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\begin{document}

\IBVShead{5612}{4 March 2005}

\IBVStitle{UBVRI Analysis of the Eclipsing Binary V1128 Tauri}

\IBVSauth{Hawkins, Nathan C.$^{1,2}$; Samec, Ronald G.$^{1,2}$; Van Hamme, Walter$^4$; Faulkner, Danny R.$^{2,3}$}

\IBVSinst{Astronomy program, Department of Physics Bob Jones University, Greenville, SC 29614, USA}
\IBVSinst{Visiting Astronomer, SARA Observatory, Kitt Peak, AZ}
\IBVSinst{U of South Carolina, Lancaster, SC}
\IBVSinst{Florida International University, Miami, Fl}

\SIMBADobj{V1128 Tau}

\begintext

\vspace*{-1cm}

As a part of our study for solar-type eclipsing binaries, we observed the variable 
V1128 Tauri [GSC 664 694, HIP 17878; $\alpha$(2000)= 03\hr 49\mm 27\fsec8, $\delta$(2000)= +12\deg 54\arcm 44\arcs].  
The variability of V1128 Tau was discovered by HIPPARCOS (ESA 1997).  According to the TYCHO 
catalog (ESA 1997), V1128 Tau is a solar-type binary, with a spectral type of G0.  Our preliminary
standard star work has confirmed this. We obtained a $B-V = 0.606 \pm 0.039$. 
Timings of minimum light have been published by Heged\"us et al. (2003), and Tas et al. (2003).  
Tas et al. give the following ephemeris:
\begin{equation}
{\rm HJD\ Tmin\ I} = 2452236.060963 \pm 0.000014 + (0.30537332 \pm 0.00000002
{\rm d)\times E}.
\end{equation}

Our observations were made with the Southeastern Association for Research in Astronomy (SARA) 0.9-m reflector 
and AP7 CCD at Kitt Peak, on 24-27 December, 2003, by RGS, DRF, and NCH.  Standard $UBVR_CI_C$ filters were used.  
Between 70 and 100 high precision observations were taken in each pass band.  The stars [GSC 664 1304, HIP 17876, $\alpha$(2000)= 03\hr 49\mm 27\fsec5, $\delta$(2000)= +12\deg 54\arcm 32\arcs, $B-V = 0.726 \pm 0.052$] and 
[GSC 666 710, $\alpha$(2000) = 03\hr 49\mm 38\fsec7, $\delta$(2000)= +12\deg 54\arcm 01\arcs, $B-V = 0.854 \pm 0.072$] were used as 
the comparison and check stars, respectively.  A finding chart for V1128 Tau, the comparison star, and 
check star is given as Figure 1.  The light curves are given in Figure 2, 
as normalized flux versus phase.

Three precision mean epochs of minimum light were determined from eclipse timings in all five pass bands, 
using parabola fits: HJD Tmin I = 2453000.6523 $\pm$ 0.0002 and HJD Tmin II = 2452998.6665 $\pm$ 0.0002 and
2453000.8044 $\pm$ 0.0003. From our observations, we calculated the following linear ephemeris, which we 
then used to phase our data:
\begin{equation}
{\rm HJD\ TMin\ I} = 2453000.6522 \pm 0.0004 + 0.30530 \pm 0.00009 
{\rm \times E}
\end{equation}
A linear fit to all available timings of minimum light gives:
\begin{equation}
{\rm HJD\ TMin\ I} = 2453000.6533 \pm 0.0001 + 0.305373219 \pm 0.000000037 
{\rm \times E}
\end{equation}

Due to the fact that the $O-C$ plot seemed to indicate a period change, we also calculated a quadratic fit 
to all available timings:
\begin{equation}
{\rm HJD\ Tmin\ I} = 2453000.6525 \pm 0.0002 + 0.30537273 \pm 0.00000011 
\times {\rm E}  
\end{equation}
$$\hspace*{7cm}- 0.000000000034(\pm 0.000000000007) \times {\rm E}^2$$
 

\IBVSfig{9cm}{5612-f1.eps}{}
\IBVSfigKey{5612-f1.eps}{V1128 Tau}{finding chart}


Figure 3 gives the $O-C$'s calculated from the linear portion of equation (4), with the quadratic 
term shown overlaying.  The plot shows indications of a variable, decreasing period, just as one would 
expect in the case solar-type binaries due to magnetic braking.  Although the timings cover only about
15000 orbits, the quadratic term is already very significant.  A complete table of minima and linear and
quadratic residuals are given as Table 1. The linear residuals are calculated from equation (3) and
the quadratic ones are calculated from equation (4). Further observations, as well as archival searches 
for photographic minima, are needed to confirm this behavior.

