Anton Tikhonov / Saint-Petersburg State University

1. Anton Tikhonov /Saint-Petersburg State University Anatoly A. Klypin/New Mexico State University Properties of voids in the Local Volume and the Limit of appearance of a galaxy in DM halo The observational discovery ((Gregory & Thompson 1978; Joeveer et al. 1978; Kirshner et al. 1981) was soon followed by the theoretical understanding that voids constitute a natural outcome of structure formation via gravitational instability (Peebles 1982; Hoffman & Shaham 1982). Emptiness of voids: do we have a problem? Cosmological simulations predict many small DM halos in voids and it seems that observations are failing to find a substantial number of dwarf galaxies inside voids. Statistics of voids in catalogs of galaxies; formation of DM structures in voids; physics of galaxies in voids.

2. Description of the Local Volume galaxy sample In his Catalog and Atlas of Nearby Galaxies, Tully (1988) noted the presence in the Local Supercluster (LSC) that consists of number of intersecting filaments of the so-called Local void which begins directly from the boundaries of the Local Group and extends in the direction of North Pole of the LSC by ~ 20 Mpc. The Local void looks practically free from galaxies. Later, Karachentsev (1994) published an updated version of the LV list, which contained 226 galaxies with VLG < 500 km/s. Over the past few years, special searches for new nearby dwarf galaxies have been undertaken basing on the optical sky survey POSS-II/ESO/SERC, HI and infrared surveys of the zone of avoidance, ‘‘blind’’ sky surveys in the 21 cm line, HIPASS and HIJASS. At the present time, the sample of galaxies with distances less than 10 Mpc numbers about 550 galaxies. For half of them the distances have been measured to an accuracy as high as 8-10% (Karachentsev et al., 2004=Catalog of Neighboring Galaxies). Over the last 5 years, snapshot surveys with Hubble Space Telescope (HST ) have provided us with the TRGB distances for many nearby galaxies. The absence of the effect of “God's fingers”' in the Local Volume because of the virial motions of galaxies simplifies the analysis of the shape and orientation of nearby voids.

3. After recent systematic optical, IR, and HI surveys, the total number of known galaxies within 10 Mpc has increased from 179 to 550. About half this Local Volume (LV) sample is now been imaged with HST, yielding the galaxy distances with an accuracy of about 8%. For the majority of the LV galaxies we currently have H fluxes that allow us to reconstruct the star formation history of our neighbourhood. For the late-type LV galaxies their HI masses and angular momentum follow the linear relation in the range of 4 orders, which is expected for rotating gaseous disks being near the gravitational instability threshold. The data obtained on the LV galaxies imply important cosmological parameters, in particular, the mean local matter density and HI mass density, as well as SFR density. LV parameters important for cosmology. In spite from the presence of local voids, the average density of luminositywithin the radius of 8 Mpc around us exceeds 1.5 - 2.0 times the global luminosity density. Almost the same excess is also seen in the local HI massdensity. About 2/3 of the LV galaxies belong to the known virializedgroups like the LG. Because the average virial mass-to-luminosity ratio forthem is 40 Msun/Lsun, the mean local mass density within 8 Mpc turns out tobe 0.10 in units of the global critical density. This quantity is 2 - 3 times aslow as the global density of matter, Ωm = 0.27. To remove the discrepancybetween the global and local quantities of Ωm, we assume that the essentialamount of dark matter ( 70%) exists outside the virial radius of the groups. I.D. Karachentsev, 2007

5. 3D grid (to refer the nodes of this grid to this or that void). • Empty seed sphere of largest possible radius is identified. • Expansion of seed spheres by spheres with radius • Rsph > 0.9 Rseed • and with centers inside already • fixed part of a void. • Next seed sphere is determined. Process continues until Rseed > threshold. • Voids are thick enough throughout their volumes. • Voids are divided into lying completely inside boundaries • and voids touching when constructed the sample boundaries. 2D-case of point-like distribution. Seed circles and voids growing from them are shown. The numerals indicate the order of identification of voids Void detection algorithm

6. Distribution of six large minivoids within the LV-sphere of radius 7.5 Mpc. ¼ of Local Volume is occupied by Void N1 in Aquila. It is the front part of the Local (Tully) void

7. The peak in luminosity function, isolated galaxies. • Tidal Index TIi = max[ log(Mk/D3ik) ] + C • For every galaxy i, we found its main disturber, producing the highest tidal action or a maximum density enhancementΔρk ~ Mk/D3ik • Inside 8 Mpc around MW there are about 420 galaxies (known today). Galaxies in the peak (Babs~ -14) have morphological de Vaucouleur type 7-10 (dwarf Irregulars). Large M(HI)/Mtotal. Isolated galaxies with Babs ~ -14 have an order higher HI/LB and SFR/LB with the respect to galaxies in more dense environment. M25/L = 3.8 Msun/Lsun, total galaxy mass MT = 2.5 M25

