\documentstyle[twoside,epsf]{article}
\input ibvs2.sty
\begin{document}
\IBVShead{6134}{30 March 2015}
\IBVStitle{LO Andromedae -- A W-Type Overcontact Eclipsing Binary}
\IBVSauth{Nelson, Robert H.$^{1,2}$; Robb, Russell M.$^{2,3}$}
\IBVSinst{1393 Garvin Street, Prince George, BC, Canada, V2M 3Z1, email: bob.nelson@shaw.ca}
\IBVSinst{Guest investigator, Dominion Astrophysical Observatory, Herzberg Institute of Astrophysics, National Research Council of Canada}
\IBVSinst{Department of Physics and Astronomy, University of Victoria, Victoria, B.C., Canada, V8P 2W7}
\SIMBADobj{LO And}
\begintext
The variability of LO And (= TYC 3637-416-1= NSV 14569 = NSVS 3561083 =
CSV 8853 = WR 136) was discovered photographically by Weber (1963), who
classified the system as a probable Cepheid variable. Diethelm \&
Gautschy (1980) determined a period of 0.190429~days (half the modern
value) and supplied a full photoelectric light curve displaying only one
minimum. The General Catalogue of Variable Stars (Samus et al.,
1985-2013) lists the type as EW and a period of 0.3804427~days, with a
reference to Kreiner (2004). From 1995 to 2014 there have been numerous
eclipse timings. G\"urol \& M\"uyessero\u{g}lu (2005) [hereafter G\&M (2005)]
presented five new times of minima of their own, collected a total of 15
photographic (pg), 164 visual (vis), 17 photoelectric (PE), and 10
charge-coupled device (CCD) eclipse timings from the literature, and performed
the first period study of the system. Plotting an eclipse timing (ET)
diagram (a.k.a. O$-$C diagram), they first determined a quadratic fit (which
they attributed to mass exchange), noting that it was not sufficient to
explain the period variation completely. They then went on to solve for
the parameters of the orbit of the putative third star, listed in Table 1.
(They considered, then rejected, that an alternate explanation might be
magnetic cycles -- the Applegate effect (Applegate, 1992)).
Assuming that the residual variation is due to the light time effect (LTE)
resulting from a third orbiting body, the new times of minima, $T$ can be
predicted by the equation
\begin{equation}
T = {\rm HJD}_0 + P_0 E_0 + (c_0 + c_1 E + c_2 E^2) + \Delta T
\end{equation}
\noindent where ${\rm HJD}_0$ (= 24 45071.059) is the starting epoch, $P_0$ (=
0.38043556~days) is initial period, $c_0$, $c_1$ and $c_2$ are the
coefficients for the quadratic fit, and $\Delta T$ is the time delay due to
orbital motion of the close eclipsing pair about the centre of mass of the
triple system. The latter is given by (Irwin, 1952, 1959):
\begin{equation}
\Delta = A \frac{(1-e^2) \sin(\nu + \omega) }{ ( 1+e \cos \nu) + e \sin \omega}
\end{equation}
\noindent where $A$ = semi-amplitude = $\frac{1}{2}[({\rm O}-{\rm C})_{\rm max} -
(O-C)_{\rm min}] = (a_{13} \sin i_3)/c$; $i_3$ = inclination of the 3rd star
orbit (90\deg = edge-on); $e$ = eccentricity; $\nu$ = true anomaly; $c$ =
speed of light, and $\omega$ = argument of periastron.
