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4. Results: V(R), sigmaM(R), M(R)

In Fig. 1 we present the rotation curves of the 25 galaxies for which we have calculated mass models. The results in Fig. 1 (and subsequent figures) can be easily misinterpreted if they are taken at face-value; in the curve of M81, for example, the rotation of the bulge has not been taken into account because of the large non-circular motions found there. Table 1 contains the most important information concerning the interpretation of the results for the individual galaxies.

Figure 1

Figure 1. Rotation curves of 25 galaxies of various Hubble types.

Table 1 is set up in the same way as table l of chapter 2. To facilitate comparison the same sequence of galaxies has been used. In column 1 we give the name of the galaxy, columns 2 and 3 contain notes on the large and small scale deviations from circular motion as inferred from the velocity field and in column 4 we describe some characteristics of the HI distribution. In column 5 we have coded for each galaxy the main types of non-circular motion which influence the rotation curve analysis: A = arms, B = oval distortion, C = warp, D = large scale asymmetry. In a number of cases optical data have been used for the rotation curve in the inner regions. The symbol OR indicates that this has been done; R indicates radio data only. The addition of a U indicates that we consider the determination of the rotation curve in the inner parts unsatisfactory. The reference to the optical information is given in column 5 as well.

Table 1.

Galaxy Large scale Small scale HI character Remarks

  deviation deviation    
N3718 double profiles   strong outer arms  
M81 asymmetry density waves envelope; arms ADRU
N4151 oval   strong outer arms B ORU 1
N4736 oval   gas in ring t, R OR 2
M31 double profiles arm motions arms + extensions A OR 3
N891     southern tail RU
N2841 warp   large envelope C RU
N4565     warp C RU
N5383 oval     B RU
N4258 oval narrow features strong outer arms B R
N5055 warp   large envelope C OR 4
M51 interaction arm motions arms D RU
N7331 warp   warp C OR 5
N253        
N3198   oval + warp small "tail" R
N3359 oval?      
N5033 warp? peculiar arm   C OR 4
N5907     warp C RU
N7640        
N300 warp?   large envelope  
M33 warp density waves? envelope, clouds C R
I342 oval?? ? asymm.envelope BDRU
N2403       RU
N4244     warp C RU
M83 warp   envelope,"tail" C RU
M101 asymmetry arm motions arms,asymmetry D R
N6946        
N2805 warp?   asymmetry  
N4631     warp + features C RU
N4236 oval?      
I2574        
N3109     large envelope ? RU
HoII        
N4449 strange velocity gradient large envelope  
Galaxy     warp R

A = arms, B = oval distortion, C = warp, D = large asymmetry R = 21-cm points only, OR = optical + 21-cm points U = uncertain in the inner parts numbers indicate references: (1): Fricke and Reinhardt (1974), (2) Chincarini and Walker (1967), (3) Rubin and Ford (1970) (we ignored the dip), (4) Van der Kruit and Bosma (1978), (5) Rubin et al. (1965)

We present the resulting curves of sigmaM(R), derived from Nordsieck's method, in Fig. 2, the cumulative mass curves, M(R) are shown in Fig. 3. In table 2 we give the results of the mass models in tabular form. We have included the parameters of the spheroids and disks of Shu et al.'s method which fit the rotation curve best. We also included some of the parameters which we will discuss in detail in the next chapter.

Figure 2

Figure 2. Mass surface density distributions for 25 galaxies.

Figure 3

Figure 3. Cumulative mass, M(R), as function of R for 25 galaxies.

Table 2.

Galaxy Delta Rox Mo Ho Eo Vm R(sigma = 50)
  Mpc kpc       km s-1 kpc

N3718              
M81 3.25 13.0 9.8 11.1 23.1 217.3 11.9
N4151 13.8 19.6 7.6 9.9 8.2 146.3 12.2
N4736 6.0 10.0 5.3 3.8 9.1 186.0 8.5
M31 0.69 29.5 29.4 90.7 79.7 232.9 24.8
N891 13.75 23.6 19.7 46.3 44.2 211.8 19.4
N2841 9.0 36.1 49.7 219.9 185.0 273.0 32.1
N4565 1.5.0 38.4 43.8 190.5 132.9 246.4 29.9
N5383 31.3 26.8 20.6 50.9 41.4 200.7 17.9
               
N4258 6.6 29.4 19.5 50.1 34.2 187.4 19.5
N5055 8.0 41.1 25.3 80.3 50.1 199.3 17.3
M51 9.7 11.8 7.1 6.6 14.7 203.3 8.7
N7331 14.0 30.3 31.4 105.6 81.1 227.1 26.9
               
