\documentstyle[twoside, epsf]{article}

\input ibvs2.sty

\begin{document}

\IBVShead{5715}{17 July 2006}

\IBVStitle{The Classical Algol XZ UM\lowercase{a} --- Observations and Analysis}

\IBVSauth{Nelson, R.H.$^{1,2}$; Terrell, D.$^3$; Gross, J.$^4$}

\IBVSinst{1393 Garvin Street, Prince George, BC, Canada, V2M 3Z1, e-mail:~bob.nelson@shaw.ca}

\IBVSinst{Guest investigator, Dominion Astrophysical Observatory, Herzberg Institute of Astrophysics, National Research Council of Canada}

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

\IBVSinst{Sonoita Research Observatory, Box 131, Sonoita, AZ 85637, USA, e-mail:~johngross3@msn.com}

\SIMBADobj{XZ UMa}
\IBVStyp{ EA }

\begintext

XZ UMa (= SV*BV 32 = BD+50 1651 = TYC 3429 1530, 9\hr31\mm24\fsec5,
+49\deg28\arcm03\arcs, J2000.0) is listed in the General Catalogue of
Variable Stars, 4th Edition (Kholopov, 1985) as type EA/SD, period = 1.22232
days, spectral type A5 + F9, and referenced to Remus (1956), who provided
the chart (and is presumably the discoverer), and to the authors of the GCVS
(who presumably determined the period).

No published light curves or analysis could be found (although there are
catalogue parameters given---see Brancewicz \& Dworak (1980) and Svechnikov \&
Kuznetsova (1990)), nor is there any evidence of any existing radial
velocities, so this system was selected for study.

Times of minima have been continuously observed since about 1970; an $O-C$
plot (Nelson, 2005a) reveals continuous changes in the period, alternately
increasing and decreasing, which suggests a sinusoidal relationship of
period 7770 days.  (However, this relationship---if it exists---has been
observed over only one putative sine period and is therefore highly
speculative.)

The following elements (calculated from the last few hundred cycles) were
used for phasing:
$${\rm 
JD~Hel~Min~I} = 53048.7928(32) + 1.2223115(10) \times E.$$
Eleven high-resolution (10 \AA/mm) spectra were taken by one of the authors
(RHN) in April 2005 at the Dominion Astrophysical Observatory (DAO) in
Victoria, British Columbia, Canada.  The spectral range was 4997--5260 \AA{}.  A
log of observations and the derived heliocentric radial velocities is
presented in Table 1 and a list of IAU Standard Radial Velocity Stars
(Roberts \& Boksenberg, 1986) from which the XZ UMa radial velocities were
derived is given in Table 2.

Intermediate reductions (overscan removal, cosmic ray cleaning, setting
apertures, fitting background, summation of counts, reduction to 1
dimension, calibration from Fe-Ar arc spectra, and finally dispersion
correction) were performed by ‘Ravere’, software developed by one of the
authors (Nelson, 2005b).  Final determination of radial velocities was
performed by ``Broad'', software developed by the same author that uses the
Rucinski broadening functions (Rucinski, 2004).  As expected, there was some
scatter in the values for a given XZ UMa spectrum from the various radial
velocity standard spectra.  The mean and standard deviation were taken and
those values lying outside twice the sample standard deviation were
rejected.  In this way, the standard deviations for each radial velocity
determination of $V_1$ and $V_2$ averaged 6.5 and 8.5 km/s (resp.); the rms
deviations from the best-fit WD radial velocities were 7.5 and 11.0 km/s
(resp.).  Conversions from geocentric radial velocities (relative to that of
IAU standard stars) to heliocentric radial velocities was accomplished by
one of the authors (RHN) using his own software.

