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$\begin{figure} \par\includegraphics[width=8.4cm,clip]{5940fig1.eps} \end{figure}$ Figure 1: Top: Lomb-Scargle (LS) periodogram of the VHE runwise flux for LS 5039 (chance probability to obtain the LS power vs. frequency). Inset: zoom around the highest peak (pre-trial probability $\sim$ 10^-20), which corresponds to a period of 3.9078 $\pm$ 0.0015 days, compatible with the ephemeris value of $3.90603\pm 0.00017$ days (vertical red line at 0.2560 days^-1 on the inset) from Casares et al. (2005). The post-trial chance probability of the orbital period peak is found to be less than 10^-15 (see Fig. 3). Middle: LS periodogram of the same data after subtraction of a pure sinusoidal component at the orbital period of 3.90603 days. The orbital frequency peak has been removed as expected, as well as significant satellite peaks (see text). Bottom: LS periodogram of the HESS source HESS J1825-137 observed simultaneously in the same field of view. The middle and bottom panel results are consistent with that expected of white noise over the range of frequencies sampled. The dotted lines correspond to a 10^-2 pre-trial chance probability.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{5940fig2.eps} \end{figure}$ Figure 2: Top: normalised Rayleigh Statistic (deJager 1994) periodogram calculated from run-wise HESS fluxes for LS 5039. The middle and bottom panels depict the NRS after subtraction of the orbital period and for HESS J1825-137, respectively (as for the Lomb-Scargle test in Fig. 1).
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{5940fig3.eps} \end{figure}$ Figure 3: Density function of the chance probability of the Lomb-Scargle power determined by Monte-Carlo and resampling methods after subtraction of the orbital period sinusoid. The expected exponential density functions are also indicated (solid lines). In the Monte-Carlo method, $\sim$ 10⁶ random time series were generated to produce a distribution of the highest Lomb-Scargle power. The highest power obtained after these iterations reaches just above 20, well below the power of 62 obtained from the unshuffled lightcurve at the orbital period. An extrapolation of the curves is therefore used to estimate the chance probability for powers above 20.
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In the text

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{5940fig4.eps} \end{figure}$ Figure 4: The orbital geometry (Casares et al. 2005) viewed from directly above LS 5039. Shown are: phases ( $\phi$ ) of minimum (periastron) and maximum (apastron) separation between the two components; epochs of superior and inferior conjunctions of the compact object representing phases of co-aligment along our line-of-sight of the compact object and stellar companion. The orbit is actually inclined at an angle in the range $13^\circ < i < 64^\circ$ with respect to the view above. VHE $\gamma$ -rays (straight black lines with arrows) can be absorbed by optical photons of energy $h\nu _\epsilon$ , when their scattering angle $\theta$ exceeds zero.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{5940fig5.eps} \end{figure}$ Figure 5: Top: integral $\gamma$ -ray flux (F>1 TeV) lightcurve (phasogram) of LS 5039 from HESS data (2004 to 2005) on a run-by-run basis folded with the orbital ephemeris of Casares et al. (2005). Each run is $\sim$ 28 min. Two full phase ( $\phi$ ) periods are shown for clarity. The blue solid arrows depict periastron and apastron. The thin red dashed lines represent the superior and inferior conjunctions of the compact object, and the thick red dashed line depicts the Lomb-Scargle Sine coefficients for the period giving the highest Lomb-Scargle power. This coefficient is subtracted from the light curve in Fig. 1 middle panel. Middle: fitted pure power-law photon index (for energies 0.2 to 5 TeV) vs. phase interval of width $\Delta \phi =0.1$ . Because of low statistics in each bin, more complicated functions such as a power-law with exponential cutoff provide a no better than a pure power-law. Bottom: power-law normalisation (at 1 TeV) vs. phase interval of width $\Delta \phi =0.1$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{5940fig6.eps} \end{figure}$ Figure 6: Very high energy $\gamma$ -ray spectra of LS 5039 for two broad orbital phase intervals (defined in the text): INFC $0.45<\phi \leq 0.9$ (red circles); SUPC $\phi \leq 0.45$ and $\phi >0.9$ (blue triangles). The shaded regions represent the 1 $\sigma$ confidence bands on the fitted functions (Table 1). Both spectra are mutually incompatible with the probability that the same spectral shape would fit both simultaneously being $\sim$ $2\times 10^{-6}$ . A clear spectral hardening in the region 0.3 to $\sim$ 20 TeV is noticed for the INFC phase interval.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{5940fig7.eps} \end{figure}$ Figure 7: Top: integral flux (E>1 TeV) vs. time (MJD) for LS 5039 on a run-by-run basis. Bottom: after subtraction of the orbital period of 3.9063 days (this is achieved by subtraction of the Lomb-Scargle coefficients for the selected period). The average flux (dashed lines) for the post-subtracted light-curve is consistent with a steady source with a chance probability of $4\times 10^{-2}$ . In addition, the average flux levels determined exclusively for 2004 and 2005 data differ at a 2 $\sigma$ level (statistical errors) but are consistent when factoring in systematic errors of $\sim$ 10% on a run-by-run basis.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{5940fig8.eps} \end{figure}$ Figure 8: Energy spectra of LS 5039 separated into the same broad phase intervals as for Fig. 6. INFC $0.45<\phi \leq 0.9$ (red circles); SUPC $\phi \leq 0.45$ and $\phi >0.9$ (blue triangles), comparing results from the semi-analytical Model + Hillas (filled markers) and Hillas-only (open markers) analyses (Aharonian et al. 2006b), respectively. The Hillas-only analysis has made use of an independent calibration chain.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{5940fig2.eps} \end{figure}$	Figure 2: Top: normalised Rayleigh Statistic (deJager 1994) periodogram calculated from run-wise HESS fluxes for LS 5039. The middle and bottom panels depict the NRS after subtraction of the orbital period and for HESS J1825-137, respectively (as for the Lomb-Scargle test in Fig. 1).
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