DOUBLE-LINED SPECTROSCOPIC BINARY STARS IN THE RAVE SURVEY

The goal of the classification pipeline is to separate different types of spectra and to discover spectra with systematic or other observational errors. It is required that the value of the S/N is greater than 13. That limit was set in Z08 where it was shown that the estimation of atmospheric parameters for spectra at lower S/N becomes unreliable and only the major spectral lines are still distinguishable. It seems reasonable to assume that classification would also become unreliable below that limit.

Next, the minimal and maximal flux values are verified. If the minimal value (of any single pixel) is negative, the spectrum is rejected since it has clearly undergone some problems in background subtraction. On the other hand, the limits on maximal values are more problematic because rejecting spectra with emission lines is not our goal. Taking that into account, we set the upper limit to 1.5 by inspecting the normalized flux distribution of a large number of spectra. It showed that less than 1% of the spectra have their maximum flux above that value, mostly as a result of an artifact. Such spectra are not immediately excluded but are flagged as potential cosmic-ray hit candidates. Emission-line objects (see Figure 1(h)) are identified later.

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In the next step, several properties of the CCF between the observed spectrum and the synthetic template are calculated and evaluated. The template spectrum is interpolated based on the library of synthetic spectra by Munari et al. (2005). We always construct the CCF using the same template. In our experience, this allows for an easier classification of unusual spectra (e.g., coronal emission, binaries, etc.) because in those cases the resulting CCF is not influenced by the erroneous formally best-matching normal star template, calculated by the parameter estimation pipeline. For the template, we use the average case of a dwarf with T_eff = 5800 K, log(g) = 4.4, and M/H = 0.0 (i.e., close to solar values). The calculation of the CCF is done with the same template for all observed spectra. This means that the peaks of CCFs of hotter stars, for example, will be weaker but it is of no concern since we are only interested in the particular shape of the CCF and not in its strength. For the same reason, the exact values of the selected atmospheric parameters of the template spectrum are not important and the properties of the CCF do not depend strongly on the values of those parameters. The observed spectrum is then re-binned to the template's wavelength range for an easier calculation. Z08 also showed that the projected rotational velocity (vsin i) is not recoverable for a slowly rotating star, while the amount of α-enhancement ([α/Fe]) is unreliable and cannot be trusted for individual objects. Therefore, both parameters are set to zero. Another reason why a more careful selection of rotational velocity is not important is the fact that the width of the core of the CCF is much wider than the error of the typical rotational velocity estimate.

The wings of the CCF contain information about the oscillations of the spectral continuum. By comparing the asymptotic values of the wings, it is possible to eliminate all spectra that have uneven continuum and are unsuitable for modeling. Figure 1(b) shows a relatively high S/N spectrum with a strongly oscillating continuum. While the left wing converges to zero as it does in the case of a well-behaved single star spectrum, the right one does not. The difference of the two levels is a useful method for the detection of badly normalized spectra.

Distinguishing between different types of stellar objects (e.g., binary stars, emission stars, fast rotators) is harder than detecting spectra plagued by observational and systematic errors. Spectral features in the former might look similar in some cases (split major lines in spectra of stars with chromospheric emission and double-lined binary spectra, for example). Counting the number of peaks of the CCFs is extremely efficient in the detection of potential SB2 binaries (Figure 1(c)). If the CCF has more than one central peak, the spectrum is clearly double-lined and probably comes from an SB2. In the case of blended SB2-like spectra, the CCF does not show two distinct peaks but is still asymmetric (Figure 1(d)). Unfortunately, CCFs of spectra of stars with chromospheric emission (Figure 1(f)) look similar to the previous case. Discriminating between those two classes is possible by measuring the width of the CCF and the level of asymmetry. The width of the CCF for a spectrum showing chromospheric emission cores is equal to that of the underlying star without the emission-line cores. The level of asymmetry is calculated by comparing the area under the left and right half of the CCF. It turns out that CCFs of blended binary candidates are wider and more asymmetric than those of stars with emission-line cores. The border values were set by inspecting a visually classified sample of both types. Stars with emission-line cores usually have stronger narrow metallic lines that help to distinguish between both types. In cases where spectral lines of an SB2 candidate are too blended, the detection of binarity is impossible. Further details on this topic are described in the following section.

