THE OPTICAL LUMINOSITY FUNCTION OF VOID GALAXIES IN THE SDSS AND ALFALFA SURVEYS

The SDSS (Fukugita et al. 1996; Gunn et al. 1998; Lupton et al. 2001; Strauss et al. 2002; Blanton et al. 2003) is a wide-field multifilter imaging and spectroscopic survey covering a quarter of the northern Galactic hemisphere in the five-band SDSS system: u, g, r, i, and z. Once each image is classified, follow-up spectroscopy is done on galaxies with r-band magnitude r < 17.77. Spectra obtained through the SDSS are taken using two double-fiber-fed spectrographs and fiber plug plates covering a portion of the sky 149 in radius with minimum fiber separation of 55 arcsec.

For the optical data in this work, we utilize the Korea Institute for Advanced Study Value-Added Galaxy Catalog (KIAS-VAGC) of Choi et al. (2010). The KIAS-VAGC catalog is based on the SDSS DR7 (Abazajian et al. 2009) spectroscopic targets in the main galaxy sample and contains 707,817 galaxies.

The ALFALFA Survey (Giovanelli et al. 2005a, 2005b) is a large-area, blind extragalactic H i survey with sensitivity limits allowing for the detection of galaxies with H i masses down to M_HI = 10⁸ M_⊙ out to 40 Mpc. The most recent release of the ALFALFA Survey (α.40; Haynes et al. 2011), covers ∼2800 deg² across two regions in the northern Galactic hemisphere, called the Spring Sky (07^h30^m < R.A. < 16^h30^m, 04° < decl. < 16° and 24° < decl. < 28°), and two in the southern Galactic Hemisphere, called the Fall Sky (22^h < R.A. < 03^h, 14° < decl. < 16° and 24° < decl. < 32°). The H i detections in this catalog are categorized as either Code 1, 2, or 9. Code 1 objects are reliable detections with high signal-to-noise ratio (S/N > 6.5); Code 2 objects have S/N < 6.5 and coincide with optical counterparts with known redshift similar to the H i detected redshift; and Code 9 objects are high-velocity clouds.

To obtain the optical properties of the H i sources, we use the cross-reference catalog of 12,468 ALFALFA H i sources with the most probable optical counterpart from the SDSS DR7 supplied by Haynes et al. (2011). Because we are interested in each galaxy's environment, we must limit our sample to objects found in the region accessible to the DR7 void catalog of Pan et al. (2012), the NGC region. We limit our sample to Code 1 detections within z ≤ 0.05 because of radio frequency interference beyond this redshift range.

For our detections, we query the SDSS DR7 database to obtain all information needed for the analysis in this work, such as color, ICI, absolute magnitude, and surface brightness. Because we compare optically selected galaxy LFs to H i selected galaxy LFs, we must remain consistent in how we determine absolute magnitudes, M_r. Therefore, we K-correct the magnitudes and band-shift each H i source's M_r to z = 0.1 using K-correct version 4.4 (Blanton & Roweis 2007), as done in the KIAS-VAGC. Because not all ALFALFA detections have optical spectroscopy, we adopt the 21 cm redshift for determining each galaxy's comoving distance and r-band absolute magnitude. Approximately 200 of ∼7000 of the galaxies in the ALFALFA sample are matched to SDSS galaxies for which SDSS spectra were not taken. The differences between optical and H i redshifts are typically less than 50 kpc s⁻¹. Only a handful of galaxies have H i-to-optical redshift differences in the range 50–200 kpc s⁻¹. These differences are consistent with the velocity widths of ${M}^{*}$ galaxies, so the effect on the faint-end slope of the LF will be negligible.

