The variability of V2197 Cyg (NSVS 5761314, TYC 3167-1279-1), amongst many others, was discovered photographically by Margoni & Stagni (1984, hereafter M&S) who gave coordinates, magnitude ranges in B and V , finder charts for all 99 stars, elements (epoch, period), and preliminary light curves for about half the stars (but not for V2176 Cyg, their #58). Andronov et al. (1993) performed U,B, V,R, and I photometry of this and three other M&S stars; they went on in Andronov et al. (1994) to identify the system as an eclipsing variable, also giving the elements (including period = 0.46771 d) and eclipse duration. Skiff (1997) identified the M&S variables with those in the IRAS and GSC catalogues. Hoffman et al. (2008) provided an updated period, quoted 2MASS colours, and classified the system as \u3b2 Lyrae. Since then, there have been a number of eclipse timings but no light curve analysis.Peer reviewed: YesNRC publication: Ye

Nelson, Robert H.

Robb, Russell M.

Information Bulletin on Variable Stars

Robert H., Nelson

Russell M., Robb

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V2197 Cyg: a semi-detached eclipsing binary?

Robert H. Nelson

Russell M. Robb

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V2197 Cyg - A Semi-Detached Eclipsing Binary?

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COMMISSIONS G1 AND G4 OF THE IAUINFORMATION BULLETIN ON VARIABLE STARSVolume 63 Number 6203 DOI: 10.22444/IBVS.6203Konkoly ObservatoryBudapest06 April 2017HU ISSN 0374 – 0676V2197 Cyg – A SEMI-DETACHED ECLIPSING BINARY?NELSON, ROBERT H.1,2; ROBB, RUSSELL M.2,31 1393 Garvin Street, Prince George, BC, Canada, V2M 3Z1, email: bob.nelson@shaw.ca2 Guest investigator, Dominion Astrophysical Observatory, Herzberg Institute of Astrophysics, National Re-search Council of Canada3 Department of Physics and Astronomy, University of Victoria, Victoria, B.C., Canada, V8P 2W7The variability of V2197 Cyg (NSVS 5761314, TYC 3167-1279-1), amongst many oth-ers, was discovered photographically by Margoni & Stagni (1984, hereafter M&S) who gavecoordinates, magnitude ranges in B and V , finder charts for all 99 stars, elements (epoch,period), and preliminary light curves for about half the stars (but not for V2176 Cyg,their #58). Andronov et al. (1993) performed U, B, V, R, and I photometry of this andthree other M&S stars; they went on in Andronov et al. (1994) to identify the system asan eclipsing variable, also giving the elements (including period = 0.46771 d) and eclipseduration. Skiff (1997) identified the M&S variables with those in the IRAS and GSCcatalogues. Hoffman et al. (2008) provided an updated period, quoted 2MASS colours,and classified the system as β Lyrae. Since then, there have been a number of eclipsetimings but no light curve analysis.Light curve and radial velocity data have been acquired, but before any analysis couldbe performed, the first task was to examine the period variation. An eclipse timing differ-ence (O–C) plot using all available data and the elements of Kreiner (2004) is reproducedin Fig. 1.It will be seen that, even though all data are electronic (PE or CCD), there is a fairamount of scatter–larger than most of the error ranges. Clearly there must be unexplainedphysical reason for this discrepancy; future accurate data are required to sort out truerelationship. In the meantime, the line of best fit must suffice. In view of the fact thatall data were taken between cycles 7000 and 9000 (approximately), any errors due touncertainties in the period are likely to be small.A slightly different set of elements, specified in equation (1) was used in all phasing.JD (Hel) Min I = 2457514.9187(5) + 0.4657489(1)E (1)In August of 2012, the lead author took 82 frames in V , 79 in RC (Cousins) and 77in the IC (Cousins) band at his private observatory in Prince George, BC, Canada. Thetelescope was a 33 cm f/4.5 Newtonian on a Paramount ME mount; the camera was anSBIG ST-10XME. Standard reductions were then applied. The variable, comparison andcheck stars are listed in Table 1. The coordinates and magnitudes for all three stars are2 IBVS 6203Figure 1. V2197 Cyg – eclipse timing (O–C) diagram. Legend: filled circles – photoelectric; blackdiamonds – CCD. The open square represents a rejected reading.Table 1: Details of variable, comparison and check stars.Object GSC RA (J2000) Dec (J2000) V (mag) B − V (mag)Variable 3167-1279 20h50m16.s321 37◦56′45.