Relationships between Hi Gas Mass, Stellar Mass, and the Star Formation Rate of HICAT+WISE (H i-WISE) Galaxies

The principal source of data for our analysis is HICAT, which is derived from HIPASS (Barnes et al. 2001; Meyer et al. 2004). HIPASS is a blind survey below a declination δ of +2°, performed with the Parkes 64 m radio telescope using a 21 cm multibeam receiver. HICAT contains 4315 H i sources selected from HIPASS and is 99% complete at a peak flux of 84 mJy and an integrated flux of 9.4 Jy km s⁻¹ (Meyer et al. 2004; Zwaan et al. 2004).

For each H i source in HICAT, we search for optical counterparts using the position and velocity measurements in HICAT. Since the HIPASS data has a spatial resolution of 155, it is necessary to obtain more accurate positions for the H i sources before searching for their mid-infrared counterparts in the WISE frames. To this end, we search for optical counterparts in the spectroscopic sample of Bonne et al. (2015), the NASA/IPAC Extragalactic Database (NED),⁴ HYPERLEDA (Makarov et al. 2014), and HOPCAT (Doyle et al. 2005). In order to accurately match the H i sources with their optical counterparts, we cross-check the velocity measurements from HICAT with the velocity provided from the above sources for all possible positional matches. We describe each source below—as well as the matching process—in detail.

In our preliminary search for optical counterparts, we use the spectroscopic sample of Bonne et al. (2015), which covers the full survey area of HICAT and provides velocities (predominantly from the r_F ≤ 15.60 2MASS selected 6dF Galaxy Survey, 6dFGS; Jones et al. 2009), morphologies, and WISE photometry from the All-Sky public-release archive (Cutri et al. 2013a) for 13325 galaxies. For each source, we select the best match to this sample within 5' and 400 km s⁻¹ of the respective HICAT position and velocity, resulting in 1043 optical counterparts of 4315 H i sources.

To obtain additional optical counterparts, we then search in NED and HYPERLEDA for galaxies within 10' and 400 km s⁻¹ of their respective HICAT positions and velocities. As NED and HYPERLEDA draw information from catalogs such as HICAT, it must be ensured that the velocities extracted from these databases are sourced from optical or high-resolution H i radio observations and not sourced from HICAT, and hence that HICAT velocities are not being cross-matched to themselves.

HOPCAT (Doyle et al. 2005) is used as our last source for optical matches. The matches from HOPCAT cannot be cross-checked with known velocities, but are categorized as "good guesses" by Doyle et al. (2005; see the reference for details on HOPCAT and its matching criteria). We do not use HOPCAT as our primary source for optical matches because Bonne et al. (2015), NED, and HYPERLEDA described above provide more recent velocity measurements from 6dFGS and other surveys that were not available at the time HOPCAT was compiled. The final number of galaxies taken from each source described here is listed in Table 1. In total, optical counterparts were obtained for 3719 H i sources. However, 147 of these were found to be multi-galaxy systems and were thus excluded from our analysis.

WISE was launched in 2009 December, and mapped the entire sky in four mid-infrared bands: W1, W2, W3, and W4 (3.4, 4.6, 12, and 22 μm; Wright et al. 2010). Once WISE depleted its cryogen in 2010 October, it was then operated in a "warm" state using the two short bands and then placed in hibernation for well over 2 yr. As part of the NEOWISE program, WISE was reactivated in 2013 September and continues to observe in the W1 and W2 bands (Mainzer et al. 2014). The point source sensitivities of W1, W2, W3, and W4 in Vega magnitudes are 16.5, 15.5, 11.2, and 7.9, respectively (Wright et al. 2010), in which W4 is approximately two orders of magnitude more sensitive than the IRAS.

We have measured new WISE photometry for the optical counterparts of the HICAT source using the procedure described in Jarrett et al. (2013). We chose to do this because the profile-fit photometry data in the ALLWISE public-release archive (Cutri et al. 2013a) of the (degraded resolution) mosaics is optimized for point sources (e.g., Jarrett et al. 2013; Cluver et al. 2014, and references therein). Therefore, resolved sources such as our sample galaxies are either measured as several point sources, or their flux is underestimated by the PSF photometry (mpro). The WISE default catalogs do include extended source photometry for 2MASS Extended Source Catalog (2MXSC; Jarrett et al. 2000) galaxies, but the elliptical apertures (gmag) miss a significant fraction of the flux (Cluver et al. 2014).

All measurements are carried out on WISE image mosaics that are constructed from single native frames using a drizzle technique (Jarrett et al. 2012), resampled with 1 sq. arc pixels (relative to a 6 arcsec FWHM beam). Photometry for each individual HIPASS galaxy, principally flux measurements and surface brightness characterizations, are conducted using the system developed by T. H. Jarrett specifically for WISE data (Jarrett et al. 2013, see Section 3.6). The system estimates photometric errors from the formal components, including the sky background variance and the local sky level, instrumental signatures, and the absolute calibration. The error model also takes into account the correlation between resampled pixels through a correction factor, which is detailed in the WISE Explanatory Supplement (see Section 2.3.f, Cutri et al. 2013a). As detailed in Jarrett et al. (2013), the shape (inclination) and orientation were determined at a fixed 3σ isophotal level, which provides a robust and relatively accurate (<5%) estimate, although this assumes symmetry and a fixed shape to the 1σ edge of the galaxy.

