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5. Common halos

Most galaxies are in more or less large clusters. In the analytic, hierarchical CDM scenario, halos are the result of the merging of smaller, less massive, denser, previously formed halos. Once the new large halo is formed, violent relaxation erases any internal substructure, and therefore halos within halos should not be expected from this type of model. As an exception, visible galaxies may survive the merging process, and therefore we might expect to find several visible galaxies in a halo. High resolution N-body simulations have, however, been able to resolve some sub-structures, or subhalos, within dark matter halos (Colin et al. 1999; Benson et al. 1999 and others) even if tidal disruption, spatial exclusion of subhalos, dynamical friction and other effects complicate the global picture. In view of these difficulties and given the number of free parameters inherent to these calculations, let us keep the classical scenario in which: a) no subhalos exist within a halo; b) several visible galaxies may reside in the same halo; c) a halo can have no visible galaxy; d) no visible galaxy can exist outside a halo. This picture is fully compatible with the essentials of hierarchical CDM models, even if the above mentioned particular models keep track of subhalos. The purpose of this argument is to comment on the possible picture in which a large percentage of spiral galaxies are embedded in common halos, instead of each having their own.

Common halos could be present in clusters and associations at all levels, from binary systems to rich clusters. The hypothesis of common halos is not new (see the review by Ashman 1992, for instance). Let us briefly consider the different systems:

a) Dwarf irregular satellites around a bright galaxy. Following White & Rees (1978), when the halos of the first small galaxies are disrupted to form bigger units, the residual gas may again be able to cool and collapse to form a larger central galaxy. The model naturally predicts the existence of small satellites around big galaxies. Therefore, this and some subsequent models implicitly assume that the satellites have no halo of their own, but are instead in the halo of the bright galaxy, even if observations seem to indicate that these satellites are DM rich (e.g. Ashman 1992).

b) Binary galaxies. In the well-known paper by Kahn & Woltjer (1959), it was considered, as an alternative interpretation, that the unseen mass was forming a common envelope. van Moorsel (1987), observing HI in binaries, suggested that the data were consistent with a common dark matter envelope surrounding the pair system. Charlton & Salpeter (1991) concluded that extremely extended halos, with radii of around 1 Mpc, were present in their sample of binaries. This could also be the case of the M31-Milky Way pair; both could lie in a common halo that has arisen from the mergers of the early smaller halos of the two galaxies.

c) The Local Group. If the 35 galaxies, or more, members of the Local Group conserved their own halos, there could be a problem with available volume. To calculate the filling factor, i.e. the volume of the halos of the 35 galaxies divided by the total volume of the Local Group, we face the problem that we do not actually know the individual volumes. But for an exploratory calculation, we may assume that all halos have the same volume, irrespective of type and luminosity. To justify this assumption, let us consider that R200 is the halo size. From its definition (the radius enclosing a sphere with mean density 200 times the critical density) it is easily deduced that R200 $ \propto$ M2001/3 for all galaxies. A relation should exist between M200 (the mass of a sphere with radius R200, which can be taken as the mass of the halo) and the luminosity L, an observational quantity. Salucci & Persic (1997) give M200 $ \propto$ L0.5, in which case R200 $ \propto$ L0.17, i.e. R200 is "nearly" independent of the luminosity. White et al. (1983) and Ashman (1992) propose M200/L $ \propto$ L-3/4, in which case R200 $ \propto$ L0.08; in this case, the exponent (0.08) is so small that the adoption of constant R200 for all galaxies is a good first approximation. Let us take R200 $ \sim$ 250kpc as a typical value. Let us adopt the zero-velocity surface radius (1.18 Mpc; van den Bergh 1999) as the radius of the Local Group halo. The filling factor obtained is then 0.33. This figure is so high that individual halos would be in contact, and eventually merge. Therefore, a picture more in consonance with the theory is that there is only one large previously formed common halo. This rough calculation just considers the most optimistic situation. The filling factor would be higher if the Local Group were non spherical as suggested by Karachentsev (1996) and if there were many more galaxies belonging to the Local Group. Discoveries of new members have recently been reported and many low surface brightness galaxies would not have been detected if they had not been in the close vecinity of the Milky Way. Moreover, consider that in a sphere of 500 kpc around the Milky Way there are 11 galaxies and around M31 there are 15 galaxies. Under the assumption that each galaxy has its own halo of about 200 kpc, we obtain filling factors much higher than unity. Another observation suggesting that the Local Group has a common halo is the observation that the high-velocity clouds have their kinematic centre in the Local Group barycentre (López-Corredoira, Beckman & Casuso 1999).

d) Small compact groups. The evidence and necessity of common halos is specially clear in the case of Hicson Compact Groups (HCG; Hickson 1982; Mamon 1995). HCG contain few galaxies, four or slightly more, and are very compact, with the intergalactic distance and the whole apparent size of the group being much smaller than the size of typical halos. From the dynamical point of view, given the small velocity dispersion, the system would collapse in less than 109 years, after which the members would merge and form a large elliptical (Barnes 1989; Diaferio, Geller & Ramella 1994 and others) but in fact they are noticeably stable and there are few signs of interaction and merging. These facts led Athanassoula, Makino & Bosma (1997) to assume a massive, not excessively concentrated common DM halo. Gómez-Flechoso & Domínguez-Tenreiro (1997) included a common DM halo in their N-body simulations to stabilize the groups. Common envelope material is found in X-rays (Ponman & Bertram 1993) and atomic hydrogen (Verdes-Montenegro et al. 1997 and references therein). In HCG 49, Verdes-Montenegro et al. (1999) showed that the HI common envelope is rotating with a highly symmetrical pattern, following a large-scale potential that is not due to any particular galaxy member. Perea et al. (1999) have studied faint satellite galaxies at large distances from the members but belonging to the HCG. They found that the common halo is about four times more massive than the galaxy members. We therefore conclude that a great deal of evidence clearly indicates that HCG are embedded in large common halos.

e) Rich clusters. White & Rees (1978), Navarro, Frenk & White (1996) and many other theoretical models had as objectives the obtention of halos with different sizes, with rich clusters being the largest considered. Clearly, rich clusters could be the best example of visible galaxies moving in a large DM cluster, from the point of view of hierarchical CDM scenarios.

