Atomic Gas Scaling Relations of Star-forming Galaxies at z ≈ 1

The GMRT-CATz1 survey (Chowdhury et al. 2022b) used ≈510 hr with the upgraded GMRT 550–850 MHz receivers to carry out a deep Hi 21 cm emission survey of galaxies at z = 0.74–1.45, in three sky fields covered by the DEEP2 Galaxy Survey (Newman et al. 2013). The three DEEP2 fields covered by the CATz1 survey contain seven subfields of size ≈52' × 28', each of which was covered using a single GMRT pointing. The design, the observations, the data analysis, and the main sample of galaxies of the GMRT-CATz1 survey are described in detail in Chowdhury et al. (2022b). We provide here a summary of the information directly relevant to this paper.

The observations for the GMRT-CATz1 survey were obtained over three GMRT observing cycles. The data of each subfield from each observing cycle were analyzed separately. This was done to prevent systematic effects present in the data of one cycle (e.g., low-level radio-frequency interference, deconvolution errors, etc.), from affecting the quality of the data from the other cycles (see Chowdhury et al. 2022b for a detailed discussion). The analysis resulted in two to three spectral cubes for each of the seven DEEP2 fields. The cubes have channel widths of 48.8 kHz, corresponding to a velocity resolution of 18–25 km s⁻¹, over the redshift range z = 0.74–1.45. The FWHMs of the synthesized beams of the spectral cubes are 40–75 over the frequency range 580–830 MHz, corresponding to spatial resolutions in the range 29–63 kpc ¹ for galaxies at z = 0.74–1.45.

The GMRT-CATz1 survey covers the Hi 21 cm line for 16,250 DEEP2 galaxies with accurate spectroscopic redshifts (velocity errors ≲62 km s⁻¹; Newman et al. 2013) at z = 0.74–1.45. We excluded (i) red galaxies, identified using a cut in the (U − B) versus M_B color–magnitude diagram (Willmer et al. 2006; Chowdhury et al. 2022b), (ii) radio-bright AGNs, detected in our radio-continuum images at >4σ significance with rest-frame 1.4 GHz luminosities L_{1.4 GHz} ≥ 2 × 10²³ W Hz⁻¹ (Condon et al. 2002), (iii) galaxies with stellar masses M_* < 10⁹ M_⊙, and (iv) galaxies whose Hi 21 cm subcubes were affected by discernible systematic effects (Chowdhury et al. 2022b). This yielded a total of 11,419 blue star-forming galaxies with M_* ≥ 10⁹ M_⊙ at z = 0.74–1.45, the main sample of the GMRT-CATz1 survey. The survey provides a total of 28,993 Hi 21 cm subcubes for the 11,419 galaxies. The subcube of each galaxy covers a region of ±500 kpc around the galaxy location, with a uniform spatial resolution of 90 kpc, and a velocity range of ±1500 km s⁻¹ around its redshifted Hi 21 cm frequency, with a channel width of 30 km s⁻¹. The median spectral rms noise on the 28,993 Hi 21 cm subcubes is 297 μJy per 30 km s⁻¹ velocity channel, at a spatial resolution of 90 kpc.

We note that the average Hi 21 cm emission signal from the sample of 11,419 galaxies is consistent with being unresolved at a spatial resolution of 90 kpc (Chowdhury et al. 2022b). Further, the compact resolution of 90 kpc ensures that the average Hi 21 cm emission signal does not include a significant contribution from companion galaxies in the vicinity of the target galaxies (Chowdhury et al. 2022b).

The stellar masses of the individual DEEP2 galaxies were obtained using a relation between the stellar mass ² and the absolute rest-frame B-band magnitude (M_B ), the rest-frame (U − B) color, and the rest-frame (B − V) color (Weiner et al. 2009). The relation was calibrated using a subset of the DEEP2 galaxies with K-band estimates of the stellar masses (Weiner et al. 2009). The SFRs of the individual galaxies were inferred from their M_B values and rest-frame (U − B) colors, via the SFR calibration of Mostek et al. (2012); these authors used the SFRs of galaxies in the Extended Groth Strip (obtained via spectral energy distribution (SED) fits to the rest-frame ultraviolet, optical, and near-IR photometry; Salim et al. 2009) to derive the SFR calibration for the DEEP2 galaxies. Mostek et al. (2012) found that the scatter between the SED SFRs of Salim et al. (2009) and the SFRs obtained via the calibration based on the M_B and (U − B) values is ≈0.2 dex. ³

We estimate the average Hi mass and the average SFR of subsamples of galaxies by stacking, respectively, the Hi 21 cm line luminosities and the rest-frame 1.4 GHz continuum luminosities. The procedures used in stacking the Hi 21 cm emission signals and the rest-frame 1.4 GHz continuum emission signals are described in detail in Chowdhury et al. (2022a, 2022b). We provide here, for completeness, a brief review of the procedures.

