NEW β LYRAE AND ALGOL CANDIDATES FROM THE NORTHERN SKY VARIABILITY SURVEY

Eclipsing binaries offer a unique opportunity to determine stellar parameters with a high degree of accuracy due to the constraints on the geometry of the system. Among other things, eclipsing binaries offer a direct measurement of the radius of each star if the period, inclination, and radial velocity of each star is known. The eclipsing binaries discussed here are generally β Lyrae and Algol-type systems. Algols are distinguished mainly by their light-curve shape, which features a near constant brightness outside of eclipse, and unequal primary and secondary minima. β Lyrae type eclipsing variables are usually distinguished by light curves that are continuously varying between eclipses due to ellipsoidal variations. Due to the difficulty in distinguishing between the two due to light-curve shape alone, both variable types will be referred to as "β Lyraes" in this paper.

β Lyrae type systems may contain binaries of very different evolutionary states. These states range from two main-sequence stars in tight orbits, to semidetached binaries with mass transfer, to binaries with a highly-evolved secondary and a less-evolved primary yielding large ellipticity effects. Some binaries classified as β Lyrae do not eclipse at all, with the light variation coming from the ellipticity effects alone. β Lyrae itself (β Lyrae A) is a complicated system that is not fully understood. It is generally believed that β Lyrae A is a mass-transferring system where the mass gainer is embedded in a thick accretion disc (Huang 1963). However, no published accretion disc model fits both photometric and spectroscopic data. Linnell (2000) proposed a thick accretion disc model with two temperatures which produces accurate fits to UBV photometry, yet still fails to fit IR light curves and some spectral features. Recent data suggest the presence of circumstellar dust and bipolar jets (Ak et al. 2007). Finding and observing more of these types of objects may help constrain some of the current models and address the complexities in other β Lyrae type systems.

Similar to β Lyrae type variables, systems of Algol-type may contain binaries in a wide variety of evolutionary states. However, the most common class of objects described as Algols are semidetached interacting binaries with a cool F-K giant or subgiant secondary star filling its Roche lobe and transferring mass onto a hot B-A dwarf. For many Algols it is believed that the current secondary star was originally the more massive primary star, but mass transfer has reversed their identities (Kopal 1955). Finding more of these types of Algols are important in understanding accretion structures and morphologies (Richards & Albright 1999). Another interesting subclass of Algol systems are the detached, low-mass, main-sequence pairs (M_1,2 < 1 M_☉, T < 5500 K), with only nine well-studied systems known at the beginning of 2007. As outlined by López-Morales (2007) (see their Table 2 and references therein), those systems reveal that the observed stellar radii are consistently ≈ 10% larger than that predicted by stellar models (Baraffe et al. 1998), possibly as a result of unaccounted-for effects due to metallicity and magnetic activity. Thus, finding more of these systems and obtaining multi-color light curves and radial velocity curves will allow for tighter constraints of stellar models.

The Robotic Optical Transient Search Experiment (ROTSE-I; Akerlof et al. 2000) was a project whose main goal was to detect the so-called orphan gamma-ray bursts (GRBs) and provide follow-up for high energy missions with rapid optical observations. With nearly a year in baseline, observations nearly nightly, and all-sky coverage, the project is an excellent resource for finding variable stars, and in particular short-period eclipsing binaries. The database contains about 14 million unique objects. After Fourier analysis and manual selection, to be discussed later, we have identified 448 new β Lyrae/Algol-type candidates. The majority of these candidates, as we will see, are β Lyrae type candidate variables, with the rest being Algol-type candidates. The current number of confirmed β Lyrae type systems is about 300 (Samus & Durlevich 2004), while the current number of confirmed Algol-type systems is about 500 (Budding et al. 2004). Thus if these candidates are confirmed, the number of known β Lyrae systems will greatly increase, while the number of Algol-type systems will increase modestly.

