The shape of the outer Milky Way should be heavily influenced by the shape of our heavy halo. Simulations of the formation of collisionless halos indicate that they should be highly triaxial, with a tendency to pro-lateness. If our halo were as strongly triaxial as these simulations suggest, the outer disk would have ellipticity ϵ disk ≃ 0.06.

Simulations of galaxy formation which include an appropriately small fraction of gaseous matter give rise to halos of much smaller ellipticity, and predict ϵ disk ≃ 0.02. These simulations are not as reliable as purely collisionless simulations, and we should treat their results with some caution. However, it is not incredible that a small fraction of gas could radically reduce the ellipticity of a halo by making the system's potential more centrally concentrated.

The distribution of the apparent ellipticities of spiral galaxies indicates that their disks have slightly eliptical disks, ϵ disk ≃ 0.05. This may merely reflect ephemeral features such as spiral arms, however. The velocity fields of disks provide a more robust probe of the ellipticity ϵ Φ of galaxy potentials. The narrowness of the Tully–Fisher relation places an interesting upper limit ϵ Φ < 0.1. More detailed studies of individual velocity fields will be required if we are unambiguously to demonstrate ϵ Φ > 0 in some cases.

It is a tall task to determine the structural parameters of one's own galaxy much less any deviations from axisymmetry. Nonetheless, after hard work, the existence of asymmetries has been reported and discussed in the literature from a wide variety of sources (most recently, Nakai & Nishiyana 1994). Now, in order to understand Milky Way evolutionary history, it is our job to determine the origin and intrinsic structure of these asymmetries.

Galactic and extragalactic astronomers often mean different things by “halo” the former mean the spheroidal distribution of metal poor stars around the Milky Way (MW), the latter mean the massive, dark component providing the large dynamically inferred mass in and around galaxies. This review will focus on massive, dark halos. Despite the title of this conference, we cannot restrict our attention to the shape of the MW halo: very little would be to say. We must turn to cosmological simulations and to observations of external disk galaxies in the hope of deriving a representative picture.

The problem of axisymmetric Jeans stability of a stellar disk was essentially completely solved in the classic paper by Toomre (1964). While his analysis was strictly local, the stability criterion it yielded has been found to be remarkably reliable in global studies; I review earlier results and give a further example in Sellwood (1995, hereafter S95). Toomre (1974) concluded that the MW is safely stable to axisymmetric Jeans modes.

We have obtained counts of stars near the tip of the red giant branch of M31, and have used these counts to estimate the surface brightness of the halo of M31 down to a level of μV ∼ 30 mag arcsec–2 (R ∼ 20 kpc). The surface brightness along the minor axis of the M31 halo is well-represented by a single de Vaucouleurs law (0.2 ≃ R[kpc] ≃ 20). Alternatively, the outer halo of M31 can also be modelled by a power-law density distribution of the form ρ(R) ∞ R –5. This result suggests that the globular cluster component of the halo of M31 (for which ρ ∞ R –3) is more extended than the stellar halo of this galaxy. At μv à 28 mag arcsec–2 (R à 10 kpc), the axial ratio of the halo of M31 is found to be c/a = 0.55 ± 0.05.

A new era for the field of Galactic structure is about to be opened with the advent of wide-area digital sky surveys. In this article, I will review the status and prospects for research for 3 new ground-based surveys: the Sloan Digital Sky Survey (SDSS), the Deep Near-Infrared Survey of the Southern Sky (DENIS) and the Two Micron All Sky Survey (2MASS). These surveys will permit detailed studies of Galactic structure and stellar populations in the Galaxy with unprecedented detail. Extracting the information, however, will be challenging.