The stacked Hi 21 cm spectral cube of a given subsample of galaxies was computed by taking a weighted average of the individual Hi 21 cm subcubes, in luminosity–density units, of the galaxies in the subsample. During the stacking analysis, each Hi 21 cm subcube is treated as arising from a separate "object." The weights were chosen to ensure that the redshift distributions of the different subsamples are identical; the specific choices of weights for the different stacks are discussed in Sections 3.1 and 3.3. For each subsample, we then fitted a second-order polynomial to the spectra at each spatial pixel of the stacked Hi 21 cm cube, and subtracted this out to obtain a residual cube; the polynomial fit was performed after excluding spectral channels in the velocity range ±250 km s⁻¹. For each subsample, the rms noise at each spatial and velocity pixel of the stacked Hi 21 cm cube was obtained via Monte Carlo simulations (Chowdhury et al. 2022b). Finally, for each subsample, the average Hi mass was obtained from the measured velocity-integrated Hi 21 cm line luminosity. ⁴ The velocity integral was carried out over a contiguous range of central velocity channels containing emission at ≥1.5σ significance, after smoothing the stacked Hi 21 cm subcubes to a velocity resolution of 90 km s⁻¹.

The average SFR of each subsample was computed by stacking the rest-frame 1.4 GHz luminosity density of the galaxies in the subsample (e.g., White et al. 2007; Chowdhury et al. 2022a). We used the GMRT 655 MHz radio-continuum images of the DEEP2 subfields to extract subimages around each of the 11,419 galaxies of the full sample. We convolved all subimages to an uniform spatial resolution of 40 kpc, regridded them to a uniform grid with 5.2 kpc pixels spanning ±260 kpc, and converted the flux-density values (in jansky) to rest-frame 1.4 GHz luminosity–density values (in watts per hertz), assuming a spectral index of α = −0.8 (Condon 1992), with S_ν ∝ ν^α . The stacked rest-frame 1.4 GHz luminosity density of a subsample of galaxies was computed by taking a weighted median of the individual subimages, with the weights being the same as those used during the Hi 21 cm stacking of the subsample. Finally, the stacked rest-frame 1.4 GHz continuum luminosity density of a subsample of galaxies is converted to an estimate of the average SFR of the subsample, using the relation SFR (M_⊙ yr⁻¹) = 3.7 × 10⁻²² × L_{1.4 GHz} (W Hz⁻¹) (Yun et al. 2001). The errors on our measurements of the average SFRs include both the statistical uncertainty and a 10% flux-scale uncertainty (Chowdhury et al. 2022b).

We divide our sample of 11,419 galaxies (28,993 Hi 21 cm subcubes) into three stellar-mass subsamples with 1.0 ×10⁹ M_⊙ < M_* ≤ 6.0 × 10⁹ M_⊙ ("Low"), 6.0 × 10⁹ M_⊙ < M_* ≤1.3 × 10¹⁰ M_⊙ ("Intermediate"), and M_* > 1.3 × 10¹⁰ M_⊙ ("High"). ⁵ The number of galaxies and Hi 21 cm subcubes in each subsample are provided in Table 1. The redshift distributions of the three stellar-mass subsamples are different (see Figure 1). We correct for this difference by assigning weights to each Hi 21 cm subcube such that the redshift distribution of each stellar-mass subsample is effectively identical. Specifically, the weights ensure that the effective redshift distributions of the intermediate- and high-stellar-mass subsamples are identical to that of the low-stellar-mass subsample; the mean redshift of the final redshift distribution is 〈z〉 = 1.01. We use these weights while computing all average quantities for the three stellar-mass subsamples.