To arrive at an independent solution, we first pre-modeled with Binary Maker 2.0 (Bradstreet 1992) and obtained 
preliminary solutions in all five pass bands independently.  Both detached and semi-detached configurations 
were tested.  Parameters derived from the initial Binary Maker solutions were then used as the starting 
values for a simultaneous 5-color synthetic light curve solution using the Wilson Code (Wilson \& Devinney 
1971, Wilson 1990, 1994).

Our solution indicates that the system is a W-type W UMa system; the cooler star is almost twice the 
mass of the hotter component ($m2/m1 = 1.944 \pm 0.004$). The mass ratio is constrained by the totality of 
the primary eclipse.  The W-type phenomena is indicative of strong (saturated) magnetic activity on the 
primary component, which masks the true temperature of the star.  The components fill their Roche lobe 
to only 18.5\%.  Other parameters include the temperatures, $T_1$ = 6000 K (fixed) and $T_2$ = 5830 K, 
and orbital inclination of 85\deg. 

The observed O'Connell effect is more evidence for magnetic spot activity; our model includes a single 
large magnetic region on the surface of the secondary, less massive component, with a mean temperature 
factor of 0.89 of the surface temperature (5220 K).  The position and size of the region is given 
by the parameters: co-latitude = 125\deg, longitude = 266\deg, and radius = 25\deg.


\begin{table}
\normalsize
\centerline{{\bf Table 1:} Epochs of Minimum Light, V1128 Tau}
\begin{center}
\begin{tabular}{rrrrcl}
\hline
        Epochs &        &   Linear  &  Quadratic &         & \\
        2400000+ &  Cycles&  Residuals&  Residuals &  Weight & Reference\\
\hline
       48500.0620	& $-$14738.0  	& $-$0.0008    	& 0.0001   	& 1.0	& ESA 1997\\
       51822.5237 	& $-$3858.0   	& 0.0002    	& $-$0.0003   	& 1.0	& Heged\"us et al. 2003\\
       51830.4633 	& $-$3832.0   	& 0.0001    	& $-$0.0004   	& 1.0	& Heged\"us et al. 2003\\
       51830.6165 	& $-$3831.5   	& 0.0007     	& 0.0001   	& 1.0	& Heged\"us et al. 2003\\
       52236.4578 	& $-$2502.5   	& 0.0009     	& 0.0008   	& 1.0	& Tas et al. 2003\\
       52236.4578 	& $-$2502.5   	& 0.0010     	& 0.0008   	& 1.0	& Tas et al. 2003\\
       52236.6096 	& $-$2502.0   	& 0.0000    	& $-$0.0002   	& 1.0	& Tas et al. 2003\\
       52236.6101 	& $-$2502.0   	& 0.0005     	& 0.0004   	& 1.0	& Tas et al. 2003\\
       52240.4271 	& $-$2489.5   	& 0.0004     	& 0.0002   	& 1.0	& Tas et al. 2003\\
       52240.4274 	& $-$2489.5   	& 0.0007     	& 0.0005   	& 1.0	& Tas et al. 2003\\
       52248.3670 	& $-$2463.5   	& 0.0006     	& 0.0004   	& 1.0	& Tas et al. 2003\\
       52248.3672 	& $-$2463.5   	& 0.0008     	& 0.0006   	& 1.0	& Tas et al. 2003\\
       52254.3201 	& $-$2444.0  	& $-$0.0011    	& $-$0.0013   	& 1.0	& Tas et al. 2003\\
       52254.3205 	& $-$2444.0  	& $-$0.0007    	& $-$0.0008   	& 1.0	& Tas et al. 2003\\
       52258.2906 	& $-$2431.0  	& $-$0.0005    	& $-$0.0006   	& 1.0	& Tas et al. 2003\\
       52258.2906 	& $-$2431.0  	& $-$0.0004    	& $-$0.0006   	& 1.0	& Tas et al. 2003\\
       52258.4440 	& $-$2430.5   	& 0.0003     	& 0.0001   	& 1.0	& Tas et al. 2003\\
       52258.4444 	& $-$2430.5   	& 0.0006     	& 0.0005   	& 1.0	& Tas et al. 2003\\
       52263.3298 	& $-$2414.5   	& 0.0001     	& 0.0000   	& 1.0	& Tas et al. 2003\\
       52263.3301 	& $-$2414.5   	& 0.0004     	& 0.0002   	& 1.0	& Tas et al. 2003\\
       52263.4819 	& $-$2414.0  	& $-$0.0005    	& $-$0.0007   	& 1.0	& Tas et al. 2003\\
       52263.4819 	& $-$2414.0  	& $-$0.0005    	& $-$0.0006   	& 1.0	& Tas et al. 2003\\
       52277.2233 	& $-$2369.0  	& $-$0.0009    	& $-$0.0011   	& 1.0	& Tas et al. 2003\\
       52277.2235 	& $-$2369.0  	& $-$0.0007    	& $-$0.0009   	& 1.0	& Tas et al. 2003\\
       52277.3762 	& $-$2368.5  	& $-$0.0007    	& $-$0.0008   	& 1.0	& Tas et al. 2003\\
       52277.3771 	& $-$2368.5   	& 0.0002     	& 0.0000   	& 1.0	& Tas et al. 2003\\
       52277.3772 	& $-$2368.5   	& 0.0003     	& 0.0001   	& 1.0	& Tas et al. 2003\\
       52313.2582 	& $-$2251.0  	& $-$0.0001    	& $-$0.0002   	& 1.0	& Tas et al. 2003\\
       52314.3272 	& $-$2247.5   	& 0.0001     	& 0.0000   	& 1.0	& Tas et al. 2003\\
       52315.2437 	& $-$2244.5   	& 0.0006     	& 0.0005   	& 1.0	& Tas et al. 2003\\
       52536.4871 	& $-$1520.0   	& 0.0011     	& 0.0012   	& 1.0	& Tas et al. 2003\\
       52536.4872 	& $-$1520.0   	& 0.0011     	& 0.0013   	& 1.0	& Tas et al. 2003\\
       52563.5116 	& $-$1431.5   	& 0.0000     	& 0.0002   	& 1.0	& Tas et al. 2003\\
       52563.5119 	& $-$1431.5   	& 0.0003     	& 0.0005   	& 1.0	& Tas et al. 2003\\
       52565.3429 	& $-$1425.5  	& $-$0.0010    	& $-$0.0008   	& 1.0	& Tas et al. 2003\\
       52565.3435 	& $-$1425.5  	& $-$0.0003    	& $-$0.0001   	& 1.0	& Tas et al. 2003\\
       52565.4967 	& $-$1425.0   	& 0.0002     	& 0.0003   	& 1.0	& Tas et al. 2003\\
       52565.4968 	& $-$1425.0   	& 0.0003     	& 0.0005   	& 1.0	& Tas et al. 2003\\
       52565.4976 	& $-$1425.0   	& 0.0011     	& 0.0013   	& 1.0	& Tas et al. 2003\\
       52565.4977 	& $-$1425.0   	& 0.0012     	& 0.0014   	& 1.0	& Tas et al. 2003\\
       52608.2474 	& $-$1285.0  	& $-$0.0013    	& $-$0.0011   	& 0.5	& Tas et al. 2003\\
       52608.2484 	& $-$1285.0  	& $-$0.0003    	& $-$0.0001   	& 0.5	& Tas et al. 2003\\
       52608.4011 	& $-$1284.5  	& $-$0.0004    	& $-$0.0001   	& 1.0	& Tas et al. 2003\\
       52608.4013 	& $-$1284.5  	& $-$0.0001    	& 0.0001   	& 0.5	& Tas et al. 2003\\
       52998.6665    	& $-$6.5  	& $-$0.0019    	& $-$0.0011   	& 1.0	& Present Observations\\
       53000.6523     	& 0.0  	        & $-$0.0010	& $-$0.0002   	& 1.0	& Present Observations\\
       53000.8044     	& 0.5  	        & $-$0.0016    	& $-$0.0008   	& 1.0	& Present Observations\\
\hline
\end{tabular}
\end{center}
\end{table}