As detailed in T. H. Jarrett et al. (2013, 2018, in preparation), isophotal measurements at the W1 1σ level typically capture more than 96% of the total light for bulge-dominated galaxies, and to a lesser extent (≥90%) for late-type galaxies, and most notably in the W3 and W4 bands as much as 20% of the light can be missing with low surface brightness galaxies. Hence, total fluxes are important in order to estimate the dust-obscured star formation activity in the W3 and W4 bands. The total flux is estimated by fitting a double Sérsic function to the axisymmetric radial profile, consisting of an inner bulge and an outer disk. Integrating the composite Sérsic model from the 1σ isophote to the edge of the galaxy (3 disk scale lengths) recovers the light that is below the single-pixel noise threshold; details of the fitting process may be found in Jarrett et al. (2013). The error model for the total fluxes includes the goodness of fit, as well as the previous sky estimation per pixel estimates, and typically adds 4%–5% to the isophotal flux uncertainty.

Lastly, each galaxy mosaic is visually inspected, and if necessary, bright stars and nearby galaxies are manually masked out, and the apertures are adjusted. Figure 1 compares our new WISE photometry for HICAT galaxies with the previously available archival fluxes and illustrates the impact of the new photometry on derived quantities. For example, for W1 ∼ 12 mag galaxies our W1 and W3 magnitudes are on average systematically brighter by ∼1.4 mag and 1.1 mag than the default photometry pipeline magnitudes. Figure 2 shows four examples of the WISE mosaics that have been cleaned of neighboring objects, as well as the elliptical apertures used for photometry.

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We apply an S/N threshold of 5 in the W1 and W2 bands, an S/N threshold of 3 in the W3 band, and reject confused sources or H i sources consisting of multiple galaxies. Consequently, we measure good W1–W2 photometry for 3275 H i sources and good W1–W2–W3 photometry for 2831 H i sources. We find 20 H i sources that do not meet any of our WISE signal-to-noise thresholds and 147 H i sources are multi-galaxy sources. From top to bottom, Figure 2 shows examples from HICAT of a "well-behaved" source, a multi-galaxy source, and two visually flagged sources. A full list of parameters for HICAT+WISE (H i-WISE) is given in Table 8 in the Appendix. The 147 H i sources that are found to be multi-galaxy systems are excluded from Table 8.

Figure 3 illustrates the WISE colors of HICAT galaxies, along with the expected colors of different types of galaxies, and clearly demonstrates that HIPASS is dominated by star-forming spiral galaxies, with relatively few ellipticals and luminous infrared galaxies (LIRGs). The galaxies with intermediate disk colors in the active galactic nucleus (AGN)/LIRGs region may harbor dust-obscured AGNs and Seyferts (Jarrett et al. 2011; Huang et al. 2017).

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The W1 and W2 bands are dominated by light from K- and M-type giant stars, and thus trace the continuum emission from evolved stars with minimal extinction at low redshifts. Consequently, these bands are good tracers of the underlying stellar mass of a galaxy (Meidt et al. 2012; Cluver et al. 2014). However, the W2 band is also sensitive to hot dust, as well as 3.3 $\mu {\rm{m}}$ polycyclic aromatic hydrocarbon (PAH) emission from extreme star formation and AGNs. W1 contains the 3.3 $\mu {\rm{m}}$ PAH emission, but it is typically weak for normal star-forming galaxies (Ponomareva et al. 2018). As such, the aggregate stellar mass will be overestimated in the presence of an AGN (Jarrett et al. 2011; Stern et al. 2012; Meidt et al. 2014). In order to mitigate this problem, we exclude AGNs from our analysis that are identified in the AGN catalog of Véron-Cetty & Véron (2010).

Stellar masses were estimated following the GAMA-derived stellar mass-to-light ratio (${M}_{* }/{L}_{W{1}_{\mathrm{Sun}}})$ relation of Cluver et al. (2014):

$$\begin{eqnarray}&&{\mathrm{log}}_{10}{M}_{* }/{L}_{W{1}_{\mathrm{Sun}}}=-1.96(W1-W2)-0.03,\end{eqnarray} \tag{ 1 }$$

which depends on the "in-band" luminosity relative to the Sun,

$$\begin{eqnarray}&&{L}_{W{1}_{\mathrm{Sun}}}={10}^{-0.4(M-{M}_{\mathrm{Sun}})},\end{eqnarray} \tag{ 2 }$$

where M is the absolute W1 magnitude and M_Sun = 3.24 (Jarrett et al. 2013). Equation (1) was determined using the Galaxy and Mass (GAMA; Driver et al. 2009) survey with stellar masses derived assuming a Chabrier (2003) IMF (Taylor et al. 2011; Cluver et al. 2014), and limited to galaxies with −0.05 < W1 − W2 < 0.30, so we restrict the input colors for Equation (1) accordingly. The W1–W2 color dependence takes into account morphological dependence on the M/L and other factors, such as metallicity (Cluver et al. 2014). To determine the W1–W2 color, apertures are matched between the two bands. We typically use the W2 elliptical isophotal aperture as the fiducial since it is less sensitive than W1 and usually 10% to 15% smaller in radial extent. This is particularly the case for galaxies whose mid-infrared emission is dominated by stellar light (see Cluver et al. 2017; Jarrett et al. 2017).

The consistency of our stellar masses and those from other studies can be tested using the MPA-JHU catalog (Brinchmann et al. 2004)⁵ for the Sloan Digital Sky Survey (SDSS; York et al. 2000). By construction, our WISE stellar masses agree with the SED stellar masses determined by GAMA (Driver et al. 2009; Taylor et al. 2011), with a 1σ scatter of just 0.2 dex, and the GAMA ${M}_{* }$/L agree with the MPA-JHU ${M}_{* }$/L, with a bi-weight mean and 1σ scatter in the difference between ${M}_{* }$/L of −0.01 and 0.07 dex. For dwarf galaxies the difference MPA-JHU between and UV-optical SED stellar masses (Huang et al. 2012) is zero with the objects lying within ±0.35 dex ${M}_{\odot }$ (Maddox et al. 2015, and private correspondence). Thus, we do not expect large offsets between the stellar masses we have obtained from WISE and those which have been used in recent studies of H i galaxies.

