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\newcommand {\kms}{km\,s$^{-1}$}                % km/s
\newcommand {\Msun}{${\rm M_{\odot}}$}          % Msun
\newcommand {\Rsun}{${\rm R_{\odot}}$}          % Rsun

\input ibvs2.sty

\begin{document}
\IBVShead{4645}{28 October 1998}

\IBVStitle{HD 13654: Probably not an eclipsing binary}

\IBVSauth{C.~LLOYD$^1$, R.D.~PICKARD$^2$, R.H.~CHAMBERS$^2$}

\IBVSinst{Space Science Department, Rutherford Appleton Laboratory,
Chilton, Didcot, Oxon.\ OX11 0QX, UK, e-mail: cl@ast.star.rl.ac.uk}
\IBVSinst{Crayford Manor House Astronomical Society, The Manor House,
Mayplace Road East, Crayford, Kent DA1 4HB, UK, e-mail: rdp@star.ukc.ac.uk}

\SIMBADobj{HD 13654}
\IBVStyp{ A3V+(F?) }
\IBVSkey{spectroscopy, radial velocity, period}
\IBVSabs{Radial velocity variations of HD 13654 reveal three possible}
\IBVSabs{periods. From dynamical considerations and knowledge of the}
\IBVSabs{spectral type, A3V, it is shown that the most likely period is}
\IBVSabs{0.82486$\pm$0.00003 days. The mass of the secondary is probably}
\IBVSabs{$ 0.7 < m_{2} < 1.5 $ and the inclination $ 28 < i < 60 $degrees.}

\begintext

Munari (1992) drew attention to HD 13654 as a possible eclipsing,
spectroscopic binary on the basis of radial velocity variations and
spectroscopic changes. The primary has a well determined spectral type of
A3V but this was apparently replaced on one of the ten spectra by a
late-type star of spectral type around G9. The interpretation of this
change was that the late-type secondary had eclipsed the primary. Given
the large velocity amplitude, $\sim$ 140 \kms, and likely orbital period,
a few days, this interpretation seemed appropriate. The blue spectra
showed no contamination by the secondary but a red spectrum did show some
absorption lines attributable to the secondary. The luminosity change
during eclipse is not known but as the secondary is only weakly visible
in the red the difference is likely to be at least one or two magnitudes.

In an effort to identify past eclipses in this system the Hewitt Camera
Plate Archive, held by the Crayford Manor House Astronomical Society, has
been searched. Details of the camera and archive are given by Howarth
(1992). The brightness of HD~13654 was estimated visually, using a fixed
microscope and light table, on 35 plates taken between 1964 and 1989. The
plates are unfiltered and a variety of panchromatic emulsions have been
used, Ilford HP3, FP4, HPS and Kodak Professional Royal Pan 4141, which
give a very broad band pass. The comparison stars used were BD+58\deg 419
(A2), BD+58\deg 426 (B9) and occasionally BD+58\deg 427 (A0), and are of similar
colour to HD~13654. On all the plates HD~13654 was found to be slightly
fainter than BD+58\deg 419 at V $\simeq$ 9.8, with no significant variation.
No eclipses consistent with the spectroscopic changes were seen. It is
possible that the times of the plates were unfortunately placed and real
eclipses have been missed. If the eclipse occupies 0.1 in phase, then
there is a probability of 0.025 that all 35 plates will miss an eclipse.
While this chance is not impossibly small it is very suggestive that the
system does not eclipse. Through correspondence with Dr Munari it now
appears that there is some doubt over the eclipse spectrum, which may not
have been of the correct star.

According to the Hipparcos and Tycho Catalogues (1997) HD 13654 is
considered to be a suspected variable with a range in $V_{\rm T}$ of 9.5
-- 10.8. However, closer inspection of the Tycho measurements reveals
that the errors are very large, particularly for the faint values, and
show no significant variation.

\vfill\eject

\IBVSfig{8cm}{4645-f1.eps}{Least squares sine periodogram of the
radial velocity measurements}

The nine velocity measurements given by Munari have been subjected to a
period analysis using a least squares sine periodogram. Although the
number of measurements is rather small for this exercise the method is
well suited to irregularly spaced, but high signal-to-noise data, much
more so that the discrete Fourier methods. Given the large variation
there is every expectation that this approach should reveal the correct
period, the problem would lie in identifying it among the aliases. In the
event aliasing is not too severe. The periodogram is given in Figure 1
and shows the relative standard error of the residuals as a function of
trial frequency. Three periods are clearly identified above the rest,
these are 9.8, 6.5 and 0.8 days. The periodogram was also calculated with
the time of the eclipse spectrum included, using the systemic velocity,
but it showed a much poorer reduction in the errors, such that no
particular period could be clearly identified, suggesting that this
velocity is inconsistent with the rest.

