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5 BD +13$^\circ$13 = SAO 91772 = LN Peg

5.1 Brief history

LN Peg was identified as a chromospherically active binary by Bergoffen et al. (1988), who discovered the strong CaII K emission and radial-velocity variations of this star. Latham et al. (1988) computed a single-lined circular orbit with a period of 1.844 days. However, Pasquini & Lindgren (1994) detected CaII K emission from both the primary and the secondary.

Rodonó et al. (1994) discovered the system's light variability and from their few observations found a period consistent with the orbital period. From photometry obtained during two observing seasons, Henry et al. (1995) identified four possible periods. They concluded that the one at 1.852 days represents the rotational period because it most closely agrees with the orbital period.

5.2 Orbital elements

The primary and secondary components of LN Peg seen in our spectra are called Aa and Ab, respectively, while the two stars together are called component A.

Two new sets of observations have been obtained for LN Peg. The Vienna group collected 39 spectra during a single, extensive 1996-1997 observing run at the NSO. From November 1993 through October 1998, FCF obtained 13 observations at KPNO. Also available for analysis are the velocities of Latham et al. (1988) and three velocities of Fleming et al. (1989), which are on the same velocity system.

Assuming the orbital period of Latham et al. (1988), a preliminary set of orbital elements was determined for the NSO velocities of the primary, component Aa, with BISP and refined with SB1. Agreement with the orbital elements of Latham et al. (1988) was excellent except for the center-of-mass velocity, which was 7 kms-1 more negative, suggesting that the system is triple. This possibility was confirmed when a combined solution of the NSO and KPNO data produced systematic velocity residuals.

An SB1 solution of all the velocities of Aa, but with zero weight given to the Latham et al. (1988), Fleming et al. (1989), and KPNO data, resulted in residuals that were analyzed to determine the period of the long-term velocity variations. Because of the spacing of the data, two possible periods emerged, 4.3 and 8.6 years. With BISP a set of preliminary long-period orbital elements was computed for each period. Then, with one velocity given zero weight, GLS was used to obtain a simultaneous solution of the short- and long-period orbits. Within their errors, the orbital elements of the short-period orbit are the same for both solutions. However, the long period orbits are rather different. For example, the 4.3-year period has $e= 0.054\pm 0.064$ while the 8.6-year period has $e = 0.49\pm 0.05$.Since the weighted sum of the residuals squared for the 8.6-year solution is 15% larger than for the 4.3-year solution, we have assumed that the 4.3-year solution is correct. However, we note that orbits with such long periods have no propensity toward zero eccentricity, so additional observations will be necessary for a definitive decision.

Absorption lines of the secondary, component Ab, are visible at red wavelengths. They are also rotationally broadened but are much weaker than those of Aa, making velocity measurements difficult. Thus, a GLS solution of the NSO and KPNO velocities of Ab was obtained with only the short-period semiamplitude varied. All other orbital elements were fixed at the values obtained for Aa. Six NSO velocities with residuals greater than 9 kms-1 were given zero weight.

The short- and long-period orbital elements are given in Table 5. The short-period eccentricity is quite small $0.054\pm 0.064$, but has been retained because in triple systems the third star may cause a non-zero eccentricity (Mazeh & Shaham 1979; Söderhjelm 1984) in the short-period orbit. For the tables and figures each measured velocity has been separated into a short- and long-period component, which consists of the short- or long-period calculated velocity plus one-half of the computed residual. Thus, the sum of those separated short- and long-period velocities for each date of observation results in the actually measured velocity. The short-period velocities and residuals to the computed fit are listed for both components in Tables A1 and A2 in the (electronic) Appendix, respectively, while those for the long period are in Tables A3 and A4, respectively. Included in those tables are the velocities of Latham et al. (1988) and Fleming et al. (1989). The computed short-period orbit compared with our velocities is shown in the upper panel of Fig. 3, while a similar comparison for the long-period velocities of the primary is in the lower panel of Fig. 3. For the short-period orbit a time of conjunction with the primary behind the secondary is HJD $2\, 446\, 348.080$.The standard error of an observation of unit weight is 1.0 kms-1.

 
\begin{figure}
\includegraphics [angle=-90,width=8.7cm]{lnpeg_sh.eps}

\includegraphics [angle=-90,width=8.7cm]{lnpeg_lo.eps}
\end{figure} Figure 3: Radial-velocity curves of LN Peg. The upper panel is for the short-period orbit (Aa-Ab), the lower panel for the long-period orbit of LN Peg A (only for Aa). Open symbols are NSO McMath-Pierce data, filled symbols are from KPNO, pluses from Latham et al. (1988), and crosses from Fleming et al. (1989)  
Our results for LN Peg demonstrate that new observations are valuable not only to confirm old orbital elements but also to detect additional components. This is particularly true when an initial orbital solution has been determined from observations obtained over only one or two observing seasons.


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