A&A 404, 365-372 (2003)
J. F. González 1,2 - E. Lapasset1
1 - Complejo Astronómico El Leoncito (CASLEO), San Juan, Argentina
2 - Observatorio Astronómico de Córdoba (OAC), Argentina
Received 21 February 2003 / Accepted 24 March 2003
We apply the two-dimensional cross-correlation technique TODCOR to derive spectroscopic orbits for the two B-type double-lined spectroscopic binaries HD 66066A and HD 315031, previously mentioned as blue straggler candidates of the open clusters NGC 2516 and NGC 6530, respectively. Reliable radial velocities for both components are measured even for orbital phases for which the separation between the spectral lines are about 0.5 times the quadratic sum of the full-width at half-maximum of the lines. Both binaries have circular orbits and the orbital periods are 1.67 and 1.38 days for HD 66066A and HD 315031, respectively. We calculate minimum masses with errors of 3-5% and obtain the projected radii from the line widths. We derive absolute stellar parameters which are consistent with the age and distance of the clusters. Both binary systems are formed by main-sequence stars and it is expected that they will experience mass-transfer between their components before the end of the core H-burning stage. HD 315031 is likely a triple system as suggested by the variation of the center-of-mass velocity.
Key words: techniques: radial velocities - binaries: spectroscopic - stars: individual: HD 66066A, HD 315031 - open clusters and associations: individual: NGC 2516, NGC 6530
Several close spectroscopic binaries have been discovered as a result of our spectroscopic program on bright main-sequence stars in open clusters (González & Lapasset 2000, 2001, 2002). In this paper we present the orbital analysis of two double-lined spectroscopic binaries (SB2), HD 66066A and HD 315031, belonging to the clusters NGC 2516 and NGC 6530, respectively. Both stars are blue straggler candidates included in Ahumada & Lapasset's (1995) catalogue, although according to recent photometric studies they may be considered as normal main-sequence stars.
HD 66066A ( 5822, [J2000.0]) is near the center of the open cluster NGC 2516. It was reported as a double-lined spectroscopic binary by González & Lapasset (2000). In the Color-Magnitude diagram it is located not far from the turnoff point but clearly below it, with a visual magnitude V=7.18 mag (Dachs & Kabus 1989). It is the brightest component of a visual pair with a 5 5 separation (h4031, Innes 1927). The combined light of this double star reaches 6.77 mag (Dachs & Kabus 1989), locating it close to the blue straggler region. The individual visual magnitudes tabulated in the Tycho Catalogue (ESA 1997) are 7.07 and 7.91 mag, resulting 6.66 mag for the whole system.
HD 315031 ( 0428, [J2000.0]) is a 8.3 mag star belonging to the open cluster NGC 6530. It was mentioned as binary by Walker (1957), according to unpublished spectroscopic observations by R. J. Trumpler. Hiltner et al. (1965) classified the spectrum of HD 315031 as B2 IV. No spectroscopic observations of this star have been reported since then. Van den Ancker et al. (1997) suggested the binarity of HD 315031 based on its abnormal position in the Color-Magnitude diagram and its high membership probability deduced from polarimetric observations.
In Sect. 2 we present our spectroscopic observations and describe the method of reduction and RV measurement. In Sect. 3 we calculate the orbital parameters while in Sect. 4 we derive absolute stellar parameters for the stellar components and discuss the physical and evolutionary status of the systems. Finally, the last section summarizes the main results.
We obtained 19 and 28 echelle spectra of HD 66066A and HD 315031 respectively, between 1996 and 2002 at the Complejo Astronómico El Leoncito (CASLEO), San Juan, Argentina. We used the 2.15 m telescope and the echelle spectrograph REOSC, with a spectral resolution of 13 300. Exposure times were typically 1.5 min for HD 66066A and 8 min for HD 315031, reaching a maximum signal-to-noise ratio between 40 and 100. The depths of metallic and He I lines for these stars are of the order of 4-10% of the continuum level, resulting an effective signal-to-noise ratio of about 3-8 for the useful spectral features. As example, Fig. 1a shows two typical rectified spectra of HD 66066A.
