Physical Parameters of Late-type Contact Binaries in the Northern Catalina Sky Survey
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Physical Parameters of Late-type Contact Binaries in the Northern Catalina Sky Survey
Weijia Sun,
1, 2, 3, 4
Xiaodian Chen,
2, 5, 6
Licai Deng,
2, 5, 6 and Richard de Grijs
3, 4, 7 Department of Astronomy, School of Physics, Peking University, Beijing 100871, China Key Laboratory for Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road,Chaoyang District, Beijing 100012, China Department of Physics and Astronomy, Macquarie University, Balaclava Road, Sydney, NSW 2109, Australia Centre for Astronomy, Astrophysics and Astrophotonics, Macquarie University, Balaclava Road, Sydney, NSW 2109, Australia School of Astronomy and Space Science, University of the Chinese Academy of Sciences, Huairou 101408, China Department of Astronomy, China West Normal University, Nanchong 637002, China International Space Science Institute–Beijing, 1 Nanertiao, Hai Dian District, Beijing 100190, China
ABSTRACTWe present the physical parameters of 2335 late-type contact binary (CB) systems extracted fromthe Catalina Sky Survey (CSS). Our sample was selected from the CSS Data Release 1 by strictlylimiting the prevailing temperature uncertainties and light-curve fitting residuals, allowing us to almosteliminate any possible contaminants. We developed an automatic Wilson–Devinney-type code toderive the relative properties of CBs based on their light-curve morphology. By adopting the distancesderived from CB (orbital) period–luminosity relations (PLRs), combined with the well-defined mass–luminosity relation for the systems’ primary stars and assuming solar metallicity, we calculated theobjects’ masses, radii, and luminosities. Our sample of fully eclipsing CBs contains 1530 W-, 710 A-,and 95 B-type CBs. A comparison with literature data and with the results from different surveysconfirms the accuracy and coherence of our measurements. The period distributions of the various CBsubtypes are different, hinting at a possible evolutionary sequence. W-type CBs are clearly located ina strip in the total mass versus mass ratio plane, while A-type CBs may exhibit a slightly differentdependence. There are no significant differences among the PLRs of A- and W-type CBs, but the PLRzero points are affected by their mass ratios and fill-out factors. Determination of zero-point differencesfor different types of CBs may help us improve the accuracy of the resulting PLRs. We demonstratethat automated approaches to deriving CB properties could be a powerful tool for application to themuch larger CB samples expected to result from future surveys.
Keywords: binaries: close — methods: data analysis — stars: fundamental parameters INTRODUCTIONLate-type contact binary systems (CBs), also known as W Ursae Majoris (W UMa) variables, are eclipsing binarieswhere both components fill their Roche lobes. Hence, they are in ‘contact’ with each other, thus allowing mass andenergy transfer (Lucy 1968). The components’ close separation facilitates relatively short orbital periods, with mostsystems having periods between 0.25 and 0.5 days. Another natural outcome of their proximity is the variability oftheir light curves. The latter are effective tools to study CB formation and evolution.Previous studies have revealed that CBs are embedded in a common envelope (Lucy & Wilson 1979) with bothcomponents having similar temperatures (Kuiper 1941), although the systems may undergo periodic thermal-relaxationoscillations (Flannery 1976; Robertson & Eggleton 1977). However, an unresolved mystery remains as to whether anevolutionary sequence exists among different types of CBs. Only limited sample sizes, encompassing just tens of CBswith common characteristics, have thus far been available for comparative research (e.g., Qian 2001; Yakut & Eggleton2005; Yildiz & Do˘gan 2013). The large sample size is essential to constrain evolutionary models of CBs (Stepien 2006),
Corresponding author: Weijia Sun, Xiaodian [email protected], [email protected] a r X i v : . [ a s t r o - ph . S R ] F e b as well as their angular-momentum loss properties and nuclear evolutionary pathways, particularly as regards anyimpact these may have on the resulting orbital periods (Chen et al. 2016a; Jiang 2019) and the evolutionary productsof the different CB types (Yang & Qian 2015; Li et al. 2019).Since Eggen (1967) first proposed to use CBs as distance indicators, various studies have attempted to establishperiod–luminosity (PL)–color (PLC) relations (Rucinski 1994; Chen et al. 2016b). Chen et al. (2018a) managedto achieve a distance accuracy of 7% using infrared passbands . This may be further improved if we can excludethe possible impact associated with using different subtypes and any dependence on the CBs’ physical parameters.However, this will only be feasible based on large sample sizes.The sample of known CBs was recently significantly increased thanks to new data from several sky surveys thatprovide high-cadence, long-term, high-precision photometric observations in a range of passbands, including, e.g., theCatalina Sky Survey (CSS; Marsh et al. 2017), the Wide-field Infrared Survey Explorer catalogue (
WISE ; Chen et al.2018b), the All-Sky Automated Survey for Supernovae (ASAS-SN; Jayasinghe et al. 2018), the Northern Sky VariabilitySurvey (NSVS; Gettel et al. 2006), and the Asteroid Terrestrial-impact Last Alert System (ATLAS; Heinze et al. 2018).As sample sizes increased, researchers have taken advantage of the data from various surveys and constructed genuineCB samples for further statistical study (Rucinski 1995; Norton et al. 2011; Marsh et al. 2017). However, most previousstudies dealing with large samples of CBs were limited to analyses of their light-curve morphology (e.g., periods andamplitudes), which is rather different from deriving the intrinsic properties of the stellar components. Moreover, futuresurveys using, e.g., the Zwicky Transient Facility (ZTF; Bellm et al. 2019) and the Large Synoptic Survey Telescope(LSST; LSST Science Collaboration et al. 2009) will likely result in enormous numbers of newly discovered CBs, thusposing a challenge to our ability to derive stellar parameters based on individual light-curve solutions.In this paper, we develop an automated Wilson–Devinney-type (W–D; Wilson & Devinney 1971; Wilson 1979) codeto derive physical parameters from the CB light curves, and we apply our method to a large CB sample from theCSS Data Release 1 (CSDR1 ; Drake et al. 2014). Armed with distance information obtained from PLR analysis ininfrared passbands (Chen et al. 2018a), we can estimate the intrinsic properties—masses, radii, and luminosities—of2335 CBs.This article is organized as follows. In Section 2, we describe the data and candidate selection. The details of themethod and the input parameters, as well as the selection criteria applied to obtain our final catalog, are discussedin Section 3. We performed a series of tests to verify the accuracy and consistency of our measurements, which wereport in Section 4. Section 5 presents a discussion of the CB-subtype classification, their evolutionary states, andimplications for the PLRs, which is followed by a summary in Section 6. DATA AND CANDIDATE SELECTIONWe used CB data from the CSDR1, the northern-sky section of the CSS. The survey used three telescopes to coverthe sky between declinations δ = − ◦ and +70 ◦ at Galactic latitudes | b | > ◦ . The unfiltered observations weretransformed to V CSS magnitudes (Drake et al. 2013). The CSDR1 collected ∼ ,
000 periodic variables based ontheir analysis of 5.4 million variable star candidates, with a median number of observations per candidate systemof around 250. Because of limitations to the aperture photometry obtained, the V -band zero-point uncertainty is ∼ . − .
