4 The bar of NGC 3359

The bar of NGC 3359 has a deprojected total length of 2.9 arcmin (which corresponds to $\sim$9 kpc). Around 17$\%$ of the total H$\alpha$ flux from the galaxy comes from the bar, which exhibits a string of very bright, prominent H II regions, or "hotspots''.

According to Friedli & Benz (1993) and to Friedli et al. (1994) strong flows of gas are predictable along a bar which is at a formative stage. The hotspots in this case can be explained as due to the star formation in the gas which has not contributed to the intense star formation at the ends of the bar (due to interstellar shocks) but falls towards the centre as its angular momentum is absorbed in the shocks and in the more general bar potential. This gas can be trapped in the inner resonant structure of the galaxy, producing massive stars and hence the hotspots.

Properties of bars related to their velocity structures include their metallicity gradients. In a general study of metallicity gradients in galaxies, Vila Costas & Edmunds (1992) showed that the gradients within the bars of barred galaxies are much lower (almost zero) than those in the external discs. In NGC 3359, however, Martin & Roy (1995) found a higher gradient within the bar, using oxygen as the abundance probe. They attributed this effect to the fact that in NGC 3359 the bar is still forming, so that there has not been time for turbulence to smooth out the intrinsic gradient due to a radially differential star formation rate. A related effect of this type of mixing in the disc is the reduced star formation symmetry in the arms of barred spirals compared with non-barred spirals, as reported in Rozas et al. (1998b).

In our residual velocity map, the zone around the bar is noticeable for the high values of its residuals (v > 30 km s^-1) found after subtracting off the rotational model. In Fig. 12 we show an integrated profile along the bar (with a integration size of 5 pixels, which represents 2.8 $^{\prime \prime }$), which clearly shows the amplitude of the residuals, (up to 30 km s^-1 and 35 km s^-1 in the NE and SW zones respectively) and their symmetry with respect to the bar centre.

Figure 10: Map of the velocity dispersion in the H$\alpha$ emission of NGC 3359, with isointensity contours superposed. Darker shading corresponds to higher velocity dispersions

Figure 11: Radial distribution of the velocity dispersion in annuli of width 8 $^{\prime \prime }$

Figure 12: Integrated profile of the residual velocity of the H$\alpha$ emission along the bar of NGC 3359

Figure 13: Diagram showing the cuts made along and perpendicular to the bar over the H$\alpha$ intensity map of the bar

Figure 14: Position velocity diagrams of the H$\alpha$ emission perpendicular to the bar of NGC 3359. The rotation curve, projected in the direction of the slice, has been overlaid in the panel of the cut which passes through the dynamical centre

Figure 15: Position velocity diagrams of the H$\alpha$ emission parallel to the bar of NGC 3359. The rotation curve, projected in the direction of the slice (parallel to the bar), has been overlaid in the panel of the cut which passes through the dynamical centre

These residuals are also detected in cuts made along and perpendicular to the H$\alpha$ bar (PA 28$^\circ$) through the data in the original cube, and they are much too strong to be artifacts. The positions of these cuts are indicated with a diagram in Fig. 13.

We show the velocities along the perpendicular cuts in Fig. 14. In the graph, in the upper left hand corner we see the distance measured from the dynamical centre, positive to the NE, negative to the SW. Given the orientation of the bar with respect to the major axis, these cuts should show the projection of the rotation curve in the direction of the bar. In the upper panels, to the N of the dynamical centre (see Fig. 13), we should see positive velocities, and in the lower pannels after the dynamical centre, to the S, negative velocities; however at +9.6 $^{\prime \prime }$ N of the dynamical centre the velocity at peak intensity suddenly goes more negative, and then rises to 0 km s^-1. This is consistent with the existence of negative residual velocities in the NE section of the bar. From the dynamical centre in the SW direction the opposite effect is seen; between -9.6 $^{\prime \prime }$ and -12.8 $^{\prime \prime }$: there is a displacement of the peak emission to positive velocities corresponding to the positive residuals we observe in the map of residuals. These coincide not only in position along the bar, but also in velocity amplitude. One should be aware that the kinks in the countours at -50 km s^-1 in the botton 3 panels of Fig. 14, are artificial due to the fact that we used the original data cube to derive the position-velocity diagrams (before "cleaning'' the noise in the data cube) in order to preserve the information at low signal levels.

