HIghMass – High HI Mass, HI-rich Galaxies at z$\sim$0
Sample Definition, Optical and H$\alpha$ Imaging, and Star Formation Properties

The ALFALFA survey achieves its spectral mapping via a drift scan technique with the Arecibo L-band feed array (ALFA) on the Arecibo 305 m antenna (Giovanelli et al., 2005). The final 3-D spectral cubes yield a median HI centroiding accuracy of $\sim$20^′′ (dependent on signal-to-noise ratio) and a resolution of $\sim 3.5^{\prime}$. In addition to properties of the detected HI signals, ALFALFA survey catalogs also include, where applicable, an assignment of the most probable optical counterpart (OC) to each HI source. The HIghMass sample galaxies have been selected from the 2011 ALFALFA catalog, $\alpha$.40 (Haynes et al., 2011), covering 40% of the final survey area and including $\sim$16,000 high-quality detections. For the area of overlap, the $\alpha$.40 catalog included crossmatches of the OCs to the SDSS Data Release 7 (Abazajian et al., 2009).

Because of the high sensitivity of the Arecibo telescope, the $\alpha$.40 catalog includes over 2800 galaxies with $M_{\rm HI}>10^{10}~M_{\odot}$. Among these, the HIghMass sample selects the most gas-rich, relative to their stellar mass. To derive $f_{\rm HI}$, we estimate $M_{*}$ by spectral energy distribution (SED) fitting to seven GALEX-SDSS bands (Huang et al., 2012a, b). Similar to Figure 2(c) of Huang et al. (2012b), the left panel of Fig. 1 shows the $f_{\rm HI}$ vs. $M_{*}$ diagram for the SDSS-GALEX-$\alpha$.40 sample, but weighted by the $V/V_{\rm max}$ values, where $V$ is the overlapped survey sky volume and $V_{\rm max}$ is the maximum distance at which an HI source can be detected by ALFALFA. Relatively HI-poor galaxies are observable in a smaller $V_{\rm max}$ than the total survey volume, so that they are assigned a higher weight above unity. This approach corrects for the ALFALFA survey incompleteness (Haynes et al., 2011) in order to mimic the scaling relations derived from a volume limited sample (Huang et al., 2012b). It is similar to what was applied in Baldry et al. (2004), accounting for the fact galaxies of a given absolute magnitude can be observed only within a certain redshift range. Black contours and grayscales represent the SDSS-GALEX-$\alpha$.40 common sample. The sharp lower edge of the general distribution arises because only the galaxies with weights below 60, or equivalently with $M_{\rm HI}\gtrsim 10^{8.2}~M_{\odot}$, are included. The gray long dashed line in Fig. 1 shows the approximate lower limit of $M_{\rm HI}=10^{8.2}~M_{\odot}$. The solid blue curve illustrates the weighted running average defined by the SDSS-GALEX-$\alpha$.40 galaxies, in agreement with the result derived from the GASS survey at $M_{*}>10^{10}~M_{\odot}$ (Catinella et al., 2013, final data release, cyan dash-dotted line). The decreasing trend of $f_{\rm HI}$ with $M_{*}$ confirms the expectation that massive galaxies are mostly gas poor. The hint of a $f_{\rm HI}$ bimodal distribution as driven by the higher portion of gas-poor galaxies at the high stellar mass end will be more prominent if the ALFALFA detections with higher weights (i.e., the HI poor galaxies with $M_{\rm HI}\lesssim 10^{8.2}~M_{\odot}$ detected only nearby) are included in this plot. The $f_{\rm HI}$ bimodal distribution is consistent with the bimodal distribution in an optical color-magnitude diagram, as well as the fact that the relative number of red galaxies increases among massive galaxies with $M_{*}\gtrsim 10^{10}M_{\odot}$.

As an HI-selected population, galaxies detected by ALFALFA are strongly biased towards gas-rich systems with the HIghMass galaxies being the extreme cases. The black lines in Fig. 1 corresponds to the selection criteria of HIghMass galaxies: (i) has an $M_{\rm HI}>10^{10}~M_{\odot}$, lying above the dashed line; and (ii) has an $f_{\rm HI}$ more than than 1$\sigma$ above the running average in a given $M_{*}$ bin, lying above the dotted line. These selection criteria are partly motivated by the semi-analytic model prediction in Boissier & Prantzos (2000) that those galaxies which reside in high-$\lambda$ DM halos have preferentially higher gas fractions at fixed circular velocity. To avoid unreliable measures, we visually inspected these galaxies to eliminate cases in which the HI fluxes suffer from confusion in the ALFA beam or those in which the SDSS magnitudes suffer from significant shredding or blending. The final HIghMass program sample consists of 34 galaxies, listed in Table 1. Different subsets are observed in our comprehensive multiwavelength observing programs, accounting for the technical feasibility. For instance, targets close to bright stars were avoided in our GALEX program (GI-6; Haynes PI); targets close to strong continuum sources or with low HI fluxes were avoided in the HI synthesis mapping conducted with the Jansky Very Large Array (JVLA), the Giant Meterwave Radio Telescope (GMRT) and the Westerbork Synthesis Radio Telescope (WSRT).

The 34 HIghMass galaxies are shown superposed on the ALFALFA population as colored symbols in Fig. 1 with separate symbols identifying the galaxies included in our HI synthesis program (20 filled symbols) and those with narrowband H$\alpha$ imaging (31 open squares: KPNO11). Most of these objects are also included in other multiwavelength programs with other facilities (GALEX, Isaac Newton Telescope, warm-Spitzer, Herschel, IRAM 30-m, CARMA, SMA). The $f_{\rm HI}$ ranges between 0.24 and 9.2, with 20/34 having $f_{\rm HI}>1$. Because ALFALFA does not provide the angular resolution needed to resolve the HI disks, we have obtained HI synthesis maps of 20 objects which could be feasibly mapped with existing HI synthesis instruments, including eight observed with the GMRT (in 2009; Chengalur PI; downward triangles in Fig. 1; and in 2011; Adams PI; upward triangles), two with the WSRT (in 2011; Haynes PI; diamonds), and last ten with the JVLA (in 2011; Haynes PI; circles). By mapping the distribution and velocity of the HI gas, these observations will yield clues on the origin and nature of the HIghMass galaxies via the constraints on their DM halos placed by gas dynamics (Hallenbeck et al., 2014). In addition, recent accretion of intergalactic medium (IGM) or minor mergers of faint companions may leave signatures in the HI morphology or velocity fields.

The HIghMass sample was also targeted for medium-depth observations (1200 sec) with the GALEX satellite, but only NUV observations were obtained because of the early failure of the GALEX FUV detector. However, existing GALEX archival data give insight into the intriguing behavior in some of the HIghMass galaxies. GALEX images reveal that SF in more gas-rich galaxies often extends much farther in radius than had previously been appreciated (Thilker et al., 2007). Whereas only two faint loose spiral arms are seen in optical images of UGC 9234 in the HIghMass sample, an extended UV disk hosting irregular and patchy SF is clearly evident, indicative of recent gas inflow and disk regrowth. It is known that the extent of the UV disk (normalized to the optical size) is strongly correlated to the integrated $f_{\rm HI}$, as expected if that the amount of HI regulates the growth of SF disk in the outskirt of galaxies (Cortese et al., 2012). In combination with the resolved HI column density maps, dust maps available from Herschel observations, insights into the underlying stellar population from Spitzer, and CO fluxes from the IRAM 30-m telescope for significant subsets of the HIghMass sample, future work with the resolved SF measures derived from both UV photometry and H$\alpha$ imaging will address the questions concerning the gas-SF interplay. We will study the HI-to-H₂ transition and the empirical K-S relation in more detail to explore how such massive HI disks can exist without having converted the bulk of gas into stars yet.

