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Astron. Astrophys. 363, 869-886 (2000)

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5. Gas kinematics

Fig. 2b shows the overlay of isovelocity contours with the peak brightness map derived from the 12CO(1-0) data. As previously stated, the observed kinematics is consistent with that of a gas disk in counter-rotation with respect to the more massive stellar disk I . In contrast, molecular clouds corotate with the less massive stellar disk II, the ionized gas, and the HI component. Counter-rotation of molecular gas is best displayed in Fig. 5a, representing the position-velocity diagram seen in 12CO(1-0) along the major axis of NGC 3593. We have superposed the radial velocities of ionized gas, derived from the H[FORMULA] and NII nebular lines, with the radial velocities of the stars, derived from stellar absorption lines (data from B96 ). There is a basic agreement between the ionized gas and molecular gas rotation curves, except for the eastern side of the CND. Between [FORMULA]=5-15", the ionized gas curve shows radial velocities significantly lower than the ones derived from CO. This might be simply explained by a peak of dust extinction towards [FORMULA]=10" which would affect only the H[FORMULA] measurements (see Fig. 4b). However the [FORMULA] map shows that the estimated extinction is similar on both sides of the major axis.

[FIGURE] Fig. 5. a (top): We show the 12CO(1-0) position-velocity (p-v) diagram along the major axis of NGC 3593 (the common line contours and grey scale is 0.01, 0.035, 0.07, 0.12, 0.17, 0.24 to 0.44Jybeam-1 by steps of 0.1Jybeam-1). The empty star markers show the stellar radial velocities given by B96, re-scaled to [FORMULA]=630kms-1. Filled circles denote measurements of the ionized gas velocities obtained by B96 with the same reference. b (bottom): A zoomed view of the 12CO(1-0) p-v plot along the X axis defined in Fig. 2b, showing the departure from circular motions ([FORMULA]) across the one-arm spiral (indicated by the arrow; see text for details).

Although the observed kinematics is dominated by circular motions, especially in the CND (see Fig. 2b), isovelocities show a wavy pattern at the passage of the one-arm spiral. This indicates the presence of streaming motions in the gas, linked with a form of density wave instability. Deviations from circular motion can be clearly identified in the southwest quadrant of the image, i.e. along the S-R, as a systematic kink in the isovelocities which appear redshifted across the CO arm (See Fig. 2b). The shift is better illustrated in Fig. 5b, which shows a position-velocity diagram across a strip oriented along PA=-107o (denoted as the x axis in Fig. 2b). At the passage of the CO arm in the southwest quadrant (at [FORMULA]x[FORMULA]-22[FORMULA]), velocities are clearly redshifted from [FORMULA] (the projected average value of the circular velocity field for [FORMULA]). Rather than an overall shift, we detect a neat gradient towards redder velocities going across the CO arm in the S-R region.

Fig. 2b shows weak indications that the velocity shift might be inverted on the northern side of the disk, following the passage of the CO arm in the N-R at ([FORMULA], [FORMULA])=(+5",+9"). However the velocity shift along the N-R is by far less systematic than the one observed along the dominant S-R and should be attributed a lower weight.

In the next section we analyze the sign of the streaming motions expected for a trailing/leading [FORMULA] wave in the frame of a standard density wave theory, our objective being to explain the non-circular motions associated with the NGC 3593 CO arm.

5.1. The signature of [FORMULA] waves on the gas flow

Shu et al. (1973) developed a kinematical model to derive the perturbations in the flow of interstellar gas due to a spiral wave of variable strength. The Shu et al. model has been usually applied to the case of progressive two-arm ([FORMULA]) spirals. Here we study the case of one-arm ([FORMULA]) trailing/leading spirals for two extreme values for the pattern speed ([FORMULA]), and define what we call the slow and the fast mode solutions. In the slow (fast) solution we are mostly inside (outside) corotation of the modes. It is expected that the sign of velocity perturbations will change across the corotation resonance; the latter explains our exploratory search. In the fast solution we chose a value of [FORMULA]=100km/s/kpc, which implies corotation lies well inside the nuclear disk of the model galaxy: RCOR=2.5 kpc, for [FORMULA]=250kms-1. On the other hand, the slow mode is characterized by [FORMULA]=0km/s/kpc, which pushes corotation outside the disk.

