obtained typical gas depletion timescales of ≈0.5–1 Gyr (e.g., Saintonge et al. 2011; Tacconi et al. 2013; Genzel et al. 2015; Schinnerer et al. 2016) for main-sequence galaxies at z ≈ 0–4. At high redshifts, the molecular gas depletion timescale shows only a weak dependence on redshift and stellar mass, but a strong dependence on the sSFR (Genzel et al. 2015). However, at low redshifts, this timescale has been found to depend on stellar mass: the molecular gas depletion timescale is larger by a factor of ≈6 in the highest-mass galaxies (Saintonge et al. 2011). We note that a recent study of molecular gas in absorption-selected galaxies at z ≈ 0.7 has found evidence for significantly longer molecular gas depletion timescales, ≳10 Gyr (Kanekar et al. 2018), very different from those seen in emission-selected star-forming galaxies.

In the local universe, Saintonge et al. (2011) used the COLD GASS galaxy sample, comprising of galaxies at 0.025 < z < 0.05 with stellar mass M_⋆ ≥ 10¹⁰ M_⊙, to study the dependence of the atomic gas depletion time on galaxy properties. They found that the average atomic gas depletion timescale is ≈3 Gyr (albeit with considerable scatter) for the COLD GASS galaxies, with little dependence on parameters like the stellar mass, the sSFR, etc. (see also Schiminovich et al. 2010). The molecular and atomic gas depletion timescales are similar in the highest-mass COLD GASS galaxies, with red colors and high surface densities, while the molecular gas depletion timescale is nearly an order of magnitude lower than the atomic gas depletion timescale in low-mass galaxies, with high sSFRs and low stellar surface density (Saintonge et al. 2011). Similarly, extending to lower stellar masses, M_⋆ ≥ 10⁹ M_⊙, the galaxies of the xGASS "representative sample" of Catinella et al. (2018) have a median atomic gas depletion time of ≈5 Gyr, for objects with detections of H i 21 cm emission.

In the case of the DEEP2 galaxies, Kanekar et al. (2016) stacked the H i 21 cm emission from 868 galaxies at z ≈ 1.3 to obtain an upper limit of M_{H i}(3σ) ≤ 2.1 × 10¹⁰ M_⊙ on their average H i mass. We have stacked the rest-frame 1.4 GHz radio continuum emission from the same 868 galaxies, to obtain an SFR of (24.2 ± 3.7) M_⊙ yr⁻¹. Combining this with the upper limit of Kanekar et al. (2016) on the H i mass then implies a 3σ upper limit of ≈0.87 Gyr on the atomic gas depletion time, in main-sequence star-forming galaxies at z ≈ 1.3. Interestingly enough, the atomic gas depletion timescale is comparable to the molecular gas depletion timescale (≈0.7 Gyr) in similar star-forming galaxies at a similar redshift (Tacconi et al. 2013; Genzel et al. 2015). The DEEP2 galaxies of the subsample of Kanekar et al. (2016) have stellar masses ≳10⁹ M_⊙, similar to those of the xGASS sample, but have far shorter atomic gas depletion times. The short inferred gas depletion time of the DEEP2 subsample emphasizes the need for replenishment of the atomic gas content of high-z main-sequence galaxies. Atomic hydrogen thus appears to be a transient phase in star-forming galaxies at high redshifts, with the conversion from the atomic to the molecular phase taking place on a timescale comparable to the timescale for the conversion of the molecular gas to stars. This is consistent with the speculation of Saintonge et al. (2011), that, at high redshifts, the bottleneck for star formation does not lie in the conversion of atomic gas to molecular gas.

Krumholz et al. (2008, 2009) carried out a theoretical modeling of the formation of molecular hydrogen from the atomic phase in galactic disks, considering the atomic to molecular transition to take place in a thin spherical layer, separating a purely molecular region from a region with a negligible molecular fraction (see also Krumholz 2013), and finding reasonable agreement with observational data on local samples of galaxies. We use this model to examine conditions in the DEEP2 galaxies that might yield the observed atomic and molecular gas depletion timescales of <0.87 Gyr and ≈0.7 Gyr, respectively. In chemical equilibrium, the atomic and molecular gas depletion timescales are related by

$$\begin{eqnarray}&&{\rm{\Delta }}{t}_{{\rm{H}}{\rm{I}}}={\rm{\Delta }}{t}_{{{\rm{H}}}_{2}}/{R}_{{{\rm{H}}}_{2}},\end{eqnarray} \tag{ 8 }$$

where Δt_{H i} and ${\rm{\Delta }}{t}_{{{\rm{H}}}_{2}}$ are the atomic and molecular gas depletion timescales, and ${{R}}_{{{\rm{H}}}_{2}}$ is the atomic-to-molecular mass ratio, with

$$\begin{eqnarray}&&{R}_{{{\rm{H}}}_{2}}={f}_{{{\rm{H}}}_{2}}/[1-{f}_{{{\rm{H}}}_{2}}],\end{eqnarray} \tag{ 9 }$$

and ${f}_{{{\rm{H}}}_{2}}$ is the H₂ fraction.

Equations (10)–(12) of Krumholz (2013) relate ${f}_{{{\rm{H}}}_{2}}$ to the total gas surface density ${{\rm{\Sigma }}}_{0}$, the clumping factor f_c, and the metallicity. Krumholz (2013) note that the gas clumping factor depends on the scale over which the surface density is averaged, with f_c ≈ 1 on scales of ≈100 pc, and f_c ≈ 5 on scales of ≈1 kpc. We will assume f_c ≈ 5 averaged over the DEEP2 galaxies. Finally, we assume that the DEEP2 galaxies have, on average, solar metallicity.

For the DEEP2 galaxies, the gas depletion timescales are Δt_{H i} < 0.87 Gyr, and ${\rm{\Delta }}{t}_{{{\rm{H}}}_{2}}\approx 0.7\,\mathrm{Gyr}$ (Tacconi et al. 2013), implying ${R}_{{{\rm{H}}}_{2}}\geqslant 0.8$. Using this and f_c ≈ 5 in Equations (10–12) of Krumholz (2013) then yields an average total gas surface density of Σ₀ ≳ 6 M_⊙ pc⁻². Overall, within the model of Krumholz (2013), the average gas surface density in the DEEP2 galaxies must be relatively high to account for the similar atomic and molecular gas depletion timescales.