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\IBVShead{5994}{27 July 2011}

\IBVStitle{V456 Cyg -- A Detached Eclipsing Binary}

\IBVSauth{Nelson, Robert H.$^*$} 

\IBVSinsto{1393 Garvin Street, Prince George, BC, Canada, V2M 3Z1 email: b-o-b.nelson@shaw.ca [remove dashes]}
\IBVSinsto{$^*$Guest investigator, Dominion Astrophysical Observatory, Herzberg Institute of Astrophysics, National Research Council of Canada}

\SIMBADobj{V456 Cyg}

\begintext

V0456 Cyg [=TYC 3152-323-1 = AN 172.1935 = BD+38\deg 4107, 
RA = 20\hr 28\mm 50\fsec845, Dec = 39\deg 09\arcm 13\farcs69 (J2000)] 
was first reported to be variable by Morgenroth (1935) who 
classified it as an Algol-type and supplied a finder chart plus magnitude 
range, but no period.  The first available reference to a period is due to 
Savedoff (1951) who listed a period of 0.89 days for this system (amongst many 
others).  Whitney (1959) reported a much improved period of 0.8911906 days, not
far off the modern value of 0.8911956 days.  Wood and Forbes (1963) reported 
quadratic and even cubic parameters for the ephemerides for these and 332 other
systems, but modern period studies with photoelectric and CCD times of minima 
indicate a constant period for this system (Nelson 2011).  Zakirov and 
Eshankulova (2006) took UBVR photoelectric observations and apparently solved 
by Lavrov's Direct Method (no reference was given; paper is not available).

In September of the years 2006 and 2007 the author took eight medium resolution
(10~\AA/mm reciprocal dispersion) spectra at the Dominion Astrophysical 
Observatory (DAO) in Victoria, British Columbia, Canada; he then used the 
Rucinski broadening functions (Rucinski, 2004) to obtain radial velocity (RV) 
curves (see Nelson et al., 2006 and Nelson 2010 for details). The spectral range was
approximately 5005-5260 \AA. A log of DAO observations and RV results is 
presented in Table 1.

\begin{table}[h]
\caption{Observation log}
\small
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
DAO&Mid Time&Exposure&Phase at&V1&V2\\
Image \#&(HJD-2400000)&(sec)&mid-exp&(km/s)&(km/s)\\
\hline
13043&53988.8632&3600&0.758&148.8&-174.4\\
13045&53988.9063&3600&0.807&136.1&-164.5\\
13076&53989.8656&3600&0.883&95.6&-120.7\\
13151&53994.7636&3600&0.379&-101.2&116.6\\
13222&54000.8693&3600&0.230&-146.9&172.2\\
13224&54000.9114&3600&0.277&-146.6&172.5\\
11195&54366.7578&2718&0.789&147.9&-167.2\\
11254&54369.7784&3326&0.179&-129.3&153.9\\
\hline
\end{tabular}
\end{center}
\normalsize
\end{table}


On three nights in May of 2008, one night in August of 2008, and nine nights in
July of 2010, the author took a total of 151 CCD images of the field in B, 152 
in V and 148 in Rc (Cousins) at his private observatory in Prince George, 
British Columbia, Canada. The telescope was a 33cm f/4.5 Newtonian on a 
Paramount ME mount; the detector was a SBIG ST-7XME CCD cooled to -20\deg C.  
Reduction software was MIRA by Mirametrics, Inc., and either sky or box flats 
were used.  A list of the Variable (GSC 3152-323), Comparison (GSC 3152-491) 
and Check (GSC 3152-365) stars appears in Table 5 (available only 
electronically).

\IBVSetable{5994-t5.tex}

The following elements were used for phasing throughout (see Nelson, 2011 for 
the O-C relation):

