2 Main steps of the method, and choice of the sample

The main steps are:

(1). Find the position of the innermost point of a spiral arm and measuring its coordinate ($\rho_{0}, \theta_{0}$) relative to the image center and to the major axis.

(2). Vary the value of the inclination $\gamma$ around $\arccos(d_{25}/D_{25}$) and fit the spiral arm starting from that innermost point with a logarithmic spiral curve to get its winding parameter $\Lambda$such that $\mu=\arctan(m/\Lambda)$, where m is the number of arms, with a least square method. D₂₅ and d₂₅ are taken from the Third Catalog of Bright Galaxies by de Vaucouleurs et al. (1991, RC3). They are the apparent major and minor isophotal diameters measured at or reduced to the surface brightness level $\mu_{B}=25.0$ blue mag per square arc second.

(3). Determine the inclination and the corresponding winding parameter by comparing the fitted spiral curve with the image.

(4). Calculate the thickness of the galactic disk h, by

$$h=\frac{2r_{0}}{\sqrt{m^{2}+\Lambda^{2}}},$$ (1)

$$r_{0}=\frac{\rho_{0}\sqrt{\sin^{2}\theta_{0}+\cos^{2}\theta_{0}\cos^{2}\gamma}}{\cos\gamma},$$ (2)

where m is the number of the arms (see Peng 1988).

(5). The thickness of the galactic disk, H in kpc, is

H=hd,

where d is the distance of the galaxy

$$d=\frac{v_{\rm opt}}{H_{0}},$$ (4)

where H₀ is the Hubble constant taken as 75 km/s/Mpc, and $v_{\rm opt}$,the mean heliocentric radial velocity in km/s derived from optical observations, is taken from the RC3.

Our statistical sample contains 71 galaxies, selected from more than 600 northern spirals having a determined $(B-V)_{\rm T}^{0}$ (i.e., the total color index corrected for galactic and internal extinction and redshift) in RC3 according to one single criterion: their images have distinguishable spiral arms. The mean Hubble type indexes (T) of these galaxies are from 2 to 6, and they have $\log(D_{25}/d_{25}$) less than 0.76.

Our data reduction and analyses were done with IRAF installed in the Sun Workstation at the Laboratory of Astronomical Data Analysis of Nanjing University.