The data used in the analysis are from the ROTSE-I project, which is archived in the SkyDOT database (http://skydot.lanl.gov; Woźniak et al. 2004). ROTSE-I consisted of four Canon 200 mm lenses mounted on a single platform. Its combined field of view was about 16 × 16 deg², with a limiting magnitude of ∼15 and a saturation magnitude of ∼9.5 in unfiltered light. While awaiting notification of the detection of a GRB by earth-orbiting satellites, it acquired twice nightly unfiltered images of the entire northern sky. The initial data from ROTSE-I were released as the Northern Sky Variability Survey (NSVS) in 2004 (Woźniak et al.) and include digital sky images obtained from 1999 April 1 to 2000 March 30. Star positions in the NSVS catalog have errors of ∼0.3°, and blending normally occurs inside 84''. The NSVS database consists of about 2 terabytes of data with 225,000 separate images. Photometric calibration images were taken each night. Field-flattened images were then passed through a photometric reduction routine called Source Extractor (SExtractor; Bertin & Arnouts 1996) that produced light curves for about 14,000,000 objects.

Using the Two Micron All Sky Survey (2MASS), color information can be obtained for the β Lyrae type candidates. However, these colors were taken at random phases for all the candidate objects, and thus are most likely the colors outside of eclipse. Since many Algols have red giant companions, and the 2MASS survey was conducted in the near-IR, the resulting colors should be dominated by the red giant secondary.

To find candidate eclipsing binary systems, we first used some simple statistics already compiled in the SkyDOT database. Since the database has photometric errors as high as ∼0.08 at R = 13.5, we required at least a 0.1 mag standard deviation around the median magnitude in the object's light curve to be classified as a variable star candidate. We also required the median magnitude to be less than 13.5 to avoid low signal-to-noise (S/N) data, and require at least 30 observations of the object to exist in order for Fourier analysis to be reliable. The observations used do not have the standard NSVS error flags (Woźniak et al. 2004) as well as APINCOMPL (which rejects incomplete or corrupted aperture data).

We did not impose a bright magnitude limit (though ROTSE-I saturates at ∼9.5), as the minimum of 30 "good" observations is a sufficient selection criterion for bright stars. By imposing these simple conditions, the number of variable star candidates is immediately reduced from 14 million to around 100,000 objects.

The next step in the analysis method is to determine the period of the candidate. This is primarily done by Fourier analysis. A Fourier transform is taken of each candidate's light curve and the power spectrum is analyzed. The Fourier method used takes into account unevenly sampled data and is the same code used by McNamara (1987), developed by Scargle (1982) and Horne & Baliunas (1986). The periods implied by the top two power peaks and their closest two harmonics (half and twice the frequency) are then further analyzed using the phase dispersion minimization (PDM; Stellingwerf 1978) routine in the vicinity of the Fourier peaks. The PDM analysis identifies the correct period in almost all cases with the rest being caught by manual inspection. PDM is much more accurate and dependable than Fourier analysis when studying mainly nonsinusoidal waveforms such as Algol light curves because it is not sensitive to the shape of the light curve. However, PDM requires a large amount of computing power and is not practical for 100,000 objects. Thus, the PDM routine was only used to fine-tune the period. Many of the 100,000 variable star candidates are not variable stars, yet pass the previous tests. This is caused by the influence of nearby neighbors on the derived magnitudes or a few bad data points. Thus, an additional step must be made to eliminate candidates that do not have a well-defined period. This is done by taking the ratio of the strongest Fourier peak determined by previous methods to the 30th strongest peak. The 30th strongest peak is assumed to be a measure of the Fourier "noise." We determined, by trial and error that this ratio needs to be at least 1.5 for objects with orbital periods less than 50 days and 1.2 for periods greater than 50 days. This ensures a well-defined periodic structure to the light curve. Using the 30th strongest peak is somewhat arbitrary. However, the 30th peak is still among the relatively significant peaks, thus a peak with a ratio of 1.5 will be very significant. This method was chosen because we wanted as few false positives as possible while still generating many genuine variable star candidates. The ratio of 1.5 was determined by analyzing a sample of 100 known variable stars in the database and maximizing the number that were detected by the algorithm. Other methods such as taking the average Fourier signal level away from any peaks and sidelobes proved less effective because it is difficult to create a computer algorithm that can find this location in the Fourier spectrum, especially when the signal is multi-periodic. We acknowledge that many small amplitude variable star candidates will be missed by our process, but extracting them using our methods would have required sifting through significantly more false positives, and finding every small amplitude variable star is not the focus of this paper.

