3 Distances

We inferred the distances to Cepheids using the light-curve parameters derived as described above and the following procedure suggested by Berdnikov et al. (1996b):

(1) We use the period-colour relation by Dean et al. (1977) to determine the intrinsic colour, (<B> - <V>)₀, and the colour excess:

E_B-V = (<B> - <V>) - (<B> - <V>)₀.

In the absence of accurate <B> magnitude we first determine the intrinsic colour $(<V>-<m_{\lambda}>)_0$ = $<M_V>-<M_{\lambda}>$ (log P) using PL relations <M_V>(log P) and $<M_{\lambda}>$(log P) from Berdnikov et al. (1996b). We then calculate the corresponding colour excess $E_{V-m_{\lambda}}$ and convert it into E_B-V using interstellar extinction law parameters from Berdnikov et al. (1996a,b).

(2) If the mean magnitude, <K>, is not available directly from observations, it is derived from formula (5) or an appropriate formula from Table 7 in Berdnikov et al. (1996b) based on known <V> and $<m_{\lambda}>$. Here $m_{\lambda}$can be any of the B, R, I, $R_{\rm C}$, or $I_{\rm C}$ filters. The galactocentric distance of the star, which is required to allow for the abundance gradient in the disk, is calculated from the preliminary heliocentric distance inferred from <B>, <V>, and log P. To this end, we use PL relation of Berdnikov & Efremov (1985) and adopt R₀ = 7.1 kpc, where R₀ is the distance of the Sun from the Galactic centre. Note that we derived the formulas used to infer <K> from, say, <B>, <V>, log P, and $R_{\rm g}$ - R₀ without adopting any specific value for the abundance gradient in the galactic disk. Each of these formulas simply establishes a relation between two observed colours (e.g., <V> - <K> and <B> - <V>), the period, P, and the difference of galactocentric distances of the star ($R_{\rm g}$) and the Sun (R₀). The coefficients at $R_{\rm g} - R_0$, if combined with some relation connecting abundance differences into colours, can be used to estimate the abundance gradient.

(3) <K> is then corrected for interstellar extinction:

$$<K>_0\,\,=\,\,<K> - 0.274 \cdot E_{B-V}.$$

(4) The absolute magnitude of a star is then determined from the following formula:

$$<M_K>\,\,=\,\,-5.462 - 3.517 \cdot ({\rm log} P -1).$$

(5) The true distance modulus is then calculated as:

$$DM_0\,\,=\,\,<K>_0 - <M_K>.$$

(6) And, finally, the distance $r_{{\rm hel}}$ (in kpc) is given by:

$$r = 10^{0.2 \cdot (DM_0 - 10)}.$$

The distances thus derived are on a short distance scale consistent with an LMC distance modulus of 18.25 (Berdnikov et al. 1996b).

3.1 The catalogue

The resulting light-curve parameters and distances of 455 Galactic classical Cepheids are summarised in the table. The first column of the table gives the name of the Cepheid; the second column, its variability type according to GCVS (Kholopov et al. 1985-1987). The third column gives the fundamental period P₀, which is equal to the observed variability period for most of the Cepheids (DCEP or CEP type in GCVS). We assumed that small-amplitude Cepheids (DCEPS type in GCVS) are first-overtone pulsators and therefore calculated their fundamental periods by dividing the GCVS value by a factor of 0.716 - 0.027 $\cdot$ log P as found by Alcock et al. (1995) and slightly modified by Feast & Catchpole (1997). Note that we give P₀ only up to the second digit after the decimal point to save the space because this precision is sufficient for distance determination. More accurate period values can be found in the GCVS or in our data bank on the INTERNET at:

ftp.sai.msu.su/pub/groups/cluster/cepheids/

The fourth column gives the heliocentric distance, $r_{{\rm hel}}$. The fifth column indicates how the intensity-mean <K> magnitude was derived. k means that it is known directly from observations; bv, rc, ic, and i, that it wass inferred from observed <B> and <V>, V and $R_{\rm C}$, V and $I_{\rm C}$, V and I, respectively. The subsequent columns give light-curve parameters - amplitude, Amp, magnitude at maximum light, MAX, and intensity-mean magnitude, <m>, for each of the filters B, V, R, I of the Johnson system and filters $R_{\rm C}$ and $I_{\rm C}$of the Cron-Cousins system.