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We separately stacked the Hi 21 cm emission and the rest-frame 1.4 GHz continuum emission of the galaxies in the three stellar-mass subsamples, following the procedures of Section 2.2. Figure 2 shows the stacked Hi 21 cm emission images, the stacked Hi 21 cm spectra, and the stacked rest-frame 1.4 GHz continuum images of the three subsamples. We obtain clear detections of the average Hi 21 cm emission signal in all three cases, at 4.2–4.9σ statistical significance. We also detect the stacked rest-frame 1.4 GHz continuum emission at high significance (>28σ) in all three subsamples. The average Hi masses and the average SFRs of galaxies in the three subsamples are listed in Table 1. We find that the average SFR and the average stellar mass of the galaxies in the three subsamples are in excellent agreement with the star-forming main sequence at z ≈ 1 (see Table 1; Whitaker et al. 2014; Chowdhury et al. 2022a).

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We use the extended GALEX Arecibo Sloan Digital Sky Survey (SDSS) (xGASS; Catinella et al. 2018) to compare our measurements of the Hi properties of star-forming galaxies at z ≈ 1 to those of galaxies in the local universe. The xGASS survey used the Arecibo telescope to measure the Hi masses of a stellar-mass-selected sample of galaxies with M_* > 10⁹ M_⊙ at z = 0.01–0.05. The stellar masses and SFRs of the xGASS galaxies used in this work were obtained from the publicly available catalog of the xGASS representative sample. The stellar masses in this catalog are from Kauffmann et al. (2003) and Brinchmann et al. (2004), while the SFRs were computed using a combination of GALEX near-ultraviolet (NUV) and Wide-field Infrared Survey Explorer mid-infrared (MIR) data or via SED fits for galaxies for which MIR data were not available (Catinella et al. 2018).

The main sample of the GMRT-CATz1 survey consists of blue, star-forming galaxies at z = 0.74–1.45. In order to ensure a fair comparison between the Hi properties of the GMRT-CATz1 galaxies and those of the xGASS galaxies, we limit the xGASS sample to blue galaxies, with NUV−r < 4. We divide the xGASS galaxies into three stellar-mass subsamples, using the same "Low," "Intermediate," and "High" stellar-mass ranges as for the DEEP2 galaxies. Further, for each xGASS subsample, we use weights to ensure that the stellar-mass distribution within the subsample is effectively identical to that of the corresponding (Low, Intermediate, or High) subsample at z ≈ 1. In passing, we note that the average Hi masses of xGASS galaxies in the three stellar-mass subsamples obtained using a cut in the SFR–M_* plane to select main-sequence galaxies are consistent with the values obtained by selecting blue galaxies with NUV−r < 4.

The average Hi masses of the blue xGASS galaxies in the three stellar-mass subsamples are listed in Table 2; the errors on the averages were computed using bootstrap resampling with replacement. The table also lists, for comparison, the GMRT-CATz1 measurements of the average Hi masses of blue galaxies in the same stellar-mass subsamples at z ≈ 1. We find that, across the stellar-mass range 10⁹–2.4 × 10¹¹ M_⊙, the average Hi mass of the z ≈ 1 galaxies is higher than that of local universe galaxies, by a factor of ≈3.1–4.5.

We determined the M_HI–M_* relation at z ≈ 1 by fitting a power-law relation to our measurements of the average Hi mass of blue star-forming galaxies in the three stellar-mass subsamples at z ≈ 1, following the procedures in the Appendix. We find that the M_HI–M_* relation for main-sequence galaxies at z ≈ 1 is

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{log}\left[{M}_{{\rm{H}}\,{\rm\small{I}}}/{M}_{\odot }\right] & = & (0.32\pm 0.13)\mathrm{log}\left[{M}_{* ,10}\right]\\ & & +\,(10.183\pm 0.056),\end{array}\end{eqnarray} \tag{ 1 }$$

where M_*,10 = M_*/10¹⁰ M_⊙. In order to compare the M_HI–M_* relation of blue star-forming galaxies at z ≈ 1 to that of blue star-forming galaxies at z ≈ 0, we also fitted a power-law relation, using the procedures of the Appendix, to the measurements of 〈M_HI〉 in blue xGASS galaxies in the three stellar-mass subsamples of Table 2, with stellar-mass distributions identical to those of the subsamples of galaxies at z ≈ 1. We find that the best-fit M_HI–M_* relation for blue galaxies at z ≈ 0 is $\mathrm{log}\left[{M}_{{\rm{H}}\,{\rm\small{I}}}/{M}_{\odot }\right]\,=(0.38\pm 0.05)\mathrm{log}\left[{{M}_{* }}_{,10}\right]+(9.634\pm 0.019)$. ⁶

