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Astron. Astrophys. 345, 787-812 (1999)

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6. Interpretation of the [FORMULA] features

Model [FORMULA] diagrams depend on the location of the observer in the galactic plane, which is described by his galactocentric distance [FORMULA] in initial units and the angle [FORMULA] between the line joining himself to the centre and the major axis of the bar, and on his velocity [FORMULA]. We assume here that the observer lies in the plane [FORMULA] and that [FORMULA] is purely azimuthal.

The phase space coordinates of the SPH particles have been stored every 2 Myr in order to realise a posteriori [FORMULA] diagram movies for any arbitrary values of these parameters with a high temporal resolution. To compare these movies with the observations and decide for an optimum model, some reference points have been overlayed on the movies to localise the features seen in the CO and HI data (Table 2). In each movie, the view point is at rest relative to the rotating frame of the bar, i.e. [FORMULA] and [FORMULA] remain constant. The contribution of each SPH particle to the [FORMULA] frames is weighted by its inverse squared distance relative to the observer to mimic the flux decline of point sources (all model [FORMULA] diagrams in this paper are computed this way, except the one in Fig. 21). A direct consequence of the asymmetries developing in our simulations is that model [FORMULA] diagrams computed for diametrically opposite view points always considerably differ.


Table 2. Reference points overlayed in the [FORMULA] diagram movies to locate the main observed features indicated in Fig. 1 and the Carina arm.

Two models from these movies, l10t2066 and l10´t2540, illustrated and confronted to the observations in Fig. 15, have especially retained our attention. In both cases, the inclination angle of the bar is [FORMULA] and no velocity rescaling has been applied. The circular velocity of the observer is set to the mean azimuthal velocity of his surrounding SPH particles, i.e. to 203 km s-1 for l10t2066 and 197 km s-1 for l10´t2540. The model l10´t2540 is selected as one of the models which best reproduce the overall [FORMULA] observations within the solar circle. Even if the agreement is rather qualitative, this model offers a solid basis to interpret the data. Fig. 16 highlights the spiral arms which trace the [FORMULA] features in the model and Fig. 17 shows the velocity field of the gas. Fig. 18 also provides a qualitative key-map to spatially locate observed [FORMULA] sources in the Galactic plane.

[FIGURE] Fig. 15. Confrontation of a selection of two models with observed gas kinematics. Top: 12CO and HI [FORMULA] diagrams integrated over [FORMULA] and [FORMULA] respectively; the data are from Dame et al. (1999) for the CO, and Hartmann & Burton (1997), Burton & Liszt (1978) and Kerr et al. (1986) for the HI. Middle: synthetic [FORMULA] diagrams of models l10t2066 and l10´t2540 for a bar inclination angle [FORMULA], including all particles within [FORMULA]. Bottom: face-on projections of the gas spatial distribution in these models, rescaled such as to put the observer at [FORMULA] kpc ([FORMULA] symbol). In these units, corotation lies at [FORMULA] kpc (l10t2066) and 4.4 kpc (l10´t2540). The model on the left reproduces almost perfectly the connecting arm, while the model on the right provides a fair global qualitative agreement to the data.

[FIGURE] Fig. 16. Link between the spiral arms in the [FORMULA] plane and the [FORMULA] features in model l10´t2540. The spiral arms and their [FORMULA] traces are depicted by the true phase space coordinates of the gas particles, using all particles within a narrow band of 300 pc centred on the maximum surface density curve of each spiral arm. In the upper plot, closer structures relative to the observer have been overlayed on the more distant ones. The nuclear ring is not represented.

[FIGURE] Fig. 17. Velocity field of model l10´t2540 in the rotating frame of the bar. The subtracted solid rotation does not take into account the bar offcentring. The grey curves indicate the location of the spiral arms.

[FIGURE] Fig. 18. Radial velocity contours in model l10´t2540 as a function of longitude and distance relative to the observer, whose location and circular velocity are as in Fig. 15. The spacing of the contours is 20 km s-1 and the thick contour is the zero velocity curve (labels are given in km s-1). Only the particles within [FORMULA] have been considered. Note the very sharp velocity gradient when crossing the axis shocks.

