Absolute dimensions of the early F-type eclipsing binary V506 Ophiuchi
We report extensive differential -band photometry and high-resolution spectroscopic observations of the early F-type, 1.06-day detached eclipsing binary V506 Oph. The observations along with times of minimum light from the literature are used to derive a very precise ephemeris and the physical properties for the components, with the absolute masses and radii being determined to 0.7% or better. The masses are and for the primary and secondary, the radii are and , and the effective temperatures K and K, respectively. The orbit is circular and the stars are rotating synchronously. The accuracy of the radii and temperatures is supported by the resulting distance estimate of pc, in excellent agreement with the value implied by the trigonometric parallax listed in the Gaia/DR2 catalog. Current stellar evolution models from the MIST series for a composition of match the properties of both stars in V506 Oph very well at an age of 1.83 Gyr, and indicate they are halfway through their core hydrogen-burning phase.
Subject headings:binaries: eclipsing; stars: evolution; stars: fundamental parameters; stars: individual (V506 Oph); techniques: spectroscopic; techniques: photometric
The variability of V506 Oph (TYC 993-1631-1, Gaia/DR2 4486661994344201344, , SpT F1 v) was discovered photographically by Hoffmeister (1935), who classified it as an Algol-type eclipsing system. The binary orbital period of 1.06 days was first established by Soloviev (1937). Aside from the many times of minimum light measured since, CCD light curves have been reported ocassionally in the more recent literature (Pojmanski & Maciejewski, 2004; Lapham & Snyder, 2007; Kochanek et al., 2017), sometimes only in graphical form, but there is no detailed study of the system as yet.
Here we report extensive new photometric observations of V506 Oph as well as radial-velocity measurements, which we combine to determine the physical properties of the system for the first time. The spectroscopic observations and velocity measurements are presented in Section 2. In Section 3 we combine them with times of minimum light from the literature to derive an accurate linear ephemeris as well as the spectroscopic elements. The photometric observations are reported in Section 4, and subjected to a detailed light curve analysis in Section 5. The physical properties of the stars, derived in Section 6, are then compared with predictions from recent stellar evolution models in Section 7. Final remarks are given in Section 8.
V506 Oph was observed spectroscopically with two different instruments. Between 2010 May and 2017 February we monitored the binary with the Center for Astrophysics | Harvard & Smithsonian (CfA) Tillinghast Reflector Echelle Spectrograph (TRES; Szentgyorgyi & Fűrész, 2007; Fűrész, 2008) attached to the 1.5m Tillinghast reflector at the Fred L. Whipple Observatory on Mount Hopkins, Arizona. This bench-mounted, fiber-fed instrument delivers spectra with a resolving power of covering the wavelength range 3900–9100 Å in 51 orders. We gathered 48 spectra with signal-to-noise ratios (S/N) near the Mg i b triplet (5187 Å) ranging from 21 to 74 per resolution element of 6.8 km s. Wavelength calibrations relied on exposures of a Thorium-Argon lamp taken before and after each science frame, and the reductions were performed with a dedicated pipeline.
Radial velocities from the CfA spectra were measured with the two-dimensional cross-correlation technique TODCOR (Zucker & Mazeh, 1994). Templates appropriate for each star were taken from a library of pre-computed synthetic spectra based on model atmospheres by R. L. Kurucz (see Nordström et al., 1994; Latham et al., 2002). For this analysis we used only the 100 Å wide order centered on the Mg i b triplet, as previous experience indicates it contains most of the velocity information and because our synthetic templates are limited in coverage to a narrow region surrounding that feature. We selected the best templates by running grids of cross-correlations over wide ranges in effective temperature () and rotational broadening ( when seen in projection), at fixed solar metallicity and values of the surface gravity , close to our final determinations in Section 6. Following Torres et al. (2002) we selected the template parameters giving the highest cross-correlation value averaged over all observations, with weights set by the strength of each exposure. In this way we estimated the temperatures to be K and K for the primary (the marginally more massive star) and secondary, which are the same within their uncertainties. They correspond approximately to spectral type F1. The uncertainties are based on the scatter from the individual spectra, with an extra 100 K added in quadrature, to be conservative. The rotational velocities were determined to be km s for both stars. Thus the spectroscopic properties are essentially identical. The light ratio at the mean wavelength of our observations (see Zucker & Mazeh, 1994) was found to be . The resulting radial velocities in the heliocentric frame are listed in Table 1 along with their uncertainties.