The right panel of Fig. 1 illustrates the trend of HI mass fraction as a function of stellar mass surface density, $\mu_{*}$ for the ALFALFA population (contours and grayscale) with the HIghMass galaxies identified individually as in the left panel. Catinella et al. (2010) found $\mu_{*}$ to be one of the optical-derived quantities that can be used to predict accurately the $f_{\rm HI}$ in galaxies, in addition to the NUV$-r$ color, or the specific SFR defined as SSFR $\equiv$ SFR/$M_{*}$. We follow Catinella et al. (2013) to define $\mu_{*}\equiv M_{*}/(2\pi r^{2}_{50,z})$ for the parent SDSS-GALEX-$\alpha$.40 sample, where $r_{50,z}$ is the radius containing 50 percent of the Petrosian flux in z-band measured by the SDSS pipeline. No inclination correction is applied to obtain face-on values because the Petrosian flux is determined within circular apertures by the standard procedure. However, we have reprocessed the photometry on the SDSS images with elliptical apertures (see Appendix B), so that $\mu_{*}\equiv M_{*}/(2\pi r^{2}_{50,z}~q)$ for the HIghMass galaxies, where $q$ is the minor-to-major axial ratio. The running average as determined by our SDSS-GALEX-$\alpha$.40 sample (blue solid line) lies slightly above the GASS result (cyan dash-dotted line, Catinella et al., 2013). This small discrepency can be easily explained by the fact that the ALFALFA survey extends to a lower $M_{*}$ range while the $f_{\rm HI}$ at fixed $\mu_{*}$ is overall higher for less massive galaxies (Catinella et al., 2010). In comparison with the parent ALFALFA sample, the HIghMass galaxies have extraordinarily high $f_{\rm HI}$ at given $M_{*}$, but overall lower $\mu_{*}$ (see Section 6). In an $f_{\rm HI}$ vs. $\mu_{*}$ diagram, because the $f_{\rm HI}$ value generally increases with decreasing $\mu_{*}$ for the overall population, the HIghMass galaxies are not outliers in the right panel of Fig. 1, i.e., they follow the global scaling relation between $f_{\rm HI}$ and $\mu_{*}$.

Table 1 presents the existing data for selected observations and basic properties for the full sample of 34 HIghMass galaxies. Columns are as follows:

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  Col(1): ALFALFA catalog identifier (also known as the AGC number).

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  Col(2): Other name resolution by NED; same as AGC numbers in the UGC cases.

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  Col(3) and (4): J2000 position of the OC assigned to the HI source, in degrees.

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  Col(5): Galaxy morphology classification according to NED. The presence of a strong bar is denoted by ‘B’ based on the the data release for Galaxy Zoo 2 (Willett et al., 2013).

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  Col(6): The HI line width $W_{50}$, in km s^-1, taken from the $\alpha$.40 catalog (Haynes et al., 2011).

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  Col(7): The HI disk rotational velocity $V_{\rm rot}$, in km s^-1, taken to be the deprojected $W_{50}$ using the axial ratio of the optical disk to correct for inclination (see Section 6).

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  Col(8): The systemic heliocentric recessional velocity $cz$, in km s^-1.

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  Col(9): The adopted distance in Mpc, taken from the $\alpha$.40 catalog (Haynes et al., 2011).

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  Col(10): The logarithm of the $M_{\rm HI}$ and its error, in $M_{\odot}$, taken from the $\alpha$.40 catalog (Haynes et al., 2011).

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  Col(11): Type of archival GALEX images used in Section 4, AIS = all sky imaging survey; MIS = medium imaging survey; DIS = deep imaging survey; GII = guest invited investigation; null if outside of footprint.

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  Col(12): Source of H$\alpha$ images, K = our KPNO 2011 run; K* = KPNO 2012 run by Angie Van Sistine; G = GOLDmine data (Gavazzi et al., 2003); null if too far away.

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  Col(13): Code for our HI synthesis mapping programs as discussed in Section 2.1.

Histograms in panel (a)-(d) of Fig. 2 show, respectively, the distributions of the heliocentric recessional velocity, observed HI line width, logarithm of the $M_{\rm HI}$, and NED morphology classification in the Third Reference Catalog (RC3) system (de Vaucouleurs et al., 1991, available for 28 galaxies). Adopting an intrinsic axial ratio of $q_{0}=0.2$, the inclination $\cos i$ is inferred by $\sqrt{(q^{2}-q_{0}^{2})/(1-q_{0}^{2})}$. The rotational velocity of the HI disk, $V_{\rm rot}$, is thus estimated by $(W_{50}/2)/\sin i$. The resulting $V_{\rm rot}$ values, overlaid in Panel (b) by the filled histogram, are large, consistent with their status as HI massive disk galaxies (see Panel c). The only early type galaxy in the sample, UGC 4599, is a face on S0 galaxy with an outer ring where active star forming regions are found. The total asymptotic magnitudes in the B band are available from RC3 for 21 galaxies, ranging from 15.73 mag to 12.60 mag, with a median of 14.35 mag. The final two panels in Fig. 2 show the RC3 B-band absolute magnitude and logarithm of the $M_{\rm HI}/L_{B}$, assuming $B=5.47$ for the sun. These B-band magnitudes are systematically brighter than our reprocessed SDSS magnitudes (measured inside elliptical Petrosian apertures, see Appendix B), but the differences are within the uncertainty. The final set of 34 HIghMass galaxies span a range of colors, morphologies, luminosities, $M_{*}$, and SFRs (see Section 4).

Fig. 3 illustrates the unweighted distribution of the parent $\alpha$.40-SDSS sample (contours and points) on an optical color-magnitude diagram; the HIghMass galaxies are superposed with the same colored symbols as in Fig. 1. The approximate dividing line which separates the “red sequence” from the “blue cloud” as presented by Baldry et al. (2004) is shown as the dash-dotted curve. In this plot, the SDSS magnitudes of the parent sample are the DR8 pipeline values, but those of the HIghMass galaxies are our reprocessed measurements (see Appendix B). The vast majority of the galaxies in the $\alpha$.40-SDSS population are found in the blue cloud region. Similarly, most of the HIghMass galaxies, especially the GMRT09 and JVLA11 targets, are exceptionally blue given their high luminosities. Only three HIghMass galaxies lie in the red sequence above the division, UGC 6066, UGC 9234, and UGC 4599. UGC 6066 is an edge-on red spiral and UGC 4599 is an S0 galaxy; they have the earliest morphological types in the HIghMass sample. Although the stellar light in both UGC 9234 and UGC 4599 is dominated by red central regions, the first galaxy has two loose arms and the second one has an outer ring, both being blue and LSB features along which multiple star-forming regions are identified in our continuum-subtracted H$\alpha$ images (see Appendix A). The huge HI reservoirs in both of these red galaxies are apparently involved in the current re-growth of the outer features. Future work will investigate the star formation histories of these systems exploiting other multiwavelength datasets.

In recent years, a number of other surveys have amassed a significant body of H$\alpha$ imaging data on selected populations of star-forming galaxies, including the GOLDmine survey of the Virgo cluster and Coma superclusters (Gavazzi et al., 2003). Out of the HIghMass galaxies, UGC 7686 happens to be a background galaxy in the Virgo direction so that is imaged by the GOLDmine survey. However, the ALFALFA galaxies are biased against cluster environments (Martin et al., 2012). Another ALFALFA-related H$\alpha$ program, H$\alpha$3 (Gavazzi et al., 2012), is in fact lacking in objects with $\log M_{\rm HI}>9.75~M_{\odot}$, because of the well-known cluster HI deficiency and the relatively small volume sampled.