In hierarchical cosmologies, dark matter coronas arise from the gravitational collapse of density peaks in a random perturbation field. The result is a triaxial, slowly rotating, centrally concentrated dark corona (Dubinski and Carlberg, 1991; Dubinski, 1992). Binney (1978) was the first to consider the effects of triaxial coronas around disk galaxies, showing that they might explain the observed warps and apparent twists seen in many disks. In external galaxies these deformations of density and velocity fields are modeled with a system of circular annuli, each of which has its own inclination and line of nodes (LON). By examining warped systems in a variety of reference frames, Briggs (1990) has mentioned that galaxy kinematics uniquely specifies a new reference frame in which there is a common LON for orbits within the transition radius and also a differently oriented straight LON for the gas outside the transition radius, which is approximately equal to the Holmberg radius of the galaxy.

I have recently started an observing program to study the distribution of dynamically old giant stars in the disk, looking for (i) large amplitude spiral arms and (ii) small amplitude corrugations.

1. (i) Theoretical studies of spiral density waves usually assume that the mass density contrast is weak and the waves linear. Recent observations in red and near-IR light (e.g., Elmegreen and Elmegreen 1984; Rix and Zaritsky 1994), coupled with stellar population models, suggest otherwise. In the Galaxy, we can compare observations of diffuse NIR light and of individual stars, eliminating the need for population modeling. Moreover, we can estimate distances to stars to learn about 3D structure.

2. (ii) Recent work by Malhotra (1994a; 1994b) has shown that the midplane of the molecular and atomic gas differs from the nominal (Galactic latitude b = 0°) plane by up to 50 pc in the inner Galaxy. Various observations (Djorgovski & Sosin 1989, Freudenreich et al 1994, Carney & Seltzer 1993) show that the stellar distribution also deviates from b = 0. We will choose fields to test the possibility that the stars behave like the gas. This constrains theories of the corrugations; e.g., if old stars participate then magnetic fields aren't the cause.

The Diffuse Infrared Background Experiment (DIRBE) on-board the Cosmic Background Explorer (COBE) satellite has provided striking new images of the Galactic bulge at effective wavelengths of 1.25, 2.2, 3.5, and 4.9μ (Hauser 1993, plate 3; Arendt et al. 1994; Weiland et al. 1994). The bulge, defined here as the spheroid within the |l| < 20° and |b| < 10° region around the Galactic center, and its stellar content have been subjects of considerable interest since they contain important clues about the dynamical and star-formation history of our Galaxy. The morphology of the Galactic bulge is much harder to ascertain than that of bulges in many external galaxies, because of our location in the Galactic plane amid the obscuration by interstellar dust. In spite of this difficulty, there has recently been an accumulating body of evidence that the stellar distribution in the bulge is bar shaped, i.e. that the bulge is not rotationally symmetric in the plane of the disk (see Blitz 1993 for a review of the subject). The existence of a bar in our Galaxy would have important implications for the dynamics of the Galaxy. A bar would provide a mechanism for sweeping gas from the disk into the Galactic center “feeding” a central black hole (e.g. Shlosman, Frank, & Begelman 1989). It would also provide a mechanism for generating spiral arms, and a basis for estimating the mass of the halo relative to that of the disk (e.g. Combes & Sanders 1981 and references therein).

It seems by now well-established that in the central kpc the Galaxy is not axisymmetric (Gerhard 1995, Dwek 1995). The kinematics of many different tracers, as well as the distribution of sources on the sky, all point to an elongated distribution of matter and of the potential, with the long axis of the distortion pointing somewhere in the first Galactic quadrant. It is therefore tempting to reconsider our data concerning this part of the Galaxy in terms of ‘the’ Bar. But to what extent should we (or is it useful to) distinguish between the bar and the stellar bulge of old?

There is now substantial evidence for a rotating bar in the inner Galaxy. This is an important change in our perception of the Galaxy because it changes the ways in which we have to think about its evolutionary history.

The analysis of the first three years of the OGLE data revealed 12 microlensing events of the Galactic bulge stars, with the characteristic time scales in the range 8.6 < t 0 < 80 days, where t 0 = RE/V. A complete sample of nine events gave the optical depth to gravitational microlensing larger than (3.3 ± 1.2) × 10–6, in excess of current theoretical estimates, indicating a much higher efficiency for microlensing by either bulge or disk lenses. The lenses are likely to be ordinary stars in the Galactic bar, which has its long axis elongated towards us. At this time we have no evidence that the OGLE events are related to dark matter. The OGLE color magnitude diagrams reveal the presence of the Galactic bar and a low density inner disk region ∼ 4 kpc in radius. A catalogue of a few thousand variable stars is in preparation.

