\alpha.40: the Galaxy Population

The Arecibo Legacy Fast ALFA Survey: The Galaxy Population Detected by ALFALFA

Shan Huang, Martha P. Haynes, Riccardo Giovanelli Center for Radiophysics and Space Research, Space Sciences Building, Cornell University, Ithaca, NY 14853. shan@astro.cornell.edu, haynes@astro.cornell.edu, riccardo@astro.cornell.edu Jarle Brinchmann Sterrewacht Leiden, Leiden University, NL-2300 RA Leiden, The Netherlands jarle@strw.leidenuniv.nl

Making use of HI 21 cm line measurements from the ALFALFA survey () and photometry from the Sloan Digital Sky Survey (SDSS) and GALEX, we investigate the global scaling relations and fundamental planes linking stars and gas for a sample of 9417 common galaxies: the -SDSS-GALEX sample. In addition to their HI properties derived from the ALFALFA dataset, stellar masses () and star formation rates (SFRs) are derived from fitting the UV-optical spectral energy distributions. 96% of the -SDSS-GALEX galaxies belong to the blue cloud, with the average gas fraction . A transition in SF properties is found whereby below , the slope of the star forming sequence changes, the dispersion in the specific star formation rate (SSFR) distribution increases and the star formation efficiency (SFE) mildly increases with . The evolutionary track in the SSFR– diagram, as well as that in the color magnitude diagram are linked to the HI content; below this transition mass, the star formation is regulated strongly by the HI. Comparison of HI- and optically-selected samples over the same restricted volume shows that the HI-selected population is less evolved and has overall higher SFR and SSFR at a given stellar mass, but lower SFE and extinction, suggesting either that a bottleneck exists in the HI to H conversion, or that the process of SF in the very HI-dominated galaxies obeys an unusual, low efficiency star formation law. A trend is found that, for a given stellar mass, high gas fraction galaxies reside preferentially in dark matter halos with high spin parameters. Because it represents a full census of HI-bearing galaxies at , the scaling relations and fundamental planes derived for the ALFALFA population can be used to assess the HI detection rate by future blind HI surveys and intensity mapping experiments at higher redshift.

Subject headings:
galaxies: evolution – galaxies: fundamental parameters – galaxies: ISM – galaxies: star formation – radio lines: galaxies – surveys

1. Introduction

In the last decade, the galaxy catalogs contributed by legacy programs like the Sloan Digital Sky Survey (SDSS) and the Galaxy Evolution Explorer (GALEX) satellite extragalactic surveys have enabled us to quantify properties associated with the stellar populations of galaxies in the local universe. Through their statistically-based insight into the stellar component and the interrelationship of the physical parameters, these surveys have provided quantitative clues of importance to our understanding of the formation and evolution of galaxies (e.g. Brinchmann et al., 2004; Salim et al., 2007). The bimodal distribution evident in the color-magnitude diagram (Baldry et al., 2004; Schiminovich et al., 2007) suggests a likely evolution scenario whereby galaxies in the blue cloud form stars vigorously and grow through mergers and later, after depleting their gas reservoirs, then migrate to the red sequence. This picture is also supported by tracers of the star formation history (SFH): e.g., the specific star formation rate (SSFR), the star formation rate (SFR) per unit stellar mass, is seen to vary with the total stellar mass (Brinchmann et al., 2004). The star-forming sequence (high SSFR) is associated with actively star forming blue cloud galaxies. Indeed, the stellar mass appears to be the crucial quantity governing the star formation (SF) along this sequence. In the absence of mergers or other events that trigger a starburst, blue galaxies on the sequence evolve towards higher stellar mass and lower SSFR, and eventually become red and dead.

In statistical terms, all surveys are biased by the properties that define them. For example, optical surveys are biased in terms of optical flux and possibly surface brightness. The SDSS legacy galaxy redshift sample has an apparent -band Petrosian magnitude limit of 17.77, as well as a surface brightness limit of 23.0 mag arcsec at the half light radius in (Strauss et al., 2002). In contrast, blind HI surveys are unbiased by optical characteristics but have their own limitations in terms of HI line emission sensitivity, usually as a function of HI line width (Martin et al., 2010; Haynes et al., 2011). Because increases with decreasing , HI-selected samples are more inclusive of star-forming galaxies than optical samples of similar depth. Indeed, since almost all star-forming galaxies contain neutral gas, an HI-selected sample can approach a full census of star-forming galaxies. For example, West et al. (2010) demonstrated the HI-selection identifies galaxies with lower surface brightness, smaller absolute magnitudes, bluer colors and smaller stellar masses than those used in typical SDSS studies. However, the limitation with an HI-selected sample is that it will miss the early type galaxies, which contain very little neutral gas (Garcia-Appadoo et al., 2009). Furthermore, analysis of the spatial correlation function shows that the HI-selected galaxies represent the least clustered population on small scales (Martin et al., 2012), a fact important for interpreting the results of future HI intensity mapping experiments.

Exploiting the mapping capability of the Arecibo L-band feed array (ALFA) and the sensitivity of the Arecibo 305 m antenna, the Arecibo Legacy Fast ALFA (ALFALFA) survey (Giovanelli et al., 2005a, b) is an ongoing blind HI survey, aimed at mapping 7000 square degrees of high galactic latitude sky between and in declination. When complete, the survey will detect more than 30,000 galaxies out to redshift of 0.06 with a median recessional velocity, , of (Haynes et al., 2011). Compared to the HI Parkes All Sky Survey (HIPASS: Barnes et al., 2001; Meyer et al., 2004; Wong et al., 2006), ALFALFA is 8 times more sensitive, its spectral coverage extends over 1.6 times the bandwidth of HIPASS, and the angular resolution of ALFA is 4 times better than that of the Parkes multifeed receiver. The combination of sensitivity and spectral bandwidth enables ALFALFA to detect thousands of massive HI disks with . In addition, the Arecibo spectral backend yields a finer velocity resolution than characterized HIPASS, making it possible to detect sources with HI line widths as narrow as . As discussed in Haynes et al. (2011) and earlier papers in the ALFALFA series, the median centroiding accuracy of the HI sources is allowing the identification of most probable optical counterparts in 97% of cases. ALFALFA provides the first full census of HI-bearing objects over a cosmologically significant volume of the local universe (Martin et al., 2010) so that its population includes the very rare objects missing from the smaller volumes sampled by previous blind HI surveys. It enables the study of the characteristics of HI-selected galaxies in comparison with the galaxy populations included in the SDSS and GALEX surveys.

The 2011 ALFALFA catalog, ‘’, covers of the final targeted sky area (Haynes et al., 2011), giving HI masses, systemic velocities and HI line widths for 16000 high quality detections (§2.1). In addition to the HI line parameters, the catalog also includes an assignment of the most probable optical counterpart (OC) to each HI line detection. Haynes et al. (2011) discuss the process of assigning OCs to the HI sources, and where the footprints of the surveys overlap, the HI sources are cross-referenced to the SDSS Data Release 7 (DR7: Abazajian et al., 2009), permitting the derivation of properties associated with the stellar components of the HI-bearing galaxies detected by ALFALFA. As shown by Haynes et al. (2011), the population is highly biased against red-sequence objects.

In this paper, we investigate further the nature of the stellar counterparts of the HI line detections, adding to the optical SDSS data photometric measures from the GALEX catalog (§2.2). By combining the measurements of the gaseous and stellar components, we characterize the galaxy population and study in §3 global trends within it. SED-fitting to the seven bands from the UV to optical is applied to derive the principal stellar properties, including the stellar masses (§3.1) and SF (§3.2). To understand better the characteristics of the gas-bearing galaxies and the potential bias associated with HI-selection, we define a volume-limited sub-sample extracted from the catalog with a similar one extracted from the SDSS-DR7 (§4.1) and compare the two in §4.2 in terms of survey depth (§4.2.1), extinction (§4.2.2), color (§4.2.3), SF behavior (§4.2.4), etc. The empirical distribution of the halo spin parameter is derived in §5, which suggests that the HI-selected galaxies favor high spin parameter halos. Our conclusions are summarized in §6.

Throughout this paper, we adopt a reduced Hubble constant . A Chabrier (2003) IMF is adopted.

2. Sample and Data

2.1. ALFALFA parent sample

The HI parent sample used here is drawn from the catalog presented in Haynes et al. (2011). The catalog covers two regions in the Spring sky (i.e., the Virgo direction, , and ) and two in the the Fall sky (i.e., the anti-Virgo direction, , and ). As discussed in Haynes et al. (2011), ALFALFA HI line detections are categorized according to their signal-to-noise ratio (S/N) and corresponding reliability. Code 1 sources have S/N 6.5 and are highly reliable. Another set of entries, designated as “code 2” sources, or “priors”, have lower S/N but coincide with a likely OC at the same redshift. Most of these sources are likely to be real (Haynes et al., 2011). The catalog includes 15041 extragalactic HI sources, 11941 with code 1 and 3100 with code 2. In this paper, we consider both the code 1 and 2 detections and adopt the HI measures, distances and HI masses presented in the presented by Haynes et al. (2011). It is important to note that 70% of the ALFALFA sources are new HI detections proving that previous targeted surveys based on optical selection (magnitude, size and morphology), most notably the extensive collection contained in the Cornell digital HI archive (Springob et al., 2005), missed large segments of the local gas-bearing population.

In particular, one of the most surprising results of ALFALFA to date is the richness of the high HI mass galaxy population (Martin et al., 2010). With its combination of sensitivity and depth, ALFALFA reveals that there still exists at a population of massive galaxies which retain massive HI () disks. Some, in fact, contain a dominant fraction of their baryons in HI gas. As the most HI massive local galaxies, they are the analogs of the massive disks detected at (Catinella et al., 2008) and those that will dominate the deep surveys being planned for even higher with the EVLA, APERTIF, ASKAP and MeerKAT and eventually the Square Kilometre Array (SKA). By design, ALFALFA provides a census of HI bearing galaxies within a cosmologically significant volume over a wider dynamic range of HI masses than previous studies. It thus serves as the reference HI-selected population.