|(2,400,000+)||(km s)||(km s)||(km s)||(km s)||Phase|
Note. – Phases are calculated from the reference time of primary eclipse in Table 4.
V506 Oph was also observed at Fairborn Observatory in southeast Arizona near Washington Camp, between 2012 February and 2018 May. For this we used the Tennessee State University 2m Astronomical Spectroscopic Telescope (AST) and a fiber fed echelle spectrograph (Eaton & Williamson, 2007). The detector was a Fairchild 486 CCD having 4K4K pixels 15 m in size, which results in echelle spectra that have 48 orders and cover a wavelength range of 3800–8260 Å (Fekel et al., 2013). Because of the faintness of the system, we used a fiber diameter that produced a spectral resolution of 0.4 Å, but even so, given the weakness and very significant line broadening of the features, many of the spectra did not have a high enough S/N to provide meaningful results. However, we were able to obtain useful velocity measurements from 17 AST spectra that had a resolving power of 15000 at 6000 Å and an average S/N of about 40.
A description of the general radial velocity reduction of the Fairborn AST spectra has been given by Fekel et al. (2009). In particular for V506 Oph we used a solar line list that consisted of 168 mostly neutral Fe lines that cover a wavelength range of 4920–7100 Å. The individual lines were fitted with a rotational broadening function (Sandberg Lacy & Fekel, 2011). Unpublished velocities of several IAU solar-type radial velocity standards show that velocities obtained with our Fairchild CCD have a offset relative to the velocities of Scarfe (2010). Thus, 0.6 km s has been added to each velocity. We list these measurements in Table 2. We estimate the uncertainties to be 3.2 and 2.6 km s for the primary and secondary, respectively, from the scatter of a preliminary spectroscopic orbital solution.
|(2,400,000+)||(km s)||(km s)||Phase|
Note. – Velocity uncertainties are esimated to be 3.2 and 2.6 km s for the primary and secondary, respectively. Phases are calculated from the reference time of primary eclipse in Table 4.
Rotational broadening fits of the stellar lines in our 17 spectra result in values of for both components. From the same spectra the average equivalent width ratio of the secondary to the primary, which should be equivalent to the light ratio since the spectra appear to be very similar, is , the same as obtained from the CfA spectra.
3. Times of minimum and spectroscopic orbit
Times of minimum light for V506 Oph have been recorded since 1928 by photographic, visual, and photoelectric/CCD techniques. We collect all 176 measurements of which we are aware (84 for the primary and 92 for the secondary) in Table 3, with their uncertainties when published.
Note. – The uncertainties in the second column are taken directly from the original publications. Scale factors for these errors determined from our joint solution with the spectroscopy are given in the text. The ‘Eclipse’ column refers to the primary (1) or secondary (2) minimum. ‘Type’ is “pg”, “v”, or “pe” for photographic, visual, or photoelectric/CCD observations. Sources are: (1) https://www.bav-astro.eu/index.php/veroeffentlichungen/service-for-scientists/lkdb-engl; (2) http://var2.astro.cz/ocgate/?lang=en; (3) Lapham & Snyder (2007), with the unrealistically small formal uncertainties multiplied by 30; (4) Lacy (2007). (This table is available in its entirety in machine-readable form.)