08 mag from field to field. The photometric uncertainties were determined by employing an empiricalrelationship between the source fluxes and the observed photometric scatter. Typical values range from 0.05 to0 .
10 mag, mainly depending on the target brightness.The initial CB sample was selected as described by Drake et al. (2014). Based on the Stetson variability index ( J W S )and its standard deviation ( σ J ), the authors selected a sample of variable stars from the reduced photometric data.For classification purposes, a Lomb-Scargle-type (Lomb 1976; Scargle 1982) periodogram analysis was applied to allvariable candidates. Those with significant periodic patterns were subsequently studied using the Adaptive FourierDecomposition method (Torrealba et al. 2015) to derive their best-fitting periods. Finally, the remaining candidateswere visually inspected and classified based on their periods, light-curve morphologies, and colors.Drake et al. (2014) found 30,743 CBs (EW-type stars) in the CSDR1. To estimate their temperatures from multi-band photometry, we cross-matched the sample with the American Association of Variable Star Observers’ (AAVSO)Photometric All-Sky Survey (APASS; Henden & Munari 2014). This is a survey in the B, V , and Sloan g (cid:48) , r (cid:48) , and This was improved to 6% based on
Gaia
Data Release 2 measurements (Chen et al. 2019). http://nesssi.cacr.caltech.edu/DataRelease/ i (cid:48) passbands. Its Data Release (DR) 9 covers almost the entire sky (Henden et al. 2016) and provides high-accuracyAPASS photometry without any offsets (Munari et al. 2014). Following cross-matching, we found 13,726 CB candidatesfor which both CSDR1 and APASS photometry had been obtained. Comparison with the LINEAR data of Palaversaet al. (2013), for which Drake et al. (2014) found that 98.3% of CBs had the same classification, suggests only a minorcontribution from contaminants. Given that the candidates used in our subsequent analysis comprise a subset of theinitial sample (candidates with poor mass-ratio determinations or low inclinations were ignored; see Section 3.3), wealso expect a low to a negligible level of contamination in our CB sample. LIGHT-CURVE SOLUTIONSTo model the W UMa light curves, we used a W–D-type approach. Our program executes two subroutines, onefor generating light and radial velocity curves based on a given set of physical parameters and the other allowingadjustments of the light- and velocity-curve parameters using differential corrections. We adopted ‘Mode 3,’ appropriatefor over-contact binaries, with both component stars filling their Roche lobes. The component stars can still havedifferent surface brightnesses if they are in geometric contact without being in thermal equilibrium.3.1.
Effective temperatures
The effective temperature is one of the W–D code’s primary input parameters. Light curve morphologies can placetight constraints on the T /T temperature ratio, but not on the individual component temperatures. Therefore, weestimated the effective temperatures based on the CB’s spectral type, as inferred from its intrinsic color, using thede-reddened ( B − V ) APASS photometry.We adopted the relevant E ( B − V ) reddening values from the 3D dust extinction map derived from Pan-STARRS1and 2MASS photometry by (Green et al. 2019). Distances to our sample CBs were obtained on the basis of theChen et al. (2018a) PLRs for 12 optical to mid-infrared bands based on 183 nearby W UMa-type CBs with accurate Tycho – Gaia parallaxes. These authors determined the distances to field CBs by combining the PLR distances basedon W ISE/ W , Gaia / G mean (DR 1), and Two Micron All-Sky Survey (2MASS)/ JHK s photometry (Chen et al. 2018a,their Section 5.2).The reddening in the B and V passbands was calculated by employing A λ /E ( B − V ) coefficients from Schlafly &Finkbeiner (2011, their Table 6), for R V = 3 .
1; here, A λ denotes the extinction in a given bandpass λ . The median E ( B − V ) value is 0.037 mag, while 90% of our sample objects have reddening values lower than 0.15 mag.We then used the empirical relation between the intrinsic color, ( B − V ) , and the average temperature, T , fromPecaut & Mamajek (2013) to estimate the color temperature, T color . This approximate estimation is sufficient, sinceit only affects the determination of the absolute temperatures, while it has a minor effect on other key parameters,including the mass ratio, relative radii, and the system’s inclination. To better illustrate this, we compared thetemperatures derived here with those obtained from a low-resolution spectroscopic survey undertaken with the LargeSky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST; Luo et al. 2015). LAMOST (Cui et al. 2012; Denget al. 2012; Zhao et al. 2012) is a reflective Schmidt telescope located at Xinglong Observatory north of Beijing, China,with an effective aperture of 3.6-4.9 m and a field of view of 5 ◦ (diameter). It has 4000 fibers covering its focal plane.Its wavelength coverage is 3650 − R ∼ T color ) and spectroscopic data ( T spec ), as well as the residual, ∆ T = T color − T spec . Thereis no significant bias apparent toward any temperature. The root-mean-square error (RMSE) is 352 K, which is closeto the mean error in the temperature determination (324 K) for CBs derived from SDSS colors (Marsh et al. 2017).The color index is commonly used as a proxy for the temperature of the primary component. However, thisapproximation will introduce biases in temperature for both components. To alleviate this problem, we assignedthe color temperature to the system’s combined light rather than just to the primary star. We hence introduce thecombined temperature, T c , as T c = L p + L s L p /T p4 + L s /T s4 (1)where L p ( T p ) and L s ( T s ) are the luminosities (temperatures) of the primary and secondary components, respectively.In practice, we adopted T color for the primary star’s temperature in the first run, and we then obtained the corre-sponding luminosities and temperatures for both components. Next, we calculated T c and the ratio of T c and T color , T s p ec ( K ) T color (K) − ∆ T ( K ) Figure 1.
Temperature measurements based on intrinsic colors ( B − V ) and spectroscopic data. The black dashed line is theone-to-one linear relation. The residual temperature, ∆ T = T color − T spec , is displayed in the bottom panel. The root-mean-square error (RMSE) is 352 K. using Eq. 1 and α = T c /T color , respectively. We subsequently corrected the individual temperatures by dividing themby α . These new temperatures were taken as input for a second run, which yielded a new solution that retained thecombined temperature, T c , close to the color temperature, T color .3.2. Other parameters
Marsh et al. (2017) found that a photospheric temperature of 6200 K separates CBs into two groups. Systemswith temperatures greater than 6200 K generally have smaller amplitudes ( (cid:46) . T > g = 0 .
32 and g = 1 . A = 0 . A = 1 .
