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Dark Matter Problem in Disk Galaxies

In the generic CDM cosmogony, dark-matter halos emerge too lumpy and centrally concentrated to host observed galactic disks. Moreover, disks are predicted to be smaller than those observed. We argue that the resolution of these problems may lie with a combination of the effects of protogalactic disks, which would have had a mass comparable to that of the inner dark halo and be plausibly non-axisymmetric, and of massive galactic winds, which at early times may have carried off as many baryons as a galaxy now contains. A host of observational phenomena, from quasar absorption lines and intracluster gas through the G-dwarf problem point to the existence of such winds. Dynamical interactions will homogenize and smooth the inner halo, and the observed disk will be the relic of a massive outflow. The inner halo expanded after absorbing energy and angular momentum from the ejected material. Observed disks formed at the very end of the galaxy formation process, after the halo had been reduced to a minor contributor to the central mass budget and strong radial streaming of the gas had died down.


INTRODUCTION
High resolution simulations of galaxy formation, incorporating realistic CDM initial conditions of dark halo formation, generally confirm the existence of a universal density (NFW) profile in the outer regions of galaxies (Navarro, Frenk & White, 1997). Moreover, some groups are now reporting significant central dark matter density cusps that are as steep as ∝ r −β with β ≈ 1.5. The existence of even a more modest cusp (β ≈ 1, as in the original NFW result) implies that at the current epoch L * galaxies have two to three times too much dark matter within a 2 to 2.5 disk scale lengths (Navarro & Steinmetz, 2000). This conclusion applies both to the Milky Way, where the mass of the disk can be dynamically estimated from the motions of stars near the Sun, and to an ensemble of nearby spirals, for which the Tully-Fisher relation effectively measures a M/L ratio that can be compared with values predicted by stellar-synthesis models. The Tully-Fisher slope and dispersion are accounted for by the high resolution simulations, but the normalization is discrepant, by about a factor of 3 in M/L at given surface brightness, rotation velocity and luminosity (Navarro & Steinmetz, 2000).
Two further problems encountered with the cold dark matter hypothesis are (i) that the scale-lengths of disks are predicted to be too small by a factor ∼ 5 , and (ii) an order of magnitude more satellites are predicted than are observed (Moore et al, 1999).
Both of these problems are closely related to the persistence of substructure in high-resolution N-body simulations of hierarchical models of dark halo formation.
There are two possible avenues for resolution of these problems. One approach is to tinker with the particle physics. One may abandon the idea that CDM is weakly interacting. There are CDM particle candidates for which annihilation rates are of order the weak rate but for which scattering crossections are of the order the strong interaction (Carlson et al, 1992;. Such dissipative CDM may erase both the CDM cusps and clumpiness (Spergel & Steinhardt, 1999), but at the price of introducing an unacceptably spherical inner core in massive clusters (Miralda-Escude, 2000). One may suppress the small-scale power on subgalactic scales, either by invoking broken scaleinvariance (Kamionkowski & Liddle, 1999) or warm dark matter (Sommer-Larsen & Dolgov, 1999), in the hope that the structure of massive dark halos will be modified.
Here we adopt the less radical approach of exploring astrophysical alternatives. We accept the fundamental correctness of the CDM picture, and ask (i) could excess dark matter be ejected from the optical galaxy? and (ii) why do baryons in galaxies currently have more specific angular momentum than predicted by the simple CDM picture. We argue that these questions are connected, and that both may be resolved if galaxies have first absorbed and then ejected a mass of baryons that is comparable to their current baryonic masses. An earlier paper argued that baryonic winds can imprint cores within dwarf galaxy dark halos (Navarro, Eke & Frenk, 1996). Here we propose that energy and angular momentum surrendered by the ejected baryons have profoundly modified the dark halo within the current optical massive galaxy. In this picture most protogalactic material remained gaseous until the period of mass ejection was substantially complete -this conjecture is tenable because we have no reliable knowledge of either the rate at which, or the efficiency with which, stars form in a protogalactic environment.
In Section 2 we argue for massive galactic outflows. In Section 3 we ask how the dark halo was modified as a result of processing the material prior to ejection. Section 4 is concerned with the implications for the star-formation rate within a gaseous bar. Section 5 sums up our arguments.

INFLOW AND OUTFLOW
A primary problem with the conventional picture of galaxy formation is that in all simulations, the baryons lose much of their angular momentum as they fall into dark-matter haloes (Katz & Gunn, 1992;Weil, Eke & Efstathiou, 1998) rather than conserving it as semi-analytic models of galaxy formation typically assume (Kauffmann, White & Guiderdoni, 1993;Granato et al, 2000). Consequently, whereas in semi-analytic galaxy-formation models, the baryons are marginally short of angular momentum to account for the observed disk sizes, in reality they will fall short by an order of magnitude.