We classify all of our galaxies as void or wall detections by comparing the comoving coordinates of each to the void catalog of Pan et al. (2012). This void catalog uses the galaxy-based void-finding algorithm of Hoyle & Vogeley (2002), VoidFinder (also see El-Ad & Piran 1997). We briefly discuss the algorithm here. In a map of SDSS DR7 galaxies with M_r < −20.1 in the northern Galactic hemisphere, we calculate each galaxy's third-nearest neighbor. If the third-nearest neighbor is at least 7 h⁻¹ Mpc away, the galaxy is removed from the map and is considered a "potential void galaxy." Once all "potential void galaxies" have been removed, VoidFinder grows spheres in the empty regions of the map. If a sphere has a minimum radius of 10 h⁻¹ Mpc and lies completely within the survey mask, it is considered a true void. We then place the "potential void galaxies" back into the map. If these "potential void galaxies" lie within one of the true void spheres, we classify it as a "void galaxy"; otherwise, we classify it as a "wall galaxy." We compare the locations of all of our galaxies against the locations of the void spheres. If a galaxy lies within a large-scale void in this catalog, we classify the galaxy as a "void galaxy"; otherwise, we classify the galaxy as a "wall galaxy." The void catalog contains 1054 voids, the largest of which are ∼30 h⁻¹ Mpc in effective radius. The median effective radius of all voids within the catalog is ∼17 h⁻¹ Mpc. See Pan et al. (2012) for further details regarding the statistical properties of the voids in SDSS DR7. Because we require each sphere to lie completely within the mask, we risk misclassifying true void galaxies along the edges as wall galaxies. From the optically selected sample, we identify 75,063 (21%) void galaxies and 274,436 (77%) wall galaxies within z < 0.107. The remaining galaxies (2%) lie along the survey edges and are excluded because of the potential misclassification issues.

Similarly, for the H i selected sample, we positionally compare each H i detection's comoving coordinates to the void catalog. We identify 2611 (35%) void detections, 4566 (60%) wall detections, and 390 (5%) detections located near the survey edges.

For the sake of comparing the effects of the selection biases between the SDSS and ALFALFA samples, we make an optically selected subsample that we call SDSS_nearby. For SDSS_nearby, we limit ourselves to galaxies within z < 0.05. We further limit the sample to galaxies within 07^h30^m < R.A. < 16^h30^m, 04° < decl. < 16° and 24° < decl. < 28°, to ensure we only use galaxies within the same volume as our ALFALFA sample. We compare the magnitude-limited (r < 17.6) SDSS_nearby galaxy locations to the void catalog of Pan et al. (2012). We identify 7058 (25%) void galaxies, 20,148 (73%) wall galaxies, and 537 (2%) galaxies living near the survey edges. The reader should keep in mind that a "void" sample from an H i survey and a "void" sample obtained from an optical survey contain fundamentally different galaxies.

Previous studies on the types of galaxies typically found by blind H i surveys reveal late-type, mostly blue galaxies with high star-formation rates and specific star-formation rates (Toribio & Solanes 2009). Huang et al. (2012) provide an in-depth comparison of optically and H i selected samples and show that galaxies detected in H i tend to have low star-formation efficiencies. Here we briefly compare the environmental differences of an H i selected sample from the ALFALFA Survey and an optically selected sample from the SDSS catalog covering the same volume of sky (SDSS_nearby).

In Figure 1 we compare the optical u−r color distribution of SDSS_nearby (upper) and ALFALFA (lower) galaxies. We obtain galaxy colors using SDSS model magnitudes. The feature that is most evident is the deficiency of red galaxies in the ALFALFA sample compared to the SDSS sample. The void and wall SDSS color distributions are bimodal with the second peak appearing as a result of the highly populated red sequence, whereas the H i color distributions are unimodal with only a slight presence of the red sequence in the ALFALFA wall sample. While a majority of the ALFALFA detections are blue, we notice the void population on average tends to be bluer than the wall population. Hoyle et al. (2012) notice a similar trend toward bluer colors in the SDSS void sample. In both survey samples, we notice significantly fewer red galaxies in the void populations than those in walls.

