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Home All issues Volume 609 (January 2018) A&A, 609 (2018) A11 Full HTML
Open Access
Issue
A&A
Volume 609, January 2018
Article Number A11
Number of page(s) 12
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/201731645
Published online 22 December 2017

© ESO, 2017

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Any overdense region in the Universe is driven by the competition between its self-gravity and the cosmic expansion, and therefore can be characterized by an idealized zero-velocity surface that separates these zones. de Vaucouleurs (1958, 1964, 1972) presupposed systematic deviations from linearity in the velocity-distance relation and interpreted these deviations as a local phenomenon caused by the Virgo complex. The expected effect has only subsequently been supported by observations. Peebles (1976) found the virgocentric infall signal using the field galaxy data available at that time (Sandage & Tammann 1975).

Lynden-Bell (1981) and Sandage (1986) focussed on the Local Group of galaxies. They showed that, in the simplest case of the spherically symmetric system in the empty Universe with Λ = 0, the radius of the zero-velocity surface R0 and the total mass of the group MT0\hbox{$M^0_T$} are related as MT0=(π2/8G)×R03×T0-2,\begin{equation} M^0_T= (\pi^2/8G)\times R^3_0\times T^{-2}_0, \end{equation}(1)where G is the gravitational constant and T0 is the age of the Universe (Lynden-Bell 1981; Sandage 1986). In the standard cosmological ΛCDM model, where Ωm is the mean cosmic density of matter and H0 the Hubble parameter, the relation between R0 and MT becomes MT=(π2/8G)×R03×H02/f2(Ωm),\begin{equation} M_T=(\pi^2/8G)\times R^3_0\times H^2_0/f^2(\Omega_{\rm m}), \end{equation}(2)where the dimensionless parameter f(Ωm)=(1−Ωm)-1−Ωm2(1−Ωm)−32cosh-1(2Ωm−1)\begin{equation} f(\Omega_{\rm m})=(1-\Omega_{\rm m})^{-1}-\frac{\Omega_{\rm m}}{2} (1-\Omega_{\rm m})^{-\frac{3}{2}} \cosh^{-1}\left(\frac{2}{\Omega_{\rm m}}-1\right) \end{equation}(3)changes in the range from 1 to 2/3 while varying Ωm from 0 to 1. Taking the Planck model parameters Ωm = 0.315, Ωλ = 0.685 and H0 = 67.3 km s-1 Mpc-1 (Planck Collaboration XVI 2014), we obtain the relation (MT/M⊙)0.315=1.95×1012(R0/Mpc)3,\begin{equation} (M_T/M_{\odot})_{0.315} = 1.95\times 10^{12} (R_0/{\rm Mpc})^3, \end{equation}(4)which is by 1.50 times more than the classical estimate from Eq. (1).

This method was sucessfully applied to determine masses of the Local Group (Ekholm et al. 2001; Karachentsev et al. 2002, 2009; Teerikorpi et al. 2005), M81 group (Karachentsev & Kashibadze 2006), CenA group (Karachentsev et al. 2006), as well as the Virgo cluster (Tully & Shaya 1984; Karachentsev & Nasonova 2010; Karachentsev et al. 2014) and the Fornax cluster (Nasonova et al. 2011).

It is important to stress that the R0 method estimates the total mass of a group independently of mass estimates based on virial motions. Notably, the corresponding total mass MT is confined on the linear scale of R0, which is three to four times as large as the virial radius of a group or cluster, Rvir.

thumbnail Fig. 1

Distribution of 45 Milky Way satellites by their spatial distances and radial velocities relative to the Milky Way. Dashed lines correspond to the parabolic velocity for a point mass of 1 × 1012M⊙.

The implementation of the R0 method became possible with wholesale measurements of distances to nearby galaxies from luminosities of the red giant branch stars (TRGB) with accuracy of ~ 5% attainable by the Hubble Space Telescope. In the Local Volume, limited to 11 Mpc, there are about a thousand known galaxies; most of these galaxies have measured radial velocities with a typical accuracy less than 5 km s-1. About one-third of the Local Volume population already has accurate TRGB distance estimates. The compilation of observational data on these objects is presented in the Updated Nearby Galaxy Catalog (Karachentsev et al. 2013) and its latest electronic version1 (Kaisina et al. 2012). For a typical galaxy of the Local Volume with a distance of ~ 6 Mpc, the TRGB distance error of ~ 300 kpc is comparable with a virial radius of the group, thus its location can be confidently fixed relative to the group centroid and zero velocity surface. Other methods of secondary importance are the Tully & Fisher (1977) relation distances or the brightest stars distances with an accuracy of ~ (20−30)%, which do not provide an opportunity to determine R0 value even for the nearest groups.