Figure 3(A) shows the M_HI–M_* relations for blue star-forming galaxies at z ≈ 1 and z ≈ 0. We find no statistically significant evidence for an evolution in the slope of the M_HI–M_* relation from z ≈ 1 to z ≈ 0. However, we find clear evidence that the relation has shifted downwards from z ≈ 1 to z ≈ 0. Specifically, our measurements show that the M_HI–M_* relation of blue star-forming galaxies at z ≈ 1 lies a factor of 3.54 ± 0.48 above the local universe relation.

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In passing, we emphasize that the M_HI–M_* relations of this Letter, at both z ≈ 0 and z ≈ 1, were obtained by fitting a relation to measurements of 〈M_HI〉 in three stellar-mass subsamples. This approach is different from that typically followed for galaxies at z ≈ 0, where the M_HI–M_* relation is obtained by fitting to estimates of $\langle \mathrm{log}\,{M}_{{\rm{H}}{\rm\small{I}}}\rangle$ in multiple stellar-mass subsamples (e.g., Saintonge & Catinella 2022). The difference arises from the fact that the averaging in a stacking analysis is carried out on the Hi masses themselves, rather than on the logarithm of the Hi masses; in general, the logarithm of the average value of a given quantity is not the same as the average of the individual logarithms (e.g., Brown et al. 2015). Care must hence be taken when comparing scaling relations obtained from simulations with those obtained from stacking analyses such as the present work, or when comparing the scaling relations from stacking analyses with those based on direct measurements of M_HI, and hence on estimates of $\langle \mathrm{log}\,{M}_{{\rm{H}}{\rm\small{I}}}\rangle$. Specifically, the scaling relations obtained from the stacking analysis yield the mean HI mass at a given stellar mass. Conversely, for a log-normal distribution of HI masses, the scaling relations obtained from direct measurements yield the median HI mass at a given stellar mass. Further, again for a log-normal distribution of HI masses with scatter σ, $\langle \mathrm{log}{{M}}_{{\rm{H}}{\rm{I}}} \rangle =\mathrm{log} \langle {{M}}_{{\rm{H}}{\rm{I}}} \rangle -\frac{\mathrm{ln}10}{2}{{\sigma }}^{2}$. Assuming that the scatter of the scaling relation at z ≈ 1 is independent of M_* and that it is equal to the scatter of 0.4 dex measured at z = 0 (Catinella et al. 2018), the "direct" M_HI–M_* relation would be offset downward from Equation (1) by 0.184 dex.

The availability of cold gas regulates the star formation activity in a galaxy. The Hi depletion timescale (t_dep,HI), defined as the ratio of the Hi mass of the galaxy to its SFR, quantifies the approximate timescale for which the galaxy can sustain its current SFR, in the absence of accretion of fresh Hi from the CGM. In other words, accretion of gas from the CGM on a timescale of ≈t_dep,HI is required to sustain the current star formation activity of the galaxy.

We define the "characteristic" Hi depletion timescale of a sample of galaxies as 〈t_dep,HI〉 ≡ 〈M_HI〉/〈SFR〉. We combined the average SFRs of galaxies in the three subsamples with their average Hi masses to estimate the characteristic Hi depletion timescale, 〈t_dep,HI〉 ≡ 〈M_HI〉/〈SFR〉, of galaxies at z ≈ 1, as a function of their average stellar masses. Table 1 lists the 〈t_dep,HI〉 values of the galaxies in the three stellar-mass subsamples at z ≈ 1, while the estimates of 〈t_dep,HI〉 are plotted against the average stellar mass in Figure 3(B). For comparison, the figure also shows the characteristic Hi depletion timescale of the xGASS galaxies in the same three stellar-mass subsamples, while Table 2 compares the values of 〈t_dep,HI〉 for the galaxies at z ≈ 0 and z ≈ 1. We find that the characteristic Hi depletion timescale of blue star-forming galaxies at z ≈ 1 is ≈2–4 times lower than that of similar galaxies with the same stellar-mass distribution at z ≈ 0.

