Aller au contenu

Est ce que le soleil se déplace t'il dans l'espace

Messier4

Par Messier4
dans Astronomie & Astrophysique

Messages recommandés

Messier4

Messier4

Posté
Posté

:)

Bonjour,

je souhaiterais savoir si le soleil se déplace t'il dans l'espace?

Car je ne comprends pas comment il peut tounre autour de nous vu qu'il et toujours à la même place.

merci

Smith

Smith

Posté
Posté
:)

Bonjour,

je souhaiterais savoir si le soleil se déplace t'il dans l'espace?

Car je ne comprends pas comment il peut tounre autour de nous vu qu'il et toujours à la même place.

merci

De mieux en mieux...:mdr:

kiwi74

kiwi74

Posté
Posté
:)

Bonjour,

je souhaiterais savoir si le soleil se déplace t'il dans l'espace?

Car je ne comprends pas comment il peut tounre autour de nous vu qu'il et toujours à la même place.

merci

 

Au bûcher !!!!!!!!!!!!!!!!!!!! :mad:

 

 

 

 

 

:be:

Lomic

Lomic

Posté
Posté

ah oui là ça pousse fort quand même :D va finir en trou noir la géante rouge ;)

schnucki

schnucki

Posté
Posté

Je ne comprend pas comment un spécialiste de la lune, des planètes et du ciel profond ne sait pas ca, :?:, c´est désolent :confused::(, mon fils de dix ans, il sait lui:be:

CATLUC

CATLUC

Posté
Posté

Salut Newton,

J'ai bien compris ce que c'était qu'un trou noir et que en premier il fallait effectuer un recherche sur google et après sur le forum si je ne comprenais pas ce qu'été un trou noir.

merci

 

Faudrait mettre en pratique maintenant.:mad:

schnucki

schnucki

Posté
Posté
Messier,

 

le soleil ne tourne pas autour de nous

c'est la Terre qui tourne autour de lui, comme toutes les planètes ;)

 

Mauvaise réponse:b::p, le mouvement qui laisse le plus à penser que le soleil bouge, comme le sous entend messier4, c´est le mouvement de la terre sur elle-même au quotidien, et pas son déplacement annuel autour du soleil.

Messier4

Messier4

Posté
  • Auteur
Posté
Salut Newton,

J'ai bien compris ce que c'était qu'un trou noir et que en premier il fallait effectuer un recherche sur google et après sur le forum si je ne comprenais pas ce qu'été un trou noir.

merci

 

Faudrait mettre en pratique maintenant.:mad:

 

Salut Catluc,

Je te remercie pour tes conseils.

Mais je vais mettre cela en pratique de suite, sachant que je viens juste de me rendre compte que j'avais une bibliothèque complète de livre sur l'astronomie.

Merci

:)

Messier4

Messier4

Posté
  • Auteur
Posté

Salut christel,

merci pour cette info, je connais bien ciel et espace.

Car j'achète la revue mensuel tous les mois.

merci

CATLUC

CATLUC

Posté
Posté
Salut christel,

Car j'achète la revue mensuel tous les mois.

merci

 

Ouf il était super Sylvain du CNED après tout.:confused:

syncopatte

syncopatte

Posté
Posté
Salut syncopatte,

A tu une réponse à ma question ou pas?

merci

 

Evidemment:

 

THE ASTRONOMICAL JOURNAL, 118:337-345, 1999 July

© 1999. The American Astronomical Society. All rights reserved. Printed in U.S.A.

THE SOLAR MOTION RELATIVE TO THE LOCAL GROUP STÉPHANE COURTEAU AND SIDNEY VAN DEN BERGH

Dominion Astrophysical Observatory, Herzberg Institute of Astrophysics, National Research Council, 5071 West Saanich Road, Victoria, BC V8X 4M6, Canada

Received 1999 March 4; accepted 1999 March 17 ABSTRACT New data on the membership of the Local Group (LG) are used, in conjunction with new and improved radial velocity data, to refine the derivation of the motion of the Sun relative to the LG. The Sun is found to be moving with a velocity of V = 306 ± 18 km s-1 toward an apex at l = 99° ± 5° and b = -4° ± 4°. This finding agrees very well with previous analyses, but we discuss the possibility of a bias if the phase-space distribution of LG galaxies is bimodal. The LG radial velocity dispersion is 61 ± 8 km s-1. We use various mass estimators to compute the mass of the LG and the Andromeda subgroup. We find MLG = (2.3 ± 0.6) × 1012 Modot.gif, from which M/LV = 44 ± 12 (in solar units). For an assumed LG age of 14 ± 2 Gyr, the radius of an idealized LG zero-velocity surface is r0 = 1.18 ± 0.15 Mpc. The LG is found to have 35 likely members. Only three of these have (uncertain) distances gsim.gif1.0 Mpc from the LG barycenter. Barring new discoveries of low surface brightness dwarfs, this suggests that the LG is more compact and more isolated from its surroundings than previously believed.