\begin{table}
\begin{center}
\begin{tabular}{lccl}
\hline
Quantity&G\&M (2004)&This study&unit\\
\hline
Constant, $c_0$&1.00&4.68&$10^{-3}$ days\\
Slope, $c_1$&0&$-$9.69&$10^{-6}$ days/cycle\\
Quadratic coeff., $c_2$&1.281&1.167&$10^{-10}$ days/cycle$^2$\\
Amplitude, $A = a_{13} \sin i /c$&0.00829&0.00755&days\\
$a_{13} \sin i$&1.435&1.31&astron. units\\
Eccentricity, $e$&0.275&0.262&---\\
Period, $P_3$&37.08&29.6&years\\
Arg. of periastron, $\omega$&198&80.4°rees\\
Periastron time, $T_{\rm p}$&41919.1&46431.0&HJD$-$2400000\\
$dP/dt$&2.46&2.24&$10^{-7}$ days/year\\
Mass transfer rate, $dm_1/dt$&+1.686&+1.537&$10^{-7}$ M$_\odot$/year\\
Mass function, $f(m_3)$&0.002150&0.00256&M$_\odot$\\
Mass, $m_3$&0.21&0.22&M$_\odot$\\
\hline
\end{tabular}
\caption{Parameters for the quadratic + LTE fit from the analysis of G\&M (2005) and the present paper, plus some derived quantities.}
\end{center}
\end{table}
With the benefit of 48 new PE and CCD subsequent eclipse timings, we have re-
determined a quadratic + LTE fit using the linear elements (HJD$_0$, $P_0$) given
above; both sets of resulting parameters are given in Table 1, column 3. An
ET difference plot is displayed in Figure 1. Weights of 0.1 were assigned to
the visual estimates, and 1 to the photographic, photoelectric and CCD eclipse
timings. The residuals from quadratic fits of both studies are displayed in
Figs. 2 and 3. (Note that the latter two cannot be displayed in the same
figure because constants $c_0$, $c_1$ and $c_2$ are different in each case.)
It will be seen that, visually, the present solution fits the augmented data set better than that of G\&M (2005). As in their work, we have solved for the intrinsic rate of period change, $dP/dt$ by equation 3.
\begin{equation}
\frac{dP}{dt} = 2 c_2 \left(\frac{365.24}{P_0}\right)~.
\end{equation}
One can show, under the conditions of mass and angular momentum conservation for the system as a whole, for masses $m_1$, $m_2$ and period $P$, that:
\begin{equation}
(m_1 m_2)^3 P = {\rm constant}
\end{equation}
Therefore, differentiating equation 4, one obtains:
\begin{equation}
\frac{dm_1}{dt} = \frac{1}{3P\left(\frac{1}{m_2}-\frac{1}{m_1}\right)}\frac{dP}{dt}~.
\end{equation}
Both values of $dm_1 /dt$ (from G\&M (2005) and from this work) are presented in Table~1.
We have also solved for the mass function defined in Mayer (1990), assuming that the orbital inclination of the third-star orbit, $i_3$ is the same as the inclination of the binary pair orbit, $i$ given in Table 5.
\begin{equation}
f(m_3) = \frac{(a_{13} \sin i)^3 }{P_3^2} = \frac{(m_3 \sin i_3)^3 }{ (m_1 + m_2 + m_3)^2}~.
\end{equation}
From equation (6) one can iterate for $m_3$:
\begin{equation}
m_3 = \frac{a_{13} \sin i_3}{\sin i_3}\left(\frac{m_1 + m_2 + m_3}{P_3}\right)^{\frac{2}{3}}~.
\end{equation}
The corresponding values for $m_3$ are also presented in Table 1.
It should be firmly borne in mind, however, that -- due to the scatter in the
early timings (before cycle 10000) -- all the fit parameters and derived
quantities are very tentative, and that new data over the next decade or so
may very well render their values obsolete. By comparison, a much more robust
quadratic + LTE fit, in the case of ER Orionis, may be found in Nelson (2015).
The O$-$C file for LO And may be obtained from the AAVSO website (Nelson,
2013).
\IBVSfig{6cm}{6134-f1.eps}{Eclipse timing diagram for LO And showing the fit of G\&M (2005) [dashed line] and that of the present study [solid line]. }
\IBVSfigKey{6134-f1.eps}{LO And}{other}
\IBVSfig{5cm}{6134-f2.eps}{Residuals from the quadratic fit of G\&M (2005) plus their LTE fit. See Fig. 1 for the legend.}
\IBVSfigKey{6134-f2.eps}{LO And}{other}
\IBVSfig{5cm}{6134-f3.eps}{Residuals from the quadratic fit of this study plus our LTE fit. See Fig. 1 for the legend.}
\IBVSfigKey{6134-f3.eps}{LO And}{other}
Using the 2003 Wilson-Devinney code (see references below), G\&M (2005) went
on to perform a light curve analysis on $B$ \& $V$ photometric data that they
had obtained at Ankara University Observatory. They determined a value for
the important parameter mass ratio $(q=m_2/m_1)$ indirectly by the ``$q$-search"
method. [The latter entails fixing the mass ratio for a range of
values, varying the remaining parameters (such as orbital inclination $i$,
temperature $T_2$, system potential $\Omega$, light value $L_1$, and -- if
used -- spot parameters) to obtain solutions. The residuals from the best fit
obtained in each case versus the corresponding value of $q$ are plotted, and
the $q$ corresponding to the minimum is adopted.] The problem with the
$q$-search method is that the value of q obtained is not as robust as that
obtained spectroscopically, and, in the case of overcontact binaries
undergoing partial eclipses, the value of $q$ obtained is only determinable to
about $\pm10\%$. (Terrell \& Wilson, 2005).
