In the paper [Elyiv A.A., Karachentsev I.D., Karachentseva V.E., Melnyk, O.V., Makarov D.I. 2013, Astrophysical Bulletin, 68, 1] we have realized one of the algorithms for void identification. For the analysis we used a sample of 10 502 galaxies with radial velocities below 3500 km/s (<48 Mpc). The sample selected from HyperLeda and NED databases and includes both the northern and southern hemispheres, except for the low galactic latitudes | b | < 15◦. In order to have the same conditions for the void identification both in the near and far regions of volume, we have excluded from the analysis the dwarf galaxies with absolute magnitudes fainter than MK = −18.4. This threshold is roughly equivalent to the luminosity of the Small Magellanic Cloud-type dwarfs. The distribution of 7596 bright galaxies with VLG = 0–3500 km/s in equatorial coordinates you can see on map Fig.1.
We calculated Cartesian equatorial coordinates X, Y, Z for each of the 7596 galaxies. In the sample volume we searched for a sphere with maximum radius R, which does not contain galaxies. For this purpose, we scanned all volume with step 1.5 Mpc as a compromise between the accuracy and required machine time. The boundary condition was following, the center of the empty sphere could not be located in the cone of the Milky Way |b| < 15◦ and not further then 48 Mpc from the observer. Next, the limiting conditions were supplemented with a new constraint: the center of the sphere has to be located outside the volume, occupied by all the previous spheres. This procedure was repeated until the radius of the smallest void has reached R = 6 Mpc. The result is a collection of 179 empty spherical volumes with the radii from 12 to 6 Mpc. Some of them partially overlap each other and form complicate structures like “dumbbells”, a “boomerangs” and “strings”. The slices of volume from X=-48 Mpc to +48 you can see in final_faint.gif. Dark and green zones are voids and galactic cone. Black and red dots are bright galaxies with luminosity above threshold and faint galaxies, respectively.
Such method includes a few free parameters. One of them is the minimum distance of the void center to the boundaries of the volume, as well as the minimum distance between the centers of the voids. Another parameter is the threshold absolute magnitude of the dwarf galaxies (MK = −18.4), the possible presence of which in the empty volume is ignored. The third parameter is the minimum radius of the spherical void (in our case Rmin = 6.0 Mpc), which limits the algorithm proceeding.
Large voids which consist with overlapped empty spheres form three groups of hypervoids: HV1, HV2 and HV3 with 56, 22 and 5 spherical voids, respectively. Some parameters of these hypervoids: the total volume, the minimum and maximum distance to hypervoid surface, the distance to the centroid of the hypervoid and its position in the sky are listed in Table 1 below.
The largest HV1 hypervoid, starting from the Local Group in the Hercules–Aquila region, reaches the boundary of the considered volume and, passes round the Local Volume in a horseshoe shape. The horseshoe shape of the low-density regions, covering the Virgo cluster is clearly visible in Fig. 6 of Courtois et al. [H. M. Courtois, Y. Hoffman, R. B. Tully, and S. Gottloeber, ApJ, 744, 43 (2012).].
Three diagrams below (XY_virgo_larger.jpg, YZ_virgo_larger.jpg, XY_virgo_larger.jpg) show the HV1 in more details in three projections with respect to the super-galactic plane. Since the hypervoid has a complex structure, we show it from the direction of negative and positive axes perpendicular to the considered plane, in the left and right panels of the figure, respectively. The distances to the particular plane are characterized by the scale under the figure. The upper, middle and bottom panels show the projection on the SGX–SGY, SGX–SGZ, SGY–SGZ planes, respectively. Concentric circles have an increment of 10 Mpc. In the SGX–SGZ and SGY–SGZ projections we can clearly see that the hypervoid envelopes the Local Group.
Summing up the volume of voids presented in Table 1, we deduce that they occupy about 30% of the considered volume of the Local Universe within 40 Mpc. This estimation takes into account the fact that the spherical voids belonging to hypervoids overlap.
Searching for nearby voids we have excluded from consideration 2906 dwarf galaxies. If this population was homogeneously distributed in the volume of the Local Universe, the expected number of dwarf galaxies in the voids would amount to about 1000. Their real number in voids is 48 which not reach even a 10% of expected number. This means that the empty volumes, devoid of galaxies with normal luminosity remain almost empty when considering the dwarf galaxies as well.
Founded voids contain 48 late-type dwarf galaxies with absolute magnitudes in the range of MB = [−13.0, −16.7]. These galaxies have active star formations and gas reserves per luminosity unit by about 2–3 times higher than those in the dwarf galaxies of the same type, located in denser environments.
We have defined the contours of the nearby voids and identified the dwarf population there in the space of radial velocities. The presence of collective motions of galaxies with the amplitudes of 300 km/s can lead to significant distortion of void shapes and the global pattern of their distribution. Obviously, this situation will gradually become clearer as more and more individual distances of galaxies will be obtained.
The full list of voids is available by the request via a contact form on our contacts page.