Independent spectroscopic orbital solutions from the CfA and Fairborn velocities gave elements consistent with each other, except for a minor difference in the center-of-mass velocities that is of no consequence and is likely due to instrumental shifts. We therefore combined these data sets. Furthermore, as the times of minimum light spanning nearly 87 years constrain the ephemeris far better than our radial velocities can, we used the two kinds of observations together in a joint orbital solution to derive the final ephemeris and spectroscopic elements simultaneously. For the times of minimum without published uncertainties we adopted errors of 0.0175, 0.0146, and 0.0035 days for the photographic, visual, and photoelectric/CCD measurements, respectively, determined by iterations so as to achieve reduced values near unity for each type of observation. In a similar manner we determined appropriate scaling factors to be applied to the published visual errors of 1.09 and 1.28 for the primary and secondary measurements, and scale factors for the photoelectric/CCD errors of 1.17 and 1.65. Initial fits allowing for separate epochs of primary and secondary minumum showed no evidence of eccentricity, so the final fit assumed none. We also allowed for possible velocity offsets between the primary and secondary stars separately for the CfA and Fairborn data (, ), which in the case of the CfA data may result from template mismatch. We additionally solved for a systematic offset between the CfA and Fairborn velocity zero points (), to account for possible instrumental shifts as indicated above. The results are listed in Table 4, and shown graphically in Figure 1 together with the observations and residuals.
|Min I ()|
|CfA , (km s)||2.91, 3.26|
|CfA ,||48, 48|
|Fairborn , (km s)||3.20, 2.60|
|Fairborn ,||17, 17|
Note. – and represent the primary minus secondary velocity offsets, and the global CfA minus Fairborn shift. The minimum masses and semimajor axis are expressed in units of the nominal solar mass and radius (, ) as recommended by 2015 IAU Resolution B3 (see Prša et al., 2016).
Differential photometry of V506 Oph in the band was performed with the URSA WebScope at the University of Arkansas at Fayetteville and with the NFO WebScope near Silver City, New Mexico (see Lacy et al. 2014 for technical details). V506 Oph (var) was measured along with two nearby comparison stars (comp; TYC 993-762-1, , , and TYC 993-0780-1, , ). Differential magnitudes were measured with the application Measure written by author Lacy. The two comparison star fluxes were combined and the differential magnitudes were calculated as varcomps. We obtained 8345 URSA images between 2003 July and 2012 June on a total of 129 nights, and 7475 NFO images between 2005 January and 2013 June on a total of 234 nights. Exposures were 120 sec long, and square photometric apertures with sizes of 30″ and 22″ were used for URSA and NFO, respectively. The Gaia/DR2 catalog lists 7 nearby stars within 30″ of V506 Oph, but they are all at least 8 magnitudes fainter and therefore do not contaminate the photometry.
Examination of the raw data revealed that the NFO measurements suffer from small systematic errors typically less than 0.02 mag, caused by imprecise centering from night to night and variations in responsivity across the field of view (see Lacy et al., 2014). We corrected this by applying nightly offsets based on a preliminary light curve solution using the URSA data alone, which shows no such effects for V506 Oph. The full data sets are given in Table 6 (URSA) and Table 6 (NFO, including corrections). The resultant light curves are displayed in Figure 2.
|Note. — (This table is available in its entirety in machine-readable form.)|
|Note. — (This table is available in its entirety in machine-readable form.)|
5. Light curve analysis
The URSA and NFO photometry of V506 Oph was analyzed using version 2013 of the Wilson-Devinney LC program (Wilson & Devinney, 1971; Wilson, 1979, 1990) called within a Markov Chain Monte Carlo (MCMC) scheme. Our method of solution used the emcee111ttp://dan.iel.fm/emcee . code of Foreman-Mackey et al. (2013), which is a Python implementation of the affine-invariant MCMC ensemble sampler proposed by Goodman & Weare (2010). We typically used 100 walkers and uniform priors within suitable limits for all fitted quantities.