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In Figure 2 we present the r-band absolute magnitude distributions of the SDSS_nearby (upper) and ALFALFA (lower) samples. As shown in Hoyle et al. (2012), we see a shift toward fainter magnitudes in the SDSS void sample. The H i void galaxy sample detects relatively more dwarf galaxies than does the optically selected sample. This is because the SDSS spectroscopic main galaxy sample is biased against faint, low-surface-brightness patchy galaxies, which are more easily detectable in an H i survey. Because of the relative abundance of dwarf galaxies in the H i sample, we suspect that the LF of ALFALFA galaxies will have a much steeper slope than the optically selected sample. We also see that the H i selected wall galaxies are slightly brighter than the typical optically selected wall galaxies on average. A typical galaxy in a wall will experience gas stripping phenomena (tidal stripping, mergers, ram pressure stripping, and so on), thereby reducing the H i fraction of its baryonic content. This reduced H i fraction will contain just enough H i to be detected by a radio survey for only the largest or brightest galaxies in the walls. We suspect that the shift toward brighter galaxies in the mean of the distribution of the ALFALFA wall sample compared to the SDSS_nearby wall sample will result in the ALFALFA wall LF having a somewhat brighter characteristic magnitude than that of SDSS_nearby.

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As galaxies evolve, they are thought to move from the blue cloud to the red sequence after star formation has been quenched. Galaxies in voids are typically less evolved—and, therefore, fainter and more gaseous—than similar-sized galaxies in walls. This makes void galaxies easy targets for radio surveys. As we will show later in Section 4.3.1, ALFALFA prefers less-evolved galaxies, regardless of environment.

The LF is a measure of the number of galaxies per Mpc³ in a magnitude range dM_r centered at magnitude M_r. For each measurement of the LF, we find the best-fit parameters of a Schechter (1976) function of the form

$$\begin{eqnarray}{\rm{\Phi }}({M}_{r}) & = & 0.4\mathrm{ln}10{{\rm{\Phi }}}^{*}{10}^{0.4({M}^{*}-{M}_{r})(\alpha +1)}\\ & & \times \mathrm{exp}(-{10}^{0.4({M}^{*}-{M}_{r})}).\end{eqnarray} \tag{ 1 }$$

We estimate the LF of our SDSS and ALFALFA void and wall samples using the SWML method of Efstathiou et al. (1988). For details on how we apply the method, see Moorman et al. (2014), in which we detail the two-dimensional version of the SWML. The SWML method does not retain information about the normalization of the LF; therefore, we adjust the amplitude according to the number density of the particular sample of interest. For each sample, the wall volume is estimated by taking the difference between the total volume of interest and the volume of the voids within. We estimate the best-fit Schechter parameters (the normalization factor ${\rm{\Phi }}*$, the characteristic magnitude ${M}^{*}$, and the faint-end slope α) to our functions over the magnitude range −22.0 < M_r < −13.0 using a least-squares estimator.

We estimate errors for each optical LF from three sources. The first source is Poisson error, which accounts for ∼70% of the uncertainties in each bin. These errors affect the brightest and faintest ends more so than the intermediate-magnitude bins because we have less information in the outermost bins. That is, extremely bright galaxies are uncommon in the universe, and the faintest galaxies are difficult to detect beyond the very nearby universe.

The second source is the error in each bin introduced from the SWML method, described in Efstathiou et al. (1988). These errors account for about 30% of the total bin uncertainties. As with the Poisson errors, we have less information about the galaxy distribution in the brightest and faintest bins, making the uncertainties larger in these bins.

The third source is an error estimate accounting for the inhomogeneity of large-scale structure, using the jackknife method of Efron (1982). For this source of error, we divide our region of interest into 18 subregions and calculate the LF of the galaxy sample, excluding one of the 18 regions for each iteration. We estimate the variance in each bin after all iterations. The jackknife errors account for less than 1% of the total error. This suggests that the SWML method is relatively robust against large-scale structure.

