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\IBVShead{5742}{15 December 2006}

\IBVStitle{Photometry of the Algol-type Binary Z Draconis}

\IBVSauth{Terrell, D.}

\IBVSinsto{Dept.\ of Space Studies, Southwest Research Institute,
1050 Walnut St., Suite 400,\\ \indent  Boulder, CO 80302, USA,
e-mail: terrell@boulder.swri.edu}

\SIMBADobj{Z Dra}
\IBVStyp{  EB  }
\IBVSkey{photometry}
\IBVSabs{BVRcIc photometry of the Algol-type binary Z Draconis is reported.}
\IBVSabs{Simultaneous analysis of the photometry and previously published}
\IBVSabs{radial velocities yields the absolute dimensions of M1 = 1.47 Msun,}
\IBVSabs{M2 = 0.43 Msun, R1 = 1.48 Rsun and R2 = 1.78 Rsun.}

\begintext

Ceraski (1903) first reported the eclipsing nature of Z Draconis, concluding that it was
an Algol-type binary. Russell \& Shapley (1914) analyzed the photoelectric observations
of Dugan (1912) and gave a rough estimate of a distance of 1000 light years for the system.
No other published light curves since that of Dugan appear to exist, although the system's
times of minimum have been reasonably well observed, as can be seen in the $O-C$ diagram
given by Kreiner et al.\ (2001) based on available times of minimum. Struve (1947)
measured radial velocities of the primary.

Z Dra was observed with a 0.25-m Schmidt--Cassegrain telescope and a Santa 
Barbara Instrument
Group ST-7XE CCD camera with $BVR_CI_C$ filters. Calibration (bias, dark, flat) and aperture 
photometry were done with IRAF (Tody, 1993).

Differential photometric observations were made on seven nights in the period 2005 February to 2005 March. GSC 4396-1170
was used as the comparison star and GSC 4396-0455 was the check star.  The Johnson $B-V$ values, based on Tycho
$B_T-V_T$ values transformed according to Bessell (2000), are $0.52 \pm 0.05$ for the comparison star and $0.80 \pm
0.12$ for the check star. The Johnson $B-V$ for the variable, again based on Tycho data, is $0.45 \pm 0.06$. The
standard deviation for comparison minus check observations was 0.02 magnitudes in $B$ and 0.01 magnitudes in $V$, $R_C$
and $I_C$. The instrumental differential magnitudes for Z Dra are available from the IBVS web site as 5742-t2.txt ($B$),
5742-t3.txt ($V$), 5742-t4.txt ($R_C$) and 5742-t5.txt ($I_C$).
\IBVSedata{5742-t2.txt} 
\IBVSedata{5742-t3.txt}
\IBVSedata{5742-t4.txt}
\IBVSedata{5742-t5.txt} 
\IBVSdataKey{5742-t2.txt}{Z Dra}{photometry}
\IBVSdataKey{5742-t3.txt}{Z Dra}{photometry}
\IBVSdataKey{5742-t4.txt}{Z Dra}{photometry}
\IBVSdataKey{5742-t5.txt}{Z Dra}{photometry}

The new photometric data and the radial velocities of Struve (1947) were analyzed simultaneously with the PHOEBE program
(Pr\v{s}a \& Zwitter, 2005 ) which uses the most recent release of the 2003 version the Wilson--Devinney program (WD;
Wilson \& Devinney, 1971; Wilson, 1979).  WD's mode 5 was employed, as appropriate for Algol-type binaries. The gravity
darkening exponents were fixed at 0.32 and the bolometric albedos were set to 0.5 for both stars. The logarithmic limb
darkening law was used with coefficients from Van Hamme (1993).The mean effective temperature of of the primary was
initially set equal to 8083 K based on the A5 spectral type given by Struve (1947) and the calibrations of Flower
(1996).  The reader should note that the temperatures are not accurate to 1~K as this figure might imply but are
uncertain by approximately 200~K. The resulting mass and radius of the primary were 1.49 $M_\odot$ and 1.49 $R_\odot$,
values that are significantly lower than expected for an A5 V star and more in line with an F4 V star, which is the
classification given in the GCVS. The Tycho and 2MASS colors of the system are also in better agreement with the later
spectral type, so another solution assuming $T_1=6725~K$ was performed and the results are presented in Table 1. The
derived value for the time derivative of the orbital period ($\dot{P}$) was adjusted to allow for a period difference
over the nearly six decades of time between the photometric and spectroscopic observations. The $O-C$ diagram of times
of minimum (Kreiner et al., 2001) shows complex behavior so the derived value of $\dot{P}$ is useful only as an
indicator of the long-term trend of the period changes.