The galaxies in the HIghMass program can be most easily distinguished from very local surveys, e.g, the survey of 52 dwarf-dominated galaxies in the local volume (Karachentsev & Kaisin, 2010), the surveys of 140 local irregulars by Hunter and collaborators (Hunter & Elmegreen, 2004), or the 11 Mpc H$\alpha$ UV Galaxy Survey (11HUGS; Kennicutt et al., 2008), by its inclusion of massive and luminous galaxies which are too rare to be included in surveys of such limited volume. Note that Hunter & Elmegreen (2004) have used 74 spiral galaxies spanning the range of morphologies from Sab to Sd as compiled by Kennicutt (1983) for comparison. However, the $\log M_{\rm HI}/L_{B}$ distribution of that Sab-Sd sample peaks around $-1$, which is significantly HI poorer than our galaxies with similar Hubble types (see Fig. 2f). Instead, the less massive blue compact dwarfs (BCDs) in Hunter & Elmegreen (2004) have comparable $\log M_{\rm HI}/L_{B}$ values to our galaxies (see Fig. 4 in their paper). This can be understood as a result of the general increasing trend of $f_{\rm HI}$ with decreasing $M_{*}$.

Most H$\alpha$ surveys covering the complete morphological spectrum have also been limited to distances of less than 30 Mpc, including the SIRTF Nearby Galaxies Survey (SINGS; Kennicutt et al., 2003), the H$\alpha$ Galaxy Survey sampling 334 galaxies (H$\alpha$GS; James et al., 2004), and the JCMT Nearby Galaxies Legacy Survey of 156 nearby galaxies (NGLS; Sánchez-Gallego et al., 2012). Similar to ours, the sample of the last survey has been HI flux selected in order to avoid an SFR-driven selection while ensuring that the galaxies have a rich ISM. The Hubble-type distributions of spirals from these surveys are similar, peaking around Sc; in fact, the HIghMass sample has a larger fraction of galaxies with later types, consistent with the well-known correlation between high $f_{\rm HI}$ and late-type morphology. However, even a volume out to 30 Mpc contains few truly massive HI disks, with only a handful of galaxies of $M_{\rm HI}>10^{10}~M_{\odot}$ found in those surveys.

An exception is the Survey for Ionization in Neutral-Gas Galaxies (SINGG; Meurer et al., 2006), consisting of 468 galaxies selected from the HI Parkes All-Sky Survey (HIPASS; Meyer et al., 2004). All of their targets are detected in H$\alpha$, confirming that non star-forming galaxies with $M_{\rm HI}\gtrsim 10^{7}~M_{\odot}$ are very rare. SINGG includes galaxies as distant as 80 Mpc, although the majority still have $cz<3000$ km s^-1. By comparison, only one of the HIghMass galaxies, UGC 4599 has $cz<3000$ km s^-1, whereas our median $cz=$ 7660 km s^-1 ($D\sim$100 Mpc). While SINGG Release 1 (Meurer et al., 2006) includes 13 HIPASS sources with $10<\log M_{\rm HI}<10.3$ and 3 more with $10.3<\log M_{\rm HI}<10.6$ (none with $\log M_{\rm HI}>10.6$), multiple galaxies luminous in H$\alpha$ are found to be associated with a single HI source for 9/16 of them. In contrast, we have dropped targets with massive companions to minimize such kind of confusion. As a result, the HIghMass galaxies, being extremely HI massive, are underrepresented by even the SINGG sample.

In addition, there are several H$\alpha$ surveys of particular galaxy types. Analysis of Interstellar Medium of Isolated Galaxies (AMIGA; Verdes-Montenegro et al., 2005) compiles 206 galaxies from the Catalog of Isolated Galaxies (CIG; Karachentseva, 1973). Only UGC 5711 in our sample is included in the CIG. Schombert et al. (2011) present a recent H$\alpha$ imaging survey for a large sample of LSB galaxies. Although the optical color of their galaxies are blue, being comparable to the dwarf galaxies and gas-rich irregulars, their SSFRs are a factor of ten less than other galaxies of the same baryonic mass (Schombert et al., 2011). In contrast, the HIghMass galaxies exhibit healthy ongoing SF globally (see Section 6), neither do they belong exclusively to the isolated population.

The $f_{\rm HI}$ vs. $M_{*}$ correlation obtained by the GASS survey (Catinella et al., 2010) is illustrated along with the ALFALFA population in Fig. 1. The parent sample of GASS is defined by the intersection of the footprints of the SDSS primary spectroscopic survey, the projected GALEX medium imaging survey (MIS) and the ALFALFA region. Further selection criteria include a stellar mass cut ($10<\log M_{*}/M_{\odot}<11.5$) and a redshift cut ($0.025<z<0.05$). The final GASS targets are randomly drawn from this parent sample in a manner which balances the distribution across $M_{*}$, but any sources already detected by ALFALFA are not re-observed. By design, the less massive objects with $\log M_{*}<10$ but high gas fractions are not probed by the GASS. Above this $M_{*}$ cutoff, HIghMass galaxies fall within the extreme tail of the $f_{\rm HI}$ distribution in each $M_{*}$ bin, which are likely to be excluded statistically from the GASS target list. Given the $f_{\rm HI}$ and $M_{*}$ measurements, there is only one galaxy, UGC 8802, lying above the dotted line in our Fig. 1, out of the 250 galaxies in total from the GASS final data release (Catinella et al., 2013). This galaxy meets all our selection criteria. Lying north of Dec.$\sim 35^{\circ}$, it is outside of the footprint of the $\alpha$.40 catalog, but has comparable physical properties to the HIghMass galaxies, e.g., low and evenly distributed SFR surface density, strong color gradient, and extremely high SSFR in the outer disk (Moran et al., 2010).

Finally, motivated by the study of GASS galaxies, a project entitled “Bluedisk” has been devoted to obtaining HI maps of 25 nearby galaxies predicted to have unusually high $f_{\rm HI}$ (Wang et al., 2013). The sample is selected from the SDSS DR7 MPA/JHU catalogue, using the follow criteria: $10<\log M_{*}/M_{\odot}<11$, $0.01<z<0.03$, Dec. $>30^{\circ}$, with high signal-to-noise ratio (S/N) NUV detection in the GALEX imaging survey, and have high $f_{\rm HI}$ relative to the average trend as predicted from measurements of $\mu_{*}$, NUV$-r$ color, and $g-i$ color gradient of the galaxy. Given their final measurements of $M_{*}$ and $M_{\rm HI}$, however, only one target with the lowest $M_{*}$ among their “gas-rich” sample (see black crosses in Fig. 1) sits above the dotted line, denoting one of the selection criteria of the HIghMass galaxies. Again, the HIghMass sample is more extreme than the “Bluedisk” galaxies.

In summary, because of their rarity, the HIghMass galaxies form a unique sample of exceptionally gas-rich massive HI disks and their study will benefit future HI surveys of their higher redshift counterparts which are likely to dominate the planned deep field surveys by the SKA and its pathfinders. The expected number of resolved detections peaks in the HI mass bin of $\sim 10^{10}~M_{\odot}$ (Duffy et al., 2012), for both the ASKAP WALLABY survey (out to $z=0.26$, with a mean redshift of 0.05 at S/N = 6) and the DINGO DEEP survey (out to $z=0.26$, with a mean redshift of 0.12 at S/N = 6). Therefore, the HighMass galaxies are representative of this class of object, in terms of HI mass. Meanwhile, there is an ongoing study of 53 SDSS-selected galaxies at $0.16<z<0.26$, using $\sim$400 hr Arecibo telescope time (Catinella & Cortese, in prep). Those HI bearers at $z\sim 0.2$ are found to be HI-rich, blue, and of low stellar mass surface densities, sharing similar properties with the HIghMass galaxies (see below). Preliminary analysis shows that the stellar massive HIghMass galaxies align with those $z\sim 0.2$ HI detections in the $f_{\rm HI}$ vs. $M_{*}$ plot (Fig. 1), and can be their low redshift analogues (private communication). The HIghMass galaxies will be studied along with the $z\sim 0.2$ HI bearers to further illustrate this (Catinella & Cortese, in prep).