Wide and shallow spectral lines are a signature of hot stars, where the otherwise dominant Ca ii triplet is weak or absent and lines from the hydrogen Paschen series dominate. The CCF between such a spectrum and a template spectrum of a colder dwarf is wide and with low amplitude (Figure 1(g)). Since lines get wider and shallower with increasing temperature, it becomes increasingly difficult to recognize SB2 binary candidates among early A-type and hotter stars, even if they are observed at quadratures and close to edge-on inclinations. Fortunately, the fraction of hot stars among the high galactic latitude field RAVE stars is almost negligible. Relatively low amplitude and very wide CCFs are also observed in spectra of contact binaries. Most of the lines in such spectra display very little contrast with the underlying continuum: in addition to their intrinsic shallowness they are further widened by rapid rotation (Figure 1(e)). They too can be recognized by inspecting the asymmetry of the CCF. Fast rotating stars are another type of object that shows similar CCFs. According to Glebocki & Stawikowski (2000), the average projected rotational velocity becomes significant (greater than 30 km s^-1 on average) for stars earlier than type F5, setting a limit at T_eff = 6600 K. If some wide-lined spectrum that does not have a clear two-peaked CCF has a temperature above this limit, it is considered to be a fast rotator rather than a blended binary.

Peculiar types of stars are harder to classify since spectral features of such objects span a wide range of appearances. CCFs of special cases (Figures 1(h)–(j)) all look different from normal single star spectra. All such peculiar objects were flagged and later eye-checked to avoid any misclassification. A detailed description of the classification procedure along with the computer code is available upon request from the authors.

It is desired that the synthetic sample mimics the observed one as closely as possible. We expect that metallicity ([M/H]) and barycentric radial velocity are both distributed the same way for binary stars as they are for single stars, with the latter values measured by Z08. The similarity between the metallicity distribution among single and binary stars is discussed by Latham (2003). Additionally, we expect that both components should have roughly the same chemical composition and are both of the same age.

Although in the RAVE survey the number of dwarfs and giants is roughly similar, we assumed that only main-sequence binary stars are likely to be double-lined. For binaries of intermediate masses, it is highly unlikely to find one consisting of two giant components. There are two reasons for this: (1) to reach the giant stage at the same time, two stars must be almost equally massive (to within 1%) and (2) the lifespan of a giant is much shorter than the lifespan of a dwarf. Combining both criteria makes the probability of finding a giant–giant SB2 very small. Additionally, the morphology of a spectrum of a giant star is similar to a spectrum of a dwarf star with similar effective temperature. So even if we would be dealing with an SB2 spectrum of two giants, the classification method should not have any trouble recognizing that.

As a starting point for constructing a synthetic binary spectrum we took a distribution of temperature, metallicity, and radial velocity for single star dwarfs where we only included spectra with S/N >20 and log(g)>3.5 from the observed sample of 222,563 stars (from the internal release not yet publicly available) that had been previously confirmed as normal single stars by the classification method. After drawing random picks for the first star's temperature T_eff,1 and [M/H] from those distributions both values were randomly varied for typical errors of both measurements, σ_T = 300 K and σ_[M/H] = 0.2. This was done in order to make both distributions smoother. Using the two values, we found a complete set of parameters (mass, radius, and I magnitude) for the first star from a Yonsai–Yale isochrone (Yi et al. 2001) of appropriate iron abundance and an age of 200 Myr. This particular age was chosen so that all stars are already settled on the main sequence and the hotter ones still did not have time to turn to giants, setting the corresponding upper mass cutoff at approximately 3 solar masses. The age dependence of the stellar parameters for the stars on the main sequence can be neglected and the selection of the age of the isochrone is not very important. Similarly, we also neglected the minor effect of α-enhancement and its value was kept fixed at zero during the calculation of all spectra. This provides us with all the necessary parameters for the construction of the synthetic spectrum of the first component. Now we randomly select a luminosity ratio η, which is defined as