The orbital parameters of the three most likely periods are given in
Table 1, together with derived values of the minimum mass of the
secondary and minimum inclination of the system, assuming that the
secondary in the less massive and less luminous component. The mass of
the A3V star is assumed to be 2.1 \Msun\ (Allen 1973). It is immediately
obvious that in a system with a period of 9.8 days the secondary exceeds
this mass, so either the primary should be of an earlier spectral type or
both stars should be visible with a similar spectral type. As only a
single A-type spectrum is seen it means the 9.8 day period can be
eliminated. It is also the least likely of the possible periods.

\vskip 4mm

\centerline{\normalsize Table 1: Orbital solutions}
\vskip2mm
\begin{center}
\begin{tabular}{ccccccc}
\hline
Period & K & $f(m)$ & $\sigma$ & $a_{1}\sin i$ & minimum & minimum \\ 
(days) & \kms\ &\Msun\  & \kms\ & \Rsun\ & mass & inclination \\
\hline
0.82486$\pm$0.00003 & 69$\pm$6 & 0.028 & 7.3 & ~1.12 & 0.11 & 22~ \\
6.4938$\pm$0.0033~~~ & 85$\pm$7& 0.414 & 6.3 &10.91 &2.04 & 67~ \\
9.8048$\pm$0.0052~~~ & 86$\pm$7& 0.648 & 7.9 &16.66 &2.55 & 90$^{*}$\\
\hline
\end{tabular}

$^{*}$ Strictly undefined as the minimum mass is larger that the 2.1 \Msun\
assumed
\end{center}

\IBVSfig{8cm}{4645-f2.eps}{
Radial velocity curve from the data of Munari using the 0.82486 day period.}

The 6.5 day period gives the smallest residuals but the minimum mass of
the secondary is only marginally less than that assumed for the primary.
It therefore seems very unlikely that there would be a sufficient
luminosity difference between the two for the secondary to pass
unnoticed. Also, for this minimum mass, the inclination would be 90
degrees and the system would be eclipsing. If the photographic results
are to be believed, the system is probably not eclipsing and avoiding this
condition would increase the minimum mass, and with it, the visibility of
the secondary.

For the 0.82 day period, both the minimum mass of the secondary and
minimum inclination are correspondingly lower, so it is possible for the
system to contain a secondary that is spectroscopically invisible.
Assuming that the secondary is at least one magnitude fainter than the
primary it will have a mass $m_{2} <$ 1.5 \Msun\ and the system will have
an inclination, $i > 28$ degrees. However, the size of the system and
radii of the components ($r_{1}=1.9, r_{2}=1.3$ \Rsun) means that system
will be eclipsing for $i > 56$ degrees. Depending on the precise values
of all the relevant parameters (for $m_{2}=0.7$ \Msun, $r_{2}=0.7$ \Rsun\
then $i > 60$ degrees will eclipse) there is still a range of
inclinations, $i \sim 28 - 60$ degrees, where the system does not eclipse
and stars of appropriate masses and luminosities may be accommodated.
The orbital solution for this period is shown in Figure 2.

Irrespective of the periods suggested by the periodogram, dynamical
arguments point to a short period; with 0.82486 days as the most likely
candidate from the period analysis. Periods of less than one day are
relatively common for A-type binaries and a wide range of secondaries is
possible. Given the weak visibility of the secondary it is probably
towards the lower end of the possible mass range, $ 0.7 < m_{2} < 1.5$
\Msun, giving an F or G star, with $28 < i < 60$ degrees.


It is a pleasure to thank Dr Munari for helpful correspondence on this
system.


\vfill\eject

\references

Allen C.W., 1973, {\it Astrophysical Quantities, Third edition}, Athlone
Press

Howarth J.J, 1992, {\it J.BAA},  {\bf 102}, 343

Munari U., 1992, {\it IBVS}, No.\,3715 

\end{document}