N253              
N3198 9.0 25.7 9.2 14.7 9.0 140.0 11.6
N3359              
N5033 14.0 35.8 26.9 86.1 58.8 209.1 22.4
N5907 11.5 30.7 26.3 75.8 67.1 225.9 20.1
N7640              
               
N300              
M33 0.72 5.4 0.75 0.19 0.27 85.0 4.4
I342 4.0 22.8 12.9 24.1 18.6 169.7 16.1
N2403 3.25 11.7 3.7 2.7 2.6 119.9 9.4
N4244 3.6 12.3 2.7 1.7 1.5 105.8 7.2
M83 8.9 38.5 18.9 48.4 25.3 163.5 16.8
M101 7.2 13.6 9.9 12.6 18.7 194.2 12.7
N6946              
               
N2805              
N4631 5.2 9.9 4.2 2.9 4.5 146.4 9.8
N4236 3.25 11.7 1.3 0.60 0.33 71.9 4.7
               
I2574              
N3109 2.2 20.4 0.91 0.45 0.10 45.9 -
               
HoII              
N4449              
               
Galaxy   12.7 12.7 7.5 34.3 232.5 ~ 14

Delta distances from references in table 2.1 or with H = 75 km s-1 Mpc-1
x radius of the last measured point on the rotation curve
units of Mo (mass within Ro), Ho (angular momentum within Ro), and Eo (kinetic energy of rotation within Ro) are 1010 Modot, 1013 Modot kpc km s-1, and 1014 Modot km-2 s-2 respectively.

Table 2. (continued)

Galaxy m A1 A2 A3 B1 B2 B3 M relative mass in spheroid
    kpc kpc kpc       1010 Modot % of Mf

N3718                  
M81 A 0.8 2.8 3.2 1032 284.5 123.9 11.5 2.9
N4151 A 1.2 9.0 12.8 4616 111.1 17.11 15.9 10.0
N4736 A 1.2 5.0 5.0 1322 226.8 50.96 8.9 14.9
M31 A 2.0 15.0 17.0 919.8 109.4 19.99 52.3 12.7
N891 C 14.0   12.6 97.47   26.41 36.1 10.0
N2841 A 10.5 39.3 31.4 248.4 29.45 12.16 124.0 13.9
N4565 A 13.1 39.3 26.2 164.6 20.86 13.69 90.5 13.4
N5383 A 13.7 31.9 22.8 132.2 16.09 12.38 49.5 15.0
N4258 A 6.0 16.0 18.0 79.16 47.07 16.68 40.9 7.7
N5055 A 3.5 19.4 23:2 493.4 78.12 10.58 40.6 19.0
M51 C 4.8   4.2 224.3   80.13 11.8 6.5
N7331 A 8.1 20.4 24.4 226.6 47.64 15.04 83.3 7.8
N253                  
N3198 D     6.5     39.73 10.3 0
N3359                  
N5033 A 3.4 10.9 17.0 502.5 120.8 18.69 44.1 9.4
N5907 B 6.7 13.4 11.2 184.9 81.35 31.46 35.6 10.2
N7640                  
N300                  
M33 C 1.2   3.5 279.6   45.88 2.1 0.89
I342 B 11.2 23.3 14.8 95.83 26.35 17.48 26.0 11.5
N2403 C 9.5   9.4 73.32   22.39 10.2 6.2
N4244 C 5.2   4.7 64.35   40.13 4.0 2.1
M83 C 16.0   15.0 69.06   16.50 24.4 12.2
M101 C 6.0   7.0 173.2   47.75 19.1 4.7
N6946                  
N2805                  
N4631 B 3.0 10.1 8.8 367.5 74.90 23.92 10.5 12.6
N4236 D     6.6     20.50 2.8 0
I2574                  
N3109 D     10.4     8.26 1.8 0
HoII                  
N4449                  
Galaxy C 1.9   6.5 1170   58.10 22.9 5.7

models: A: ns1 = 5, e1 = .866; ns2 = 5, e1 = .98; nT = 1
  B: ns1 = 5, e1 = .98; ns2 = 5, e2 = .998; nT = 1
  C: ns1 = 5, e1 = .98 (for Galaxy e1 = .866) nT = 1
  D: nT = 1
  Al, A2, A3 are the scalelength of spheroid 1, spheroid 2 and disk, resp.
  Bl, B2, B3 units km s-1 kpc-l are the fitted parameters

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