2.2. Optical and UV counterparts of ALFALFA HI sources

In addition to the HI measurements, Haynes et al. (2011) attempt to identity the most probable optical counterpart (OC) of each HI line source in the catalog. Ancillary information such as redshift coincidence, angular size, color and morphology is used in making the OC assignment. As discussed by Haynes et al. (2011), the process is not perfect, particularly for low signal-to-noise sources for which the centroiding accuracy can exceed 30 and in regions of source confusion. Nonetheless, the vast majority of OC assignments are probably valid and thus permit the comparison of the stellar and gaseous components of the ALFALFA population.

2.2.1 SDSS photometry

Towards this aim, Haynes et al. (2011) also provide a cross reference of the assigned OCs with the SDSS-DR7 (Abazajian et al., 2009) where the two surveys have overlapping sky footprints. The northern Fall region is not covered by the SDSS legacy imaging survey DR7. Of the 15041 HI source included in the catalog, 201 have no OC assigned by Haynes et al. (2011), 2310 lie outside the DR7 footprint, and 60 appear to be in the region of the SDSS imaging survey but cannot be associated with an object in the SDSS photometric database. In most of the latter cases, the OC is evident in the SDSS images but is projected close to a bright foreground star or contaminated by its glare.

As discussed by numerous authors e.g., West et al. (2010), gas rich nearby galaxies are often blue and patchy with the result that their overall optical emission is shredded among several photometric objects by the SDSS pipeline measurements. The ALFALFA-SDSS cross-reference given in Table 3 of Haynes et al. (2011) includes a photometric code that identifies objects with suspicious SDSS photometry, and we exclude such objects (293/12470) from the SED-fitting. For the others, we require that model magnitudes are available in all five SDSS bands (u, g, r, i, z) and retrieve the SDSS photometric parameters from the standard SDSS-DR7 database.

The current catalog used here relies on the optical identifications and photometry derived from the SDSS-DR7 database as cross-referenced in Table 3 of Haynes et al. (2011). Blanton et al. (2011) have presented a new method for background subtracting the SDSS imaging which they apply to the SDSS-III DR8 images. As ALFALFA progresses, we will migrate to use of the improved SDSS pipeline. Especially for purposes of comparison with results obtained by other authors who have likewise relied on DR7, we retain the use of DR7 in the present work.

2.2.2 GALEX photometry

Using a similar approach, we have conducted a separate cross-match of the ALFALFA OCs to the GALEX UV photometric catalog. The imaging mode of the GALEX instrument surveys the sky simultaneously in two broad bands, one in the FUV (effective wavelength of 1516) and a second in the NUV (effective wavelength of 2267). The GALEX field of view is in diameter (Morrissey et al., 2007), although image quality deteriorates in the outer annulus beyond a radius of . We use the GALEX GR6 data release, with its improvements to flat fielding, adjustment to the photometric zero-point, etc. Given the poorer image resolution ( FWHM), compared to that of the SDSS, as well as the lower UV source density, visual inspection shows that the GALEX DR6 pipeline measurements corresponding to the ALFALFA galaxies suffer less from shredding issues. We have also validated that the GALEX pipeline photometry is in close agreement with our own photometric reprocessing of the GALEX images for a sample of dwarf galaxies detected by ALFALFA (Huang et al., 2012).

The GALEX mission includes several survey modes that differ in their exposure time per tile: The All-sky Imaging Survey(AIS) is the shallowest (100 sec), while the Medium Imaging Survey (MIS, 1500 sec) is designed to maximize the coverage of the sky that is included in the SDSS. The latter also includes the Nearby Galaxy Survey (NGS), a selected set of targeted fields of similar depth as the standard MIS. A third Deep Imaging Survey (DIS) is much deeper but covers only a small solid angle. In adopting the GALEX counterparts, we give preference to sources extracted from the MIS, NGS or DIS, but make use of the AIS for those objects not included in the deeper surveys.

To cross-match the ALFALFA OCs to the GALEX catalog, we first search the position of the ALFALFA OCs for all GALEX neighbors within 36. Objects close to the GALEX field edge, i.e. with a distance from the field center , are dropped to avoid duplications with objects in overlapping tiles and known GALEX imaging artifact effects. To permit homogeneous SED-fitting to all 7 bands (FUV, NUV, ugriz), we require that UV images of comparable depth must exist for both of the UV bands; this criterion results in the adoption of AIS measurements where the MIS catalog is incomplete, e.g. because of the failure of the FUV detector. In other cases, matches are missed because the FUV and NUV sources may fail to coincide because of, e.g. astrometry error or shredding in one or both bands. Among the 14840 extragalactic ALFALFA sources with OCs 1828 (12.3%) have no GALEX counterpart returned within 36, either because they lie outside of the GALEX footprint or have no detected UV emission in both bands. 516 (3.5%) are excluded because they lie too close to a GALEX field edge and 1317 (8.9%) are not matched because all neighbors are detected only in one band but not the other. The remaining 11179 OCs are matched to the nearest neighbor in the GALEX catalog with 7752 (52.2%) matched to UV sources found in the AIS and 3427 (23.1%) to ones in the MIS. The median separation between the coordinates of the OC and the cross-matched GALEX object is only 1.6.

Although the addition of the GALEX UV photometry sets better constraints on the SF properties and dust extinction (Salim et al., 2005), the requirement that UV sources must be detected in both bands introduces an additional bias against non star-forming galaxies. SED-fitting to the SDSS bands only (Huang et al., 2012) demonstrates that 13.5% of the 12156 galaxies in the -SDSS DR7 cross-match have , and therefore belong to the quiescent population. This fraction drops to 3.9% of the 9417 galaxies that have counterparts in both the SDSS and GALEX photometric catalogs. As we discuss in §4, the HI-selection produces the stronger bias against the red sequence.

2.2.3 UV-to-optical colors of ALFALFA galaxies

Figure 1 presents the optical-UV color–color diagram derived for the 9417 galaxies which have complete entries in all three of the ALFALFA-, the SDSS-DR7 and GALEX-DR6 catalogs and for which the 7-band SED-fitting produces a valid result (see §3), denoted as the -SDSS-GALEX sample hereafter. Contours and points depict the distribution for the -SDSS-GALEX sample in high and low number density regions respectively, with typical error bars shown in the upper left corner (pipeline magnitude errors). Colors hereafter are all corrected for Galactic extinction but not internal extinction (see §4.2.2). In the optical, the SDSS pipeline extinction-corrected values are used, while at UV wavelengths, we adopt the values based on the maps of Schlegel et al. (1998), the Cardelli et al. (1989) extinction law with , and for the FUV and 8.2 for the NUV, following Wyder et al. (2007). Because of the bandwidth limit of ALFALFA, only low redshift galaxies with small K-correction are included, and we ignore this term in computing colors, i.e., no K-correction is applied.

Because it contrasts the recent SF, as indicated by the UV light, with the total past SF, as indicated by the optical light, the UV-to-optical color is a stronger diagnostic of SFH than colors derived from the optical bands only. This result is also evident in Figure 1. Based on the distribution of their GALEX-SDSS matched catalog, Salim et al. (2007) define their blue cloud galaxies as those with . Using the same cutoff, 96% of the -SDSS-GALEX galaxies lie on the blue side, suggesting that HI-selection induces a strong preference for blue star-forming galaxies, or conversely, a strong bias against red sequence galaxies. Bluewards of this division, the two colors are well correlated with a slope of , which is comparable to what was found by Wyder et al. (2007), . Although only a small population (411) of galaxies appear redward of , the () colors of the red objects increase less quickly with () and the distribution of the reddest tail is nearly flat. As discussed in §4.2.2 the degeneracy of () among the red populations is even more pronounced in an optically-selected sample with more red galaxies. Therefore, the SED-fitting to the SDSS bands only is sufficient to constrain the SF for the HI-selected blue galaxy population in general (e.g. Huang et al., 2012) but gives systematic overestimates of SFRs for optically-selected red galaxies such as those in the Virgo cluster known to have quenched SF (e.g. Hallenbeck et al., 2012), i.e., it is crucial to include the UV bands in the SED-fitting to infer the SF of the red population. As a result, we adopt the UV-optical color () rather than the optical-only () in the analysis of SF and gas properties below.

3. Global Properties of the ALFALFA Galaxy Population

To derive the global properties of the stellar components of the ALFALFA galaxies, we adopt the methodology of Salim et al. (2007). In particular, stellar masses and SFRs are derived from SED-fitting the seven GALEX/SDSS bands. Further details of the method and fitting quality as applied to the sample are found in Huang et al. (2012) which focuses on the lowest HI mass dwarf population. In addition, the Gaussian prior distribution of the effective optical depth in band, , is applied, with the mean predicted by Giovanelli et al. (1997) and a standard deviation of 0.55 dex. Such an improvement reduces the overestimate of internal extinction and SFR with decreasing stellar mass, as identified by Salim et al. (2007) (see §4.2.2 for more details), but still accounts for the effect of dust in disk systems. In this section, we discuss the results for the full -SDSS-GALEX overlap sample (9417 galaxies).

3.1. Gas and stars

Current understanding interprets the standard SDSS color magnitude diagram (CMD) in terms of an evolutionary scenario under which galaxies migrate from the blue cloud to the red sequence as they assemble their mass. This picture is further reinforced by the presence of the star-forming sequence in the SSFR vs. stellar mass diagram; more massive galaxies show lower SSFRs. Consistent with this picture, one would expect galaxies to grow increasingly gas poor and thus having lower HI fractions (defined throughout this work as ) as they assemble their mass. Therefore, blue galaxies with high gas fractions indicate disks Which are stable against collapse, making their SF much less efficient (West et al., 2009).

