The H i mass function and velocity width function of void galaxies in the Arecibo Legacy Fast ALFA Survey

We measure the HI mass function (HIMF) and velocity width function (WF) across environments over a range of masses, 7.2 < log (M-HI/M-circle dot) < 10.8, and profile widths, 1.3 log (km s(-1)) < log (W) < 2.9 log (km s(-1)), using a catalogue of similar to 7300 HI-selected galaxies from the Arecibo Legacy Fast ALFA (ALFALFA) Survey, located in the region of sky where ALFALFA and Sloan Digital Sky Survey(Data Release 7) North overlap. We divide our galaxy sample into those that reside in large-scale voids( void galaxies) and those that live in denser regions (wall galaxies). We find the voidHIMF to be well fitted by a Schechter function with normalization Phi* = (1.37 +/- 0.1) x 10(-2) y h(3) Mpc(-3), characteristic mass log(M-HI*/M-circle dot) + 2 log h(70) = 9.86 +/- 0.02, and low-mass-end slope alpha = -1.29 +/- 0.02. Similarly, for wall galaxies, we find best-fitting parameters Phi* = (1.82 +/- 0.03) x 10(-2) h(3) Mpc(-3), log(M-H I*/M-circle dot) + 2 log h(70) = 10.00 +/- 0.01, and alpha = -1.35 +/- 0.01. We conclude that void galaxiestypically have slightly lower HI masses than their non- voidcounterparts, which is in agreement with the dark matter (DM) halo mass functionshift in voidsassuming a simple relationship between DM mass and HI mass. We also find that the low-massslope of the voidHIMF is similar to that of the wall HIMF suggesting that there is either no excess of low-massgalaxies in voidsor there is an abundance of intermediate HI mass galaxies. We fit a modified Schechter function to the ALFALFA voidWF and determine its best-fitting parameters to be Phi* = 0.21 +/- 0.1 h(3) Mpc(-3), log (W*) = 2.13 +/- 0.3, alpha = 0.52 +/- 0.5, and high-width slope beta = 1.3 +/- 0.4. For wall galaxies, the WF parameters are Phi* = 0.022 +/- 0.009 h(3) Mpc(-3), log (W*)= 2.62 +/- 0.5, alpha= -0.64 +/- 0.2, and beta = 3.58 +/- 1.5. Because of large uncertainties on the voidand wall WFs, we cannot conclude whether the WF is dependent on the environment.