The previous steps produced roughly 10,000 variable star candidates. After sorting for period and making use of the magnitude ratio (MR; Kinemuchi et al. 2006), defined as

$$\begin{equation} {\rm MR} = \frac{\hbox{max.}\, \hbox{mag.}\, - \hbox{median}\, \hbox{mag.}}{\hbox{max.}\, \hbox{mag.}\, - \hbox{min.}\, \hbox{mag.}}, \end{equation} \tag{ 1 }$$

we were able to determine whether the variable star spends most of its time above or below the median magnitude. Eclipsing systems spend most of their time above the median magnitude, while pulsating stars tend to spend more time below the median or at least nearly equal time above and below. The analysis produced roughly 3000 candidate light curves that suggested they were eclipsing binaries and were then manually examined to pick obvious β Lyrae and Algol-type candidates. The most common possible misidentification is the confusion with W Ursa Majoris (W UMa) type binaries, especially with the relatively low signal-to-noise NSVS data. W UMa type systems generally have periods less than 1.2 days and β Lyrae variables generally have periods greater than 1.0 day, leading to some overlap in their periods. Algol-type variables can have periods less than a day, thus most of the possible confusion is between W UMa and Algol-type systems. RR Lyrae variables of the type RRc are also possible contaminants, as they can have similar light curves and periods to W UMa type systems if mistakenly identified with twice their period. The magnitude ratio and manual inspection were aimed to minimize contamination, as light curves with equal eclipse depths and continuous variation outside of eclipse are rejected as W UMa or RRc-type variables. RS CVn systems are another possible contaminant, as these light curves can appear similar to both RRc and β Lyrae variables. However, only the eclipsing RS CVn systems mimicking a β Lyrae system are probable contaminates, as those that do not eclipse and have somewhat sinusoidal light curves with long periods would not be misidentified as an Algol or β Lyrae. The actual period of a system could also be either twice or half that identified by the Fourier analysis. Some obvious misidentifications were corrected in the manual inspection process. However, if an Algol-type system lacks an obvious unequal secondary eclipse, it can be difficult to distinguish between that case and one where the primary and secondary eclipses have the same depth.

As a check on whether some candidates are misidentified W UMa type binaries, all candidates were modeled using the eclipsing light curve (ELC) code (Orosz & Hauschildt 2000). The ELC code utilizes a genetic algorithm, as outlined by Charbonneau (1995), in order to find best-fit solutions; the advantage is a complete, unbiased coverage of the entire solution space with rapid convergence. The parameters of interest for which we modeled were the temperatures, fill factors, mass ratio, and inclination of the systems. Since we have only a V-band light curve, we had to fix the temperature of the primary star, defined as the star which is furthest from the observer at phase 0.0 (primary eclipse), by using the 2MASS J − K color index and interpolating from the standard tables of Houdashelt et al. (2000) and Tokunaga (2000). The temperature of the secondary star was then left as a free parameter. The ELC code utilizes fill factors, defined as the volume fraction that a star occupies of its Roche Lobe, as the variable parameter to determine stellar radii. We allowed the fill factors for both stars to vary between 0.2 and 1.0. The mass ratio, defined as the mass of the primary star divided by the mass of the secondary star, was allowed to vary from 0.2 to 5.0, and the inclination was allowed to vary from 30° to 90°, with 90° representing an exactly edge-on system. Since the model atmospheres employed by the ELC code are loosely dependent on the surface gravity, we had to determine a plausible scale of the system. For this purpose only, we assumed for each system that the total mass was 2.0 M_☉, which coupled with the period obtained from the light curves allowed us to determine a physical orbital separation. For limb darkening, a square-root law was selected with coefficients taken from Van Hamme (1993). Gravity-darkening coefficients were automatically chosen by the code based on the models of Claret (2001). If the temperature of the primary was greater than 7100 K, the albedos of the stars were set to 1.0, otherwise they were set to 0.5.

The genetic algorithm used an initial population of 100 light curves with varying parameters. During each iteration, or "generation," the parameters were changed slightly and those light curves that more closely matched the target pattern were given more weight in the next generation. This process continued for 50 such generations. Resulting synthetic light curves were visually inspected and confirmed to have a good fit to the data; any light curves with poor fits were re-run with higher populations and more generations until a satisfactory fit was found. Candidates in which both fill factors are greater than 0.95 are interpreted as a highly likely W UMa system. The results from this analysis are shown in Figure 1.