Table 1

Milky Way companions with TI> −0.5.

Table 2

M31 companions.

Below we use the most complete data on distances and radial velocities of the Local Volume galaxies to estimate the zero-velocity radius around the local massive galaxies.

2. Galaxy motions around the Milky Way and M31

thumbnail Fig. 2

Distribution of 52 test particles by their differential radial velocities and projected distances from M31. Dashed lines correspond to the parabolic velocity for a point mass of 1 × 1012M⊙.

The recent surveys of large sky areas (Abazajian et al. 2009; Tonry et al. 2012; Koposov et al. 2015) led to the discovery of new Milky Way (MW) dwarf satellites with low luminosities and extremely low surface brightnesses. The recent overview by McConnachie (2012) reports 29 MW satellites with measured radial velocities and accurate distances. In recent years, this list has been expanded up to 45 objects. The corresponding data are presented in Table 1. The table columns contain (1) galaxy name; (2) equatorial coordinates J2000.0; and (3) tidal index, TI=max[log(Mn∗/Dn3)]−10.96,    n=1,2,...N,\begin{equation} TI = \max[\log(M^*_n/D^3_n)]-10.96, \,\,\,\, n=1, 2, \ldots N, \end{equation}(5)distinguishing the most significant galaxy (main disturber = MD) among N neighbouring galaxies, whose tidal force dominates the remaining galaxies with masses Mn∗\hbox{$M^*_n$} and spatial separations Dn. The constant, −10.96, is chosen in such a way that TI = 0 corresponds to a significant neighbour located on the zero velocity surface with TI< 0 galaxies ranked as isolated. Finally, Col. (4) lists the main disturber name, Col. (5) distance to a galaxy in Mpc, and Cols. (6, 7) radial velocity of a galaxy (in km s-1) relative to the Sun and relative to the MW centre with apex parameters adopted in NASA Extragalactic Database (NED). References to the used values of distances and velocities of galaxies are presented in the Local Volume Galaxies Database2.

The distribution of 45 satellites of the MW by their Galactocentric distances and radial velocities is shown in Fig. 1. The dashed lines correspond to the parabolic velocity for a point mass of 1 × 1012M⊙. The velocity distribution of satellites looks symmetrical relative to the MW centre, although two satellites with near-parabolic velocities – Tucana and LeoI – are close to the upper escape limit. Three MW satellites, Sag dIr, DDO 210, and Tucana with distances D ~ 1 Mpc and negative Θ1, belong to field galaxies. However, the MW is dynamically the most significant neighbour for each of these.

Specialized searches for faint satellites in the outskirts of the spiral galaxy M31 in the Andromeda constellation (Ibata et al. 2007, 2014; Martin et al. 2009) has proved to be notably productive. While the sample by McConnachie (2012) included 23 satellites, now their number is roughly doubled amounting up to 44. The data on these satellites are presented in Table 2, where the first six columns have the same meaning as in Table 1. The seventh column of Table 2 contains spatial distances of satellites (in Mpc) relative to M31, while eighth and ninth list the projected separation of satellites in the sky (in Mpc) and their differential radial velocities relative to M31 (in km s-1). Aside from dwarf galaxies, we tabulate also the data on eight distant globular clusters from PAndAS survey (Huxor et al. 2014) with measured radial velocities. Their spatial distances still remain unknown, and we set them equal to 0.78 Mpc.

The distribution of 44 + 8 test particles by their differential radial velocities and projected separations relative to M31 is presented in Fig. 2. The dashed lines also mean the parabolic velocity for a point mass of 1 × 1012M⊙. Similar to the MW case, the distribution of M31 satellites by their relative velocities seems to be very symmetrical; two satellites – And XIV and And XII – have near-parabolic velocities that are close to the lower escape limit.

Table 3

Total mass estimates for the Milky Way and M31 (in 1012M⊙).

Table 4

Isolated galaxies around the Local Group.