6.1. Connecting arm

The connecting arm is clearly identified with the axis shock in the near part of the bar. More precisely, this arm is build up by the gas clouds which have recently crossed the shock front at various galactocentric distances and which now collectively plunge towards the nuclear ring/disc with velocities roughly parallel to the shock front. In other words, the connecting arm traces the near-side branch of the Milky Way's dustlanes. Other models, like l10t2066 in Fig. 15, exhibit axis shocks with [FORMULA] traces resembling much more the real connecting arm than in model l10´t2540, thus reinforcing our interpretation.

The presence of the connecting arm feature in the observed [FORMULA] diagrams can be considered as a further evidence of the Galactic bar. Furthermore, its rather large domain in longitude is relevant of an extended bar, especially if the latter is seen close from its major axis (see Sect. 7). The connecting arm feature is a real concentration of gas in space and not an artifact due to velocity crowding along the line of sight, as suggested by Mulder & Liem (1986) 1. In our simulations, the gas does not always trace the full length of the axis shocks and hence it is not surprising that the emission from the connecting arm appears truncated at [FORMULA]. The [FORMULA] movies sometimes show gas lumps deposited by lateral arms in the near-side axis shock and moving precisely along the connecting arm feature. The time for the gas to travel from the endpoint of a lateral arm to the nuclear ring along the shock is of order [FORMULA] Myr and it takes about another 10 Myr for the gas not absorbed by the ring to encounter the opposite axis shock. The fraction of gas deposited in the nuclear ring is time-dependent, but has been estimated to 20% in a steady gas flow model of NGC 1530 (Regan et al. 1997). The gas mass in each branch of the axis shocks is [FORMULA] [FORMULA] or less.

According to Fig. 16, the axis shock in the far-side of the bar is predicted as an almost vertical feature in the [FORMULA] diagram, i.e. with [FORMULA] constant. Such a feature is indeed visible in the 12CO observations (Fig. 1) near [FORMULA], with only a marginal decrease of absolute longitude towards negative velocities. The longitude confinement comes from the fact that the shock line is nearly parallel to the line of sight and the velocity extension from the fact that the velocity of the gas along the shock rapidly increases when approaching the nuclear ring/disc.

6.2. 3-kpc and 135-km s-1 arms

The 3-kpc and the 135-km s-1 arms are lateral arms. The observed velocity asymmetry between these two arms happens because the latter passes closer to the centre than the former. The gas associated with the 135-km s-1 arm, moving almost parallel to the arm (Fig. 17), indeed falls deeper in the potential well of the nucleus and therefore reaches higher forbidden velocities before striking the dustlane shock.

The observed velocity asymmetry of bright emission near the positive and negative terminal velocity peaks could have a related origin: the gas from the 3-kpc arm, after crossing the dustlane shock further out than its counterarm, starts to fall towards the nuclear ring/disc with a higher potential energy and therefore will approach the latter with higher velocities, producing an enhanced velocity peak. Model l10´t2540 however does not exhibit such a velocity asymmetry. This asymmetry could also arise from a relative radial motion between the nuclear ring/disc and the LSR, produced either by the oscillations of the density centre (see Sect. 5.1) or by a radial velocity component of the LSR with respect to the Galactic centre, possibly induced by the bar itself (Raboud et al. 1998), or both.

The inner branch of the molecular ring, with tangent point at [FORMULA], is the outer extension of the 135-km s-1 arm.

6.3. Bania's clumps

Observations of the gas velocity field in external barred galaxies have revealed velocity changes up to 200 km s-1 across the bar leading dustlanes, demonstrating that these dustlanes are associated with very strong shocks. Such velocity fields have been measured for example in NGC 6221 (Pence & Blackman 1984), NGC 1365 (Joersaeter & van Moorsel 1995; Lindblad et al. 1996), NGC 3095 (Weiner et al. 1993), NGC 1530 (Regan et al. 1997; Reynaud & Downes 1998) and NGC 7479 (Laine et al. 1999). Fig. 19 shows how the gas velocity field is affected by the near-side branch of the axis shocks in model l10t2066. The shock occurs near [FORMULA] kpc and is followed downstream by a huge gas concentration. Both velocity components, parallel and perpendicular to the shock front, undergo an abrupt velocity gradient across the shock layer. The velocity change is however larger for the parallel component, reflecting the shearing nature of the axis shocks, and is comparable to the values observed in external galaxies. In NGC 1530, Reynaud & Downes (1998) found that the velocity change increases towards the nuclear ring, but this property is hard to infer from our models because the shock fronts are not well resolved in the low density part.