3.1.1 HI versus stellar mass

In the last decades, many studies have investigated how the HI content varies with stellar properties in galaxies, such as morphology, luminosity, size and SF activity (Gavazzi et al., 1996; Boselli et al., 2001; Kannappan, 2004; Disney et al., 2008; Garcia-Appadoo et al., 2009; West et al., 2009, 2010; Toribio et al., 2011). Despite the complex interplay of dynamics, SF, chemical enrichment and feedback etc., the stellar and HI components, as well as the dark matter halo, exhibit correlations with each other. However, many of these studies have relied on relatively small and/or inhomogeneous samples limited to the very nearby universe. Although the main scaling relations were known, constraints on the accuracy of these relationships, as well as the quantification of their scatter are still not well determined. Based on an H narrow-band imaging survey of 400 galaxies selected from ALFALFA, Gavazzi et al. (2012a, b) also investigate the relationships between HI and newly-formed stars, emphasizing the study of environment effects. Here we focus on the nature of the population detected by the ALFALFA survey.

Figure 2 illustrates the relationships of the HI mass and (the vertical axes) with the stellar mass and color (horizontal axes). The contours and points outline the distributions of the galaxies in the -SDSS-GALEX sample; the blue diamonds and solid lines trace the average values and in bins of , with a bin size of 0.5 dex in panels (a), (c) and (d). The number of galaxies in each stellar mass or () color bin is given at the bottom of panels (c, d). Typical error bars of individual galaxies are shown in the corners of panels (a) and (d). The Spearman’s rank correlation coefficients of the relation, , are shown in the upper right corner of all panels. Compared to similar studies that have previously probed the global scaling relations involving (e.g. Bothwell et al., 2009; Catinella et al., 2010), the sample offers a more complete statistical sampling of the full range of HI and stellar masses. As discussed in Haynes et al. (2011), ALFALFA’s combination of sensitivity, sky coverage and bandwidth yields a sample that probes a wide dynamical range in HI mass (7-11 dex with a mean of 9.56 dex), from the most massive giant spirals with to the lowest HI mass dwarfs with log . In fact, the stellar mass range that is probed is slightly wider: 6–11.5 dex, with a mean of 9.43 dex. As an HI-selected sample, -SDSS-GALEX demonstrates the ability to recover galaxies with small .

Figure 2(a) shows the distribution of with . The cyan dash-dotted line traces the linear fit to the GASS sample of high stellar mass galaxies (; Catinella et al., 2010):

Note that those authors chose to calculate rather than because the value is depressed by the contribution of gas-poor galaxies in their -selected sample; a similar effect results in their adoption of rather than . In contrast, an HI-selected sample such as ours does not sample the low HI fraction massive objects so that, as a function of , and adequately trace the main distribution. Moreover, as pointed out in Cortese et al. (2011), the distribution of is closer to log-normal than Gaussian, and thus they also prefer to .

We confirm the previous findings that increases with . However, the correlation does not appear to be a simple linear one, i.e. is smaller at the high mass end. The linear fit to the blue diamonds in Figure 2(a) is


This trend is consistent with the idea that once AGNs are turned on in massive galaxies, gas is lost due to AGN feedback. The fact that is lower in massive SF/AGN composites than in purely SF galaxies of the same mass may be the cause of a similar break in slope of the star-forming sequence (see §3.2, at a slightly higher transition mass, ). Furthermore, compared to the high stellar mass GASS galaxies, the ALFALFA population is overall more gas-rich for the same stellar mass (log ) and traces a steeper slope in the vs. scaling relation, i.e. there is a systematically larger discrepancy in the typical HI content of the ALFALFA and GASS populations in the largest bins. Besides the change in slope, there appears to be an increased scatter in the distribution below log , a regime only poorly sampled by other studies. In fact, Huang et al. (2012) point out that at the lowest HI masses, ALFALFA detects a population of dwarf galaxies with low for their ; some of these objects are dwarf ellipticals/spheroidals (dE/dSph) galaxies in the Virgo cluster and may have accreted their current gas supply only recently (Hallenbeck et al., 2012). The HI gas can be easily removed in low mass systems due to their shallow potential wells, so that the galaxy migrates onto the red sequence as its SF quenches.

Figure 2(c) shows how the HI fraction depends on . The cyan dash-dotted line again traces the GASS result for the high stellar masses (Catinella et al., 2010), while the green (upper), red (lower) and yellow (middle) dashed lines trace the separate samples of HI-normal galaxies, ones in Virgo and outside-Virgo respectively from Cortese et al. (2011) who looked for trends among galaxies in different environments. Again, the known trend that higher galaxies have lower is clearly evident, with a correlation coefficient . depends more strongly on than on () partly because the same measure of the enters also in the computation of . Compared to other findings, the ALFALFA population uniformly includes galaxies which are more gas rich for a given . Their extraordinarily high indicates little integrated past SF, while their blue colors may be attributed to a SFH that steadily rises to the present day or a truly young stellar component (Garcia-Appadoo et al., 2009).

Both the GASS and Cortese et al. (2011) samples include galaxies that have lower and lie below the ALFALFA HI detection threshold. For example, the Virgo cluster is well known to contain a significant population of HI deficient galaxies (Davies & Lewis, 1973; Giovanelli & Haynes, 1985; Solanes et al., 2002) whose HI line flux densities are too low for them to be detected by the short ALFALFA observations; their detections were made using longer duration, target Arecibo observations. The offset of the ALFALFA population from the other samples is therefore as expected. However, it is interesting to note that the scaling of with log derived here and by Cortese et al. (2011) for the HI-normal galaxies, while they do not coincide in amplitude, do show comparable slopes at intermediate masses, and perhaps the same is true for all samples at log . A “fast”, shallow survey like ALFALFA derives the same trend as one which relies largely on much deeper, pointed observations. The flattening off of at log is traced only by the ALFALFA dwarfs (Huang et al., 2012).

It is important to note that the nearby, low mass galaxies are the ones most susceptible to shredding by the SDSS pipeline so that, statistically, their stellar masses are more likely to be underestimated, resulting in an extreme tail of galaxies with unrealistically high . By exclusion of objects with suspect SDSS photometry as noted by Haynes et al. (2011), the most egregious cases have been excluded from this analysis. Similar problems with the use of the SDSS pipeline measurements have much less effect on the main distribution. At the same time, source confusion within the ALFA beam (FWHM ) is more likely among more distant systems so that the (and ) of some high sources may be overestimated. However, other than cases of major mergers, the highest galaxies are always significantly more massive than their small companions, so that the change in , if the contribution from companions is removed, would only be small. Overall, the trend of falling with increasing seen in the ALFALFA galaxies is well defined. For the ALFALFA population overall, the median . HI-selected galaxies are uniformly gas rich for their stellar mass following a scaling relation over the range of stellar mass .

In Figure 2(c), the number density of points drops sharply on the upper edge of the main distribution: there is a real cutoff in the galaxy population with even higher than ALFALFA detects. The increased dispersion in the contours on the lower edge of the distribution with substantial numbers of outliers with lower than the main population confirms that, because of its HI-selection, ALFALFA misses much of the gas-poor galaxy population. Longer integration times would obviously detect galaxies of lower and thus lower at constant . The GASS observing strategy (Catinella et al., 2010) is specifically designed to probe to constant by conducting significantly longer but targeted HI observations. The GASS program thus characterizes the overall population of galaxies selected by stellar mass at the high mass end. The ALFALFA survey, on the other hand, samples well the full dynamical range of the HI-rich (for their stellar mass) population

Figures 2(b, d) explore the variation of and with (). Definitions of diamonds and lines in panel (d) are the same as in panel (c). As noted in Figure 1, nearly all ALFALFA galaxies are blue, and the population is highly biased against the red sequence. While there is a wide spread in , there is little trend of with color (). In fact, there are 128 -SDSS-GALEX red galaxies () with , including the early type galaxies with quenched SF but unusually high HI masses (e.g. AGC 260442), the edge on galaxies with significant internal extinction (e.g. UGC 6312 has a dust lane evident in the SDSS image), and even the “red spirals” found in the Galaxy Zoo (Masters et al., 2010), e.g. UGC 9624 and UGC 9283. There are 116 red galaxies () with ; most are early type “dead” galaxies. Cortese et al. (2011) found that the blue cloud galaxies have the same regardless of environment, whereas for the red galaxies, Virgo members are significantly gas poorer than HI-normal systems (see dashed lines in Figures 2d). In particular, their fit for HI-normal galaxies (green) agrees well with the main trend for the galaxies.

In contrast, is a strong function of color among the ALFALFA population ( in panel d), at least among the blue cloud galaxies, i.e. the bluer galaxies tend to have higher HI fractions. However, this trend gradually flattens for the very red galaxies (), i.e. the very red galaxies among the ALFALFA population have higher than would be predicted by extrapolation of the trend traced by the blue galaxies. Compared to the vs. () trends derived by Catinella et al. (2010) or Cortese et al. (2011), traced by the dash-dotted and dashed curves respectively in panel (d), the offset of blue diamonds on the blue side is small, but the deviation becomes systematically larger in the redder bins. Such a change in behavior can be partly explained by the fact that ALFALFA detects only a very small subset of these red galaxies. The presence of HI in this small population of otherwise “red and dead” galaxies is most easily explained if their HI gas has been acquired only recently, as has been invoked previously to explain the HI in ellipticals (e.g., Wardle & Knapp, 1986; Morganti et al., 2006), and the annular HI distributions seen in many S0s (e.g., van Driel et al., 1988; Donovan et al., 2009). Deep HI synthesis imaging of the SAURON and ATLAS samples of early-type galaxies shows that HI is commonly detected in galaxies which do not reside in cluster cores (e.g., Oosterloo et al., 2010; Serra et al., 2012). A significant fraction of non-cluster early-types contain some cool HI gas, with the large spread in HI content likely due to differences in their accretion histories.