3. Orbital masses of the Milky Way and M31

For a massive galaxy surrounded by small satellites, the orbital mass estimate is expressed as Morb=(32/3π)×(1−2e2/3)-1×G-1×⟨ΔV2×Rp⟩,\begin{equation} M_{\rm orb}=(32/3\pi)\times(1-2e^{2}/3)^{-1}\times G^{-1}\times\langle\Delta V^2\times R_p\rangle, \end{equation}(6)where ⟨ ΔV2 × Rp ⟩ is the mean product of squared radial velocity difference of a satellite with its projected distance from the main galaxy and e is the orbit eccentricity (Karachentsev & Kudrya 2014). This relation is obtained under the assumption of uniformly random orientation of satellite orbits relative to the line of sight. With the typical eccentricity value of ⟨ e2 ⟩ = 1/2 (Barber et al. 2014) the relation (6) becomes Morb=(16/π)×G-1×⟨ΔV2×Rp⟩.\begin{equation} M_{\rm orb}=(16/\pi)\times G^{-1}\times \langle\Delta V^2 \times R_p\rangle. \end{equation}(7)Applying Eq. (7) to the assembly of the MW and M31 satellites, we get values for orbital masses Morb(MW) =1.51×1012M⊙ and Morb(M31) =1.69×1012M⊙. Since in the case of MW satellites we observe their 3D distances, then project distances, the orbital mass estimation should be reduced by a factor of (π/ 4) yielding Morb(MW) =1.18×1012M⊙. Hence, the ratio of mass estimates for these two galaxies reaches Morb(MW)/Morb(M31)≃0.70.\begin{equation} M_{\rm orb}({\rm MW})/M_{\rm orb}({\rm M31})\simeq0.70. \end{equation}(8)This value is quite close to the ratio Morb(MW)/Morb(M31) = 0.82 obtained by Karachentsev & Kashibadze (2006) from a minimum value for scatter of peculiar velocities with respect to the Hubble regression line, while varying the centroid position between the MW and M31.

A comparison of the derived total masses of the MW and M31, their combined mass, and the mass ratio with other mass estimates in the recent literature is presented in Table 3. These estimates were based on kinematics of satellites and globular clusters assuming that the MW and M31 haloes follow the standard NFW profile or fit the kinematics of high-velocity stars and blue horizontal branch stars. Our present measurements are in good agreement with the median values given in the last line of Table 3. An essential part of the mismatch between the different estimates in Table 3 may arise from the observed orbital anisotropy of the MW and M31 satellites (Ibata et al. 2013; Pawlowski et al. 2014) and from the uncertain dynamical status of two MW satellites, Leo I and Tucana, and the two M31 satellites, And XIV and And XII. Excluding these objects reduces the mass estimates by 14−15% in both cases.

4. Hubble flow around the Local Group

The proximate velocity field around the Local Group was considered in most detail by Karachentsev & Kashibadze (2006) and Karachentsev et al. (2009). For a sample of 30 galaxies with TRGB distances from 0.7 to 3.0 Mpc with respect to the Local Group centre, it was shown that the Hubble flow is characterized by the local Hubble parameter Hloc = (78 ± 2) km s-1 Mpc-1, the radial velocity dispersion σv ≃ 25 km s-1, and the radius of zero-velocity surface R0 = (0.96 ± 0.03) Mpc. The minimal value of σv corresponded to the barycentre position of Dc = (0.55 ± 0.05)DM31 = 0.43 Mpc, determining the mass ratio of MMW/MM31 ≃ 0.8 stated above.

thumbnail Fig. 3

Models of major and minor attractor. O represents an observer, C represents the centre of a galaxy group, and G represents a test particle (a galaxy).

thumbnail Fig. 4

Distribution of isolated galaxies by distances and velocities relative to the Local group barycentre assuming the minor attractor model. Upper panel: barycentre position locates at x = Dc/DM31 = 0.55 towards the M31. The solid circles indicate galaxies that have the MW or M31 as the main disturber. Lower panel: Hubble flow around the LG at the barycentre position of x = Dc/DM31 = 0.43. The grey wedges trace the companion positions under different x, where their thin end corresponds to the barycentre coinciding with M31. Solid and dotted lines in the insert indicate the velocity dispersion as a function of x with and without the Leo A, respectively.

