On The Period and Light Curve of the A-Type W UMa Binary GSC 3208 1986
aa r X i v : . [ a s t r o - ph . S R ] A p r COMMISSIONS G1 AND G4 OF THE IAUINFORMATION BULLETIN ON VARIABLE STARS
Volume 63 Number 6262 DOI: 10.22444/IBVS.6262 Konkoly ObservatoryBudapest27 March 2019
HU ISSN 0374 – 0676
ON THE PERIOD AND LIGHT CURVE OF THEA-TYPE W UMA BINARY GSC 3208 1986
EATON, JOEL A. ; ODELL, ANDREW P. ; POLAKIS, THOMAS A. Dept of Physics and Astronomy, NAU Box 6010, Flagstaff AZ 86011 USA; e-mail: WCorvi @ yahoo.com Command Module Observatory, 121 W. Alameda Dr., Tempe, AZ 85282 USA; e-mail: [email protected]
Abstract
We present a new period study and light-curve solutions for the A-Type W UMa binary GSC3208 1986. Contrary to a previous claim by R.G. Samec et al. of a rapidly decreasing period, thesystem’s period is increasing moderately on a timescale of 2E6 years. The light curve is variable onthe time scale of years, which can be understood by changes in how much it overfills its Roche lobe.
Contact binaries are binaries close enough that their components are enclosed in acommon, probably convective envelope (Lucy 1968). The best known members of thisclass are the W Ursae Majoris systems (Binnendijk 1970), although there are other rarerbinaries that may be in marginal contact (e.g., Ka lu˙zny 1983, 1986a–d; Siwak et al.2010). Binnendijk (pp. 218-221) defined two varieties of these W UMa systems, A-types,with transit primary eclipses, and W-types, with occultation primaries. Given the directdependence of the ratio of radii on mass ratio in contact binaries, these A- and W-typeclasses correspond to q = M / M less than and greater than 1.0, respectively.GSC 3308 1986 ( α (2000)=22 h m . s δ (2000)=+41 ◦ ′ . ′′
9) is a faint A-type W UMabinary observed and analyzed by Samec et al. (2015a; hereafter
SAMEC ). SAMEC obtainedfour nights of photometry ( σ B ≈ q =0.24, and that the staroverfills its Roche lobe by 39%. These properties are not surprising for such a system, but SAMEC also derived a very rapid period decrease , corresponding to a timescale of 3 × years. This seems unlikely for what they claim is an “ancient” contact system, especiallyif caused by magnetic braking, their favored period-change mechanism. EPHEMERIS:
Suspecting that the radical period decrease might result from R. G.Samec’s previously documented (Odell et al. 2011) error of confusing Modified Julian Date(Heliocentric Julian Date - 2,400,000.5) with Reduced Julian Date (HJD - 2,400,000.0)in data from the Northern Sky Variability Survey (NSVS, see Wozniak et al. 2004), weobtained the archival data from the NSVS and SuperWASP (SWASP, see Butters et al.2010) web sites. We have subsequently obtained new light curves for 2017 and 2018(Polakis; BVRI on the UBV/Cousins system; Table 1, given as file 6262-t1.txt on theIBVS web site) and added the published photometry of Liakos & Niarchos (2011) and
IBVS
SAMEC to give nine seasonal light curves. Using these, we find a very different result than
SAMEC . We have derived new effective times of minimum for these nine epochs by fittingthose seasonal light curves with the Wilson-Devinney code to measure phase shifts withrespect to the ephemeris of Eq. 1. These are listed in Table 2; the errors given are the σ ’scalculated by the W-D code multiplied by a factor of three per Popper (1984). Table 2. O − C Residuals for linear and quadratic elements (days)Epoch (Obs) Cycle (Obs-Calc) (Obs-Calc) Source of dataRJD (N) linear quadratic(Eq. 1) (Eq. 2)51464.1096 ± ± ± ± ± ± ± ± ± In analyzing the period, we first used a preliminary linear ephemeris derived by Odellfrom the NSVS plus Polakis 2017 data, namelyHJD T min
I = 2 , , . . × N , (1)to phase all the data into annual/seasonal light curves, then derived the deviations ofthe phases from this linear ephemeris with the W-D code as noted above, and then fitthose deviations with a second-order polynomial to determine the following quadraticephemeris:HJD T min I = 2 , , . . × N + 1 . × − × N . (2)In this equation the numbers in parentheses are errors in the last decimal place, and N isthe cycle number. Fig. 1 shows the deviations from Eq. 1 and the quadratic fit. SPECTRA:
Odell obtained two spectra of GSC 3208 1986 with the Boller&Chivens Spec-trograph on the Steward Observatory 90-inch telescope around 1 June 2015, specificallyat HJD 2,457,173.9734 (phase 0.55) and HJD 2,457,174.8694 (phase 0.76). These spectracovered the wavelength range 3900–4750 ˚A and are consistent with the F3 V spectral typeof
SAMEC . They give radial velocities for the components of RV =22.1 ± − forthe phase near conjunction and RV =86.9 ± − and RV =-298 ±
25 km s − for thequadrature. These values give a crude indication of the velocity amplitudes of the com-ponents, K =91 ±
16 km s − and K =294 ±
25 km s − with γ =-4 km s − . The resultingspectroscopic mass ratio q =0.30 ± ∼ consistent with the photometric mass ratio. LIGHT CURVE:
The extensive observations from SWASP give us the opportunity tosolve well-defined light curves for the three years, 2007, 2006, and 2004. The data for 2007are by far the best and most numerous, so we will concentrate on them. Consequently,we have formed 200 normal points derived from the roughly 11,300 SWASP observationsfor 2007, giving them in Table 3 (available through the IBVS website as )as orbital phase (based on Eq. 1), magnitude, and a standard deviation of the mean foreach magnitude. The typical normal point has an uncertainty of σ =0.0019 mag (S.D.), BVS Figure 1. (O-C) Diagram for GSC 3208 1986. nominally giving about the same total weight as the photometry published by
SAMEC , butthe SWASP data cover enough time to average out the typical wavelength-independentobservational errors of data taken on a mere four nights. These data represent a broadband in the optical, corresponding roughly to V of the U BV system. Fig. 2 shows theSWASP light curves for 2007 (Table 3) with a representation of the solution of Table 4plotted as a solid line.
Figure 2.
Light-Curve Solution for SWASP, normal points for 2007.
We have solved this light curve with the Wilson-Devinney code [2003 version; seeWilson & Devinney (1971); Wilson (1990,94)], finding the elements in the second col-umn of Table 4. These are roughly consistent with
SAMEC ’s solution (Table 4, Col. 4).In calculating this solution we adopted
SAMEC ’s temperature of the primary, convective
IBVS gravity darkening (Lucy 1967), convective reflection effect (Rucinski 1969), the Kurucz-atmospheres option in the W-D code, and a linear limb-darkening coefficient from VanHamme (1993). We accounted for a slight O’Connell effect in the normal points with asmall dark spot on the leading hemisphere of the primary component. The small χ indi-cates the model fits the data as well as can be expected. For completeness, we calculateda solution for 2007 with radiative gravity darkening and reflection effect, because in thepast there was some inkling that these hotter A-type systems might be radiative, but thefit was much worse, by a factor of two in χ . This radiative solution had a significantlylower fillout, 13%, as expected from the well-known correlation between fillout and gravitydarkening.The other two years of SWASP data had somewhat different light curves which wehave solved by varying those elements of the 2007 solution that might conceivably changeon the timescale of a few years. Some elements, such as q and i , cannot change materiallyon such a short timescale, so we are left with temperatures and fillout that might change.Keeping q , i , T fixed, we get the solution in Col. 3 of Table 4 for 2004. A greater depthof both eclipses in 2004 led to a larger overfilling of the Roche lobe. The solution for2006 had a marginally larger fillout, 39%, for the worst data of the three years ( σ =0.014mag). The differences between 2007 and 2004 might conceivably result from a change inthe photometric band of the observations, but it would require a shift at least as greatas from V to B between the two years. A shift of this magnitude is rather unlikely (seeButters et al. 2010, Fig. 1).All of these solutions imply that the standard overcontact model fits GSC 3208 1986well. Values of T mult , which measures the ratio of T as measured in W-D, Mode 3, to itsvalue for W-D, Mode 1, (no break in temperature at the neck between the components),are 1.0 for all practical purposes, so the temperature varies smoothly over the surface asdetermined by the gravity-darkening law. The solution for a radiative envelope, however,does not have this property and gives a significantly worse fit, so the envelope is not likelyto be radiative. Table 4.