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To identify low-mass, main-sequence Algol candidates, the ELC code was again used. Assuming an initial system mass of 2.0 solar masses, the orbital separation, a, can be calculated using the period from the Fourier analysis and Kepler's third law. Using the radius, R, from the ELC code, the fractional radius, f, of each component can be calculated, defined as f = R/a. Masses were then extracted using the models of Baraffe (1998) based on 2MASS temperatures and assuming [M/H] = 0.0 and an age of 1 Gyr. The separation was again computed using these masses, and final radii were computed by multiplying the fractional radii by the new separation. This analysis yielded 37 candidates with the characteristics of main-sequence eclipsing binaries.

After manual inspection of the light curves, the candidates' coordinates were queried in SIMBAD to check for previous identifications. Table 1 presents new β Lyrae/Algol-type candidates. The 409 stars in this table are absent from SIMBAD, the Combined General Catalogue of Variable Stars (CGCVS; Samus & Durlevich 2004), the New and Suspected Variable Star list,³ other recent major lists of suspected variables from the NSVS (Otero 2008; Damerdji et al. 2007), or their coordinates returned a nonvariable source from the SIMBAD. Almost all our variable stars are included in the Tycho-2 catalog (Hog et al. 2000), but not classified as variable. Table 1 columns include the right ascension (R.A.) and declination (decl.) of each object, the NSVS object identification number, its period determined by Fourier and PDM methods described above, the J − H, H − K, and K magnitudes extracted from the 2MASS database, the mean ROTSE unfiltered magnitude, the average photometric error of the object, the primary and secondary eclipse depths, the time of minimum of the deepest eclipse in MJD, and whether it is a low-mass binary candidate or W UMa contaminants according to the procedure discussed in the previous section. Table 2 shows what we call the "Refined" β Lyrae type systems. The 94 stars in this table fall in one or more of three categories: (1) the star was not classified as an Algol or β Lyrae variable in SIMBAD or the CGCVS, (2) the β Lyrae's period listed in the CGCVS differed significantly from the period derived in the present study, or (3) the system is listed as a variable star, but no period is given. The columns are the R.A., decl., NSVS ID, the period of the object (if any) from the CGCVS, the period we determined, the J − H, H − K, and K 2MASS magnitudes, the observed time of minimum, the CGCVS classification of the system, and our classification. Table 3 consists of 103 stars and includes the known β Lyrae/Algol-type variables extracted from the NSVS database with updated times of primary minimum. The columns include the R.A., decl., NSVS ID, reference period, our period, the time of minimum of the deepest eclipse in MJD, and the reference that lists the previously noted position and period of the object.

The majority of our candidates show continuous variation outside of eclipses, consistent with a β Lyrae classification. An example of such a system is shown in Figure 2. Light curves with little or no variation outside of eclipse, similar to Algol itself, are less common. An example of such a system is shown in Figure 3. Many light curves are somewhere between these two examples, where it is hard to determine if there are ellipsoidal variations present due to the photometric errors. In the manual inspection process we attempted to discard candidates with periods less than 1 day that had nearly equal eclipse depths and constant variation outside of eclipse as these were most likely W UMa type binaries. However, there is often uncertainty as to whether or not the light curve is flat outside of eclipse or if one eclipse is actually much deeper than observed due to poor temporal coverage and low S/N for faint eclipsors. An example of such a candidate is shown in Figure 4.

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One noteworthy object is NSVS 8574015, whose light curve is shown in Figure 5. This candidate is unusual because the variation outside of the primary eclipse is greater than what one would expect from photometric errors alone. This object was observed with the New Mexico State University's (NMSU) 1 m telescope, and it was found that the variations in the NSVS light curve are due to a pulsating component (Figure 6). The pulsating component is likely a δ Scuti-type variable of short (∼26 min) period.

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Another candidate that was identified as a β Lyrae, but later rejected, is NSVS number 7178256 (Figure 7). It has a light curve similar to that of the eclipsing pulsating system with unusual scatter outside of eclipse. However, this object is a recently discovered bright cataclysmic variable with a deep eclipse (Sing et al. 2007). Thus, our analysis method is capable of identifying other interesting, yet somewhat unrelated objects.