Current estimates of the acquisition of angular momentum by perturbations in the expanding universe seem robust, as is the prediction that collapsing baryons will surrender much of their angular momentum. Hence, we should take seriously the expectation that protogalaxies early on will contain a considerable mass of low-angular momentum baryons. What becomes of this material? Some of it will have been converted into the galaxy's bulge and central black hole. However, the mass of low-angular momentum material to be accounted for is comparable to the mass of the current disk, on account of the substantial factor by which infalling baryons will have been short of angular momentum. The bulge and central black hole of the Milky Way, by contrast, between them contain less mass than the disk by a factor ∼ 5. In galaxies of later Hubble type, such as M33, the factor can be substantially greater.
Star formation is always associated with conspicuous outflows, which are thought to be generically associated with accretion disks. Hence, it is likely that a significant fraction of a protogalaxy's low angular momentum baryons are ejected in a wind that is powered by star formation, magnetic torques and black hole accretion. Observations of star-burst galaxies such as M82 lend direct support to this conjecture (Axon & Taylor, 1978;Dahlem, Weaver & Heckman, 1998). We conclude that the observed disks of galaxies plausibly formed from the higher angular momentum tail of the conventional distribution. In terms of a sphericallysymmetric infall model, we imagine that the baryons that started out close to the centre of the protogalaxy were mostly ejected. Galactic disks are formed from the baryons that were initially confined to the perifery of the volume from which the final galaxy's dark matter was drawn, or even came from outside this volume -the theory of primordial nucleosynthesis assures us that ∼ 90% of all baryons lay outside the spheres conventionally containing galactic dark matter, so there is no shortage of material to work with. On account of its large galactocentric radius, the material to which we are appealing will initially have had more angular momentum than the disk into which it was destined to settle.
X-ray observations of early-type galaxies and clusters of galaxies provide strong support for the conjecture that forming galaxies blow powerful winds. In clusters of galaxies, the metal-enriched ejecta are directly observed because they have been trapped by the cluster potential. The wide spread in the X-ray luminosities of the hot atmospheres of giant elliptical galaxies has been used to argue persuasively that early winds can escape the potentials of many galaxies, but not those of the most massive systems, with the consequence that the ejected gas sometimes falls back into the visible galaxy and gives rise to a 'cooling flow' (D'Ercole et al, 1989).
Independent arguments point to massive outflows early in galactic evolution. The narrow dispersion in the colourmagnitude diagrams of cluster ellipticals, both now and at redshifts z ∼ 1 (Jorgensen et al, 1999), implies that the galaxies' colours are not heavily contaminated by metalpoor stars. Early outflows would prevent such contamination (Kauffmann & Charlot, 1998), (Ferreras & Silk, 2000). Moreover, bulges and the nuclei of elliptical galaxies are enhanced in α-elements (C, O, Mg) relative to Fe (Kuntschner, 2000). This observation seems to require suppression of star formation from material that has been enriched in Fe by type Ia supernovae. It is often assumed that this suppression is achieved by converting all the protogalactic gas to stars before many type Ia supernovae have exploded, but it could be also be achieved by a supernova-driven wind. Models of the chemical evolution of disks (Prantzos & Silk, 1998) similarly yield an acceptably small number of metal-poor stars in the old disk if a supernova-driven wind carries metalenriched gas out of the galaxy. Finally, the detection of old halo white dwarfs with a frequency and mass range similar to that inferred for MACHOs from the LMC microlensing experiments (Ibata et al, 1999) will, if spectroscopically confirmed (Ibata et al, 2000), require a substantial protogalactic outflow phase to eliminate from the protogalaxy heavy elements that would otherwise pollute stars that formed later and are observed to have low metalliciticies.
Galactic outflows will have delivered heavy elements to the intergalactic medium (Lehnert, Heckman & Weaver, 2000). This process not only accounts for the observed metallicities of intracluster gas (Renzini, 1997), but may also be responsible for the metallicities of the low-density gas that is primarily detected through Lyα absorption in quasar spectra. It is possible at low z, significant enrichment of the IGM and ICM might come from dwarf galaxies, although the low metallicities of the dwarfs argue against this unless the luminosity function is exceptionally steep. At the redshifts z ∼ > 2 at which the enriched IGM material is observed, most of the stars in the nearby dwarf galaxies will not have formed, so the more luminous galaxies would have necessarily had to dominate unless a new population of early-forming dwarfs is invoked. However semi-analytic theory predicts that at z ∼ > 2, most star formation is confined to locations at which luminous galaxies now reside (Baugh et al., 1998), (Benson et al., 2000). These locations are far removed from the low-density gas that is observed to contain heavy elements. Galactic winds could be responsible for transporting the heavy elements from the location of the bulk of star formation, to where they are observed. Moreover, extended metal-enriched absorption systems might arise from expanding shells that form in galactic winds in the same way that shells form around planetary nebulae. Thus, many lines of argument suggest that outflows from both spheroids and disks were common, and therefore that significantly more baryons were involved in the formation of a given galaxy than it now contains.