To calculate the H i mass, we use the published integrated 21 cm flux (F_{H i}) as follows:

$$\begin{eqnarray}&&{{M}}_{{\rm{H}}{\rm{I}}}[{{M}}_{\odot }]=\displaystyle \frac{2.356\times {10}^{5}}{1+{z}}\times {{D}}_{{L}}^{2}\times {{F}}_{{\rm{H}}{\rm{I}}}[{\rm{J}}{\rm{y}}\,{\rm{k}}{\rm{m}}\,{{\rm{s}}}^{-1}],\end{eqnarray} \tag{ 3 }$$

where D_L is the luminosity distance to the galaxy in megaparsecs and z is the redshift measured from the H i spectrum (e.g., Lutz et al. 2017). The uncertainty in the H i mass (Δ${M}_{{\rm{H}}{\rm{I}}}$) is estimated using the method suggested by Doyle & Drinkwater (2006):

$$\begin{eqnarray}&&{\rm{\Delta }}{F}_{{\rm{H}}{\rm{I}}}=0.5\times {F}_{{\rm{H}}\,{\rm{I}}}^{1/2},\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&{\rm{\Delta }}{M}_{{\rm{H}}{\rm{I}}}={M}_{{\rm{H}}{\rm{I}}}\displaystyle \frac{{\rm{\Delta }}{F}_{{\rm{H}}{\rm{I}}}}{{F}_{{\rm{H}}{\rm{I}}}}.\end{eqnarray} \tag{ 5 }$$

The W3 and W4 bands are sensitive to the interstellar medium, AGNs, and star formation (e.g., Calzetti et al. 2007; Jarrett et al. 2011; Cluver et al. 2014, 2017). W4 emission is dominated by warm dust, and for star-forming galaxies W4 luminosity can be used to predict Balmer-decrement-corrected Hα luminosity with an accuracy of 0.2 dex (Brown et al. 2017). However, W4 lacks sensitivity and 39% of HICAT sources lack W4 detections.

WISE W3 luminosity includes contributions from PAHs, nebular emission lines, silicate absorption, and warm dust, all of which are associated with star formation in galaxies. For ∼L* star-forming galaxies, Cluver et al. (2017) found that PAHs and warm dust make 34% and 62.5% contributions, respectively, to the observed W3 luminosity. That said, we expect the contribution of PAHs to the W3 luminosity to decrease with decreasing galaxy mass due to the mass–metallicity relation of galaxies. Also, W3 better predicts the total infrared luminosity (and hence SFR) than W4 (Cluver et al. 2017). WISE W3 is thus a good SFR indicator, and can be used to obtain the Balmer-decrement-corrected Hα luminosity with an accuracy of 0.28 dex (i.e., Brown et al. 2017).

Although the W3 band traces emission from star formation, it may also have contributions from evolved stellar populations. For ∼L* galaxies located at the center of the star-forming main sequence, the stellar continuum contributes 15.8% of the W3 light and we subtract it from our data using the W1 photometry and the method of Helou et al. (2004). To account for this, we therefore scale the W1 integrated flux density, and subtract it from the W3 total flux to give an estimate of the W3 emission from the ISM, W3_PAH (Cluver et al. 2017). We use the prescription in Table 4 from Brown et al. (2017) to estimate the Balmer-decrement-corrected Hα (${L}_{{{\rm{H}}}_{\alpha },\mathrm{Corr}}$):

$$\begin{eqnarray}\mathrm{log}{L}_{W{3}_{\mathrm{PAH}}}\,[\mathrm{erg}\ {{\rm{s}}}^{-1}] & = & (40.79\pm 0.06)+(1.27\pm 0.04)\\ & & \times \ (\mathrm{log}{L}_{{{\rm{H}}}_{\alpha },\mathrm{Corr}}\,[\mathrm{erg}\ {{\rm{s}}}^{-1}]-40),\end{eqnarray} \tag{ 6 }$$

with a 1σ scatter of 0.28 dex. SFRs are estimated by scaling the Kennicutt (1998) calibration to a Chabrier (2003) IMF:

$$\begin{eqnarray}&&\mathrm{SFR}\,[{M}_{\odot }\,{\mathrm{yr}}^{-1}]=(4.6\times {10}^{-42})\times {L}_{{{\rm{H}}}_{\alpha },\mathrm{Corr}}\ [\mathrm{erg}\,{{\rm{s}}}^{-1}].\end{eqnarray} \tag{ 7 }$$

The uncertainty in SFR is dominated by the scatter in the relationship between WISE W3 luminosity and Balmer-decrement-corrected Hα luminosity and therefore the uncertainty in log(SFR) ∼ 0.28 dex (Brown et al. 2017).

We use the SFR calibration from Brown et al. (2017) because it provides better SFR estimates for a broad range of galaxies—including LIRGs and blue compact dwarfs galaxies—compared to the prior literature. Also, Cluver et al. (2017) compared the SFR calibrations from the prior literature to their calibration derived from total infrared luminosity and found the SFR calibration from Brown et al. (2017) to agree with their own.

We use HICAT to form the basis of the H i-selected sample. Out of 3513 HICAT sources, 2826 have good W1 and W2 photometry. Of these, 2396 also have good photometry for the W3 band, and 2342 galaxies in this category have significant W3_PAH flux (W3 flux with the stellar continuum subtracted). Figure 4 shows the percentage of H i sources with WISE counterparts as a function of H i mass. We achieve a HICAT-WISE match completeness of 80% for H i mass >10^9.5 ${M}_{\odot }$.