′′29 12.04(17) +0.17(22)Comparison 3167-0649 20h50m32.s961 37◦57′48.′′77 10.47(4) +0.30(6)Check 3167-1451 20h50m13.s62 37◦55′54.′′3 11.66(na) 1.28(na)from the Tycho Catalogue (Hog et al. 2000) and the 2MASS catalogue, (Cutri et al. 2003),except for the magnitudes of the check star, for which there was no reference in SIMBAD.In September of 2011, 2013, and 2014, the lead author then took a total of 7 mediumresolution (R ∼ 10000 on average) spectra of V2197 Cyg at the Dominion AstrophysicalObservatory (DAO) in Victoria, British Columbia, Canada using the Cassegrain spec-trograph attached to the 1.85 m Plaskett Telescope. He used the 21181 grating with1800 lines/mm, blazed at 5000 Å giving a reciprocal linear dispersion of 10 Å/mm inthe first order. The wavelengths ranged from 5000 to 5260 Å, approximately. A log ofobservations is given in Table 2. (The last value for V2 listed in the table, –270.7 km/s,was not used in the modelling on the grounds that it was deviant by more than 3σ fromthe curve of best fit; however, it is plotted in Fig. 6 for reference.)Frame reduction was performed by software ‘RaVeRe’ (Nelson 2009). See Nelson etal. (2014) for further details.Radial velocities were determined using the Rucinski broadening functions (Rucinski2004; Nelson 2010b; Nelson et al. 2014). An Excel worksheet with built-in macros (writtenby him) was used to do the necessary radial velocity conversions to geocentric and back toheliocentric values (Nelson 2010a). The resulting RV determinations are also presentedin Table 2. For all the data, the results were corrected typically 5 % up to allow forthe small phase smearing. Correction was achieved by dividing the RVs by the factorf = (sinX)/X; whereX = 2π t/P , and where t denotes exposure time and P denotesthe orbital period. For spherical stars, this correction is exact; in other cases, it can beshown to be close enough for any deviation to fall below observational errors. The meanIBVS 6203 3Table 2: Log of DAO observations.DAO Mid Time Exposure Phase at V1 V2Image # (HJD−2400000) (sec) Mid-exp (km/s) (km/s)7849 55808.9875 3561 0.229 –148.0 +159.88141 55820.6522 3600 0.274 –142.0 +172.08153 55820.9065 3600 0.820 +89.4 –217.98217 55825.8105 2876 0.350 –134.4 +140.59629 56544.6973 3600 0.857 +77.8 –205.69638 56544.8504 3600 0.186 –131.0 +174.024359 56906.9975 3600 0.745 +97.9 –270.7rms errors for RV1 and RV2 were 9.1 and 14.0 km/s, respectively, and the overall rmsdeviation from the (sinusoidal) curves of best fit was 12.3 km/s. The best fit yielded thevalues K1 = 123.0(8) km/s, K2 = 214.3(1.1) km/s and Vγ = −30.8(6) km/s, and thus amass ratio qsp = K1/K2 = M2/M1 = 0.574(5).One of the authors (R.M.R.) obtained a spectrum of V2197 Cyg at the DominionAstrophysical Observatory (DAO) with the 1.85 m telescope and the 2131 Cassegrainspectrograph, operating at a reciprocal dispersion of about 60 Å/mm and 0.9 Å/px.The start time of the exposure was 2013 June 22 at UT+09:25:33 and lasted 666 s (JD2456465.8927), corresponding to phase 0.66. The strength of the G-Band and Hydrogenlines indicate F3(±1)V. A comparison spectrum of 48 Boo (F3V) observed with the sameconfiguration is plotted for comparison in Fig. 2, where the spectra have been scaled andoffset an arbitrary amount. The spectrum of V2197 Cyg has been smoothed with a 3point running average. The lines are (left to right) Ca II K-line, Ca II H-line blendedwith Hǫ, Hδ, and Hγ.Figure 2. Classification spectra.Next, the lead author (R.H.N.) used the 2003 version of the Wilson-Devinney (WD)light curve and radial velocity analysis program with Kurucz atmospheres (Wilson andDevinney 1971; Wilson 1990; Kallrath et al. 1998) as implemented in the Windows front-end software WDwint (Nelson 2009) to analyze the data. Using the spectral type of F3V,4 IBVS 6203Table 3: Limb darkening values from Van Hamme (1993) for T1 = 6820 K and T2 = 5037 K.Band x1 