3.1.2 Predictors of HI gas fraction

The tight correlation between and () can be used as a predictor of given measures of color, i.e., the ‘photometric gas fraction’ technique (Kannappan, 2004). Furthermore, a ‘fundamental plane’ of has been identified by the GASS survey (Catinella et al., 2010), where the stellar mass surface density is defined as and is the radius containing 50% of the Petrosian flux in the -band. Their best fit ‘plane’ is

and the scatter of such a predictor is reduced relative to the correlation with the additional parameter . Because colors essentially trace the SSFRs (see also §3.2), similar predictors are calibrated by Zhang et al. (2009) for an optically-selected sample as:

It should be noted that no correction for internal extinction is applied in those analyses, although it is well known that the inner disks of spirals are optically thick (e.g., Giovanelli et al., 1995). We discuss the need for an internal extinction correction below in §4.2.2. The predicted by these formulae are plotted on the horizontal axes in Figures 3(a-c), respectively. Compared to the ALFALFA measurements of the (vertical axes), they all predict systematically smaller . This reaffirms that the HI-selected sample is biased towards the gas rich population. The deviation from the one-to-one dashed line increases with in the case of the GASS calibration (Figure 3a). The Zhang et al. (2009) estimators (Figure 3b and c) systematically underpredict of the -GALEX-SDSS galaxies by 0.3 dex.

Exactly which scaling relation to use to predict the properties of a population depends of course on what the scientific objective is. For example, the scaling relations for an optically-selected sample may be valid for a stellar mass selected population. However, the relations derived for ALFALFA give better predictions for the HI detection rate for future SKA surveys which will likewise be HI-selected. Previous simulations of SKA detection rate are mostly based on the HIPASS results locally (e.g., Abdalla & Rawlings, 2005; Obreschkow et al., 2009). But HIPASS suffered from limitations in its volume sensitivity, and in fact, ALFALFA detects more HI sources at the high end (Martin et al., 2010). Based on the -GALEX-SDSS galaxies, linear regression gives:


Note that for comparison with other authors, the colors used here are corrected for Galactic extinction but not for internal extinction. In Figures 3(d-f), the ALFALFA measures are plotted against the values predicted by equations (2)-(4), with the correlation coefficients 0.88, 0.87 and 0.87 respectively. The systematic offset is removed according to our best fit and the correlations are as tight as the Catinella et al. (2010) ( 0.88) and the two different Zhang et al. (2009) ( 0.87 and 0.86) results. Among the three planes, the correlation has the least scatter and it is also tighter than the correlation ().

Note that the fundamental plane found here is noticeably different from the GASS relationship (Catinella et al., 2010). The main trend in Figure 3(d) reveals a break in slope at , whereas the GASS relation is confined to only below this critical . Although the GASS sample is complete in the massive domain, it does not probe the lower stellar mass, gas rich systems. Blindly applying the fundamental plane defined by the massive gas-poor galaxies through extrapolation into the gas-rich regime results in serious underprediction of . Because of the change in slope, the deviation from (Catinella et al., 2010) is systematically larger in the high galaxies.

Because the HI population is so overwhelmingly dominated by blue cloud dwellers and since HI is presumably a constituent of a galaxy’s disk, not its bulge or halo, it seems appropriate to explore scaling relations which are tied more heavily to the galaxy’s disk. Hence, we define a disk stellar mass surface density , where is the radius containing 90% of the Petrosian flux in the -band. Compared to , is based on the -band flux with higher S/N and less bulge contribution. In addition, adopting colors corrected for internal extinction (see §4.2.2), we derive improved predictors as follows:


The values given by equation (5)-(7) are plotted on the horizontal axes in Figures 3(g-i). They show less scatter from the one-to-one dashed line with better 0.90. We suggest that scaling laws which incorporate properties which reflect the disk nature of the HI distribution, and specifically the above relations, provide the most appropriate approach to predicting the characteristics of HI-selected populations.

3.1.3 Assessing the molecular gas H contribution

ALFALFA is an extragalactic HI line survey and, as such, probes only the neutral ISM. Yet, the process of SF in most galaxies is more directly coupled to the molecular gas, and the question of which gas component – HI, H or total gas – correlates best with SF is still debated. To account for the full gas content, we thus need to assess the expected contribution of molecular gas to the total gas mass in the ALFALFA population galaxies.

An outgrowth of the GASS survey of high stellar mass galaxies, COLD GASS is a legacy survey which has measured the CO(1-0) line of 350 randomly selected GASS sample galaxies (0.025 0.05) with the IRAM 30m telescope. COLD GASS has uncovered the existence of sharp thresholds in galaxy structural parameters such as , concentration index and () color, above which the detection rate of the CO line drops suddenly. These thresholds correspond approximately to the transition between the blue cloud and red sequence (Saintonge et al., 2011b). Even though Catinella et al. (2010) found some red sequence galaxies with a surprisingly large HI component, none of the 68 galaxies in the first installment of COLD GASS with are securely detected in CO. At the same time, only 1.4% of the -GALEX-SDSS galaxies have , so that the HI-selected galaxies should have a high detection rate in CO.

Under the assumption that molecular gas forms out of lower density clouds of atomic gas, one might naively expect a tight correlation between and . However, within the subsample of galaxies detected both in HI and CO by COLD GASS, the fraction varies greatly, from 0.037 up to 4.09; the two quantities are only weakly correlated (Saintonge et al., 2011a). The relative proportions of molecular and dense atomic gas in giant molecular clouds depend on the cloud column density and metallicity (Krumholz et al., 2008), and the clouds could even be primarily atomic if the metallicity is sufficiently low (Ostriker et al., 2010).

Of all the parameters that Saintonge et al. (2011b) investigated, the mean molecular gas fraction () among the COLD GASS galaxies correlates most strongly with their () color, with

although it is weaker than the correlation, probably because H resides in the inner region where extinction is higher, whereas HI dominates in the outer disks (Saintonge et al., 2011a). At the same time, they find that is only a weak decreasing function of . As a result, although ALFALFA probes a lower stellar mass range than COLD GASS does, the correlation above can still be roughly applied to the -GALEX-SDSS galaxies. Specifically, since the -GALEX-SDSS galaxies have a mean () of 2.24, the results of COLD GASS predict a mean of 0.082 for the HI-selected population, higher than the 0.066 of the COLD GASS detections.

We note that although is only a weak decreasing function of , clearly decreases with increasing , i.e., the fraction appears to decline in less massive galaxies (see also Blanton & Moustakas, 2009). For luminous galaxies, a substantial fraction of the gas is sometimes in molecular form, but the detection of CO in low mass galaxies has been shown to be very difficult (e.g., Leroy et al., 2009). Therefore, we conclude that for the ALFALFA population and thus ignore its contribution to the total gas fraction, focusing instead on the well-determined atomic gas fraction .

3.2. Star formation properties

In addition to the stellar mass, SED-fitting also yields an estimate of the current SFR averaged over the last 100 Myr. Salim et al. (2005) have shown the importance of including the GALEX UV bands, especially the FUV, to reduce the uncertainties in SFRs derived from SED-fitting. In addition to the SFR itself, several other quantities of physical interest also become available. For example, the SSFR, defined as , compares the current SFR with that in the past (as measured by ), and thus is well correlated with the birthrate-, or parameter, defined as . Both the SSFR and the parameter describe the SFH. At the same time, normalization of the SFR by instead of yields the star formation efficiency (SFE), defined as . The SFE compares the current SFR with its potential in the future, the latter regulated by , the available fuel. The reciprocal of the SFE is the Roberts time, (Roberts, 1963; Sandage, 1986), the timescale for depletion of the HI gas reservoir, assuming a constant SFR at the current level.

Figure 4 shows a montage illustrating how the SF related properties, , , (y axes) vary with , and the () color (x axes). As before, contours and points trace the -SDSS-GALEX population. Spearman’s rank correlation coefficients are shown in the lower left corners of all panels. Typical error bars of individual galaxy estimates are plotted in the lower right corners of panels (a, e, i). In the bottom row, tracing the SFE, the cyan dashed line shows the average value obtained by Schiminovich et al. (2010) for the high stellar mass GASS sample, while the green dash-dotted line marks the value corresponding to the Hubble timescale.

3.2.1 The SFR and SSFR in HI-selected Galaxies

Among the ALFALFA population and in agreement with previous studies, e.g. Salim et al. (2007), SFRs generally increase but SSFRs decrease with increasing stellar mass (Figure 4a, d). Similar trends are also evident with (Figure 4b, e), albeit with larger scatter, especially in the vs. distribution (). The trend of decreasing SSFR with increasing stellar mass suggests the “downsizing” scenario of structure formation (Cowie et al., 1996), such that the high galaxies form most of their stars in the first  Gyr after their formation (Bell et al., 2003) and today exhibit relatively suppressed SF. In contrast, the low mass systems in such a picture remain active in SF throughout their histories. Under a hierarchical dark matter halo assembly scenario in which the low mass structures form first and then merge to form massive galaxies, the “downsizing” concept suggests a late epoch of gas replenishment and regrowth in low mass systems.

Although an HI-selected sample like ALFALFA is biased against massive galaxies with low SFRs and low SSFRs (see also §4.2.4), there is a hint in Figures 4(a, d) that the number density of such galaxies increases in the regime in comparison to the intermediate mass range (). The presence of some points in the lower right corner of the vs. plot suggests that at least some objects with large stellar masses and detectable HI but very low SFRs are included in the ALFALFA population. More importantly however, there is not a comparably rich population of massive HI disks with low SFRs, i.e., the number density of galaxies in the lower right corner of Figure 4b is lower than that in the lower right corner of 4a. Where there is a lot of HI, there is always some SF.

As evident in Figure 4(c), the expected correlation between and (), that galaxies bluewards of have higher SFRs than ones redwards of that value (e.g. Salim et al., 2005), is not so well defined by the ALFALFA population (), mainly because ALFALFA detects only a few very red galaxies. In particular, we lack sufficient dynamic range in () to probe the trend along the red sequence seen in optically-selected samples that galaxies bluer in () have higher SFRs, especially if colors after extinction correction are plotted.

