2 Velocity field and rotation curve

We determined intensity-weighted mean velocities in order to make maximum use of the information contained in spectra with limited signal-to-noise ratios. Noise was further suppressed by only using data from the areas delineated by the cleaning masks (cf. Paper I). The intensity-weighted velocity fields of our galaxy sample are shown in Fig. 4.

We have determined rotation curves by iteratively fitting to the observed velocity field the parameters found with the tilted-ring method (Warner et al. 1973), incorporated in the GIPSY packages as the task ROTCUR (Begeman 1987). Note that the inclination and the location of the kinematic center can be determined only if the rotation curve flattens at the outer radii (i.e. shows the onset of differential rotation). In order to obtain robust solutions, we performed a large number of fits where each parameter was free in 25 to 30 fits, allowing calculation of the rms scatter of each parameter at all radii. Solution of $v(r)\sin~i$ can also directly be compared to observed major axis position-velocity maps (Sect. 3). Although the product $v(r)\sin~i$ is well-constrained, the separate solutions for v(r) and i in general are not unique. In particular, at inclination angles $\leq$$50^\circ$, v(r) and i cannot be fitted independently (Begeman 1987).

Depending on galaxy HI extent and surface brightness, we performed fits on full-resolution (13.5'') or low-resolution (30'') data. As a consistency check, we used both low and full resolution data for DDO 47, DDO 48 and NGC 2976. The results are presented in Tables 1 and 2. In total, 13 out of 29 galaxies in the sample could so be fitted. For the remainder, a complete analysis was not feasible. There, we required the rotation center to coincide with the HI center of mass which was found to be correct at least for all the objects listed in Table 1. In addition, we assigned to these objects a low ($30^\circ$), average ($60^\circ$) or high ($80^\circ$) inclination based on the appearance of the HI isophotes. The results of fits to the high-resolution data, but restricted by these assumptions, are given in Tables 3 and 4. The center coordinates in Table 3 are those of the HI-intensity-weighted mean position in $\alpha_{1950}$ and $\delta_{1950}$. They typically change only by a few arcseconds if different intensity thresholds are applied. The errors quoted for position angle and systemic velocity represent their scatter between different radii. Note that the velocities listed in Table 4 have not been corrected for inclination. These $v(r)\sin i$ values, as indeed also the position angle, depend only weakly on the assumed inclination.

   

Table 3: HI disk parameters from restricted tilted-ring/HI isophote fits; inclination assumed.