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To measure the distribution of H i masses and SFRs as a function of stellar mass and morphology, we generate a stellar mass-selected sample of spiral galaxies (the spiral sample). The spiral sample is drawn from the Bonne et al. (2015) catalog, which achieves a 99% completeness in redshifts and morphologies for galaxies with K_tot < 10.75. We maximize H i completeness by limiting the sample to spiral galaxies (defined with de Vaucouleurs T-type ≥ 0) with redshift ≤0.01 and remeasured W1 magnitude <10. Our spiral sample consists of 600 galaxies.

For 435 of our spiral galaxies we obtained H i fluxes from HICAT, while for a further 121 galaxies we obtained archival H i fluxes from Paturel et al. (2003), Huchtmeier & Richter (1989), Springob et al. (2005), and Masters et al. (2014). The details of the H i counterparts are provided in Table 2. As we illustrate in Figure 5, 93% of the spiral galaxies have H i detections.

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The aforementioned W1 and redshift limits are chosen because of the brightness limitation of the parent sample and the detection sensitivity of HICAT. While the notional limit for the Bonne et al. (2015) is K_tot ≤ 10.75, this limits the W1 ≤ 11.5 and galaxy numbers decline at W1 > 10. Table 3 lists the number of galaxies in our sample, the number with H i detections and the percentage with H i detections with and without the redshift and W1 magnitude limits applied. Removing the redshift and magnitude limits from the spiral sample decreases the percentage of galaxies with H i detections to 50%, but has little impact on measured relations we describe in Section 5.

Table 4.  Median H i Mass and 1σ (68%) Scatter as a Function of Stellar Mass for the Spiral Sample, and the GASS Spiral Sample

	Spiral Sample				GASS Spiral Sample
log(${M}_{* }$)	log(${M}_{{\rm{H}}{\rm{I}}}$)	1σ	Total	% H i	log(${M}_{{\rm{H}}{\rm{I}}}$)	1σ	Total	% H i
(${M}_{\odot }$)	(${M}_{\odot }$)	(${M}_{\odot }$)		Detections	(${M}_{\odot }$)	(${M}_{\odot }$)		Detections
9.25	9.14	0.42	31	97
9.75	9.41	0.37	129	95
10.25	9.59	0.43	225	92	9.53	0.47	130	89
10.75	9.61	0.46	174	97	9.73	0.38	111	94
11.25	9.93	0.54	38	92	9.88	0.55	64	83

Note. Median H i masses are not calculated for stellar mass bins with a H i completeness ≤50%.

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In order to compare the H i mass, stellar mass, and SFR relationships of this work to those of GASS (Catinella et al. 2010, 2012, 2013), which uses a stellar mass-selected sample, we have also produced such a sample (${M}_{s}$ sample). The GASS sample is designed to measure the neutral hydrogen content of 1000 galaxies to investigate the physical mechanisms that regulate how cold gas responds to different physical conditions in the galaxy and the processes responsible for the transition between star-forming spirals and passive ellipticals (Catinella et al. 2010).

The ${M}_{s}$ sample selection is identical to that of the spiral sample except that it lacks the T-type criterion. The ${M}_{s}$ sample contains 839 galaxies, of which 590 have an H i counterpart. The details of the H i counterparts are provided in Table 2. Figure 5 shows that the fraction of galaxies with an H i measurement drops at the higher stellar masses, where the number of H i-poor ellipticals increases.

The relationship between H i mass and stellar mass for the H i-selected sample is illustrated in Figure 6. The H i mass is a strong function of stellar mass among the H i sample (Spearman's rank correlation, r_s, = 0.64) and the least-squares fit to the medians, represented by an orange line in Figure 6, is

$$\begin{eqnarray}&&\mathrm{log}\,{M}_{{\rm{H}}{\rm{i}}}=0.51\ (\mathrm{log}\,{M}_{* }-10)+9.71.\end{eqnarray} \tag{ 8 }$$

We fit 68% of the H i masses within 0.5 dex of our best-fit relation.

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H i mass versus stellar mass relations for the H i-selected sample and previous studies (Catinella et al. 2010; Huang et al. 2012; Maddox et al. 2015) are also plotted in Figure 6. Our sample and the ALFALFA samples of Huang et al. (2012) and (Maddox et al. 2015) are H i-selected, while the GASS sample of Catinella et al. (2010) is stellar mass-selected. We find the relations for the H i–selected samples are qualitatively similar, with median H i mass increasing with stellar mass. In contrast, the H i versus stellar mass relation measured with the GASS sample (Catinella et al. 2010) is up to 0.5 dex lower than those derived from H i-selected samples, as the GASS sample includes galaxies with low H i masses (including ellipticals). There are also discrepancies in the H i versus stellar mass relations measured with different H i-selected samples. We do not see the break in the relation at a stellar mass of 10⁹ ${M}_{\odot }$ that was previously observed by ALFALFA (i.e., Huang et al. 2012; Maddox et al. 2015).⁶ Below a mass of 10⁹ ${M}_{\odot }$ our sample is less than 70% complete for WISE counterparts, and thus we may not be reliably measuring H i mass versus stellar mass in this mass range. However, even if this was not an issue we believe this sample would produce a biased relation, as it (by construction) excludes galaxies that have high stellar masses but low H i masses (i.e., many elliptical galaxies).

The H i and stellar mass distribution for the spiral sample is shown in Figure 7. The median H i mass increases with stellar mass with a least-squared fit of

$$\begin{eqnarray}&&\mathrm{log}\,{M}_{{\rm{H}}{\rm{I}}}=0.35\ (\mathrm{log}\,{M}_{* }-10)+9.45,\end{eqnarray} \tag{ 9 }$$

with 68% of the H i masses within 0.4 dex.