In that approach, we considered the so-called minor attractor model, illustrated by the upper panel of Fig. 3. Here, a galaxy group with centre, C, is separated by a distance, Dc, from the observer, O, and moves away along the line of site with the velocity, Vc. In the outskirts of the group there is a galaxy, G, with distance, Dg, and radial velocity, Vg. If the angle between C and G is θ, then their mutual separation is expressed as R2=Dg2+Dc2−2Dg×Dc×cosθ,\begin{equation} R^2=D_g^2+D_c^2 -2D_g\times D_c\times\cos \theta, \end{equation}(9)and the projected differential velocity is given by Vgc=Vg×cosλ−Vc×cosμ,\begin{equation} V_{gc}=V_g\times\cos\lambda-V_c\times \cos\mu, \end{equation}(10)where μ = λ + θ, and tanλ=Dc×sinθ/(Dg−Dc×cosθ).\begin{equation} \tan\lambda = D_c \times \sin\theta/(D_g-D_c \times \cos\theta). \end{equation}(11)In this scheme we assumed peculiar velocities of galaxies in the vicinity of a group to be small compared with velocities of the regular Hubble flow.

Yet, there is another possibility, which is the major attractor case (see lower panel of Fig. 3); this case is characterized by predominating infall towards the centre of a group or a cluster. If Vi is the infall velocity than Vg=Vc×cosθ−Vi×cosλ,\begin{equation} V_g=V_c\times\cos\theta-V_i\times\cos\lambda, \end{equation}(12)and the velocity of a galaxy relative to the group centre is expressed as Vi=[Vc×cosθ−Vg]/cosλ.\begin{equation} V_i=[V_c\times\cos\theta-V_g]/\cos\lambda. \end{equation}(13)Evidently the difference between these two models would be insignificant if the galaxy lays almost strictly behind (λ ≃ 0) or in front (λ ≃ 180°) of the group centre.

The last few years astronomers have detected some new dwarf galaxies in the vicinity of the Local Group (KKs3, LeoP, and KK258) and measured their accurate TRGB distances and radial velocities. For some galaxies (KKR25 and Tucana), old inexact values of radial velocities were corrected and distances were refined. This circumstance has motivated us to redefine parameters of the local Hubble flow.

To reduce the role of virial motions, we excluded galaxies with TI> 0 from consideration; thus, the MW and M31 satellites with distances DMW< 0.8 Mpc were consequently excluded. The data on the rest field galaxies with DMW< 3.5 Mpc are presented in Table 4. The columns of Table 4 contain (1) galaxy name; (2) distance (in Mpc) from the Milky Way; (3) heliocentric radial velocity (in km s-1); (4) distance from the Local Group barycentre located at Dc = 0.43 Mpc; (5, 6) velocity (in km s-1) relative to the barycentre in the case of minor and major attractor, respectively; (7) tidal index; (8) the main disturber name; and (9) λ in degrees (see Fig. 3).

The distribution of 35 isolated galaxies by distances and velocities relative to the Local Group barycentre for the case of minor attractor is presented in the upper panel of Fig. 4. As shown in the Table 4 data, only 14 galaxies of 35 have the MW or M31 as the main disturber; they are denoted by solid circles. With reference to these objects, the zone affected gravitationally by the Local Group reaches Rc ≃ 2.5 Mpc, while more distant field galaxies are influenced by other massive neighbours of the Local Group, such as M81, NGC 253, and NGC 5128.

According to Peirani & de Freitas Pacheco (2008), Falco et al. (2014), and Penarrubia & Fattahi (2017), the radial velocity profile around the spherically symmetrical group or cluster can be expressed as V(R)=H0×R−H0×R0×(R0/R)1/2,\begin{equation} V(R)=H_0\times R-H_0\times R_0\times (R_0/R)^{1/2}, \end{equation}(14)where R0 is the radius of the zero-velocity surface to be found. The solid line in Fig. 4 corresponds to Eq. (14) with parameters defined from the least squares method, R0 = 0.95 ± 0.03 Mpc, H0 = 90 ± 2 km s-1 Mpc-1, and σv = 42 km s-1. The errors of R0 and H0 parameters were estimated using the Monte Carlo method, assuming that distance errors for galaxies are distributed normally with a typical value of ~ 5%. The peculiar velocity dispersion in the upper panel of Fig. 4 is contributed mostly by distant galaxies, which are disturbed by the neighbouring groups. Considering the only 14 galaxies in the zone affected gravitationally by the Local Group, we obtain the following parameters for the surrounding Hubble flow: R0 = 0.85 ± 0.03 Mpc, H0 = 79 ± 3 km s-1 Mpc-1, and σv = 23 km s-1. In the major attractor model, these parameters vary slightly, since λ values for these 14 galaxies are small (see the last column in Table 4).