In order to improve on this study, one of the authors (R.H.N.) secured, in the
months of September in 2007, 2009, 2010, and 2013, a total of 13 medium
resolution ($R\sim 10000$ on average) spectra of LO And at the Dominion
Astrophysical Observatory (DAO) in Victoria, British Columbia, Canada using
the Cassegrain spectrograph attached to the 1.85 m Plaskett Telescope. He
used the 21181 grating with 1800 lines/mm, blazed at 5000~\AA~giving a
reciprocal linear dispersion of 10 \AA/mm in the first order. The wavelength
ranged from 5000 to 5260~\AA, approximately. A log of observations is given
in Table 2. The following elements were used for both RV and photometric
phasing:
\begin{equation}
{\rm JD~(Hel)~Min~I} = 24~56226.6792 + 0.380441888458~E
\end{equation}
\begin{table}
\begin{center}
\begin{tabular}{cccccc}
\hline
DAO&Mid Time&Exposure&Phase at&$V_1$&$V_2$\\
Image \#&(HJD$-$2400000)&(sec)&Mid-exp&(km/s)&(km/s)\\
\hline
11183&54365.9451&3600&0.019&1.7&---\\
11188&54365.9897&3600&0.136&$-$58.9&185.1\\
11203&54366.9663&3600&0.703&62.8&$-$256.0\\
11205&54367.0166&3600&0.835&76.2&$-$248.9\\
11211&54367.6466&3600&0.491&$-$2.6&---\\
11213&54367.6717&617&0.557&19.7&---\\
11219&54367.7539&3600&0.773&69.5&$-$259.5\\
11262&54369.8917&3600&0.393&$-$45.5&---\\
19073&55100.8404&3600&0.708&86.7&$-$277.8\\
19149&55102.9667&3600&0.297&$-$68.6&247.2\\
17272&55469.6910&3600&0.240&$-$69.8&278.2\\
9670&56545.9697&3600&0.262&$-$91.1&258.3\\
9692&56546.9266&3600&0.778&67.7&$-$294.9\\
\hline
\end{tabular}
\caption{Log of DAO observations}
\end{center}
\end{table}
Frame reduction was performed by software {\sc RaVeRe} (Nelson 2009). See
Nelson et al. (2014) for further details. Radial velocities were determined
using the Rucinski broadening functions (Rucinski, 2004, Nelson, 2010b, Nelson
et al., 2014). An Excel worksheet with built-in macros (written by him) was
used to do the necessary radial velocity conversions to geocentric and back to
heliocentric values (Nelson 2010a). The resulting RV determinations are also
presented in Table 2. These results were corrected 7.7\% up in this case to
allow for the small phase smearing. Correction was achieved by dividing the
RVs by the factor $f = (\sin X) / X$; where $X = 2\pi t / P$ and $t$ denotes
exposure time, and $P$ denotes the orbital period. For spherical stars, this
correction is exact; in other cases, it can be shown to be close enough for
any deviation to fall below observational errors. The mean rms error for each
RV is 8.3~km/s and the rms deviation from the curves of best fit is 11.4~km/s.
The best fit yielded the values $K_1 = 76.4(2.8)$~km/s, $K_2 = 272.4(3.3)$~km/
s and $V_\gamma = 3.7(1.9)$~km/s.
In May-July of 2012, the same author (R.H.N.) took a total of 169 frames in
$V$, 172 in $R_{\rm c}$ (Cousins) and 169 in the $I_{\rm c}$ (Cousins) band at
his private observatory in Prince George, BC, Canada. The telescope was a 33
cm f/4.5 Newtonian on a Paramount ME mount; the camera was an SBIG ST-10XME.