0, which is a reasonable approximationgiven that Rafert & Twigg (1980) found that the expected bolometric albedo for stars with radiative envelopes is 1.0,while the average value for those with convective envelopes is around 0.5. We adopted the logarithmic limb-darkeninglaw of (Klinglesmith & Sobieski 1970); its coefficients have been tabulated by (van Hamme 1993).Since we have no information about the metallicity of our CBs, we adopted solar metallicity. This is statisticallyacceptable since our sample is located within 2 − P/ d t = 0), because uniform orbital period changes are unusual among CBs (e.g., Kreiner 1977; Qian 2001).Next, the dimensionless surface potential Ω was calculated using the formulation of Wilson (1979). Note that forover-contact binaries Ω is fixed to the same value as Ω , and thus we used the same potential Ω for both the primaryand secondary stars.We did not consider the effect of starspots, for reasons of clarity and simplicity. This is a generally accepted practicesince spots usually have only subtle effects on the shape of a light curve. Spots are usually included to explainasymmetries when one light-curve maximum is higher than the other, an effect also known as the O’Connell effect. Asexplained in Section 3.3, we removed those solutions that did not fit the light curves well. Therefore, any CBs thatare strongly affected by the O’Connell effect have already been excluded from our sample. We remind the reader thatone should exercise caution in reaching the simplistic conclusion that our sample CBs may be free from spots becausethe hypothetical distribution of spots is by no means uniquely determined by the CB light curves.We also assumed that the third-light contribution is negligible. Any tertiary component does not affect the estimationof the relative parameters (including the mass ratios and inclinations) but only the luminosities and masses. D’Angeloet al. (2006) performed a spectroscopic search for third members in their sample of CB systems. They found that theuncertainty in total luminosity introduced by a tertiary component is smaller than 0.15 mag, leading to an increase inthe uncertainty in the derived masses of only ∼ The q -search method Using the periods derived by Drake et al. (2014), we converted our light curves from the time domain to the phasedomain.Next, we used Gaussian Process (GP) models to fit the photometric data and reject the outliers. GP modeling,which is well suited to time-series modeling, is routinely and widely applied to the light curves of transits (e.g., Gibsonet al. 2012b,a; Evans et al. 2013) and variable stars (e.g., Roberts et al. 2012; McAllister et al. 2017). For our purposes,we selected a GP kernel composed of a Mat´ern component and an amplitude factor, as well as observational noise.The Mat´ern kernel with ν = 3 / σ ); 2 σ outliers were rejected to allow for a robust light-curve analysis.To constrain the CB mass ratios, q = m /m , we employed a q -search method, i.e., we analyzed how the meanresidual changes for different, fixed q values, adopting the q value corresponding to the minimum mean residual asthe best light-curve solution (see Fig. 2, top row). This is an effective approach to estimating CB mass ratios withouthaving access to information pertaining to the radial velocity curves (Terrell & Wilson 2005). It has been widelyapplied (e.g., Chen et al. 2016b; Yang et al. 2017; Zhou et al. 2018). Next, we adopted the standard error given by theW–D code through the Method of Multiple Subsets (MMS) as the uncertainty associated with the relevant derivedproperty (except for q ; see Section 4.).To be more specific, we first fixed the value of q , leaving as free parameters the inclination i , the secondary star’stemperature T , and the respective bandpass luminosities of the secondary star L . The W–D program iterated throughthe Levenberg–Marquardt procedure (Levenberg 1944; Marquardt 1963) to find the best solution, as well as the meanresidual, within a given number of iterations. In the second step, we repeated the same procedure for different q values,from 0.05 to 10. The step width used was variable so as to balance the need for our computational resources and theresulting numerical precision (step widths of 0.02, 0.05, and 0.25 from q = 0 .
05 to 0.5, from q = 0 . q = 2 to 10, respectively). The total number of fixed q values was 85. Note that, under certain conditions, the W–Dcode did not converge. We skipped the corresponding q value and continued the calculation from the next q value. CBswith fewer than 60 q values were removed from our sample and subsequently ignored. Having thus obtained the best q value, we relaxed the constraint on the mass ratio and carried out a final run based on all final, adjusted parametervalues simultaneously to calculate the respective standard errors.3.4. Absolute parameters
Thanks to the high-precision CB PLRs derived by Chen et al. (2018a), we can now derive accurate absolute magni-tudes for our sample CBs. To derive the absolute parameters, such as a system’s semi-major axis ( A ) and its absolutestellar component masses, we must adopt a number of basic assumptions, imposed by the lack of spectroscopic data.We hence assumed that the luminosities and masses of the primary stars are commensurate with loci on the zero-ageMS (ZAMS). This is a reasonable assumption (Yakut & Eggleton 2005). Yildiz & Do˘gan (2013) compiled a list of − . − . − . − . − . − . l og R e s i du a l CSS J095501.1-014745 − . . . . . . . . . . . . . M ag n i t ud e ( m ag ) − . − . − . − . − . − . − . l og R e s i du a l CSS J094939.5-020655 − . . . . . . . . . . . . . M ag n i t ud e ( m ag ) Figure 2.
Two examples of the q -search diagram. (top) Mean residual versus q . Red dots represent the best q correspondingto the smallest residuals. (bottom) Observations and best-fitting solutions of the light curves. Blue dots show the observationaldata and their photometric errors, while orange crosses are outliers that were rejected through GP regression. The best solutions(red curves) were derived based on the q values given in the first row.