[FIGURE] Fig. 19. Spatial density and velocity profiles along four slits perpendicular to the "connecting arm" in model l10t2066. The upper and lower velocity curves respectively stand for the velocity components parallel ([FORMULA]) and perpendicular ([FORMULA]) to the shock front. The profiles are derived by standard SPH summation, e.g. from Eq. (3) for [FORMULA], and for [FORMULA]. The vertical distribution of the dense post-shock gas everywhere peaks within 10 pc from that plane.

Bania's (1977) clump 2 and an other vertical feature near [FORMULA] (see Fig. 1) could represent gas lumps which are just about to cross the near-side dustlane shock somewhere between the 3-kpc arm and the nuclear ring/disc: the upstream part still moves with the small quasi-apocentric velocities of the pre-shock orbits, while the downstream part has been accelerated to the high inwards post-shock velocities, giving rise to a steep radial velocity gradient (Fig. 18) and a velocity stretch of over 100 km s-1 in the observations. Contrary to the [FORMULA] trace of the far-side dustlane shock, these features might be really concentrated in space and not result from an accumulation of gas along the line of sight. For the [FORMULA] lump, this interpretation is supported by the fact that all emission from the lump originates at nearly constant latitude, as expected from a spatially confined source, and that the part of the connecting arm at the same longitude as the lump appears at almost the same latitude as the lump itself (see Fig. 2). Furthermore, this lump also has a small mass relative to the connecting arm and will therefore essentially adapt its momentum to that of this arm. For clump 2, with a mean latitude differing by more than [FORMULA] from that of the connecting arm (at similar [FORMULA]) and a total mass of nearly [FORMULA] [FORMULA] (Stark & Bania 1986), our interpretation is more speculative. However, if this clump is indeed close to the apocentre of its orbit, it will enter very slowly the shock line, where gas is moving at very high speed (over 200 km s-1), and thus receive a significant impulse when integrated over time. Moreover, the clump complex may move on a kind of looped quasi-[FORMULA] orbit and therefore will self-dissipate its energy if its size is comparable to that of the loops, whatever its mass. If the connecting arm indeed traces the near-side dustlane, the identification of clump 2 with such a dustlane, as proposed by Stark & Bania (1986), is ruled out (unless the Milky Way has a double bar). But it should be noted that the axis shock assigned to the connecting arm in model l10´t2540 can produce an [FORMULA] trace resembling much more that of clump 2 if the bar inclination angle is reduced to [FORMULA] (see Fig. 22).

Clump 1, composed of several clouds which are not bound to each other (Bania et al. 1986), is the southern terminus part of the 135-km s-1 arm which penetrates the far-side dustlane shock. According to model l10´t2540, its dynamics should be rather subtle: a part of its gas is absorbed by the dustlane, resulting in a huge velocity change like those described above, from [FORMULA] km s-1 to [FORMULA], and the other part, corresponding to the portion of clump 1 at [FORMULA], is gliding outwards along but without crossing the shock front until apocentre is reached (see the magenta segment in Fig. 16). The momentum injected by this cloud into the axis shock gas bends the outer segment of the shock. Since the far-side dustlane is nearly aligned with the line of sight, the vertical feature near [FORMULA] is in fact a superposition of dustlane gas moving along this line and of clouds with shock induced velocity gradients (see Fig. 20). Clump 1 must be a very perturbed and compressed region, and hence a potential site of star formation a priori. An indicator of "readiness" for star formation is given by the 12CO [FORMULA] to [FORMULA] ratio, tracing dense molecular clouds, which is indeed particularly high for this clump (Hasegawa 1997, private communication). However, the strong shearing in the shock may prevent any star formation to proceed (e.g. Reynaud & Downes 1998). The bulk of this clump, owing to its large mass and impact velocity, may also cross the shock front without being too much affected.

[FIGURE] Fig. 20. Typical path in the [FORMULA] and [FORMULA] planes of an SPH particle in simulation l10. The points show the positions of the particle from [FORMULA] to 2200 Myr with a constant time interval of 2 Myr. The [FORMULA] plot is in the bar rotating frame with the origin at the density centre and with the bar inclined by [FORMULA] relative to [FORMULA] (like in Fig. 15), and the [FORMULA] plot is viewed from [FORMULA] kpc. The particle is chosen to pass through the intersection of the near-side lateral arm and axis shock at [FORMULA] Myr, i.e. through [FORMULA] kpc in the lower left frame of Fig. 15. Note the larger velocity gap between the points when the particle crosses the far-side axis shock.