\begin{table}
\begin{center}
{\normalsize Table 1}

\begin{tabular}{ccccrr}
\hline
DAO  &  Start time  &  Exposure  &  Phase at  &  $V_1$  &  $V_2$ \\
Image \#  &  (HJD${} - 240000$)  &  (sec)  &  mid-exp  &  (km/s)  &  (km/s) \\
\hline
3139  &  53487.6569  &  3000 & 0.081  &  $-$78   &  67   \\
3141  &  53487.7072  &  3600 & 0.122  &  $-$104  &  93   \\
3143  &  53487.7570  &  3600 & 0.163  &  $-$120  &  125  \\
3146  &  53487.8125  &  3600 & 0.209  &  $-$127  &  149  \\
3007  &  53481.7576  &  3600 & 0.255  &  $-$137  &  144  \\
3118  &  53486.6574  &  3600 & 0.264  &  $-$133  &  151  \\
3124  &  53486.7500  &  3600 & 0.339  &  $-$120  &  139  \\
3128  &  53486.8048  &  3600 & 0.384  &  $-$99   &  110  \\
3179  &  53489.6527  &  7200 & 0.748  &  90    &  $-$185 \\
3064  &  53483.6757  &  3600 & 0.824  &  76    &  $-$170 \\
3155  &  53488.6549  &  3600 & 0.898  &  44    &  $-$121 \\
\hline
\end{tabular}
\end{center}
\end{table}

\begin{table}
\begin{center}
{\normalsize Table 2}

\begin{tabular}{lcccr}
\hline
DAO      &  Star  &  $V$ & Sp. & RV\\
Image \#  &  HD-   &  (mag) & Type  &  (km/s)\\
\hline
3004, 3033        &  089449  &  4.78  &  F6 IV  &  6.3 \\
3036, 3069        &  102870  &  3.59  &  F8 V   &  4.3 \\
3019              &  149803  &  8.58  &  F7 V   &  $-7.5$ \\
3022, 3057, 3193  &  154417  &  6.00  &  F9 V   &  $-16.8$ \\
3026, 3061        &  187691  &  5.12  &  F8 V   &  0 \\
\hline
\end{tabular}
\end{center}
\end{table}

Photometric observations were carried out by DT and JG in the $B$, $V$ and $I_c$
bands; 754, 770 and 815 values were obtained, respectively.  The 14''\
telescope at the Sonoita Research Observatory (SRO), equipped with a Santa Barbara
Instrument Group STL-1001E camera was used to obtain the photometric data.
The usual data processing procedures (bias and dark subtraction and
flatfielding) were done using IRAF\IBVSfm. Comparison stars are listed in Table 3;
the magnitudes and colours are from the Tycho catalogue (ESA, 1997). The data are
in the SRO instrumental system

\IBVSfoot{IRAF is distributed by the National Optical
Astronomy Observatories, which are operated by the Association of
Universities for Research in Astronomy, Inc., under cooperative agreement
with the National Science Foundation.}

\IBVSedata{5715-t6.txt}
\IBVSdataKey{5715-t6.txt}{XZ UMa}{photometry}
\IBVSedata{5715-t7.txt}
\IBVSdataKey{5715-t7.txt}{XZ UMa}{photometry}
\IBVSedata{5715-t8.txt}
\IBVSdataKey{5715-t8.txt}{XZ UMa}{photometry}

\begin{table}
\begin{center}
{\normalsize Table 3}

\begin{tabular}{llrr}
\hline
Star  &  GSC ID  &  $V$  &  $B-V$ \\
\hline
Var    &  3429-1530  &  10.49  &  0.20 \\
Comp   &  3429-449   &  10.33  &  0.36 \\
Check  &  3429-1027  &   9.96  &  0.53 \\
\hline
\end{tabular}
\end{center}
\end{table}

We used the latest version of the Wilson--Devinney (WD) light curve and
radial velocity analysis program with the Kurucz atmospheres (Wilson \&
Devinney, 1971; Wilson, 1990; Kallrath et al., 1998) to analyze the data.  
To get started, we used the above $B-V = 0.20 \pm 0.04$; the tables of Flower
(1996) gave temperature $T_1 = 7766 \pm 240$ K; interpolated tables from Cox
(2000) gave $\log g = 4.282$; an interpolation program by Terrell (1994) gave
the (van Hamme, 1993) limb darkening values; and finally, a logarithmic
($LD=2$) law was selected, appropriate for hotter stars (Bessell, 1979).  
Fitting a double sine wave to the radial velocity data gave a mass ratio of
$q = M_2/M_1 = 0.658 \pm 0.029$ km/s and a centre of mass radial velocity $V\gamma =
-19.5 \pm 0.9$ km/s.

