3 Results

3.1 The surface photometry

The spatial distribution of the H$\alpha$+[$\rm N \;{\scriptsize II}$] emission is displayed in Fig. 1 together with the slit positions of the long-slit spectra. Most of the emission originates from knots in the spiral arm regions. These knots are the typical signatures of the presence of $\rm H \;{\scriptsize II}$ regions. The emission is also found to originate close to the dust lanes. The complex dust lane structures in the area of the bulge and bar are evident in the continuum image of NGC 6221 (Fig. 2). We estimate a bar projected radius of about 20''-25'' in agreement with Elmegreen & Elmegreen (1985).

  

Figure 1: H$\alpha$+[$\rm N \;{\scriptsize II}$] emission lines image of NGC 6221. The slit positions ($\rm PA =5^{\circ}$, $50^{\circ}$,$95^{\circ}$, $125^{\circ}$, and $155^{\circ}$) of the obtained spectra are plotted. The black bars show the position and the size of the regions (along the different slit positions) where the [$\rm N \;{\scriptsize II}$]/H$\alpha$ fluxes ratio is greater than 0.5. The image orientation and scale are indicated

  

Figure 2: Stellar continuum image of NGC 6221. The image orientation and scale are the same as in Fig. 1

From the isophotal analysis of the continuum image and the two DENIS images in the bands I and J, the position of the bar was determined. The maximum in ellipticity and the plateau of the position angle profile around $\rm PA =125^\circ$ (Fig. 3) were used as indicators of the bar component. This position angle value is also consistent with the orientation of the dust lanes in Fig. 2. P&B derive for NGC 6221 a position angle for the line-of-nodes of $118^\circ \pm 5^\circ$. They also stated that the major axis of the bar is exactly perpendicular to the line-of-nodes. We believe they confused the position angles of the major axis of galaxy with that of the bar as can be seen by Fig. 2 in this paper and by Plates 2 and 3 in their paper and from our velocity field. The uncalibrated surface brightness profile of the bar shows an exponential decrease, although heavily influenced by the presence of dust lanes.

3.2 The radial profiles of the [$\rm N \;{\scriptsize II}$]/H$\alpha$ ratio

The radial profiles of the fluxes ratio [$\rm N \;{\scriptsize II}$] ($\lambda$ 6583.4 Å)/H$\alpha$ were calculated for all position angles and are presented in Fig. 4. The value of the ratio ([$\rm N \;{\scriptsize II}$]/H$\alpha$ $\sim0.3$) indicates that the emission is mainly from $\rm H \;{\scriptsize II}$ regions, even in the bulge. The central regions where 0.5< [$\rm N \;{\scriptsize II}$]/H$\alpha$ $\leq1$ are marked as black bars along each slit position in Fig. 1. They constitute a ring-like structure with a radius of about 9'' ($\sim\! 1$ kpc for the assumed distance), which is is located at the distance from the centre corresponding to the position of a ILR due to the presence of the bar (see Sect. 3.4 for the discussion). The presence of this nuclear gaseous ring is consistent with the $\rm H \;{\scriptsize I}$ observations of Koribalsky (1996b).

 

Figure 3: NGC 6221 ellipticity and position angle radial profiles obtained from the ellipse fitting to the NTT continuum-band (crosses), DENIS I-band (filled diamonds), and DENIS J-band (open circles) images

 

Figure 4: [N II]($\lambda$ 6583.4 Å)/H$\alpha$ emission line fluxes ratios of NGC 6221 as a function of radius for the position angles 5$^\circ$ (major axis), 50$^\circ$, 95$^\circ$(minor axis), 125$^\circ$ (bar major axis) and 155$^\circ$

3.3 The ionized gas and stellar kinematics

The measured ionized gas and stellar kinematics of the galaxy NGC 6221 are presented for the observed position angles in Figs. 5-9.

In all the spectra we found an offset of 4''-5'' between the stellar kinematical centre (obtained from the position of the maximum intensity of continuum) and the gaseous kinematical centre (estimated from the maximum emission of the H$\alpha$ and [$\rm N \;{\scriptsize II}$] lines).

The position of the gaseous kinematical centre coincides with that estimated by P&B. For the systemic velocity we measured $V_{\rm sys} = 1465\pm10$ while P&B obtained a slightly larger value of $1475\pm5$. If we use the emission lines data as reference for the centre, we find for all intermediate position angles that the folded velocity and velocity dispersion curves of ionized gas and stars present strong asymmetries. On the other hand, using the absorption lines data as reference for the centre the asymmetries of the folded kinematical profiles are minimized. In the following the absorption line data are therefore used to give the true centre for both ionized gas and stars.

