\documentstyle[twoside, epsf]{article}

\input ibvs2.sty

\begin{document}

\IBVShead{5112}{12 June 2001}

\IBVStitle{The Nature of the Eclipsing Binary LD~328}

\IBVSauth{Lloyd, C.$^1$; Hager, T.$^2$; Henden, A.A.$^3$; James, N.D.$^4$; Kaiser, D.H.$^5$; Lubcke, G.C.$^6$}

\IBVSinst{Space Science \& Technology Department, Rutherford Appleton
Laboratory, Chilton, Didcot,\\ \indent Oxon.\ OX11 0QX, UK,
e-mail: {\tt cl@astro1.bnsc.rl.ac.uk}}

\IBVSinst{34 Mount Tom Road, New Milford, Connecticut 06776, USA,
e-mail: {\tt thager@pcnet.com}}

\IBVSinst{Universities Space Research Association/U.S. Naval
Observatory, P.O. Box 1149, Flagstaff,\\ \indent Arizona
86002-1149, USA, e-mail: {\tt aah@nofs.navy.mil}}

\IBVSinst{11 Tavistock Road, Chelmsford, Essex CM1 6JL, UK
e-mail: {\tt ndj@blueyonder.co.uk}}

\IBVSinst{2631 Washington Street, Columbus, Indiana 47201, USA,
e-mail: {\tt dhkaiser@sprynet.com}}

\IBVSinst{3817 Patrick Henry Way, Middleton, Wisconsin 53562, USA,
e-mail: {\tt gil2@ix.netcom.com}}

\SIMBADobjAliasJ2000{LD 328}{GSC 3256-0458}{00 26 49.09 +49 40 35.7}
\IBVStyp{ EA }
\IBVSkey{Algol-type - photometry}
\IBVSabs{CCD observations have been made of the eclipsing binary LD 328}
\IBVSabs{covering the full light curve in V and the primary minimum in the}
\IBVSabs{red. Additional accurate multi-colour photometry is available at}
\IBVSabs{secondary eclipse and out of eclipse. Modelling suggests that the}
\IBVSabs{system contains late A-type primary and a G-type secondary,}
\IBVSabs{filling its Roche lobe.}

\begintext

LD~328 (GSC 3256-0458, 00\hr26\mm49\fsec09, +49\deg40\arcm35\farcs7
(USNO A2.0)) was discovered as an eclipsing binary by Dahlmark (1999).
An analysis of the historical photographic observations, Dahlmark's
data, and recent visual and CCD observations shows that the star is an
Algol variable with a period of 1\fday0838485, increasing at,
$\dot{P}/P=5.6\times 10^{-7}$~yr$^{-1}$ (Lloyd et al.\ 2001). In this
paper the CCD observations are described in more detail and are used to
model the system.

The CCD observations have been calibrated using a comparison sequence
derived from $BV(RI)_{\rm C}$ observations from the USNO Flagstaff
Station 1.0-m telescope and a SITe/Tektronix $1024\times1024$ CCD (see Table 1).
LD~328 was observed at two phases which provide multi-colour photometry
at secondary eclipse and out of eclipse (see Table 2). The comparison
stars were calibrated on one photometric night and have an estimated zero
point error of 0\fmm02. Additional field photometry is available at
\begin{center}
{\tt ftp://ftp.nofs.navy.mil/pub/outgoing/aah/sequence/ld328.dat}.
\end{center}
Further CCD observations in $V$ only have been made by Hager, Lubcke and Kaiser
using 0.25-m, 0.28-m and 0.35-m SCTs respectively, all equipped with
ST-9E CCDs, and together with the Flagstaff observations they cover the
complete light curve. Observations around primary eclipse were also made
by James using an unfiltered Starlight Xpress SX CCD on a 0.30-m
telescope. These have been calibrated using the $R$ magnitudes of the
comparison stars. The light curves in $V$ and $R$ are shown in Figures 1 and
2 respectively, using the current period given above.