$$\begin{equation} \eta =10^{\frac{2}{5}(I_1-I_2)}, \end{equation} \tag{ 2 }$$

where I₁ and I₂ are the brighter star's and the fainter star's I magnitudes, respectively. This ratio is selected from an interval of [0, 1]. From there on it is straightforward to find the position on the same isochrone with a matching I magnitude of the second component. Distributions of stellar masses, radii, mass ratios, and luminosity ratios in the final sample are shown in Figure 2.

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The orbital period was chosen randomly from a distribution fitted to observations in Duquennoy & Mayor (1991),

$$\begin{equation} f(\log P)=\frac{dN}{d\log P}=C \exp \left\lbrace \frac{-(\log P- \overline{\log P})^2}{2\sigma ^2_{\log P}}\right\rbrace, \end{equation} \tag{ 3 }$$

where $\overline{\log P}=4.8$ and σ_log P = 2.3 and P is in days. A similar distribution was also found in numerical simulations of star cluster evolution by Bate (2009). A limit on the short period was selected at 0.2 day, because the period distribution for eclipsing binary stars in Malkov et al. (2006) shows a strong cutoff there. On the longer end, we took a generous limit of two years. At such long orbital periods, the orbital velocities become so small that the fraction of detectable binaries becomes negligible. For a binary system of two solar twins on a circular orbit, the maximal velocity amplitude is equal to 30 km s^-1 for a period of two years. Knowing the orbital period, the semimajor axis and orbital velocities were calculated using Kepler's third law. We assumed that all systems have circular orbits. This only holds true for very short period systems (P < 10 days). The eccentricity of systems with P < 500 days can be significant with a mean of about 0.3, according to Duquennoy & Mayor (1991). Nevertheless, the differences of orbital velocities of such systems compared to the velocities of similar systems with circular orbits are small in most cases, justifying the upper assumption. The orbital phase and orbital inclination to the line of sight were selected randomly.

The rotational velocities of both stars were calculated by assuming that the stars co-rotate with the system's orbital rotation. The minimal rotational velocity was set at 20 km s^-1, similar to the value typically obtained by RAVE's parameter estimation pipeline for slowly rotating single stars. While this value is unrealistically high, it simulates the marginally lower resolving power of the observed spectra compared to the synthetic ones, where the difference is easily compensated for by slightly wider lines of faster rotators. Some of the close binary systems were removed from the simulation since their rotational velocity exceeded the highest velocity supported by the spectra library from Munari et al. (2005). The overall number of such systems is very small and their omission should not affect the end results of the simulation.

Synthetic spectra were then scaled according to the luminosity ratio η, Doppler-shifted to their projected orbital velocities, summed and normalized, and finally, the barycentric radial velocity drawn from the distribution shown in Figure 3 was applied. To simulate the observational errors, Gaussian noise was added to the binary spectrum according to the randomly selected value of S/N from the distribution also shown in Figure 3. Errors in the normalization of the continuum were simulated by introducing five cosine functions with random phases, frequencies, and amplitudes matching typical variations in observed spectra. We generated 10⁶ such binary spectra that were then classified with the method described in the previous section.

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One of the results yielded by the simulations is the distribution of system periods at which the binarity is detectable. The limitations on the short- and long-period ends come from two different factors. The spectral lines of short-period binaries are widened because of the co-rotation of both components. Another reason for the widening is velocity smearing during the exposure which becomes significant only for the systems with the shortest periods (P < 1 day). Combining both effects can blend the lines of even a relatively well-separated system, making detection more difficult. On the long-period end, the detection probability is affected by the limited resolving power of the spectrograph and the fact that binarity detection strongly depends on the noticeable double peaks of the relatively wide Ca ii triplet lines. For example, a binary system of solar twins orbiting around each other on a circular orbit with a period of one year and seen along a line of sight close to orbital plane is just on the threshold of detection when observed at a quarter phase.