On the other hand, the is a strong function of the () color (Figure 4f), with the Spearman’s rank correlation coefficient . This is also the tightest among all the correlations shown in Figure 4. It is natural to expect that () is closely tied to the . Since the luminosity largely reflects the SF and the -band luminosity the stellar mass, the () color, as the ratio of the two, serves as a proxy for the . Given the fact that better characterizes the SFR than the -band, one may also expect the to correlate better with () color than with (). However, because suffers more from internal extinction and the associated corrections can be highly uncertain, extra scatter is introduced when the is used with accounting for the impact of extinction. In fact, as demonstrated in (§4.2.2) and Figure 8(b), a shift towards blue colors and an even tighter correlation between and () become apparent when extinction-corrected colors are used.

3.2.2 The star formation law in HI-selected galaxies

The underlying question linking gas to stars in galaxies, the “star formation law” (SFL), is what limits SF: the formation of molecular gas out of HI or the efficiency at which the available molecular gas is converted into stars (Schruba et al., 2011). Various forms of the SFL are studied, perhaps most common among them the empirical law describing how the SF surface density () is regulated by the gaseous surface density (e.g., in Kennicutt, 1998).

It should be noted that since most galaxies are unresolved by the ALFA 3.5′ beam, ALFALFA measures only the global HI content. Our estimate of the SFL will thus be globally averaged. Numerous recent studies focusing on more detailed observations of smaller yet representative samples have demonstrated the regulation of SF by molecular gas. For example, the HI Nearby Galaxy Survey (THINGS; Walter et al., 2008) and the HERA CO Line Extragalactic Survey (HERACLES; Leroy et al., 2009) provide measurements of the surface densities of total gas, atomic and molecular gas, and SFR in kpc-sized regions within a number of nearby galaxies. Measurements of the azimuthally averaged gas and SFR profiles show that the SFR correlates better with the molecular hydrogen component than with the total gas density within the optical disk (e.g. Bigiel et al., 2008), suggesting that the SFR is controlled by the amount of gas in gravitationally bound clouds and that H is directly important for cooling. Krumholz et al. (2011a) collated observations of the relationship between gas and SFR from resolved observations of Milky Way molecular clouds, from kpc-scale observations of Local Group galaxies, and from unresolved observations of both disk and starburst galaxies in the local universe and at high redshift. Those authors showed that the data are consistent with a simple, local, volumetric SFL and that the SFR is simply 1% of the molecular gas mass per local free-fall time. Furthermore, Schruba et al. (2011) found a tight and roughly linear relationship between IR (inferring ) and CO (inferred ) intensity, with . This relation does not show any notable break between regions that are dominated by molecular gas and those dominated by atomic gas, although there are galaxy-to-galaxy variations in the sense that less massive galaxies exhibit larger ratios of SFR-to-CO, an effect which may due to depressed CO relative to H in low metallicity galaxies. Similarly, Bigiel et al. (2011) demonstrated a roughly constant H consumption time ().

However, other works show that the relationship between SF and gas varies systematically depending on the local environment. Bigiel et al. (2010a, b), found an evident correlation between SF and HI in the outer disks of spirals and in dwarf galaxies where HI is likely to dominate the ISM. Given the poor correlation between HI and SFR found inside star-forming disks, this finding strongly hints that different physics governs the formation of star-forming clouds, and that the HI column is perhaps the key environmental factor in setting the SFR (Bigiel et al., 2010a). Furthermore, the SFL is likely to have a distinct form in the atomic-gas-dominated regime (e.g. , theoretically by Ostriker et al., 2010, where is the midplane density of stars plus dark matter). Therefore, we may expect a steeper dependence of on if there is a dropoff in the stellar and dark matter density with radius. There is no single universal slope predicted for the SFL in the diffuse-gas-dominated regime. In low gas surface density or low metallicity regions where gas is significantly atomic, thermal and chemical processes become dominant in determining where stars can form, and the gravitational potential of the stars and dark matter may have a significant effect. Similarly, the model developed by Krumholz et al. (2009b) suggests becomes a steep function of when complexes of gas become primarily atomic, for low ISM surface density. Observations also confirm steeper slopes for the low density outer HI-dominated regions of spiral galaxies, as well as dwarf galaxies, compared to the inner molecular-dominated regions of spirals (Bigiel et al., 2010a).

The increasing SFR with HI mass evident in Figure 4(b) suggests the regulation of SF by the HI gas, with a correlation coefficient of . The red dash-dotted line in Figure 4(b) shows the linear fit to the -SDSS-GALEX galaxies, with a slope of 1.19, suggesting a global, atomic, volumetric SFL. The close to unit slope indicates a SFE close to constant as a function of . The correlation between SFR and appears to be in conflict with the earlier finding that most galaxies show little or no correlation between and (Bigiel et al., 2008). The high galaxies represented by the ALFALFA population appear to obey an unusual SFL which may not only depend on the H, but also on the HI, stellar and dark matter properties. Additional observational and theoretical work is needed to evaluate how the SF efficiency of bound clouds depends on the relative amounts of cold HI versus molecular gas.

3.2.3 The SFE in HI-selected galaxies

Figures 4(g-i) illustrate the distribution of the with , and the () color. The timescale for atomic gas depletion for the majority of the ALFALFA galaxies is shorter than the Hubble time , and comparable to it for many of those with low stellar masses, .

For the high stellar mass GASS population, Schiminovich et al. (2010) found that, unlike the SSFR which decreases with increasing stellar mass, the SFE remains relatively constant with a value close to  yr , or equivalently  Gyr. This value is longer than the molecular gas depletion timescale (see §3.2.2). Furthermore, those authors also found little variation in the SFE with stellar mass surface density , the () color or the concentration index, a result which they interpreted as an indication that external processes or feedback mechanisms which control the gas supply are important for regulating SF in massive galaxies. Considering that , an interesting implication of the weak correlation between the SFE and the stellar mass is that the fit to the versus distribution would have a similar slope to that of the vs. , specifically for and for (see equations 1 in §3.1). However, the red dash-dotted line in Figure 4(d) shows the linear fit to the ‘star-forming sequence’ defined by the -SDSS-GALEX galaxies:


The differences in the slopes suggest that is a weak increasing function of in the low range but remains relatively constant above ; this trend is also evident in the bottom row of panels(). The mild trend of increasing SFE with stellar mass seen in Figure 4(g) was not evident in the GASS study (Schiminovich et al., 2010) because the GASS sample includes only galaxies with .

Rather than a simple continuous scaling relation, the change of slope given in equation (8) and evident in Figure 4(d), suggests that a transition mass exists at in the way in which star formation scales with total . A similar transition mass at in SSFR is adopted by Salim et al. (2007) for their blue galaxies with . Those authors suggested that the lower SSFR is a consequence, at the high end, of a population of systems which are both star-forming and have AGN, thereby yielding lower SSFRs than pure SF galaxies of the same mass. Similarly, Kannappan et al. (2009) identified a “threshold” stellar mass of several times , below which the number of blue sequence E/S0 galaxies sharply rises. Those authors matched the threshold to the mass scale below which the mean HI content of low- galaxies increases substantially both on the red sequence and within the blue cloud. Abrupt shifts in the SFE and gas richness near the “threshold mass” have been linked to the interplay of gas infall, supernova-driven winds, and changes in mass surface density. However, it is important to note that such a threshold falls below the “transition” mass characteristic of the ”green valley”, identified in the, e.g., versus and relations, at a stellar mass proposed in many other works (e.g. Kauffmann et al., 2003; Baldry et al., 2004; Bothwell et al., 2009; Catinella et al., 2010) and suggested to be indicative of the SF quenching in massive galaxies as they migrate from the blue cloud to the red sequence.

Perhaps surprisingly, the ALFALFA galaxies have on average lower SFE, or equivalently, longer , compared to the optically-selected population, with a mean of  yr , or equivalently  Gyr, compared to the  Gyr derived for the GASS galaxies. We note that the average value was volume corrected in Schiminovich et al. (2010), but not in Figure 4(g-i). However, we confirm that the volume correction (see §4.1) results in only subtle changes in the mean as a function of for the -SDSS-GALEX galaxies, and it is still longer than  Gyr. As we demonstrate in §4.2.4, the HI-selected galaxies have, on average, higher SFRs at a fixed stellar mass, so that the lower SFEs must result from their higher HI masses rather than from less active states of SF. This result reaffirms the general conclusion that HI-selected samples are strongly biased towards the most gas-rich galaxies. In agreement with the low SFEs characteristic of the ALFALFA population, Bigiel et al. (2008) have seen a decrease in SFE in the HI-dominated THINGS galaxies. Furthermore, Bigiel et al. (2010a) found that the SFE decreases with galactocentric radius among the THINGS sample across the outer disks beyond the optical radius, where HI dominates the ISM, with well above Hubble time. In the THINGS dwarf galaxies, the contribution of H to the total gas budget is generally small even in the inner disks, also corresponding to a low SFE (Bigiel et al., 2010a). All these results are consistent with the conclusion that SFEs are low, on average, in HI-rich systems.

However, we note that the low HI SFE may not be in conflict with the usual H SFL. The HI-selected high galaxies may still follow the normal behavior of how stars form from H, but rather that a bottleneck exists in the process by which star-forming molecular clouds assemble. The conversion of HI to H depends on environment inside a galaxy and the relative abundance of HI and H is key to setting the SFR (Bigiel et al., 2010b). Although the low HI SFE suggests the inefficiency of HI-to-H conversion, the HI-to-H ratio cannot be arbitrarily high. Ostriker et al. (2010) assumed an equilibrium state, in which cooling balances heating and pressure balances gravity. This balance can be obtained by a suitable division of the gas mass into star-forming (gravitational bound) and diffuse components such that their ratio is proportional to the vertical gravitational field. If too large a fraction of the total surface density is in diffuse gas, the pressure will be too high while the SFR will be too low. In this situation, the cooling would exceed heating, and mass would drop out of the diffuse gas component to produce additional star-forming gas.

Close examination of the vs. diagram in Figure 4(g) also reveals a considerable number of outliers with relatively high SFE at the high end, falling well above the main distribution. In general, high SFEs have been measured in starburst galaxies and interacting systems which are consuming their gas reservoirs on very short timescales. However, a close inspection of 13 -SDSS-GALEX galaxies with shows that 9 of them are members of the Virgo Cluster. Ram pressure stripping results in strong HI deficiency and very short in these extreme outliers. In contrast, the outliers below the main distribution can either be red, massive, low SSFR galaxies against which ALFALFA is strongly biased, or abnormally gas rich (for their stellar mass) but quiescent ones. The latter include candidates of recent re-accretion or systems in which the HI gas is somehow inhibited from forming stars. We return to this point in §5.