Key words: galaxies: clusters: general; galaxies: kinematics and dynamics; galaxies: spiral; Local Group

 

1. INTRODUCTION The motion of the Sun relative to the other members of the Local Group (LG) has been studied for many decades, with investigations by Humason, Mayall, & Sandage (1956), Yahil, Tammann, & Sandage (1977, hereafter YTS77), Sandage (1986), Karachentsev & Makarov (1996), and Rauzy & Gurzadyan (1998 and references therein; hereafter RG98). YTS77 and many others have stressed the importance of understanding the solar motion relative to the LG in the context of the large-scale motions of galaxies. The reliability of measurements of peculiar motions in the universe, or residual motion from the uniform Hubble expansion, depends in part on accurate knowledge of the motion of the solar system relative to any standard inertial frame. This inertial rest frame is usually taken as the centroid of the Local Group of galaxies or the reference frame in which the dipole of the cosmic microwave background (CMB) vanishes (Kogut et al. 1993). The motion of the Sun relative to the CMB can be decomposed into a sum of local and external components:1

 

df1.gif

 

 

VSunrarr.gifLSR is the motion of the Sun relative to the nearby stars that define a local standard of rest (LSR), and the motion VLSRrarr.gifGSR is the circular rotation of the LSR about the Galactic center, which is directed toward l = 90° and b = 0°. Externally, VGSRrarr.gifLG is the motion of the Galactic center (or Galactic standard of rest) relative to the LG centroid, which is caused by nonlinear dynamics within the LG (mostly infall of the Galaxy toward M31). Finally, VLGrarr.gifCMB is the peculiar velocity of the LG in the CMB rest frame, induced by gravitational perturbations in the universe.

Recent discoveries of new candidate members of the LG, and the deletion of former candidates, have allowed us to revise the solution for the solar motion relative to the LG, VSunrarr.gifLG, to assess Group membership, and to compute a new value for the mass of the LG. Three criteria are usually invoked to assess the probability that a galaxy is associated with the LG: (1) The distance to that galaxy from the LG barycenter should be less than (or comparable to) the radius at the zero-velocity surface (Lynden-Bell 1981; Sandage1986), (2) the galaxy should lie close to the ridgeline solution between radial velocity and the cosine of the angle from the solar apex relative to well-established LG members, and (3) it should not appear to be associated with any more distant group of galaxies centered well beyond the limits of the LG. We examine these criteria below.

This paper is organized as follows: First, in § 3, we compute a new solution for the motion of the Sun relative to LG members. Then in § 4 we estimate the radius of the zero-velocity surface, and we assess LG membership in § 5, based on the three criteria listed above. We conclude in § 6 with a brief discussion and summary and a digression on the detectability of small groups like the LG using X-ray telescopes.

Recent studies of the membership in the LG also include van den Bergh (1994a, 1994b), Grebel (1997), and Mateo (1998). The reader is referred to van den Bergh (2000, hereafter vdB2000) for a comprehensive review of the nature of the LG and the question of membership in it.

1 Our notation is analogous to that of RG98.

2. DATA A listing of information on the 32 probable (and three possible) members of the LG that were isolated using the criteria discussed above is given in Table 1. Columns (1)ndash.gif(3) give the names and David Dunlap Observatory morphological types (van den Bergh 1966, 1994b) for each LG member. Equatorial (J2000.0) and Galactic coordinates are listed in columns (4)ndash.gif(7). Various photometric parameters taken from vdB2000 (visual color excess, absolute visual magnitude, and true distance modulus) are listed in columns (8)ndash.gif(10). Column (11) gives the heliocentric radial velocity of each galaxy in kilometers per second, and column (12) lists the cosine of the angle between each galaxy and the solar motion apex in the rest frame of the LG. Columns (13) and (14) give the distance of a galaxy from the Sun and from the LG barycenter in megaparsecs. Finally, column (15) gives the main reference to each of the radial velocities quoted in column (11). The LG suspects at large distances (footnoted in Table 1) are Aquarius (DDO 210), with a distance from the LG center of 1.02 ± 0.05 Mpc (Lee 1999), Tucana, at sime.gif1.10 ± 0.06 Mpc (vdB2000), and Sag DIG, with a poorly determined LG distance of 1.20 Mpc lsim.gifD lsim.gif 1.58 Mpc (Cook 1987). Uncertain entries in Table 1 are followed by a colon.

tb1.t.gifTABLE 1 OBSERVATIONAL DATA ON LOCAL GROUP MEMBERS

The positions of LG members in Cartesian Galactocentric coordinates are shown in Figure 1. The velocity components, X, Y, Z, of an object point toward the Galactic center (l = 0°, b = 0°), the direction of Galactic rotation (l = 90°, b = 0°), and the north Galactic pole (b = + 90°), respectively.

fg1.t.gif

FIG. 1.mdash.gifPositions of LG members in Galactic Cartesian coordinates, as viewed from two orthogonal directions. The left side shows a sphere of radius r0 = 1.18 Mpc (corresponding to the zero-velocity surface of the LG) as a solid line. The dotted line shows a sphere of radius rh = 450 kpc, which encompasses both the Andromeda and Galaxy subgroups. Both spheres are centered on the LG barycenter at X = -220, Y = +361, and Z = -166 kpc. For clarity, not all the LG members have been labeled. Filled circles represent galaxies within the Andromeda/Galaxy volume; LG members outside of this sphere are plotted as crosses. The Galaxy, M31, and M33 are shown with a spiral galaxy symbol.