$$	JD_{Hel} Min I = 54637.8691(19) + 0.89119559(17)d \times E $$

The author used the 2004 version of the Wilson-Devinney (WD) light curve and 
radial velocity analysis program with the Kurucz atmospheres (Wilson and 
Devinney, 1971, Wilson, 1990, Kallrath, et al., 1998) as implemented in the 
Windows software WDwint (Nelson, 2009) to analyze the data.  To get started, a
spectral type A2 (SIMBAD, no reference given) and a temperature T1 = 9000 $\pm$
150 K were used; interpolated tables from Cox (2000) which gave log g = 4.195 
were used; an interpolation program by Terrell (1994) gave the (van Hamme, 
1993) limb darkening values; and finally, a square root (LD=3) law for the 
extinction coefficients was selected, appropriate for hotter stars (Bessell, 
1979).  (The stated error in T1 corresponds to one half spectral sub-class.)  
At first, radiative envelopes were chosen for both stars, appropriate for 
hotter stars, but shifting to convective envelopes for star 2 gave a much 
better fit ($\Sigma \omega^{2}_{res}$ = 0.00559 for rad-conv versus $\Sigma \omega^{2}_{res}$ = 0.00808 for rad-rad). 
 The parameters are listed in electronic Table 6 (the last three columns are 
explained below).

\IBVSetable{5994-t6.tex}

Mode 2 (for detached stars) was chosen, based on the general appearance of the 
light curves.   Convergence by the method of multiple subsets was reached in a 
small number of iterations.  In particular, the mass ratio q = M2/M1 was held 
fixed because this value (0.8487 $\pm$ 0.0036) was well determined from the RV 
curves; in contrast, it is not well constrained from the photometric data.  

A plot of the B,V and R light curves, and WD fit is shown later. It is 
important at this stage to raise the issue that there was a problem in that the
derived values for absolute parameters such as mass and stellar radius.  They 
were simply too low to fit with the primary spectral type A2, and more closely 
fit those of a primary spectral type A8.  As indicated above, the spectral type
of A2 given in SIMBAD is without reference.  However, the quoted infrared 
magnitudes J = 10.244 and H = 10.17 (from the 2MASS survey) yield J-H = 0.074 
implying the spectral type of A2 (Covey, et al., 2007).  As there is no 
indication of a classification spectrum in the references, the spectral type 
must be regarded as uncertain.

Next, the lower primary temperature T1 = 7640 K (equivalent to A8 V spectral 
type) was adopted and new extinction coefficients produced (also listed in 
Table 6).  The usual runs in differential corrections mode were repeated and a 
new solution found.  In view of the uncertainty as to primary spectral type it 
seemed advisable to present both solutions.

A plot of the B,V and V light curves, and WD fit are shown in Figures 1 and 2; 
careful comparisons reveal only very slight differences in the fits.  The RVs 
are shown in Fig. 3. (the plots from the two models are almost identical) and a
three dimensional representation from Binary Maker 3 (Bradstreet, 1993) is 
shown in Fig. 4 (electronic only).

Third light was tested for and found to be insignificant.  Next, non-zero 
eccentricity was tested for; a value of 0.0016 +/- 0.0006 resulted.  This is a 
very low value and is worth ignoring.

Final WD output parameters for each model are listed in Table 2 for both models.

The WD output fundamental parameters and errors are listed in Table 3  
along with those from the properties of zero age main sequence stars (ZAMS; 
Cox, 2000).  Most of the errors are output or derived estimates from the WD 
routines. The error in q was derived from the rms deviations of points from the
best-fit double sine curves.  In estimating the distance, galactic extinction 
was allowed for using the formula \hfill\break
$A_V = 3 E(B-V) = R \times \lbrack (B-V)_{data} - (B-V)_{tables} \rbrack$.

This last method is relatively crude in that the colour index, B-V was taken 
from Tycho data; the stated error in each is 0.052 and 0.056 magnitudes, 
translating to $\pm$ 0.076 in the difference (but this may be a worst-case 
scenario).  The tabular values are uncertain to around 0.015 magnitudes 
(corresponding to one half a spectral sub-class), and lastly, the value R=3 is 
an approximation -- it varies from place to place and many authors favour the 
value 3.1.  This last uncertainty accounts for an error of only a few pc and is
therefore well within the error estimate of 56 or 57 pc for the distance.

