3. Secondary comparison stars (C₂)

The C₂ of differential photometry is observed to confirm the constant brightness of C₁, and to determine the brightness of C₁. Even for a C₂ of unknown brightness, the differential magnitudes ${\Delta}m_{C_1-C_2}$ can confirm the short-term constant brightness of  C₁. But this does not test the long-term constant brightness of C₁. For example, a low inclination late-type spotted C₁ with long-term variability might not exhibit short-term variability. If the brightness of C₂ is known, the C₁ brightness is obtained, and the long-term constancy of C₁ can eventually be verified with respect to the other available data. It is crucial for the long-term differential photometry of any variable star (O) that the constant brightness of the chosen C₁ and C₂ combination is confirmed with high accuracy. Such a combination should be consistently used in all subsequent differential photometry of O. To achieve this goal, we compiled numerous references of the UBVRI magnitudes (and errors) for all C₁ and C₂ of V 1794 Cyg (Tables 1 and 2). Furthermore, Table 2 contains new data for the two most frequently used C₁ (SAO 50313 and SAO 50205). We will show that the best combination for V 1794 Cyg would be C₂=57 Cyg with C₁=SAO 50313 or SAO 50205.

Earlier C₁ and C₂ combinations for V 1794 Cyg appear arbitrary (see Table 3). The position of V 1794 Cyg  in the vicinity of the North America Nebula (NGC 7000) and the Pelican Nebula (IC 5070) offers numerous C₁ and C₂ alternatives. Four secondary (16 Cyg B, 57 Cyg, SAO 50257, SAO 50326) and three primary comparison stars (SAO 50313, SAO 50205, SAO 50260) have been used. Furthermore, the primary comparison star SAO 50313 was once used as C₂ (SET=38). The C₂ of each SET is specified in Table 3 (Col. 5), where "Absolute'' denotes absolute photometry. No C₂ was observed or specified during some subsets.

Figure 1: aceg) The UBVR magnitudes of SAO 50313 during individual subsets (Table 2: $\pm 1 \sigma$ errors). The weighted mean and error are outlined with the continuous and the dashed line, respectively. bdf) Other measurements with respect to the reference number (i.e. no epoch)

Figure 2: The UBVRI magnitudes of SAO 50205, otherwise as in Fig. 1

1. Secondary comparison star 16 Cyg B

16 Cyg B (HD 186427, SAO 31899) was used as a C₂ only once (SET=28). The long-term UBV are constant (Table 1), but the RI show some scatter. The Cousins RI by Rakos & Franz (1988) transformed to the standard Johnson system (Bessell 1979) agree with Moffett & Barnes (1979). Thus the RI by Johnson et al. (1966) induce the large errors of the long-term mean RI (Table 1). 16 Cyg B is a close "solar analog''-candidate (Neckel 1986: G3V, $T_{\mathrm{eff}} \! = \! 5735 {\mathrm{K}}$, $B-V = 0\hbox{$.\!\!^{\rm m}$ }66$, $U-B = 0\hbox{$.\!\!^{\rm m}$ }20$). Since the upper limit of the solar luminosity variations is $\pm 0\hbox{$.\!\!^{\rm m}$ }001$ (Willson & Hudson 1991), detection of photometric variability in this "solar analog''-candidate would be surprising. 16 Cyg B has been the standard star in many photometric studies (e.g. Moffett & Barnes 1979; Skiff 1993). The angular separation of $\Delta_{\mathrm{sep}}\!=\!13\hbox{$.\!\!^\circ$ }6$ between 16 Cyg B and V 1794 Cyg requires a large extinction correction, and thus it is an inconvenient C₂ for differential photometry.

2. Secondary comparison star 57 Cyg

57 Cyg (HD 199081, SAO 50180, $\Delta_{\mathrm{sep}}=0\hbox{$.\!\!^\circ$ }2$) has been the most frequently used C₂ for V 1794 Cyg. The UBV measurements indicate constant long-term brightness. But the RI have been measured only once (Johnson et al. 1966). 57 Cyg is an early-type B5V spectroscopic binary with $P_{\mathrm{orb}}=2\hbox{$.\!\!^{\rm d}$ }854825$, but not an eclipsing binary (Hilditch 1973; Batten et al. 1978; Giuricin et al. 1984). Since the masses are nearly equal ( $M_1 \! / \! M_2 \! \! = \! \! 1.125$), and the orbital inclination is $i \! \simeq \! 48^{\circ}$, the upper limit for B changes is $\sim 0\hbox{$.\!\!^{\rm m}$ }02$ (Hilditch 1973). The differential UBVmagnitudes ${\Delta}m_{C_1-C_2}$ of our APT photometry revealed no periodicity with P_orb, nor any significant periodicity between $0\hbox{$.\!\!^{\rm d}$ }4$ and 50^d. Finally, we confirmed the P_orb for the v_raddata in Hilditch (1973). That 57 Cyg was successfully used as C₂ by Percy & Welch (1983) in studying the low amplitude photometric variability in early-type supergiants also supports short-term constant brightness. Our APT differential UBV photometry of SAO 50313 and SAO 50205 with respect to this C₂confirmed constant short-term brightness. Because the UBV magnitudes are accurate and the RI magnitudes are available, we conclude that 57 Cyg is currently the best C₂ choice for V 1794 Cyg. Furthermore, 57 Cyg is the only early-type C₂ in Table 1, all others being late-type stars with convective outer envelopes possibly sustaining starspots.

3. Secondary comparison star SAO 50257

SAO 50257 (HD 199512, $\Delta_{\mathrm{sep}}\!=\!1\hbox{$.\!\!^\circ$ }7$) is a K1-2 giant or subgiant (Yoss 1961; Straizys et al. 1989). There are only two V measurements (Table 1). The single B measurement is inaccurate (Turon et al. 1992), but agrees with $B\!\sim\!m_{\mathrm{pg}}\!= \!7\hbox{$.\!\!^{\rm m}$ }6$ (Fehrenbach et al. 1987). The short-term differential magnitudes SAO 50313 minus SAO 50257 were constant (Bopp et al. 1983; Kaluzny 1984). But SAO 50257 is an unsuitable C₂, because its long-term constant brightness is uncertain, and the URI magnitudes unknown.

4. Secondary comparison star SAO 50326

The spectral-type of SAO 50326 (HD 200060, $\Delta_{\mathrm{sep}}\!=\!1\hbox{$.\!\!^\circ$ }1$) is K2III (McClure 1970; Schmitt 1971; Straizys et al. 1989). The few UBV measurements reveal no long-term variability (Table 1). Heckert & Stewart (1992) detected no short-term variability in the differential UBV(RI)_C magnitudes SAO 50313 minus SAO 50326. But this C₂ is unsuitable, because its RI magnitudes are unknown.