In passing, we note that the characteristic Hi depletion timescale, 〈M_HI〉/〈SFR〉, for a sample of galaxies may be different from the average of the depletion timescales of the individual galaxies, 〈M_HI/SFR〉. Indeed, for the xGASS galaxies, we find that the 〈M_HI/SFR〉 values in the three stellar-mass subsamples are higher than the corresponding 〈M_HI〉/〈SFR〉 values by factors of ≈1.2–1.6. However, this does not affect the results of this Letter because we consistently compare the characteristic depletion timescales of the different galaxy subsamples, at both z ≈ 1 and z ≈ 0.

We obtained the t_dep,HI–M_* relation at z ≈ 1 by combining our estimate of the M_HI–M_* relation at z ≈ 1 (Equation (1)) with a relation for the star-forming main sequence at z ≈ 1 from Whitaker et al. (2014). These authors provide best-fitting relations to the star-forming main sequence for the redshift ranges z = 0.5–1.0 and z = 1.0–1.5; we interpolated the best-fit parameters between the two redshift intervals to find that the main-sequence relation at z ≈ 1 is $\mathrm{log}\left[\mathrm{SFR},/,(,{M}_{\odot },\,,{\mathrm{yr}}^{-1},)\right]\,=0.976\,+\,0.720\mathrm{log}\left[{{M}_{* }}_{,10}\right]\,-0.205\mathrm{log}{\left[{{M}_{* }}_{,10}\right]}^{2}.$ Combining this relation with the M_HI–M_* relation of Equation (1), we find that the t_dep,HI–M_* relation for main-sequence galaxies at z ≈ 1 is: ⁷

$$\begin{eqnarray}&&\begin{array}{l}\mathrm{log}\left[{t}_{\mathrm{dep},{\rm{H}}\,{\rm\small{I}}}/\mathrm{Gyr}\right]=(0.207\pm 0.056)\\ \quad +\,(-0.40\pm 0.13)\mathrm{log}\left[{{M}_{* }}_{,10}\right]+0.205\mathrm{log}{\left[{{M}_{* }}_{,10}\right]}^{2}.\end{array}\end{eqnarray} \tag{ 2 }$$

We emphasize that Equation (2) was not obtained by fitting a relation to our measurements of the characteristic Hi depletion timescale in the three M_* subsamples. However, Figure 3(B) shows that our measurements of 〈t_dep,HI〉 in the three subsamples are consistent with the t_dep,HI–M_* relation of Equation (2).

Overall, we find that blue star-forming galaxies at z ≈ 1, with stellar masses in the range M_* ≈ 10⁹–2.4 × 10¹¹ M_⊙, have larger Hi reservoirs than those of blue galaxies at z ≈ 0, by a factor of 3.54 ± 0.48. However, the evolution of the star-forming main sequence by a factor of ≈10 from z ≈ 0 to z ≈ 1 (e.g., Whitaker et al. 2014) implies that the characteristic Hi depletion timescales of blue star-forming galaxies at z ≈ 1 are lower, by factors of ≈2–4, than those of local galaxies. The results of this Letter thus extend the findings of the earlier GMRT Hi 21 cm stacking studies (Chowdhury et al. 2020, 2021, 2022a, 2022b) that blue star-forming galaxies at z ≈ 1 have a large average Hi mass but a short characteristic Hi depletion timescale to the entire stellar-mass range M_* ≈ 10⁹–2.4 × 10¹¹ M_⊙.

The Hi fractions (f_HI ≡ M_HI/M_*) of galaxies in the local universe and their specific SFRs (sSFR ≡ SFR/M_*) are known to be correlated, with a scatter of ≈0.5 dex (Catinella et al. 2018); this is one of the tightest atomic gas scaling relations at z ≈ 0 (Catinella et al. 2018). The locations of galaxies in the f_HI–sSFR plane are indicative of the efficiency with which their Hi is being converted to stars. In this section, we investigate the redshift evolution of the relation between f_HI and sSFR, for blue star-forming galaxies, from z ≈ 1 to z ≈ 0.