All of the H$\alpha$ and R imaging reported hereafter was obtained in Feb–Mar 2011 over 5 nights (2 other nights were lost to bad weather), using the T2KB detector on the 2.1-m telescope at KPNO. The CCD has a pixel scale of 0.43^′′ pixel^-1 and a chip size of 2048 $\times$ 2048, so that all our targets can be easily imaged by a single pointing. The detector was used in the 3.1 $e^{-}$ ADU^-1 gain mode. The standard R filter is used to provide broadband imaging along with continuum subtraction for the narrowband images. Due to the wide spread of $cz$, a series of eight H$\alpha$ filters are used, in ascending central wavelength, kp1564, kp1565, kp1495, kp1566, kp1496, kp1497, kp1498, and kp1517. Their bandpasses are superimposed on the velocity histograms in Fig. 2(a) by dotted lines in colors, with peak transmission $\sim 75\%$. The H$\alpha$ filter for each source is selected to be the one whose central wavelength best matches the $cz$ of HI line; in all cases, the FWHM of the filters ($\sim 75~\rm\AA$) are sufficient to cover the velocity width of the HI line. However, in most cases, the [NII]$\lambda\lambda$6548 and [NII]$\lambda\lambda$6584 are also contained within the filter bandpass. For the sake of clarity, while we will correct for this contamination when we calculate the SFR from the H$\alpha$ luminosity in Section 4, we generically refer to H$\alpha$ as the total detected H$\alpha$+[NII] flux in this section. Because of the lack of an appropriate H$\alpha$ filter, the most distant HIghMass galaxy UGC 8797 could not be observed. Two other HIghMass galaxies UGC 12506 (the lone ALFALFA fall sky target, an image of which has been kindly provided to us by A. van Sistine and J. Salzer) and UGC 7686 (which had an extant H$\alpha$ image from the GOLDmine) were also not observed in this run.

We utilized an observing mode consisting of three H$\alpha$ exposures (15 min each) and two or three R band exposures (3 min each). Calibration frames included afternoon bias and dome flat fields. Observations of galaxies were bracketed by standard star exposures of both spectrophotometric standards HD19445, HD84937, and BD +26 2606 (Oke & Gunn, 1983), and Landolt (1992) standards (in both R and I bands yielding the color term), at regular intervals throughout the night to calibrate the flux zero points. Galaxies requiring the same H$\alpha$ filter were grouped into observations on the same nights to minimize standard star exposures. There were three clear nights under photometric conditions; on these the standard stars were imaged and then galaxy frames taken on the other non-photometric nights were calibrated by bootstrapping to the photometric frames. The smoothed images (see Appendix A) have an average seeing of $\sim 1.^{\prime\prime}5$. Unfortunately, none of the images of UGC 4599 were taken on photometric nights and a very bright star near UGC 190277 causes serious bleeding on the CCD. As a result, the final H$\alpha$ measurements to be presented are for 29 HIghMass galaxies. Unsurprisingly, H$\alpha$ emission is detected in all of our targets as HI-selected galaxies.

Details of the image reduction, continuum subtraction, surface photometry, and external checks of the H$\alpha$ data quality can be found in Appendix A. Here we present the H$\alpha$ and R-band measurements from our KPNO images of 29 HIghMass galaxies in Table 2. The [NII] and extinction corrections are applied only when calculating SFRs in this work; hence any H$\alpha$ EW values and line fluxes here are in fact for H$\alpha$+[NII], uncorrected for internal or Galactic extinction, but corrected for continuum over-subtraction (see Appendix A). However, we have checked that none of these corrections affect the qualitative results to be addressed. Columns are as follows:

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  Col(1): The ALFALFA catalog identifier (also known as the AGC number).

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  Col(2): KPNO H$\alpha$ filter used in our observing run.

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  Col(3): $\theta$, the position angle (measured eastward from North) and its associated error, measured on the R-band image, in units of degrees.

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  Col(4): $\epsilon$, the ellipticity and its associated error measured on the R-band image, defined as $1-b/a$.

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  Col(5): $\mu_{0}$, the disk surface brightness extrapolated to the galaxy center as measured on the R-band image, in units of mag arcsec^-2, and not corrected for inclination (see Section 5).

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  Col(6): $r_{\rm d}$, the disk scale length measured on the R-band image, in units of arcsec.

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  Col(7): $r_{\rm d,out}$, the disk scale length of the outer disk (see Section 5); the value is null if only a single disk is fit.

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  Col(8): $r_{\rm petro,50}$, the semi-major axis of the ellipse that encompasses 50% of the R-band Petrosian flux, in units of arcsec.

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  Col(9): $r_{\rm petro,90}$, the semi-major axis of the ellipse that encompassess 90% of the R-band Petrosian flux, in units of arcsec.

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  Col(10): $d_{25}$, the major axis of the ellipse defined by the R-band isophote of 25 mag arcsec^-2, in units of arcsec.

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  Col(11): $R$, the R-band magnitude and its associated error in the Johnson-Cousins system; with or without superscription if the magnitudes are measured as mag₈ (the magnitude extrapolated to 8$r_{\rm d}$) or the Petrosian magnitude. See Appendix A for the definitions of the two types of global magnitudes and validation of their consistency. These magnitudes are not corrected for internal or Galactic extinction.

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  Col(12): Logarithm of the line flux of H$\alpha$+[NII] and its associated error, in units of erg s^-1 cm^-2; with (without) superscription if measured as mag₈ (Petrosian magnitude).

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  Col(13): Equivalent width (EW) of the H$\alpha$+[NII] lines and its associated error, in units of Å. See Appendix A for details of its derivation.

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  Col(14): Logarithm of the SFR derived from the H$\alpha$ luminosity (see Section 4), in units of $M_{\odot}$ yr^-1, with all corrections applied.

In addition to our own broadband R magnitudes, we use public SDSS images to provide magnitudes at its filter bands. However, because of their relatively large size, low surface brightness and patchy nature, we use our own photometric analysis of the SDSS magnitudes rather than relying on the standard SDSS pipeline which is not optimized for systems of these characteristics. Details of the photometry reprocessing, an internal comparison with the KPNO measurements, and external checks of data quality (including a comparison with the SDSS pipeline derived values) can be found in Appendix B. Here we present our SDSS measurements for all 34 HIghMass galaxies, along with the SED fitting derived quantities to these five bands in Table 3. All magnitudes are in the AB system. Columns are as follows:

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  Col(1): The ALFALFA catalog identifier (also known as the AGC number).

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  Col(2)-Col(6): Magnitudes and their associated errors in the five SDSS bands, respectively; with (without) superscription if measured as mag₈ (Petrosian magnitude) and not corrected for internal or Galactic extinction.

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  Col(7): $\cos i$, where $i$ is the inclination of the disk. A $\cos i$ value close to zero corresponds to a large correction term for surface brightness deprojection (see Section 5), whereas a $\cos i$ value close to unity corresponds to a large uncertainty in the $V_{\rm rot}$ estimate (see Section 6).

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  Col(8): $\mu_{e}(r)$, the r-band face-on surface brightness at the half light radius, in units of mag arcsec^-2 (see Section 5).