\IBVSfig{20cm}{5612-f2.eps}{}
\IBVSfigKey{5612-f2.eps}{V1128 Tau}{light curve}


\IBVSfig{9cm}{5612-f3.eps}{}
\IBVSfigKey{5612-f3.eps}{V1128 Tau}{O-C diagram}


Our solution is shown overlaying the phased, flux-normalized data in Figure 2; while a geometrical 
representation of V1128 Tau is given in Figure 4. Out tabled solution is given in Table 2. 
Tas et al. (2003) has published a large collection of B,V data using 3 different telescopes and 
detectors over two observing seasons. A Wilson solution was calculated on the combined curves. 
Their solution is of W-type with an inclination of 85\deg\ and a mass ratio of $m1/m2 = 2.2$. They also 
showed asymmetries in the light curves indicating spot activity in the system. The differences between Tas et al. (2003) and the present
solution arise due to a combination of the following factors. Tas et al.'s (2003) solutions are based only 
on B and V observations, while ours is based on $UBVR_CI_C$, thus giving a better fix on the parameters, 
especially those related to temperature. They used one dimensional limb darkening coefficients, 
while we used two dimensional coefficients as well as bolometric albedos. Tas et al.'s (2003) choice of 
coefficients was different from ours. We used Van Hamme's coefficients which are included with the 
Wilson code based on Kurucz atmospheres and the temperature of the primary component.  
Our primary component temperature was fixed at 6000 K, better reflecting its K0 spectral type. 
We also allowed our spot to adjust in latitude. Also, it is best not to combine
light curves from different seasons for active W UMa binaries.