100 CBs with well-determined parameters and found that their primary components are more similar to normal MSstars than the systems’ secondary components. These authors found that the primary stars occupy loci in both the M – L and M – R diagrams that make them resemble ZAMS stars as if they were detached eclipsing binaries, while thesecondary stars do not exhibit such properties.Using the luminosity fraction of the primary star f V = L V1 / ( L V1 + L V2 ) derived in the previous section, for eachCB we calculated the V -band luminosities of both component stars. Next, we converted these V -band luminositiesto bolometric luminosities using the relevant bolometric correction (BC; Pecaut & Mamajek 2013). We obtained theBC V for each star based on the effective temperature derived in Section 3.3, i.e., M i, bol = M i,V + BC V ( T i ), where i corresponds to 1 or 2 in reference to the primary and secondary stars, respectively. We subsequently used the M – L relation ( L ∝ M . ; Yildiz & Do˘gan 2013) to infer the masses of the primary stars. The intercept of the M – L relationwas derived by fitting the CBs in the Yildiz & Do˘gan (2013) catalog. The masses of the secondary stars were thendetermined based on the best-fitting mass ratios (Section 3.3). The orbital major axes, A , were converted to absoluteunits using Kepler’s Third Law. Therefore, we can deduce the absolute radii of the primary and secondary stars ( r , r ) based on their relative measurements ( r /A , r /A ). The errors associated with these absolute parameters werecalculated through error propagation analysis. 3.5. Selection Criteria
It is widely acknowledged that the q values derived from spectroscopic studies may be different from those basedon photometric analyses (e.g., Yakut & Eggleton 2005). Rucinski (2001) have pointed out that the reliable methodto determine the mass ratio should be based on radial velocity observations. In that case, the q sp parameter is givenby the ratio of velocity semi-amplitudes of both components. In fact, the q ph parameter, i.e., the mass ratio obtainedfrom light-curve analysis alone, might not be reliable. Spectroscopic q sq values are usually preferred if the results arenot mutually consistent.However, determination of q ph has been shown to be reliable nevertheless for the special conditions pertaining tosystems exhibiting total eclipses (Mochnacki & Doughty 1972; Wilson 1978; Rucinski 2001). In this case, the depth ofthe light-curve minima primarily depends on the mass ratio and much less on the fill-out factor. Combined with theduration of the totality, which allows for an estimation of the system’s inclination, fully eclipsing binaries can break thedegeneracy among the different physical parameters and yield an accurate mass ratio. In the ground-breaking study ofTerrell & Wilson (2005), the authors simulated the light curves for various physical parameters and demonstrated thatthe eclipse properties (complete versus partial) govern photometric mass ratios for over-contact and semi-detachedbinaries. Only for CBs exhibiting total eclipses can accurate radii be derived based on Roche geometry, which henceresults in accurate q ph parameters. Subsequently, Hamb´alek & Pribulla (2013) expanded the simulations to coverthe full parameter space spanned by the mass ratio, the orbital inclination, and the fill-out factor to investigate theuniqueness of the photometric light-curve solutions. They addressed the importance of the presence of third light andalso confirmed the result of Terrell & Wilson (2005) that q ph is robust for fully eclipsing over-contact and semi-detachedsystems. Under these circumstances, the severe degeneracy among multiple physical parameters, most notably betweenthe mass ratio and the fill-out factor, can be broken.Therefore, we applied additional selection criteria to our sample CBs to obtain a highly reliable sample. First, wevisually checked the best-fitting solutions and excluded those that did not match well. The light curve of a typicalCB should exhibit continuous brightness variations as a function of time and have nearly equal eclipse depths. In ournext step, we neglected all CBs with inclinations below 70 ◦ . Hamb´alek & Pribulla (2013) pointed out that the numberof similar (i.e., degenerate) light curves decreases with increasing inclination, and so photometric light curves are noteffective tools to analyze systems seen under low inclinations. CBs characterized by a large tilt of their orbital planewith respect to the observer ( i > ◦ ) can have substantial variations in their brightness because of orbital eclipses.The final selection criterion was that only fully eclipsing systems were included in the final catalog to ensure a robustdetermination of the mass ratio, q ph . To achieve this, we regarded CBs with inclination angles i > arccos | ( r − r ) /A | to have total eclipses and their q ph to be well-determined. A side effect of applying this criterion is that it will inevitablydisfavor high-mass-ratio CBs. Therefore, a deficiency of CBs with q ∼ VALIDATIONThe reliability of our results is predominantly determined by the quality of our measurements, which renders val-idation of great importance. To assess the performance quality of our method, two tests were designed, to evaluatethe final accuracy and precision, respectively. ‘Accuracy’ here refers to how close our derived values are to the ‘true’value, while ‘precision’ reflects how close our results are to each other. Sections 4.1 and 4.2 address, respectively, theaccuracy and precision of the physical parameters q .In our accuracy test, we compared our results with spectroscopic measurements from the literature. In general, q sp values based on spectroscopic velocity curves are usually considered the ‘correct’ means to evaluate the ‘true’ massratios, while q ph might be influenced by other properties. Thus, such a direct comparison can tell us directly whetherthere are any discrepancies between our results and the ‘true’ values, and obtain a reasonable approximation to theuncertainties associated with a range of physical parameters. In the precision test, we applied our methodology toASAS-SN data to check whether the parameters derived from various sky surveys are biased with respect to eachother. This way, we can assess the coherence of our measurements across different data sources.4.1. Accuracy testing with spectroscopic measurements
In this section, we will perform a direct comparison between our results and literature data. Since our CSS-based CBs are generally fainter than the CBs in the Pribulla et al. (2003) catalog, we did not find any matchingcandidates. Instead, we collected ASAS-SN CB light curves for which literature measurements from Pribulla et al.(2003) were available. These CBs were cross-matched with APASS and
Gaia
DR2 (based on their coordinates) toderive color indices and absolute distances. Next, we derived the light curve solution and selected a sample withreliable measurements adopting the same selection criteria as before. The final step was to estimate the scatter invarious parameters (e.g., q and f ) compared with their values in the literature. The systematic uncertainty estimated Table 1.
Relative Physical Parameters of our Sample CBsID Period T a T a i Ω b q f c L V1 /L V , tot Subtype(day) (K) (K) ( ◦ )CSS J223201.5+342945 0 . ±
38 5771 88 . ± .
50 6 . ± .
09 0 . ± .
09 0 . ± .
15 0 . ± .
01 WCSS J090725.9-032447 0 . ±
32 6008 80 . ± .
42 7 . ± .
08 0 . ± .
09 0 . ± .
13 0 . ± .
01 WCSS J223244.6+322638 0 . ±
35 5409 80 . ± .
98 7 . ± .
06 0 . ± .
09 0 . ± .
09 0 . ± .
01 WCSS J165813.7+390911 0 . ±
28 5022 86 . ± .
85 9 . ± .
05 0 . ± .
09 0 . ± .
07 0 . ± .
01 WCSS J001546.9+231523 0 . ±
37 6157 72 . ± .
28 13 . ± .
10 0 . ± .
09 0 . ± .
15 0 . ± .
01 WCSS J222607.8+062107 0 . ±
128 6587 75 . ± .
27 8 . ± .
23 0 . ± .
09 0 . ± .
36 0 . ± .
02 WCSS J042755.0+060421 0 . ±
41 73 . ± .
67 1 . ± .
02 0 . ± .
09 0 . ± .
28 0 . ± .
01 WCSS J080529.8+005305 0 . ±
50 5699 73 . ± .
61 10 . ± .
08 0 . ± .
09 0 . ± .
12 0 . ± .
01 WCSS J225217.2+381800 0 . ±
30 5902 76 . ± .
04 7 . ± .
08 0 . ± .
09 0 . ± .
13 0 . ± .
01 WCSS J163458.9-003336 0 . ±
38 5601 74 . ± .
16 8 . ± .
08 0 . ± .
09 0 . ± .
12 0 . ± .
01 WCSS J012559.7+203404 0 . ±
35 5764 78 . ± .
51 7 . ± .
05 0 . ± .
09 0 . ± .
07 0 . ± .
01 WCSS J041633.5+223927 0 . ±
43 80 . ± .
91 2 . ± .
02 0 . ± .
09 0 . ± .
18 0 . ± .
01 WCSS J145924.5-150145 0 . ±
39 83 . ± .
43 2 . ± .