Three parameters, i.e. R0, H0, and σv, characterizing the local cosmic expansion, moderately depend on the position of the LG barycentre. Above, we used the barycentre location at the distance of Dc = 0.55DM31 = 0.43 Mpc, corresponding to the mass ratio of MM31/MMW = 1.2. This ratio matches well with the medians in Table 3. However, Penarrubia et al. (2014) found that the minimal scatter of nearby galaxies within 3 Mpc around the LG is achieved with MM31/MMW = 0.75. The authors have concluded that their analysis rules out models in which M31 is more massive than our Galaxy with about 95% confidence. To check this statement, we calculated σv for 14 nearest isolated galaxies as a function of the position of the LG barycentre x = Dc/DM31 on the line connecting the MW with M31. The data on σv and R0 are presented in Table 5. The lower panel of Fig. 4 shows the local Hubble diagram for 14 galaxies at various M31-to-MW mass ratios. Each galaxy is drawn by grey wedge with caliber inversely related to the dispersion σv at given barycentre position; thus its thinner end indicates the barycentre position at M31. The insert in the figure shows the velocity scatter of galaxies respect to the best-fitting regression line. The solid and dotted lines in the insert represent the behaviour of σv for a case of included or excluded Leo A, respectively. This dwarf galaxy is a marginally isolated object with the tidal index TI = +0.03. The derived minimums of these two lines fix the M31-to-MW mass ratio near 0.7 and 1.0, respectively, not allowing a firm assessment of which galaxy mass is dominated. Over the range of MM31/MMW = [1/3−3] the value of the zero velocity radius is changing within R0 = 0.86−0.96 Mpc. Thus, the observed coldness of the local Hubble flow leads us to measure the radius of the sphere separating the Local Group from the global cosmic expansion with ~ 5% error. According to (4), the radius R0 = 0.91 ± 0.05 Mpc yields the total mass estimate for the Local Group MT = (1.5 ± 0.2) × 1012M⊙ with an unprecedented accuracy, although this quantity lies below all values of M(MW+M31) in Table 3. The mismatch becomes slightly less dramatic when the Planck model parameters in (4) replace the WMAP parameters as follows: Ωm = 0.24, Ωλ = 0.76, and H0 = 73 km s-1 Mpc-1 (Spergel 2007); this increases the coefficient in (4) from 1.95 to 2.12.

As noted by Chernin et al. (2004), the actual deviation of the binary shape of the Local Group from the spherical symmetry produces a minor bias in the R0 and mass estimate. According to N-body simulations by Penarrubia et al. (2014), neglecting the quadrupole potential overestimates the Local Group mass up to ~ 30%.

Table 5

Parameters of the local Hubble flow as a function of the LG barycentre position.

5. Other massive galaxies in the Local volume

Considering the Hubble flow around other giant galaxies of the Local Volume, we selected 15 galaxies with stellar masses M∗> 3 × 1010M⊙ and accurate distances. Their overview is presented in Table 6 with objects ranging by their distances from the observer. For each of these 15 galaxies, surrounded by a suite of satellites, the second most massive member of its group is also indicated. In some cases, i.e. M31 and the Milky Way, NGC 5128 (CenA) and NGC 5236, Maffei 2, and IC 342, the second galaxy is comparable in mass with the first galaxy and acts itself as the centre of a dynamically separated subgroup.

Table 6

Giant galaxies in the Local Volume.

Table 7

Isolated galaxies around the nearby group centres.

The columns of Table 6 contains (1) galaxy name; (2, 3) its supergalactic coordinates; (4) the galaxy distance from the MW; (5) its radial velocity relative to the Local Group centroid; (6) logarithmic stellar mass; (7) logarithmic orbital mass according to Karachentsev & Kudrya (2014); (8) number of satellites of the main galaxy with measured radial velocities and accurate distances.

