The Hubble flow around the Local Group
I. D. Karachentsev
O. G. Kashibadze
D. I. Makarov
R. B. Tully
Institute for Astronomy of Hawaii
, 2680 Woodlawn Drive, Honolulu,
HI 96822, USA
Special Astrophysical Observatory of the Russian Academy of Sciences
, Nizhnij Arkhyz, KChR, 369167,
A B S T R A C T We use updated data on distances and velocities of galaxies in the proximity of the Local Group (LG) in order to establish properties of the local Hubble flow. For 30 neighbouring galaxies with distances 0.7 < DLG < 3.0 Mpc, the local flow is characterized by the Hubble parameter Hloc = (78 2) km s1 Mpc1, the mean-square peculiar velocity v = 25 km s1, corrected for errors of radial velocity measurements (4 km s1) and distance measurements (10 km s1), as well as the radius of the zero-velocity surface R0 = (0.96 0.03) Mpc. The minimum value for v is achieved when the barycentre of the LG is located at the distance Dc = (0.55 0.05) DM31 towards Andromeda galaxy (M31) corresponding to the Milky Way (MW)-to-M31 mass ratio MMW/MM31 4/5. In the reference frame of the 30 galaxies at 0.7-3.0 Mpc, the LG barycentre has a small peculiar velocity (24 4) km s1 towards the Sculptor constellation. The derived value of R0 corresponds to the total mass MT(LG) = (1.9 0.2) 1012 M with m = 0.24 and a topologically flat universe, a value in good agreement with the sum of virial mass estimates for the MW and M31.
1 I N T R O D U C T I O N
The studies of the Hubble flow of galaxies in the neighbourhood
of the Local Group (LG) have been out of favour with cosmologists.
The main reason has been a lack of reliable data on distances to
even the nearest galaxies outside the LG. Early on, Lynden-Bell
(1981), Sandage (1986, 1987) and Giraud (1986, 1990) noted that
the behaviour of the Hubble flow at distances D (1 3) Mpc
allows one to find the total mass MT of the LG independently of virial
mass estimates for the Milky Way (MW) and Andromeda galaxy
(M31) based on the motions of their companions. A decelerating
influence of the LG on nearby galaxies causes the Hubble regression
V |D to cross the line of zero velocity at a non-zero distance R0.
In the case of spherical symmetry with = 0, the radius of the
zero-velocity surface R0 can be expressed via the LG mass and the
age of the Universe T0 by a simple relation
MT(LG) = (2/8G)R30T02,
Rizzi et al. (2007).
McConnachie et al. (2008).
Tully et al. (2006).
Silva et al. (2005).
Kopylov et al. (2008).
Dolphin et al. (2002).
Karachentsev et al. (2006).
2 O B S E RVAT I O N A L DATA O N T H E
N E I G H B O U R I N G G A L A X Y F L OW
The usage of the wide-field survey of the Andromeda
neighbourhood (Ibata et al. 2001; Ferguson et al. 2002; Irwin et al. 2005)
and the Sloan survey archive led to the discovery of a couple of
dozen new companions to the MW and M31, doubling the total
number of identified dwarf galaxies in the LG. Nowadays, there are
47 members in the LG with known distances and radial velocities
which permit improved derivations of the virial masses of the MW
In close proximity of the LG, there are 30 more galaxies with
distances from the group centroid within 0.7 < DLG < 3.0 Mpc.
Their main observational properties are listed in Table 1. The
lower boundary was accepted to be 0.7 Mpc in order to
exclude companions to the MW and M31 not participating in the
cosmological expansion. The upper boundary was adopted to
be 3.0 Mpc in order to exclude members of the nearby groups
around IC342, M81 and Centaurus A, with their centres located
at 3.3, 3.6 and 3.7 Mpc from us, respectively. Approximately,
the same distance range was used by Karachentsev et al. (2002)
and Karachentsev & Kashibadze (2006) while finding R0 and v
In the last years, new galaxies have also been discovered in the
volume just beyond the LG, but at a much lower rate than in the
close proximity to the MW and M31. Improving galaxy distances
based on the luminosity of the tip of red giant branch (TRGB) with
respect to the distances from Karachentsev et al. (2002) leads to six
galaxies: SDIG, NGC 247, UGCA 92, NGC 1569, UGC 8638 and
ESO 383-87 to be placed beyond DLG = 3.0 Mpc. Other galaxies
within the volume (ESO 410-005, HIZSS003, UGC 4879) have their
radial velocities and/or distances newly measured. The improved
observational data motivated us to reconsider the properties of the
local Hubble flow.