02 0 . ± .
09 0 . ± .
10 0 . ± .
01 ACSS J051056.2+041919 0 . ±
60 70 . ± .
33 1 . ± .
02 0 . ± .
09 0 . ± .
26 0 . ± .
01 ACSS J130111.2-132012 0 . ±
56 88 . ± .
84 1 . ± .
01 0 . ± .
09 0 . ± .
19 0 . ± .
01 ACSS J130425.1-034619 0 . ±
16 89 . ± .
38 2 . ± .
01 0 . ± .
09 0 . ± .
05 0 . ± .
01 ACSS J141923.2-013522 0 . ±
89 88 . ± .
29 2 . ± .
02 0 . ± .
09 0 . ± .
20 0 . ± .
01 ACSS J065701.5+365255 0 . ±
31 76 . ± .
81 2 . ± .
02 0 . ± .
09 0 . ± .
10 0 . ± .
01 ACSS J162327.1+031900 0 . ±
58 78 . ± .
31 1 . ± .
01 0 . ± .
09 0 . ± .
22 0 . ± .
00 BCSS J153855.6+042903 0 . ±
39 84 . ± .
31 2 . ± .
01 0 . ± .
09 0 . ± .
12 0 . ± .
00 B(This table is available in its entirety in machine-readable form in the online journal. A portion is shown here for guidance regarding its formand content.) a Temperatures without uncertainty estimates were derived using the photometric method described in Section 3.1, while values with uncer-tainties were obtained from the W–D code. b Ω = Ω = Ω . c Fill-out factor, defined by Ruci´nski (1973): f = (Ω − Ω o ) / (Ω i − Ω i ), where Ω i and Ω o are the inner and outer Lagrangian surface potentialvalues, respectively. from the ASAS-SN data also applies to our CSS-based results, because both surveys share the same passband ( V ),while the typical sampling cadence and the photometric uncertainties are comparable.In the left-hand panel of Fig. 3, we present a comparison of the mass ratios q of literature values and the solutionswe derived from ASAN-SN. Note that we also included literature results based on photometric light curves. Thisis a reasonable practice, since Pribulla et al. (2003, their Fig. 1) confirmed the consistency of q ph and q sp for totaleclipses. Forty of the CBs we obtained light curve solutions for based on ASAS-SN data had either q sp or q ph measurements available. The mass ratios calculated based on ASAS-SN light curves, q ASASSN , are in good agreementwith their literature counterparts, q lit . The corresponding Pearson correlation coefficient is 0.78, indicating a stronglinear correlation between both measurements. The mean difference in the mass ratios, ∆ q = q ASASSN − q lit = − . σ = 0 . σ , as the actual uncertainty in the mass ratio for our CSS data set.We additionally checked our determinations of the fill-out factor, f , which may also suffer from degeneracies: see theright-hand panel of Fig. 3. Except for some points with relatively large error bars, there is a good linear correlationbetween f lit and f ASASSN . This is strong evidence supporting, based on the photometric precision of ASAS-SN (orCSS), that we can derive accurate measurements of physical parameters that are not severely biased.
Table 2.
Absolute Physical Parameters of our Sample CBsID m m r r L L A ( M (cid:12) ) ( M (cid:12) ) ( R (cid:12) ) ( R (cid:12) ) ( L (cid:12) ) ( L (cid:12) ) ( R (cid:12) )CSS J223201.5+342945 1 . ± .
03 0 . ± .
09 0 . ± .
03 0 . ± .
01 0 . ± .
17 0 . ± .
10 2 . ± . . ± .
03 0 . ± .
11 1 . ± .
04 0 . ± .
02 1 . ± .
47 0 . ± .
16 2 . ± . . ± .
03 0 . ± .
09 1 . ± .
03 0 . ± .
01 0 . ± .
19 0 . ± .
08 2 . ± . . ± .
03 0 . ± .
09 1 . ± .
03 0 . ± .
01 0 . ± .
24 0 . ± .
06 1 . ± . . ± .
03 0 . ± .
09 1 . ± .
03 0 . ± .
01 0 . ± .
23 0 . ± .
05 1 . ± . . ± .
03 0 . ± .
13 1 . ± .
05 0 . ± .
02 3 . ± .
65 1 . ± .
24 2 . ± . . ± .
04 0 . ± .
10 1 . ± .
04 0 . ± .
01 1 . ± .
43 0 . ± .
07 2 . ± . . ± .
03 0 . ± .
11 1 . ± .
04 0 . ± .
01 1 . ± .
44 0 . ± .
10 2 . ± . . ± .
03 0 . ± .
11 1 . ± .
04 0 . ± .
02 2 . ± .
47 0 . ± .
18 2 . ± . . ± .
03 0 . ± .
10 1 . ± .
04 0 . ± .
01 1 . ± .
33 0 . ± .
09 2 . ± . . ± .
03 0 . ± .
12 1 . ± .
04 0 . ± .
02 2 . ± .
56 0 . ± .
18 2 . ± . . ± .
04 0 . ± .
11 1 . ± .
04 0 . ± .
02 2 . ± .
68 0 . ± .
21 2 . ± . . ± .
04 0 . ± .
13 1 . ± .
05 0 . ± .
02 3 . ± .
99 1 . ± .
30 3 . ± . . ± .
04 0 . ± .
13 1 . ± .
05 0 . ± .
02 3 . ± .
78 0 . ± .
11 2 . ± . . ± .
03 0 . ± .
12 1 . ± .
05 0 . ± .
02 2 . ± .
57 0 . ± .
09 2 . ± . . ± .
03 0 . ± .
08 0 . ± .
02 0 . ± .
01 0 . ± .
13 0 . ± .
07 1 . ± . . ± .
05 0 . ± .
11 1 . ± .
04 0 . ± .
02 1 . ± .
68 0 . ± .
11 2 . ± . . ± .
03 0 . ± .
09 1 . ± .
03 0 . ± .
01 0 . ± .
21 0 . ± .
06 2 . ± . . ± .
04 0 . ± .
15 1 . ± .
06 0 . ± .
02 6 . ± .
46 0 . ± .
09 3 . ± . . ± .
05 0 . ± .
12 1 . ± .
04 0 . ± .
02 2 . ± .
96 0 . ± .
10 2 . ± . Precision testing with ASAS-SN
We also performed a consistency test to verify whether our measurements are coherent among different surveys. Asubsample of 877 CBs was randomly selected from our catalog and we made a comparison of the physical parameters( q ) derived based on CSS and those based on ASAS-SN data. The result of the comparison (Fig. 4) is shown as aHess diagram to better illustrate the relative density of data points. The mass ratio measurements demonstrate aremarkable consistency among various surveys. The scatter in this correlation ( σ = 0 .
05) could be taken as the theinternal error associated with our method, which is smaller than the σ = 0 .