GSC 3208 1986: Light-Curve SolutionsParameter 2007-SWASP 2004-SWASP 2012-SAMEC 2017-Polakis 2018-Polakis(1) (2) (3) (4) (5) (6) x = x (fixed) 0.51 0.51 Non-linear 0.63,0.51,0.41,0.33 0.63,0.51,0.41,0.33 g (fixed) 0.32 0.32 0.32 0.32 0.32 A bol (fixed) 0.50 0.50 0.50 0.50 0.50 i (deg) 85.60 ± ± q ( M / M ) 0.2424 ± ± ± ± ± ± ± ± ± ± ± ± T (K, fixed) 6875 6875 6875 6875 6875 T (K) 6757 ±
22 6789 ±
10 6760 ± ? 6745 ±
11 6725 ± T mult ± ± σ (mag) 0.0019/point 0.0066/point ∼ ∼ ∼ χ /DOF 1.2 1.1 ∼ ∼ ∼ r spot (deg) 1.7 1.7 T spot (black) (black) BVS You may have noticed that the quoted errors of our solution for 2007 and
SAMEC ’ssolution for 2012 are inconsistent, although the two data sets have roughly the same weight( σ ). This probably results from the way such uncertainties are calculated. If wecalculate the uncertainty of each element independently of all the others, we get values forthe 2007 SWASP solution similar to those quoted by SAMEC . However, if we let elements q , i , Ω, T , and the x ’s vary simultaneously, we get the uncertainties listed. Adding g and A bol to the mix gives even bigger uncertainties, doubling the reported uncertainty ofΩ. This result confirms Popper’s (1984) insinuation that the uncertainties derived by theW-D code are misleading. It also points to the intuitive truth that our assumptions aboutlimb darkening, gravity darkening, and reflection effect will inevitably bias the results forall these contact and near-contact binaries.ACKNOWLEDGMENTS: We thank Steward Observatory for allocating the telescopetime to obtain the spectra we used. This paper makes use of data from the DataRelease 1 of the WASP data (Butters et al. 2010) as provided by the WASP consor-tium, and the computing and storage facilities at the CERIT Scientific Cloud, reg. no.CZ.1.05/3.2.00/08.0144, which is operated by Masaryk University, Czech Republic. It alsouses data from the Northern Sky Variability Survey created jointly by the Los AlamosNational Laboratory and University of Michigan.References:Binnendijk, L., 1970, ARA&Ap , , 217 DOIButters, O. W. et al., 2010, A&A , L10 (SuperWASP)Ka lu˙zny, J., 1983,
AcA , , 345Ka lu˙zny, J., 1986a, AcA , , 105Ka lu˙zny, J., 1986b, AcA , , 113Ka lu˙zny, J., 1986c, AcA , , 121Ka lu˙zny, J., 1986d, PASP , , 662Liakos, A., Niarchos, P., 2011, IBVS , 5999, 2Lucy, L. B., 1967,
ZsfAp , , 89Lucy, L. B., 1968, ApJ , , 1123 DOIOdell, A.P., Wils, P., Dirks, C., Guvenen, B., O’Malley, C.J., Villarreal, A.S., Weinzettle,R.M., 2011, IBVS , 6001Popper, D. M., 1984, AJ , , 132 DOIRucinski, S.M., 1969, AcA , , 245Samec, R. G., Kring, J. D., Robb, R., Van Hamme, W., Faulkner, D. R., 2015a, AJ , ,90 ( SAMEC ) DOISamec, R. G., Benkendorf, B., Dignan, J. B., Robb, R., Kring, J., Faulkner, D. R., 2015b, AJ , , 146 DOISiwak, M., Zola, S., Koziel-Wierzbowska, D., 2010, AcA , , 305Van Hamme, W., 1993, AJ , , 2096 DOIWilson, R.E., Devinney, E.J., 1971, ApJ , , 605 DOIWilson, R. E., 1990, ApJ , , 613 DOIWilson, R. E., 1994, PASP , , 921 DOIWozniak, P. R. et al., 2004, AJ ,127