\begin{table}
\caption{Final WD output parameters}
\small
\begin{center}
\begin{tabular}{|@{\hspace{3pt}}l@{\hspace{3pt}}|@{\hspace{3pt}}c@{\hspace{3pt}}|@{\hspace{3pt}}c@{\hspace{3pt}}|@{\hspace{3pt}}c@{\hspace{3pt}}|@{\hspace{3pt}}c@{\hspace{3pt}}|@{\hspace{3pt}}l@{\hspace{3pt}}|@{\hspace{3pt}}c@{\hspace{3pt}}|@{\hspace{3pt}}c@{\hspace{3pt}}|@{\hspace{3pt}}c@{\hspace{3pt}}|@{\hspace{3pt}}c@{\hspace{3pt}}|}
\hline
WD&Mod. 1&Mod. 1&Mod. 2&Mod. 2 & WD&Mod. 1&Mod. 1&Mod. 2&Mod. 2\\
Quantity&Value&Error&Value&Error & Quantity&Value&Error&Value&Error\\
\hline
T1 (K)&9000&170&7640&90 & V$_{\gamma}$ (km/s)&-0.50&0.19&-0.50&0.19\\
T2 (K)&7696&170&6667&90 & r1 (pole)&0.279&0.001&0.258&0.001\\
$\Omega_1$&4.398&0.01&4.696&0.01 & r1 (point)&0.298&0.001&0.271&0.001\\
$\Omega_2$&4.644&0.01&4.305&0.01 & r1 (side)&0.285&0.001&0.262&0.001\\
q = M2/M1&0.8487&0.0036&0.8487&0.0036 & r1 (back)&0.293&0.001&0.268&0.001\\
i (deg)&84.29&0.09&82.78&0.06 & r2 (pole)&0.236&0.001&0.260&0.001\\
L1/(L1+L2) (B)&0.739&0.001&0.666&0.001 & r2 (point)&0.247&0.001&0.278&0.001\\
L1/(L1+L2) (V)&0.704&0.001&0.634&0.001 & r2 (side)&0.240&0.001&0.265&0.001\\
L1/(L1+L2) (R)&0.681&0.001&0.608&0.001 & r2 (back)&0.245&0.001&0.274&0.001\\
a (solar radii)&5.712&0.007&5.730&0.008 & $\Sigma \omega^{2}_{res}$&0.00556&&0.00653&---\\
\hline
\end{tabular}
\end{center}
\normalsize
\end{table}

\begin{table}
\caption{Models 1 \& 2}
\small
\begin{center}
\begin{tabular}{|@{\hspace{2.5pt}}l@{\hspace{2.5pt}}|@{\hspace{2.5pt}}c@{\hspace{2.5pt}}|@{\hspace{2.5pt}}c@{\hspace{2.5pt}}|@{\hspace{2.5pt}}c@{\hspace{2.5pt}}|@{\hspace{2.5pt}}c@{\hspace{2.5pt}}|@{\hspace{2.5pt}}c@{\hspace{2.5pt}}|@{\hspace{2.5pt}}c@{\hspace{2.5pt}}||@{\hspace{2.5pt}}c@{\hspace{2.5pt}}|@{\hspace{2.5pt}}c@{\hspace{2.5pt}}|@{\hspace{2.5pt}}c@{\hspace{2.5pt}}|@{\hspace{2.5pt}}c@{\hspace{2.5pt}}|@{\hspace{2.5pt}}c@{\hspace{2.5pt}}|@{\hspace{2.5pt}}c@{\hspace{2.5pt}}|}
\hline
 & \multicolumn{6}{c}{Model 1}& \multicolumn{6}{c|}{Model 2} \\
\hline
Fund.&Star 1&Star 1&Star 1&Star 2&Star 2&Star 2 &Star 1&Star 1&Star 1&Star 2&Star 2&Star 2\\
Quantity&Tabular&WD&Error&Tabular&WD&Error &Tabular&WD&Error&Tabular&WD&Error\\
\hline
Sp. Type&A2 V&---&---&A8 V&---&--- &A8 V&---&---&F4 V&---&---\\
Temp. (K)&9000&9000&167&7640&7696&87 &7640&7640&87&6765&6664&58\\
Mass (M$_{\odot}$)&2.50&1.71&0.09&1.75&1.45&0.09 &1.75&1.73&0.04&1.44&1.46&0.03\\
Rad. (R$_{\odot}$)&2.09&1.63&0.008&1.58&1.37&0.008 &1.58&1.51&0.008&1.34&1.53&0.008\\
M bol&1.10&1.80&0.18&2.29&2.85&0.07 &2.29&2.68&0.08&3.40&3.25&0.08\\
Log g (cgs)&4.195&4.24&0.014&4.284&4.32&0.012 &4.284&4.32&0.002&4.342&4.23&0.002\\
Lum. (L$_{\odot}$)&25.7&15.7&1.6&7.60&5.97&0.42 &7.60&6.98&0.50&3.36&4.13&0.29\\
Dist. (pc)&---&496&57&---&---&--- &---&483&56&---&---&---\\
\hline
\end{tabular}
\end{center}
\normalsize
\end{table}