x2 y1 y2Bol 0.639 0.643 0.249 0.160V 0.696 0.797 0.284 0.107RC 0.622 0.735 0.291 0.165IC 0.537 0.647 0.280 0.183the tables of Cox (2000), and those of Flower (1996) gave a temperature T1 = 6820±200 Kand log g1 = 4.328 ± 0.012. (The quoted errors refer to one and one half spectral sub-classes.) An interpolation program by Terrell (1994, available from Nelson 2009) gave theVan Hamme (1993) limb darkening values; and finally, a logarithmic (LD = 2) law for thelimb darkening coefficients was selected, appropriate for temperatures < 8500 K (ibid.).The limb darkening coefficients are listed below in Table 3. (The values for the secondstar are based on the later-determined temperature of 5037 K and assumed spectral typeof K2.) Convective envelopes for both stars were used, appropriate for cool stars (hencevalues gravity exponent g = 0.32 and albedo A = 0.500 were used for each).From the shape of the light curve, it was clear that the system was in near contactbut the difference in the depths of the two minima indicate that the stars are not inthermal contact. Various modes were tried: mode 3 (contact), mode 2 (detached), mode 5(Algol) and, finally mode 6 (double contact). Convergence was obtained by the method ofmultiple subsets: (a, Vγ, L1), (T2, q), (i, T2) and (T2, Ω1). The net result was residuals (or,more correctly, sums of residuals squared) that were nearly identical, making it difficult tochoose between the scenarios. A useful procedure was to proceed with mode 6 (because thepotentials were fixed from the mass ratio, thereby reducing the number of free parameters),find the optimum using differential corrections, then switch to another mode, makingslight adjustments in potentials Ω1 and Ω2 as necessary to satisfy the conditions for thatmode, then proceeding with differential corrections once again. This led to the bestminimum. Mode 3 failed because differential corrections wanted increases in potentialΩ1 that would force star 1 inside the Roche lobe (i.e., Ω1 > Ωi where the latter is theinner critical potential), and in any case, the unequal depths of minima precluded thismode. Mode 2 (detached) also failed for the same reason, except that this time, differentialcorrections wanted potential Ω2 > Ωi, that is for the secondary to be at or inside the Rochelobe. Therefore only mode 5 (semi-detached) and mode 6 (double contact) remained.In the first set of iterations when the fit was near, the sigmas for each dataset wereadjusted, based on the output of WD (viz. computed from the sum of residuals for eachdataset plus number of points). The same values were then used throughout in order thatresults from the different iterations could be compared.It would seem that mode 5 (semi-detached) gave the best solution, but only by a verysmall margin. Also, in view of the errors in the data, it seems clear that another dataset might well favour a different mode. Therefore one cannot in confidence differentiatebetween the two modes. On the other hand, all produce virtually identical fundamentalparameters—certainly well within the estimated errors.Detailed reflections were tried, with nref = 2, but there was little—if any—differencein the fit from the simple treatment. There are certain uncertainties in the process (seeCsizmadia et al. 2013; Kurucz 2002). On the other hand, the solution is very weaklydependent on the exact values used.Solutions were tested for third light; suggested corrections were smaller than estimatedIBVS 6203 5Table 4: Wilson-Devinney parameters.WD Quantity Mode 5 Mode 6 error unitTemperature T1 6820 6820 [fixed] KTemperature T2 5037 5037 12 Kq = m2/m1 0.595 0.595 0.018 —Potential Ω1 3.0551 3.0542 0.063 —Potential Ω2 3.0542 3.0542 —Inclination, i 80.20 80.20 0.07 degSemi-maj. axis a 3.182 3.182 0.056 R⊙Syst. velocity, Vγ –25.2 –25.2 0.6 km/sPhase shift 0.0011 0.0011 0.0001 —L1/(L1 + L2) (V ) 0.8743 0.8744 0.0002 —L1/(L1 + L2) (RC) 0.8455 0.8456 0.0002 —L1/(L1 + L2) (IC) 0.8195 0.8197 0.0002 —r1 (pole) 0.3996 0.3997 0.0023 orb. rad.r1 (point) 0.5253 0.5532 0.1387 orb. radr1 (side) 0.4229 0.4231 0.0032 orb. rad.r1 (back) 0.4517 0.4519 0.0052 orb. rad.r2 (pole) 0.3136 0.3136 0.0022 orb. rad.r2 (point) 0.4468 0.4468 0.0085 orb. radr2 (side) 0.3277 0.3277 0.0024 orb. rad.r2 (back) 0.3599 0.3599 0.0023 orb. rad.