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  Col(9): $A_{r}$, the r-band internal extinction and its associated error, derived by SED fitting using the five SDSS bands (prior $A_{r}$ distribution applied; Huang et al., 2012b), in units of mag.

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  Col(10): $M_{r}$, the final r-band absolute magnitude after applying all corrections. We adopt the $E(B-V)$ measurements by DIRBE (Schlegel et al., 1998) to account for foreground reddening, and the internal extinction is corrected given the $A_{r}$.

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  Col(11): Logarithm of the stellar mass and its associated error, derived by SED fitting, in units of $M_{\odot}$ (see Section 4).

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  Col(12): Logarithm of the stellar mass surface density in units of $M_{\odot}$ kpc^-2 (see Section 2.1); the value is null if the radius containing 50 percent of the Petrosian flux in z-band is undetermined.

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  Col(13): Logarithm of SFR and its associated error, derived by SED fitting, in units of $M_{\odot}$ yr^-1 with all corrections applied (see Section 4).

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  Col(14): Logarithm of the birth-parameter, $b\equiv{\rm SFR}/\langle{\rm SFR}\rangle$, and its associated error, derived by SED fitting (see Section 5 and 6).

Through a coincidence of dust and stellar population evolution physics, the dust-age-metallicity degeneracy actually helps in the estimate of $M_{*}/L$ from optical colors (Taylor et al., 2011). While H$\alpha$ is recognized as an instantaneous indicator sensitive to SF activity over the timescale of $\sim$10 Myr, images obtained in the SDSS u-band respond to variations in the SFR over 100-500 Myr. Our future study of the Spitzer IRAC imaging will trace the low-mass star population which dominates the mass budget in galaxies, so as to better constrain the $M_{*}$. In this section, we make use of the photometry derived in Appendix B to perform SED fitting to the five SDSS bands in order to obtain the $M_{*}$ and SFR estimates.

Further details of the method and fitting quality for the $\alpha$.40–SDSS (DR7) sample are found in Salim et al. (2007) and Huang et al. (2012a). We use the Bruzual & Charlot (2003) stellar population synthesis code to construct the model SEDs, adopting a Chabrier (2003) IMF. Random bursts are allowed to be superimposed on a continuous star formation history (SFH). We correct the observed magnitudes for Galactic reddening and implicitly apply $K$-corrections by convolving the redshifted model SEDs with SDSS bandpasses in the rest frame. The full likelihood distributions of parameters are derived following a Bayesian approach, so that the errors due to model degeneracies are properly characterized by the width of the resulting probability density functions. In addition, the Gaussian prior distribution of the effective optical depth in the V band, $\tau_{V}$, is applied, accounting for the fact that the extinction depends not only on the inclination but also on the luminosity of galaxy (Giovanelli et al., 1997). As a result, the fitting-derived internal extinction is improved (Huang et al., 2012b), in terms of both systematic and random uncertainties. Although dust has little effect on the $M_{*}$ estimates, the uncertainty of the extinction correction can be the dominant term in the estimate of the SFR from optical or UV SFR indicators, e.g., H$\alpha$. Approximately half of the starlight emitted in the optical and UV is absorbed by interstellar dust and re-radiated at infrared wavelengths (Kennicutt & Evans, 2012), so that it is important to assume a prior $\tau_{V}$ distribution to better constrain the extinction. Our SED fitting-derived measures of $M_{*}$, SFR(SED), and $A_{r}$ are given in Table 3. We also follow the same fitting procedure as for the $\alpha$.40–SDSS (DR8) sample, yielding physical quantities of the general population to be presented together with the HIghMass galaxies in Section 6.

H$\alpha$ emission traces stars with masses greater than $\sim 15~M_{\odot}$ and hence provides a measure of very recent massive SF. In addition to the need to assume an IMF to extrapolate the number of high mass stars (relevant for most SFR indicators), H$\alpha$-based SFRs need large and uncertain extinction corrections (like UV and other blue indicators, e.g., [OII] and H$\beta$). Central AGN may also contribute to the observed H$\alpha$ line emission (like [OII], [OIII], radio, and IR indicators). The specific drawbacks of H$\alpha$-based SFRs is contamination in most of the filters used in the observations by the [NII]$\lambda\lambda$6548 and 6584 $\rm\AA$ lines. In general, the largest systematic errors are dust attenuation and sensitivity to the population of the upper IMF in regions with low absolute SFRs (Kennicutt & Evans, 2012). Given their integrated SFRs, the incomplete IMF sampling has no impact on the HIghMass galaxies, and, the uncertainties in the internal extinction corrections to the H$\alpha$ fluxes dominate over photometric errors as the main error in the derived SFRs.

We derive the SFR from the H$\alpha$ luminosity adopting a recent H$\alpha$ calibration in Kennicutt & Evans (2012),

Here, the last term converts a Kroupa IMF used in their work to a Chabrier (2003) IMF used by us (Bell et al., 2003). We note that the correction for stellar absorption underlying the H$\alpha$ emission is already taken care of by the continuum subtraction (Kennicutt et al., 2008). In addition to the (1) continuum over-subtraction and (2) Galactic extinction corrections explained in Appendix A, the following corrections are applied on the observed $L_{\rm H\alpha}$:

(3) [NII] contamination: Although SDSS spectra are available for 33/34 of the HIghMass galaxies, they are limited by the small aperture (3 arcsec) of the fibers, covering only the nuclear regions in the majority. Additionally, according to the BPT diagram (Brinchmann et al., 2004), there are five AGNs, two low S/N LINERs, and two composite galaxies with both AGN and SF contributions among our sample. The nuclear [NII]/H$\alpha$ ratios are most likely to deviate from the overall values. Alternatively, we adopt the scaling relation between [NII]/H$\alpha$ and $M_{B}$ given by Kennicutt et al. (2008),

where $M_{B}$ comes from the combined SDSS magnitudes, assuming $h=0.75$ as in Kennicutt et al. (2008). Despite a large scatter, we have confirmed this relation to be systematically consistent with the SDSS flux measurements, excluding the AGNs. We further adopt a line ratio [NII]$\lambda\lambda$6584/[NII]$\lambda\lambda 6548=3$ to exclude the [NII]$\lambda\lambda$6584 contribution in five galaxies because it falls outside of the H$\alpha$ filter.

(4) Dust extinction correction: We make use of the continuum extinction given by the SED fitting and assume a constant ratio between the nebular line and stellar continuum extinctions at the same wavelength, $A_{r}=0.44A_{\rm H\alpha}$ (Calzetti et al., 2000). Due to the same concern raised by the small fiber aperture, we choose here not to rely on the Balmer decrement derived from the SDSS spectra in order to infer $A_{\rm H\alpha}$. Use of the Balmer decrement may lead to an underestimate of the extinction because lines of sight with low extinction are more heavily weighted within the beam (Kennicutt & Evans, 2012), or an overestimate of the extinction induced by the fact that the disk central regions are less transparent (Giovanelli et al., 1994). In the future, we plan to explore this issue further with long-slit optical spectroscopy and Herschel data.

The final SFR(H$\alpha$) values with these corrections applied are presented in the last column of Table 2. The SFR(H$\alpha$)s for the HIghMass galaxies range from 0.34 to 21 $M_{\odot}~{\rm yr^{-1}}$, with a median value of 2.5 $M_{\odot}~{\rm yr^{-1}}$, significantly higher than the median SFR found by the other H$\alpha$ surveys, e.g., 11HUGS, H$\alpha$GS, or SINGG. The difference cannot be attributed to the different corrections we applied because a comparison of the $L_{\rm H\alpha}$ distributions (only continuum over-subtraction corrected and Galactic extinction corrected) show as well that the HIghMass galaxies tend towards high $L_{\rm H\alpha}$. This result is in contrast with previous understanding that HI-selected galaxies have somewhat lower $L_{\rm H\alpha}$ and SFRs (Sánchez-Gallego et al., 2012), but agree with the finding in Huang et al. (2012b) that the HI-rich galaxies have, on average, higher SFRs at fixed $M_{*}$.