Figure 4 compares the distribution of the input binary systems and those recovered by our analysis. The dashed lines show the distribution of periods given in Equation (3), while the shaded gray histogram shows the input period distribution. The systems with the shortest periods are missing partly because it was not possible to model spectra of fast rotating cool stars and partly because we removed all systems that exhibited Roche overflow, i.e., in which the stellar radii became greater than the radius of the Roche lobe R_L given by Eggleton (1983),

$$\begin{equation} \frac{R_L}{a}\approx \frac{0.49q^{2/3}}{0.6q^{2/3}+\ln (1+q^{1/3})}, \end{equation} \tag{ 4 }$$

where a denotes the semimajor axis and q denotes the mass ratio. The solid line in Figure 4 shows the number of systems that were confirmed as binaries by our classification method. The number of modeled systems is small below P ⩽ 1 day and predictions there should not be trusted. The detection ratio becomes very high for systems with periods between 1and10 days. For systems with periods between 10and100 days, the detection rate is still significant. For P ⩾ 100 days the number of recovered binaries rapidly drops, becoming negligible at 1 yr.

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The dependence of the ratio between the number of properly classified and all binary systems (detection ratio) on various parameters is shown in Figure 5. For all synthetic spectra the classification was done at only one orbital phase, i.e., for a "single shot." A tight relation between mass ratio q and luminosity ratio η comes from the fact that only main-sequence stars were included in the simulation sample. More interestingly, both S/N diagrams (q–S/N and S/N–η) show that the detection is almost independent of the S/N as long as η ≳ 0.3 or equivalently q ≳ 0.75. The detection ratio is equal to the simulation average of ∼31%. A slightly worse detection is observed at S/N <20, while the seemingly lower detection ratio at S/N >80 is a consequence of the small number of such systems in the simulation.

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The detection clearly depends strongly on the system period P and the difference between the projections of the orbital velocities of stars Δv_orb. The detection ratio is higher than 80% for 0.8 days < P < 2 days as long as η ≳ 0.3. It seems that it begins to decrease at shorter periods but this again comes from the fact that very few systems were modeled in this region. For P < 30 days, the detection is still better than 50% and falls toward 0 at roughly 1 yr. The unexpectedly high yield of binaries at short periods and η < 0.3 can be explained as the result of the incorrect classification of rapidly rotating cool stars as blended binaries.

The same properties can be seen on the diagrams that show the dependence of the detection ratio on the velocity difference. At Δv_orb > 40–50 km s^-1, the probability of detection is greater than 90% as long as η ≳ 0.3. Observed spectra sometimes have a slightly lower resolving power than the model ones because of non-optimal focusing. Taking that into account it is safe to take 50 km s^-1 as a lower limit. Below that value the probability for detection quickly vanishes.

The simulation shows that the target population consists mostly of binary systems with relatively well-separated spectral lines (Δv_orb > 50 km s^-1) and mass ratios close to unity (q > 0.75). Consequently, this implies that only shorter period binaries with P < 1 yr will be detected, independent of the S/N, and additionally justifies the circular orbit assumption.

Since the orbital period is not measurable from a single observation, it is convenient to plot the distribution of orbital periods for all systems with a given Δv_orb (shown in Figure 6). The range of orbital periods at lower velocities is greater than at higher velocities, meaning that it is possible to guess the system's period more precisely for binaries with better separated lines.

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The fraction of SB2 binaries that are classified as normal single stars in the observed sample is of minor concern for studies of Galactic structure. Mistakenly treating a blended SB2 spectrum as a single one does not yield extremely wrong results because the centroid of the blended correlation peaks should be close to the systemic velocity. As for the atmospheric parameters, the similarity of both components ensures that the single star spectrum fit will still be some average of both spectra and will thus not be far from the proper solution for each component. Usually, only the rotation velocity is overestimated, but this parameter is not measurable from RAVE spectra with noteworthy precision anyway.