In order to bring out the asymmetries in the gas velocity curves we compare them with the empirically derived curve of circular velocity projected onto the different position angles. We adopted the equation of the rotation curve of a galaxy represented as a sequence of flattened spheroids of Brandt (1960) as applied by Bettoni & Galletta (1997) for their sample of barred galaxies. The parameters of the curve were found by the best fit to the major axis NE side of ionized gas rotation curve (which has the more regular pattern) assuming a galaxy inclination of $44^\circ$ (RC3). The resulting curve has been folded for the major axis SW side. Then it has been projected onto the remaining the position angles assuming that the mean motions were symmetric with respect to the galaxy rotation axis. These projected curves (see Figs. 5-9) allow us to estimate when ionized gas and stars deviate from circular motions.

3.3.1 The major axis $\rm (PA =5^\circ)$

The kinematics of the ionized gas and stars measured along the NGC 6221 optical major axis is shown in Fig. 5.

  

Figure 5: The kinematics of the ionized gas (open circles) and stars (filled squares) measured along NGC 6221 major-axis ($\rm PA =5^{\circ}$). The observed heliocentric velocity curves and the velocity dispersion profiles are shown in the top and in the bottom panel respectively. The errorbars of the gas velocities and velocity dispersions smaller than symbols are not plotted. The solid line represents the model circular velocity, as explained in the text

The ionized gas kinematics extends to about 80'' ($\sim\! 11$ kpc) on the receding NE side and to about 55'' ($\sim\! 8$ kpc) on the approaching SW side. We found that our gas rotational velocity data agrees within the errors with the measurements obtained by P&B along their spectrum G $\rm (PA =14^\circ )$ and deprojected to our position angle. We obtain more detailed measurements in the central region where the velocity gradient is strong ($\Delta v_{\rm gas} =$ 350 $\rm km\;s^{-1}$ for $\Delta r=20''$). The velocity dispersion of the gas shows within the bulge a peaked trend for |r|<5 with a maximum value of about 130 $\rm km\;s^{-1}$. In the outer region dominated by the disk component the velocity dispersion is found to be constant at a value of about 50 $\rm km\;s^{-1}$. Similar peaked velocity dispersion profiles are also found in bulges of elliptical (e.g. Zeilinger et al. 1996) and lenticular galaxies (e.g. Bertola et al. 1995). For 15''<|r|<25'' the gas velocity curve is very asymmetric as shown by the comparison with the empirical circular velocity curve. In this radial range the gas velocity along the receding side is about 20 $\rm km\;s^{-1}$ lower than the circular velocity. It is about 60 $\rm km\;s^{-1}$ higher along the approaching side. An abrupt change in the slope of the gas velocity curve and a local maximum in the gas velocity dispersion is also observed at about 17''. No emission is detected for 25''<r<50''.

The stellar kinematics data extend from about 35'' ($\sim 5$ kpc) on the NE side to near the centre of the galaxy. The velocities of the stars follow closely the trend of the velocities of the gas. The stellar velocity dispersion profile is peaked with a central value of about 200 $\rm km\;s^{-1}$. At larger radii it drops off to a value of about 70 $\rm km\;s^{-1}$ along the NE side. For the SW side it was not possible to measure the stellar kinematics due to the poor S/N ratio of the absorption lines.

The stellar kinematics of the bulge is found to be consistent with a hot stellar system ($v/\sigma\simeq0.3$ at $\epsilon\simeq0.2$). The fact that the velocity dispersion of the gaseous component is of the same order as that of the stellar one indicates a significant contribution of random motions to the dynamical support of the gas as dicussed by Bertola et al. (1995) for a sample of S0 galaxies.

3.3.2 The intermediate axis at $\rm PA =50^\circ$

The kinematics of ionized gas and stars measured along the NGC 6221 $\rm PA =50^\circ$ is shown in Fig. 6.

  

Figure 6: Same as Fig. 5 for $\rm PA =50^\circ$

The gas kinematics is observed to about 70'' ($\sim\! 10$ kpc) on the NE side and to about 85'' ($\sim\! 12$ kpc) on the other side. For this intermediate axis our gas velocity data agrees within the errors with those of P&B (spectrum J). The central velocity gradient ($\Delta v_{\rm gas} =$ 300 $\rm km\;s^{-1}$ for $\Delta r=20''$) is lower than on the major axis. The gas velocity dispersion has a central maximum of about 120 $\rm km\;s^{-1}$. It decreases slowly to about 40 $\rm km\;s^{-1}$ with the distance from the centre.

