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\IBVShead{4135}{28 December 1994}                      % Use it with dummy or empty arguments

% Call for macro \title {Title of the paper}
\title{A PRE-MAIN-SEQUENCE COMPANION TO AR AURIGAE?}

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    A recent analysis of the well-known bright eclipsing binary AR
Aurigae (HD\,34364, HR\,1728, V$_{max}$ = 6.15, B9VpHgMn + B9.5V, P$_{AB}$ = 4\fd 13
days) suggests that the secondary star is still contracting towards
the ZAMS, while the primary star appears to be exactly on the ZAMS
(Nordstr\"om \& Johansen 1994). Moreover, AR Aur is a triple system,
the existence of the as yet unseen third star being inferred from a
light-time effect in the observed minima with a period of $\sim$24 years
(Chochol et al. 1988, Nordstr\"om \& Johansen 1993).

    AR Aur A (2.5 M$_{\odot}$) and B (2.3 M$_{\odot}$) are of considerable interest as
coeval and nearly equal-mass stars apparently just arriving on the
ZAMS. Given the remaining observational uncertainties in the absolute
dimensions, it is of interest to verify this scenario by other means.
Direct detection of star C would support this scenario and provide an
estimate of the mass of star C and the inclination between the two
orbital planes. This note discusses how this test could be made.

    Models by Mazzitelli (1989) have been used to estimate the radius
({\it R}$_C$), temperature ({\it T}$_C$), and luminosity ({\it L}$_C$) 
for star C at an age of 4$\times$10$^6$ yr (the time for star A to 
reach the ZAMS from the birthline), for
different assumed values of {\it i}, the inclination of the long-period
orbit (the eclipsing pair has {\it i} = 88\fdg 5). The results are given in
Table 1. Values of {\it i} less than 30\degr are not listed, since the mass
of star C ({\it M}$_C$) would be high enough for C to make a detectable 
contribution at visible wavelengths, contrary to what is observed. Assuming
black-body radiation, the luminosity of star C can then be computed
for any wavelength and normalised to units of {\it L}$_A$ + {\it L}$_B$; thus, the
quantity {\it l}$_C$ (``third light") plotted in Figure 1 and given for some
standard photometric passbands in Table 1 is {\it l}$_C$ = {\it L}$_C$/({\it L}$_A$
+ {\it L}$_B$).
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\centerline{Table 1. Model properties for AR Aur C at an age of 4$\times$10$^6$ years}
\vskip 1mm
\begin{center}
\begin{tabular}{ccccccccccc}
\hline
{\it i}&{\it M}$_C$&{\it R}$_C$&{\it T}$_C$&{\it l}$_C$({\it R})&{\it l}$_C$({\it I})&
{\it l}$_C$({\it J})&{\it l}$_C$({\it H})&{\it l}$_C$({\it K})&{\it l}$_C$({\it L})&
{\it l}$_C$({\it M})\\
\hline
\\
90\degr & 0.523& 1.097& 3825&  0.01&  0.01&  0.02&  0.03&  0.03&  0.05&  0.05\\
70\degr & 0.559& 1.129& 3877&  0.01&  0.01&  0.02&  0.03&  0.04&  0.05&  0.06\\
60\degr & 0.611& 1.172& 3953&  0.01&  0.01&  0.02&  0.03&  0.04&  0.05&  0.06\\
50\degr & 0.698& 1.218& 4090&  0.01&  0.02&  0.03&  0.04&  0.05&  0.06&  0.07\\
40\degr & 0.847& 1.348& 4321&  0.01&  0.03&  0.04&  0.05&  0.07&  0.08&  0.09\\
30\degr & 1.124& 1.553& 4682&  0.02&  0.05&  0.06&  0.09&  0.10&  0.12&  0.14\\
\hline
\end{tabular}
\end{center}
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\centerline{2}
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\centerline{\epsffile{4135-f1.ps}}
\centerline{Figure 1. Fractional light of star C as a function}
\centerline{of assumed orbital inclination and wavelength.}
\vskip 3mm
If the light contribution from star C is significant, the depth of the
minima in the light curves of the eclipsing pair AB will be reduced.
The question we wish to address is the following: Given the
photometric elements, radii and inclination, from our previous
analysis of light curves of AB at wavelengths where third light is
negligible, at what (larger) wavelength could we observe a reduction
in eclipse depth due to star C relative to what we would predict
without it?

  Using the {\it b}$_F$ (4747 \AA) light curve and analysis tools from our
previous study, we have studied this question by adding specified
amounts of third light and then redetermining {\it l}$_C$ from the light curve,
gradually reducing the number of points used. We find that we can
recover {\it l}$_C$ rather accurately with a surprisingly few observations of
the precision of the {\it b}$_F$ light curve, 0.01 mag: Typical standard errors
are 0.01 with 40 points, 0.02 with just 10 well-distributed points on
the light curve (about half near both mid-eclipses, half outside
eclipse). This remarkable economy is possible because the existing
high-quality analysis provides an accurate prediction of the eclipse
depths in the absence of third light. The errors in {\it l}$_C$ scale, of
course, with the mean errors of the actual new observations, which
will also depend on the wavelength of observation.

  The dotted line in Figure 1 indicates the usable wavelength for which
0.04 of third light is measurable with certainty. For inclinations
close to 90\degr\ (i.e., near co-planarity of the orbits), the K band
(2.2 $\mu$m) is just at the detection limit for star C with 1\%
photometry. In the L and M bands (3.5 and 5 $\mu$m), detection will be
easier, but photometry probably correspondingly more difficult. The N
band (9 $\mu$m) should be avoided, as dust emission might be
significant.


  Deviations from the ephemeris derived earlier for the eclipsing pair
AB:
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\centerline{Min\,I = HJD\,2\,438\,402.1847 + 4\fd 1346662$\times$E}
\vskip 1mm

\noindent due to motion in the AB-C orbit are not more than 12 minutes, and
secondary minima occur midway between primary eclipses since the AB
orbit is circular. In planning follow-up photometry, observers should
be aware of the problems with variable comparison stars described in
Nordstr\"om \& Johansen (1994). It is proposed to use two of the
reliable stars: 
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\centerline{3}
\vskip 2mm
\noindent HR\,1734, HR\,1738, or HR\,1749. HR\,1734 has a faint (m$_V$ =
11.8) companion at a distance of 3\farcs 8, which always should be
included.
\vskip 1cm


% Call for macros \authors - \authorsrightcol - \endauthors
\beginauthors
\authorsrightcol
K. T. JOHANSEN
B. NORDSTR\"OM
The Niels Bohr Institute of 
Astronomy, 
Physics and Geophysics
Astronomical Observatory
Brorfeldevej 23
DK-4340 T\o ll\o se
Denmark
\endauthors

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\references

Chochol D., Juza K., Mayer O., Zverko J., Ziznovsky J., 1988, {\it Bull.
  Astron. Inst. Czech.}, {\bf 39}, 69
  
Mazzitelli I., 1989, in Low-Mass Star Formation and Pre-Main-Sequence
  Objects, B. Reipurth (ed.), ESO Conference and Workshop Proceedings
  No. 33, p. 433
  
Nordstr\"om B., Johansen K.T., 1993, {\it IBVS}, No.\,3871

Nordstr\"om B., Johansen K.T., 1994, {\it A}\&{\it A}, {\bf 282}, 787


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