 

We have calculated distances of individual galaxies relative to the LG barycenter by (1) assuming that most of the LG mass is concentrated in the Andromeda and Galactic subgroups, (2) adopting a distance to M31 of 760 kpc (vdB2000), and (3) assuming that M31 is 1.5 times more massive than the Milky Way (Mateo 1998; Zaritsky 1999 and references therein). Lacking more detailed information about the mass constituents of the LG, it seems reasonable to expect that the local center of mass will be situated on the line between our Galaxy and M31 in the direction of M31. The LG barycenter is located at 0.6 times the distance to M31, at 454 kpc toward l = 121fdg.gif7 and b = -21fdg.gif3.In Galactic Cartesian coordinates this corresponds to X = -220, Y = +361, and Z = -166 kpc.

Histograms of the differential and cumulative distance distributions of the LG members relative to its barycenter are shown in Figures 2 and 3, respectively. These figures show that all probable LG members have distances lsim.gif850 kpc from the dynamical center of the LG. Taken at face value, this suggests that the core of the LG may be smaller and more isolated from the field than has generally been assumed (e.g., Jergen, Freeman, & Bingelli 1998; Pritchet 1998).

fg2.t.gif

FIG. 2.mdash.gifHistogram showing the distribution of measured distances of all known LG members from the LG dynamical center. It is seen that the membership drops steeply beyond DLG sime.gif 0.85 Mpc. The density of galaxies near DLG = 0 is small because the center of the LG is situated between the Andromeda and Galactic subgroups, where few galaxies are found.

 

fg3.t.gif

FIG. 3.mdash.gifCumulative distance distribution of all known LG members. This histogram shows that the core of the LG has lsim.gif0.85 Mpc. Half of the known members of the LG are seen to located within 450 kpc of the adopted barycenter.

 

3. SOLAR MOTION RELATIVE TO LOCAL GROUP MEMBERS Using the line-of-sight velocities and positions of probable LG members (Table 1), we compute a new solution for the bulk motion of the Sun relative to the LG centroid. The computation of a bulk flow vB is independent of estimated distances to any of the galaxies, or the exact shape of their orbits, provided that the spatial and velocity distributions are independent (see, e.g., YTS77; RG98). If the three-dimensional velocity distribution is invariant under spatial translations, one can further assume that the global velocity field can be decomposed into the sum of a bulk flow vB and a three-dimensional random isotropic Maxwellian distribution with a velocity dispersion sigma.gifv. The bulk flow statistics reduces to the maximization of the likelihood function

 

df2.gif

 

where vimg1.gif is the observed radial velocity of galaxy k and the components {img2.gifimg3.gif}j=1,2,3 are the direction cosines of that galaxy. The inferred solar apex corresponds to the direction that minimizes scatter in the distribution of radial velocities versus cos thetas.gif, where thetas.gif is the angle between the solar apex and the unit vector toward each galaxy.

Details on such techniques and confidence in the estimators can be found in YTS77 and RG98 (our estimator is identical to that developed by RG98). The observational errors in the radial velocities are relatively small, and they are insignificant compared with the residual velocity dispersion. They are therefore neglected. Here we adopt the values quoted by the main source in column (15) of Table 1. Standard deviations for the amplitude and direction of the solar motion and for the residual velocity dispersion of the LG are estimated by bootstrap resampling of the input data(these are also available from the Hessian matrix of secondderivatives). The errors quoted correspond to the 1 sigma.gif dispersion for each parameter.

A maximum likelihood solution, giving equal weight to all 26 objects with measured heliocentric radial velocities, yields a solar motion with Vodot.gif = 306 ± 18 km s-1 toward an apex at l = 99° ± 5° and b = -3° ± 4°. The residual radial velocity dispersion in the LG is sigma.gifr = 61 ± 8 km s-1. Assuming the velocity distribution of LG galaxies to be isotropic, the three-dimensional velocity dispersion in the LG is sime.gif106 km s-1.

A comparison with other published solutions for the motion of the Sun relative to the LG barycenter is given in Table 2. With the exception of RG98, most solutions are found to be in agreement with each other to within their quoted errors. For example, our solution seldom differs by more than 1 km s-1 from YTS77, with a maximum deviation of ±2 km s-1.

tb2.t.gifTABLE 2 SOLAR MOTION RELATIVE TO THE LOCAL GROUP

The good agreement among most published solutions is not fortuitous. The dynamics of the LG are heavily dominated by systems that were already included in the sample of Mayall (1946, the earliest reference cited here). The addition of new members, especially to the Galaxy subgroup (which now accounts for half of all known LG members with a measured redshift), has not altered the solar motion solution in any significant way. Moreover, most studies of solar motion relative to LG galaxies have assumed a uniform potential that governs LG dynamics. The solar motion amplitude measured by Sandage (1986) assumes a two-to-one mass ratio between M31 and our Galaxy. A lower mass ratio of 1.5, as we advocate here, would yield an even lower amplitude.