08 reported in Section 4.1. This behavioris what one can expect when comparing with an external catalog. Although there is a lack of CBs with a high massratios, this test is sufficient to illustrate the coherence of our measurements, i.e., that it is not strongly biased by thephotometric uncertainties. A more robust test could be done by comparison with a high-precision survey (e.g., theZwicky Transient Factory, ZTF). However, the number of available objects with high-cadence light curves covering theentire phase space is limited. Therefore, we did not include a comparison with the ZTF, but we will explore the ZTFin a future paper. DISCUSSION5.1.
CB subtypes
Equipped with this information about the relative parameters of our sample CBs, we now can classify them intoseveral subtypes. Traditionally, CBs are divided into two subtypes: A-type systems (where the more massive staris hotter) and W-type systems (where the less massive star is hotter). A further subdivision, referred to as B-typeCBs, has been proposed to describe systems that exhibit a significant temperature difference between the primaryand secondary components (Lucy & Wilson 1979). These latter CB systems are in marginal contact with each other0 . . . . . . q lit . . . . . . q A S A SS N σ : 0.085 p -value: 0.78 q sp q ph . . . . . . f lit . . . . . . f A S A SS N σ : 0.12 p -value: 0.83 Figure 3.
Comparisons of (left) mass ratio q and (right) fill-out factor f (right) of literature values and the solutions we derivedfrom ASAN-SN data. The black dashed lines are the one-to-one linear relations for q and f . The root-mean-square error, σ ,and the Pearson correlation coefficients for these parameters are included in the bottom right-hand corners of the panels. In theleft-hand panel, mass ratios from spectroscopic and photometric sources are marked in blue and orange colors, respectively. and cannot attain thermal equilibrium. We adopted the criterion that B-type CBs should exhibit a temperaturedifference between their components over 1000 K, while A- and W-type CBs are classified based on their masses andtemperatures. Our sample contains 1530 W-, 710 A-, and 95 B-type CBs.Figure 5 shows the distribution of the bolometric luminosity ratio, λ = L /L , of our CBs as a function of q . TheCB subtypes occupy different regions in the diagram. A- and W-type systems reside close to the correlation foundby Lucy (1968), λ = q . . Lucy (1968) argued that the apparent ratio of the CBs’ luminosities does not followthe MS relation, λ = q . , but that it is instead proportional to the ratio of the surface areas. This suggests thatmass exchange may be significant among A- and W-type systems. However, B-type CBs are located between Lucy’srelation and the λ = q . line, in essence since B-type CBs are binary systems that have not yet attained thermalequilibrium. Note that this is different from our assumption for the primary stars adopted in the previous section.Here, we consider the luminosity ratios of the primary and secondary components. On the one hand, if the prevailingenergy transfer is sufficient, they should have attained the same temperature but different sizes. On the other hand, ifthe energy transfer is not sufficient, both components resemble independently evolved stars, which would thus followthe λ = q . relation. In other words, we only ascertain whether the luminosity ratios follow either of the knowntrends. We also found that W-type CBs have generally higher luminosity ratios than their A-type counterparts for agiven mass ratio. This is expected because the T /T temperature ratio is higher for W-type systems.Csizmadia & Klagyivik (2004) introduced the concept of H-type CBs, characterized by high mass ratios, q ≥ . β = L , obs L , ZAMS , (2)where L , obs is the observed luminosity of the primary star, L , obs = L tot / (1 + q . (cid:16) T T (cid:17) ) = L tot / (1 + λ ), followingthe model of Lucy (1968), and L , ZAMS is the luminosity of the primary star if both stars follow the MS M – L relation, L , ZAMS = L tot / (1 + q . ). It is straightforward to show that β = 1 + q . q . (cid:16) T T (cid:17) = 1 + αλ . λ , (3)1 . . . . . . q CSS . . . . . . q A S A SS N σ : 0.05 p -value: 0.85 0 . . . . . . . . Figure 4.
Hess diagram of the mass ratios derived from CSS ( q CSS ) and ASAS-SN data ( q ASASSN ). Colors represent thelogarithm of the number of objects in each bin. The red dashed line is the one-to-one linear relation. The root-mean-squareerror, σ , and Pearson correlation coefficients are included in the bottom right-hand cornerc of the panels. where α = (cid:16) T T (cid:17) . . Note that the M – L relation we have adopted (Yildiz & Do˘gan 2013) is slightly different fromthat of Csizmadia & Klagyivik (2004), and hence the indices are not exactly the same. We adopted the former relationsince it provided better fits to our data.We present the distribution of our CB sample’s transfer parameters β versus their luminosity ratios λ in the left-hand panel of Fig. 6. We classified all systems with high mass ratios ( q ≥ .
72) as H-type stars. As expected, onlytwo CBs were marked as H types due to our selection criterion aimed at only selecting CBs with total eclipses. Formost systems, both parameters exhibit a good correlation that can be represented well by Eq. 3, with α ranging from0.5 to 2. Note that α depends sensitively on the ratio of the components’ surface temperatures, suggesting that thesurface temperatures of the primary and secondary stars in the majority of A-, B-, and W-type CBs are very similar.These subtypes are enclosed by an envelope corresponding to the minimum rate of transfer at a given luminosity ratio( α = 0). It has been suggested (Kalimeris & Rovithis-livaniou 2001) that the energy transfer rate is a function of theluminosity of the secondary star. However, Csizmadia & Klagyivik (2004) found that the former parameter is alsorelated to the mass ratio. In the middle panel, we redrew the figure by color-coding the data according to the CBs’mass ratios. The deviation of high- q CBs from the envelope ( α = 0) shows a clearly increasing trend as q becomeslarger, attaining significance for q > .
6. In fact, Csizmadia & Klagyivik (2004) corrected their β values to account forthe influence of different mass ratios, i.e., β corr = β − . q . , leading to a correlation between β corr and the bolometric2 . . . . . . q . . . . . . L u m i n o s i t y r a t i o λ WAB
Figure 5.
Luminosity ratio ( λ ) versus mass ratio ( q ) distribution of our CB sample. Open orange squares, open blue triangles,and solid green triangles represent A-, W-, and B-type CBs, respectively. The solid line is the MS M – L , i.e., λ = q . ; thedashed line is Lucy’s relation, λ = q . . luminosity ratio. In the right-hand panel, we adopted this practice and indeed confirmed their results. That is, wedid not find any evidence indicating that CBs with mass ratios greater than 0.72 are special. Therefore, we did notinclude H-type CBs as a subtype in our classification.5.2. Periods and evolutionary state
One of the key parameters defining a given CB system is its orbital period, which is commonly used as a proxy forits evolutionary state (e.g., Qian 2001). As mass transfer proceeds, a binary system’s orbital separation continues toshrink, thus leading to a decrease in the orbital period.Figure 7 shows the distribution of orbital periods for the different CB subtypes. The period distribution of B-type CBs peaks around 0.45 day, which is distinct from the distributions of the other subtypes. B-type CBs arelikely in the non-thermal-contact state of the relaxation oscillations and a semidetached phase (Lucy & Wilson 1979).Approximately one-quarter of B-type systems have relatively short periods. However, note that the prevailing selectioneffects are rather complicated. In fact, they may favor the detection of systems exhibiting large amplitudes. On theother hand, high- q CBs are likely rejected because of our focus on selecting objects exhibiting total eclipses.3 . . . . . . λ . . . . . . T r a n s f e r p a r a m e t e r β WABH . . . . . . λ . . . . . . T r a n s f e r p a r a m e t e r β . . . . . . λ C o rr ec t e d T r a n s f e r p a r a m e t e r β c o rr . . . . . . . Figure 6. (left) Transfer parameter β versus luminosity ratio λ . Symbols are as in Fig. 5. Dashed lines show the expected β curves for different α values. Red solid dots represent H-type CBs, defined as high mass-ratio binary systems, q > .