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However, as Figure 7 illustrates, at a given stellar mass the median H i mass increases with T-type while the dispersion decreases with T-type. For example, for the 10¹⁰ to 10^10.5 ${M}_{\odot }$ stellar mass bin, the median H i mass and the 1σ spread of galaxies for all spirals is 10^9.53 ${M}_{\odot }$ ± 0.47 dex, for T-type 0 to 2 is 10^9.26 ${M}_{\odot }$ ± 0.59 dex, and for T-type 6 to 8 is 10^9.72 ${M}_{\odot }$ ± 0.31 dex. The increasing spread of H i masses with decreasing T-type for spiral galaxies may be part of a broader trend, as Serra et al. (2012) concluded that the H i mass distribution for early-type galaxies was far broader than that for spirals. They suggest this scatter reflects the large variety of H i content of early-type galaxies, and confirms the lack of correlation between H i mass and luminosity.

In Figure 7, we compare our H i mass–stellar mass distribution of our spiral sample to that from GASS (Catinella et al. 2010), using GASS galaxies that we have classified as spirals with Galaxy Zoo 1 (GZ1; Lintott et al. 2011). Using the GZ1 classifications and a 70% vote threshold, we find GASS comprises 305 spirals, 273 ellipticals, and 182 galaxies with uncertain morphology.⁷ We repeat our analysis on the GASS sample, using the same stellar mass bins and H i median mass calculations with stellar mass bins with 10 or more galaxies and an H i detection rate >50%. The estimated median H i masses for the spiral sample and the GASS spiral samples are listed in Table 4. The median H i masses for the GASS spiral sample increases with stellar mass similar to our spiral sample. The median H i mass of the spiral samples differs by about 0.08 dex on average. To explain the relationship between H i mass and stellar mass of the spiral samples we turn to the halo spin parameter models of Obreschkow et al. (2016) in Section 7.

In Figure 8, we present H i mass versus stellar mass for our ${M}_{s}$ sample and the equivalent stellar mass-selected sample of GASS (Catinella et al. 2010). The estimated median H i masses of the ${M}_{s}$ sample and the GASS sample are listed in Table 5. For the ${M}_{s}$ sample the H i mass increases with the stellar mass for the stellar mass bins ≤10^10.5 ${M}_{* }$ and then flattens for the highest stellar mass bin. The estimated H i mass median for the highest stellar mass bin may be underestimated, as the H i completeness for this bin is only 58% and our assumption that all nondetections are below the median could be in error.

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Table 5.  Median H i Mass and 1σ (68%) Scatter as a Function of Stellar Mass for the ${M}_{s}$ Sample and the GASS Sample

	${M}_{s}$ Sample				GASS Spiral Sample
log(${M}_{* }$)	log(${M}_{{\rm{H}}{\rm{I}}}$)	1σ	Total	% H i	log(${M}_{{\rm{H}}{\rm{I}}}$)	1σ	Total	% H i
(${M}_{\odot }$)	(${M}_{\odot }$)	(${M}_{\odot }$)		Detections	(${M}_{\odot }$)	(${M}_{\odot }$)		Detections
9.25	9.10	0.50	34	91
9.75	9.56	0.27	145	86
10.25	9.48	0.41	272	79	9.14	0.64	299	68
10.75	9.03	0.89	299	58	9.32	0.62	292	63
11.25			84	50			168	50

Note. Median H i masses are not calculated for stellar mass bins with an H i completeness ≤50%.

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At stellar masses greater than 10¹⁰ ${M}_{\odot }$, median H i mass is almost constant with stellar mass, and our measurements agree with those of GASS to within 0.3 dex. This is in contrast with the trend shown in Figure 7 for the spiral sample. The obvious explanation, given the prior literature (e.g., Catinella et al. 2010; Huang et al. 2012), is that this is due to the increasing fraction of gas poor early-type galaxies at high ${M}_{* }$, as illustrated in the top panel of Figure 8. Serra et al. (2012) found that early-type galaxies host less H i than spiral galaxies, but have a broader range of H i masses. For example, Serra et al. (2012) found that elliptical galaxies have H i mass from 10⁷ to 10⁹ ${M}_{\odot }$ (the lower limit is uncertain as this overlooks H i nondetections in their sample), while the H i mass distribution for spirals peaks at ∼2 × 10⁹ ${M}_{\odot }$, with a small number of galaxies below 10⁸ ${M}_{\odot }$. Combining this result with our previous findings from our spiral sample, we conclude that as one moves from early-type to late-type galaxies, median H i mass increases while the scatter in H i mass decreases. Within an individual T-type, H i mass typically increases with stellar mass, and it is the increasing fraction of early-types with increasing stellar mass that explains the roughly constant median H i masses measured for the ${M}_{s}$ sample.

A key conclusion from the previous sections is that sample selection impacts measured H i mass versus stellar mass relations, and, to illustrate this, in Figure 9 we plot H i mass–stellar mass relations for H i-selected samples, spiral galaxy samples, and stellar mass-selected samples, including data from both our work and the literature. For all values of stellar mass, H i-selected samples have a higher H i mass than spiral-selected and stellar mass-selected samples. This is because H i surveys are designed to sample a large number of H i-rich systems, and therefore lack the sensitivity to detect the H i-poor galaxy population. For example, HIPASS can detect galaxies with H i masses >10⁹ ${M}_{\odot }$ at z = 0.01; however, elliptical galaxies have H i masses ≤10⁹ ${M}_{\odot }$ (Serra et al. 2012), and would thus be largely missing from HIPASS samples at these redshifts. Even the late-type galaxies in Figure 7 have H i masses as low as 10⁸ ${M}_{\odot }$, and thus some are missing from HIPASS-selected samples at z > 0.01. Similar selection effects apply to ALFALFA, albeit at higher redshifts. This is not surprising and indeed was a motivation for studies such as GASS, but does illustrate that H i mass versus stellar mass relations have a strong dependence on sample selection.