|Figure 1: Observed spectra and cross-correlation function (CCF) for the binary HD 66066A at orbital phases (left-hand panels) and (right-hand panels). a) Rectified unfiltered spectra. b) Countour plot of the 2-dim CCF. c) Sections of the 2-dim CCF passing through the maximum. These sections correspond to the right lines in b). d) Classic 1-dim CCF using a low-rotation template.|
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We estimated the spectral types to be B7 III + B7-8 for the binary HD 66066A, and B0.5 V + B1-2 V for HD 315031. Previous works classified the former as B8.5 III (Dachs 1972), B8.5 IV (Dachs & Kabus 1989), and B8 V (Garrison & Gray 1994), and the latter as B2 IVn (Hiltner et al. 1965). The full-width at half-maximum of the metallic lines are about 90 and 60 km s-1 for the primary and the secondary components of HD 66066A respectively, and 80 and 60 km s-1 in the case of HD 315031.
Table 1: RV of the binary HD 66066A: heliocentric Julian Date, orbital phase, RV, error and residual observed minus computed.
Table 2: Radial velocities of HD 315031.
The RV measurements were carried out by means of two-dimensional correlations using observed spectra of standard stars as templates. As described in González & Lapasset (2000), we obtained template spectra for each binary component by convolving high signal-to-noise spectra of low-rotating stars of appropriate spectral-type with computed rotational profiles. In a previous step, we derived the projected rotational velocity of the components by comparing binary spectra taken at quadrature phases with the standard spectrum convolved with various rotational profiles. For the templates of both components of the binary HD 66066A we used an observed spectrum of star HR 7287 (B8 III) broadened to km s-1 and km s-1for the primary and the secondary components, respectively. In the case of HD 315031, we employed star HR 6787 (B0 V) with a rotational profile of 52 km s-1 for the primary template and HR 6165 (B2 V) with 42 km s-1 for the secondary.
RVs for both components were measured using our own version of TODCOR. Following the algorithms of Zucker & Mazeh (1994), we computed the two-dimensional cross-correlation function (CCF) from the three one-dimensional correlations involving the object and the two templates spectra. Single cross-correlations were calculated by convolving filtered spectra. The radial velocities for the two components were computed by fitting a double parabola to the correlation maximum, and their errors were derived from the asymmetric-noise, the height of the correlation peak and its width. The error computations proposed by Tonry & Davis (1979) for single cross-correlations, were applied to the sections of the CCFs parallel to the axes. In this way for each spectrum we estimated the individual error of the RV of each component.
For these RV determinations we selected spectral regions with the most conspicuous metallic or He I lines. We used the spectral windows 445.8-453.3 nm and 490.0-508.0 nm for HD 66066A, which include several lines of Fe II, Ti II, Mg II, Si II, and He I. For HD 315031, we considered the range 452.0-473.2 nm, dominated mainly by He I, Si III, and O II lines. Firstly, we applied two-dimensional cross-correlations to well resolved spectra with the aim of obtaining the luminosity-ratio of the components. The mean value resulted for HD 66066A and for HD 315031. Then, we fixed this parameter and computed the RVs of the two components for all the spectra. Tables 1 and 2 list the measured RVs.
As example, Fig. 1 shows the CCF of HD 66066A corresponding to two different orbital phases. The left-hand panels correspond to a spectrum taken closer to the quadrature while the right-hand panels are near the conjunction phase. For comparison Fig. 1d shows the classic CCF of the object spectra with the B8 III template. For this correlation we used a lower rotational profile (20 km s-1) in order to improve the resolution of the two components. In spectra where the two set of spectral lines are well resolved (left panels) the difference between the velocities obtained using TODCOR (Figs. 1b and c) and by fitting two Gaussians to the classic CCF (Fig. 1d) are generally of the same order as the measurement errors. Nevertheless, in spectra with strongly blended lines (right-hand panels) the advantage of TODCOR is clear. This technique made possible to compute reliable velocities in spectra with components separated only by 0.47 times the quadratic sum of the full-width at half-maximum of the spectral lines. In such conditions, no results were obtained by the classic method, even when in this case a lower-rotation template was used.
|Figure 2: RV curves of HD 66066A. Circles and triangles represent the velocities of the primary and secondary, respectively. The continuous lines display the calculated radial velocities.|
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The last two columns of Tables 1 and 2 list the differences (O-C) between the observed and computed RVs. The RV residuals do not show any trend with the orbital phase but they clearly depend on the signal-to-noise ratio of the spectra. In the case of HD 66066A, for example, the rms of the residuals is 2.2 km s-1 in high signal-to-noise spectra (S/N > 70) and 5.8 km s-1 in spectra with higher noise level.