∑ω2res 0.02513 0.02519 — —errors. Therefore third light was eliminated. In spite of the fact that spots might beexpected on one or other stars, no attempt was made to include them, as there was noneed. It seems likely that any indication of a spot occurring on the secondary would beoverwhelmed by the light of the primary.The two acceptable solutions are presented in Table 4. For the most part, the errorestimates are the formal errors provided by the WD routines and are known to be low;the actual errors may be several times the quoted ones. However, it is a common prac-tice to quote these estimates, and we do so now. Also, estimating the uncertainties intemperatures T1 and T2 is somewhat problematic. A common practice is to quote thetemperature difference over—say—1.5 spectral sub-classes (assuming that the classifica-tion is good to one spectral sub-class). In addition, various different calibrations havebeen made (Cox 2000, page 388–390 and references therein; and Flower 1996), and thevariations between the various calibrations can be significant. Here a spectral type (forstar 1) was determined to be F3(±1) sub-classes. Then the uncertainty over one andone half spectral sub-classes gives an uncertainty of ±200 K to the absolute temperaturesof each. The modelling error in temperature T2, relative to T1, is indicated by the WDoutput to be much smaller, around 12 K.The light curve data and the fitted curves are plotted in Figures 3–5. The residuals(in the sense observed-calculated) are also plotted, shifted upwards by 0.40 units.The radial velocities and the fit are plotted in Fig. 6. A three-dimensional representa-tion from Binary Maker 3 (Bradstreet, 1993) is depicted in Fig. 7.6 IBVS 6203Figure 3. V light curves for V2197 Cyg – data, WD fit, and residuals.Figure 4. RC light curves for V2197 Cyg – data, WD fit, and residuals.Figure 5. IC light curves for V2197 Cyg – data, WD fit, and residuals.IBVS 6203 7Figure 6. Radial velocity curves for V2197 Cyg – data and WD fit.Figure 7. Binary Maker 7 representation of the system – at phases 0.75 and 0.97.The WD output fundamental parameters and errors are listed in Table 5 using the datafrom the mode 5 solution (and are virtually identical with those from mode 6). From itstemperature, star 2 was assumed to be spectral class K2. Most of the errors are outputor derived estimates from the WD routines. From Kallrath & Milone (1999), the fill-outfactor is f = (ΩI −Ω)/(ΩI −ΩO), where Ω is the modified Kopal potential of the system,ΩI is that of the inner Lagrangian surface, and ΩO, that of the outer Lagrangian surface,was also calculated.To determine the distance r, the analysis proceeded as follows: first the WD routinegave the absolute bolometric magnitudes of each component; these were then convertedto the absolute visual (V ) magnitudes of both, MV,1 and MV,2, using the bolometriccorrections BC = –0.120 and –0.420 for stars 1 and 2 respectively. The latter were takenfrom interpolated tables constructed from Cox (2000). The absolute V magnitude wasthen computed in the usual way, getting MV = 3.39 ± 0.12 magnitudes. The apparentmagnitudes in the B and V passbands were B = 12.10 ± 0.01 mag and V = 11.65 ±0.01 mag (presumed errors), taken from the Andronov et al. (1993). The colour excess(in B–V) was obtained in the usual way, by subtracting the tabular value of B–V (for thatspectral class) from the observed value. This gave E[B–V ] = +0.07 ± 0.08 magnitudes.Hence, for the mode 5 solution, a distance r = 407 pc was calculated from the standard8 IBVS 6203Table 5: Fundamental parameters.Quantity Observed Tables error unitTemperature, T1 6820 6820 200 KTemperature, T2 5037 5026 200 KMass, m1 1.25 1.48 0.02 M⊙Mass, m2 0.75 0.74 0.01 M⊙Radius, R1 1.36 1.38 0.02 R⊙Radius, R2 1.07 0.80 0.02 R⊙Mbol,1 3.41 3.45 0.02 magMbol,2 5.24 5.98 0.02 maglog g1 4.27 4.33 0.01 cgslog g2 4.25 4.51 0.03 cgsLuminosity, L1 3.57 4.54 0.07 L⊙Luminosity, L2 0.66 0.36 0.01 L⊙Fill-out factor 1 –0.0003 — — —Fill-out factor 2 0 — — —Distance, r 407 — 50 pcrelation:r = 100.2(V −MV −AV +5) pc (2)The errors were assigned as follows: δMbol,1 = δMbol,2 = 0.02, δBC1 = 0.015, δBC2 =0.120 (the variation over 1.5 spectral sub-classes), δV = 0.02, all in magnitudes. Com-bining the errors rigorously (i.e., by adding the variances) yielded an estimated error inr of 51 pc.The distance estimate is in statistical agreement with the value of 320 ± 50 pc fromthe Gaia Catalogue1 (Gaia Collaboration 2016, Lindegren et al. 2016).For comparison, the tabular values for the fundamental parameters, taken from Cox(2000) for F3 and K2 main sequence stars, are given in Table 5. Of course, these applyto detached stars, which these are not; however, comparisons are useful. Star 1 is seen tobe undermassive and underluminous for F3 (and the same for F4 which has a tabulatedmass of 1.44 M⊙ and a luminosity of 4.04 L⊙) while star 2 has a larger radius (which isto be expected for one that fills its Roche lobe) and a higher luminosity (a function ofits larger radius). The luminosities are fairly close but display differences, as one wouldexpect for interacting stars.In conclusion, the fundamental parameters of this system have been determined, albeitto a somewhat lower level of precision than one would like, mostly due to the uncertaintyin the spectral class and the degree of interstellar absorption. Also, more accurate pho-tometric data might enable one to distinguish definitively between the various modes.Acknowledgements: It is a pleasure to thank the staff members at the DAO (especiallyDmitry Monin, David Bohlender, and the late Les Saddlmyer) for their usual splendidhelp and assistance.This work has made use of data from the European Space Agency (ESA) mission Gaia1https://www.cosmos.esa.int/web/gaia/gaia-dataIBVS 6203 9(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and AnalysisConsortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Fundingfor the DPAC has been provided by national institutions, in particular the institutionsparticipating in the Gaia Multilateral Agreement.The eclipse timing (O–C) Excel file may be found online at Nelson (2016).References:Andronov, I. L., Chinarova, L. L., Kolesnikov, S. V., Shakhovskoy, N. M.. Shvechkova,N. A., 1993, IBVS, No. 3933Andronov, I. L., Chikrigin, A. V., Kimeridze, G. N, 1994, Odessa Astron. Pub., 7, 89Bradstreet, D.H., 1993, “Binary Maker 2.0 – An Interactive Graphical Tool for Pre-liminary Light Curve Analysis”, in Milone, E.F. (ed.) Light Curve Modelling ofEclipsing Binary Stars, pp 151-166 (Springer, New York, N.Y.)Cox, A. N., ed, 2000, Allen’s Astrophysical Quantities, 4th ed., (Springer, New York, NY)Csizmadia, S., Pasternacki, T., Dreyer, C., Cabrera, A., Erikson, A., Rauer, H., 2013,A&A, 549, A9 DOICutri, R.M., et al., 2003, VizieR On-line Data Catalog: II/246Flower, P. J., 1996, AJ, 469, 355 DOIGaia Collaboration, Prusti, T. et al. 2016, A&A, 595, A1 DOIHoffman, D. I., Harrison, T. E., Coughlin, J. L., McNamara, B. J., Holtzman, J. A, TaylorG. E., and. Vestrand, W. T., 2008, AJ, 136, 1067 DOIHøg, E., et al., 2000, A&A, 355, L27Kallrath, J., Milone, E. F., 1999, Eclipsing Binary Stars–Modeling and Analysis (Springer-Verlag)Kallrath, J., Milone, E.F., Terrell, D., and Young, A.T., 1998, ApJ, 508, 308 DOIKreiner, J.M., 2004, AcA, 54, 207Kurucz, R.L., 2002, Baltic Astron., 11, 101Lindegren, L. et al., 2016, A&A, 595, A4 DOIMargoni, R., Stagni, R., 1984, A&AS, 56, 87Nelson, R.H., 2009, Software, http://www.variablestarssouth.org/profilegrid blogs/software-by-bob-nelson/Nelson, R.H., 2010a, Spreadsheets, http://www.variablestarssouth.org/profilegrid blogs/spreadsheets-by-bob-nelson/Nelson, R.H., 2010b,“Spectroscopy for Eclipsing Binary Analysis” in The Alt-Az Initia-tive, Telescope Mirror & Instrument Developments (Collins Foundation Press, SantaMargarita, CA), R.M. Genet, J.M. Johnson and V. Wallen (eds)Nelson, R.H., 2016, Bob Nelson’s O–C Files, http://www.aavso.org/bob-nelsons-o-c-filesNelson, R. H., Şenavcı, H.V. Baştürk, Ö., Bahar, E., 2014, New Astron., 29, 57 DOIRucinski, S. 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V2197 Cyg - A Semi-Detached Eclipsing Binary?

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