Name	HI center of mass		i	$\rm PA_{kin}$	$v_{\rm sys}$	$D_{\rm HI}$	$q_{\rm HI}$	$\rm PA_{HI}$	Scale
	$\alpha_{1950}$	$\delta_{1950}$	$^\circ$	$^\circ$	$~{\rm {km~s^{-1}}}$	arcsec		$^\circ$	kpc/'
[1]	[2]	[3]	[4]	[5]	[6]	[7]	[8]	[9]	[10]
D 22	$\rm 2^h29^m47\fs2$	$\rm 38^\circ27'35''$	80	$\rm 178\pm 1$	$\rm 564 \pm 2$	157 $\pm$ 9	0.47 $\pm$ 0.04	181 $\pm$ 2	2.9
D 43	$\rm 7^h24^m50\fs2$	$\rm 40^\circ52'19''$	30	$\rm 296\pm 4$	$\rm 355 \pm 1$	145 $\pm$ 3	0.93 $\pm$ 0.03	335 $\pm$ 11	1.4
D 46*	$\rm 7^h38^m00\fs9$	$\rm 40^\circ13'30''$	30	$\rm 273\pm 4$	$\rm 363 \pm 2$	189 $\pm$ 5	0.97 $\pm$ 0.05	226 $\pm$ 45	1.4
D 47*	$\rm 7^h39^m 03\fs1$	$\rm 16^\circ55'13''$	30	$\rm 319\pm 8$	$\rm 272 \pm 1$	403 $\pm$ 4	0.85 $\pm$ 0.01	266 $\pm$ 3	0.58
D 48*	$\rm 7^h54^m46\fs8$	$\rm 58^\circ10'39''$	80	$\rm 357\pm 3$	$\rm 1086 \pm 1$	245 $\pm$ 12	0.33 $\pm$ 0.02	354 $\pm$ 2	4.6
N 2537*	$\rm 8^h09^m42\fs3$	$\rm 46^\circ08'32''$	30	$\rm 171\pm 2$	$\rm 446 \pm 1$	219 $\pm$ 5	0.80 $\pm$ 0.04	261 $\pm$ 6	1.9
D 52	$\rm 8^h25^m06\fs4$	$\rm 42^\circ01'17''$	60	$\rm 5 \pm 3$	$\rm 394 \pm 1$	204 $\pm$ 9	0.58 $\pm$ 0.04	359 $\pm$ 3	1.5
D 63	$\rm 9^h36^m01\fs9$	$\rm 71^\circ25'07''$	30	$\rm 38\pm 15$	$\rm 140 \pm 2$	307 $\pm$ 6	0.76 $\pm$ 0.02	5 $\pm$ 2	1.0
N 2976*	$\rm 9^h43^m11\fs7$	$\rm 68^\circ09'06''$	60	$\rm 321 \pm 2$	$\rm 3 \pm 2$	316 $\pm$ 5	0.62 $\pm$ 0.01	326 $\pm$ 1	1.0
D 64	$\rm 9^h47^m26\fs3$	$\rm 31^\circ43'19''$	60	$\rm 97\pm 7$	$\rm 517 \pm 1$	210 $\pm$ 11	0.56 $\pm$ 0.05	84 $\pm$ 4	1.8
D 68	$\rm 9^h53^m52\fs8$	$\rm 29^\circ03'42''$	60	$\rm 29\pm 10$	$\rm 504 \pm 3$	300 $\pm$ 9	0.56 $\pm$ 0.03	19 $\pm$ 2	1.8
D 73	$\rm 10^h06^m39\fs5$	$\rm 30^\circ23'50''$	60	$\rm 66\pm 3$	$\rm 1378 \pm 2$	135 $\pm$ 3	0.94 $\pm$ 0.03	38 $\pm$ 15	5.2
D 83*	$\rm 10^h33^m54\fs7$	$\rm 31^\circ48'24''$	60	$\rm 55\pm 3$	$\rm 584 \pm 1$	190 $\pm$ 4	0.55 $\pm$ 0.02	56 $\pm$ 2	2.6
D 87*	$\rm 10^h46^m16\fs3$	$\rm 65^\circ47'34''$	60	$\rm 239\pm 5$	$\rm 339 \pm 1$	246 $\pm$ 5	0.86 $\pm$ 0.03	224 $\pm$ 6	1.0
M 178	$\rm 11^h30^m45\fs1$	$\rm 49^\circ31'06''$	-	-	-	91 $\pm$ 4	0.70 $\pm$ 0.06	146 $\pm$ 7	1.5
N 3738	$\rm 11^h33^m04\fs7$	$\rm 54^\circ48'10''$	60	$\rm 270$	$\rm 225 \pm 4$	182 $\pm$ 6	0.80 $\pm$ 0.05	274 $\pm$ 10	1.5
D 101	$\rm 11^h53^m07\fs1$	$\rm 31^\circ47'41''$	-	-	-	-	-	-	2.1
D 123*	$\rm 12^h23^m45\fs9$	$\rm 58^\circ35'52''$	18	$\rm 198 \pm 5$	$\rm 723 \pm 1$	240 $\pm$ 2	0.97 $\pm$ 0.01	197 $\pm$ 13	3.3
M 209	$\rm 12^h23^m50\fs2$	$\rm 48^\circ46'25''$	30	$\rm 225$	$\rm 285 \pm 8$	125 $\pm$ 5	0.86 $\pm$0.08	206 $\pm$ 20	1.4
D 125	$\rm 12^h25^m14\fs0$	$\rm 43^\circ46'17''$	60	$\rm 135\pm 2$	$\rm 195 \pm 1$	281 $\pm$ 3	0.66 $\pm$ 0.02	118 $\pm$ 2	1.3
D 133*	$\rm 12^h30^m27\fs6$	$\rm 31^\circ48'54''$	30	$\rm 350 \pm 5$	$\rm 331 \pm 1$	296 $\pm$ 5	0.86 $\pm$ 0.02	18 $\pm$ 5	1.5
D 165	$\rm 13^h04^m40\fs2$	$\rm 67^\circ58'20''$	-	135	22	253 $\pm$ 5	0.79 $\pm$ 0.03	93 $\pm$ 4	1.3
D 166	$\rm 13^h11^m00\fs0$	$\rm 36^\circ28'36''$	30	$\rm 41\pm 9$	$\rm 942 \pm 3$	200 $\pm$ 3	0.75 $\pm$ 0.02	46 $\pm$ 3	4.7
D 168*	$\rm 13^h12^m14\fs7$	$\rm 46^\circ11'07''$	60	$\rm 276\pm1$	$\rm 191 \pm 2$	366 $\pm$ 5	0.82 $\pm$ 0.02	304 $\pm$ 3	1.0
D 185*	$\rm 13^h52^m53\fs5$	$\rm 54^\circ08'24''$	80	$\rm 39\pm 5$	$\rm 137 \pm 3$	302 $\pm$ 13	0.37 $\pm$ 0.02	17 $\pm$ 1	2.0
D 190	$\rm 14^h22^m48\fs2$	$\rm 44^\circ45'09''$	60	$\rm 149\pm 6$	$\rm 149 \pm 1$	201 $\pm$ 4	0.86 $\pm$ 0.03	150 $\pm$ 7	1.7
D 216	$\rm 23^h26^m02\fs9$	$\rm 14^\circ28'02''$	60	135	-	286 $\pm$ 17	0.32 $\pm$ 0.02	130 $\pm$ 1	0.29
D 217*	$\rm 23^h27^m32\fs8$	$\rm 40^\circ43'03''$	30	$\rm 43\pm 8$	$\rm 432 \pm 2$	472 $\pm$ 5	0.75 $\pm$ 0.01	27 $\pm$ 2	2.7