Fig. 4 shows the comparison of the values of the SFR derived from the SEDs, SFR(SED), and from the H$\alpha$ luminosity, SFR(H$\alpha$)s, for the HIghMass galaxies. For the majority, the two quantities are in rough agreement within the uncertainties. Therefore, the standard calibration of the H$\alpha$ SFR indicator, assuming a Chabrier (2003) IMF, is applicable to our galaxies. However, for a few sources, the SFRs derived from SED-fitting result in much lower values by almost a factor of ten. In such cases, huge error bars on the SFR(SED)s result from broad probability density functions of the SFR estimates, suggesting that the SFR(H$\alpha$) values represent the more realistic result. We further assess this conclusion by referring to the GALEX archive for NUV measurements; note that FUV measures which would also be useful are available for a smaller subset. With a poorer resolution ($\sim 4$ arcsec FWHM) and a larger impact from dust extinction, the NUV images are less valuable for the purpose of tracing SFRs than our high quality H$\alpha$ data, but we can use them here to judge the relative reliability of SFR(SED) and SFR(H$\alpha$). Excluding the shredded pipeline NUV magnitudes, we apply corrections for Galactic extinction, internal extinction (self-consistent values given by the SED fitting), and $K$-corrections. The end result is that the inferred SFRs from the final NUV luminosity, adopting a Kennicutt & Evans (2012) calibration, reach better agreement with the higher values of SFR(H$\alpha$) than with the SFR(SED)s.

In summary, we have double checked the robustness of the SFR(SED)s and SFR(H$\alpha$)s, adopting a conservative error analysis to conclude that the H$\alpha$-derived SFRs provide more reliable measures of the SFR in those cases where the two approaches differ. We conclude that there is no evidence that the exceptional gas fractions of the HIghMass galaxies result from abnormal levels of SF at least among the massive stars. We can also rule out a significant decaying or rising SF history in the last $\sim$10 Myr relative to the last 100-500 Myr.

On an SFR vs. $M_{*}$ diagram, star forming galaxies form a narrow band, the so-called “main sequence” of SF; an even tighter correlation has been identified on a similar SSFR vs. $M_{*}$ plot (e.g. Salim et al., 2007). $M_{*}$ appears to be the crucial quantity governing the SF along this sequence. In the absence of mergers or other events that trigger a starburst, it has been suggested that blue galaxies on the SF sequence evolve towards higher $M_{*}$ and and lower SSFRs. In this scenario, the tightness of the SF sequence, with an rms scatter of less than 0.3 dex, indicates that the SF of “main sequence” galaxies is not driven mainly by merger-induced starbursts but rather by a continuous mass-dependent process that is gradually declining with time, e.g., smooth gas accretion (Bouché et al., 2010). Huang et al. (2012b) have previously presented the results for the ALFALFA parent population, confirming the expectations that SFRs generally increase but SSFRs decrease with increasing stellar mass.

Whereas the SF sequence reflects directly the relationship between the accretion rate and the halo mass (Bouché et al., 2010), the DM halo should play a more fundamental role than the stellar mass in the regulation of disk growth. For this reason, we examine the SF behavior of the ALFALFA sample overall, and the HIghMass galaxies in particular, as a function of the disk rotational velocity, $V_{\rm rot}$, taken to be the deprojected HI line width using the axial ratio of the optical disk to correct for inclination. Within some scaling factor that accounts for the (unknown) extent of the HI disk, we expect $V_{\rm rot}$ to provide a measure of the dynamical mass of the DM halo, more reliable for example than $M_{*}$ alone, in order to characterize the overall gravitational effect leading to material infall and thus SF. This expectation is particularly justified here since $f_{\rm HI}>1$ in 20/34 of the HIghMass galaxies. We could also derive the dynamical masses ($M_{\rm dyn}$) from the values of $V_{\rm rot}$ and the optical disk size, but because the axial ratios are less vulnerable to shredding by the SDSS DR8 pipeline relative to the disk size measurements (see Appendix B), we choose to present the results simply using $V_{\rm rot}$ rather than $M_{\rm dyn}$. We note however that the qualitative results to be drawn from this analysis will not be altered if any of $M_{*}$, $M_{\rm dyn}$, or $M_{*}+M_{\rm HI}$ is used instead of $V_{\rm rot}$.

Fig. 8 shows the parameter space occupied by the HIghMass galaxies (colored symbols) as compared to that by the general ALFALFA population (black contours and gray dots). The $x$-axis is $V_{\rm rot}$ in all panels with $y$-axes showing SFR, SSFR, and SFE, respectively from top to bottom. In order to make the plots here, we adopt SFR(H$\alpha$)s for the HIghMass sample if available, but use SFR(SED)s otherwise. Note that our parent sample here is defined by galaxies included in that $\alpha$.40 catalog and with SDSS photometry from the SDSS/DR8.

In the SFR vs. $V_{\rm rot}$ diagram (top panel), the HIghMass galaxies in general lie slightly above the running average as defined by the ALFALFA galaxies. The only extreme outlier beneath the SF sequence is the only early type galaxy in our sample, UGC 4599, having an SFR of 0.01 $M_{\odot}$ yr^-1 in the center region (the outer ring is excluded from the Petrosian aperture because of the existence of the central bulge, see Appendix). This happens to be the only KPNO target without standard star frames bracketed, so that the estimate of the SFR comes from SED fitting. However, there are SF regions situating along the outer ring of this galaxy as evident in the continuum-subtracted H$\alpha$ image (uncalibrated). Recent work by Finkelman & Brosch (2011) derived the SFR within the entire ring to be 0.04 $M_{\odot}~{\rm yr}^{-1}$ from GALEX UV flux. Those authors concluded that both a merger between two HI-rich galaxies and the cold accretion of gas from the IGM can account for the observed properties of this galaxy, as well as the huge amount of HI detected. It is very possible that the SFR(SED) value obtained in the current work is an underestimate in this relatively red galaxy (see discussion in Section 4). Except for UGC 4599, the current SFRs range from 0.34 (UGC 8089, a LSB galaxy with low $M_{*}$) to 21 (UGC 8475, a well-developed spiral), and have a median of 2.5 $M_{\odot}$ yr^-1, in rough agreement with the range derived from Sc galaxies but higher than that of the Sa galaxies in Caldwell et al. (1991). Again, we emphasize that the majority of the HIghMass galaxies are not crouching giants. Instead of being quiescent objects like Malin 1, most have blue outer disks and exhibit healthy onging SF, as gauged by their $V_{\rm rot}$ via this standard scaling relation. Although they have slightly lower surface brightnesses, they are different from the extreme LSB galaxies which typically have lower SSFRs by a factor of ten than other galaxies of the same baryonic mass (Schombert et al., 2011).

In the middle panel, the upward deviation of the HIghMass galaxies from the general trend is even more evident. The HIghMass galaxies have only moderate to high current SFRs but significantly higher SSFRs at fixed $V_{\rm rot}$. Given the fact that $M_{*}$ represents the integrated past SF, this offset can either due to a higher ratio of current to past-averaged SFR and/or the HIghMass galaxies have formed the bulk of their stars more recently relative to the typical ALFALFA galaxy, and thus have a shorter integrated SFH.