In conclusion, it seems clear that spectral type A8 on the ZAMS better fits the
derived mass for the primary star. Other quantities including the luminosity L
are well within bounds for a main-sequence star. On the other hand, star 2 
seems to be somewhat evolved, as its radius and luminosity are too high for a 
ZAMS star. Reference to triply-interpolated evolutionary tracks from the 
Geneva group reveal no fit at all for solar metallicity Z = 0.02 (Schaller et 
al., 1992)) but a possible fit for Z = 0.04 (Schaerer et al., 1993). Taking 
into account the estimated errors for L and T, an age between 0.5 and 1.00 Gy 
is feasible. There is no easy explanation as to how the stars could be at such 
disparate ages, however.


Acknowledgements:
It is a pleasure to thank the staff members at the DAO (especially Dmitry Monin
and Les Saddlemyer) for their usual splendid help and assistance.

\vskip -2mm

\IBVS2fig{7cm}{5994-f1.ps}{V456 Cyg: B,V and R Light Curves -- Data and WD Fit (Model 1)}{5994-f2.ps}{V456 Cyg: B,V and R Light Curves -- Data and WD Fit (Model 2)}
\IBVSfigKey{5994-f1.ps}{V456 Cyg}{light curve}
\IBVSfigKey{5994-f2.ps}{V456 Cyg}{light curve}

\vskip -3mm

\IBVSfig{6cm}{5994-f3.ps}{V465 Cyg: Radial Velocity Curves -- Data and WD Fit}
\IBVSfigKey{5994-f3.ps}{V456 Cyg}{radial velocity curve}

\IBVSefigure{5994-f4.ps}
\IBVSecomment{Binary Maker 3 representation of the system -- at phases 0.75 and 0.97}
\IBVSfigKey{5994-f4.ps}{V456 Cyg}{}

\IBVSetable{5994-t4.tex}

\vskip -5mm

\small

\references

Bessell, M.S., 1979, PASP, 91, 589

Bradstreet, D.H., 1993, in: Light Curve Modelling of Eclipsing Binary Stars, ed. Milone, E.F., (Springer, New York), 151  \BIBCODE{1993IAUCB..21..151B}

Covey, K.R., et al., 2007, Astron. J., 134, 2398

Cox, A.N., 2000, Allen's Astrophysical Quantities, 4th ed., (Athlone Press, London).

Kallrath, J., Milone, E.F., Terrell, D., and Young, A.T., 1998,  
ApJ, 508, 308.

Morgenroth, O., 1935, AN, 255, 425

Nelson, R.H. et al., 2006, IBVS 5715

Nelson, R.H., 2009, Software by Bob Nelson, \\
http://members.shaw.ca/bob.nelson/software1.htm

Nelson, R.H., 2010, in: The Alt-Az Initiative, Telescope Mirror \& Instrument Developments, eds.: R.M. Genet, J.M. Johnson and V. Wallen, (Collins Foundation Press, Santa Margarita, CA), 479

Nelson, R.H., 2011, Bob Nelson's O-C Files, 
http://www.aavso.org/bob-nelsons-o-c-files

Rucinski, S. M., 2004, IAU Symp., 215, 17

Savedoff, M.P., 1951, Astron. J., 56, 1

Schaller, G., Schaerer, D., Meynet, G., Maeder, A., 1992, A\&ASS 96, 269

Schaerer, D., Meynet, G., Maeder, A., Schaller, G., 1993, A\&ASS, 98, 523

Terrell, D., 1994, Van Hamme Limb Darkening Tables, vers. 1.1.

van Hamme, W., 1993, AJ, 106, 2096

Whitney, B.S., 1959, Astron. J., 64, 258

Wilson, R.E., Devinney, E.J., 1971, ApJ, 166, 605

Wilson, R.E., 1990, ApJ, 356, 613

Wood, B.D., Forbes, J.E., 1963, Astron. J., 68, 257

Zakirov, M.M., Eshankulova, M.U., 2006, Kinematika Fiz. Nebesn. Tel., 22, 363

\endreferences

\normalsize

\end{document}