Aside from the galaxies presented in Table 6, the Local Volume contains another two massive galaxies – NGC 2903 (log M∗ = 10.82) and NGC 6946 (log M∗ = 10.76). But their distances measured from the luminosity of brightest stars are not yet sufficiently accurate. In total, the 15 giant galaxies have about 500 satellites in their suites, but, as shown in the last column of Table 6, only 102 satellites outside the Local Group have accurate estimates of distances and velocities. Among the second most massive members of 15 groups, three galaxies – NGC 4242, NGC 4597 and NGC 6684 – have Tully-Fisher distances with accuracy of ~ 20% (denoted with column signs). In 11 of 15 groups, the main galaxy exceeds its satellites twice or more in mass, allowing us to estimate its halo mass from the orbital motions. This approach is not worthwhile in the case of the rich group Leo I, where NGC 3379, NGC 3368, and several other bright members have compatible luminosities.

Despite the great efforts to measure highly accurate TRGB distances of nearby galaxies from Hubble Space Telescope data, many neighbouring groups stay still poorly explored. For example, in the outskirts of giant galaxies NGC 4594 (Sombrero), NGC 5055, and NGC 3115, no satellites have reliable distance estimates.

6. Cosmic flow around the synthetic (stacked) nearby group

thumbnail Fig. 5

Hubble diagram for the synthetic group of the Local Volume, assuming the minor attractor model. Upper panel: distances and velocities of satellites are calculated relative to the main galaxy in a group. Lower panel: distances and velocities of satellites are calculated relative to the barycentre of a pair of the most massive galaxies in each group.

Table 8

Parameters of the Hubble flow around the nearby synthetic group under various assumptions.

Seeking to use as much information as possible about companion motions around the nearby massive galaxies outside their virial zones, we combined the data on companions of various galaxies into the single synthetic group. To be included into the consolidated group, a galaxy should satisfy the following four conditions: (1) a companion has accurate estimates of distance and radial velocities; (2) the companion distance from the main galaxy, RMG, is less than 3.5 Mpc; (3) the companion belongs to field galaxies, having TI< 0; and (4) the companion has a proper aspect, when its position angle λ between the vector of companion radial velocity and the line joining it with the main galaxy (see Fig. 3) lays within λ< 45° or λ> 135°.

These conditions are satisfied for 66 galaxies of the Local Volume; the corresponding data are presented in Table 7. Its columns contain: (1) name of the main galaxy acting as the centre of its suite; (2) name of a companion galaxy; (3) companion galaxy distance from the group barycentre; (4, 5) companion galaxy velocity relative to the group barycentre in the case of minor or major attractor; (6, 7) tidal index of the galaxy and the name of its main disturber; and (8) position angle of the companion as indicated in Fig. 3.

The Hubble diagram for the synthetic group of the Local Volume for the minor attractor model with distances and velocities calculated relative to the main galaxy is shown in the upper panel of Fig. 5. The cosmic flow around the synthetic group is characterized by the Hubble parameter H0 = (76 ± 2) km s-1/Mpc, velocity dispersion σv = 62 km s-1, and radius of the zero velocity surface R0 = 0.83 ± 0.03 Mpc. As one can see, the radius R0 turned out to be quite small, corresponding to the effective mass of the synthetic group of ~ 1.1 × 1012M⊙. To estimate how various factors influence R0, we constructed another series of Hubble diagrams. An alternative Hubble diagram with distances and velocities calculated relative to the group barycentre rather than from the main galaxy itself is presented in the lower panel of Fig. 5. The barycentre is supposed to lie between the two most massive galaxies of each group given in Table 6. In this case the local Hubble parameter is H0 = (85 ± 2) km s-1 Mpc, peculiar velocity dispersion σv = 57 km s-1, and radius R0 reaches R0 = 0.93 ± 0.02 Mpc.

As follows from the data on Table 6, the nearby galaxy groups differ substantially in their stellar and virial masses, M∗ and Morb, which can lead to a systematic bias in the averaged R0 estimate. To verify this effect, we normalized distances of companions around each group to its individual radius R0, assuming R0∝M∗1/3\hbox{$R_0\propto M_*^{1/3}$} or R0∝Morb1/3\hbox{$R_0\propto M_{\rm orb}^{1/3}$}. After that we did not find any decrease in peculiar velocity dispersion in the synthetic Hubble diagram.

