Tobias C Hinse edited untitled.tex  over 8 years ago

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\section{Generating 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. A total of five new timings were reported by \cite{Ramsay1994} but only one were listed in 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}. All new measurements obtained by \cite{Potter_2011} were taken directly from their Table 1. Some remarks are at place. In Table \ref{NewTimingData} we list the original uncertainty as $\sigma_{lit}$ in the first column. We also list the uncertainty obtained from the scatter of the data around a best-fit linear regression line. We have calculated three scatter metrics: a) the root-mean-square, root-mean-square (RMS),  b) the standard deviation (STD)  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{bevingtonformula}  \end{equation}  \noindent  where $N$ is the number of data points, $(a,b)$ denotes the two parameters for a linear line and $(x_{i}, y_{i})$ is a given timing measurement with $x_{i}$ being the eclipse cycle number. This procedure likely provides a more realistic determination of timing uncertainties for several reasons. For a given measurement series the same telescope/instrument has been used most likely under similar weather conditions (does not apply for satellite based observations). In addition, the same technique to measure the mid-eclipse time has been applied for each published timing series. However, this approach is valid only for data sets with three or more timing measurements. For two or less measurements we have adopted the timing uncertainty as quoted in the literature. The above approach also justifies the inclusion of any data point with a reasonable timing accuracy. The technique of inferring uncertainties from the scatter distribution has also limitations. The most important one is the time length over which the data spans. If the series of measurements spans over a too long time interval, then the scatter likely contains an astrophysical signal (additional bodies, mass transfer, etc.). We have looked into this. Most of the time series measurements spans only a few days. The longest time interval is spanned by data obtained from 1.9m/HIPPO measurement \cite{Potter_2011} spanning almost two years. In that case we have taken the timings as quoted by \cite{Potter_2011}. Final remarks: We have tested the change in scatter metrics when unit weights or weights of the form $1/\sigma_{i}^2$ were used with $\sigma_{i}^2$ given by the published uncertainty in the literature. We found no change or influence at all. Also for each fit we used the published period to calculate cycle numbers. No ephemeris were given in the works of \cite{BaileyCropper_1991}. We have therefore used their cycle numbers in order to determine the scatter around a best-fit line. Also we chose the zero-epoch reference point to be more or less close to the center of a given measurement series. Finally, we have rejected the timing measurement HJD 2,44,7132.93600 of \cite{Ferrario_1989} due to a too large timing uncertainty obtained from a shallow eclipse in J-band data.  \begin{table}   \begin{tabular}{ c c c c c c }  \hline  BJD(TDB) &$\sigma_{lit}$ & RMS & STD & Eq. (XXX) Eq.~\ref{Bevingtonformula}  & Remarks \\ \hline   2455506.427034 & 0.0000100 & 0.0000100 & 0.0000100 & 0.0000100 & HIPPO/1.9m, \cite{Potter_2011}, no RMS,STD,Eq.(6.15) determination \\   2455478.485831 & 0.0000100 & 0.0000100 & 0.0000100 & 0.0000100 & HIPPO/1.9m, \cite{Potter_2011}, no RMS,STD,Eq.(6.15) determination \\