Standard reductions were then applied. The comparison star (the same as for
G\&M, 2005) and check star are listed in Table 3. The coordinates and
magnitudes are from the Tycho Catalogue, Hog et al. (2000).
\begin{table}
\begin{center}
\begin{tabular}{cccccc}
\hline
Object&GSC&RA (J2000)&Dec (J2000)&$V$ (mag)&$B-V$ (mag)\\
\hline
Variable&3637-0416&23\hr 27\mm 06\fsec672 &45\deg 33\arcm 22\farcs00&11.25&+0.70\\
Comparison&3637-0299&23\hr 26\mm 26\fsec518 &45\deg 30\arcm 37\farcs77&10.53&+1.00\\
Check&3636-0116&23\hr 25\mm 56\fsec429 &45\deg 32\arcm 28\farcs82&10.18&+1.26\\
\hline
\end{tabular}
\caption{Details of variable, comparison and check stars.}
\end{center}
\end{table}
For classification purposes, one of the authors (R.M.R.) took two low
resolution spectra, on 2013 March 9 (HJD=24~56360.4608) and 2013 June 22
(HJD=24~56465.3077). He used the 1.85 m Plaskett telescope at the Dominion
Astrophysical Observatory (DAO) in Victoria, British Columbia, Canada with the
Cassegrain spectrograph in the 2131 configuration, resulting in a reciprocal
dispersion of 60 \AA/mm. The two spectra were very similar. The strength of
the Calcium H\&K lines, G-band, H$\gamma$, Fe\,I~4384, Ca\,I~4227, and H$\delta$
lines all indicated a F5 $\pm$1 spectral classification for LO And.
R.H.N. used the 2003 version of the Wilson-Devinney (WD) light curve and
radial velocity analysis program with Kurucz atmospheres (Wilson and Devinney,
1971, Wilson, 1990, Kallrath, et al., 1998) as implemented in the Windows
front-end software {\sc WDwint} (Nelson, 2009) to analyse the data. To get started,
the spectral type F5 V, mentioned above, was adopted. Interpolated tables
from Cox (2000) gave a temperature $T1 = 6650 \pm 100$ K and
$\log g = 4.355$. An interpolation program by Terrell (1994, available from
Nelson 2009) gave the Van Hamme (1993) limb darkening values; and finally, a
logarithmic (LD=2) law for the limb darkening coefficients was selected,
appropriate for temperatures $<$ 8500 K (ibid.).
From the GCVS 4 designation (EW) and from the shape of the light curve, mode 3
(overcontact binary) mode was used. Early on, it was noted that the maxima
between eclipses were unequal. This is the O'Connell effect (Davidge \&
Milone, 1984, and references therein) and is usually explained by the presence
of one or more star spots. Accordingly, one was added first to star 1, and
this gave good results. (Moving the spot to star 2 gave poorer results and
was abandoned.)
Convergence by the method of multiple subsets was reached in a small number of
iterations. (The subsets were: ($a$, $L_1$), ($T_2$, $q$), and ($V_\gamma
$, $i$, $q$). The spots were handled separately.) Convective envelopes for
both stars were used, appropriate for cooler stars (hence values gravity
exponent $g = 0.32$ and albedo $A = 0.500$ were used for each). Detailed
reflections were tried, with $n_{\rm ref} = 3$, but there was little -- if any
-- difference in the fit from the simple treatment. The limb darkening
coefficients are listed in Table 4. There are certain uncertainties in
the process (see Csizmadia et al., 2013, Kurucz, 2002). On the other hand,
the solution is weakly dependent on the exact values used.