The resulting values of H0, σv, and R0 parameters for all discussed cases are presented in Table 8; i.e. distances and velocities calculated relative to the main galaxy or group barycentre and the minor or major attractor model. These data allow us to conclude, first, that changing a model from a minor attractor to major attractor increases the R0 estimate and causes a significant increment in dispersion, and, second, that accounting for the second most massive galaxy in a group leads to a notable growth of the R0 estimate.

7. Discussion

As our estimates suggest, galaxies in the infall zone between the virial radius and the R0 are relatively small in number, ~ 15%. This circumstance, inherent for the Local Group and for other nearby groups, opts for estimating R0 value within minor attractor model. The low value of peculiar velocity dispersion resulting in this case is also an oblique argument for such a choice.

The second most massive galaxy plays an essential role in the kinematics of several nearby groups, often forming a dynamical subsystem. So, deciding on a barycentre of the two most bright galaxies as the reference point for distances and velocities of companions seems to be more preferable than the main galaxy itself. Hence, we adopt the value of 0.93 ± 0.02 Mpc as the optimal estimate for R0 radius of the cumulative group (see the lower panel of Fig. 5). The corresponding mass is log (MT/M⊙) = 12.20 with a formal error of ~ 0.04 dex. Averaging orbital mass estimates from Table 6 and considering the representation of each group in the Hubble diagram, we obtain the mean logarithmic mass log (Morb/M⊙) = 12.42 ± 0.07. So, the mass of the synthetic group derived from outer motions of surrounding galaxies turned out to be ~60% of the expected mass from inner orbital motions of satellites. A probable source of this discrepancy was discussed by Chernin et al. (2013) and Karachentsev & Kudrya (2014).

As noted by Chernin et al. (2013), the estimate of the total mass of a group includes two components, MT = Mm + MDE, where Mm is the mass of dark and baryonic matter and MDE is the mass, negative in magnitude, which is determined by the dark energy with the density of ρDE, MDE=(8π/3)×ρDE×R3.\begin{equation} M_{\rm DE}= (8\pi/3)\times\rho_{\rm DE}\times R^3. \end{equation}(15)On the scale of virial radius, the contribution of this component in the group mass does not exceed 1%, but in the sphere of R0 radius, the role of this kind of a mass defect becomes significant. In the standard ΛCDM model with Ωm = 0.24 and H0 = 73 km s-1 Mpc-1 the contribution of dark energy is (MDE/M⊙)=−0.85×1012×(R0/Mpc)3,\begin{equation} (M_{\rm DE}/M_{\odot})= -0.85\times 10^{12} \times (R_0/ {\rm Mpc})^3, \end{equation}(16)i.e. about 30% of the Local Group mass determined by orbital motions. This correction essentially reduces the observed discrepancy between the mass estimates for the Local Group, as well as for other nearby groups, derived via internal (virial) and external galaxy motions.

Another possible explanation might be caused by the existence of unrelaxed (tidal) thin planar structures of satellites seen around the MW and M31 (Kroupa 2014), which are at variance with the assumption of spherical symmetry case.

The peculiar velocity dispersion in the vicinity of the synthetic group, 57 km s-1, is twice as large as in the outskirts of the Local Group. This difference might originate from bulk motions of galaxies, which become perceptible on the scale of ~ 5−10 Mpc. A giant galaxy is not necessarily the main disturber for neighbouring field galaxies. Indeed, this is the case for only a portion of companion objects presented in Table 7. Another portion, which are comprised of mostly distant field galaxies (shown by open circles), are gravitationally influenced by a massive galaxy from another neighbouring group.

thumbnail Fig. 6

Distribution of barycentres of 15 nearby groups by their radial velocities and distances from the Local Group centre. The solid line corresponds to the regular Hubble flow with Hubble parameter H0 = 73 km s-1 Mpc-1.