The stellar parameters and radial velocities were obtained by fitting the observed binary spectra with the synthetic spectra from the library. While many methods exist for fitting single star spectra (see, e.g., Koleva et al. 2009, and references therein), none of them was reportedly used on SB2 spectra. Modeling binary spectra is more complex than modeling single star spectra for obvious reasons. The number of free parameters is more than twice as large. In our case, where we neglected all minor effects, the total number of parameters was 10: effective temperatures of both stars, their surface gravities, rotational velocities, metallicity, which was assumed to be the same for both stars, both Doppler shifts, and the luminosity ratio.

The common way of finding the best-fitting solution is to define a criterion for the goodness of fit, which is usually the sum of squares of the difference between the observed (o) and modeled (m) spectra, where the sum goes through all wavelength bins.

Our fitting procedure works as follows. First, the approximate Doppler shifts and luminosity ratio are obtained with the TODCOR method (Zucker & Mazeh 1994). The parameters of both template spectra for the calculation of the CCF are always the same. With roughly known velocities and luminosity ratio, a better solution is searched for using a MultiNest algorithm (Feroz et al. 2009). This method has two big advantages over more traditional algorithms like the Nelder–Mead simplex. The final solution of the latter depends on the initial starting point on the grid of synthetic spectra. Moreover, because we are using a linear interpolation of synthetic spectra between the grid points, descending methods have a bias for finding a solution close to some grid point. Parameter space sampling methods on the other hand have a better feel for the area surrounding the global minimum and therefore a better chance of finding it.

Unfortunately, none of the tested methods gave reasonable results in performing a completely unconstrained fitting. It often happened that the method returned a solution consisting of a giant and a dwarf both with similar temperatures and a luminosity ratio close to unity. While this solution might formally be the best-fitting one, it is still not physically feasible and cannot be trusted. To overcome the problem we limited the solutions to the main-sequence stars, the same as we did in the construction of the synthetic sample for the described simulation (see Section 3.1). This simplification gave more reasonable solutions (Table 1).

The errors of the Δv_orb are similar to the errors of measured radial velocities for single stars. Generally, they are larger for blended cases, where positions of lines are harder to locate and for faster rotating stars that have wider lines. Errors on individual spectral types and luminosity ratio were estimated from four re-observations. The objects T_9474_01354_1, T_8045_00353_1, T_8510_01121_1, and T_4916_01130_1 were all observed twice on different nights. The average effective temperature difference between the two solutions for the same object is equal to 130 K with a standard deviation of 44 K, similar to what is returned by the MultiNest method. The errors depend on the S/N and the separation of the lines (Doppler shifts). They are greater when the lines are closer together. The average difference of the luminosity ratio is equal to 0.08 with a standard deviation of 0.08. Here, the dependence on line separation is much greater. When lines are separated well (Δv_orb ≳ 100 km s^-1 for both measurements) the errors are smaller than 5%, but are proportionally higher in the blended case of T_9474_01354_1 (more than 20%). This holds true only if the main-sequence assumptions can be justified.

While the spectra listed in Table 1 do not show any special features, some of those in Table 2 do and can be grouped together.

4.2.1. Ca ii Emission

Six different objects (one observed twice) show chromospheric emission in the Ca ii lines, similarly to what is sometimes observed in the same lines of single stars. All iron lines, especially the ones at 8515 Å, 8647 Å, and 8688 Å, show duplicity (Figure 7), although they are harder to identify in some of the noisier spectra. All seven spectra are consistent with G-type stars. The Ca ii triplet lines of both components are too shallow, which indicates that some of the flux originates from emission processes. These stars are probably members of the RS CVn group of binaries with active chromospheres. G spectral types and emission cores in the Ca ii lines are their distinctive features, with the active chromospheres powered by intense magnetic fields generated by tidal interaction between the two components (Foing et al. 1989; Eker et al. 2008). Object T5844_00340_1 was observed twice in the span of one month and shows changes in the positions of lines. Iron lines in C0232159_055451 are hardly observable, but shapes of the Ca ii triplet lines are consistent with other objects of this kind.

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4.2.2. Contact Binaries

4.2.3. HD 101167