6.4. Tilt of the gaseous disc

A further observational argument supporting our interpretation of the dominant [FORMULA] features is the fact that the connecting arm and the portion of the 3-kpc arm at positive longitude, located in the near-side of the bar according to the models, have their maximum emission below the Galactic plane (i.e. at [FORMULA]), and that the dustlane near [FORMULA] and the negative longitude part of the 135-km s-1 arm, located in the far-side of the bar, above this plane (i.e. [FORMULA]; see Fig. 2). Hence structures predicted to be spatially close to each other by the models are indeed found at similar latitude in the observations.

Consequently, the gaseous disc within the central [FORMULA] kpc is tilted relative to the plane [FORMULA]. Referring to Fig. 2, emission of the connecting arm at [FORMULA], i.e. where b stops to decrease as [FORMULA] increases, occurs near [FORMULA]. Approximating the dustlanes by a straight line across the Galactic centre with an in-plane inclination angle of [FORMULA] (see Sect. 7), the source of this emission is tilted by [FORMULA] out of the Galactic plane, corresponding to a distance of about 120 pc below this plane. Similarly, the far-side dustlane ends at [FORMULA] with [FORMULA], implying a tilt [FORMULA] and a height of [FORMULA] pc. A similar tilt is also apparent on the 12CO longitude-latitude map of Dame et al. (1987; 1999), where the dustlanes contribute only very little to the total emission. Blitz & Spergel (1991) have inferred an apparent [FORMULA] central tilt of the bar major axis from balloon 2.4 µm observations of the Galactic bulge within [FORMULA] and [FORMULA]. However, such a tilt has not been confirmed by the more recent near-IR COBE/DIRBE maps (Weiland et al. 1994). In the dust subtracted K-band map (Paper I), the latitude centroid as a function of longitude, excluding the high extinction zone [FORMULA], only shows a significant tilt when regions beyond [FORMULA] from the Galactic plane are included, but then the tilt is likely an artifact due to the growing contribution of zodiacal light. The small tilt angle derived here is not generated by a position of the Sun above the Galactic plane, which is only of order [FORMULA] pc (Humphreys & Larsen 1995 and references therein), and concerns gas on a larger scale than the 180-pc molecular ring, for which an apparent tilt angle of [FORMULA] has been estimated, also with negative latitude in the first Galactic quadrant (Uchida et al. 1994a; Morris & Serabyn 1996).

Larger tilts of the inner [FORMULA] kpc gaseous disc, of [FORMULA] and based on expanding or elliptical motion models, have been reported in the past (e.g. Cohen 1975; Burton & Liszt 1978; Liszt & Burton 1980). More recently, Burton & Liszt (1992) have updated and improved their tilted disc model into a flaring warp with a central disc coplanar to the Galactic plane. The warp is rectilinear in each radius and the tilt of its midplane is given by [FORMULA], where [FORMULA] is the galactocentric azimuth relative to the Sun defined positive in the direction of Galactic rotation, [FORMULA] the azimuth of the line of nodes and [FORMULA] the maximum tilt angle. This model predicts a tilt angle of about [FORMULA] at [FORMULA], in agreement with the tilt derived for the Galactic dustlanes.

The departure of the dustlanes from the plane [FORMULA] does not appear to increase linearly with galactocentric distance, but seems to stabilise or gently decline at larger distance, rendering its description by a constant tilt somewhat oversimplistic.

6.5. Central molecular zone

This part of the [FORMULA] observations is probably the most complex and the most difficult to understand. Binney et al. (1991) have given a detailed description of the gas flow in a rotating barred potential in terms of the closed [FORMULA] orbits, associating the terminal velocity curves in the observed [FORMULA] diagrams with the envelope of non self-intersecting such orbits and the parallelogram structure of the 180-pc molecular ring with the innermost orbit of this kind, called the "cusped [FORMULA]" orbit, where shocks would transform most of the atomic gas into molecules and force the gas to plunge onto the more viable orbits of the [FORMULA] family.