The Optical Gravitational Lensing Experiment (OGLE, Udalski et al. 1994a; Paczynski et al. 1994b – these proceedings; and references therein) is an extensive photometric search for the rare cases of gravitational microlensing of Galactic bulge stars by foreground objects. It provides a huge data base (Szymański & Udalski 1993), from which color-magnitude diagrams have been compiled (Udalski et al. 1993, 1994b). Here we discuss the use a of well-defined population of bulge red clump stars to investigate the presence of the bar in our Galaxy. The results of our earlier studies are described by Stanek et al. (1994).

We present radial velocities for approximately 40 stars in each of four optically obscured, off-axis fields toward the Galactic bulge. The mean heliocentric radial velocity and velocity dispersion are −75 ± 24 km s–1 and 127 ± 16 km s–1 2 ± 23 km s–1 and 127 ± 14 km s–1, −14 ± 22 km s–1 and 126 ± 14 km s–1, and −31 ± 28 km s–1 and 153 ± 17 km s–1 for fields located at 299, 288, 171, and 160 pc projected radius, respectively. The dispersions generally match Kent's (1992) axisymmetric mass model but may be higher than the model's predictions at small projected radius.

Evidence for the bar structure in our Galaxy has been shown by Blitz and Spergel (1991b) based on the near-infrared maps of the bulge, by Nakada et al. (1991) based on IRAS point source catalogue, and more clearly by recent COBE maps. However, no clear “dynamical” signature of the bulge bar has been found yet. At optical wavelengths, stellar radial velocities of the bulge stars were observed only at the optical windows and were not observed for the entire region of the bulge because of the dust extinction in this direction.

While the existence of a central bar in our Galaxy now seems to be well established, its parameters (such as position angle, extension, axis ratio, angular speed etc…) still remain controversial. The large amount of photometrical and stellar kinematical data becoming now available within ∼ 30° of the Galactic Centre should provide potentially new constraints on these parameters. Unfortunately, a detailed barred model of the Milky Way, which would offer a powerful work frame to interpret such observations, does not exist yet. We therefore report here on a first attempt at constructing a 3D dynamically self-consistent barred model of the Galaxy. The idea is to follow the time evolution of a set of 400,000 particles initially distributed according to a plausible axisymmetric mass model of the Milky Way and in virial equilibrium, hoping that a bar will form spontaneously. Gas is not included so far, but will be introduced as a next step in this ongoing work. Some results presented at this meeting will be only quickly summarised here and explained in some more details elsewhere (Fux et al. 1995 and A&A paper in preparation).

Many features of the Milky Way appear weird or unique, because of the peculiar point of view. However the same features are observed more easily and clearly in nearby galaxies. The Milky Way appears to cumulate many dynamical features, such as a bar, a nuclear disk, a perpendicular nuclear bar (?), lopsidedness, an inner ring (molecular ring at 5kpc), a peanut-shape bulge, a warp, and a polar ring. By comparison with external galaxies, and also results from N-body simulations, we can infer the most probable bar angular velocity and length, and interpret the ring features.

It is well known that the existence of H I and CO gas at “forbidden” velocities in longitude-velocity (l–V) diagrams of the inner Galaxy (e.g. Liszt & Burton 1980, Liszt 1992) is inconsistent with circular motion in an axisymmetric potential. Gas flow in a barred potential could be consistent with the observations, however. We have compared the observations to 2-D hydrodynamical simulations of gas flows in a family of barred potentials. The gas flow pattern is very sensitive to the assumed potential, and the l–V distribution of cool gas in the inner Galaxy places strong constraints on several parameters of the Milky Way bar.