The result by RG98 differs more substantially from all others because of the different nature of their approach. As a first step, RG98 recognize the existence of the two main dynamical substructures within the LG, namely, the Galaxy subgroup (13 galaxies)2 and the Andromeda subgroup (seven galaxies). For each subgroup, RG98 estimate a bulk flow using equation (2). They find, in Galactocentriccoordinates, VGalsubrarr.gifSun = (94 ± 64, -354 ± 42, 37 ± 33)km s-1, or |VGalsubrarr.gifSun| = 368 ± 28 km s-1 toward(l = 285° ± 11°, b = +6° ± 5°), and VAndsubrarr.gifSun = (-127 ± 541, -143 ± 267, 301 ± 254) km s-1, or |VAndsubrarr.gifSun|= 357 ± 218 km s-1 toward (l = 228° ± 180°, b =+58° ± 65°). The error bars for the bulk flow estimate of the Andromeda subgroup are large because of the small number of galaxies involved in the statistics, and because of the narrow angular size of the subgroup on the sky (i.e., bulk flow components perpendicular to the M31 line of sight are poorly constrained). RG98 compute the global bulk flow of the LG as the mean motion of its main dynamical substructures, equally weighted, i.e., VLGrarr.gifSun = (VGalsubrarr.gifSun + VAndsubrarr.gifSun)/2, which yields VLGrarr.gifSun =(-17 ± 303, -249 ± 155, 169 ± 144) km s-1, or|VLGrarr.gifSun| = 301 km s-1 toward (l = 266°, b = +34°). The residual velocity dispersion is sigma.gifr = 110.3 km s-1. Error bars are thus larger in RG98's treatment because of the poor estimate of the M31 subgroup's bulk flow.

RG98 suggest that the phase-space distribution of LG galaxies is bimodal. Application of bulk flow statistics from equation (2) to a uniform LG distribution may therefore be biased. Indeed, with the exception of RG98, the results quoted in Table 2 apply if the velocity distribution function of selected LG galaxies is the sum of a three-dimensional bulk flow, plus a random component that does not correlate with the spatial position of galaxies. However, solar motion solutions that assume a uniform three-dimensional structure for the LG may be biased if the Andromeda subgroup bulk flow VAndsubrarr.gifSun differs significantly from that of the Galaxy subgroup VGalsubrarr.gifSun.

This suggestion is supported by RG98's analysis and corroborated by our own reexamination of this issue. Our analysis, based on equation (2), also suggests that the Andromeda subgroup would partake of a different, stronger bulk motion than the Galaxy subgroup. But, given the large errors in the apex parameters of the Andromeda subgroup, it would be premature to make any claims based on these results. In any case, the poor number statistics do not allow a rejection or confirmation of this hypothesis. All solutions that account for subgrouping or a uniform structure of the LG agree to within their 1 sigma.gif confidence interval.

2 RG98's "Milky Way" subgroup does not include the newly discovered Sagittarius dwarf spheroidal.

3.1. Summary of Corrections to Radial Velocities The correction to heliocentric radial velocities Vhel for a solar apex of direction (la, ba) and amplitude Va in any reference frame can be expressed as

 

df3.gif

 

where l and b are the Galactic coordinates to the observed galaxy. The peculiar motion of the Sun relative to the LSR is 16.5 km s-1 toward l = 53° and b = + 25° (Delhaye 1965; see also Crampton 1968), or X = +9, Y = +12, and Z = +7 km s-1 (note the typographical error in eq. [1] of Braun & Burton 1999). Therefore,

 

df4.gif

 

 

The Galactic rotation has an amplitude Y = 220 ± 20 km s-1 (X = 0, Z = 0) toward l = 90° and b = 0° (IAU1985 convention; see Kerr & Lynden-Bell 1986). Therefore,the corrected radial velocity of a galaxy in the Galactic standard of rest is

 

df5.gif

 

 

The corrections given above are widely used and accepted (de Vaucouleurs et al. 1991, hereafter RC3). We also found (see § 3) the correction for motion of the Sun relative to the LG centroid as

 

df6.gif

 

under the assumption that the velocity distribution function in the LG can be described as bulk flow plus a random isotropic Maxwellian component. Applying the same premises, not to the LG as a whole as we did, but to the two main LG substructures, RG98 find (see also Table 2)

 

df7.gif

 

 