In order to test these scenarios, we characterize the shape of the SFH and estimate the formation time, again by SED fitting. The relevant parameters are defined as follows: $T_{\rm form}$ is the time since the galaxy first started forming stars; $T_{\rm wm}$ is the mass-weighted age; $\gamma$ is the timescale of the SFH so that the continuous component of SFH is given as $e^{\gamma t}$; and $b$-, the birthrate-parameter, is the present SFR (averaged over the last 100 Myr) divided by the past average SFR, accounting for the bursts in SFH. Due to model degeneracies, these four parameters are poorly constrained by the SED fitting of five optical bands, with typical uncertainties being 60%. Despite this caveat, it is indicative that the HIghMass galaxies in general started to form stars more recently, with a median $T_{\rm form}$ of 4.16 Gyr, in comparison with a value of 4.51 Gyr for the ALFALFA galaxies. This also suggests that the HIghMass galaxies have overall younger stellar population (median $T_{\rm wm}=$ 2.28 vs. 2.54 Gyr). The median timescales of SF are comparable between the two populations, with a median of $\gamma=$ 0.41 for both, seemingly in contradiction with the prediction that the galaxies in high $\lambda$ halos have longer timescales of SF, or equivalently, that their SFHs decline more slowly. However, taking into account the possibility of bursts, the median $b$-parameter is higher among the HIghMass galaxies, being 0.38 (vs. 0.31 for the full ALFALFA sample). It is interesting to note that the two HIghMass galaxies with the highest $b$-parameters (AGC 203522 and AGC 248881) also have the highest EW_Hα+[NII] values among our KPNO targets, i.e., they are undergoing a burst of star formation at the present time.

The HIghMass galaxies in fact follow the standard calibration of the $f_{\rm HI}$ fundamental plane (e.g., the $f_{\rm HI}$–SSFR–$\mu_{*}$ correlation in Huang et al., 2012b), despite the higher than average $f_{\rm HI}$ at fixed $M_{*}$, $M_{\rm dyn}$, $M_{*}+M_{\rm HI}$, or $V_{\rm rot}$. This consistency suggests that the more gas-rich galaxies with higher $f_{\rm HI}$s tend to have higher SSFRs and lower surface densities by a corresponding amount, so that they follow the same $f_{\rm HI}$ fundamental plane as defined by their gas-poorer counterparts. Hence, it would be impractical to identify the gas-rich galaxies in high $\lambda$ halos by selecting outliers from the $f_{\rm HI}$ fundamental plane, because of the seemingly self-regulated process between gas supply and SF.

The upper panel of Fig. 9 confirms the finding that the HIghMass galaxies have overall lower stellar mass surface densities at fixed $V_{\rm rot}$, relative to the parent $\alpha$.40–SDSS (DR8) sample. The concentration index in the r-band, $r_{\rm petro,90}/r_{\rm petro,50}$, is plotted as a function of $V_{\rm rot}$ in the lower panel of Fig. 9. Higher values of $r_{\rm petro,90}/r_{\rm petro,50}$ correspond to bulge-dominated systems ($r_{\rm petro,90}/r_{\rm petro,50}=3.35$ for a de Vaucouleurs model; 2.29 for an exponential disk). Except for UGC 4599, all of the HIghMass galaxies can be categorized as disk systems. However, in comparison with the parent sample, the overall lower concentration indexes of the HIghMass galaxies at fixed $V_{\rm rot}$ is insignificant but rather results from the very large scatter in the concentration index vs. $V_{\rm rot}$ relation.

In summary, the moderate to high current SFRs of the HIghMass galaxies, together with their overall higher EWs, SSFRs, and $b$-parameters support the idea that SF in them has been suppressed in the past, but that they are undergoing an active period of disk growth at the current epoch. This evolutionary state is predicted to be the typical behavior of galaxies residing in high $\lambda$ DM halos by semi-analytical models (e.g., Boissier & Prantzos, 2000). And/Or, the HIghMass galaxies appear to have been forming the bulk of their stars at later times, possibly as triggered by gas infall events. Future work will explore evidence for gas infall in the HI synthesis maps and better determine the SFH via NIR photometry from warm-Spitzer.

Among the various forms of applicable SFLs, the most commonly studied is the empirical K-S relation which attempts to describe how the SFR surface density $\Sigma_{\rm SFR}$ is regulated by the gas surface density, e.g., $\Sigma_{\rm SFR}\propto\Sigma_{\rm HI+H_{2}}^{\alpha}$, where the exponent is determined globally to be $\alpha=1.4\pm 0.15$ in Kennicutt (1998). By definition, K-S relation gives the surface density of SF efficiency, $\Sigma_{\rm SFE}\equiv\Sigma_{\rm SFR}/\Sigma_{\rm gas}\propto\Sigma_{\rm gas}^{\alpha-1}$, and the reciprocal of the SFE is the SF timescale. Within the optical disk where H₂ dominates, it has been established that the $\Sigma_{\rm SFR}$ correlates better with the $\Sigma_{\rm H_{2}}$ than with the total gas density (Leroy et al., 2008; Bigiel et al., 2008), indicating that SF occurs exclusively in the molecular phase of the ISM. In spirals, the $\Sigma_{\rm SFE}$ of H₂ alone is nearly constant with an H₂ depletion time of $\sim$2 Gyr (Leroy et al., 2008; Bigiel et al., 2011; Schruba et al., 2011), i.e., $\alpha=1$ at a resolution of $\sim$kpc. Controversial results are found in low-metallicity dwarf galaxies and in the outer parts of large spirals, where the ISM is mostly atomic. The HI-based $\Sigma_{\rm SFE}$ is much smaller, with a SF timescale of $\sim$100 Gyr and, in systems where HI dominates, the K-S relation is likely to have a distinct form, e.g., $\Sigma_{\rm SFR}$ also begins to correlate with the $\Sigma_{\rm HI}$ (Bigiel et al., 2010; Krumholz, 2013).

In the current work, we only inspect the global HI-based SFE ($\equiv{\rm SFR}/M_{\rm HI}$) and the corresponding gas depletion timescale $t_{R}\equiv{\rm SFE^{-1}}$. The distribution of $t_{R}$ is known to be broad, ranging from 0.3 Gyr (on the scale of starbursts) to 100 Gyr (many times the Hubble time, $t_{H}=13.6$ Gyr). Huang et al. (2012b) have already shown that as an HI-selected sample, the ALFALFA galaxies have overall lower SFEs, or equivalently longer $\langle t_{R}\rangle=8.9$ Gyr, relative to an optically-selected sample. The bottom panel of Fig. 8 shows the distributions of HIghMass galaxies and the ALFALFA parent sample on an SFE vs. $V_{\rm rot}$ diagram. The horizontal dash-dotted line in green corresponds to $t_{R}=t_{H}$; the cyan dashed line on top marks the average SFE derived from the GASS sample ($t_{R}=3$ Gyr, Schiminovich et al., 2010).

Contrary to the expectation that the high $f_{\rm HI}$ results from a low efficiency of SF in the HIghMass galaxies, their HI-based SFEs are moderate relative to the parent ALFALFA sample (see Fig. 8). The median SFE is $10^{-9.83}$ yr^-1 ($t_{R}=6.8$ Gyr), which is slightly higher than the average of the ALFALFA population overall, but still lower than that of the stellar mass-selected GASS galaxies. The $t_{R}$ distribution is confirmed to be broad. However, except for the early-type UGC 4599 which has a $t_{R}$ comparable to the $\Sigma_{\rm SFE}$ obtained in spiral outer disks (100 Gyr), the global HI depletion timescales are not extremely long in comparison with the H₂ depletion time (2 Gyr), with 74% of the sample having $t_{R}<t_{H}$. The majority of the HIghMass galaxies with $t_{R}>t_{H}$ are in our list of LSB galaxies, including AGC 188749, AGC 190796, AGC 190277, UGC 8089, and UGC 9234, in support of the correlation between lower surface density and lower SFE.

