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Astron. Astrophys. 317, 36-42 (1997)

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3. Analysis and results

3.1. HI data

3.1.1. Full ring H I analysis

The circular velocity ( V ) was measured by fitting the five orientation parameters consisting of the kinematic centre position ( x,y ), inclination ( i ), position angle of the line of nodes ( [FORMULA] ), and systemic velocity ( [FORMULA] ) to the measured H I velocities. We performed a nonlinear least square fit by applying the GAL task (van Moorsel & Wells 1985) of the AIPS astronomical image-processing system to concentric annuli containing the velocity data. We have chosen to perform a full ring analysis, where the ring width is chosen to be [FORMULA], similar to the H I resolution. GAL weights the velocities in the sampled region using a [FORMULA] function, where [FORMULA] is counted from the line of nodes. No intensity weighting procedure was applied on the velocity data.

Leaving all parameters free in the first runs of GAL revealed small variations ( [FORMULA] ) of the dynamical centre position ( x,y ) and of the systemic velocity [FORMULA] ( [FORMULA] km s[FORMULA] ) as a function of radius. This can be explained by the inherent asymmetry of NGC 1300. The position of the dynamical centre was found to match the position of the optical centre within the errors. From the optical spectra we find no reason to assume the kinematic centre to be offset from the optical nucleus, and we thus fix the dynamical centre position ( x,y ) at the position of the optical nucleus given in Table 1.

Furthermore, when combining the H I velocity field with the optical velocity field we found a slight velocity offset between the two fields of [FORMULA] km s[FORMULA]. The assumed systemic velocity from the optical measurements was 1566 km s[FORMULA] (PH), while we adopted a value of 1573 km s[FORMULA] in order to match the H I observations better.

[FIGURE]Fig. 5. The H I rotation curve of NGC 1300. In the derivation we used the parameters given in Table 1. The error bars in radius and velocity correspond to the ring width and rms velocity values respectively

Once we fixed these three parameters, we did an extended two-dimensional parameter search for the remaining parameters ( i ) and ( [FORMULA] ) using GAL. For each run, with a given parameter setup, we achieved a root mean square ( rms ) value for the fit to each radius. Two-dimensional rms maps for each radius were constructed and analyzed. The position angle for the line of nodes was found to be insensitive to the value for the inclination i, and nearly constant outside the bar region. We estimate the position angle for the line of nodes to be [FORMULA]. The inclination, although not as accurately determined as the line of nodes, was estimated to [FORMULA], for which a global minimum rms value was found. This is in excellent agreement with JvM, although these authors used a slightly different dynamical centre ( x,y ) and systemic velocity [FORMULA].

In Fig. 4 we illustrate the variation of the different parameters as a function of radius. We also indicate our preferred parameter values as straight lines. These values were determined in the radial interval [FORMULA] where effects of the bar, and effects of low data coverage are small. The x - and y - coordinates are given as offsets in arcseconds from the position of the optical nucleus.

[FIGURE]Fig. 6. Gray scale residual map, where the axisymmetric velocity field, as described by the rotation curve in Fig. 5, has been subtracted from the observed velocity field. Black corresponds to 20 km s[FORMULA] and white to -20 km s[FORMULA]. The H I total column density contours (thin), representing the spiral arms, have been overlaid. The thick contour marks the zero residual velocity

The final parameters from our H I analysis are given in Table 1, and in Fig. 5 we present the resulting H I rotation curve. The turnover radius ( [FORMULA] ) closely corresponds to the bar extent.

A residual map, presented in Fig. 6, was constructed by subtracting the axisymmetric velocity field, described by the rotation curve in Fig. 5, from the observed H I velocity field. The H I total column density contours have been overlaid in order to indicate spiral arm positions. The zero residual velocity is marked by the thick contour.

In the bar region we find residual velocities of the order of [FORMULA] km s[FORMULA], consistent with elliptical streaming aligned with the bar major axis. Furthermore, following the H I arm emanating from the eastern end of the bar, we see negative residuals at the arm position where the arm is detectable, i.e. for a winding angle of [FORMULA]. The largest residuals ( [FORMULA] km s[FORMULA] ) are found in the part of the arm situated south of the bar. The arm starting at the western end of the bar displays a similar behaviour, but now with positive residuals.

3.1.2. Wedge-based H I analysis

An alternative way of sampling the observed H I velocities when fitting the observational parameters, is to restrain the fit to an angular interval, a wedge.