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While the relationship between SFR and H i mass is the principal focus of the paper, we are also able to measure the local (z ≤ 0.01) star-forming main sequence (MS; e.g., Noeske et al. 2007; Rodighiero et al. 2011; Wuyts et al. 2011) using the spiral sample. Measurements of the MS are enhanced by our highly complete sample, our new WISE photometry (which should mitigate aperture bias—see Section 2.2), and our ability to take advantage of a recent calibration of W3 as an SFR indicator that uses large aperture photometry (Brown et al. 2017).

In Figure 10 we present our star-forming main sequence. As expected, the median of the log SFR increases from −0.50 dex for the 10⁹ to 10^9.5 ${M}_{\odot }$ stellar mass bin to 0.14 dex for the 10¹⁰ to 10^10.5 stellar mass bin, with the scatter of individual galaxies about the median being ∼0.3 dex. For stellar mass bins above 10¹⁰ ${M}_{\odot }$, the median log SFR is roughly constant at 0.14 while the scatter of the individual galaxy SFRs about the median increases from 0.38 to 0.49 dex. The changing trend of SFR with increasing stellar mass and the increased dispersion of SFRs is evidence of mass quenching (Kauffmann et al. 2003), and this also coincides with an increasing fraction of early-type spirals (T-type ≤ 2). To mitigate the effect of mass quenching on our model fit to the MS, we only fit to galaxies with stellar mass ≤10^10.5 ${M}_{\odot }$ (shown in Figure 10(b)) and measure the MS to be

$$\begin{eqnarray}&&\mathrm{log}\,\mathrm{SFR}=0.7\ (\mathrm{log}\,{M}_{* }-10)-0.09,\end{eqnarray} \tag{ 10 }$$

with a 1σ scatter of 0.27 dex. Alternate selection criteria to mitigate the effect of mass quenching produces similar MS fits. For example, a subsample of galaxies with T-type > 2 produces a fit of log SFR = 0.61 (log M_* − 10) − 0.08 (1sσ scatter = 0.26 dex).

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Figure 10(b) and Table 6 also compare the MS relation from this work to the prior literature (Elbaz et al. 2007; Salim et al. 2007; Chen et al. 2009; Oliver et al. 2010; Zahid et al. 2012; Grootes et al. 2013), with data taken from the extensive review by Speagle et al. (2014). To shift the Speagle et al. (2014) homogenized MS relations from a Kroupa to Chabrier IMF, we apply −0.03 and −0.07 dex shifts to the stellar masses and SFRs, respectively. The blue line is the z = 0.01 MS relation given by Equation (28) from Speagle et al. (2014), and the shaded region is the "true" scatter about the MS (for more details, please refer to Speagle et al. 2014). The normalization (at log ${M}_{* }$ = 10) of our best fit is 0.04 dex smaller and the slope is 0.21 larger than the best fit for the MS of Speagle et al. (2014). Speagle et al. (2014) noted that the wide range of the MS slopes for the local universe suggests that the systematics involved are underestimated, and they estimate the magnitude of these systematics on the MS slopes to be of the order of ∼0.2 dex. As we noted earlier, our slope depends on the criterion used to reject galaxies that could be undergoing quenching, and including early-type spiral galaxies with masses above 10^10.5 ${M}_{\odot }$ reduces our slope to 0.416 (1σ scatter = 0.34), which is closer to that of Speagle et al. (2014).

Table 6.  Main-sequence Relationships

Paper	α	β	log SFR(10)	zmed	zrange	log ${M}_{* }$ Range	Survey
This Study	0.7	−7.09	−0.09	⋯	≤0.01	9.0–11.0	WISE
Zahid et al. (2012)	0.71 ± 0.01	−6.78 ± 0.1	0.32	0.07	0.04–0.1	8.5–10.4	SDSS
Oliver et al. (2010)	0.77 ± 0.02	−7.88 ± 0.22	−0.18	0.1	0.0–0.2	9.1–11.6	SWIRE
Chen et al. (2009)	0.35 ± 0.09	−3.56 ± 0.87	−0.06	0.11	0.005–0.22	9.0–12.0	SDSS
Elbaz et al. (2007)	0.77	−7.44	0.26	0.06	0.015–0.1	9.1-11.2	SDSS
Salim et al. (2007)	0.65	−6.33	0.17	0.11	0.005–0.22	9.0–11.1	GALEX-SDSS selected
Speagle et al. (2014)	0.49	−5.13	−0.03	⋯	⋯	⋯	⋯
Grootes et al. (2013)a	0.550	−5.520	−0.02	⋯	≤0.13	9.5–11	GAMA/Herschel-ALTAS
Cluver et al. (2017)b	1.05 ± 0.09	−10.40 ± 0.88	0.09	⋯	z < 0.01(<30 Mpc)	7–11.5	SINGS/KINGFISH

Notes. Column 1: reference. Columns 2 and 3: MS slope α and normalization β reported in Table 6 of Speagle et al. (2014). These best-fit parameters have been adjusted for IMF, cosmology, SPS model, and emission line corrections. Column 4: log SFR predicted by each MS relation at log ${M}_{* }$ = 10. Column 5: the median redshift. Column 6: redshift range. Column 7: stellar mass range. Column 8: survey data.

^aThe normalization was not adjusted by Speagle et al. (2014). We do not apply shifts to the stellar masses and SFRs as Grootes et al. (2013) make use of Chabrier (2003) IMF. ^bThe normalization was not adjusted for systematics by Speagle et al. (2014). The MS trend of Cluver et al. (2017) is not shown in Figure 10 because KINGFISH galaxies were chosen to cover the full range of galaxy types, luminosities and mass properties, and local ISM environments rather than being a magnitude-limited sample.