As the system is well detached we used the LC program in mode 2, along with the option of simple reflection and synchronous rotation of both components (see Section 6). The ephemeris and mass ratio of the binary were held fixed at the values in Table 4, and the primary temperature was set to 6840 K (Section 2). The main parameters of the fit were the inclination angle , the temperature of the secondary , the surface potentials and , a phase shift , and the out-of-eclipse magnitude difference at phase 0.25, . We assumed initial measurement errors for the URSA and NFO observations of 0.02 mag, and a scale factor (with a log-uniform prior) was included as an additional adjustable parameter, which we solved for self-consistently and simultaneously with the other parameters (see Gregory, 2005). Convergence of the chains was checked visually, with the additional requirement of a Gelman-Rubin statistic of 1.05 or smaller for each parameter.
The URSA and NFO data sets were initially analyzed separately. Tests indicated the best results were obtained by solving also for the linear limb-darkening coefficients of each star (, ), as well as the gravity-darkening exponents (, ). More complicated limb-darkening laws did not provide any improvement. The albedos for both components were held fixed at a value of 0.5, commonly adopted for convective stars, as experiments with other values gave poorer results. No significant third light was detected, consistent with the fact that the Gaia/DR2 catalog (Gaia Collaboration et al., 2018) lists no companions within the photometric apertures that are bright enough to affect the light curves.
The independent URSA and NFO solutions gave similar results, so for our final solution we solved both light curves together imposing a common geometry as well as a single value of and the limb- and gravity-darkening parameters for each star, for a total of 14 free parameters. The resulting light elements are presented in Table 7, and the adopted model is shown in Figure 2 overlaid on the observations.
|, (mag)||0.01079, 0.00944|
|Note. — The parameter values listed correspond to the mode of the posterior distributions, and the uncertainties are the 16% and 84% (1) credible intervals.|
To guard against the possibility that the uncertainties returned by our MCMC procedure are underestimated because of residual systematic errors (i.e., time-correlated or “red” noise) in the NFO data, or even in the URSA data, we carried out a residual permutation exercise as described next. The light curve residuals from our adopted solution were shifted by an arbitrary number of time steps (separately for URSA and NFO) and added back into the model curve at each time of observation (with wrap-around) to create synthetic data sets. We subjected them to a new MCMC solution in which we simultaneously perturbed the primary temperature, the mass ratio, and the albedos by adding Gaussian noise with standard deviations equal to their reported uncertainties for and , and for the albedos. We repeated this 50 times, and computed the scatter (standard deviation) of the resulting distribution for each fitted and derived parameter as a measure of the uncertainty caused by red noise. We then added this uncertainty and the internal ones from the MCMC solutions in quadrature to obtain the final errors reported above in Table 7. The derived quantities include, among others, the individual Roche lobe radii as well as , the equivalent volume radius of each star (radius of a sphere with the same volume as the Roche lobe).
6. Absolute dimensions
The combination of the spectroscopic elements in Table 4 and the light elements in Table 7 yields the physical properties for the system given in Table 8. The absolute masses and radii are determined with relative precisions of about 0.7% each. The averages of the measured projected rotational velocities from the CfA and Fairborn spectra agree well with the expected values for synchronous rotation (listed in the table), within the errors.
|(K)||6840 150||6780 110|
|Dist. modulus (mag)|
|Gaia/DR2 distance (pc)|
|Synchronous projected rotational velocity assuming spin-orbit alignment.|
|Average measured projected rotational velocity from CfA and Fairborn Observatory.|
|Note. — The masses, radii, and semimajor axis are expressed in units of the nominal solar mass and radius (, ) as recommended by 2015 IAU Resolution B3 (see Prša et al., 2016), and the adopted solar temperature is 5772 K (2015 IAU Resolution B2). Bolometric corrections are from the work of Flower (1996), with conservative uncertainties of 0.1 mag, and the bolometric magnitude adopted for the Sun appropriate for this scale is (see Torres, 2010). See text for the source of the reddening. For the apparent visual magnitude of V506 Oph out of eclipse we used (Henden & Munari, 2014; Henden et al., 2015).|
Consistent estimates of the reddening in the direction of V506 Oph were obtained from five different sources: 0.083 (Burstein & Heiles, 1982), 0.099 (Drimmel et al., 2003), 0.091 (Amôres & Lépine, 2005), 0.086 (Schlafly & Finkbeiner, 2011), and 0.083 (Green et al., 2018). The straight average with a conservative uncertainty is mag, from which the extinction is mag.
