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As a test the CURVEFIT routine has been used in a similar manner. The resulting reduced chi2 was also 95.22 matching and confirming the result from the previous section. The /NODERIVATIVE keyword does not change anything and expressions for the partial derivative has been included. The RMS also agrees with the results obtained from LINFIT. However, the formal $1\sigma$ uncertainties in the best-fit parameters (TZERO and PERIOD) are one magnitude smaller compared to the equivalent values obtained from LINFIT. The data and the best-fit line (obtained from LINFIT) is shown in Fig.~\ref{linearfit} with the residuals plotted in Fig.~\ref{linearfit_res}. There is absolutely no difference when using the results from CURVEFIT.  \section{Linear \subsection{Linear  ephemeris - conclusion} After fitting a straight line and visually inspecting the residual plots I cannot see any convincing trend that should justify a quadratic ephemeris (linear + a quadratic term). What I see is a sinusoidal variation around the best-fit line. Relative to the linear linear the first timing measurement arrives 20s earlier than expected. Then the trend goes down and increases again to 40s at E=0, then decreases again to a minimum to around 20s and increases again thereafter. There is no obvious quadratic trend from looking at the residuals in Fig.~\ref{linearfit_res}.  \section{Quadratic ephemeris} 
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\subsection{Quadratic ephemeris using MPFIT}  I have also used MPFIT to fit a quadratic ephemeris to the Potter et al. (2011) timing data. The resulting $\chi^2$ is 3718.94 with (42-3) degrees of freedom yielding a reduced $\chi^2$ of 95.36. This is identical to the results obtained with CURVEFIT and thus confirmed independently. This is really surprising. The RMS scatter of data around the quadratic ephemeris is around 31 seconds. I will not state the best-fit values for the three model parameters (and their uncertainties) as obtained from MPFIT.  \subsection{Quadratic ephemeris - conclusion}  Based on the above result I cannot see that the residuals relative to a linear ephemeris allow the inclusion of a secular term accounting for a quadratic ephemeris. The $chi^2$ increases with an extra parameter which is not what is expected. I will continue now and fit a 1- and 2-companion model.  \section{linear + 1-companion LTT model using MPFIT}