This model is confronted to several problems. The most frequently reported one (e.g. Kuijken 1996; Morris & Serabyn 1996) is the asymmetry of the observed 180-pc parallelogram, and in particular the substantial [FORMULA] km s-1 forbidden velocity near [FORMULA], which cannot be fully accounted for by projection effects of the cusped [FORMULA] orbit. Other problems are: (i) when viewed in the full [FORMULA] data cube, the 180-pc parallelogram appears more as an assemblage of larger scale features rather than forming a distinct unity (see e.g. Fig. 4 in Morris & Serabyn 1996); for instance, its upper edge is observed to extend continuously well beyond the longitude range of the postulated parallelogram and joins the connecting arm through the positive terminal velocity peak, (ii) the terminal velocity peaks and the parallelogram cannot both be generated by the same cusped [FORMULA] orbit because the formers occur well outside the longitude boundaries of the latter, (iii) the longitudinal edges of the parallelogram near [FORMULA] and [FORMULA], assimilated to the bar leading shocks in the model, should define rather clear [FORMULA] features as in our models, yet these edges are more disordered than the other edges of the parallelogram, and (iv) the cusped [FORMULA] orbit of the stellar dynamical models in Paper I generally does not match the HI terminal velocity peaks; the models providing the best agreement always arise in young and not completely stabilised bars, whereas in older bars the cusped [FORMULA] orbit presents velocity peaks at fairly larger absolute longitudes than observed.

Fig. 21 shows that the dustlane shocks are indeed responsible for the positive and negative terminal velocity peaks, but that they do not coincide with the leading edges of the cusped [FORMULA] orbit, which produces velocity peaks at higher absolute longitude and with lower velocity amplitude. Gas on the shocks move along non-periodic orbits with much smaller pericentre than the cusped [FORMULA] orbit. Thus the Milky Way's cusped [FORMULA] orbit is probably much larger than in the Binney et al. model, explaining why these authors find a very small corotation radius of 2.4 kpc. The asymmetries in our models make the cusped [FORMULA] orbit slightly uncertain. In particular, there is a small range of Hamiltonians where the [FORMULA] orbits only loop at one extremity. However, studies of Galactic [FORMULA] orbits generally represent the true Milky Way's potential by bisymmetric models and therefore are also concerned with similar uncertainties.

[FIGURE] Fig. 21. Cusped [FORMULA] orbits in the instantaneous frozen rotating potential, superposed on the spatial gas distribution of model l10t2066 (left ), and the corresponding traces in the [FORMULA] diagram (right ). The solid line orbit is obtained imposing reflection symmetry on the potential with respect to the vertical axis through the centre of mass, and the other orbits are based on the exact potential rotating about the centre of mass, the dashed and dotted orbits having single cusps at opposite ends. The crosses indicate the Lagrangian points [FORMULA], [FORMULA], [FORMULA] and [FORMULA], and the thin solid lines the corotation circle, based on the radius of the Lagrangian points [FORMULA] and [FORMULA], and the longitudes of its tangent points. Note that in the particle representation used here, the [FORMULA] plot looks different from the one in Fig. 15 because the weights of the inverse squared distance relative to the observer are not taken into account. For example, the molecular ring is more difficult to distinguish without this correction.

The gas on the dustlanes falling onto the nuclear ring from large distances does not necessarily merge with the ring, but rather passes round of it and lands on the opposite dustlane closer to the nuclear ring, merging with it only at the next passage or after repeating the whole cycle once more (Fig. 20; see also Fig. 10a in Fukuda et al. 1998). The farther out the gas on the dustlanes originates, the more it passes away from the nuclear ring. The upper and lower edges of the 180-pc parallelogram could represent such gas streams which precisely brush the nuclear ring/disc, loosing only little mass to it. The mass transfer would appear in the [FORMULA] plot like vertical bridges between the streams and the nuclear disc. An example of such bridges is detectable in the high resolution 12CO data (e.g. Morris & Serabyn 1996) near [FORMULA] and for V between 100 and 200 km s-1. The brushing streams finally crash in the dustlanes where they are abruptly decelerated. The right longitudinal edge of the 180-pc parallelogram, at [FORMULA], could be a trace of this process. However it is not very clear why this edge is located at lower absolute longitude than the bright emission near the negative terminal velocity peak, corresponding to gas with about maximum velocity on the far-side dustlane, i.e. why the gas on this dustlane slows down before being striked by the positive velocity stream round the nuclear ring. Uchida et al. (1994b) have reported on a large scale shock front in the AFGL 5376 region, which is close to the southern end of the parallelogram upper edge, but which they consider as a support of the expanding molecular ring hypothesis.

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© European Southern Observatory (ESO) 1999

Online publication: April 28, 1999