The RC3 does not include any corrections for galaxy motions in the frame of the LG, on account of their ill-defined nature. This was perhaps a wise decision. De Vaucouleurs et al. (1976, hereafter RC2) report the "old" solar apex solution (300 sin l cos b), but modern solutions (Table 2) show deviations from the RC2 formulation as large as ±87 km s-1, as already noted by YTS77. Perhaps even more important are the deviations that exist between our solution and that of RG98. The maximum deviations (eqs. [6], [7], and [8]) are ±154 km s-1 toward (l = 145°, b = + 60°) and (l = 325°, b = -60°). These are shown in Figure 4, with negative and positive residuals represented by stars and circles, respectively.

fg4.t.gif

FIG. 4.mdash.gifAitoff projection in Galactic coordinates showing the residuals between our solution for the solar motion relative to the LG (eq. [6]) and that of RG98 (eq. [7]). The size of the symbols is linearly proportional to the magnitude of the residual, the largest ones being +154 km s-1 in the direction (l = 145°, b = + 60°), and -154 km s-1 toward (l = 325°, b = -60°). Positive and negative residuals (this paper; RG98) are shown with circles and stars, respectively.

 

In choosing a reference frame for cosmological studies, one may transform heliocentric radial velocities to the CMB frame (e.g., Kogut et al. 1993). Under the assumption that the CMB dipole is kinematic in origin, and not the product of any external force field, this operation carries little uncertainty. On the other hand, the transformation to the LG rest frame is free of any assumptions about the origin of the CMB dipole and minimizes the effect of the mass distributed outside the sample. Modern solutions for solar motion with respect to LG galaxies that assume a uniform LG potential and a fixed LG barycenter are robust. These studies yield nearly identical solutions (e.g., Table 2). However, this result can be due either to the homogeneous nature of the LG or to the fact that we are making similar erroneous assumptions. The kinematic method described above can lead to biased results if the phase-space galaxy distribution is not homogenous. The use of a dynamical method to reconstruct the orbits of individual LG galaxies could provide a potentially more accurate description of the motion of the LG center of mass. Such a method, based on least-action principles, has been proposed (Shaya, Peebles, & Tully 1995), but it depends on a reliable knowledge of the galaxy distribution outside the LG, which is lacking at present. Clearly, it is the prerogative of the astronomer to adopt (and justify) whatever cosmological rest frame he or she prefers.

Given that the mean motion of the LG is consistent with the combined motion of its two main substructures, we will adopt the "standard" solution (eq. [6]) as the best description of solar motion relative to the LG. However, one should keep in mind the main caveats/assumptions for this solution, as we reiterate in § 6.

4. MASS OF THE LOCAL GROUP If we assume that the LG is in virial equilibrium and that its velocity ellipsoid is isotropic (sigma.gif2 = 3sigma.gifimg4.gif), then the mass of the LG can be computed from its velocity dispersion (Spitzer 1969; see also Binney & Tremaine 1987, eqs. [4]ndash.gif[80b]) as

 

df8.gif

 

where rh is the radius in kpc containing half the mass as measured from the center of the isotropic distribution. The numerical value of rh can be estimated from the cumulative distance distribution of LG members shown in Figure 2. We find that rh sim.gif 450 kpc. This number-weighted figure is clearly an upper limit to the actual mass-weighted estimate. If M31 accounts for approximately 60% of the mass in the LG, a simple mass distribution model gives rh sime.gif 350 kpc. Using this value and sigma.gifr = 61 ± 8 km s-1, we find MLG = (2.3 ± 0.6) × 1012 Modot.gif.

It is of interest to tally the mass of individual LG components. To compute the mass of the Andromeda subgroup, we use the projected mass method of Bahcall & Tremaine (1981) and Heisler, Tremaine, & Bahcall (1985; see also Aceves & Perea 1999). In the absence of specific information on the distribution of orbital eccentricities, the projected mass estimator is given by

 

df9.gif

 

where R is the projected separation from M31 (assuming DM31 = 760 kpc) and Vimg5.gif is the radial velocity in the frame of M31. Table 3 gives the relevant parameters for all seven known members of the Andromeda subgroup. We find that the Andromeda subgroup has a mass of (13.3 ± 1.8) × 1011Modot.gif, the lower and upper bounds corresponding to the virial and projected mass estimates, respectively, following the notation of Heisler et al. (1985).