Figure 6 reproduces the distribution of barycentres of 15 nearby groups listed in Table 5 by distances and radial velocities relative to the Local Group centre. The straight line corresponds to the regular Hubble flow with H0 = 73 km s-1 Mpc-1. Barycentres of the groups with DLG< 6 Mpc situated in the supergalactic plane (i.e. in the Local Sheet; Tully et al. 2016) demonstrate a small scatter of radial velocities. More distant groups, around M 101, NGC 5055, NGC 2683, NGC 3115, and NGC 3379 at supergalactic latitudes | SGB | > 10° (denoted with asterisks), exhibit negative peculiar velocities about −200 km s-1. These velocities are caused by the observed expansion of the Local Void with an amplitude of ~ 260 km s-1 (Tully et al. 2016). Also, the group around Sombrero (NGC 4594) is located just near the zero-velocity surface of the Virgo cluster. Its positive peculiar velocity reflects the group fall towards the cluster. Apparently, some portion of these bulk motions manifest themselves as extra peculiar velocities of the Local Volume galaxies in the panels of Fig. 5. Ignoring these non-virial coherent motions may lead to the overestimation of galaxy masses based on the Numerical Action Method (Peebles 2017).

Our conclusion that the peripheral regions of the Local Group and other neighbouring groups do not contain a large amount of dark matter seems to be the most important result of this work. The bulk of mass is concentrated within the virial radius of these groups. The same inference was made for the nearest Virgo cluster (Karachentsev et al. 2014) from the observed infall of galaxies towards the cluster centre. Yet further evidence is provided by Kourkchi & Tully (2017), who have considered infall zones and collapsed cores of halos in the Local Universe.

A review of available observational data on distances and radial velocities of the Local Volume galaxies shows that the population of outskirts of the nearby groups has not yet been covered with highly accurate distance measurements. There are groups, for example around the giant Sombrero galaxy, totally lack reliable distance estimates, even for close probable satellites. The systematical measurements of TRGB distances with the Hubble Space Telescope within the Local Volume have the potential to provide meaningful data on the distribution of the dark matter on the scales of ~ 1 Mpc.

Acknowledgments

The authors are grateful to Elena Kaisina for updating the Local Volume Galaxies Database (https://www.sao.ru/lv/lvgdb/), Dmitry Makarov for the renewed data on galaxy tidal indices, and Brent Tully for reviewing the manuscript and for his helpful comments. This work is supported by the Russian Science Foundation grant No. 14–12–00965.

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All Tables

Table 1

Milky Way companions with TI> −0.5.

In the text
Table 2

M31 companions.

In the text
Table 3

Total mass estimates for the Milky Way and M31 (in 1012M⊙).

In the text
Table 4

Isolated galaxies around the Local Group.

In the text
Table 5

Parameters of the local Hubble flow as a function of the LG barycentre position.

In the text
Table 6

Giant galaxies in the Local Volume.

In the text
Table 7

Isolated galaxies around the nearby group centres.

In the text
Table 8

Parameters of the Hubble flow around the nearby synthetic group under various assumptions.

In the text

All Figures

thumbnail Fig. 1

Distribution of 45 Milky Way satellites by their spatial distances and radial velocities relative to the Milky Way. Dashed lines correspond to the parabolic velocity for a point mass of 1 × 1012M⊙.
In the text
thumbnail Fig. 2

Distribution of 52 test particles by their differential radial velocities and projected distances from M31. Dashed lines correspond to the parabolic velocity for a point mass of 1 × 1012M⊙.
In the text
thumbnail Fig. 3

Models of major and minor attractor. O represents an observer, C represents the centre of a galaxy group, and G represents a test particle (a galaxy).
In the text
thumbnail Fig. 4

Distribution of isolated galaxies by distances and velocities relative to the Local group barycentre assuming the minor attractor model. Upper panel: barycentre position locates at x = Dc/DM31 = 0.55 towards the M31. The solid circles indicate galaxies that have the MW or M31 as the main disturber. Lower panel: Hubble flow around the LG at the barycentre position of x = Dc/DM31 = 0.43. The grey wedges trace the companion positions under different x, where their thin end corresponds to the barycentre coinciding with M31. Solid and dotted lines in the insert indicate the velocity dispersion as a function of x with and without the Leo A, respectively.
In the text
thumbnail Fig. 5

Hubble diagram for the synthetic group of the Local Volume, assuming the minor attractor model. Upper panel: distances and velocities of satellites are calculated relative to the main galaxy in a group. Lower panel: distances and velocities of satellites are calculated relative to the barycentre of a pair of the most massive galaxies in each group.
In the text
thumbnail Fig. 6

Distribution of barycentres of 15 nearby groups by their radial velocities and distances from the Local Group centre. The solid line corresponds to the regular Hubble flow with Hubble parameter H0 = 73 km s-1 Mpc-1.
In the text

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