Figure 16: Low resolution (16'') map of the residuals in the bar zone, with ellipses chosen to conform to the predicted orbits of the gas around the bar

In Fig. 15 we show the cuts parallel to the bar, ordered NW to SE. The most illustrative cut is that which passes through the dynamical centre. In this panel, we show the velocity rotation curve, projected in the direction of the cut (parallel to the bar). We can see how, in the SW of the bar, where the peak intensity shows negative velocities, the intensity contours have offsets to positive velocities. The opposite effect is seen in the NE. These elongations can be readily explained if there are two components of velocity at the corresponding points on the bar. The existence of these components: red-shifted in the SW and blue-shifted in the NE, coincides with a well-defined gradient in the residual velocity field. The cut at -3.0 $^{\prime \prime }$ from the dynamical centre is of particular interest; here we are in a direction between the major and minor axes of the galaxy, but even so the maxima in the velocities of the regions have the same radial velocity. The residual non-circular motions are "compensating'' the differences in projected velocity which we would expect for a simply rotating disc at these positions.

The velocity gradient observed could well be due to the projection along the line of sight of the velocity of the gas-flow round the stellar bar of the galaxy. To determine the orientation of this stellar bar we have used infrared images in J and K, the symmetry of whose isophotes yields a position angle of 15$^\circ$. The outer isophotes in an I band image suggest a value of 7$^\circ$, used by Ball (1992), but the internal isophotes in this band give a value of 15$^\circ$, equal to those in J and K (Paper I). Roberts et al. (1979) demonstrated that the presence of a non-axisymmetric potential in a spiral galaxy, of barred form in the inner zone, and spiral in the outer, will give rise to a gas response in the inner part of the disc in the form of non-circular motion along quasi-elliptical stream-lines. They predict that a strong velocity gradient across the bar can be the result of the highly oval gas circulation driven by the barlike potential field in the inner parts, and predicts too, supersonic velocities at both sides of the bar. Following this predictive model we assumed that the strong velocity gradient observed across the bar, (which is plotted in Fig. 17 as a function of the azimuthal angle in the plane of the galaxy) was due to the projection (in the plane of the sky) of the tangential component of the velocity gas flow (assumed to be in elliptical orbits).

For NGC 3359 we have assumed as a first approximation that the observed residuals are the projection of fluxes of this form, without extra components. We have taken the orbits of the gas around the bar to follow ellipses with axial ratio cos $(70\hbox{$^\circ$ })=0.34$, which is the best fit to the bar isophotes. We integrated the map of residual velocities obtained with the low resolution (16 $^{\prime \prime }$) data cube, a procedure adopted to overcome the problem posed by the patchy nature of the emission from the ionized gas, using two concentric annuli, centred on the dynamical centre, with PA = 15$^\circ$, and effective i = 70$^\circ$, divided into sectors of 20$^\circ$ which enabled us to obtain a mean velocity value for each sector (see Fig. 16). With the values of the projected velocities as a function of the azimuthal angle, the inclination angle of the bar and that of the galaxy (53$^\circ$), we performed a deprojection to infer the in-plane velocities which produce the projected values observed for the external annulus.

Figure 17: Mean modulus of the velocity gas flow around the bar, as a function of azimuthal angle in the plane of NGC 3359 (upper panel); mean projected velocity for each sector of the projected bar annulus as a function of azimuthal angle (middle panel) and estimated errors (lower panel). The angles are measured in a clockwise direction in the plane of the galaxy

The results are shown in Fig. 17. In the upper panel we plot the modulus of the tangential velocity component of the assumed elliptical gas flow, obtained using the mean projected velocity as (middle panel) a function of azimuthal angle in the plane of NGC 3359. The origin of the graph axis is in the NE of the bar, and the angles are measured clockwise. Results show a high degree of symmetry, in the sense that maximum values of the velocity occur at an angular separation of $\sim$ 180$^\circ$, which corresponds to either side of the bar, as predicted by Roberts et al. (1979), if the observed velocity gradient is in fact due to the gas flow, caused by the shocks at the ends of the bar. The gas flux shows a velocity gradient across the bar, reaching maximum values of  40 km s^-1 for the annulus with width 34 $^{\prime \prime }$ and major axis 67 $^{\prime \prime }$ in length. We will confirm this kinematic analysis with the study of other gaseous components (Boonyasait et al. 1999, in preparation).