Using this value of , the distance to the system was inferred from radii and temperatures, the out-of-eclipse brightness of (Henden & Munari, 2014; Henden et al., 2015), and bolometric corrections from Flower (1996), and is pc. This is very nearly the same as the more precise distance of pc inferred from the Gaia/DR2 parallax (Gaia Collaboration et al., 2018), and the agreement speaks indirectly to the combined accuracy of our radii and effective temperatures.
As an additional check on the spectroscopic temperatures, we collected brightness measurements of the combined light of the binary from the literature in the Johnson-Cousins and 2MASS systems (Droege et al., 2006; Skrutskie et al., 2006; Henden & Munari, 2014; Henden et al., 2015), rejecting others that are known to have been taken in eclipse. We constructed six non-independent color indices, corrected them for reddening following Cardelli et al. (1989), and used color-temperature calibrations by Casagrande et al. (2010) to infer photometric temperatures from each index. The weighted mean of the six values, K, is very close to the average of the spectroscopic temperatures (6810 K), supporting the accuracy of those values. The temperature difference between the components is measured much more precisely from the light curve analysis than from the CfA spectra, and is K.
7. Comparison with theory
The very precise absolute dimensions of V506 Oph offer an opportunity to test current stellar evolution models. Mass-radius and mass-temperature diagrams are shown in Figure 3, in which the observations are compared against model isochrones from the MESA Isochrones and Stellar Tracks series (MIST; Choi et al., 2016), which is based on the Modules for Experiments in Stellar Astrophysics package (MESA; Paxton et al., 2011, 2013, 2015). To our knowledge there is no spectroscopic determination available for the metallicity of V506 Oph. We find that a slight adjustment in the metallicity of the models from solar to provides an excellent fit to both radii and both effective temperatures at the measured masses. The age of the system according to these models is 1.83 Gyr, which is shown by the thick dashed line in Figure 3.
Evolutionary tracks for the measured masses are seen in Figure 4, and indicate the components are halfway through their main-sequence lifetimes. The uncertainty in the location of the tracks due to the mass errors is shown at the bottom, and corresponds to only about K in this diagram.
V506 Oph has been listed as a possible member of the sparse open cluster Collinder 359 (Melotte 186) (Sahade & Frieboes, 1960; Sahade & Berón Dàvila, 1963), although the location of the binary nearly 7° from the cluster center makes this rather unlikely a priori. Curiously, many of the V506 Oph properties appear consistent with membership. For example, the recent study by Cantat-Gaudin et al. (2018) listed the parallax of Collinder 359 as mas, corresponding to a distance of about pc, which is consistent with what we obtain for the binary ( pc; Table 8). Kharchenko et al. (2005) reported the mean radial velocity of the cluster to be , though based on measurements for only two stars. This is also tantalizingly close to the center-of-mass velocity we measured for V506 Oph, . The mean proper motion components of Collinder 359 listed by Cantat-Gaudin et al. (2018) are mas yr and mas yr based on the Fourth U.S. Naval Observatory CCD Astrograph Catalog (UCAC4; Zacharias et al., 2013). Those of V506 Oph in the same catalog are mas yr and mas yr, which differ at about the 2.5 level from the cluster mean. However, if the 30 Myr age of Collinder 359 reported by Kharchenko et al. (2005) is accurate, then V506 Oph cannot be a member, as we find it to be much older (1.83 Gyr).
V506 Oph joins the ranks of the detached eclipsing binaries with the very best determined properties (see, e.g., Torres et al., 2010). Its value for testing models of stellar evolution would be significantly enhanced by a spectroscopic determination of the metallicity, although this may be challenging given the significant line broadening of both stars.
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