4. Statistical properties of flatness of spiral
galaxies

1. Dependence on color.

Figures 1 (click here) and 3 (click here) present the correlation between flatness of spiral galaxy (H/D₀) and (B-V)_T⁰, Figs. 2 (click here) and 4 (click here) show the correlation between the scaleheight of spiral (H) and (B-V)_T⁰. Results obtained by van der Kruit and Searle's method are also plotted in Figs. 3 and 4 for comparison. It is obvious that the results obtained by different methods are consistent.

  
Figure 1: Flatness of spiral galaxy plotted versus the corrected B-V color

  
Figure 2: Scaleheight of spiral galaxy plotted versus the corrected B-V color

  
Figure 3: Flatness of spiral galaxy plotted versus the corrected B-V color, the data (black circle) are from van der Kruit and Searle's papers

  
Figure 4: Scaleheight of spiral galaxy plotted versus the corrected B-V color, the data (black circle) are from van der Kruit and Searle's papers

  
Figure 5: Flatness of spiral galaxy plotted versus the corrected U-B color

  
Figure 6: Scaleheight of spiral galaxy plotted versus the corrected U-B color

  
Figure 7: Flatness of spiral galaxy plotted versus the total magnitude in the B system

  
Figure 8: Scaleheight of spiral galaxy plotted versus the total magnitude in the B system

  
Figure 9: Flatness of spiral galaxy plotted versus the Hubble sequence

  
Figure 10: Scaleheight of spiral galaxy plotted versus the Hubble sequence

  
Figure 11: The image of NGC 1096 and with superimposed fitting logarithmic spiral curves

The equations of the regression are

   

N r < /TD>

Fig. 1 70 0.708 0.302

Fig. 2 70 0.504 0.302

Fig. 3 77 0.665 0.288

Fig. 4 77 0.539 0.288

The regression coefficients, and their errors are given in Table 2 (click here). r in Col. 5 of Table 2 is the correlation coefficient and (=0.01) the lowest correlation coefficient.

From Figs. 1 (click here) and 3 (click here), one could see a trend that flatter galaxies are bluer, and the strong correlation is encouraging. A similar tendency can be found from Figs. 2 (click here) and 4 (click here) that the smaller the scaleheight of a galaxy is, the bluer the galaxy is. Figure 5 (click here) plots flatness of spiral galaxy as a function of the corrected U-B color ((U-B)_T⁰), which the total color index taken from RC3 corrected for differential galactic and internal extinction (to "face-on'') and for redshift between U and B bands. The dependence of scaleheight of spiral on (U-B)_T⁰ is illustrated in Fig. 6 (click here).

2. Dependence on magnitude.

Figure 7 (click here) shows the correlation between flatness of spiral galaxy and the total "face-on'' magnitude B_T⁰, taken from RC3, corrected for Galactic and internal absorption and for redshift in the B system. The correlation of scaleheight of spiral with B_T⁰ is shown in Fig. 8 (click here). It is interesting to find that the flatter galaxies look brighter, and that the smaller the scaleheight of a galaxy is, the brighter the galaxy looks.

3. Dependence on Hubble type.

The tightness of the spiral pattern, in addition to the disk resolution and bulge-to-disk ratio, are the fundamental criteria in Hubble's (1926) classification of spirals. It would be suggestive to see the dependence of flatness of spiral galaxies on the Hubble types, which is shown in Fig. 9 (click here). Although the scatter is quite significant, one can still find a trend that spirals become flatter along the Hubble types Sab - Scd. Part of this scatter can be attributed to the estimated dispersion of flatness among the individual galaxies themselves. An additional dispersion of comparable magnitude is expected from the discrete binning of the measured Hubble types. Kennicutt (1981) has already noted that different Hubble classifications based on different weighting of arm morphology of disk resolution will lead to inconsistencies if the data sets are

indiscriminately mixed. On the other hand, we have not found any correlation of scaleheights of spirals with T, as Fig. 10 (click here) indicates.