Figures 4(h, i) illustrate that the barely changes with either or color ( and respectively) and the scatter in both correlations is large.

3.2.4 Linking the gas fraction to SF

As first discussed by Roberts (1963), it is not surprising that SF appears to be regulated by gas content. We have already argued that the vs. diagram (Figure 4d) is similar to the vs. one (Figure 2c), both showing similar slopes along the main trend; the distributions of and in given stellar mass bins also become broader at both the high- and low- mass ends. Hence, the star-forming sequence in the former diagram can also be understood as a sequence of gas-depletion in the latter one.

Previously, Kannappan (2004) also linked the to bimodalities in galaxy properties. She suggested that the bimodality in SFHs may be intimately related to changes in , and the transition in SF modes at , found by those authors, is not a cause but an effect of changing , as predicted in cold-mode accretion scenarios. Figure 5 illustrates these relationships by showing the averaged of galaxies which lie in different loci in the CMD (left panel) and the vs. diagram (right panel). Contours indicate the number density within the -SDSS-GALEX sample in each grid point in the map, while the shade scale traces the mean HI fraction, . As mentioned in §2.2.3, 96% of ALFALFA galaxies lie on the blue side of the optical-NUV CMD, whereas a smaller fraction (84%) lie on the blue side of an optical-only CMD (see §4.2.3 below). Some of this difference can be attributed to the greater impact of shredding on the SDSS pipeline magnitudes relative to that of the GALEX photometry. Because of the color gradient of galaxies (outer disks are bluer), the shredded central redder object is identified as the OC. As a result, the adopted photometric object may be redder in () than the galaxy as a whole actually is. Moreover, the -band is not as sensitive and thus yields photometry with large uncertainties for some of the galaxies. Additionally, the () color is a stronger diagnostic of the SFH. For similar reasons, the of grid points in regions of low number density should be interpreted with caution. However the general trends (1) that the red-sequence is associated with low and (2) that blue cloud galaxies are gas rich are clearly evident. At a given , redder () colors, on average, indicate lower . Furthermore, such a variation of along the () axis is more evident in the fainter range: at , whereas at . Therefore, the correlation of () and at a given is hard to see in a sample with only massive galaxies, e.g. GASS (Wang et al., 2011).

Similarly, the right panel of Figure 5 illustrates how the HI fraction varies in the -SSFR plane. As galaxies assemble their stellar mass and evolve along the star forming sequence, represented by the contours of high number density, their HI fractions decrease. In addition, for fixed , galaxies with lower SSFRs have, on average, lower . Again this is more clearly evident at the low stellar mass end, and is consistent with the broadening in both the and distributions at low (Huang et al., 2012). In contrast, the variation of along the axis at a given is less evident for galaxies with . These two trends suggest that, for low systems, high galaxies are more likely to be starburst galaxies (defined as high SSFR galaxies), whereas galaxies in the high regime selected by high are less likely to be starbursts. In summary, Figure 5 clearly demonstrates that the color, SF and gas evolution of galaxies are closely related to one another, as expected. Moreover, the regulation of SF by is stronger in the less massive galaxies.

4. The Impact of Optical Versus HI-selection

Future surveys of HI in galaxies at intermediate to high redshifts that will be enabled by the next generation of centimeter-wavelength radio telescopes (e.g. the SKA) will aim to infer the gas evolution from high redshift populations to the local well-studied ones. It is important therefore to understand the fundamental properties of local HI-selected galaxies, as represented by the ALFALFA catalog, and their biases relative to the overall galaxy population. In §3, we examined the global properties of gas, stars and SF within the ALFALFA galaxies themselves. They form an HI-rich, blue and less evolved population with low SFE; these characteristics are more pronounced in lower mass systems. and are linked to the SF related quantities, demonstrating the role that HI plays in the regulation of galaxy evolution along the star forming sequence. To understand how the HI-selected population is biased relative to ones selected by stellar mass or optical flux, in this section we construct samples from both the and SDSS catalogues and then compare their similarities and differences.

4.1. Construction of control samples

In order to ensure the galaxies contained in each of the optically- and HI-selected samples are both representative of their respective population and fair enough to permit comparison with the other, we construct subsamples of both and the SDSS in the same sky volume within their common footprint. The volume-limits imposed are similar to those discussed by Martin et al. (2010). Comparable selection criteria are applied with a further requirement that acceptable GALEX pipeline photometry must also be available, so that stellar masses and star formation properties can be derived robustly via SED-fitting.

4.1.1 ALFALFA selected sample,

As discussed by Martin et al. (2010), radio frequency interference from the San Juan airport FAA radar transmitter at 1350 MHz makes ALFALFA blind to HI signals in a spherical shell Mpc wide centered at a distance of Mpc. Therefore, as did those authors, we exclude 568 galaxies of the sample presented in §3 which lie beyond 15000 km s ( hereafter). To maximize the overlap of contiguous sky coverage between the current ALFALFA and SDSS DR7, we consider only the two regions in the northern Galactic hemisphere (, and , , see Figure 6c). Applying these restrictions yields a sample within a sky volume of , a sky area of 1989 deg and including 7638 -SDSS-GALEX galaxies.

Next, a weight, , is assigned to each galaxy, where is given by the maximum distance, , at which an HI source can be detected by ALFALFA, if , with for the galaxies which can be detected all the way outwards to the . Because the ALFALFA sensitivity depends not only on the integrated HI line flux density,  [Jy km s], but also on the HI line profile width,  [km s], specifically, the fit to , the limiting integrated HI line flux density that can be detected at S/N above 4.5 (code 1 and 2, 25% complete), as given in Haynes et al. (2011), is:

Then, can be calculated given and , based on the standard equation . In order to characterize the stellar component of the galaxies, we also perform a cross-match to the SDSS and GALEX databases. The application of such a weight scheme, or volume correction, is equivalent to resampling the galaxies by their HI properties ( and ) alone, thereby reemphasizing the impact of HI-selection.

To further trim the sample, we drop galaxies whose weight , i.e., we consider only galaxies that could be detected in more than 1.67% of the survey volume. This cutoff corresponds approximately to a lower limit of (see Figure 6). There is not a hard cutoff because also plays a role. The galaxies with are all relatively nearby (, or assuming Hubble flow, , ), and are low HI mass galaxies less representative of the survey overall. Further motivations for applying such a weight cutoff include: (a) for these very local sources, distance dependent quantities, e.g. , have large uncertainties due to their peculiar velocities; (b) such galaxies are also underrepresented in the SDSS redshift sample (see below); (c) for resolved, patchy dwarf systems especially, the SDSS pipeline magnitudes can suffer from shredding. The lowest HI mass systems have been considered separately in Huang et al. (2012).

The final HI-selected sample referred to as includes 7157 galaxies.

4.1.2 SDSS selected sample,

To construct an optically-selected control sample out of the same sky volume, , we queried the SDSS DR7 in the same RA and Dec ranges for photometric objects which have valid model magnitudes and were also spectroscopic targets. We also require them to (a) have a spectral classification of “galaxy”; (b) have an SDSS redshift, , determined with high confidence; (c) lie within the same redshift range as , ; (d) have Galactic extinction-corrected -band model magnitudes brighter than 17.77. 24379 galaxies meet these criteria. Note the redshifts adopted for this sample use the SDSS measurement, whereas that for the comes from the HI line measures. Given the and coordinates, distances are estimated in the same manner as for the sample using a local flow model for  km s, and Hubble distance otherwise (Haynes et al., 2011). Following the same procedure as for , we searched for GALEX cross-matches, and applied similar SED-fitting to the UV/optical bands.

To match the weight cutoff of the HI-selected sample, we also calculate weights for the SDSS-selected sample but here according to their optical fluxes. In this case, is the maximum distance at which the object, given its -band flux, could be included in the SDSS main galaxy redshift sample. As for the HI-selected sample, we drop galaxies with weights greater than 60. Given the magnitude limit of the SDSS redshift survey ( 17.77 mag), such a weight cut directly corresponds to an -band absolute magnitude limit of mag. Furthermore, since the mass-to-light ratio varies only mildly with color, the luminosity cut approximately translates to a stellar mass lower limit of . Finally, a small number of galaxies are removed because they are included in the catalog but have been previously noted by individual inspection to have suspect photometry (Haynes et al., 2011). The final optically-selected sample referred to as includes 16817 galaxies, of which 34% are cross-matched to the catalog (see §2.2). The remainder are missed by ALFALFA either because they are (1) gas poor, (2) lie at a sufficient distance that their HI line flux densities falls below the HI sensitivity limit, or (3) for some other reason, e.g. their HI spectrum is contaminated by RFI or was not sampled at all (small gaps in ALFALFA coverage), or they correspond to one “child” of a shredded photometric parent object, but another photometric child is favored as the best match to the ALFALFA detection.

We note that the distributions of weight, , for both the samples highly peak at 1, and that the weight cut of 60 applied to each dataset is confirmed to be high enough to retain the main populations. Especially for the , 69% of the galaxies have a unit weight, i.e. can be detected outwards to the edge of as we defined here. The number of galaxies in bins associated with a weight above 1 drops more rapidly among the sample, confirming that the SDSS is deeper than ALFALFA.

4.2. Comparison of control samples

4.2.1 Basic properties

Figure 6 illustrates the comparison of quantities relevant to sample selection between the and the populations. In panels (a-c), red points denote galaxies in , whereas blue points denote galaxies in . In the histograms, red lines illustrate the distribution of and blue lines trace ; above each histogram, separate panels show the fraction of galaxies that are cross-matched to in each bin. The numbers in each subset are indicated in panels (a) and (b).