tb3.t.gifTABLE 3 THE ANDROMEDA SUBGROUP

From the inferred motion of nearby satellites, Zaritsky (1999) shows that the Galactic subgroup has a massof (8.6 ± 4.0) × 1011Modot.gif. Thus, the two major subgroups have a combined mass of (21.9 ± 4.4) × 1011Modot.gif. This may be compared to the virial mass of (23 ± 6) × 1011 Modot.gif found above for the entire LG. This agreement may be fortuitous if the LG is not in virial equilibrium or if the LG potential is nonisotropic. However, taken at face value, this result suggests that most of the dark and luminous mass in the LG is locked into the Andromeda and Galactic subgroups, unless the intracluster dark matter is distributed in a highly flattened shape. The timing argument by Kahn & Woltjer (1959), which is based on the motion of the Galaxy toward M31, yields a minimum LG mass of about 18 × 1011 Modot.gif. Sandage (1986), using a similar argument for the deceleration of nearby galaxies caused by the LG, finds a maximum mass for the LG equal to 5 × 1012 Modot.gif, with a best-fit value of 4 × 1011 Modot.gif. He also arrives at this low value by using the dispersion as a virial velocity to compute a virial mass for the LG. The formula he used for the virial mass differs by a factor of 7.5 from ours (eq. [8]), introduced by replacing sigma.gif2 = 3sigma.gifimg4.gif for an isotropic velocity ellipsoid and considering the half-mass radius, rh, instead of the ill-defined gravitational radius rg. Sandage also used an estimate for rg that is too small by a factor of about 2 (if rh sime.gif 0.4rg). This explains the discrepancy "by a factor of 7" (compared with Kahn-Woltjer) discussed by Sandage. Moreover, his result, that MLG = 4 × 1011 Modot.gif based on a velocity perturbation analysis of the LG, assumes a formation age of 18.1 Gyr (H0 = 55 km s-1 Mpc-1 for an Omega.gif = 0 universe) and that MM31 = 2MGal. Adoption of revised figures, H0 = 65 km s-1 Mpc-1 and MM31 = 1.5MGal, yields a model-data comparison that agrees perfectly well with MLG = (2.3 ± 0.6) × 1012 Modot.gif (see Sandage 1986, Fig. 11). Thus, both calculations in Sandage (1986) are consistent with a higher value for MLG, equal to the one we measure.

From the absolute magnitudes of LG galaxies listed in Table 1, we compute the total luminosity of the LG to be LV = 5.2 × 1010 Lodot.gif,3 corresponding to MV(LG) = -22.0. Combined with our estimate of the virial mass and assuming a 10% error in LV, we measure M/LV = 44 ± 12 in solar units.4 It is perhaps worth noting that M31 and the Galaxy together provide 86% of the luminosity of the LG. The uncertainty in MV(Galaxy) and in MV(M31) contributes significantly to the error of the integrated luminosity of the LG.

Finally, one can compute the radius of the zero-velocity surface, r0, that separates Hubble expansion from cluster contraction at the present epoch (Lynden-Bell 1981; Sandage 1986). As the universe expands, the zero-velocity surface moves outward with time. If the total random components of the velocity field cancel out, one can write, from equation (7) of Sandage (1986),

 

df10.gif

 

 

Assuming that the age of the LG is 14 ± 2 Gyr, and using our estimate of the virial mass of the LG, we find r0 = 1.18 ± 0.15 Mpc. The value of r0 given above can now be used to assess LG membership.

3 Adopting MVodot.gif = +4.82 ± 0.02 (Hayes 1983).

4 Sandage (1986) finds M/L sim.gif 25 for MLG sim.gif 3 × 1012 Modot.gif. His lower M/L estimate is based in part on a higher estimate for the total luminosity of the Local Group.

5. LOCAL GROUP MEMBERSHIP On the basis of the membership criteria listed in § 1, van den Bergh (1994b) concluded that it was safe to exclude the following galaxies from membership in the LG: (1) the Sculptor irregular (=UKS 2323-326), (2) Maffei 1 and itscompanions, (3) UGCA 86 (=A0355+66), (4) NGC 1560, (5) NGC 5237, and (6) DDO 187. A particularly strong concentration of LG suspects, including objects 2, 3, 4, and 5 listed above, occurs in the direction of the IC 342/Maffei Group (van den Bergh 1971; Krismer, Tully, & Gioia 1995), which Krismer et al. place at a distance of 3.6 ± 0.5 Mpc. Cassiopeia 1, regarded as an LG suspect (Tikhonov 1996), also appears to be a member of the IC 342/Maffei Group. Van den Bergh & Racine (1981) failed to resolve LG suspect LGS 2 on large reflector plates. They conclude that this object is either a Galactic foreground nebula, or an unresolved stellar system at a much greater distance than that of M31 and M33. Another longtime LG suspect is DDO 155 (=GR 8). However, observations by Tolstoy et al. (1995) have resulted in the discovery of a single probable Cepheid, which yields a distance of 2.2 Mpc, so that this galaxy would lie outside of the LG boundary. The spiral galaxy NGC 55 has recently been listed as a possible LG member by Mateo (1998). However, it appears preferable to follow in the footsteps of de Vaucouleurs (1975), who assigns this galaxy to the Sculptor (South Polar) Group. Côté, Freeman, & Carignan (1994) show that NGC 55 is located close to the center of the distribution of dwarf galaxies associated with the South Polar Group. Furthermore, photometry in J, H, and K by Davidge (1998) shows that NGC 55, NGC 300, and NGC 7793 are located at comparable distances. Sandage & Bedke (1994, panel 318) write, "NGC 55 is very highly resolved into individual stars, about equally well as other galaxies in the South Polar Group such as NGC 247 and NGC 300. Evidently, NGC 55 is just beyond the Local Group." Finally, Jergen et al. (1998) place NGC 55 on the near side of the Sculptor Group. We have also excluded the galaxies NGC 3109, Antlia, Sextans A, and Sextans B from membership in the LG. These objects, which have measured distances of 1.36, 1.33, 1.45, and 1.32 Mpc, respectively (vdB2000), are located relatively close together on the sky. Their mean distance from the barycenter of the LG, which is situated about 450 kpc away in the direction toward M31, is 1.7 Mpc. Furthermore, these galaxies have a mean redshift of 114 ± 12 km s-1 relative to the Vrndash.gifcos thetas.gif relation derived in § 3 (see vdB2000). These data suggest that NGC 3109, Antlia, Sextans A, and Sextans B form a physical grouping that is receding from LG and that lies just beyond the LG zero-velocity surface (van den Bergh 1999). We note that NGC 3109, Sextans A, and Sextans B were also excluded by YTS77 on the basis of their solar motion solutions. Zijlstra & Minniti (1999) find that the LG candidate IC 5152 is located at 1.8 ± 0.2 Mpc, which places it outside the LG zero-velocity surface.