72. H-typeCBs are clearly located away from the envelope ( α = 0). (middle) As the left-hand panel, but color-coded by mass ratio, q .(right) Corrected transfer parameter, β corr , versus λ . The color bar on the right applies to the middle and right-hand panels. Whether or not the CB subtypes represent an evolutionary sequence is the subject of debate (Maceroni & van ’t Veer1996; Awadalla & Hanna 2005; Eker et al. 2006; Gazeas & Niarchos 2006; Yildiz & Do˘gan 2013). Tentative evidencesuggests that, if an evolutionary sequence exists, it should reflect an evolution from A- to W-type systems. Gazeas& Niarchos (2006) found that A-type CBs generally have longer periods compared with W-type systems for a givenorbital angular momentum. This supports the argument that evolution from A- to W-type systems may be associatedwith simultaneous mass and angular momentum loss. Evolution in the opposite direction is less likely since there isno injection of mass or angular momentum from outside of the CB systems. Figure 7 shows that, although the perioddistributions of A- and W-type CBs largely overlap, A-type systems tend to have longer periods. Even though thisdistribution has not been corrected for selection effects, there is no evidence that A-type CBs are more affected byselection biases and, therefore, this may reveal a general property of the period distribution.Our result supports the notion that A-type systems are less evolved than W-type systems, which might be becauseA-type CBs have not gone through the mass-reversal stage. However, a number of studies disagree with this scenario.Hilditch et al. (1988) claimed that W-type CBs are not evolved MS stars and that A-type systems have almost reachedthe terminal MS age. Yildiz & Do˘gan (2013) estimated that the initial masses of A- and W-type CBs are different byassuming that mass transfer starts near the terminal MS age. They found that semi-detached systems with a massivesecondary component ( > . (cid:12) ) will form A-type CBs, while systems with a less massive secondary component( < . (cid:12) ) will evolve to the contact phase because of the rapid evolution of angular momentum, and hence formW-type CBs. Thus, evolutionary connections among the various CB subtypes, if any, are still unclear.In Fig. 8, the total CB mass, M tot , is shown as a function of q . Most A- and W-type CBs are located in a strip.This region is delineated by the black dashed lines, defined by the 5% and 95% percentiles of M tot for each q bin,where 0 . (cid:54) q (cid:54) m/ d q = 0 . ± .
02, which is consistent with van ’t Veer (1996) towithin 1 σ . However, close inspection revealed that the story might not be that simple. In the middle and right-handpanels of Fig. 8, we show the Hess diagrams for W- and A-type CBs, overplotted with the same black dashed lines asin the left-hand panel. It is clear that although W-type CBs are located in a well-defined strip, a non-trivial fractionof A-type stars lie outside of this region. Moreover, the strip-like morphology for A-type CBs is much less obviouscompared with their W-type counterparts, and even if similar boundaries exist for A-type CBs, the dominant slopeappears different. This difference is also tentatively visible in Li et al. (2008, their Fig. 4), where low-mass-ratio( q (cid:47) .
6) A-type CBs were generally found close to the high-mass boundary.This trend, suggesting that (at least for W-type CBs) the lower the total mass of the CBs is, the smaller their massratio becomes, could be a natural product of their dynamical evolution in the absence of mass reversal (Lomb 1976;4 . . . . . P r o b a b ili t y D e n s i t y AWB
Figure 7.
Orbital-period distributions for different CB subtypes.
Flannery 1976; Robertson & Eggleton 1977; Vilhu 1982). However, other models (Stepien 2006; Paczy´nski et al. 2007)imply that mass-ratio reversal of the progenitors occurs during the system’s evolution. Our current sample may notallow us to differentiate between both scenarios.Li et al. (2008) claimed that W-type systems are generally found in a region with intermediate-mass ratios between0.3 and 0.7, while A-type systems occur much less commonly in this area. Instead, the latter are located in twoseparate regions of parameter space ( q (cid:54) . q (cid:62) . ∼
100 objects) and limited to the solar neighborhood ( (cid:46)
300 pc), while here our sample is drawnfrom a larger volume, extending to distances of 2 − q regime is similar to those published previously.5.3. Period–luminosity relations . . . . . q . . . . . . . M t o t ( M (cid:12) ) AWB . . . . . q . . . . . . . M t o t ( M (cid:12) ) W-type 0 . . . . . q A-type 0 . . . . . . . . Figure 8.
Total CB mass, M tot , as a function of mass ratio, q . Symbols are as in Fig. 5. Black dashed lines represent theedges of the strip defined by the 5% and 95% percentiles of M tot for each q bin, where 0 . (cid:54) q (cid:54) Equipped with such a large CB sample, we can now study whether there are any systematic differences in thePLRs for different subtypes. Using the distances estimated by Bailer-Jones et al. (2018) based on
Gaia
DR 2 (GaiaCollaboration et al. 2018) parallax measurements, we constructed the PLRs for W-, A-, and B-type CBs: see Fig. 9.Chen et al. (2018a) found that W G -band counterparts because the mid-infrared W M W , mean = ( − . ± . P − log 0 .
4) + (2 . ± . , σ = 0 .
23 mag N = 1130A : M W , mean = ( − . ± . P − log 0 .
4) + (2 . ± . , σ = 0 .
24 mag N = 457B : M W , mean = ( − . ± . P − log 0 .
4) + (2 . ± . , σ = 0 .
