According to models of evolution in the hierarchical structure formation scenarios, voids of galaxies are expected to expand. The Local Void (LV) is the closest large void, and it provides a unique opportunity to test observationally such an expansion. It has been found that the Local Group, which is on the border of the LV, is running away from the void center at ~260 km/s. In this study we investigate the motion of the galaxies at the far-side border of the LV to examine the presence of a possible expansion. We selected late-type, edge-on spiral galaxies with radial velocities between 3000 km/s and 5000 km/s, and carried out HI 21 cm line and H-band imaging observations. The near-infrared Tully-Fisher relation was calibrated with a large sample of galaxies and carefully corrected for Malmquist bias. It was used to compute the distances and the peculiar velocities of the LV sample galaxies. Among the 36 sample LV galaxies with good quality HI line width measurements, only 15 galaxies were selected for measuring their distances and peculiar velocities, in order to avoid the effect of Malmquist bias. The average peculiar velocity of these 15 galaxies is found to be -419+208-251 km/s, which is not significantly different from zero. Due to the intrinsically large scatter of Tully-Fisher relation, we cannot conclude whether there is a systematic motion against the center of the LV for the galaxies at the far-side boundary of the void. However, our result is consistent with the hypothesis that those galaxies at the far-side boundary have an average velocity of ~260 km/s equivalent to what is found at the position of the Local Group.
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