We calculate the LF of our SDSS void and wall galaxies down to M_r ∼ −13 using the methods outlined in Section 3. In Figure 3, we present our estimates of the void (red) and wall (black) galaxy LFs with the best-fitting Schechter functions. The parameters associated with the best-fit Schechter functions are $\mathrm{log}{{\rm{\Phi }}}^{*}=-3.40\pm 0.03$ log(Mpc⁻³), ${M}^{*}$ = −19.88 ± 0.05, and α = −1.20 ± 0.02 for void galaxies, and $\mathrm{log}{{\rm{\Phi }}}^{*}=-2.86\pm 0.02$ log(Mpc⁻³), ${M}^{*}$ = −20.80 ± 0.03, and α = −1.16 ± 0.01 for wall galaxies. An explanation of uncertainties may be found in Section 3.2. Much like the void and wall LF results found using a previous partial data release of the SDSS (Hoyle et al. 2005), we find about a one-magnitude shift in ${M}^{*}$ toward fainter galaxies in voids. It is obvious from Figure 3 that the faint-end slopes of both the void and wall LFs are underestimated. For a more accurate estimation of the faint-end slopes, we fit a power law to the LF values fainter than M_r = −18. These power-law slopes correspond to a slope of α = −1.25 ± 0.02 for void galaxies and α = −1.27 ± 0.02 for wall galaxies. There is no statistically significant difference between the slopes of the void and wall LFs down to M_r ∼ −13, indicating that there is no relative excess of void dwarfs compared to the wall distribution. This faint-end slope result is consistent with the predictions of Cui et al. (2011), whose simulations show that the faint ends of the LF should remain the same between the most underdense and overdense regions. This conflicts with the predictions of Mathis & White (2002), although these authors neglect SNe feedback and background UV radiation, which should be included when calculating the infall rate of cold gas for low-mass halos. The faint end of the void and wall LFs starts to stray from a classic Schechter function once we reach the dwarf regime (M_r > −17). This variation does not appear in the analysis of Tempel et al. (2011) because the authors exclude galaxies fainter than M_r = −17. Excluding these dwarf galaxies from our analysis, we find a faint-end slope that closely matches that of Tempel et al. (2011).

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We notice a feature at the bright end (M_r = −20.1) of both the void and wall LFs: the void LF drops in amplitude, while the wall LF increases in amplitude. These features are an artifact of the void identification process. The void catalog is defined by a volume-limited sample corresponding to galaxies with M_r < −20.1. By defining the void catalog using galaxies brighter than this magnitude, we will see a significant decrease in the number of bright (M_r < −20.1) void galaxies and an increase in the number of bright wall galaxies.

4.1.1. Comparing to Previous Observations and Simulations

As mentioned earlier, the predicted halo mass function has a steep slope of α = −1.8, whereas the observed LFs (estimated here and in other works) have much shallower slopes of α ∼ −1.2 to −1.3. Blanton et al. (2005) show that the faint end of the LF can be steepened to α ∼ −1.5 with the inclusion of low-luminosity/low-surface-brightness galaxies. To avoid the optical selection bias against low-surface-brightness galaxies, we estimate the optical LF of a sample of H i selected galaxies from the ALFALFA sample.

We divide the ALFALFA galaxy sample into void and wall galaxies and estimate the r-band LF presented in Figure 4. It is clear from the figure that the H i selected LFs are not well fit by a simple Schechter function, but for the sake of comparison between the LFs in this work and others, we provide the best-fitting parameters to a Schechter function found using a least-squares estimator. For the void sample, we estimate the best-fitting Schechter parameters to be $\mathrm{log}{{\rm{\Phi }}}^{*}=-4.43\pm 0.09$ log(Mpc⁻³), ${M}^{*}$ = −20.74 ± 0.18, and α = −1.20 ± 0.05. For the wall galaxy sample, we estimate $\mathrm{log}{{\rm{\Phi }}}^{*}=-3.71\pm 0.04$ log(Mpc⁻³), ${M}^{*}$ = −20.77 ± 0.09, and α = −0.84 ± 0.05. See Section 3.2 for an explanation of uncertainties. The curves in Figure 4 show the Schechter functions associated with these best-fit parameters; however, the Schechter fits underestimate both the bright and faint ends of the ALFALFA LFs.