\begin{table}[!b]
\centering
\caption{Comparison star photometry near LD~328}
\begin{tabular}{cccccc}
\hline
 Star & RA (2000) Dec & $V$ & $B-V$ & $V-R_{\rm C}$ & $R_{\rm C}-I_{\rm C}$ \\
\hline
GSC3256-0691 & 0\hr27\mm02\fsec28 +49\deg38arcm49\farcs8 & 12.486 & 0.552 & 0.327 & 0.341 \\
GSC3256-0138 & 0 27 12.08 +49 43 06.6 & 13.511 & 0.533 & 0.332 & 0.340 \\
GSC3256-0274 & 0 26 44.72 +49 45 59.6 & 12.736 & 0.542 & 0.331 & 0.328 \\
\hline
\end{tabular}
\label{ld328:comp}
\end{table}

\begin{table}[b!]
\centering
\caption{Multi-colour photometry of LD~328}
\begin{tabular}{cccccc}
\hline
 HJD & Phase & $V$ & $B-V$ & $V-R_{\rm C}$ & $R_{\rm C}-I_{\rm C}$ \\
\hline
 2451930.6207 & 0.611 & 13.283 & 0.523 & 0.336 & 0.342 \\
 2451931.5851 & 0.501 & 13.428 & 0.478 & 0.308 & 0.316 \\
\hline
\end{tabular}
\end{table}

\IBVSfig{8cm}{5112-f1.eps}{The phase diagram of the CCD $V$-band data showing
the individual observations of Lubcke (filled circles), Kaiser (open
circles), Henden (filled squares) and Hager (open squares). The modelled
light curve has been over plotted}

\vskip-11pt
Very little is known about LD~328. There is no spectral type available
and the only accurate photometry is that presented here. It is possible
to estimate the unreddened colours of the primary from the $B-V$,
$V-R_{\rm C}$ and $R_{\rm C}-I_{\rm C}$ colours derived at secondary
minimum, assuming that it lies on the main sequence, and that the
secondary component makes no significant contribution at this phase.
Values for the unreddened main sequence have been taken from AQ4 (Cox
1999). The contribution of the secondary is obviously small as the star
is only slightly bluer at secondary minimum compared to the out of
eclipse colours. Unfortunately the unreddened colours are poorly
constrained and are consistent with main-sequence stars of spectral
type A or F\@. Any contribution from the secondary will tend to make the
primary appear of a later spectral type.

The $V$-band light curve of the system has been modelled using the {\sc
Light2} code (see Hill et al.\ 1989). A grid of models has been calculated
covering a range of temperatures for the primary component, $6\,500 <
T_{1} < 15\,000$~K corresponding approximately to spectral types F5 to B5,
and a range of mass ratios, $0.2 < q < 1.0$. For each model the
program has solved for the relative radii of both components, $R_{1}/a$,
$R_{2}/a$, the temperature of the secondary, $T_{2}$ and the inclination,
$i$. A series of models was also run with the secondary radius, $R_{2}/a$,
fixed at the Roche lobe radius, and the results are collected in Table~3. 

\IBVSfig{8cm}{5112-f2.eps}{The unfiltered CCD observations around primary
eclipse calibrated using the comparison star $R$ magnitudes, with the
modelled $R_{\rm C}$ and $I_{\rm C}$ light curves over plotted}

\vskip-11pt
The relative radii and the inclination are similar for all the
solutions and they all produce very similar fits to the light curve, so
there is no clearly preferred solution. For the smallest mass ratio,
$q=0.2$, the solutions with the secondary radius fixed or floating are
essentially identical, but for larger mass ratios the secondary lies
within its Roche lobe. For these, when the secondary radius is fixed at
the Roche lobe radius, the fits to the data are only marginally poorer,
but the solutions produce much smaller primaries and cooler
secondaries.