The stellar velocity curve is close to the gaseous one. Except for -10''<r<-3'' the stellar velocity dispersion remains higher than the gaseous one of about 20 $\rm km\;s^{-1}$. The stellar data are as extended as the gas data in the NE side and limited to about 35'' ($\sim 5$ kpc). The SW side is characterized by regions without emission lines and with low S/N absoption lines. This produces the large errors in the measurement of the velocity of the gas and makes impossible to determine the stellar kinematics.

3.3.3 The minor axis $\rm (PA =95^\circ )$

The kinematics of ionized gas and stars measured along the NGC 6221 optical minor axis are shown in Fig. 7.

  

Figure 7: Same as Fig. 5 for $\rm PA =95 ^{\circ}$ (minor axis)

The gas kinematics is measured to about 65'' ($\sim 9$ kpc) and to about 75'' ($\sim11$ kpc) on the NW and SE side respectively. The gas velocity measurements obtained by P&B along their spectrum B ($\rm PA=104^\circ$) deprojected to $\rm PA =95 ^{\circ}$ agree within the data errors with the velocities we found along this axis. If we assume an axisymmetric potential for a galaxy we expect to find a zero velocity gradient along the minor axis; nevertheless, here we observe a "wavy pattern" in the gas velocity curve at this position angle. P&B defined this behaviour as a "conspicuous S-shaped pattern" on the isovelocity contours of the gas. For |r|>30'' the gas velocity follows the circular velocity only on the NW side. The folded velocity curve is asymmetric for |r|>10'', with a maximum velocity difference between the NW and SE side of about 60 $\rm km\;s^{-1}$.

In spite of the fact that the minor axis differs by about $30^\circ$ from the bar position angle, the virtual absence of projected circular motions at this angle makes it possible to study in great detail how the bar affects the dynamics of gas and stars. The non-circular motions have an observed maximum amplitude of about 100 $\rm km\;s^{-1}$, which is found to be in agreement with the rather general predictions by Roberts et al. (1979), who estimate velocities in the range of 50 $\rm km\;s^{-1}$ to 150 $\rm km\;s^{-1}$ for bar-induced radial components of gas flow. From the analysis of Fig. 2 a projected radial extent of 20''-25'' is estimated for the bar component, and this is found to be in agreement with the kinematical data. The gaseous velocity dispersion profile in the region of the bar is found to be constant with a value of about 70 $\rm km\;s^{-1}$ distinctly different from the two preceding position angles (i.e. at $5^\circ$ and $50^{\circ}$) where the profile was peaked at the centre. Outside the bar region the gas velocity dispersion is lower than 50 $\rm km\;s^{-1}$.

From the above, we can explain the "wavy pattern" in the gas velocity curve along the minor axis as follows. For the central |r|<6'' the velocity of the gas shows a negative gradient because it follows the x₁ family orbits, a little further out the gradient is inverted on both sides of the velocity curve. This can be explained if we consider that beyond the position of the outer ILR (located at a deprojected radius $r\sim9''$) the gas follows the x₂ family orbits out to the corotation radius (at a deprojected radius $r\sim33''$). Outside the corotation the bar influence declines and the velocity of the gas tends to the systemic velocity, at least on the NW side.

The star kinematics is measured up to a distance of about 45'' ($\sim\! 7$ kpc) in the NW side and up to about 7'' ($\sim\! 1$ kpc) in the SE side. The velocity curve for the stars agrees within the error limits with the circular velocity. At this angle the velocity dispersion appears significantly higher for the stars than for the gas. The stellar velocity dispersion is higher than 90 $\rm km\;s^{-1}$ at all radii peaking to about 150 $\rm km\;s^{-1}$ in the centre. For the SE side (r>10'') of the spectra it was not possible to obtain measurements of the stellar kinematics.

3.3.4 The bar major axis ($\rm PA =125^\circ$)

The kinematics of ionized gas and stars measured along the NGC 6221 $\rm PA =125^\circ$ are shown in Fig. 8. From the photometrical data we deduced that this is the position angle of the major axis of NGC 6221 bar.

  

Figure 8: Same as Fig. 5 for PA = $125^{\circ}$ (bar major axis)

The gas kinematics extends to about 55'' ($\sim\! 8$ kpc) from the nucleus on either side. P&B did not obtain gas velocity measures for this angle. The gas velocity curve is strongly asymmetric. It follows the predicted circular velocity only along the approching SE side. On the receding NW side the observed gas velocity is lower (-50''<r<-20''), equal (-20''<r<-10'') and higher (-10''<r<0) than the circular velocity. The observed maximum deviation from the empirical circular velocity is about 80 $\rm km\;s^{-1}$ at $r\sim-3''$. The gas velocity dispersion profile has an "M-shaped" appearance due to the presence of two local maxima. It peaks at about 120 $\rm km\;s^{-1}$ in the centre and at about 140 $\rm km\;s^{-1}$ at r=-10''. For the outer regions it decreases and it becomes constant with a value lower than 40 $\rm km\;s^{-1}$.