MODIFICATION OF THE HALO
As we have seen, the infalling baryons will have lost much of their angular momentum. The lost angular momentum is taken up by the halo. In principle, acquisition of this angular momentum modifies the halo at all radii, but the modifications are small where dark matter dominates over baryons, and are profound only interior to the radius at which M disk ∼ M halo . Observationally, we know that the baryons are dominant inside the solar radius, so we expect the halo profile to be substantially modified there, precisely as the CDM model seemingly requires (Navarro & Steinmetz, 2000).
There are threee obvious mechanisms by which gas can lose angular momentum to the halo. Early on, the halo is expected to be triaxial and its principal axes will rotate slowly if at all. Gas flowing in such a potential rapidly loses angular momentum, even if its mass is small compared to the mass of the local halo (Katz & Gunn, 1992). If gas ever accumulates to the degree that it contributes a non-negligible fraction of the mass interior to some radius r, two other mechanisms for angular-momentum loss become effective: massive blobs of gas will lose angular momentum through dynamical friction (Stark et al, 1991;Navarro & Steinmetz, 1997), and a tumbling gaseous bar will lose angular momentum through resonant coupling (Hernquist & Weinberg, 1995). These last two processes operate even if the halo becomes axisymmetric, as it may do where gas contributes significantly to the overall mass budget.
During the earliest stages of galaxy formation, gas will be far from centrifugal equilibrium and will flow rapidly inwards. We assume that it loses energy faster than angular momentum, with the consequence that gas that started out at a given galactocentric radius will eventually settle to a (possibly elliptical) ring. If this ring is not substantially self-gravitating, it will evolve little if at all. Low-surfacebrightness galaxies would seem to be made up of such inert rings of gas. If the ring is significantly self-gravitating, it will continue to lose angular momentum to the local halo by a combination of dynamical friction and bar-driven resonant coupling. The dynamics of a tumbling gaseous bar embedded in a dark halo of comparable mass has yet to be carefully studied, but both analytic calculations and simulations show that, in the case of a stellar bar, resonant coupling is a rapid process: the time-scale of angular-momentum loss exceeds the bar's dynamical time by a factor of only a few (Wein-berg & Tremaine, 1984;Debattista & Sellwood, 1998). Consequently, a bar embedded in a dynamically significant halo will shrink. This shrinkage will rapidly enhance the mass fraction of baryons because concentration of the baryons will be accompanied by expansion of the local halo as it takes up energy and angular momentum shed by the bar.
These considerations suggest that, if the baryons ever become dynamically significant, they will go on losing angular momentum to the halo until they are dominant, and that dominance is achieved by a combination of the baryons moving in and the dark matter moving out. Moreover, chemical evolution models of the Milky Way disk require about half of the disk to have formed via late infall (Prantzos & Silk, 1998), which implies an extended phase of baryonic infall.
The source of the baryons is likely to be stripped satellites that are merging with the Milky Way and become dynamically disrupted. Late infall may double the mass of the disk, with the consequence that the final disk is close to maximal, and the role of dark matter within the solar circle is negligible.
In phase space, orbits at energies around the bar's corotation energy will be highly chaotic, and the strong orbital shear that is characteristic of chaos will tend to erase substructure within the halo near the corotation energy.
The coupling between baryons and dark matter is a fairly local process, essentially confined to a factor of 2 either side of the baryons' corotation radius. The processes we have described for one corotation radius presumably occurred in sequence at a series of radii that increased from very small values out to scales characteristic of present-day disk galaxies. If the arguments of the preceeding section are correct, the dark matter at any given radius r will interact locally with many different parcels of baryons during the formation process, as these parcels move through radius r on their way to the galactic centre and probable ejection from the galaxy.