The general appearance of the light curve suggested a detached or
semidetached system.  Mode 5 (semidetached---Algol) gave the best fit.  We
selected radiative values for the bolometric albedo and gravity darkening
exponents (albedo $A_1 = 1$ and gravity exponent $g_1 = 1$) for star 1 and
convective values ($A_2 = 0.5$ and $g_2 = 0.32$) for star 2 based on temperature
$T_1$ and the anticipated temperature $T_2$, respectively.

Because of the changes in the $O-C$ diagram that suggest a third body, we
attempted to adjust third light in the simultaneous light/radial velocity
curve solution. However, we could find no statistically significant value of
third light in any of the three passbands. Because of the difficulty in
recovering small amounts of third light, especially in partially eclipsing
systems like XZ UMa, our null result on third light should not be taken as
necessarily negating the third body hypothesis. We also adjusted the angular
rotation rate of the primary but we found no evidence of asynchronism.
Further, attempts with a detached configuration gave a poorer fit, hence the
detached configuration can be ruled out.

The results of the fit are listed in Table~4 and fundamental derived
quantities, in Table~5.  [Note:  `s.u.'\ = solar units.] Note also that the
errors quoted are the standard errors computed from the covariance matrix in
the differential corrections solution.

A 3-D representation generated by Binary Maker 3.03 (Bradstreet, 1993) is
presented in Figure 3.


\begin{table}
\begin{center}
{\normalsize Table 4}

\begin{tabular}{lrrr|lrr}
\hline

Quantity &\multicolumn{2}{c}{Value}& Error & Quantity & Value & Error\\
                 & Star 1 & Star 2&       &           &       &      \\
\hline
$F$              & 1.000  & 1.000 & [fixed] & $i$ (deg) & 83.96 & 0.06\\
$g$              & 1.000  & 0.320 & [fixed] & $L_1/(L_1+L_2)$ ($B$) & 0.820  & 0.001\\
$A$              & 1.000  & 0.500 & [fixed] & $L_1/(L_1+L_2)$ ($V$) & 0.728  & 0.002\\
$x$ (bol)        & 0.673  & 0.642 & [fixed] & $L_1/(L_1+L_2)$ ($I$) & 0.609  & 0.002\\
$y$ (bol)        & 0.203  & 0.166 & [fixed] & $\phi_0$              & 0.0006 & 0.00004\\
$x$ ($B$)        & 0.822  & 0.847 & [fixed] & $e$                   & 0      & [fixed]\\
$y$ ($B$)        & 0.332  & 0.059 & [fixed] & $a$ (solar radii)     & 7.02   & 0.1\\
$x$ ($V$)        & 0.716  & 0.784 & [fixed] & $V_\gamma$ (km/s)     & $-20.4$& 0.2\\
$y$ ($V$)        & 0.284  & 0.181 & [fixed] & $r_1$ (pole)          & 0.2389 & 0.0008\\
$x$ ($I$)        & 0.507  & 0.631 & [fixed] & $r_1$ (point)         & 0.2457 & 0.0009\\
$y$ ($I$)        & 0.213  & 0.225 & [fixed] & $r_1$ (side)          & 0.2416 & 0.0008\\
$T_1$ (K)        & 7766   & ---   & 240     & $r_1$ (back)          & 0.2445 & 0.0008\\
$T_2$ (K)        & ---    & 5346  & 5       & $r_2$ (pole)          & 0.3176 & 0.0004\\
$\Omega$         & 4.794  & ---   & 0.013   & $r_2$ (point)         & 0.4542 & 0.0016\\
$f$ (fill factor)&$-4.470$& 0.000 & 0.040   & $r_2$ (side)          & 0.3320 & 0.0004\\
$q = M2/M1$      & \multicolumn{2}{c}{0.626} & 0.003& $r_2$ (back)          & 0.3642 & 0.0004\\
\hline
\end{tabular}
\end{center}
\end{table}



\begin{table}
\begin{center}
{\normalsize Table 5}

\begin{tabular}{llclc}
\hline
Fund.\ Quantity & Star 1 & error & Star 2 & error\\
Spectral Type  & A7 &  & G7 & \\
\hline
Mass ($M_\odot$)      & 1.92 & 0.09 & 1.20 & 0.05 \\
Radius ($R_\odot$)    & 1.70 & 0.03 & 2.38 & 0.04 \\
$\log g$ (CGS)        & 4.26 & 0.2  & 3.76 & 0.2  \\
Luminosity ($L_\odot$)& 9.5  & 0.1  & 4.2  & 0.1  \\
Distance (pc)         & 504  & 26   &      &      \\
\hline
\end{tabular}
\end{center}
\end{table}