\begin{table}[!t]
\begin{center}
\begin{tabular}{ccccc}
\hline
Band&$x_1$&$x_2$&$y_1$&$y_2$\\
\hline
Bol&0.640&0.641&0.243&0.243\\
$V$&0.705&0.705&0.280&0.280\\
$R_{\rm c}$&0.632&0.632&0.287&0.287\\
$I_{\rm c}$&0.549&0.548&0.275&0.275\\
\hline
\end{tabular}
\caption{Limb darkening values from Van Hamme (1993)}
\end{center}
\end{table}
\begin{table}[!t]
\begin{center}
\begin{tabular}{lccccc}
\hline
&G \& M&G \& M&This work&This work&\\
WD Quantity&Value&error&Value&error&Unit\\
\hline
Temperature, $T_1$&6500&[fixed]&6650&[fixed]&K\\
Temperature, $T_2$&6465&184&6690&24&K\\
$q = m_2/m_1$&0.371&0.002&0.305&0.004&---\\
Potential, $\Omega_1=\Omega_2$&2.548&0.026&2.401&0.009&---\\
Inclination, $i$&78.67&0.62&80.1&0.6°\\
Semi-maj. axis, $a$&---&---&2.74&0.02&sol. rad.\\
$V_{\gamma}$&---&---&-3.0&0.8&km/s\\
Spot co-latitude&---&---&97&10°\\
Spot longitude&---&---&45&5°\\
Spot radius&---&---&33&2°\\
Spot temp factor&---&---&0.9765&0.005&---\\
$L_1/(L_1+L_2) (V)$&0.7061&0.0025&0.7330&0.0010&---\\
$L_1/(L_1+L_2) (R_{\rm c)}$&na&na&0.7339&0.0009&---\\
$L_1/(L_1+L_2) (I_{\rm c)}$&na&na&0.7348&0.0008&---\\
$r_1$ (pole)&0.4524&0.0058&0.4706&0.0003&orb. rad.\\
$r_1$ (side)&0.4873&0.0081&0.5103&0.0005&orb. rad.\\
$r_1$ (back)&0.5189&0.0115&0.5414&0.0008&orb. rad.\\
$r_2$ (pole)&0.2911&0.0099&0.2795&0.0012&orb. rad.\\
$r_2$ (side)&0.3055&0.0124&0.2937&0.0015&orb. rad.\\
$r_2$ (back)&0.3501&0.0251&0.3427&0.0035&orb. rad.\\
Phase shift&---&---&-0.0012&0.0004&---\\
$\Sigma\omega_{\rm res}^2$&0.04039&---&0.02872&---&---\\
\hline
\end{tabular}
\caption{Wilson-Devinney parameters}
\end{center}
\end{table}
The model is presented in Table 5. Note that estimating the uncertainties in temperatures $T_1$ and $T_2$ are somewhat problematic. A common practice is to quote the temperature difference over half a spectral sub-class (assuming that the classification is good to one spectral sub-class, which precision might be rare). In addition, various different calibrations have been made (Cox, 2000, page 388-390 and references therein, and Flower, 1996), and the variations between the various calibrations can be significant. In our case the classification is $\pm$ one sub-class. Therefore, we propose to assign an uncertainty of $\pm$ 200 K to the absolute temperatures of each, which would roughly span this range. The modelling error in temperature $T_2$, relative to $T_1$, is indicated by the WD output to be much smaller, around 24 K.)
\begin{table}
\begin{center}
\begin{tabular}{lccccc}
\hline
&G \& M&G \& M&This work&This work&\\
Quantity&Value&Error&Value&Error&unit\\
\hline
Temperature, $T_1$&6500&[fixed]&6650&200&K\\
Temperature, $T_2$&6465&184&6690&200&K\\
Mass, $m_1$&1.31&0.18&1.468&0.048&$M_\odot$\\
Mass, $m_2$&0.49&0.07&0.447&0.022&$M_\odot$\\
Radius, $R_1$&1.30&0.05&1.40&0.01&$R_\odot$\\
Radius, $R_2$&0.85&0.14&0.84&0.01&$R_\odot$\\
$M_{\rm bol}$, 1&3.67&0.08&3.45&0.02&mag\\
$M_{\rm bol}$, 2&4.62&0.39&4.53&0.02&mag\\
$\log g_1$&4.32&0.71&4.32&0.01&cgs\\
$\log g_2$&4.26&0.75&4.24&0.01&cgs\\
Luminosity, $L_1$&2.70&0.08&3.44&0.06&$L_\odot$\\
Luminosity, $L_2$&1.13&0.35&1.27&0.02&$L_\odot$\\
Fill-out factor&0.306&---&0.398&0.062&---\\
Distance, $r$&---&---&343&45&pc\\
\hline
\end{tabular}
\caption{Fundamental parameters}
\end{center}
\end{table}
\IBVSfig{7cm}{6134-f4.eps}{$V$, $R_{\rm c}$, and $I_{\rm c}$ light curves -- data and WD fit}
\IBVSfigKey{6134-f4.eps}{LO And}{light curve}
The WD output fundamental parameters and errors are listed in Table 6. Most of the errors are output or derived estimates from the WD routines. The fill-out factor $f = (\Omega^{\rm I}-\Omega)/ (\Omega^{\rm I}-\Omega^{\rm O})$, where $\Omega$ is the modified Kopal potential of the system, $\Omega^{\rm I}$ is that of the inner Lagrangian surface, and $\Omega^{\rm O}$, that of the outer Lagrangian surface, was also calculated.