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At the bright end, the best-fit Schechter function predicts the characteristic magnitudes of both the void and wall samples to be too bright. To get a realistic sense of the shift in ${M}^{*}$ between voids and walls, we fit only the bright end (−22 ≤ M_r ≤ −18) of the LFs, revealing a shift in ${M}^{*}$ toward fainter magnitudes in voids by about one-half of a magnitude (see the left panel of Figure 5). The direction of this shift is consistent with the shift in the dark matter halo mass function of the extended Press–Schechter theory (Goldberg et al. 2005). The magnitude of the shift is significantly less than the shift in the predicted halo mass function, as well as the shift in ${M}^{*}$ of the SDSS LF found in the previous section. The reason for this smaller shift is that typically the brightest galaxies in denser regions have burnt through their cool gas, lost their gas during mergers, or had it stripped away via tidal stripping, ram pressure stripping, and so on. Therefore, a survey looking for cool neutral gas will detect the brightest galaxies within denser regions far less frequently than will an optically selected sample. While an optically selected spectroscopic sample may be biased against faint, low-surface-brightness galaxies, an H i selected sample is biased against massive, red galaxies.

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At the faint end, the best-fitting Schechter function also severely underestimates the faint-end slopes of the void and wall LFs, estimating a much shallower slope than actually observed. To more accurately determine the faint-end slopes, we fit a power-law function to only the faint ends (−18 < M_r ≤ −13) of the LFs. The new faint-end slopes of the H i selected LFs (shown in the right panel of Figure 5) are α = −1.49 ± 0.03 for voids and α = −1.52 ± 0.05 for walls. We see no statistically significant difference in the faint-end slopes of the void and wall LFs. The faint-end slopes of the ALFALFA void and wall LFs appear to be independent of the large-scale environment. We suspect this is largely due to the relatively large number of late-type galaxies (which generally dominate the faint end of the LF) present in the ALFALFA sample compared to massive, elliptical galaxies. Tempel et al. (2011) find that the LF of spiral galaxies is independent of environment, while the faint-end slope of the observed elliptical galaxy LF steepens with increasing large-scale densities.

To more directly compare the void and wall distributions of the H i and optically selected samples, we need to compute the optical LF of SDSS and ALFALFA galaxies over the same volume of sky. Therefore, we measure the LF of the SDSS_nearby sample and estimate its characteristic magnitude and faint-end slope in the following way. For each sample (SDSS, SDSS_nearby, and ALFALFA), we split each LF into bright and faint ends, divided at M_r = −18. The bright end is fit with a Schechter function, from which we obtain the sample's characteristic magnitude, ${M}^{*}$. Each faint end is separately fit with a power law, from which we obtain the faint-end slope of each LF. We provide these fits to the data in Table 1. Note that the ${M}^{*}$ and α parameters in the table are not the same related parameters estimated in Equation (1).

Table 1.  Separately Fit Bright and Faint Ends

Sample	LSS	${M}_{r}^{*}$	α
SDSS	void	−19.32 ± 0.03	−1.25 ± 0.02
SDSS	wall	−20.54 ± 0.02	−1.27 ± 0.02
SDSSnearby	void	−19.30 ± 0.06	−1.31 ± 0.04
SDSSnearby	wall	−20.55 ± 0.03	−1.23 ± 0.03
ALFALFA	void	−19.95 ± 0.07	−1.49 ± 0.03
ALFALFA	wall	−20.49 ± 0.04	−1.52 ± 0.05

Notes. Best-fit power law and Schechter function parameters to the optical LFs of the SDSS and ALFALFA samples across environments. Each LF was split into a bright end and faint end, separated at M_r = −18. Each bright end was fit by a Schechter function; from this function, we extract the characteristic magnitude parameter, ${M}_{r}^{*}$. Each faint end (M_r > −18) was fit by a power-law function. From this fit, we extract the faint-end slope parameter, α.