BARS AND STAR FORMATION
Since the stars of the current disk are now on nearly circular orbits, they cannot have formed until after any tumbling gaseous bar had dissolved. Is it reasonable to have a bar without significant star formation? The dwarf galaxy NGC 2915 (Bureau et al., 1999) is an example of a dark-matter dominated galaxy with a very extended HI disk revealing a central bar and spiral structure extending well beyond the optical component. Evidently the Toomre Q of this system satisfies where Q global and Q local are the critical values of the disk instability parameter for global non-axisymmetric and local axisymmetric instabilities, respectively. One can readily imagine that as the disk forms, the gas surface density increases and the gas velocity dispersion drops, so that Q decreases, and the local Q criterion is subsequently satisfied. In the solar neighbourhood the disk satisfies and is marginally unstable. The gas disk of the Milky Way presently contains about 6 × 10 9 M⊙. In the transient bar phase, the effective Q is increased by the ratio of bar streaming velocity to gas velocity dispersion σg, which amounts to a factor of ∼ 10. Hence a gas mass of up to ∼ 10 11 M⊙ can be stabilized against star formation during the transient bar phase. It is clear that high resolution numerical simulations are required to model the coupling between the nonaxisymmetric protodisk and the dark halo. These simulations need to include the effects of baryonic dissipation and star formation. There may be possible stellar relics of an early massive bar, that would be recognizable as a disk component of old stars with significant orbital eccentricity.

CONCLUSIONS
Two serious problems currently plague the CDM theory of galaxy formation: an excess of dark matter within the optical bodies of galaxies, and disks that are too small. The second problem reflects the low angular momentum of infalling matter, and is made worse when one accepts that infalling baryons will surrender much of their angular momentum to the dark halo. In consequence, galaxies start with more low-angular-momentum baryons than they currently hold in their bulges and central black holes. We have argued that the surplus material was early on ejected as a massive wind. Many direct and indirect observational arguments point to the existence of such winds.
Although the angular momentum of the first baryons to fall in was inadequate for the formation of the disk, it was not entirely negligible, and caused the inner halo to expand when the latter absorbed it. Similarly, the angular momentum of the baryons that are now in the disk was originally larger than it now is, and the surplus angular momentum further expanded the inner halo. In short, through relieving perhaps twice the baryonic mass of the current galaxy of angular momentum and energy, the dark halo has become substantially less centrally concentrated than it was originally, and it now contributes only a small fraction of the mass within the visible galaxy. During this refashioning of its inner parts, substructure is likely to have been erased, leaving the final inner halo smoother both locally and globally.
This picture requires the baryonic mass to remain gaseous until the dark halo has been reduced to a minor contributor to the central mass, and a disk has formed in which most material is on circular orbits. This conjecture is plausible for two reasons: (i) the dark halo will be unresponsive to the collective modes of a gaseous disk, so the disk will not have growing modes until it dominates the gravitational potential in which it sits, and (ii) the enhanced orbital shear that is characteristic of closed orbits in a barred potential cannot be conducive to star formation. In any case we have little understanding of what controls the rate of star formation in a protogalaxy, and we know from the fragility of disks (Toth & Ostriker, 1992) that disks formed at the end of the formation process, after merging had all but ceased and the largest substructure had been erased from bulge and inner halo.
Existing numerical simulations of the interactions of baryons and dark matter during galaxy formation (e.g., Navarro & Steinmetz, 2000;Benson et al., 2000) lack both the mass resolution and some of the physics that is required to realise the essential ideas employed here. For example, in the simulations of Benson et al. the gravitational softening length is 10h −1 kpc, and the basic baryonic resolution element has mass ∼ 4 × 10 10 M⊙ and spurious discreteness effects will be present on mass scales several times larger. Such simulations neglect magnetic fields (which are believed to drive winds off accretion disks) and energy input by both supernovae and the central massive object. In summary, a considerable mass of low-angular momentum baryons must have been ejected. This prediction is a priori plausible, given observations of winds from starburst galaxies and outflows from Lyman-break galaxies, and given the prevalence of outflows in star-formation regions. The heavy element abundances of hot gas in clusters of galaxies and in cool, low-density gas observed at redshifts z ∼ 2 through quasar absorption lines are likely to arise through the mixing of metal-rich ejecta with primordial gas. The low-angular-momentum material having been ejected, the current disks formed from the higher-angularmomentum baryons that fell in later. Since the ejection stage commences only once M baryon ∼ M dm , in order for selfgravity to drive gas flows and the ensuing winds, thereby causing the dark-matter distribution to expand and the baryons to further contract, the visible galaxy is inevitably baryon-dominated but has a circular speed that is required, via the baryonic mass-loss and the protogalactic dynamical coupling, to approximately match that of the embedding halo. Thus the so-called 'disk-halo conspiracy' (Bahcall & Casertano, 1998) is not really a coincidence but a consequence of dynamical evolution.