Column designations [1] Object name; [2] and [3] right asccension and declination (epoch 1950) of kinematic center and its rms scatter between radii; [4] inclination in degrees (see text for explanation); [5] position angle of kinematic major axis in degrees and its rms scatter between radii; [6] systemic velocity in $~{\rm {km~s^{-1}}}$ and its rms scatter between radii; [7] major axis of ellipse fitted to the $N_{\rm HI}=3 \times 10^{20}~{\rm cm^{-2}}$ contour in the HI column density map; [8] axial ratio of the ellipse in [7]; [9] position angle of the ellipse major axis in [7]; [10] radial scale of the rotation curve in kpc/arcmin.

Notes: If no error is given, the value is a best estimate. For galaxies marked with an asterisk, more accurate values are given in Table 1; they are included here only for comparison purposes.

 

 

Table 4: Velocity $v(r) \sin(i)$ from restricted rotation curve fits.

radius	DDO 22	DDO 43	DDO 46*	DDO 47*	DDO 48*	NGC 2537*	DDO 52	DDO 63	NGC 2976*
$\arcsec$
30	$8.1\pm2.4$	$11.7\pm2.0$	$23.7\pm3.3$	$12.2\pm2.0$	$42.4\pm6.5$	$33.6\pm3.2$	$23.7\pm3.6$	$6.3\pm2.3$	$25.6\pm5.6$
60	$18.7\pm2.8$	$15.7\pm2.8$	$29.9\pm2.1$	$13.4\pm2.3$	$62.7\pm5.0$	$38.9\pm2.5$	$32.7\pm2.6$	$8.0\pm1.9$	$44.7\pm3.8$
90		$17.5\pm3.9$	$30.2\pm3.6$	$18.3\pm1.7$	$73.0\pm5.0$	$43.2\pm3.5$	$38.2\pm2.5$	$7.1\pm2.6$	$57.2\pm5.3$
120				$24.1\pm2.2$			$43.3\pm5.0$	$8.6\pm3.2$	$61.0\pm7.6$
150				$30.6\pm2.1$				$8.0\pm5.3$	$54.0\pm\ 11$
radius	DDO 64	DDO 68	DDO 73	DDO 83*	DDO 87*	NGC 3738	DDO 123*	Mk 209	DDO 125
$\arcsec$
30	$22.0\pm3.1$	$20.5\pm4.3$	$20.0\pm1.6$	$32.6\pm4.8$	$16.9\pm3.3$	$39.0\pm6.2$	$14.0\pm2.5$	$14.3\pm5.0$	$5.4\pm1.8$
60	$33.4\pm2.9$	$28.4\pm5.7$	$26.6\pm2.4$	$43.7\pm2.5$	$26.7\pm1.8$		$18.7\pm1.7$	$17.1\pm5.0$	$8.7\pm1.1$
90	$41.8\pm7.4$	$42.9\pm5.6$		$46.7\pm3.3$	$28.8\pm2.9$		$22.6\pm2.6$		$9.8\pm1.6$
120		$45.9\pm5.6$			$30.2\pm4.0$		$27.5\pm2.7$		$11.2\pm2.7$
150					$31.0\pm5.8$
radius	DDO 133*	DDO 165	DDO 166	DDO 168*	DDO 185*	DDO 190	DDO 216	DDO 217*
$\arcsec$
30	$11.5\pm3.0$	9	$22.6\pm4.3$	$10.7\pm2.5$	$11.7\pm2.2$	$12.3\pm1.8$	$1\pm1$	$24.1\pm4.7$
60	$17.7\pm1.9$	17	$30.2\pm3.1$	$20.3\pm2.4$	$22.9\pm3.0$	$19.4\pm2.1$	$4 \pm 2$	$38.1\pm3.1$
90	$22.9\pm2.8$	26	$35.4\pm5.0$	$24.8\pm2.2$	$36.2\pm3.2$	$24.7\pm2.5$	$7\pm5$	$41.3\pm2.8$
120	$26.6\pm2.2$			$35.6\pm5.5$			$7\pm5$	$43.4\pm2.9$
150				$37.3\pm6.7$				$47.0\pm2.0$

Notes: see text for fit procedure details. Velocities have not been corrected for inclination, as opposed to results presented in Table 2. For galaxies marked with an asterisk, more accurate values are given in Table 2; values given here are only for comparison purposes. The rotation velocity of DDO 165 was determined from the position-velocity map in position angle $135^\circ$.