For comparison with England (1989), we applied a wedge to the H I data using his angular interval [FORMULA] (as projected on the sky) centred on the position angle of the line of nodes (see Fig. 1). Performing the same analysis for the wedge data as for the full ring data gave us similar trends for i and [FORMULA], but with larger uncertainties.

For small radii, [FORMULA], we found, for both the ring and wedge methods, inclinations and position angles consistent with the findings of England (1989). However, for [FORMULA] the value for [FORMULA] drops to [FORMULA] and is nearly constant over the rest of the disc. A constant value for [FORMULA] is a characteristic of circular motion in an unwarped plane, and we believe this region to be more adequate for determining the orientation parameters and the associated rotation curve.

3.2. Optical data

When determining the orientation parameters of the H I data the position of the optical nucleus, i.e. the dynamical centre in NGC 1300, is of interest. A 30 0field surrounding NGC 1300 was extracted from the Digitized Sky Survey. In this field, ten stars were identified by the Hubble Guide Star Catalog (GSC). Their positions were measured from the Sky Survey by fitting 2-D Gaussian profiles. A linear fit to their GSC coordinates yielded the coordinates of six stars present in our CCD-images of NGC 1300. A subsequent linear fit of our images to these coordinates yielded the position of the optical centre stated in Table 1.

[FIGURE]Fig. 7. Radial velocities as a function of distance along the slits. The abscissae denote the distance along the slit in arcseconds, increasing in the direction of the position angle with the reference point (see Fig. 3) at the origin. We also plotted the corresponding velocities from the H I velocity field as solid lines

Fig. 7 presents data from the three additional spectral slit positions observed by us. The radial velocities of the various emission lines, as measured with Gaussian fits to the observed line profile, are plotted as asterisks. The optical velocities have been corrected for the offset previously mentioned. For comparison we also plot the corresponding H I velocities from the velocity field in Fig. 2.

We will here give a brief discussion on features seen in the spectra:

  • RED1 and RED2: The measurements clearly reveal velocity gradients across the spiral arms at distances [FORMULA] and [FORMULA] (RED1) and [FORMULA] and [FORMULA] (RED2) from the reference point. Also across the dust lane along the bar there is a velocity gradient of the order of 20-30 km s[FORMULA] in spectrum RED2. It is interesting to note that the H I observations do not fully resolve these gradients.
  • BLUE1: This spectrum crosses the nucleus and, having a position angle of [FORMULA], traces the bar major axis. For the inner [FORMULA], the observed velocity rises more than 100 km s[FORMULA], indicating a large central mass concentration. Across the spiral features at distances [FORMULA] from the nucleus, we again find rapid changes in velocity. The corresponding H I velocities suffer from beam-smearing and cannot resolve the sharp central velocity gradient.

In Fig. 8 we plot, together with the H I rotation curve, the measured optical velocities for all 16 slits. The observed velocities have been deprojected using the parameters in Table 1, with the assumption that they describe pure circular motion. Filled circles mark velocities inside a [FORMULA] wedge centred on the line of nodes, and empty circles mark velocities outside this wedge. The optical velocities are consistent with the H I rotation curve outside [FORMULA], but reach much higher values in the nuclear region. Estimating the maximum velocity to [FORMULA] km s[FORMULA] at [FORMULA] kpc, gives a mass inside 1 kpc of [FORMULA]. We believe that the spread in optical velocities inside the [FORMULA] wedge is primarily caused by noncircular motions, since observed velocity gradients are found when crossing spiral arms or dust lanes. However, even inside the wedge region we cannot neglect the contribution from errors in the radial velocities, boosted by the deprojection procedure (see also Blackman & Pence 1982).

[FIGURE]Fig. 8. The H I rotation curve of NGC 1300, together with optical velocity measurements from 16 long slits. Circular orbits are assumed in the derivation and plotting of the optical velocities. Filled circles mark velocities inside a [FORMULA] wedge centred on the line of nodes, and empty circles mark velocities outside the wedge

In order to create a velocity field from measurements along scattered slits, we utilize a method of interpolating between data points by fitting a regular set of Fourier components to the measured points in a least square fashion. This technique was conceived and developed by J. Högbom (see Lindblad P.O. et al. 1996 for details). Included in the compilation of the optical velocity field are the 13 slit observations by PH as well as the 3 new spectra presented here. The combined H I and optical velocity field is shown in Fig. 9. Comparing with the H I velocity field in Fig. 2 we clearly see the resolution improvement in the nuclear region, due to the optical data.

[FIGURE]Fig. 9. a Combined H I and optical radial velocity field. The contour interval is 10 km s[FORMULA], and the zero radial velocity level is marked by the thick contour. b Enlargement of the central region

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