The HIghMass galaxies have overall lower $\Sigma_{\rm SFR}$ and stellar surface densities, suggesting lower $\Sigma_{\rm gas}$ given the K-S relation. One may naively expect the HIghMass galaxies to have lower SFEs based on our understanding of the K-S relation. However, such a reasoning implicitly relies on several questionable assumptions. In the inner disks with higher levels of $\Sigma_{\rm SFR}$, H₂ can still be the dominant component of the ISM locally. The lower $\Sigma_{\rm SFE}$ caused by the lower $\Sigma_{\rm gas}$ is possible if the K-S relation is significantly super-linear with $\alpha>1$. This slope is highly debated due to the different background subtraction or the treatment of diffuse emission unrelated to SF. However, a number of authors obtained $\alpha$ value close to 1 (Leroy et al., 2008; Bigiel et al., 2011; Schruba et al., 2011), at least in the inner disk. The exact form of the K-S relation is less clear towards the outskirts, but the total $\Sigma_{\rm gas}$ there is not necessarily low for the HIghMass galaxies relative to the more normal spiral population. Despite the lower central surface density, disks formed in higher $\lambda$ halos have longer scale lengths so that the gas may be distributed in extended disks. In fact, except for a few cases with truncated $\Sigma_{\rm SFR}$ radial profiles, the star forming disks are traceable to large radii in most of the HIghMass galaxies. Finally, the inference of global properties such as the SFE according to the results derived from resolved samples which yield the K-S relation is subject to spatial averaging over a range of $\Sigma_{\rm gas}$, timescales and conditions within the ISM.

Although models predict that a lower SFE should lead to a higher gas fraction and vice versa (e.g., Bouché et al., 2010), the HIghMass galaxies with high $f_{\rm HI}$s do not have particularly low HI-based SFEs relative to the other galaxies. Given that the $M_{\rm H_{2}}$-to-$M_{\rm HI}$ ratios are lower than average, the H₂-based SFEs should be even higher than normal spirals. However, the global SFEs are still low in comparison with the $\Sigma_{\rm SFE}$ with the former set by the inefficient conversion of atomic to molecular gas in the far outer galaxy (Kennicutt & Evans, 2012). Future work will attempt to compare the properties of both HI and molecular distributions to probe further the K-S relation applicable in the HIghMass galaxies.

Both semi-analytical models and hydrodynamic simulations predict that the stellar disks in high $\lambda$ halos are formed to be less concentrated and more gas-rich (e.g., Mo et al., 1998; Boissier & Prantzos, 2000; Kim & Lee, 2013; Kravtsov, 2013). In support of this, the stellar disks of the HIghMass galaxies are confirmed to be extended with overall lower surface densities at fixed $M_{*}$. A quantitative angular momentum statistic, the “spin parameter” $\lambda$, can be expressed on terms of observable quantities as:

where $V_{\rm rot}$ is the rotational velocity as derived above, $r_{\rm d}$ is the scale length of the optical disk and $M_{\rm halo}$ is the mass of the associated DM halo (Hernandez & Cervantes-Sodi, 2006). We follow the same approach as in Huang et al. (2012b) to derive the empirical $\lambda$ distribution of host halos, adopting the $M_{\rm halo}$ derived from the $V_{\rm halo}-V_{\rm rot}$ relation given in Papastergis et al. (2011). Underlying assumptions include an exponential surface density profile of the optical disk, a flat disk rotation curve at $V_{\rm rot}$, an isothermal density profile of the halo (virialized), and that the potential energy of the galaxy is dominated by that of the halo. The last two assumptions are known to be unrealistic or highly uncertain, but are adopted for simplicity. Therefore, the relative $\lambda$ distributions are more indicative than the absolute values.

Although Hernandez et al. (2007) find that the $\lambda$ distribution of a disk galaxy sample selected from the SDSS is consistent with values derived from simulations, Huang et al. (2012b) have shown that the ALFALFA population overall shows a $\lambda$ distribution that is no longer lognormal and has a mean value well in excess of that predicted, implying that the HI-selected galaxies preferentially occupy DM halos of higher than average $\lambda$. In Fig. 10, we examine the statistical measures of $\lambda$ derived as above for the full HIghMass galaxies (solid line) superposed on a normalized distribution for the ALFALFA population overall (dashed line). The shaded area traces the subsets included in two of our HI synthesis imaging programs. All of the JVLA11 targets (shaded in red) are stellar massive disks ($M_{*}>10^{10}~M_{\odot}$), while the GMRT11 targets (shaded in cyan) all have $M_{*}<10^{10}~M_{\odot}$.

There is evidence that the HIghMass galaxies do indeed reside in DM halos characterized by higher than average values of $\lambda$, and the average $\lambda$ of the less stellar massive GMRT11 targets is similar to that of the JVLA11 ones. However, the significance of a departure from the rest of the ALFALFA population and possible dependence on other paramters such as $M_{*}$ or color is presently unclear, given the statistical uncertainties and small sample size. The HI synthesis maps will permit us to constrain the halo density profile. In fact, Hallenbeck et al. (2014) present UGC 12506 as a first case of a HIghMass galaxy whose spin parameter, derived from the fitting the HI velocity field, is truly high. Future work will use the halo density profiles derived from the HI maps to constrain the spin parameters of the HIghMass galaxies more directly.

It is well-known that the HI mass of disk galaxies can be depleted by interactions with environments of galaxies, especially via tidal or ram pressure stripping. Here, we examine whether or not the exceptionally gas-rich massive HI disks included in HIghMass are different from the rest of the HI-selected population. To quantify the environment we used a galaxy’s $n$th nearest neighbors as a metric. Using as the source catalog the SDSS DR7 spectroscopic catalog galaxies (Abazajian et al., 2009), the ten nearest neighbors of all of the high S/N ratio detections in the $\alpha$.40 sample were found. The catalogs were cut in R.A. and Dec., as well as redshift, such that the ALFALFA sample was volume-limited in the range 60-140 Mpc (within which 21 of the HIghMass galaxies fall), and the SDSS sample was volume-limited out to 165 Mpc, or equivalently an absolute r-band petrosian magnitude of $-$18.6. The search for neighbors then proceeded within an expanding spherical bubble (in the plane of the sky and in redshift distances), out to a limit of 45 Mpc. Finally a minimum separation of 10 arcsec was applied because such close neighbors are unlikely to be indicative of the surrounding environment and would not be distinguishable from the parent galaxy in ALFALFA survey anyway.

Measures of local galaxy density were estimated by averaging the logarithm of the 1st, 2nd, and 3rd nearest neighbor densities (similar to Baldry et al., 2006), and are plotted for the ALFALFA sample, the ALFALFA sample with stellar mass above $10^{10}~M_{\odot}$, and the HIghMass galaxies in Fig. 11. K-S tests comparing the distributions suggest that the high stellar mass sample is distinct from its parent ALFALFA sample (with a P-value of $1.1\times 10^{-16}$), with the high stellar mass galaxies typically avoiding regions of very low local density. The K-S tests for the HIghMass galaxies indicate that their environment is more similar to that of the high stellar mass galaxies (P-value of 0.71), than that of the average ALFALFA galaxy (P-value of 0.013). ALFALFA is naturally biased to blue galaxies which tend to be less clustered; Martin et al. (2012) have shown that the gas-rich galaxies detected by ALFALFA is the most weakly clustered population known. Thus, it may be surprising to conclude that the local environment of a HIghMass galaxy is not especially under dense, when compared with that of similarly stellar massive galaxies in ALFALFA. Much the same result is found when they are compared with other high HI mass galaxies within ALFALFA.