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Two interesting comparisons arise from this table. The first comes from comparing the full SDSS and SDSS_nearby fits, which gives us information on how the selected volume affects the shape of the LF. We find it interesting that reducing the area and redshift affects the void faint-end slope. The faint-end slopes of the full SDSS sample are more accurate because we are averaging over more structure. The large-scale structure within the nearby volume may be atypical of the full universe. The second comparison worth making is between the ALFALFA and SDSS_nearby fits, which gives us information on how sample selection affects the shape of the LF. We see that using an H i selected sample produces a much steeper faint-end slope than does an optically selected sample. This is due mostly to the inclusion of extremely low luminosity galaxies in H i surveys. The SDSS photometry affects the main galaxy sample target selection. The selection process is biased against low-surface-brightness galaxies, so these faint galaxies are excluded from our optical sample. (Refer to Figure 2 for a comparison of the M_r distributions of the two samples.) The power-law fits to the faint-end slopes match closely those shown in Blanton et al. (2005), who investigate the effects of extremely low luminosity galaxies on the faint-end slope of the galaxy LF. Again, these authors find that the slopes increase from α = −1.3 to α = −1.5 when adjusting for the incompleteness of the SDSS spectroscopic sample at low surface brightnesses.

In Figure 6, we present the global LF of the Spring Sky subsample of the α.40 data set, as well as that of the SDSS_nearby sample. We see in this figure, as well as in the previous subsection, that the optical LF of H i selected galaxies has a clearly different shape than that of the optically selected galaxies. The optically selected LF is reasonably well fit by a Schechter function with estimated parameters $\mathrm{log}{{\rm{\Phi }}}^{*}=-3.69\pm 0.03$ log(Mpc⁻³), ${M}^{*}$ = −20.75 ± 0.05, and α = −1.21 ± 0.02. It is clear from the figure that the H i selected global LF is not fit well by a Schechter function. The best-fit Schechter parameters are $\mathrm{log}{{\rm{\Phi }}}^{*}=-4.21\pm 0.05$ log(Mpc⁻³), ${M}^{*}$ = −21.11 ± 0.11, and α = −1.10 ± 0.03. One of the most notable aspects of the H i selected LF is a broad, dip-like feature around M_r = −18, followed by a sharp upturn at fainter magnitudes. Evidence of a similar dip and upturn is seen in Zwaan et al. (2001) in the LF of H i selected galaxies from the AHISS, though the authors only use a sample of 60 H i sources and attribute the features of the faint-end slope to low-number statistics. For the first time, we show statistically significant evidence for a population of LSB dwarf galaxies present in the H i selected optical galaxy LF.

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We suspect that the wide dip present in the ALFALFA LF is the result of a linear combination of different types of optically selected galaxies, that is, dwarfy starbursting galaxies at the faint end and gas-rich spirals at the bright end. In the next section, we will investigate different combinations of optically selected galaxies that may produce similar features and further split the H i sample to see which properties of the galaxies may be causing these features. Additionally, we wish to note that Papastergis et al. (2012) see a similar, albeit much shallower, dip feature in the baryonic mass function of ALFALFA galaxies. While these two phenomena may be related, it does not explain the severity of the dip seen in the ALFALFA galaxy LF.

Following the previous subsection, we fit the bright and faint ends separately with a Schechter function and power law, respectively. Again, the bright/faint division takes place at M_r = −18, where we see the dip-like feature. The characteristic magnitude of the H i selected sample brighter than M_r = −18 is ${M}^{*}$ = −20.48 ± 0.04. The faint-end slope, estimated via a power-law fit to the LF fainter than M_r = −18, is α = −1.47 ± 0.02. As mentioned above, the dramatic steepening of the faint-end slope of the H i selected LF is most likely due to the inclusion of extremely low luminosity/LSB galaxies (Blanton et al. 2005). Figure 7 shows the presence of a population of LSB galaxies in our ALFALFA sample that do not appear in the spectroscopic SDSS sample. The SDSS spectroscopic sample is biased against these very faint galaxies, so we do not see such a drastic upturn of the optically selected LF. Zwaan et al. (2001) find that gaseous LSB galaxies make up only 5 ± 2% of the luminosity density, suggesting that there should not be low-surface-brightness effects from an H i survey, but these galaxies dominate the shape of the LF at the very faint end, steepening the slope by ${\rm{\Delta }}\alpha$ ∼ 0.26.