The light curve data and the fitted curves are depicted in Figure 4. The presence of third light was tested for, but found not to be significant.
The RVs are shown in Fig. 5. A three-dimensional representation from {\sc Binary Maker 3} (Bradstreet, 1993) is shown in Fig. 6.
\IBVSfig{7cm}{6134-f5.eps}{LO And: radial velocity curves -- data and WD fit.}
\IBVSfigKey{6134-f5.eps}{LO And}{radial velocity curve}
\IBVSfig{5cm}{6134-f6.eps}{{\sc Binary Maker 3} representation of the system -- at phases 0.75 and 0.97.}
\IBVSfigKey{6134-f6.eps}{none}{other}
To determine the distance $r$ in column 4, we proceeded as follows: First the WD routine gave the absolute bolometric magnitudes of each component; these were then converted to the absolute visual ($V$) magnitudes of both, $M_{V,1}$ and $M_{V,2}$, using the bolometric correction BC = $-$0.140 for each. The latter was taken from interpolated tables in Cox (2000). The absolute $V$ magnitude was then computed in the usual way, getting $M_V = 3.25 \pm 0.03$ magnitudes. The apparent magnitude in the $V$ passband was $V = 11.19 \pm 0.09$, taken from the Tycho values (Hog et al., 2000) and converted to a Johnson magnitude using relations due to Henden (2001). The colour excess (in $B-V$) was obtained in the usual way, by subtracting the tabular value of $B-V$ (for that spectral class) from the observed (converted Tycho) value. This gave $E[B-V] = 0.26$ magnitudes. However, reference to the dust tables of Schlegel et al. (1998) revealed a value of $E[B-V] = 0.1711$ for those galactic coordinates. Since the $E[B-V]$ values have been derived from full-sky far-infrared measurements, they therefore apply to objects outside of the Galaxy; this value of $E[B-V]$ so derived then represents an upper limit for closer objects within the Galaxy. Hence the higher value of 0.26 cannot be regarded as reliable. Again, since the value of $E[B-V] = 0.1711$ represents an upper limit, objects closer than the edge of the galaxy should have a lower value; hence $E[B-V] = 0.086$ (half) was adopted and the error estimate also set to this value. Galactic extinction was obtained from the usual relation $A_V = R E[B-V]$, using $R = 3.1$ for the reddening coefficient. Hence, distance $r = 343$~pc was calculated from the standard relation:
\begin{equation}
r = 10^{0.2(V-M_V - A_V + 5)}~{\rm parsecs}~.
\end{equation}
The errors were assigned as follows:
$\delta M_{\rm bol,1} = \delta M_{\rm bol,2} = 0.02$,
$\delta {\rm BC}_1 = \delta {\rm BC}_2 = 0.01$
(the variation of 1.5 spectral sub-classes), $\delta V = 0.09$, $\delta E(B-V) = 0.086$, all in magnitudes, and $\delta R = 0.1$. Combining the errors
rigorously yielded an estimated error in $r$ of 45 pc.
In conclusion, the fundamental parameters of this system have been determined. One of these is the mass ratio, defined by the WD routine as $q = m_2/m_1$. As to eclipse sub-type (A or W), the deeper eclipse, by convention, defines phase 0; therefore the star eclipsed at that phase -- the primary -- is the hotter one. However, in this case, detailed modelling using a spot results in a slightly higher temperature for the secondary, making the system type-W.
It is interesting to note that G\"urol \& M\"uyessero\u{g}lu (2005), although
they noted a magnitude difference in maxima (Max II $-$ Max I) of $-0.010$ in
$V$, made no attempt to include any spots in their WD modelling. They also
the classified the system as type-A, which classification might have been
different if they had added a spot as we have done. (However, in our case, we
noted a magnitude difference (Max II $-$ Max I) $\approx +0.03$ in the $V$
band--the opposite. Clearly the spot, if it exists, has migrated in the time
interval of nine years.)
{\bf 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.
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\endreferences
\IBVSedata{6134-t7.txt}
\IBVSdataKey{6134-t7.txt}{LO And}{photometry}
\end{document}