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. Furthermore, 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 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 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. From the reduced $\chi^2$ for each data set one can scale the uncertainties such that $\chi^2_{\nu} = 1$. This is only permitted if a high confidence in the applied model is justified. We think that is the case when time stamps have been obtained over a short time interval. interval allowing us to rescale timing uncertainties.  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}  \end{equation}  \noindent  where $N$ is the number of data points, $a,b$ the two parameters for a linear line and $(x_{i}, y_{i})$ is a given timing measurement at a given epoch.  We have tested the dependence of scatter on the weight used and found no difference in the scatter metrics when applying a weight of one for all measurements. %Some text has been lost!  %Here add ideas:  %-Mention about missing Finally some additional details. We only inferred new timing uncertainties for  data %-Mention that nominal weight and unit weight has been used. Both gave same RMS scatter. sets with more than two measurements. For a given data set we used the published ephemeris (orbital period) to calculate the eclipse epochs. For the time stamps presented in \cite{BaileyCropper_1991} no ephemeris was stated. We therefore, used their eclipse cycles for the independent variable to calculate a best-fit line. We have also discarded one time stamp from \cite{Ferrario_1989} due to a too high timing uncertainty.