The Hubble flow around the Local Group

Monthly Notices of the Royal Astronomical Society, Mar 2009

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 s−1 Mpc−1, the mean-square peculiar velocity σv= 25 km s−1, corrected for errors of radial velocity measurements (∼4 km s−1) and distance measurements (∼10 km s−1), as well as the radius of the zero-velocity surface R0= (0.96 ± 0.03) Mpc. The minimum value for σv 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 s−1 towards the Sculptor constellation. The derived value of R0 corresponds to the total mass MT(LG) = (1.9 ± 0.2) 1012 M⊙ with Ωm= 0.24 and a topologically flat universe, a value in good agreement with the sum of virial mass estimates for the MW and M31.

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The Hubble flow around the Local Group

I. D. Karachentsev 1 O. G. Kashibadze 1 D. I. Makarov 1 R. B. Tully 0 0 Institute for Astronomy of Hawaii , 2680 Woodlawn Drive, Honolulu, HI 96822, USA 1 Special Astrophysical Observatory of the Russian Academy of Sciences , Nizhnij Arkhyz, KChR, 369167, Russia 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, RA (J2000.0)D 000158.1152740 000214.5+450520 001508.5391313 001531.4321048 002633.3415120 005453.5374057 010926.9+354303 070029.3041230 091602.2+525024 095926.4+304447 100000.1+051956 100307.2260936 100404.0271955 101100.8044134 115053.0+385250 121846.1794334 122741.8+432938 125840.4+141303 133044.4+545436 135433.6+041435 140710.7+350337 141556.5+230319 142443.5+443133 161347.6+542216 174706.3643825 192959.0174041 204651.8125053 220241.9511743 224149.0642512 232627.5322326 234534.0+384304 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). 122 2 16 0.97 .02 1.36 .09 2.17 .11 1.94 .11 1.96 .12 2.15 .10 3.24 .18 1.69 .17 1.10 .10 0.80 .04 1.44 .06 1.34 .06 1.25 .09 1.32 .07 2.64 .14 2.27 .19 2.74 .14 2.13 .11 2.69 .14 2.60 .19 2.14 .12 2.24 .12 2.80 .14 1.86 .12 2.44 .19 1.04 .07 0.94 .04 1.97 .12 0.88 .04 2.22 .12 2.45 .13 14.06 8.7 18.47 11.60 10.95 17.92 16.61 12.60 11.50 11.68 14.08 15.70 9.63 13.95 13.52 14.85 14.32 12.14 13.09 10.30 9.80 12.47 14.19 9.94 15.56 11.49 11.09 15.56 9.16 12.92 10.78 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 and M31. 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 parameters. 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 4 CNG 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 comments. 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 & Aparicio (2003). 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 communication). 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 foreground. 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 D = V = R0T01 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 Virgo 14 10h 8 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 E410 005 DLG, Mpc 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 galaxies. 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. E410 005 E294 010 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 m)3/2 arccosh[(2/ m) 1]. (MT/M 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 11126. R E F E R E N C E S


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I. D. Karachentsev, O. G. Kashibadze, D. I. Makarov, R. B. Tully. The Hubble flow around the Local Group, Monthly Notices of the Royal Astronomical Society, 2009, 1265-1274, DOI: 10.1111/j.1365-2966.2008.14300.x