The top row contains two Spaenhauer diagrams showing, respectively, the -band absolute magnitude (panel a) and HI mass (panel b) versus distance. The solid vertical line represents the cutoff, 15000 km s. We use the SDSS redshifts to derive distances for the and ALFALFA HI velocity for the . As discussed also by Martin et al. (2010), a survey must sample sufficient volume to detect very massive galaxies in either stellar (panel a) or HI (panel b) mass. ALFALFA for the first time provides a full census of HI-bearing objects over a cosmologically significant volume of the local universe.

As evident in Figure 6(a), SDSS is volume limited to mag. The sharp lower edge of the distribution above Mpc results from the magnitude limit of the SDSS main galaxy redshift sample; as noted before, the adopted weight cutoff corresponds to mag (horizontal dashed line). Since no limit on any optical quantity is applied to the subset, many blue points from show up faintwards of the lower edge of , as faint as . We note that the blue points lying faintwards of the lower edge of and above  Mpc are still detected by the SDSS, but most often only as photometric objects; hence their optical redshifts are generally unknown. To enable SED-fitting however, all the galaxies are required to be detected in the SDSS; the very rare “dark” HI clouds without identified OCs included in are outside the scope of this work and are not included in this discussion.

Figure 6(b) shows how increases with distance. The HI measures of all come from the catalog (5653 out of 16817 galaxies, i.e., a cross-match rate of 34%). The weight cutoff applied to the sample results in an approximate limit of (horizontal dashed line). The red points below are still detected by , but are excluded from the simply because of their high weights. Because of the way distances are derived (Haynes et al., 2011) from the observed redshifts, an insignificant difference (0.1 Mpc) of the median distance arises for the same galaxies in the overlap sample. This difference is mainly due to the fact that the galaxies may be assigned membership in group whereas such information has not been applied to the sample. A few red outliers below the main distribution indicate objects without robust SDSS redshifts.

Panel (c) shows the sky distribution of the two samples. Besides the large scale structure, the required availability of GALEX photometry also contributes to the pattern. For example, the Virgo region is densely covered by at least MIS level visits, whereas the patches of sky blank in either sample and with regular edges arise from the lack of GALEX coverage in FUV and/or NUV. The distribution of distance is shown in panel (d). The two samples roughly coincide within 100 Mpc. Above the histogram, the fraction of the galaxies that are cross-matched to is shown. The first peak in number density coincides with the Virgo cluster (16.5 Mpc), where clearly out numbers . Since the two distributions agree with each other again at larger distances 50 Mpc, the disagreement at the Virgo distance indicates a real underdensity of gas-rich detections in , reflecting the well-known HI deficiency (Davies & Lewis, 1973; Giovanelli & Haynes, 1985; Solanes et al., 2002). Beyond 100 Mpc, significantly overtakes , though the shapes of peaks or gaps still agree. This suggests that ALFALFA is capable of detecting HI massive objects at large distances, although the survey is not as deep as SDSS. Although in a given distance bin, the least massive objects contained in are even fainter than those in (i.e., the blue points below the lower edge of red distribution in panel a), ALFALFA is not as complete as SDSS at large distances.

The distributions of for both samples are shown in panel (e). The vertical solid line denotes the equivalent weight cut applied to . While peaks at a slightly fainter than , the two samples probe a similar range so that their comparison is valid.

The distributions of axial ratio, given by the SDSS pipeline measures of the exponential fit in -band, are shown in panel (f). Because the ALFALFA sensitivity depends on the HI line profile width (see §4.1), might be expected to be biased against edge-on galaxies with high values. For example, West et al. (2010) demonstrated that their Parkes Equatorial Survey (ES, a search through HIPASS cubes; Garcia-Appadoo et al., 2009) – SDSS common sample is slightly biased towards face-on galaxies, relative to an SDSS DR4 sample, with the mean equal to 0.17 and 0.21 for their ES–SDSS and DR4 samples respectively. However, panel (f) shows no such obvious bias. Both and have the same . Furthermore, the cross-match rate even slightly rises for high galaxies, with only a mild drop in the very last bin. Visual inspection shows that shredding can cause large errors in the measures by the SDSS pipeline. The sample contains more galaxies with bulges making their values appear to be smaller; in contrast, is biased against such galaxies.

4.2.2 Internal extinction in HI-selected galaxies

Previously, and in many analyses of SDSS derived samples, internal extinction is ignored. However, while the outer parts of galaxy disks are transparent, it is well established that the inner regions are optically thick at short wavelengths. Therefore, the neglect of internal extinction in disk-dominated galaxies is likely to introduce systematic inclination-dependent effects. In this section, we discuss (a) how internal extinction varies with stellar mass, (b) how internal extinction may introduce scatter into relationships involving colors and (c) how the extinction characteristics of the HI-selected galaxies compare to those derived from an optically selected sample . In the three figures associated with this section, Figure 7 - 9, typical error bars on individual points are plotted in selected panels in as well as the Spearman’s rank correlation coefficients.

Estimates of internal extinction are derived from UV/optical SED-fitting as before. The two-component dust model (Charlot & Fall, 2000) is incorporated into the construction of the library of model SEDs (Gallazzi et al., 2005); the process accounts for both the diffuse interstellar medium (ISM) and short-lived (10 Myr) giant molecular clouds. Such estimates have overall larger uncertainties among the red-sequence galaxies relative to the blue cloud ones (e.g. Saintonge et al., 2011b), and contribute to the SFR uncertainties. Furthermore, Salim et al. (2007) identified differences between the effective optical depth in band, , derived from emission-line fitting and that derived from SED-fitting, as a function of stellar mass. Specifically, at lower masses, the SED-fitting-derived value is systematically higher than the line-fitting-derived one, but the situation is reversed at the high mass end. Therefore, we applied a Gaussian prior distribution of for each model, given the absolute magnitude and axial ratio of the individual galaxies (see §3). The mean of the prior distribution is given by equation (12) in Giovanelli et al. (1997), which depends on the axial ratio and absolute magnitude, i.e. more luminous edge-on galaxies have larger extinctions.

Figures 7 (a-c) show plots of -band internal extinction versus stellar mass for the galaxies. Despite the large uncertainty, internal extinction is a weakly increasing function of in all these panels. Panel (a) shows SED-fitting-derived values before the prior distribution applied. A population of low mass red galaxies have unrealistically high (SED no prior), because of the age-extinction degeneracy. The mean of the prior distribution of internal extinction, (prior), is in panel (b). Although the (prior) values of low mass galaxies are confined to low values, a population of massive galaxies have unrealistically low (prior) likely due to the underestimate of . Visual inspection shows that shredding tends to describe sources as rounder in edge-on galaxies; dominant bulges, dust lanes and seeing effects will also lead to systematic underestimates of the axial ratio. Panel (c) plots the SED-fitting-derived values after the prior distribution is applied, (SED with prior). Both a lack of high mass galaxies with low as well as of low mass ones with high are evident in panel (c). Combining the distributions in panel (a) and (b), the (SED with prior)– correlation is the tightest of the three, with a correlation coefficient . Whereas applying the prior reduces the systematic offsets of the estimates by SED-fitting, as well as the values, it has little effect on the stellar mass values (Huang et al., 2012). Figure 7 (d) demonstrates that, as expected, the derived values of (SED with prior) are higher in more edge-on galaxies. Neglect of corrections for internal extinction will lead to the systematic underestimate of luminosity, so that hereafter we apply the SED-fitting with prior corrections.

For the subset of the galaxies (6164/7157) which are included in the MPA-JHU DR7 release of SDSS spectral measurements (http://www.mpa-garching.mpg.de/SDSS/DR7/, Brinchmann et al., 2004), we have verified that at the inferred from the Balmer decrement and from the SED fitting using an prior are in good agreement and the offset observed in Salim et al. (2007) is reduced. Above this mass the Balmer decrement leads to larger values, but this is not unexpected as the SDSS spectra observe only a small region, typically towards the center of the galaxy where metallicities and dust attenuations are higher.

Another way to explore the importance of extinction correction in a population involves examining the scatter in the – color diagram, as shown in Figure 8. Results for individual points (unweighted) for the sample are shown in the left panels and for the galaxies on the right, using the colors in the top row and in the bottom, respectively. The subscript ‘0’ in the labels indicates that the colors are corrected for internal extinction. As demonstrated in §3.2, is an intrinsically strong function of (), because NUV traces the SFR and the -band luminosity is related to the stellar mass. For the HI-selected population, comparison can be made directly of the volume-limited sample shown in Figure 8(b) with the corresponding result, uncorrected for internal extinction, shown in Figure 4(f) for the full .40-SDSS-GALEX. As evident by inspection, in addition to a shift bluewards of the points in Figure 8(b), the dispersion about the mean relation is greatly reduced when the extinction correction is applied, and the Pearson correlation coefficient likewise improves from to . This analysis indicates that the scatter in Figure 4(f) is substantially amplified by the lack of a correction for dust extinction. Other factors causing scatter include different SFHs, metallicities, as well as different population synthesis models and even IMFs (Gunawardhana et al., 2011). However, dust extinction dominates among these factors. Furthermore, the star-forming galaxies have on average bluer colors than the ones (median 1.42 versus 1.74 mag). Meanwhile, the tail of red and low SSFR galaxies in panel (a) disappears in panel (b), again reflecting the bias present in the HI-selected population. An additional result of the HI-selection is that the typical error bar in panel (b) is slightly smaller than in (a).

The lower panels in Figure 8 examine the optical SDSS colors . As discussed previously in §2.2, on average . Figure 8(c) shows that galaxies with have similar () colors, forming a vertical tail in these plots; this red tail is much less pronounced in panel (d). The adoption of () as the color index breaks down the degeneracy of () in the red range () when inferences on the SFH are inferred. Furthermore, the SSFR correlates more linearly with than with , e.g. versus in .