9. Cumulative Void Functions (CVF) of galaxy and simulated samples. We look for the limit on halo circular velocity(Vcirc) that points on halos which generally do not contain galaxies. Simulations The simulations were done by A. Klypin (NMSU) using the Adaptive Refinement Tree (ART) code (Kravtsov, Klypin & Khokhlov, 1997). Spatially flat model with a cosmological constant – ΛCDM: 1) Ωm = 1 − ΩΛ = 0.3; σ8 = 0.9; h = 0.7 (WMAP1) 2) Ωm = 0.24; σ8 = 0.75; h = 0.73 (WMAP3) • The total mass of a halo depends on its radius which is difficult to define. More robust DM halo parameter is maximum “circular velocity”Vcirc = (GM/R)1/2. This is the quantity which is more meaningful observationally. Numerically Vcirc can be measured more easily and more accurately than mass. • 1. Box 160LG 16Mpc (wmap3) ART • 2. Box 80S 14Mpc (wmap1) mass resolution = 1.0×108 h-1 Msun ,complete for halos with Vcirc > 10 km/s Min. halo consists of 20 particles. • 3. Box 64Mpc (wmap3)constrained simulation, 10243 particles, GADGET2, mass resolution 1.6 107 h-1 Msun.

10. Cumulative void-function. CVF(R) = Vcumul (R)/ Vsample, Vcumul (R) - total volume of voids with Reff > R, Vsample- total volume of sample, Reff = (3Vvoid/4π)-1/3. We tried to fit observational CVF by that of ΛCDMsimulations changing limit on Vcirc of haloes that define voids. • SDSSgalaxies, Mr < -19.7 vs. • box120 Mpc, DM haloes, Vcirc > 150 km/s • LEDAgalaxies, MB < -16 vs. • box80 Mpc, DM haloes, Vcirc > 80 km/s Good agreement of CVF of distribution of galaxies above certain luminosity with distribution of simulated haloes with Vcirc above certain limit: ΛCDMis consistent withobservations with respect to voids.

11. Limit of galaxy appearance. • CVF of Local Volume sample 1. All galaxies in sphere 7.5Mpc. • 2. complete sample MB < -12 in sphere 8Mpc. • ΛCDM LV-candidates 8 Mpc sphere • Selection criteria: 1) no haloes with Mass > • 1013Msun inside sphere 8Mpc (no clusters in sample); • 2) sphere centered on halo with • 150 < Vcirc < 250 km/s (Milky Way analog). • 3) Overdensity criteria: In 7 Mpc of Local Volume • luminosty density in B-band = 2.72 108 Lsun/Mpc3 ; • luminosty density inK-band = 6.60 108 Lsun/Mpc3 . • Overdensity in LV: ρLV / ρmean =1.5-1.8. • Different overdensity ratioin model 8Mpc “LVs” • withrespect to mean density in simulated box • (wmap1 and wmap3) of halos with Vcirc>100km/s. • 4) σH of model Hubble flow should be • consistent with that of LV

12. Box64CR (wmap3) (Gustavo Yepes, Yehuda Hoffman, Stefan Gottloeber, Anatoly Klypin) CVF of 20 realizations of 8Mpc sphere from 64/h Mpc box with different limits on Vcirc of halos that define voids.ρ100 / ρmean=1.5-1.8. Mean CVF with rms. Voids in distribution of haloes with Vcirc > 35-40 km/s are the best fit of CVF of Local Volume galaxy distribution. Vcirc = 40 ± 5km/s – limit of appearance

13. Largest voids in 8Mpc-sphere. According to ΛCDM simulations totally empty front part of Tully void is probable. 10 realizations of 8Mpc-sphere CVF of Vcirc > 40km/s are plotted on CVFs of LV (M<-12 - complete sample (red)) and all LV-galaxy sample (blue)). There are voids in ΛCDM that comparable to the largest voids in LV if we consider entire LV sample.

14. Density profiles of haloes in voids Density profiles grows toward borders of voids – voids are physical. Here are density profiles of halo (Vcirc < 40 km/s) number density in shells 0.3Mpc thick inside 10 largest voids defined by haloes with Vcirc > 40 km/s in 20Mpc-sphere simulation. Profiles are not regular (not flat in deeper part of voids) - even bumps in inner part of voids possible. Rseed approximately defines thickness of voids.

15. Distribution of small haloes inside voids • We can see inside voids in distribution of voids defined by Vcirc > 40km/s haloes • totally empty regions. Here's the picture of slice of 4Mpc on Z around center of • biggest void ( Reff = 4.1Mpc, Rseed = 3.2Mpc ) in 20Mpc-sphere simulation • defined by haloes with Vcirc > 40 km/s. There are sufficient in volume holes at • least of haloes with Vcirc > 10km/s. • Vcirc vs. distance to void border of haloes with Vc < 45 that fall inside this void. • Haloes with Vcirc > 30 km/s are close to the void border.

16. Conclusion • ΛCDM is consistent with volume functions of voids in distribution of galaxies above some luminosity in a large luminosity range. There are significant (up to few Mpc) holes in ΛCDM that are free from haloes with Vcirc > 10km/s – any haloes of astronomical interest. • Voids in distribution of halos (wmap3 cosmplogy) with Vcirc > 40 ± 5 km/s reproduce Cumulative Void Function of Local Volume galaxy sample. We can treat this value as a ‘limit of appearance’ of a galaxy in a DM halo. • MB ~ -14 isolated galaxies (having Vcirc ~ 35-45 km/s) may be on the limit of appearance. Then the bump in Luminosity Function is natural. • Dark galaxies are probably located close to borders of voids. • According to ΛCDM large empty voids in Local Volume like front part of Tully Void are probable.