Group membership can be revised by inspection of the Vrndash.gifcos thetas.gif diagram, which illustrates the motions of individual galaxies with respect to the ensemble of the galaxies in the Group. This is shown in Figure 5 for LG galaxies (see also Fig. 6). The LG radial velocity dispersion, sigma.gifr = 61 ± 8 km s-1, is shown by dotted lines. Suspected outliers lying below the 1 sigma.gif regression line are few. None of the systems presented in Figure 5 can be excluded from membership on the basis of this test. The two blueshifted systems (IC 1613 and Pisces), and a handful of redshifted LG objects, fall within 2 sigma.gif of the regression line. Membership for many recently discovered dwarf spheroidals cannot be examined with this test, because their radial velocities are not yet available.

fg5.t.gif

FIG. 5.mdash.gifObserved heliocentric velocities Vr of LG members vs. cos thetas.gif, where thetas.gif is the angular distance from the solar apex. Our solar motion solution of 306 ± 18 km s-1 toward l = 99° ± 5° and b = - 3° ± 4° is shown as the solid ridgeline. Dotted lines correspond to the residual radial velocity dispersion of ±61 km s-1 from the ridge solution. Note the large deviations of Leo I and of the Sagittarius dwarf (which is strongly interacting with the Galaxy) from the mean motion of LG members.

 

fg6.t.gif

FIG. 6.mdash.gifSame as Fig. 5, but using the solar motion solution of RG98 with Vodot.gif = 306 ± 18 km s-1 toward l = 94° ± 48° and b = -34° ± 29°. For comparison, the solid ridgeline and dotted dispersion lines are those computed for Fig. 5. Note that the dispersion around the regression relation of RG98 (eq. [7]) is twice larger (sigma.gifr = 110.3 km s-1) than that for the standard solution shown in Fig. 5.

 

Figure 1 shows that most of the LG members are concentrated in subgroups that are centered on the Andromeda galaxy and on the Milky Way system. However, a few objects, such as NGC 6822, IC 1613, Leo A, and the WLM system, appear to be free-floating Group members. Aquarius (=DDO 210), Tucana, and Sag DIG are so far from the barycenter of the LG that their membership in the LG cannot yet be regarded as firmly established, even though they lie close to the solar ridgeline in the Vrndash.gifcos thetas.gif diagram.

It might be argued that our value of sigma.gifr is biased low because the database may lack (unknown) nearby fast-moving galaxies. However, this effect is probably not important, because no galaxies are found with large blueshifts relative to the mean relationship between cos thetas.gif and apex distance.

6. DISCUSSION AND SUMMARY We have measured a new solution for the solar motion relative to LG galaxies that agrees very well with previous derivations by, e.g., YTS77, Sandage (1986), and Karachentsev & Makarov (1996). Following RG98, it is worth pointing out that these solutions are only physically meaningful under the assumption that the three-dimensional spatial and velocity distributions are independent. This would not be true if the LG potential were bimodal. This is verified by computing the motion of the Sun relative to the two main LG substructures, the Andromeda and Galaxy subgroups, and testing whether their combined motion matches that inferred relative to the entire LG. Preliminary indications suggest that the Andromeda subgroup is moving faster with respect to the Sun and in a different direction from the Galaxy subgroup. However, the error bars (mostly for VSunrarr.gifAndsub) are far too large to rule out the "standard" solution. Indeed, the combined subgroup solutions are perfectly consistent with our final derivation for the solar motion relative to all LG members with VSunrarr.gifLG = 306 ± 18 km s-1 toward an apex at l = 99° ± 5° and b = -4° ± 4°. It is worth pointing out that interpretation errors for the solar motion may linger until we obtaina better understanding of the true orbital motions of LG members and a better knowledge of the overall distribution of mass in the LG.