Therefore, the hypothesis of a common halo, as opposed to individual halos, is compatible with observations of galaxy pairs, almost essential for groups like the Local Group, compelling for compact groups and tempting for rich clusters. It is also qualitatively coherent with the scenario assumed by hierarchical CDM. In analytic and semianalytic models a large common halo is assumed to be virialized; the violent relaxation following the successive merging processes would destroy any DM substructure, though visible galaxies could remain indigest. Then isolated spirals would not possess a DM halo. Some numerical calculations have not found any subhalos within halos (e.g. Katz & White 1993; Summers, Davis & Evrard 1995) giving rise to the so-called "overmerging" problem.

Benson et al. (1999) obtain many small halos containing no visible galaxy, which could be due to feedback from supernovae, which prevents efficient galaxy formation. Though they obtain that the mass-to-light relation has a minimum for about 1012M$\scriptstyle \odot$, the number of visible galaxies in a halo greatly increases with halo mass (at least for their $ \Lambda$CDM model) indicating that large halos are indeed common halos of many galaxies. The number of visible galaxies with blue absolute magnitude brighter than about -19.5 per halo is statistically lower than unity, but this number probably increases when fainter galaxies are considered in the results of this model. The Local Group has only two galaxies brighter than -19.5.

Moore et al. (1999) and others find a DM substructure in DM halos. Following this calculation, the Milky Way would have about 500 satellites with mass $ \ge$108M$\scriptstyle \odot$, and therefore mechanisms avoiding stellar formation within so many small halos would be required, which has been discussed by Moore et al. and references therein. Internal mechanisms do not seem to be responsible: if gas is lost by star-bursts and winds in a first stage of star formation, it should be explained why galaxies outside clusters have rotationally supported disks. Moreover, the strongest star-bursts observed in nearby dwarf galaxies are insufficient. These authors also discuss the difficulties inherent in forming and maintaining disks in the presence of large amounts of substructure, as disk and small halo interactions will frequently heat disks and produce ellipticals.

Galaxies could have a very different behaviour depending on their position in a cluster. Whitemore, Forbes and Rubin (1988) found a relation between the gradient of rotation curves and the location in the cluster. Verheijen (1977) found an anomalous behaviour of rotation curves of galaxies belonging to the Ursa Major cluster. Rubin, Waterman and Kenney (1999) have found many galaxies with kinematic disturbances in the Virgo cluster, but tidal effects and accretion events can explain the observed disturbances. Individual dynamic studies of disks in clusters are difficult to interpret.

We could conclude that the existence of common halos and the non-existence of individual sub-halos are suggested both by the observations and by the theory. Following this picture then, spiral galaxies would have no halo, but rather move inside halos, orbiting off-centre in less dense and more homogeneous DM environments.

Truly isolated spiral galaxies would have their own halo but these are exceptional. van den Bergh (1999) estimated that half of all galaxies in the Universe are situated in small clusters such as the Local Group. Soneira & Peebles (1977) estimated at 15% the number of isolated galaxies. Tully & Fisher (1978) even claimed that there is no evidence for a significant number of field galaxies.

The situation would be similar for late type irregulars and for dwarf spheroidal galaxies. However, these conclusions would not serve for the DM content of elliptical galaxies. In a rich cluster, if we assume that the centres of the DM halo and of the galaxy distribution coincide, at least the giant cD ellipticals at the centre would have large quantities of DM, with the cD galaxy and the DM also being coincident. Giant ellipticals, like M87, have been considered to possess very large amounts of dark matter since Fabricant, Lecar & Gorenstein (1980) and Binney & Cowie (1981) analyzed their X-ray emission. Indeed these authors noticed that these large quantities of DM encountered could belong to the cluster itself rather than to the galaxy. Huchra & Brodie (1987) showed that the dynamics of globular clusters around M87 supported the huge mass found from X-ray observations, of the order of 1013M$\scriptstyle \odot$. It is unclear whether this conclusion about cD galaxies would also apply for normal ellipticals. In some cases, the debris from a merger of spirals could fall into the halo centre. The difference between spirals (and irregulars) and cD ellipticals would be that the former lie well outside the halo's centre while the latter coincide with it.

Therefore, we can summarize the present crossroads of the problem of rotation curves of spiral galaxies by emphasizing that, if we accept the hypothesis of common virialized halos, with no substructure, for all types of clustered visible galaxies, then there are only two alternatives:

Either hierarchical CDM models are wrong, for instance, DM is baryonic (e.g. de Paolis et al. 1997; Pfenniger & Combes 1994), in which case we would need a theory of galaxy formation.

Or they are basically valid, in which case, another explanation of the rotation curve is needed. For instance, forces other than gravitation could be involved, so that models of galaxy formation would have no "responsibility" in explaining the rotation curve. We should take into account the magnetic hypothesis (Nelson 1988; Battaner et al. 1992, Battaner & Florido 1995, Battaner, Lesch & Florido 1998). Given the success of current theoretical CDM hierarchical models in other related topics, we favour this latter possibility.

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