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4.3.1. Subsets of the Optically Selected LF

Given the dramatic differences in the overall shapes of the ALFALFA and SDSS_nearby LFs, we would like to determine if the unique shape of the ALFALFA LF is reproducible using a combination of populations from the SDSS_nearby sample. Knowing that most galaxies in an H i survey tend to be blue, late-type galaxies, we first split the SDSS_nearby sample into blue and red galaxies using the color cut from Moorman et al. (2014): $u-r=-0.09{M}_{r}+0.46$, where M_r is an object's r-band absolute magnitude. We consider a galaxy with $u-r$ color less than the value given by the equation to be blue; otherwise the galaxy is considered red. Our resulting subsamples contain 16,548 blue galaxies and 11,147 red galaxies. We estimate the LF of blue and red samples, and surprisingly, we find that the red galaxy LF produces a dip similar to, albeit much shallower than, that of the ALFALFA sample. See Figure 8 for the LFs of optically selected blue and red galaxies.

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Suspecting that the red sample is composed of both large elliptical galaxies and edge-on spirals reddened by dust, we split the SDSS_nearby red sample into two categories of morphological type. We make morphological cuts based on a galaxy's ICI, which is shown to be correlated with morphological type (Shimasaku et al. 2001). The ICI is defined to be ${c}_{\mathrm{in}}={R}_{50}/{R}_{90}$, where R₅₀ and R₉₀ are the radii containing 50% and 90% of the integrated Petrosian flux of a galaxy. In Figure 9 we present the normalized distribution of each sample's color versus morphological type via the galaxies' inverse concentration indices. It is clear from the figure that ALFALFA tends to detect fewer more-evolved galaxies than does SDSS, regardless of environment. Within the SDSS_nearby sample, it appears that the void galaxies span the range of inverse concentration indices of ICI = 0.2–0.6, whereas the wall galaxies are primarily early-type galaxies (ICI < 0.42).

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From the SDSS_nearby sample, we have 8127 red elliptical galaxies and 3020 reddened spiral galaxies. As expected, we see in Figure 10 that splitting the red sample by ICI produces two distinct functions. The early-type galaxies have a relatively flat distribution with a small dip-like feature present around M_r = −18, while the late-type galaxies are well fit by a Schechter function with a faint-end slope similar to that of the global SDSS sample. The red, late-type galaxy LF has a characteristic magnitude similar to the blue galaxy LF, but it has a shallower slope. Zwaan et al. (2001) show that their H i selected LF closely matches that of late-type galaxies found in optical surveys. We find that this is not the case for the ALFALFA LF because of the significant population of massive gas-rich galaxies mentioned in Huang et al. (2012). See Figure 11 comparing the ALFALFA LF and the SDSS_nearby late-type galaxy LF.

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4.3.2. Subsets of the H i Selected LF

No known H i selection effects could be responsible for producing such a wide dip in the galaxy LF. In attempts to directly determine what populations of galaxies could be influencing the shape of the H i selected optical LF, we divide the ALFALFA sample by color into red (1376) and blue (6234) galaxies and compute the LFs. As shown in Figure 12, the dip in the LF remains present in the H i selected red galaxy sample, and we see a much less prevalent inflection at the same magnitude for the H i selected blue galaxy sample. Splitting the red and blue distributions by morphological type, based on ICI, does not reveal the origin of the dip feature present in the ALFALFA LF. That is, no subsample of ALFALFA galaxies removes the dip feature from the LF.

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