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\IBVShead{4249}{22 September 1995}       % Use it with dummy or empty arguments
 
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{\ft AN IMPROVED EPHEMERIS FOR Z CAMELOPARDALIS}
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Z Cam is the prototype of a class of dwarf novae that show standstills in
their light curves. Kraft et al.~(1969; henceforth KKM) first established
its ephemeris. They combined radial-velocity information with observations
of periodic features in the light curve to derive a period of $0.289840
\pm 1 \times 10^{-6}$ d. Two studies by Robinson (1973a and 1973b), one
photometric and the other using H$\alpha$ emission velocities, did not yet
show any significant error in the KKM ephemeris as of the early 1970s. 
Szkody \& Wade (1981) obtained a cycle of emission-line velocities in
early 1979, when Z Cam was in standstill: they also found no difference
from the KKM ephemeris. Even so, the formal error in the KKM ephemeris has
now accumulated to greater than 0.1 cycle, so we re-established the phase. 

We obtained spectra of Z Cam using the Michigan-Dartmouth-MIT Observatory
1.3-m McGraw-Hill telescope.  We used the Mark III transmission-grating
spectrometer and a TI 4849 CCD chip (Luppino 1989); our 300 line/mm
grating gave 10 \AA\ FWHM resolution from 6400 to 9000 \AA .  On 1991
October 17 UT we obtained thirteen 15-minute exposures covering three
hours; the next night we obtained three exposures, and the night after
this we obtained a single spectrum.  Reduction followed the procedures
described in Thorstensen et al.~(1991) and the references therein. The
emission lines within our spectral range were strong; H$\alpha$ had an
equivalent width of 37 \AA\ in the sum of our spectra, and at its center
stood about twice as high as the adjacent continuum. The FWHM of H$\alpha$
was 30 \AA .  Our first night was photometric, and we reduced our spectra
to absolute flux using an observation of the white dwarf G191B2B; with a
modest extrapolation to shorter wavelengths, we derive for Z Cam $V = 13.5
\pm 0.3$ (estimated error). This is close to the mean minimum magnitude
(Szkody \& Mattei 1984).  Thus the magnitude and spectrum both show that Z
Cam was not in outburst or standstill. There were no evident changes in
the spectrum or flux during our brief observations. 

Unfortunately, the red-star features were not measurable in our spectra,
unsurprising given its rather early spectral type (G1: KKM).
We therefore measured the strong H$\alpha$ emission line using a
double-Gaussian convolution technique (Shafter 1983). The Gaussians in the
template were separated by 34 \AA\ (full width), equivalent to ${\rm 1500\
km\ s^{-1}}$. In effect, this measured the steep sides of the line
profile.  Table 1 lists the resulting velocity time series. 
We fit to our emission-line velocities a least-square sinusoid of the form
$$v(t) = \gamma + K \sin [2\pi (t - T_0)/P],$$ with the period $P$ fixed
at the KKM value.  With this convention, $T_0$ is the epoch of apparent
inferior conjunction of the line source.  This gave $\gamma = -36 \pm 3$
km s$^{-1}$, $K = 138 \pm 4$ km s$^{-1}$, and $T_0 = \hbox{HJD
}2448547.0174 \pm 0.0014$, where the uncertainties are 1-$\sigma$.  The
choice of $T_0$ is arbitrary {\it modulo} the period; the epoch given here
corresponds to the night of our most extensive observations.  The
1-$\sigma$ error of a single measurement, derived from the\break
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\centerline{2}
\vskip 1mm
\noindent  goodness of
fit, was only 11 km s$^{-1}$.  We also re-fit the H$\alpha$ velocities
from Robinson (1973b); this gave $\gamma = -44 \pm 6$ km s$^{-1}$, $K =
135 \pm 9$ km s$^{-1}$, and $T_0 = \hbox{HJD }2441355.7828 \pm 0.0028$;
the goodness-of-fit implies $\sigma = 25$ km s$^{-1}$. The good agreement
between the $K$ and $\gamma$ velocities in the two studies gives us
confidence that our phases may be compared directly. We are further
emboldened since we are measuring the same line (H$\alpha$ emission) in
the same state (quiescence) and using a broadly similar centering, which
emphasizes the outer parts of the line profile. 

The two values of $T_0$ above are 7191.2346 days apart.  This is 24811.05
cycles of the KKM period.  There is no ambiguity in the cycle count; KKM's
quoted error does not allow it, and the adequacy of the KKM ephemeris for
the intervening epochs of Robinson (1973a and 1973b) and Szkody \& Wade
(1981) makes a cycle-count error even more unlikely. Adopting 24811 cycles
for the interval gives a refined period $P = 0.2898406(2)\ {\rm d}$, where
the quoted uncertainty is inflated a bit from the formal 1-$\sigma$ value
($1.2 \times 10^{-7}$ d) and is in units of the last quoted digit.  In
Figure~1 we show the data of Robinson (1973b), folded together with ours
on this best period.  Extending this analysis back to the original KKM
radial-velocity data does not improve the accuracy much, since their
velocities show much more scatter than ours or Robinson's, and the
extension of the time base is modest;  in any case, the epoch of
emission-line conjunction given in KKM's Table 2 agrees with our phase to
within 0.01 cycle.  Given how well our period agrees with the KKM
ephemeris, which was adequate through the 1970s, there is no evidence yet
of any period change. 