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SFE, defined as SFR/${M}_{{\rm{H}}{\rm{I}}}$, quantifies the current rate of gas consumption, dividing the SFR by H i mass and SFE is expected to depend on the stellar mass of a galaxy (Schiminovich et al. 2010; Huang et al. 2012; Wong et al. 2016; Lutz et al. 2017). SFE and its inverse, the depletion time, have thus been commonly used to quantify gas consumption and test models of the stability of galactic disks (e.g., Wong et al. 2016).

To investigate the relationship between star formation and H i mass within the spiral sample, we plot in Figure 11 SFE as a function of stellar mass. In Table 7 we provide the median SFEs as a function of stellar mass, with the upper limits on the H i mass being used for the H i nondetections. The SFE remains relatively constant at a median SFE = 10^−9.57 yr⁻¹, with a 1σ scatter of 0.44 dex for spiral galaxies with stellar masses between 10^9.0 and 10^11.5 ${M}_{\odot }$. While we see evidence for mass quenching in high stellar mass spirals in Figure 10, the SFE appears to be constant for spiral galaxies falling on the MS and spiral galaxies that have (potentially) commenced quenching.

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Table 7.  The Median SFE and 1σ Values of Each Stellar Mass Bin for the Spiral Sample Shown in Figure 11

log(${M}_{* }$)	Median log(SFE)	1σ	N
(${M}_{\odot }$)	(yr−1)	(dex)
9.25	−9.72	0.51	29
9.75	−9.58	0.43	128
10.25	−9.49	0.41	222
10.75	−9.48	0.47	164
11.25	−9.56	0.39	35

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SFE versus stellar mass relations for both the spiral sample and previous studies (Schiminovich et al. 2010; Jaskot et al. 2015; Wong et al. 2016; Lutz et al. 2017) are compared in Figure 12(a). H i-selected samples (Jaskot et al. 2015; Lutz et al. 2017) exhibit an increasing SFE with stellar mass; however, this reflects their selection bias against galaxies with low H i masses. By contrast, stellar mass-selected samples (Schiminovich et al. 2010; Wong et al. 2016) exhibit a constant SFE with stellar mass; however, previous studies have measured differing values of this constant, ranging from 10^−9.65 yr⁻¹ (Wong et al. 2016) to 10^−9.5 yr⁻¹ (Schiminovich et al. 2010). Wong et al. (2016) provide two theoretically motivated relations for SFE versus stellar mass, which are both plotted in Figure 12(b). The first relation assumes that the molecular gas fraction depends only on the stellar surface mass density, while the second assumes that this fraction depends on the hydrostatic pressure. Between stellar masses of 10^9.0 and 10^11.5 ${M}_{\odot }$, the hydrostatic pressure model of Wong et al. (2016; which gives a constant SFE) shows the greatest consistency with our work and other stellar mass-selected samples.

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For the spiral sample, we find that H i mass increases with stellar mass, from 10^9.14 ${M}_{\odot }$ at a stellar mass of 10^9.25 ${M}_{\odot }$ to 10^9.93 ${M}_{\odot }$ at a stellar mass of 10^11.25 ${M}_{\odot }$ (see Figure 7). We also observe a stellar mass-dependent upper limit on H i mass. In this section, we discuss the reason for this upper limit.

Both our H i- and stellar mass-selected samples imply an upper limit for H i mass as a function of stellar mass, and such thresholds are also seen in prior literature (e.g., Maddox et al. 2015). Is this upper limit for H i mass expected from theory? Maddox et al. (2015) argue that the maximum H i fraction for galaxies with stellar masses >10⁹ ${M}_{\odot }$ is set by the upper limit in the halo spin parameter, λ. The halo spin parameter is defined as

$$\begin{eqnarray}&&\lambda \equiv {J}_{\mathrm{halo}}{E}_{\mathrm{halo}}^{1/2}{G}^{-1}{M}_{\mathrm{halo}}^{-5/2},\end{eqnarray} \tag{ 11 }$$

where J_halo is the galaxy halo's angular momentum, E_halo its total energy, and M_halo its total mass (Boissier & Prantzos 2000). Maddox et al. (2015) determined the halo spin parameter of the ALFALFA galaxies and found that, at a fixed stellar mass, galaxies with the largest H i mass also have the largest halo spin parameter (see their Figure 6). The large halo spin of a galaxy stabilizes the high H i mass disk, preventing it from collapsing and forming stars.

Maddox et al. (2015) also measured the largest spin parameter to be λ ∼ 0.2, confirming the upper limit on the halo spin parameter predicted by numerical N-body simulations of cold dark matter (Knebe & Power 2008). They concluded that the upper limit on the H i fraction is set by the upper limit of the halo spin parameter due to the empirical correlation between the halo spin parameter and the H i fraction.

Obreschkow et al. (2016) found that for isolated local disk galaxies the fraction of atomic gas, f_atm, is described by a stability model for flat exponential disks. To see if the observed upper limit to the H i fraction of the spiral sample can be explained by the upper limit of the halo spin parameter, we calculate the f_atm relationship for λ ≈ 0.112, following the method outlined in Obreschkow et al. (2016). Though λ ∼ 0.2 is the maximum spin of a spherical halo, we choose to calculate the f_atm at λ ≈ 0.112 because 99% of galaxy halos are predicted to lie below ≲0.112 (Bullock et al. 2001). We define the fraction of atomic gas as

$$\begin{eqnarray}&&{f}_{\mathrm{atm}}=\displaystyle \frac{1.35{M}_{{\rm{H}}{\rm{I}}}}{M},\end{eqnarray} \tag{ 12 }$$

where M is the disk baryonic mass (M = ${M}_{* }$ + 1.35M_{H i}) and the factor of 1.35 accounts for the universal helium fraction (Obreschkow et al. 2016). Obreschkow et al. (2016) models the rotation curve of spiral galaxies as