\begin{table}[!b]
\begin{center}
\caption{Photometric model of LD~328}
\begin{tabular}{rcclccc} \hline
 $T_{1}^*$~& $T_{2}$ & $R_{1}/a$ & $R_{2}/a$ & $i$ & $q$ & $R_1/R_\odot$\\ \hline
15\,000 & 8\,200 & 0.23 & 0.26 & 81 & 1.0 & 2.4 \\ 
15\,000 & 8\,400 & 0.22 & 0.26 & 80 & 0.5 & 2.1\\
15\,000 & 7\,700 & 0.16 & 0.30$\dagger$ & 77 & 0.5 & 1.5 \\ 
15\,000 & 8\,300 & 0.23 & 0.23$\dagger$ & 82 & 0.2 & 2.0 \\ \hline 
10\,000 & 6\,200 & 0.23 & 0.26 & 80 & 1.0 & 1.9 \\ 	 
10\,000 & 6\,300 & 0.23 & 0.25 & 81 & 0.5 & 1.7\\
10\,000 & 5\,800 & 0.16 & 0.30$\dagger$ & 76 & 0.5 & 1.2\\ 
10\,000 & 6\,300 & 0.23 & 0.23$\dagger$ & 81 & 0.2 & 1.6 \\ \hline
 8\,000 & 5\,200 & 0.24 & 0.25 & 81 & 1.0 & 1.7 \\ 
 8\,000 & 5\,400 & 0.24 & 0.25 & 81 & 0.5 & 1.5 \\ 	 
 8\,000 & 4\,900 & 0.17 & 0.30$\dagger$ & 75 & 0.5 & 1.1 \\ 
 8\,000 & 5\,600 & 0.24 & 0.23$\dagger$ & 82 & 0.2 & 1.4\\ \hline 
 6\,500 & 4\,600 & 0.22 & 0.26 & 80 & 1.0 & 1.3\\
 6\,500 & 4\,600 & 0.25 & 0.24 & 81 & 0.5 & 1.4\\ 
 6\,500 & 4\,300 & 0.17 & 0.30$\dagger$ & 75 & 0.5 & 0.9\\ 
 6\,500 & 4\,800 & 0.24 & 0.23$\dagger$ & 82 & 0.2 & 1.2\\ \hline 
\end{tabular}

\normalsize
$^*$ $T_{1}$ fixed; \quad $\dagger$ $R_{2}/a$ fixed at the Roche lobe radius
\end{center}
\end{table}

\clearpage

The models can also be used to estimate the change in colour with phase
for comparison with the observed values (Table 2). Unfortunately there is
a lack of consistency which makes it difficult to draw any firm
conclusions. The agreement tends to be better with the cooler, lower mass
ratio solutions, but it is still not as good as might be expected. 

The relative radii, $R_{1}/a$, have been converted to absolute values by
adopting consistent values of $M_1$ and $T_1$ for main-sequence stars.
For the higher mass ratios the radii derived in this way are too small
for the type of star assumed. Solutions with $R_{2}/a$ fixed are even
less consistent with the spectral type. A consistent set of values for
the mass and radius occur for a primary of spectral type later than A7,
($T_{1} < 8\,000$~K) making the secondary a low-mass, late G- or K-type
star. The secondary is probably filling its Roche lobe, as the
photometric solutions, the colours and the increasing period, all point in
this direction.

In conclusion, LD~328 appears to be a relatively cool Algol binary with
the secondary filling its Roche lobe. Much of the uncertainty in the
photometric model would evaporate with a good spectral classification.
LD~328 is potentially a very useful system as it has relatively deep
eclipses and a well determined rate of period change, and would benefit
from a more detailed photometric and spectroscopic study.

\references

Cox, A.N., 1999, ed., {\it Allen's Astrophysical Quantities, Fourth edition},
Springer Verlag

Dahlmark, L., 1999, {\it IBVS}, No.\ 4734

Hill, G., Fisher, W.A., Holmgren, D., 1989, {\it A\&A}, {\bf 211}, 81

Lloyd, C., Dahlmark, L., Guilbault, P., Hager, T., Henden, A.A., James, N.D.,
Kaiser, D.H., Kinnunen, T., Lubcke, G.C., 2001, {\it IBVS}, No.\ 5111

\end{document}