The KKM study did, however, define a phase tied to the red star in the
system; this red-star phase should have a more direct physical
interpretation than the emission-line phase.  KKM noted that the emission
lines are not precisely 180 degrees out of phase with the absorption
(presumed to represent the red star), but rather lag by an additional
0.017 d (some 20 degrees of phase).  The ephemeris quoted in KKM's
equation (1) is for the inferior conjunction of the red star; if we assume
that the 0.017 d offset still holds, we find for an updated red-star
ephemeris $$\hbox{Red star inferior conjunction} = \hbox{JD}_\odot
2448546.855 + 0.2898406(2) E,$$ where $E$ is the integer cycle count.  For
completeness we give here $$\hbox{Emission-line inferior conjunction} =
\hbox{JD}_\odot 2448547.0174 + 0.2898406(2) E.$$ 
\vskip 2mm
\qquad\hbox{
$$\vbox{\halign{\hfil # & \hfil # \quad & \hfil # & \hfil # \quad &
  \hfil # & \hfil # \quad &
  \hfil # & \hfil # \cr
\noalign{\medskip} \cr
\noalign{\vskip 3pt} 
\multispan{8}{\hfil {Table 1: H$\alpha$ Emission Velocities in Z Cam} \hfil}\cr
\noalign{\smallskip} \cr
\noalign{\vskip -3pt} 
\noalign{\hrule\smallskip} \cr
${\rm HJD^a}$ \ \  & $V$ & ${\rm HJD^a}$ \ \   & $V$
 & ${\rm HJD^a}$ \ \  & $V$  & ${\rm HJD^a}$ \ \ & $V$ \cr
   & \hidewidth ${\rm (km\ s^{-1})}$ \hidewidth &  &  
     \hidewidth ${\rm (km\ s^{-1}})$ \hidewidth &  &  
     \hidewidth ${\rm (km\ s^{-1}})$ \hidewidth & 
\multispan2\hfil ${\rm (km\ s^{-1}})$ \cr
\noalign{\smallskip}
\noalign{\hrule\smallskip} \cr
8546.881 & $  -52$ & 8546.936 & $ -171$ & 8546.981 & $ -124$ & 8547.943 & $   79$ \cr 
8546.891 & $  -84$ & 8546.948 & $ -190$ & 8546.993 & $ -109$ & 8547.954 & $  106$ \cr 
8546.903 & $ -124$ & 8546.959 & $ -171$ & 8547.004 & $  -60$ & 8547.965 & $   99$ \cr 
8546.914 & $ -132$ & 8546.971 & $ -148$ & 8547.016 & $  -42$ & 8548.958 & $ -186$ \cr 
8546.926 & $ -159$ \cr
\noalign{\medskip}
\noalign{\hrule} \cr
\noalign{\vskip 1pt}
\noalign{$\strut^{\rm a}\ $Heliocentric Julian Date of mid-integration, 
	minus 2 440 000.}
}}$$
}
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\centerline{3}

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\noindent Figure 1. H$\alpha$ radial velocities from
Robinson (1973b; squares) and this work (triangles) folded
on the refined period.  All data are plotted twice for
continuity.  The curve shown is the least-squares best fit,
and its parameters are given in the figure.  For the
horizontal axis, phase zero is apparent inferior conjunction of the
emission line source; inferior conjunction of the red star should
be at phase 0.44 in this convention (KKM).
\large
\vskip 5mm
The emission-line epoch
has rather better internal precision than the absorption-line epoch. 
Since the emission lines form in or above the accretion disk, it
seems surprising that the ephemerides from such widely separated epochs
can be phased together, and that there is no obvious phase change between
quiescence and standstill. 

\vskip 1cm

\beginauthors
John R. THORSTENSEN
Dept.~of Physics and Astronomy
Dartmouth College
6127 Wilder Laboratory
Hanover, NH 03755-3528
U. S. A.
 Internet: thorsten@dartmouth.edu
\endauthors   

\vskip -1.3in
\beginauthors
\authorsrightcol
F. A. RINGWALD
Planetary Science Institute
620 North Sixth Avenue
Tucson, AZ 85705-8331
U. S. A.
 Internet: far@psi.edu
\endauthors   
 

\references
Kraft, R. P., Krzemi\'nski, W., and Mumford, G. S., 1969, {\it ApJ}, {\bf 158}, 589 (KKM)

Luppino, G. A., 1989, {\it PASP}, {\bf 646}, 931

Robinson, E. L., 1973a, {\it ApJ}, {\bf 180}, 121

Robinson, E. L., 1973b, {\it ApJ}, {\bf 186}, 347

Shafter, A. W., 1983, {\it ApJ}, {\bf 267}, 222

Szkody, P. and Mattei, J. A., 1984, {\it PASP}, {\bf 96}, 988

Szkody, P. and Wade, R. A., 1981, {\it ApJ}, {\bf 251}, 201

Thorstensen, J. R., Ringwald, F. A., Wade, R. A., Schmidt, G. D., and 
Norsworthy, J. E., 1991, {\it AJ}, {\bf 102}, 272

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