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We have identified 37 systems as candidate low-mass, main-sequence binaries. These are noted in Table 1, column 12. The mass–radius relation of each component of these systems is shown in Figure 8. The model of Baraffe et al. (1998) and the linear fit to our systems are plotted for comparison. Errors in the radius can be assumed to be roughly the scatter of the data. Multi-color light curves and radial velocity measurements are needed to confirm these candidates as low-mass binaries. An example light curve of one of these candidates is shown in Figure 9.

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There are a few defects with the analysis method used here. Long period and small eclipse depth Algol-type systems are not detected very well using our selection criteria. The reason for this is that most Algol-type systems vary little outside of eclipse, and thus have relatively short-lived minima that are sparsely sampled. Sparsely sampled minima and shallow primary eclipse candidates generally fail our 0.1 mag sigma cutoff. This leads to the majority of the candidates being the shorter-period β Lyrae type systems. Figure 10 shows a histogram of the orbital periods of known Algol-type systems from Budding et al. (2004) and would be our expectations if our candidates were mainly Algol-type systems. Figure 11 shows a histogram of the orbital periods of known β Lyrae type variables from Samus et al. (2004). The histogram of our candidates (Figure 12) more closely resembles that of Figure 11, indicating that our sample is mostly β Lyrae type variables, as expected. The only way to extract more Algol-type variables in the NSVS using the methods outlined here is to perform Fourier analysis on every object. Taking Fourier transforms on 100,000 objects would take an excessive amount of computer power, and therefore is beyond the scope of this investigation. However, our process would recover many of the Algol-type variables in databases with better temporal coverage and/or smaller photometric errors.

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The magnitude range of the NSVS means that the maximum observed primary eclipse depth can only be about 2 mag. Deeper eclipses would be truncated by the faint end of the sensitivity range. This means that the eclipse depth listed in the tables is a lower limit for objects with sparse data around the primary eclipse. A combination of both sparse data near eclipse and an outside of eclipse magnitude of 13 could lead to a misidentification of the object as another type of variable because the true eclipse depth is not observed. Comparing the primary eclipse depths of known Algol-type systems (Figure 13) to those in the present study (Figure 14), the deeper eclipsing systems are noticeably absent from our pool of candidates.

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As mentioned, there remains some confusion with W UMa type variables, thus some of our β Lyrae type candidates could in fact be W UMa systems. The ELC analysis returned 34 candidates with both fill factors greater than 0.95, which are likely W UMa systems. The shaded region in Figure 1 is the region corresponding the fill factors greater that 0.95, and thus the likely W UMa type candidates. These probable misidentifications are indicated in Table 1.

The times of minimum can also have some small errors in them due to the fact they were determined by picking the data point closest to the center of the eclipse, determined by eye. If such a data point does not exist, a time of minimum is determined by calculating the time shift needed from a nearby data point. Therefore, the times of the minimum given in the tables are not for high-precision work such as O − C studies, but can be used to roughly predict future eclipses.

We have successfully extracted 409 new β Lyrae/Algol candidates from the NSVS in the magnitude range of approximately 10–13. Additionally, 94 known variable stars were either reclassified or had their periods updated. A total of 606 β Lyrae/Algol-type candidates have times of primary minimum determined from the NSVS. We have identified 37 new low-mass, main-sequence eclipsing binaries in the database. If confirmed, the number of such systems will greatly increase. We note that Algol-type variables are not well sampled by our extraction technique, but β Lyrae type variables were easily identified. The remaining issues include the possibility of W UMa and RS CVn eclipsing systems in the candidate lists, but these misidentifications appear to be somewhat rare, as we identified only 31 stars that appear to be misidentified as W UMa type variable stars. The candidates extracted here require spectroscopic and additional photometric observations to confirm their β Lyrae/Algol classification.

This publication makes use of the data from the Northern Sky Variability Survey created jointly by the Los Alamos National Laboratory and University of Michigan. The NSVS was funded by the Department of Energy, the National Aeronautics and Space Administration, and the National Science Foundation.