Tobias C Hinse edited untitled.tex  over 8 years ago

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\section{Compiling a new dataset}  At the present stage some inconsistencies were discovered in the reported timing uncertainties as listed in Table 1 in Potter et al. (2011). For example the timing uncertainty reported by \cite{Warren_1995} is 0.000023 days, while Potter et al. (2011) reports 0.00003 and 0.00004 days. Furthermore, after scrutinizing the literature we found that several timing measurements were omitted in Potter et al. (2011). We tested for the possibility that Potter et al. (2011) adopts timing uncertainties from the spread of data around a best-fit linear regression. However, that seems not the case: As a test, we used the five timing measurements from \cite{Beuermann1988} as listed in Table 1 in Potter et al. (2011). We fitted a linear straight line using CURVEFIT as implemented in IDL and found a scatter of 0.00004 to 0.00005 days depending on the metric used to measure scatter around the best-fit. The quoted uncertainties in Potter et al. (2011) are smaller by at least a factor of two. We conclude that Potter et al. (2011) must be in error when quoting timing uncertainties in their Table 1. Similar mistakes when quoting timing uncertainties apply to data listed in \cite{Ramsay1994}. Furthermore, after scrutinizing the literature for timing measurements of UZ For we found several timing measurements that were omitted in Potter et al. (2011). For example six eclipse timings were reported by \cite{BaileyCropper_1991} with a uniform uncertainty of 0.00006 days. However, Potter et al. (2011) only reports three of the six timings. Furthermore, a total of five new timings were reported by \cite{Ramsay1994}, but only one were listed in Potter et al. (2011). We can not come up with a good explanation why those extra timing measurements should be omitted or discarded. All of the new data points have been presented in the original works alongside with data points used in the analysis of Potter et al. (2011).  In this research we make use of all timing measurements that have been obtained with reasonable accuracy. We have therefore recompiled all available timing measurements from the literature. We list them in Table \ref{NewTimingData}. The original HJD(UTC) time stamps from the literature were converted to the BJD(TDB) system using the on-line time utilities\footnote{http://astroutils.astronomy.ohio-state.edu/time/} \citep{Eastman_2010}. Not all sources of timing measurements provide explicit information of the the time standard used. In that case we assume that HJD time stamps are valid in the UTC standard. This assumption is to some extend justified since the first timing measurement was taken in august 1983. At that time the UTC time standard for astronomical observations was widespread. All new measurements presented in \cite{Potter_2011} were taken directly from their Table 1. Some remarks are at place. By finding additional timing measurements (otherwise omitted in Potter et al. 2011) in the literature we decided to follow a different approach to estimate timing uncertainties. For measurements that were taken over a short time period one can determine a best-fit line and estimate timing uncertainties from the data scatter. The underlying assumption in this method is that no significant astrophysical signal (interaction between binary components or additional bodies) is contained in the timing measurements over a few consecutive observing nights. Therefore, the scatter around a linear ephemeris should be a reasonable measure of how well timings were measured. In other words, only a first-order effect due to a linear ephemeris is observed. Higher-order eclipse timing variation effects are negligible for data sets obtained during a few consecutive nights. The advantage is that for a given data set the same telescope/instrument were used as well as weather conditions were likely not to have changed much from night to night. Furthermore, most likely the same technique was applied to infer the individual time stamps of a given data set. In Table \ref{NewTimingData} we list the original quoted uncertainties presented in the literature as $\sigma_{lit}$. We also list the uncertainty obtained from the scatter of the data around a best-fit linear regression line. The corresponding reduced $\chi^2$ statistic for each fit is also tabulated in the third column. From the reduced $\chi^2$ for each data set one can scale the corresponding uncertainties such that $\chi^2_{\nu} = 1$ is enforced \citep{Bevington2003Book}. This step is only permitted if a high confidence in the applied model is justified. We think that this is the case when time stamps have been obtained over a short time interval allowing us to rescale interval. However, ultimately the  timing uncertainties. uncertainty depends on the sampling of the eclipse event at a sufficiently high signal-to-noise ratio.  The \cite{Imamura_1998} data set was split in two since those time stamps were obtained from two observing runs each lasting for a few days. Furthermore, we have calculated three data scatter metrics around the best-fit line: a) the root-mean-square, b) the standard deviation and c) the standard deviation as given by \cite{Bevington2003Book} and defined as \begin{equation}  \sigma^2 = \frac{1}{N-2} \sum_{i=1}^{N}(y_{i} - a - bx_{i})^2  \label{BevEq6p15} 

\section{New dataset: Linear ephemeris using MPFIT}  In the following we will consider the newly compiled data set with timing uncertainties obtained from rescaling the published uncertainties in order to ensure $\chi^{2}=1$ over short time intervals.  We have determined the following linear ephemeris using MPFIT. We followed the monte-carlo approach and determined a best-fit model by generating 10 million random initial guesses. We used best-fit parameters from LINFIT to obtain a first estimate of the initial epoch and period. Then initial guesses were drawn from a Gaussian distribution centered at the LINFIT values with standard deviation given by five times the formal LINFIT uncertainties. The linear ephemeris is shown in Fig.~\ref{Linearfit_NEW}. The resulting reduced $\chi^2$ value was 162.5 ($\chi^2 = 8448.6$ with (54-2) degrees of freedom) with the ephemeris (or computed timings) given as \begin{equation}  T(E) = BJD_{TDB}~2,450,018.703604(3) + E \times 0.08786542817(9)  \end{equation}