In Table 1, the first and second columns are the galaxy names
and their equatorial coordinates at the J2000.0 equinox, respectively.
Columns (3 and 4) are heliocentric velocities with their errors and
the velocities with respect to the LG centroid. With one
exception, all the velocities Vh are taken from the NASA Extragalactic
Database (NED) and their transformation into VLG is performed
to an isolated galaxy of the general field while a case with T I > 0
means the galaxy is in a zone of significant gravitational influence
from its neighbours. Columns (10) and (11) are peculiar radial
velocities of the galaxy with respect to two lines of Hubble regression
shown in the upper and bottom panels of Fig. 1 (see below). Finally,
the last column contains the reference to the source of data on the
galaxy distance and comments. Most of the galaxies in the close
proximity to the LG have new, more accurate distance estimates
with respect to ones given in CNG. Some cases deserve additional
ESO 410-05. This dwarf spheroidal galaxy is a companion to the
spiral NGC 55. Koribalski et al. (in preparation) found from an H I
line observation its neutral hydrogen mass to be 106 M and its
radial velocity Vh = +38 km s1.
NGC 404. An isolated lenticular galaxy with an extended H I
envelope (Rio del, Brinks & Cepa 2004). We adopted its distance to
be 3.26 Mpc as an average over three estimates made by Tonry et al.
(2001), Karachentsev et al. (2002) and Tikhonov, Galazutdinova &
UGC 4879. The distance to this relatively bright (B = 13.78 mag)
dIr-type galaxy was found by Kopylov et al. (2008) via TRGB. The
authors give its optical radial velocity to be Vh = 70 km s1.
But, we would rather use another estimate, Vh = 20 km s1,
obtained from the 21-cm-line observations by Oosterloo (private
KKR25. This isolated dSph-type galaxy was considered detected
by Huchtmeier, Karachentsev & Karachentseva (2003) in the H I line
with Effelsberg radiotelescope with Vh = 139 km s1. However,
Begum & Chengalur (2005) repeated H I observations with aperture
synthesis on the Giant Metrewave Radio Telescope (GMRT) and
failed to find any H I flux from KKR25. The previous signal was
probably due to extended emission of Galactic hydrogen in the
And XVIII. This dSph-type system was recently discovered by
McConnachie et al. (2008) who found its distance to be 1.36 Mpc
according to TRGB. The radial velocity for this galaxy has not been
measured yet. Being separated by 600 kpc from M31, And XVIII
is probably a peripheric companion to M31 on the opposite side
from the MW.
The distribution of galaxies by distances and radial velocities
with respect to the LG centroid is given at the upper panel of Fig. 1.
Each galaxy is represented by a filled circle with horizontal and
vertical bars indicating the errors of measurements of distance and
radial velocity of the galaxy. For the sake of completeness, we also
present 47 members of the LG. They fill a vertical region with
DLG < 0.7 Mpc. An inclined dotted line represents a linear relation
with the global Hubble parameter H0 = 73 km s1 Mpc1. The
solid line corresponds to the regression V LG|DLG for the canonical
LemetreTolman (LT) model
The regression line drawn for m = 0, T0 = 13.4 Gyr crosses
the zero-velocity level at R0 = 0.91 Mpc.
In the upper panel of Fig. 2, we represent the distribution of
30 galaxies from Table 1 on the sky in equatorial coordinates. The
galaxies are shown as circles with their sizes indicating the galaxy
distance while numbers and colour reflect peculiar velocity. The
irregular band of strong Galactic extinction is indicated. The nearest
groups, IC342, M81, CenA and Canes Venatici I cloud (CVnI), the
local mini-attractors, are shown as large ellipses. The data
demonstrate little visible correlation between peculiar velocities of the
galaxies and their location with respect to the neighbouring groups.