We divide our sample of 11,419 galaxies into three sSFR subsamples with sSFR ≤ 0.8 Gyr⁻¹ ("Low"), 0.8 Gyr⁻¹ < sSFR ≤ 1.3 Gyr⁻¹ ("Intermediate"), and sSFR > 1.3 Gyr⁻¹ ("High"). ⁸ The numbers of galaxies and Hi 21 cm subcubes in each subsample are listed in Table 3, while the redshift distributions of the three sSFR subsamples are shown in Figure 4. The high-sSFR subsample contains a significantly larger number of galaxies at higher redshifts than the other two subsamples; this is primarily due to the redshift evolution of the star-forming main sequence within our redshift coverage, z = 0.74–1.45 (e.g., Whitaker et al. 2014). We corrected for this difference in the redshift distributions of the subsamples by using weights such that the effective redshift distributions of the intermediate- and high-sSFR subsamples are identical to that of the low-sSFR subsample. We separately stacked the Hi 21 cm subcubes of the galaxies in the three subsamples, following the procedures of Section 2.2, using the above weights to ensure that the redshift distributions of the three subsamples are identical.

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Figure 5 shows the stacked Hi 21 cm emission images and the stacked Hi 21 cm spectra of galaxies in the three sSFR subsamples. We obtain clear detections, with ≈4.3–4.4σ statistical significance, of the average Hi 21 cm emission signals from galaxies in the three subsamples. The average Hi mass and the "characteristic" Hi fraction, 〈f_HI〉 ≡ 〈M_HI〉/〈M_*〉, of the galaxies in each subsample are listed in Table 3.

Our measurements of the characteristic Hi fraction of star-forming galaxies in the three sSFR subsamples at z ≈ 1 are shown in Figure 6; also shown for comparison are the characteristic Hi fractions of blue xGASS galaxies at z ≈ 0 (Catinella et al. 2018). Note that the average sSFR of the DEEP2 galaxies in the low-sSFR subsample is 0.5 Gyr⁻¹, while there are only three galaxies in the xGASS survey with sSFR > 0.5 Gyr⁻¹. This is because the main sequence evolves between z ≈ 1 and z ≈ 0, with the sSFR of galaxies at a fixed stellar mass being ≈10 times higher at z ≈ 1 than at z ≈ 0 (e.g., Whitaker et al. 2014).

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The straight lines in Figure 6 are the loci of constant depletion timescales on the f_HI–M_* plane. The characteristic Hi depletion timescale of main-sequence galaxies in the local universe is ≈4.5 Gyr, with a large scatter around the mean (Saintonge et al. 2017). Figure 6 shows that the characteristic Hi fractions and the average sSFRs of blue xGASS galaxies at z ≈ 0 are consistent with the 〈t_dep,HI〉 = 4.5 Gyr line. However, it is clear from Figure 6 that star-forming galaxies at z ≈ 1 do not follow the f_HI–sSFR relation of local universe galaxies. This is consistent with our earlier results (e.g., Chowdhury et al. 2020, 2021) that blue star-forming galaxies at z ≈ 1 have a low characteristic Hi depletion timescale of ≈1–2 Gyr. This evolution of the f_HI–sSFR relation from z ≈ 1 to z ≈ 0 is different from the behavior of the molecular component: the molecular gas depletion timescales in main-sequence galaxies are typically ≈0.5–0.7 Gyr at z ≈ 0–1.5, with no significant evidence for redshift evolution over z ≈ 0–1.5 (e.g., Genzel et al. 2015; Saintonge et al. 2017).

The short Hi depletion timescale of galaxies at z ≈ 1 (or, equivalently, the high Hi star-forming efficiency) is indicative of a very efficient conversion of Hi to H₂, which then directly fuels the high star formation activity. The difference between local universe galaxies (with massive Hi reservoirs but low star-forming efficiency) and star-forming galaxies at z ≈ 1 may lie in the typical Hi surface densities in the galaxies; a high Hi surface density is likely to be a requirement for efficient conversion of Hi to H₂ (e.g., Leroy et al. 2008). In other words, it appears that the efficiency of conversion of Hi to stars is different at z ≈ 1, toward the end of the epoch of peak star formation activity in the universe, from that at z ≈ 0, with the Hi in galaxies at z ≈ 1 being able to fuel star formation far more efficiently than at z ≈ 0. Measurements of the average Hi surface density profiles of the GMRT-CATz1 galaxies would allow one to test this hypothesis.