\IBVSfig{8cm}{5715-f1.ps}{}
\IBVSfigKey{5715-f1.ps}{XZ Uma}{light curve}

\IBVSfig{8cm}{5715-f2.ps}{}
\IBVSfigKey{5715-f2.ps}{XZ Uma}{radial velocity curve}

\IBVSfig{6cm}{5715-f3.ps}{}
\IBVSfigKey{5715-f3.ps}{XZ Uma}{}

XZ UMa is a classical Algol, as discussed in Giuricin et al.\ (1983), in
that the A7 primary lies in the middle of the main sequence band (Iben,
1967), and the evolved G7 secondary lies above this band (i.e., is
overluminous) by about a magnitude.  Further, the masses and stellar radii
for this system lie near the lower end of the Algol group and the period is
relatively short, as is fitting for late-type Algol systems (ibid).  
However, the mass ratio, q, lies at the upper end of the group, suggesting
that the system is still early in its mass transfer phase.  The sinusoidal
shape of the $O-C$ plot, as previously mentioned, suggests the presence of a
third body (light time effect); however, examination of the spectra does not
immediately support this hypothesis.  Further monitoring of times of minima
over the next decade or two should resolve the matter (but note Zavala, 2004
for an alternate explanation of cyclic period changes).

If there is a third body, this system would somewhat resemble the near Algol
DL Vir (EA, A3 + K0-2, $q = 0.485$), where there is evidence of a G8 III third
star (Schoffel \& Popper, 1974; Schoffel, 1977)---directly from spectra and
indirectly from $O-C$ analysis.  (The eclipsing pair is only single lined; the
mass ratio of this pair comes from analysis of the radial velocities of the
A3 and G8 stars.)  Although this system was at one time semi-detached (and
therefore underwent mass transfer), it now seems to be slightly
under-contact; it is also more evolved than XZ UMa.  However, the light
curve analysis was done using the Russell--Merrill model---an analysis with a
modern light curve synthesis code is long overdue.

Acknowledgements: It is a pleasure for RHN to thank the staff members at the
DAO (especially Les Saddlemyer) for their usual splendid help and
assistance. This research has made use of the SIMBAD database, operated at
CDS, Strasbourg, France. 

\references

Bessell, M.S., 1979, {\it PASP}, 91, 589

Bradstreet, D.H., 1993, Binary Maker 3.03, in: Milone, E.F. (ed.), Light Curve
Modelling of Eclipsing Binary Stars, pp.\ 151--166 (Springer, New York); ``Binary Maker'' software
available from http://www.binarymaker.com/

Brancewicz, H.K., \& Dworak, T.Z., 1980, {\it Acta Astron.}, 30, 501

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

ESA, 1997, The Hipparcos and Tycho Catalogues (ESA SP-1200)

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

Giuricin, G., Mardirossian, F., \& Mezzetti, M., 1983, {\it Astrophys.\ J. Suppl.\ Ser.}, 52, 35

Iben, I., 1967, {\it Ann.\ Rev.\ Astr.\ Ap.}, 5, 571

Kallrath, J., Milone, E.F., Terrell, D., \& Young, A.T., 1998, {\it ApJ}, 508, 308

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Nelson, R.H., 2005b, Software, by Bob Nelson,\\ http://members.shaw.ca/bob.nelson/software1.htm

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Terrell, D., 1994, Van Hamme Limb Darkening Tables, v1.1.,\\
http://www.boulder.swri.edu/\~{}terrell/ld/

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\endreferences

\bigskip
\bigskip

\IBVSerratum{5715}

The orbital inclination of XZ UMa had been omitted from IBVS 5715.
It should be $83.9\deg \pm 0.1\deg$.

\bigskip

Bob Nelson

\end{document}