One can note, though, that three galaxies with the largest positive
velocities (DDO99, DDO125 and DDO190) are situated in the
direction of CVnI and probably take part in the primordial collapse of
this diffuse system. In general, the distribution of Vpec demonstrates
a minor dipole effect, with an excess of negative peculiar velocities
in the Southern hemisphere.
3 R A D I U S O F T H E Z E R O - V E L O C I T Y
S U R FAC E R0
An estimate of R0 for the LG was obtained by Karachentsev &
Makarov (2001) with the use of the radial velocities for 20 galaxies
having distances from 0.7 to 3.0 Mpc. The resulting value R0 =
0.96 0.05 Mpc was derived with H0 = 70 km s1 Mpc1. Later,
with the addition of new data on nearby galaxies, Karachentsev et al.
(2002) confirmed the previous estimate by obtaining R0 = 0.94
0.10 Mpc with H0 = 72 km s1 Mpc1. A more detailed analysis
of factors affecting the estimate of R0 was done by Karachentsev
& Kashibadze (2006). Parameters of the local Hubble flow depend
on a choice of the LG barycentre position. In the paper cited above,
it was shown that the minimum value for the sum of squares of
the peculiar velocities with respect to the Hubble regression line is
achieved when the distance from the MW to the barycentre is Dc =
(0.55 0.05) DM31 in the direction towards M31 with the adopted
distance to M31 of 0.78 Mpc. Assuming Dc/DM31 = 0.55 and
H0 = 72 km s1 Mpc1, Karachentsev & Kashibadze (2006)
obtained the zero-velocity radius to be 0.96 0.03 Mpc and the
meansquare value of the peculiar radial velocities to be v = 24 km s1.
Also, their modelling of the local Hubble flow with
possible chaotic tangential velocities of the galaxies around the LG
showed that typical tangential velocities with amplitude of 35 and
70 km s1 produce a statistical uncertainty in R0 as 0.02 and
0.04 Mpc, respectively.
Improved observational data on the galaxies around the LG given
in Table 1 are used by us to make a new estimate of R0 and its
uncertainty. We consider a local value of the Hubble parameter Hloc
and the distance to the LG barycentre Dc as arbitrary parameters.
We also accept that the local peculiar velocity field might have a
dipole anisotropy with an arbitrary amplitude and direction. The
dependence of v on the distance to the barycentre Dc is shown in
Fig. 3. The requirement of the minimum value for v yields us the
following six parameters: Hloc = (78 2)kms1 Mpc1, Dc/DM31 =
0.55 0.05, the dipole amplitude (in the LG frame) Vd = (24
4) km s1 directed to RA = 336 34, = 64 10 and the
radius R0 = (0.96 0.03) Mpc.
The Hubble diagram corresponding to these parameters is
presented in the bottom panel of Fig. 1, and the distribution of the
residual (peculiar) velocities of the galaxies is shown in the bottom
panel of Fig. 2 (their numerical values are also given in Table 1).
Despite the fact that some of the galaxies shifted positions on the
Hubble diagram, the value of R0 remains almost unchanged. The
reason for the stability of the quantity R0 is mostly due to the fact
that six galaxies in the vicinity of R0: WLM, Leo A, DDO 210,
UGC 4879, Tucana and SagDIG have the average distance D LG =
(0.98 0.05) Mpc and the mean radial velocity V LG = (+4
11) km s1, fixing the value R0 with good precision.
4 P E C U L I A R V E L O C I T Y PAT T E R N A R O U N D
T H E L O C A L G R O U P
0.75 Mpc < DLG < 1.50 Mpc
1.50 Mpc < DLG < 2.25 Mpc
2.25 Mpc < DLG < 3.00 Mpc
0.75 Mpc < DLG < 1.50 Mpc
1.50 Mpc < DLG < 2.25 Mpc
2.25 Mpc < DLG < 3.00 Mpc
than the commonly accepted global Hubble parameter H0 = (73
3) km s1 Mpc1 (Spergel et al. 2007). Expected differences
between Hloc and H0 for the case of a canonical LT model for the LG
and for the case of a modified LT model with -term were discussed
by Peirani & de Freitas Pacheco (2006, 2008).
The LG barycentre position at Dc/DM31 = 0.55 0.05 in the
direction to M31 indicates that the mass ratio of the two main
LG members is close to unity and probably lies within a range
of MMW/MM31 = [2/3 1]. According to Fukugita & Peebles
(2004), the amplitude of internal rotation for the MW is Vm(MW) =
241 13 km s1 and for M31 it is Vm(M 31) = 259 5 km s1.
