2 Method of the analysis

When searching for changes in the $\gamma$-velocity caused by the orbital motion of the Cepheid around the common mass centre of the binary system, extreme care has to be taken not to mix spurious effects with the intrinsic radial velocity variation.

At first, the pulsational radial velocity curve has to be determined which necessitates knowledge of the pulsation period as accurately as possible. Use of inaccurate pulsation period causes a phase mismatch in the radial velocity curve which can give rise to increased scatter in the radial velocity curve. This, however, must not be interpreted as an orbital effect even though it appears as a vertical shift in the annual $\gamma$-velocity. Another negative consequence of the use of improper pulsation period is that it can smear any low amplitude orbital effect. The case of SV Vul clearly shows that even minor orbital $\gamma$-velocity variation can be detected if allowance is made for the continuously changing pulsation period (Szabados 1996).

If properly phased normal curves representing two different epochs are compared, only vertical shift can occur between the two curves, and this refers to the change in the mean radial velocity, i.e. to the orbital motion. This is, however, an idealistic case. In reality, the value of the radial velocity determined from the spectrum depends on both the circumstances in the stellar atmosphere having various impacts on the line profile (asymmetry, broadening, occasional emission - see e.g. Albrow & Cottrell 1996; Butler 1993; Sabbey et al. 1995), and the method of determination of the radial velocity (Vinkó et al. 1998). Coupled with the problem of uncertainty in the early radial velocities (such as Joy's 1937, pioneering work), a reasonable lower limit of $\gamma$-velocity variation that can be attributed to the membership of the Cepheid in a binary system is four km s^-1 (Szabados 1996). Based on a homogeneous and precise dataset, this lower limit can be decreased considerably, see e.g. the case of SV Vul (Szabados 1996) again, and the remark on VW Pup, later on in this paper.

In order to determine the correct value of the pulsation period, the O-C-method was applied using the photometric data which are usually more accurate and available more frequently than radial velocity observations. The O-C-diagrams have been constructed for seven Cepheids in this sample (the only exception is V495 Mon). The commonly used method of O-C-diagram need not be introduced here, as to its details, the reader is referred to Willson (1986) (general information) and Szabados (1977) (application to Cepheids).

As to the other Cepheids for which the comparison of the recent radial velocity data with the first epoch values did not indicate noticeable change in the $\gamma$-velocity, the behaviour of the pulsation period was not studied during this project.

In all seven cases for which new pulsation period was determined, the new value only slightly differs from the catalogued period. The linear elements determined by the weighted least squares fit to the moments of the photometric normal maxima are indicated in the next section. Since no period change has been detected, nor assumed for the Cepheids under study, the O-C graphs are not published here. Nevertheless, the normal maxima and the O-C-residuals utilized for the determination of the precise value of the pulsation period are given in tabular form (see Tables 2-8). These data, along with the bibliographic references may be useful for later studies and revisions of the pulsation period, keeping in mind that classical Cepheids undergo period changes of various origin (evolutionary, duplicity related, and erratic - see Szabados 1994).

The subsequent columns in the tables summarising the O-C-residuals contain the following data:
1. Moment of normal maximum; 2. Epoch as counted from the final ephemeris given among the remarks on individual variables in Sect. 3; 3. O-C-residual also calculated from the same ephemeris; 4. Weight assigned to the given photometric series when performing the least squares fit for the period determination; 5. Type of the photometric data (vis: visual; pg: photographic; pe: photoelectric); 6. Reference to the observational data.

In most cases, photographic and visual have been taken into account in order to incorporate those epochs when the first radial velocity series (Joy 1937) was obtained.

  

Table 1: List of the newly discovered SB-Cepheids

The list of the newly discovered SB-Cepheids is given in Table 1 which also contains the logarithm of the pulsation period (the precise value can be found as a remark at the respective Cepheid), the mean V-brightness and the difference between the mean values of the radial velocity determined from Joy's (1937) and the recent data (absolute value in km s^-1). This latter difference gives a qualitative estimate for the orbital effect and it is by no means the amplitude of the orbital radial velocity variation. Because of the limited number of Joy's data, the arithmetic average of the radial velocities is not strictly equal to the $\gamma$-velocity but it serves as an approximation (see Pont et al. 1994b on the goodness of $\gamma$-velocity determinations from a few data points). For V495 Mon the available data are far too small to estimate the orbital effect but in view of the homogeneity of the data-set the variation in the $\gamma$-velocity is probably real.

The Cepheids involved in this sample can be commonly characterised as neglected from an observational point of view but fortunately the distribution of the available data allows the precise determination of the pulsation period. The much less numerous radial velocity data are only sufficient for revealing the variability in the $\gamma$-velocity, the orbital elements can be determined if more radial velocity data are available.