$$\begin{eqnarray}&&{f}_{\mathrm{atm}}=\min \{1,2.5{q}^{1.12}\},\end{eqnarray} \tag{ 13 }$$

where q is the global stability parameter. This parameter is defined as:

$$\begin{eqnarray}&&q=\displaystyle \frac{j\sigma }{{GM}}=0.22\displaystyle \frac{\lambda }{0.03}{\left(\displaystyle \frac{M}{{10}^{9}{M}_{\odot }}\right)}^{-1/3},\end{eqnarray} \tag{ 14 }$$

where j is the baryonic specific angular momentum of the disk, σ is the velocity dispersion of the atomic gas and mass is in units of 10⁹ ${M}_{\odot }$. The global stability parameter is simplified by making two assumptions: first, that disk galaxies condense out of scale-free cold dark matter halos, and second, that j ∝ λ (Obreschkow & Glazebrook 2014; Obreschkow et al. 2016). Under these assumptions, Equation (13) simplifies to:

$$\begin{eqnarray}&&{f}_{\mathrm{atm}}=\min \left\{1,0.5{\left(\displaystyle \frac{\lambda }{0.03}\right)}^{1.12}{\left(\displaystyle \frac{M}{{10}^{9}{M}_{\odot }}\right)}^{-0.37}\right\},\end{eqnarray} \tag{ 15 }$$

and using Equation (12), this can be rearranged to give

$$\begin{eqnarray}\displaystyle \frac{{M}_{{\rm{H}}{\rm{I}}}}{{10}^{9}{M}_{\odot }} & = & \min \left\{\displaystyle \frac{M}{1.35\times {10}^{9}{M}_{\odot }},\right.\\ & & \quad \left.18{\lambda }^{1.12}{\left(\displaystyle \frac{M}{{10}^{9}{M}_{\odot }}\right)}^{-0.63}\right\}.\end{eqnarray} \tag{ 16 }$$

Figure 13 illustrates the comparison between Equation (16) and the empirical H i–stellar mass distribution of the spiral sample. We also include the predicted f_atm curve for λ ≈ 0.03, as this value of λ corresponds to the mode of the empirically measured halo spin parameter distribution (Bullock et al. 2001). The median bins of the spiral sample are in agreement with this prediction of f_atm, while the highest H i mass galaxies lie below the predicted upper limit for f_atm, when λ = 0.112. We find that the model of Obreschkow et al. (2016) matches well with the empirical data of the spiral sample, consistent with the hypothesis that the upper limit of the H i fraction is set by that of the halo spin parameter.

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We find that SFE is constant across two orders of magnitude of stellar mass, which agrees with the findings of Catinella et al. (2010) and Wong et al. (2016), while disagreeing with others (e.g., Huang et al. 2012; Lutz et al. 2017). Wong et al. (2016) tested two models for molecular gas content within galaxies: one where molecular gas is a function of stellar surface density and another where it is a function of hydrostatic pressure. The stellar surface density prescription (Leroy et al. 2008; Zheng et al. 2013) defines the molecular-to-atomic ratio, R_mol, as

$$\begin{eqnarray}&&{R}_{\mathrm{mol},s}=\displaystyle \frac{{{\rm{\Sigma }}}_{* }}{81{M}_{\odot }\,{\mathrm{pc}}^{-1}},\end{eqnarray} \tag{ 17 }$$

where Σ_* is the stellar surface density. The R_mol for the hydrostatic pressure prescription (Zheng et al. 2013) is defined as

$$\begin{eqnarray}&&{R}_{\mathrm{mol},p}={\left(\displaystyle \frac{{P}_{h}}{1.7\times {10}^{4}{\mathrm{cm}}^{-3}{\rm{K}}{k}_{{\rm{B}}}}\right)}^{0.8},\end{eqnarray} \tag{ 18 }$$

where P_h is the hydrostatic pressure (Elmegreen 1989) and k_B is the Boltzmann constant.

Similarly to Wong et al. (2016), we find that the constant SFE can be described by a model of the marginally stable disk, while the hydrostatic pressure model provides a better prescription for estimating the SFE and molecular-to-atomic ratio. For massive galaxies with large optical disks, previous studies (e.g., Leroy et al. 2008; Wong et al. 2013) observed a correlation between R_mol and stellar surface density. The two models given by Equations (17) and (18) also predict similar R_mol and integrated SFE for high-mass galaxies (Wong et al. 2016). But for low mass galaxies, the stellar surface density prescription does not predict the observed SFE because this prescription is unable to convert the H i to molecular hydrogen, and underestimates the amount of molecular hydrogen in regions with low stellar surface densities. Therefore, this method underestimates the SFR and SFE in dwarf galaxies. While the stellar surface density model predicts that SFE will decrease for smaller stellar mass galaxies, the hydrostatic pressure model predicts a higher molecular hydrogen content for low mass galaxies, and therefore a constant SFE with stellar mass, agreeing with the empirical data.

We note that Obreschkow et al. (2016) predict that most of the baryons in dwarf galaxies are in the form of H i gas (f_atm = 1) and therefore have low SFE because these systems are inefficient at converting their H i gas to molecular gas. We do not observe a decrease in SFE because these galaxies are below the stellar mass range probed in our spiral sample. Our lowest stellar mass bin of 10^9.0 and 10^9.5 ${M}_{\odot }$ hints at a turnover for the low mass dwarf, as predicted by Obreschkow et al. (2016). Combining the next generation of H i survey, WALLABY, with 20 cm radio continuum from ASKAP, we will measure the H i properties and SFR of ∼600,000 galaxies, including a large number of dwarf galaxies populating the low mass end of Figure 12. Observing these low stellar mass dwarfs will provide a more complete picture about H i content and how efficiently dwarfs convert H i to molecular gas.