Since masses of spiral galaxies are proportional to the power 3 to
0.4 0.5 0.6
Dc / DM31, centroid position
to the Local Void (AntiLV) by two large ellipses. Location on the
sky of these two massive attractors is not associated with the local
dipole. The behaviour of the local dipole as a function of the radius
of the sphere around the LG was analysed by Kashibadze (2008).
By varying the radius from 2 to 6 Mpc, the dipole amplitude varies
within a cap of 32 km s1 while its direction chaotically drifts over
the sky. Therefore, the value of Vd obtained can be considered as a
small random value with no clear dynamical sense.
The distribution of the peculiar velocities of the galaxies after
accounting for the dipole is presented in Fig. 4 as a function of DLG.
Here, the inclined bars correspond to the 1 errors of distances to
For 30 galaxies within DLG = 0.73.0, the mean-square
dispersion of the velocities is 27 km s1. After reduction for the mean
error of the radial velocity measurement (4 km s1) and for the
mean error of the distance measurement (10 km s1), the residual
(cosmic) dispersion drops to cv = 25 km s1. Hence, the
peculiar motion of the LG centroid with respect to nearby galaxies
(24 km s1) has an amplitude comparable with v.
The local field of peculiar velocities gives us a unique
opportunity to test whether the dispersion of the velocities depends on the
luminosities of the galaxies or on the density of their environment.
The upper and bottom panels of Fig. 5 represent variations of the
modulus of peculiar velocity with the blue absolute magnitude MB
of the galaxy and with its tidal index TI, respectively. The linear
regressions are shown as dashed lines. A slight tendency in the
increasing of the |V pec| from giant galaxies to dwarf ones is seen.
Whiting (2005, 2006) studied data on galaxies within 10 Mpc and
found no correlation between luminosity and peculiar velocity at
all. Also, the galaxies that reside in the close proximity with others,
Antlia, E294-010, E410-005, LeoA and WLM, tend to have peculiar
velocities just a bit surpassing those of isolated galaxies. The large
peculiar velocity of KKR25 is most likely an artefact (due to the
Galactic hydrogen confusion) and three dIr systems in front of the
CVnI cloud (DDO 99/125/190) might have common acceleration
towards the cloud centre.
For some cosmological problems, it is enough to know the
total dispersion of peculiar velocities inside a fixed volume without
distinguishing between virial motions and the motions of
galaxies external to a virialized group. By summarizing the data for
30 galaxies considered above with data on 47 companions to the
MW and M31, we obtain the peculiar radial velocity dispersion to be
tvot = 79 km s1 within DLG < 3 Mpc.
According to Jing, Mo & Borner (1998), Branchini et al. (2001),
Zehavi et al. (2002), Feldman et al. (2003) and others, the radial
velocity difference for a galaxy and its nearest neighbour as a
function of their spatial separation can be a useful tool for mapping the
matter distribution on scales of 1 Mpc. Implementation of this
method has been limited until now due to the poverty of
observational data on distances to galaxies. For the more extended region
of the Local Volume extending to 10 Mpc, the relation between
the difference of radial velocities |V1 V2| and spatial separations
|R1 R2| was shown in CNG (Karachentsev et al. 2004). The
behaviour of the median difference |V1 V2| versus |R1 R2|
demonstrates approximately the same value |V1 V2| 100 km s 1 within
|R1 R2| < 1 Mpc and systematic increase up to 250 km s1 with
the increasing of the spatial separations to 3 Mpc. For the 77 nearest
galaxies with known radial velocities and distances within 3 Mpc,
this relation is shown in Fig. 6. Here, the LG members (N = 47)
and the galaxies around the LG (N = 30) are denoted as open and
filled circles, respectively. Although there are not so many galaxies
considered, the precision of their distances (typically 0.12 Mpc) is
much higher than for more distant CNG. In general, the features are
seen to be the same as in the CNG sample: a virial region with |V1
V2| 100 km s 1 for |R1 R2| < 1 Mpc and then a smooth increase
of the pair-wise velocity differences with the increase of separations
because of the contribution of the Hubble component. To a first
approximation, the kinematics of the LG and its neighbourhood look
to be typical of the more extended Local Volume.