For the sake of simplicity, we neglect any nonlinear term on the response of the gas, as we mainly want to focus on the differences between the leading/trailing and the slow/fast cases. We will adopt a solution for the gas flow which is asymptotically similar to the linear solution of Lin et al. (1969). Fig. 6a,b illustrate the noncircular velocity fields of the gas flow derived for the slow one-arm ([FORMULA]) leading (6a)/trailing (6b) spiral wave. On the other hand, Fig. 6c,d illustrate the corresponding solution for the fast one-arm mode, in the leading (6c) and in the trailing (6d) case. The orientation of the model galaxy disk is defined by PA=90o (i.e., X-Y axes are parallel to the major and minor galaxy axes) and i=-30o (i.e.,northern side is closer to us). We chose specifically a disk geometry and spiral parameters identical to NGC 3593, except for the inclination angle, whose absolute value is assumed lower in order to get a more detailed picture of the velocity field in the model. The gas circulates counterclockwise in the galaxy plane. We represent the radial velocities projected onto the plane of the sky (vpert). vpert contains only the deviations from circular motion. The circular rotation [FORMULA] is modeled by the law [FORMULA]=[FORMULA]/[FORMULA], where [FORMULA]=250kms-1 and [FORMULA]=2 Kpc. The pitch angles for the leading and the trailing spirals are 170o and 10o, respectively. To keep the solution close to the linear case we assumed a scaled spiral field of moderate strength.

[FIGURE] Fig. 6. We display the non-circular velocity field of the gas flow, projected onto the sky plane (vpert), due to a slow (i.e.,[FORMULA]=0) [FORMULA] leading (a;left top) and trailing (b;left bottom) spiral wave; similarly we display the solutions for a fast ([FORMULA]=100) [FORMULA] leading (c; right top) and trailing (d; right bottom). The model galaxy disk is inclined by i=-30o (northern side is closer to us). Thin line contours and gray scale range from -12.5 -10 to 20 by steps of 2.5 km s-1 (dashed contours for negative values). X and Y axes are parallel to the major and minor galaxy axes (x[FORMULA]0 westwards, y[FORMULA]0 northwards). Isovelocities v=-100km s-1 (dashed line) and v=100 km s-1 (thick line) define the orientation of circular rotation in the disk (counterclockwise). The potential minimum locus is represented by the logarithmic spiral.

Fig. 6a,d show that the change of sign of streaming motions is the same for a leading and a trailing [FORMULA] wave only along the major axis. According to Fig. 6a,b, in the southern half of the galaxy disk, the gas should be redshifted (blueshifted) across the spiral arm in the leading (trailing) case when we are inside corotation. The opposite applies for the northern half of the galaxy disk. The differences between the leading and trailing cases vanish when we approach the major axis. In contrast, according to Fig. 6c,d, the gas should be blueshifted (redshifted) across the southern spiral arm in the leading (trailing) case when we are outside corotation.

A mere inspection of Fig. 6a-d clearly indicates that, although not quantitatively identical, the slow leading solution and the fast trailing solution both produce qualitatively similar gradients of streaming motions across the arm/interarm regions. The same applies to the fast leading and the slow trailing patterns. A comparison with observations (Fig. 2 and Fig. 5) leads us to conclude that the S-R, the dominant pattern of the gas response out of the CND, fits within the slow leading scenario of Fig. 6a. Therefore the [FORMULA] wave should be a slow trailing mode with respect to the stars of disk I.

The secondary gas response, represented by the N-R, would be better accounted by the fast trailing solution of Fig. 6d (fast leading with respect to the stars of disk I). However, as stated above, we have weaker observational support to choose between the fast and the slow trailing modes for the N-R. In summary, the observed pattern of gas streaming motions out of the NGC 3593 CND is explained in terms of a mixture of [FORMULA] modes dominated by a slow leading wave (trailing with respect to the stars). We analyze below this result in the context of self consistent numerical simulations of counterrotating disks, paying special attention to the evolutionary gas response.

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© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000