Knowing the magnitude differences in $B$ and $V$ between the two components from the light curve solution, we can
compute the intrinsic $B-V$ of the system assuming the intrinsic $B-V$ of the primary (viz.\ Terrell et al., 2005).  An
F4 star should have a $B-V$ value of about 0.40. The resulting $B-V$ of the binary is 0.45, in excellent agreement with
the observed value, so the interstellar reddening toward Z Dra is small. The estimated distance to the system is $312
\pm 28$ pc, consistent with the value of $236 \pm 80$ pc determined by Hipparcos.

\begin{center}
{Table 1. Parameters for the light/velocity curve Sslution with $T_1=6725~K$} \vskip2mm 
\begin{tabular}{ccc}
\hline
Parameter & Value & Std. error$^\dag$\\ 
\hline
$a$ & 6.38 $R_{\odot}$ & 0.06 $R_{\odot}$ \\ 
$V_\gamma$ & $-31.3$ km sec$^{-1}$ & 0.3 km sec$^{-1}$ \\ 
$i$ & 87\fdeg00 & 0\fdeg09 \\ 
$T_2$ & 4149 K & 12 K \\ 
$q$ & 0.294 & 0.002 \\ 
$\Omega_1$ & 4.64 & 0.02 \\ 
$\mathrm{HJD}_0$ & 2453430.71662 & 0.00009 \\
$P$ & 1\fday3574179 & 0\fday000007 \\
$\dot{P}$ & $-1.7 \times 10^{-9}$& $6.5 \times 10^{-11}$ \\
$L_1/(L_1+L_2)_B$ & 0.958 & 0.002 \\
$L_1/(L_1+L_2)_V$ & 0.912 & 0.002 \\
$L_1/(L_1+L_2)_{R_C}$ & 0.866 & 0.003 \\
$L_1/(L_1+L_2)_{I_C}$ & 0.820 & 0.003 \\
$M_1$ & 1.47 $M_\odot$ & 0.04 $M_\odot$\\
$M_2$ & 0.43 $M_\odot$ & 0.01 $M_\odot$\\
$R_1$ & 1.48 $R_\odot$ & 0.01 $R_\odot$\\
$R_2$ & 1.78 $R_\odot$ & 0.02 $R_\odot$\\
\hline
\end{tabular}
\vskip2mm
\begin{tabular}{c}
{\normalsize $^\dag$ Formal errors from the differential corrections solution}
\end{tabular}
\end{center}

\IBVSfig{10cm}{5742-f1.eps}{$BVR_CI_C$ light curves of Z Dra and the fits from the Wilson--Devinney solution. The curves
have been shifted vertically for clarity.}
\IBVSfigKey{5742-f1.eps}{Z Dra}{light curve ; model light curve}

All of the light curves show a slightly elevated light level compared to the theoretical curves before the ingress of
the secondary eclipse. The mean light curve of Dugan (1912), gathered over approximately 3.5 years, appears to show the
same asymmetry, perhaps indicating that this is a persistent feature. The fit to the secondary eclipse in the B light
curve is poor and the fit to both eclipses in the $I_C$ curve is also poor. The $I_C$ light curve shows a strong
asymmetry between the two maxima.  The portion of the light curve between phases 0.6 and 0.9 is noticeably flatter than
that between phases 0.1 and 0.4. Some attempts at fitting a variety of single hot and cool spots were made but none
appeared to satisfactorily fit the asymmetries of all the light curves, indicating that a single spot model is
insufficient.

A high-resolution spectroscopic study of the system is sorely needed. Since the eclipses are partial, the photometric
mass ratio is questionable (viz.\ Terrell \& Wilson, 2005) thus making this a preliminary solution. Measurement of the
radial velocities of the secondary is crucial to alleviating the concern about the mass ratio. Further photometric
observations would reveal any temporal variability of the light curve asymmetries.

This work was supported by funding from the American Astronomical Society's Small Research Grants Program.

\references

Bessell, M. S. 2000, {\it PASP}, {\bf 112}, 961

Ceraski, A.V., 1903, {\it Astron.\ Nach.}, {\bf 161}, 159

Dugan, R.S., 1912, {\it Contr.\ Princeton Obs.}, {\bf 2}

Flower, P.J., 1996, {\it ApJ}, {\bf 469}, 355

Kreiner, J.M., Kim, C.-H., Nha, I.-S., 2001, An Atlas of $O-C$ Diagrams of Eclipsing 
Binary Stars, Cracow, Poland: Wydawnictwo Naukowe Akademii Pedagogicznej

Pr\u{s}a, A., Zwitter, T., 2005, {\it ApJ}, {\bf 628}, 426

Struve, O., 1947, {\it ApJ}, {\bf 106}, 92

Terrell, D., Munari, U., Zwitter, T., Wolf, G., 2005, {\it MNRAS}, {\bf 360}, 583

Terrell, D., Wilson, R.E., 2005, {\it ApSpSc}, {\bf 296}, 221

Tody, D., 1993, {\it ASP Conf.\ Ser.}, {\bf 52}, 173

Van Hamme, W., 1993, {\it AJ}, {\bf 106}, 2096

Wilson, R.E., 1979, {\it ApJ}, {\bf 234}, 1054

Wilson, R.E., Devinney, E.J., 1971, {\it ApJ}, {\bf 166}, 605

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