5 T H E T O TA L M A S S O F T H E L O C A L G R O U P In the standard flat cosmological model with -term and matter component, it takes a form
MT = (2/8G)R03H02/f 2( m),
f ( m) = (1
m)1 ( m/2)(1
arccosh[(2/ m) 1].
Therefore, for the radius of the zero-velocity surface as R0 = 0.96
0.03 Mpc, the total mass of the LG turns out to be MT = (1.88
0.18) 1012 M . Let us compare this value with estimates of the
LG mass from the orbital motions of the MW and M31 companions.
The list of properties of the nearest groups of galaxies
(Karachentsev 2005) yields M(MW) = 0.94 1012 M and
M(M31) = 0.84 1012 M as an average of virial and orbital
estimates for the subsystems around the MW and M31. Later
estimates of the masses for the subsystems with newly found dwarf
galaxies taken into account give M(M31) = 0.71 1012 M
(Geehan et al. 2006), M(M31) = 1.1 1012 M (Tempel, Tamm
& Tenjes 2007), M(MW) = (1.1 0.2) 1012 M (Xue et al.
2008), all being not so different from previous estimates. The
total mass of the LG, found by using the motions of satellites, lies
within the range M(MW + M31) = (1.62.2) 1012 M , which
is consistent with the total mass of the LG from the motions of the
30 surrounding galaxies.
It should be noted, however, that the LG mass estimate based
on so-called timing argument (Kahn & Woltjer 1959) gives a
6 C O N C L U D I N G R E M A R K S
The recent data on radial velocities and distances for nearby galaxies
demonstrate the regularity of the Hubble flow around the LG on
scales of 13 Mpc around the LG centre. The mean-square velocity
of chaotic motions along the line of sight is about v = 25 km s1
after reduction for uncertainties of the radial velocity and distance
measurements. Approximately, the same low-amplitude peculiar
motions are seen around other neighbour groups (Karachentsev &
Kashibadze 2006). The dispersion of radial velocities of the centres
of these groups is also of the same order, 25 km s1, (Karachentsev
2005) and is about three times lower than the typical dispersion of
virial motions inside the groups. Finally, the peculiar velocity of
the LG itself with respect to nearby galaxies is found to be about
24 km s1.
According to Peebles (1980), a typical amplitude of peculiar
velocity Vpec on a scale of H0r relates to the average density of
matter m and the deviation in density from the mean as
Vpec = (H0r/3) 0m.6(1+ | |)1/4,
where the last term takes non-linear correction into account (Yahil
1985). According to Karachentsev et al. (2004) and Karachentsev
& Kutkin (2005), the density excess (found by the luminosity in K
band) in the sphere of 3 Mpc radius around the MW is = 4.5
0.5. Assuming m = 0.24, one can find Vpec/H0r = 0.416 on the
scale considered. For H0 = 73 km s1 Mpc1 and r = 3 Mpc, the
expected three- and one-dimensional peculiar velocities are 91 and
53 km s1, respectively. The observed chaotic motions of the
galaxies along the line of sight (25 km s1) are half of the expected ones
(53 km s1).
Systematic searches for new nearby galaxies and measuring their
distances and velocities allowed us to find the radius of the
zerovelocity surface for the LG with an accuracy of 0.03 Mpc, which
leads to uncertainty of the total mass of the LG within 1 Mpc of
around 10 per cent. This high precision is due to three main factors:
(1) the reliability of measuring individual distances via the TRGB
method with typical error of 7 per cent (Rizzi et al. 2007); (2) the
coldness of the local Hubble flow with a typical thermal velocity
v = 25 km s1 on the scales of 13 Mpc and (3) a large enough
number of galaxies in the distance region of (13)R0.
Among 77 galaxies with known radial velocities inside the sphere
of 3 Mpc radius, 30 of them (i.e. 39 per cent) are located outside
the hot virial region of the LG. This ratio may be important for
an understanding of cosmic structure formation on the scale of
AC K N OW L E D G M E N T S
This work was supported by RFBF grants 07-02-00005,
RFBFDFG 06-02-04017 and HST grant for the programs GO 10905 and
R E F E R E N C E S