The observed radial velocity dispersion of the LG is sigma.gifr = 61 ± 8 km s-1. Braun & Burton (1999) measured a radial velocity dispersion sigma.gifr = 69 km s-1 for the motion of intracluster compact H I high-velocity clouds (HVCs). Although close in dispersion to the LG value, HVCs exhibit an excess of infall velocities (blueshifts), suggesting that many of them may still be falling into the LG at present, contrary to bona fide LG galaxies.

Table 1 presents an updated listing of 35 probable members of the LG. Half of all the members are located within 450 kpc of the barycenter of the LG, with only three objects, Sag DIG, Aquarius, and Tucana, being more than 1 Mpc away. These results show that the (binary) core of the LG is relatively compact and well-isolated from other nearby clusters. This conclusion was already anticipated by Hubble in his Realm of the Nebulae (Hubble 1936, p. 125): "the Local Group is [a] typical, small group of nebulae which is isolated in the general field." One must, however, remain cautious about these statements in light of the surprisingly high rate of recent discoveries of new members that are low surface brightness dwarfs. These have all been discovered at distances Lt.gifr0, for obvious observational reasons, but it would be premature to exclude a significant population of low surface brightness galaxies at greater distances as well.

Adopting a half-mass radius rh = 0.35 Mpc and an LG age of 14 ± 2 Gyr yields a radius r0 = 1.18 ± 0.15 Mpc for the zero-velocity surface of the LG and a total LG mass MLG = (2.3 ± 0.6) × 1012 Modot.gif. This mass determination is valid, of course, only if the LG is in virial equilibrium. The fact that an equal number of LG members are blueshifted and redshifted relative to the adopted solar motion suggests that the LG may be at least approaching virial equilibrium. An independent "projected" mass estimate for the Andromeda subgroup, combined with mass information for the Galaxy subgroup published by Zaritsky (1999), yields nearly the same total mass for the LG, independent of any assumption about the virial nature of the LG. With this mass, the visual mass-to-light ratio (in solar units) for the LG is 44 ± 12.

Mulchaey & Zabludoff (1998) find that the velocity dispersion of clusters of galaxies and their X-ray luminosities and temperatures are related by the relations

 

df11.gif

 

 

 

df12.gif

 

where the dimensionless Hubble ratio h is given by H0 = 100 h km s-1 Mpc-1. Extrapolating these relations to small values of sigma.gifr, and adopting h = 0.65 and sigma.gifr = 61 ± 8 km s-1, one obtains T ap.gif 74 eV and LX ap.gif 4.5 × 1039 ergs s-1 for the intracluster gas in the LG. These numbers suggest that it would be difficult, with current X-ray instrumentation and because of the strong absorption by our galaxy below 0.5 keV, to detect X-ray emission from any small group like the LG.

We would like to thank Stéphane Rauzy for sharing his likelihood estimator and for useful comments on the paper.

REFERENCES

Copier coller d'ici:

http://www.iop.org/EJ/article/1538-3881/118/1/337/990091.text.html

 

Patte.

Super

Super

Posté
Posté
j'achète la revue mensuel tous les mois.

 

Encore une chance que que ce ne soit pas hebdomadaire, tu aurais dû l'acheter toutes les semaines, ou quotidien, tous les jours ...

 

Salut syncopatte,

je te remercie pour ta très longue réponse.

MERCI

 

Moi aussi, même si ya une ou deux équations qui me paraissent pas tout à fait justifiées

 

Car je ne comprends pas comment il peut tounre autour de nous vu qu'il et toujours à la même place.

 

tu nous fais bien tourner en rond, et pourtant tu es à la même place !

 

 

sachant que je viens juste de me rendre compte que j'avais une bibliothèque complète de livre sur l'astronomie.

 

Quelque part j'ai envie que tu restes sur le fofo car tu es "marrant", mais d'un autre coté, si tu restes, bin tu vas mourir !

Messier4

Messier4

Posté
  • Auteur
Posté
Encore une chance que que ce ne soit pas hebdomadaire, tu aurais dû l'acheter toutes les semaines, ou quotidien, tous les jours ...

 

 

 

Moi aussi, même si ya une ou deux équations qui me paraissent pas tout à fait justifiées

 

 

 

tu nous fais bien tourner en rond, et pourtant tu es à la même place !

 

Salut,

Je n'ai pas envie de vous faire tourner en rond car je m'en fiche un peut vois tu, et je ne suis pas prêt de mourir.

bref, à tu une idée de réponse à ma question?

merci

Will

Will

Posté
Posté

Bon, puisque tu as une bibliothèque complète de livres sur l'astronomie, tu pourras donc trouver la réponse à ta question.

 

On ferme.

Archivé

Ce sujet est désormais archivé et ne peut plus recevoir de nouvelles réponses.

Aller sur la liste des sujets

  • En ligne récemment   0 membre est en ligne

    • Aucun utilisateur enregistré regarde cette page.
×
×
  • Créer...

Information importante

Nous avons placé des cookies sur votre appareil pour aider à améliorer ce site. Vous pouvez choisir d’ajuster vos paramètres de cookie, sinon nous supposerons que vous êtes d’accord pour continuer.