The stellar kinematics is observed to about 50'' ($\sim\! 7$ kpc) on the NW side and to about 40'' ($\sim\! 6$ kpc) on the SE side. The stars rotate more slowly than gas with a higher velocity dispersion at all radii. This has a central maximum of about 160 $\rm km\;s^{-1}$, and remains higher than 80 $\rm km\;s^{-1}$ at larger radii.

3.3.5 The intermediate axis at $\rm PA=155^\circ$

The kinematics of ionized gas and stars measured along the NGC 6221 $\rm PA=155^\circ$ are shown in Fig. 9.

  

Figure 9: Same as Fig. 5 for $\rm PA=155^\circ$

The gas kinematics is measured up to 80'' ($\sim\! 11$ kpc) and up to 70'' ($\sim\! 10$ kpc) in the approaching and in the receding side respectively. P&B do not present gas velocity data at this position angle. The gas velocity curve has the same appearance as that along the major axis, with the exception of a lower velocity gradient. Along all the SE side the observed velocity differs from the circular value by about 60 $\rm km\;s^{-1}$. The gas velocity dispersion profile has a central maximum of about 140 $\rm km\;s^{-1}$ decreasing to values lower than 60 $\rm km\;s^{-1}$ for |r|>20''.

The stellar kinematics is observed to about 50'' ($\sim\! 7$ kpc) on either side of the centre. The stars rotate with similar velocity to the gaseous component. They also show the same velocity dispersion profile as the gas. The S/N ratio for the absorption lines is very low for the SE side where the stellar kinematics is measured only at about 50'' from the centre.

3.4 The location of the lindblad resonances

With the empirical curve of the circular velocity V(R) derived in the Sect. 3.3 we are able to calculate the angular velocity $\Omega(R)=V(R)/R$ and the epicyclic frequency $k(R) = (4\Omega^2+R{\rm d}\,\Omega^2/\,{\rm d}r)^{0.5}$ where R is the distance from the centre deprojected on the galaxy plane. In Fig. 10 the curves $\Omega$, $\Omega + k/2$ and $\Omega - k/2$ are plotted in the inner 70'' ($\sim\! 10$ kpc) from the centre.

If we assume the observed ring of ionized gas to be at the outer ILR we derive the pattern speed of the bar $\Omega_{\rm p}$from the condition $\Omega_{\rm p}=\Omega\,(R_{\rm OILR})-k\,(R_{\rm OILR})/2$.We have $R_{\rm OILR} = 9''$ ($\sim\! 1$ kpc) and we find for the bar of NGC 6221 that $\Omega_{\rm p}=46$ $\rm km\;s^{-1}$ kpc^-1 taking in account all the uncertainties. For this value of $\Omega_{\rm p}$ there is another intersection with the curve $\Omega - k/2$ giving the location of the inner ILR. The radius of the inner ILR is small ($R_{\rm IILR} = 3'' \sim0.4$ kpc), and its precise location is uncertain as it is comparable to the seeing resolution of our observation.

Corotation is located at the radius $R_{\rm CR}$ where the bar pattern speed and the angular velocity are equal, i.e. $\Omega_{\rm p}=\Omega\,(R_{\rm CR})$.We find that the corotation radius is at a distance $R_{\rm CR} = 33''$ ($\sim\! 5$ kpc) from the centre. This is consistent with Fig. 2 where the bar seems to finish between 20'' and 25'' corresponding to about 28''-35'' if deprojected onto the galaxy plane.

No outer Lindblad resonance (OLR) is found in the radial range of the observe gas kinematics because the condition $\Omega_{\rm p}=\Omega(R)+k(R)/2$ is not satisfied for any value of the radius R.

 

Figure 10: The angular velocity curve $\Omega$ and the derived curves $\Omega\pm k/2$ in NGC 6221. The values of the angular velocity $\Omega$ and the epicyclic frequency k are calculated from the model circular velocity deprojected on the galaxy plane. The horizontal line indicates the bar pattern speed $\Omega_p=46$$\rm km\;s^{-1}$ kpc-1. The positions of the two inner Lindblad resonances ($R_{\rm IILR}=3$$^{\prime\prime}$ and $R_{\rm OILR}=9$$^{\prime\prime}$) and of the corotation ($R_{\rm CR}=33$$^{\prime\prime}$) are showed. No OLR has been found.