The eccentricity results indistinguishable from zero for both binaries,
as it is expected as consequence of tidal
friction for systems with periods as short as these.
In fact, according to Zahn's (1977) theory, the circularization time-scale for these
binaries is less than one million years. Consequently, we adopted a fixed value for the computations of the remaining orbital parameters. Moreover, it can be assumed
that both components rotate synchronously with the orbital motion, considering that
synchronization is reached before circularization. Under this hypothesis,
the relative radius of each component is proportional to the rotational
broadening of its spectral lines:
RVs of HD 315031 showed an unusual behavior (see Table 2). The measurements from different runs are not consistent with a sole value of . We interpreted this fact as due to the presence of a third object forming a wide pair with the spectroscopic binary. So, in order to analyze the orbit of the spectroscopic system, we computed one value of for each observing run by fitting a linear relation between RVA and RVB: , where q is the mass-ratio. Then we calculated the difference between the observed velocities and the parameter of the corresponding run (Cols. 7 and 8 in Table 2) and we used these data for the period searching. During the orbital analysis, the center-of-mass velocity of every observing run was considered a free parameter. Figure 3 shows the resulting RV curves.
Table 3: Orbital and spectroscopic parameters of HD 66066A.
Table 4: Orbital and spectroscopic parameters of HD 315031.
|Figure 4: Mass-Radius diagram for the possible configurations of the components of the binary HD 66066A (solar units). For orbital inclinations in the range six locations of the primary (squares) and the secondary (triangles) components are plotted. Error bars are shown for the points corresponding to . The continuous thin curves are theoretical isochrones of Girardi et al. (2000) for solar chemical composition and , 8.15 and 8.30. The heavy lines represent the zero-age and terminal-age main-sequences.|
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From the mass-radius relation of the two components we derived the corresponding ages, temperatures, and absolute magnitudes by interpolating in the grid of stellar models of Girardi et al. (2000). The comparison of these temperature values with the observed spectral-type constraints the possible values of the orbital inclination to a quite narrow range. In fact, only those configurations in the range , are compatible with temperatures between 11 200 and 13 600 K, which correspond to spectral-types B6.5-B8.5, according to the Schmidt-Kaler's (1982) calibration. Furthermore, the absolute visual magnitude interpolated in the Girardi's models for the solution corresponding to (Mv=-1.07 for the integrated light of the system) results in a distance modulus of 8.43 mag (8.23-8.87 mag for ) which is in agreement with the photometric cluster distance: V-Mv = 8.53 (Dachs & Kabus 1989); 8.35 (Meynet et al. 1993); 8.12 (Sung et al. 2002). Finally, in the Mass-Radius diagram both components lie close to the isochrone , in coincidence with the accepted cluster age: = 8.15 (Meynet et al. 1993); 8.2 (Sung et al. 2002).
All the mentioned observational data let us to adopt the solution corresponding to as the most probable for this system within a high confidence. The uncertainty of is just an estimation of the range of the possible values of the inclination. The resulting stellar parameters are shown in Table 5. This solution is consistent with the spectroscopic parameters, the temperatures derived from spectral types, and the cluster age and distance. In other words, all the available observational information on HD 66066A is consistent with a binary system composed of two normal main-sequence stars, whose evolutionary status corresponds to the age of the cluster.
Table 5: Absolute stellar parameters of HD 66066A corresponding to an orbital inclination of .