\bigskip

We wish to thank the Southeastern Association for Research in Astronomy (SARA) for their allocation 
of observing time, as well as NASA and the American Astronomical Society for their continued support 
of our undergraduate research programs through their small research grants.

\newpage

\IBVSfig{6cm}{5612-f4.eps}{}
\IBVSfigKey{5612-f4.eps}{V1128 Tau}{other}

\begin{table}[!hb]
\centerline{{\bf Table 2:} Synthetic light curve parameters for V1128 Tau}
\begin{center}
\begin{tabular}{cc}
\hline
$\lambda_{\rm B}$, $\lambda_{\rm V}$, $\lambda_{\rm R}$, $\lambda_{\rm I}$ (nm) & 360, 440, 550, 640, 790\\
x$_{\rm 1U}$, x$_{\rm 2U}$, y$_{\rm 1U}$, y$_{\rm 2U}$ &  0.872, 0.872, 0.143,0.143\\
x$_{\rm 1B}$, x$_{\rm 2B}$, y$_{\rm 1B}$, y$_{\rm 2B}$ &  0.829, 0.829, 0.185,0.185\\
x$_{\rm 1V}$, x$_{\rm 2V}$, y$_{\rm 1V}$, y$_{\rm 2V}$ &  0.745, 0.745, 0.256,0.256\\
x$_{\rm 1R}$, x$_{\rm 2R}$, y$_{\rm 1R}$, y$_{\rm 2R}$ &  0.653, 0.653, 0.269,0.269\\
x$_{\rm 1I}$, x$_{\rm 2I}$, y$_{\rm 1I}$, y$_{\rm 2I}$ &  0.56, 0.56, 0.26, 0.26\\
g$_1$ , g$_2$           &  0.32, 0.32\\
A$_1$ , A$_2$           &  0.500, 0.500\\
xbol$_1$ , xbol$_2$     &  0.647 , 0.647\\
ybol$_1$ , ybol$_2$     &  0.221 , 0.221\\
Inclination       &  84\fdeg92 $\pm$ 0\fdeg06\\
T$_1$, T$_2$ (K)        &  6000, 5828 $\pm$ 1\\
$\omega_1$,$\omega_2$ &  5.061 $\pm$ 0.001\\
q (m$_2$/m$_1$)         &  1.944 $\pm$ 0.001\\
pshift                  &  0.998 $\pm$ 0.001\\
L$_1$/(L$_1$+L$_2$)U &  0.402 $\pm$ 0.009\\
L$_1$/(L$_1$+L$_2$)B &  0.394 $\pm$ 0.008\\
L$_1$/(L$_1$+L$_2$)V &  0.386 $\pm$ 0.009\\
L$_1$/(L$_1$+L$_2$)R &  0.382 $\pm$ 0.007\\
L$_1$/(L$_1$+L$_2$)I &  0.377 $\pm$ 0.009\\
r$_1$, r$_2$ (pole)  &  0.312 $\pm$ 0.001, 0.422 $\pm$ 0.001\\
r$_1$, r$_2$ (side)  &  0.327 $\pm$ 0.001, 0.450 $\pm$ 0.001\\
r$_1$, r$_2$ (back)  &  0.367 $\pm$ 0.005, 0.482 $\pm$ 0.002\\
fill-out             &  18.5 $\pm$ 0.1\%\\
Spot Parameters:     &  Primary Component\\
Colatitude           &  125\deg $\pm$ 1\deg\\
Longitude            &  266\deg $\pm$ 1\deg\\
Spot radius          &  25\fdeg0 $\pm$ 0\fdeg3\\
Temperature factor   &  0.998 $\pm$ 0.001\\
\hline
\end{tabular}
\end{center}
\end{table}


\pagebreak


\references

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ESA, 1997, {\it The Hipparcos and Tycho Catalogs}, SP-1200

Heged\"us, T., Borkovits, T., B\'\i r\'o, I. B., Demircan, O., Erdem, A., \c Ci\c cek, C., \"Ozdemir, S., Bulut, I.,  Soydugan, F., Soydugan, E., Degirmenci, \"O. L., Bozkurt, Z., Yakut, K., Esenoglu, H., 
Szettele, I.,  2003, {\it IBVS}, 5372

Tas, G.; Evren, S.; \c Cakirli, Ö.; \'Ibanoglu, C., 2003, {\it A\&A}, {\bf 411}, 
161

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

Wilson, R. E., 1990, {\it ApJ}, {\bf 356}, 613

Wilson, R. E., 1994, {\it PASP}, {\bf 106}, 921

\endreferences

\end{document}