24 mag N = 40These PLR slopes for A- and W-type CBs are consistent with the slopes derived by Chen et al. (2018a), to within 2 σ .This shows that CBs obey rather tight correlations between their periods and luminosities. The reason that the scatter( σ ) resulting from our fits is larger than that derived by Chen et al. (2018a), by 0.16 mag, is that the error propagatedfrom the Gaia distance uncertainties is larger; Chen et al. (2018a) placed tight constraints on the distance uncertaintiesincluded in their study. There are no signs of systematic zero-point differences among the various subtypes. The zeropoints were measured for a period of 0.4 day (see the black dashed line in Fig. 9). However, the difference between B-and other CB subtypes is greater than 3 σ . This could also be an intrinsic characteristic of B-type systems, since theyare not in thermal equilibrium. However, the significance of this result is compromised by small-number statistics,especially at the short-period end. Therefore, we will not include B-type CBs in our discussion.We also compared our distance determinations, based on the Chen et al. (2018a) PLRs, with the parallax-baseddistances of Bailer-Jones et al. (2018). The mean difference between both measurements is (cid:104) DM PLR − DM (cid:36) (cid:105) =0 .
012 mag ( σ = 0 .
027 mag), thus demonstrating the robustness of the CB PLR-based distance measurements. Onepossible explanation might be related to the intrinsic scatter in the M – L and temperature–luminosity relations orthat in the intrinsic properties, including the mass ratios, the orbital inclinations, and the fill-out factors (defining theextent to which a system’s Roche lobe is filled). We explored the contributions of these three intrinsic parameters tothe scatter to check whether the addition of a nonlinear component might be helpful to improve the accuracy of thePLRs.To construct Fig. 10, we binned our sample into bins of different mass ratios q (top), inclinations i (middle),and fill-out factors f (bottom), and we present the corresponding magnitude differences, ∆ M W = DM PLR − DM (cid:36) = M (cid:36) − M DM , in each bin. This latter parameter reflects the extent to which the luminosities are brighter than predictedby the PLRs; the smaller ∆ M W is, the brighter the CBs are compared with the expected values. The error barsin Fig. 10 indicate the 25th and 75th percentiles of the distributions in each bin. The mean difference is shown asa vertical black dashed line. There are clear signs of local nonlinearities in the top and bottom panels, suggesting a6 − . − . − . − . − . − . P (day)12345 W ( m ag ) WAB
Figure 9.
PLRs based on distances from
Gaia
DR 2 for different CB subtypes. A- and B-type CBs are offset by 1 mag and2 mag, respectively. The dashed line represents P = 0 . dependence on the mass ratio and the fill-out factor. In the middle panel, ∆ M W is consistent with the mean valuesin each inclination bin and remains flat.In the top panel, a luminosity excess for q < . q values. As the mass ratio decreases from unity to zero, the radii of the primaryand secondary Roche lobes will change accordingly if the other parameters are fixed. According to Kopal (1959, theirTables 3-1 and 3-3), the sum of r , R (where ‘R’ stands for ‘Roche lobe’) and r , R remains unchanged from q = 1 to q ≈ .
4, followed by a gentle increase toward lower values, thus leading to a significant increase in the total surfacearea of the Roche lobe, S ∝ r , R + r , R for q < .
2. Consequently, the total observed luminosities of our CBs increasetoward smaller q values. We superimposed the theoretical expectations for the effects of different q values in the toppanel, which matches our results very well. This suggests a robust detection of a q -induced zero-point shift in thePLR. A weak trend was also noticed for i , while ∆ M W decreases for smaller inclination angles. However, this effectis not so significant compared with the size of the error bar. Similarly, the slight decrease in ∆ M W toward largerfill-out factors could be related to the changes of the Roche lobes’ surface areas. We used the equations of Yakut &Eggleton (2005) to simulate this effect. The adopted q value is the sample’s median mass ratio, q = 0 .
2. As shown in7 . . . . . . q − . − . − . . . . ∆ M W ( m ag )
70 75 80 85 90 i − . − . − . − . . . . . ∆ M W ( m ag ) . . . . . . f − . − . − . − . . . . . ∆ M W ( m ag ) Figure 10.
Magnitude residuals (∆ M W = DM PLR − DM (cid:36) = M (cid:36) − M DM ) as a function of (top) mass ratio q , (middle)inclination i , and (bottom) fill-out factor f . The error bars represent the 25th and 75th percentiles of the distributions in eachbin. The horizontal black dashed line is the mean magnitude difference (cid:104) DM PLR − DM (cid:36) (cid:105) = 0 .
036 mag. Orange lines in the topand bottom panels represent theoretical models of the impact of changes in q and f , respectively. CONCLUSIONSIn this paper, we have presented estimates of the fundamental parameters of 2335 total-eclipsing CBs, based on aW–D-type code. We used the q -search method to derive the mass ratios without any knowledge of their radial velocitycurves. The absolute parameters were obtained by assuming that the primary stars of our sample CB systems followthe ZAMS. A series of tests were designed to assess the accuracy and precision of our method. Our study has shownthe tremendous potential for statistical analysis of photometric CB surveys. Our main results and conclusions aresummarized below. • Based on their masses and temperatures, our sample has been classified into three subtypes. It is composed of1530 A-, 710 W-, and 95 B-type CBs. • The period distribution reveals that B-type CBs represent a different evolutionary phase compared with the othersubtypes. A-type CBs have relatively longer periods than their W-type counterparts, tentatively suggesting thatA-type systems may be less evolved. • The distribution of total CB masses, M tot , and mass ratios define a strip in phase-space. It has a well-definededge at the lower M tot limit. Although the majority of A-type CBs also lie in the strip, there is some hintsuggesting a different distribution of A-type CBs. A large fraction of B-type CBs is located outside this strip. • It is likely that systematic differences in mass ratio and age exist between our large sample and other samplesused previously. The latter was limited to the solar neighborhood. • There are no significant differences among the PLRs of A- and W-type CBs. • We confirm that the PLR zero-point deviates toward brighter magnitudes as the q value decreases from q = 0 . q . This result mayhelp us improve the accuracy of the PLRs in future studies. • An automated approach to deriving CB properties such as that employed here is a powerful tool for applicationsto future large samples. Combined with other information, such as the ages of star cluster hosts, the fundamentalproperties of CBs can be used to understand their evolution and death throes.ACKNOWLEDGMENTSL.D. and R.d.G. acknowledge research support from the National Natural Science Foundation of China through grants11633005, 11473037, and U1631102. X.C. also acknowledges support from the National Natural Science Foundation ofChina through grant 11903045. The CSS is funded by NASA under grant NNG05GF22G issued through the ScienceMission Directorate Near-Earth Objects Observations Program. The Catalina Real-Time Transient Survey is supportedby the U.S. National Science Foundation (NSF) under grants AST-0909182 and AST-1313422. This work has madeuse of data from the European Space Agency’s (ESA)
Gaia
Gaia
Gaia
MultilateralAgreement. This research was made possible through the use of the AAVSO Photometric All-Sky Survey (APASS),funded by the Robert Martin Ayers Science Fund and NSF AST-1412587. The Guoshoujing Telescope (LAMOST)is a National Major Scientific Project built by the Chinese Academy of Sciences. Funding for the project has beenprovided by the National Development and Reform Commission. LAMOST is operated and managed by the NationalAstronomical Observatories, Chinese Academy of Sciences.9
Software:
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