Given a simple assumption of the dust and stellar geometry, a well calibrated relation (, infrared-excess defined as ; , the UV spectral slope) is sufficient to predict the (tightly correlated with ) from the UV color (characterizing the UV spectral slope, ), in starburst galaxies (Calzetti et al., 1994). However, the relation in normal star-forming galaxies has a shallower slope with larger scatter (Salim et al., 2007). This result may be due to differences in the SFH (Kong et al., 2004), or dust geometry (Cortese et al., 2006). Therefore, the loci of galaxies on an versus plot give an indication of the dust extinction behavior.

Following this approach, the two samples and are compared in Figure 9, with results for on the left and on the right, both before and after applying the weight correction (see §4.1) in the upper and bottom rows respectively. The red dashed line corresponds to the fit to star-forming galaxies derived in Salim et al. (2007), based on a typical local SDSS-GALEX cross-matched catalog. Despite the large scatter, it is on average in close agreement with the distribution of the galaxies. Galaxies closer to the fit have overall higher weights so that the correlation appears to be slightly tighter in panel (c) than in (a). However, the distribution of the galaxies is offset from the fit in panels (b) and (d), toward the lower side, i.e. for a given color, the HI-selected galaxies on average have lower extinctions. This result is also confirmed by the generally lower of the sample overall, with a median value of 1.31 mag, relative to that of , 1.46 mag. Such a deviation of the main trend from the SF-fit of Salim et al. (2007) suggests that the HI-selected galaxies have different SFHs or dust geometries.

Unfortunately, the metallicity of the stellar population is poorly constrained by the SED-fitting. Nevertheless, given the correlation between dust and metallicity (e.g. Draine et al., 2007), the lower extinction infers that the galaxies have lower metallicity. Besides the well-known mass-metallicity (gas-phase) relation (e.g. Tremonti et al., 2004), Mannucci et al. (2010) demonstrate that at lower (), metallicity decreases sharply with increasing SFR, while at high stellar mass, metallicity does not depend on the SFR. Given the bias towards high SFR of the sample at a given (see §4.2.4), the bias towards low metallicity and low extinction is expected. The gas-phase metallicity measures (oxygen abundance) from the MPA-JHU DR7 release (Tremonti et al., 2004) are available for 4211/7157 of the galaxies and 10311/16817 of the galaxies. In addition to the caveat of the small SDSS fiber aperture, the requirement of being an SDSS spectroscopic target may reduce the difference between the two subsets. The mean is only slightly higher among the galaxies (8.74) than in the galaxies (8.71). The overall lower extinction among the galaxies is consistent with the idea that HI-selected galaxies are relatively gas rich and less evolved, with more likely gas infall, lower SFE and metallicity, less dust and thus lower extinction.

4.2.3 Distribution in the intrinsic CMD

The bimodal distribution in the optical CMD (Baldry et al., 2004) has been interpreted as an evolutionary sequence, with the blue-cloud galaxies growing through mergers and the consumption of gas and later migrating to the red sequence. This evolutionary scenario also predicts that galaxies evolve from a state of low stellar mass, high SSFR and high HI fraction to the opposite. As discussed in §3.1, the HI fraction is lower in redder galaxies leading to the result that an HI-selected sample like is biased against red galaxies whereas those are commonly included in, and may even dominate, an optically-selected one like . Here, we use the CMD to quantify this bias.

Figure 10 shows the CMDs of the (left panels) and the (right panels); before and after applying weight corrections in the upper and bottom rows respectively. In these plots, absolute magnitudes and colors are corrected for internal extinction as given by the SED-fitting with the prior applied. A similar CMD for the whole -SDSS population but without corrections can be found in Figure 7 of Haynes et al. (2011). The dash-dotted curve is based on the best fit to the division of the red and blue populations derived by Baldry et al. (2004) but with shifts toward bluer colors and brighter applied in the amount of the mean extinction of the sample.

As is obvious in panels (a) and (b), the red sequence is far more pronounced in than in . Among the galaxies, only 68% lie on the blue side of the division, whereas the percentage of blue galaxies in the HI-selected population is as high as 84%. The small population of ‘red’ galaxies with HI represents candidate objects which (i) have recently migrated onto the red sequence retaining some residual gas, or (ii) will transit back to the blue cloud via late gas re-accretion (Cortese & Hughes, 2009). Note that most of the red HI-bearing galaxies optically luminous. The HI mass of the faint red galaxies is usually so low that their HI line flux densities are below the sensitivity limit of ALFALFA.

In the weight corrected diagrams (panels c and d), the peaks of number density shift to fainter in both samples. Galaxies densely occupy the faintest bins, especially in the sample. This result is consistent with the optical luminosity function of the blue population (Baldry et al., 2004). A peak of the number density on the red sequence around also coincides with the maxima of the luminosity function derived by Baldry et al. (2004). However, a second peak appears on the red sequence at the faint end. Note that the data points in Baldry et al. (2004) also suggest a rise in number density in the faintest bins of the red sequence luminosity function (see their Figure 7), though those authors ignore these objects when they fit the Schechter function. In agreement with this, Hogg et al. (2003) reported a non-monotonic density trend along the red sequence, seen as a dip in the typical density for intermediate-mass red-sequence galaxies despite higher densities at higher and lower masses. Similar to the finding of a sudden broadening in the SSFR distribution faintwards of (Lee et al., 2007), a sudden broadening in the color distribution faintwards of is seen in the sample. This increased spread suggests that, unlike the galaxies of intermediate mass in which the SF is mainly regulated by stellar mass and for which the blue population dominates in number, the gas in dwarfs can be easily removed so that SF suddenly quenches driving their migration onto the red sequence.

Figure 10(c) shows a CMD for an optically-selected population similar to Figure 2 of Baldry et al. (2004). However, is limited to whereas the low-redshift sample Baldry et al. (2004) studied has . The imposition of the volume cut here clearly decreases the presence of luminous red galaxies; the local volume is dominated by blue star-forming galaxies. This effect is also enhanced by the additional UV selection applied to the sample.

The near-absence of the red sequence among the population is clear in panel (d); as we have noted before, a blind HI survey like ALFALFA is highly biased against red sequence galaxies. Additionally, in both populations galaxies appear to be bluer as their gets fainter, though with large scatter. Such a trend is weaker but still visible after internal extinction corrections are applied. Therefore, the slope is not only due to extinction, but is intrinsic.

Besides comparing the CMDs of and , we can also study the impact of HI selection through an examination of the fraction of galaxies that are cross matched to . As was discussed in §4.1, 34% of the galaxies are cross-matched to the catalog. However, we note that such a fraction is a lower limit of the HI-detection rate of optical-UV selected galaxies in , because some objects may be a shredded photometric object of a gas bearer while another piece is cross-matched to the entry. The fraction of these objects should however not be large (see Haynes et al., 2011).

Figure 11 explores the fraction of the population included in the within the CMD (left) and the diagram (right). In the left panel, the NUV-to-optical CMD with internal extinction corrections is color coded by the fraction of galaxies in the optically-selected sample which are also included in the ; the contours trace the total number density of the galaxies. Clearly, an HI survey like ALFALFA is more efficient at detecting blue galaxies than red ones. Especially at very bright end of the blue cloud (lower left corner), the detection rate is close to 100%. Furthermore, the ALFALFA population also detects the majority of optically faint blue galaxies with the detection rate again approaching 100% (lower right corner). The latter have the highest HI fractions (see also Figure 5). HI survey is most efficient in detecting galaxies with large diameter and high values (Garcia-Appadoo et al., 2009). The general shape of the color scale variation above a cross-match rate of 40% resembles that of the number density variation on the bluer side of the blue cloud. In contrast, starting from the red edge of the blue cloud and throughout the whole red sequence region, the rate of detection by ALFALFA drops below 10% and even to 0%. These results again demonstrate that HI-selection is highly biased against galaxies on the red sequence and furthermore, that such bias begins to become pronounced on the redder portions of what still is considered the blue cloud. The precise location of this limit to some extent reflects the ‘fast’ nature of ALFALFA (only 40 seconds integration per beam); a deeper survey of comparable solid angle would probe to lower gas fractions and hence deliver a higher cross-match rate.

4.2.4 Star-formation sequence

The scaling relation that the SFR increases with among the galaxies is demonstrated in §3.2 (Figure 4a). Figure 4(d) similarly shows the well confined star forming sequence in the diagram. Based on the ES–SDSS sample, West et al. (2009) suggested that the significant offset towards bluer colors, induced by HI-selection can be explained by enhanced recent bursts of star formation. Furthermore, rising SFHs, i.e. high parameter, are required to explain the colors of HI-selected galaxies bluer than , which may result from gas infall and enhanced SF subsequently. Here, we compare the distributions of the and galaxies, on and off the star-forming sequences to explore further the impact of HI-selection.

Figure 12 examines the versus scaling relation for the optical (left) and HI (right) selected samples. The upper row shows the individual galaxies while the lower traces the weighted distributions. The cyan dashed line at shows the fit to this relation obtained by Schiminovich et al. (2010), based on the high GASS sample in all four panels:

Like , GASS is essentially an SDSS selected sample but only includes the high stellar mass end. The blue diamonds and lines represent derived for or in each stellar mass bin. Note these are different from the average trends in Figure 2 or Figure 4. The values are weighted averages in the weighted panels. The numbers of galaxies in each stellar mass bins are listed at the top of panels (a) and (b). Typical error bars are shown in panels (a, b).

The main distribution, consisting of the star forming galaxies, is associated with the parameter space inside the contours. In the un-weighted diagrams, the GASS fit is consistent with in the high mass range (panel a), but falls below the average of (panel b). This offset indicates that even when only the star forming sequence is considered, an HI-selected population has a higher SFR overall, because is not complete even within the blue population (see also Figure 11). Similarly, the blue diamonds in the weighted plot roughly coincide with the GASS fit (panel c). At the same time, the of galaxies becomes systematically larger than the GASS fit with increasing (panel d).

Below the locus of star forming galaxies, the sample contains a large population of passive galaxies visible as the cloud of points extending to very low SFRs (panel a). However, this population is barely seen in the same diagram for the galaxies (panel b), i.e. an HI-selected sample is highly biased against non-star-forming galaxies.

Because is truncated at the low mass end due to the applied weight limit (see §4.1),