4 Statistical property

4.1 Dependence on color

Figures 1 and 2 present the correlations between the flatness (H/D₀) and thickness (H) and galaxy color ($(B-V)_{\rm T}^{0}$). The integrated colors of disk galaxies are predominantly influenced by their star formation history (Searle et al. 1973), and the strong correlations observed between color and flatness or thickness point to a coupling between the flatness or thickness and the integrated star formation history of galaxies.

Figure 3 plots flatness as a function of the corrected U-B color ($(U-B)_{\rm T}^{0}$), which are taken from RC3, the total U-B color index corrected for differential galactic and internal extinction (to "face-on'') and for redshift. The dependence of thickness on $(U-B)_{\rm T}^{0}$ is illustrated in Fig. 4.

  

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

  

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

  

Figure 3: Flatness of spiral galaxy plotted versus the corrected U-B color

  

Figure 4: Thickness of spiral galaxy plotted versus the corrected U-B color

  

Figure 5: Flatness of spiral galaxy plotted versus the Hubble sequence

  

Figure 6: Thickness of spiral galaxy plotted versus the the Hubble sequence

4.2 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 is interesting to see the dependence of flatness on the Hubble type, which is shown in Fig. 5. The flatness of a spiral galaxy decreases smoothly an average along the Hubble sequence, but the dispersion in flatness among galaxies of the same Hubble type is very large. Figure 6 shows the correlation between thickness and the Hubble sequence.

4.3 Correlation between $\rm {H}_{\alpha}+[\rm {NII}]$ equivalent width and thickness

Kennicutt & Kent (1983) presented the combined results of photometric and spectrophotometric surveys of H$_{\alpha}$ emission for 200 field and Virgo cluster galaxies. Romanishin (1990) published large aperture photometric measurement of $\rm {H}_{\alpha}+[\rm {NII}]$ emission line strengths of 110 spiral galaxies. We have measured the thicknesses of some spirals observed by them. The results are listed in Table 3. We use the formula (Romanishin 1990):

EW (Romanishin's$)=1.22\times{\rm EW}$(KK's)

  

Table 3: $\rm {H}_{\alpha}+[\rm {NII}]$ equivalent width and thickness

Figure 7 shows the correlation of $\rm {H}_{\alpha}+[\rm {NII}]$equivalent width with the thickness. There might be a negative correlation between star formation activity and thickness of a galaxy, but the scatter is large and there are only 20 samples. The thicknesses of NGC 628 and NGC 5194 are from Peng's paper (Peng 1988).

  

Figure 7: $\rm {H}_{\alpha}+[\rm {NII}]$ emission line plotted versus the thickness

  

Figure 8: Thickness of spiral galaxy plotted versus the Neutral hydrogen masses

Figure 8 plots the relation between thickness and neutral hydrogen masses. The neutral hydrogen mass is derived by de Vaucouleurs et al. (1991, RC3),

$$\log({M_{\rm HI}/M_{\odot}})=5.696+(16.6-{m_{21}^{\circ}})/2.5+2.0\times\log{d}$$ (5)

where ${m_{21}^{\circ}}$, from RC3, is the 21-cm emission line magnitude and corrected for self-absorption and d, in Mpc, is the distance of a galaxy.

Figure 8 suggests that a thicker galaxy contains more neutral hydrogen, although the dispersion is large.

Acknowledgements

We would like to thank Prof. Jiehao Huang for his help in finishing this paper. We also thank Prof. Jingyao Hu for his hospitality and discussion at the Xinglong Observational Station of Beijing Observatory, and are grateful to Rui Chen, Zhaohui Ji and Zhaohui Shang for their help. We wish to thank Prof. Zongyun Li for a valuable discussion. This work is supported by the National Nature Science Foundation, the National Grand Project "Climbing Up" of China and the Doctoral Program Foundation of State Education Commission of China.