Finally, let us make some considerations about the possibility of mass-transfer between the components and with regard to the future evolution of the system. From the spectroscopic mass-ratio q, we computed the equivalent radius of the Roche lobe for the primary star: . Adopting 11.64 for the separation between the components, we find a critical volume radius of 4.58 . If the primary exceeded this size, then mass-transfer would take place towards the secondary component through the Lagrangean point L1. The pointed line in Fig. 4 gives the critical radius as function of the primary mass, computed assuming that the total mass and angular momentum are conserved. This curve is well below the terminal-age main-sequence and very close to the present radius of the primary star. Consequently, the overflow of the Roche lobe would be imminent, giving place to a case-A mass-transfer (the mass-transfer occurs during the core H-burning stage). It is not easy to assert if there is any mass-flux at present, however, being the mass-radius relation for the components compatible with normal main-sequence stars, it is probable that no significant amount of mass has been transferred yet. In any case, we can speculate that the secondary component, after accreting mass, will become a blue straggler of the cluster NGC 2516.
|Figure 5: Mass-Radius diagram for the possible configurations of thecomponents of the binary HD 315031. For orbital inclinations in the range - five locations of the primary (squares) andthe secondary (triangles) components are plotted. Error bars are shown for the points corresponding to . The continuous thin curves are theoretical isochrones of Bertelli et al. (1994) for solar chemical composition and and 7.0. The heavy lines represent the zero-age and terminal-age main-sequences.|
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In Fig. 5 possible values of masses and radii of the components are shown. The solid line shows isochrones of Bertelli et al. (1994) for and 7.0. The configuration corresponding to an inclination is in agreement with the spectral-types and the isochrone of the cluster. The temperature of the components, interpolated from the theoretical models, are TA = 27 000 K and TB = 23 400 K, corresponding approximately to B0-1 V and B1-2 V in the Schmidt-Kaler's (1982) calibration. Adopting this value for the orbital inclination with an error of 0 5, we computed the stellar parameters of Table 6. The total absolute magnitude of the system results Mv = -3.0. This value differs in 1 mag from the absolute magnitude derived from the cluster distance. In fact, using the photometric data of Sung et al. (2000) we obtain Mv = -4.04 for HD 315031.
Table 6: Absolute stellar parameters of HD 315031 corresponding to an orbital inclination of .
The volume radius of the Roche lobe is 5.9 . We estimate that before the system reach the age , the primary star will have filled its critical lobe, giving rise to mass-transfer. This is about one half of the main-sequence life-time for a single star of that mass. Consequently, also this binary will suffer case-A mass-transfer and, in the same way as HD 66066A, it might be considered a blue straggler predecessor.
Finally, we make some considerations with regard to the third component.
With the aim of inferring some physical information, we analyzed the temporal variation of
the center-of-mass velocity of the spectroscopic binary.
We subtracted the computed orbit of the spectroscopic binary from the observed RVs and thus
we obtained the center of mass velocity for every spectrum. Then we computed a periodogram with
these data founding that several periods are compatible with the observations
All of them produce residuals smaller than 6 km s-1 and 10 km s-1
for the RV of the primary and the secondary lines, respectively.
gives the smaller residuals,
about 3 km s-1 and 6 km s-1, respectively.
Even if the period is not unambiguously defined with the present observations, the RV variations are
large enough to ensure that the third body is quite massive. For several probable periods we
calculated Keplerian orbits and derived the minimum-mass for the third component using the
Both binary systems are close enough to experience mass-transfer before the primary components leave the main-sequence stage. Consequently, the secondary components will increase their masses and will became blue stragglers of their clusters, as the luminosity of the cluster turnoffs diminishes due to stellar evolution. The frequency of this kind of binary stars in clusters is an important clue for evaluating the mass-transfer hypothesis as the origin of blue stragglers. Finally, we mention that both systems are triple. HD 66066A has a visual companion that could be dynamically bounded (Dachs & Kabus 1989). On the other hand, HD 315031 showed variations of the center-of-mass RVs that can be attributed to a third body forming a wide pair with the spectroscopic binary. The high amplitude of these variations suggests a mass of 6-25 for the third component. Additional data will be collected during next observing runs in order to improve the orbital parameters of the wide system.
This work was partly supported by CONICET, ANPCYT, Secyt (UNC), and Agencia Córdoba Ciencia of Argentina.
The authors acknowledge use of the CCD and data acquisition system supported under U.S. National Science Foundation grant AST-90-15827 to R. M. Rich.
One of the spectra of HD 315031 was kindly taken by Pablo Mauas.