All Figures

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{standard_model.eps} \end{figure}$ Figure 1: Spectra from our standard model with $0^\circ$ inclination - free-free flux (dashed), synchrotron flux (dotted), and the total flux (solid). The effect of free-free absorption on the synchrotron emission in this wide system is only just evident below 300 MHz. The spectral index of the thermal spectrum is +0.6, and the optically thin part of the synchrotron spectrum is -0.5. Neither the Razin effect nor SSA are treated in this model.
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In the text

$\begin{figure} \par\vspace{15.2cm} \special{psfile=st1.6.eps vscale=50 hscale=50... ...file=st22.eps vscale=50 hscale=50 hoffset=-20 voffset=-25 angle=0}\end{figure}$ Figure 2: Intensity distributions of our standard model at $0^\circ$ inclination at 1.6 GHz (top) and 22 GHz (bottom). Both images have the same intensity scale, highlighting the relative importance of the emission from the wind-wind collision region and the stellar winds as frequency varies (see also Fig. 17). Though not shown, the emission extends to the panel boundaries. Neither the Razin effect nor SSA are included in this calculation.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{razin_frac.ps} \end{figure}$ Figure 3: The influence of the Razin effect on synthetic synchrotron spectra using the standard model at $0^\circ$ inclination for various values of $\zeta$ . The effect of free-free absorption by the circum-binary stellar wind envelope is negligible, just visible at around 200-300 MHz. No Razin (solid), $\zeta =10^{-3}$ (dotted), 10^-4 (dashed), 10^-5 (dash-dotted). All spectra are normalized to the 80 GHz synchrotron flux when no Razin effect is included.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{ssa_frac.ps} \end{figure}$ Figure 4: The effect of SSA on synthetic synchrotron spectra using the standard model at $0^\circ$ inclination for various values of $\zeta$ . The effect of free-free absorption by the circum-binary stellar wind envelope is negligible, just visible at around 200-300 MHz. No SSA (solid), $\zeta =10^{-4}$ (dotted), 10^-3(dashed), 10^-2 (dash-dotted). All spectra are normalized to the 80 GHz synchrotron flux when no SSA is included.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{ffsep3.eps} \end{figure}$ Figure 5: The effect of separation on synchrotron spectra using the standard model at $0^\circ$ inclination and $\zeta =10^{-4}$ , for D=2, 5, 20, and $80\times 10^{14}$ cm. Only the effect of free-free opacity is included.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{lum_sep1.eps} \end{figure}$ Figure 6: The effect of separation on the synchrotron luminosity for a power-law electron energy distribution in the optically thin regime. Shown are the data points at four frequencies: 1.6 (solid), 5.0 (dotted), 8.3 (dashed), 14.6 GHz (dot-dashed). The slope of this log-log plot is -1/2, as expected.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{wwcff.eps} \end{figure}$ Figure 7: The effect of separation on the free-free opacity within the wind-wind collision region, using the standard model at $0^\circ$ inclination and $\zeta =10^{-4}$ , for D=2, 5, and $20\times 10^{14}$ cm. The intrinsic synchrotron emission is shown (solid) along with the spectra of the synchrotron emission emerging from the collision zone (dotted).
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{dsep_ssa_raz.ps} \end{figure}$ Figure 8: The effect of separation on the synchrotron emission using the standard model at $0^\circ$ inclination and $\zeta =10^{-4}$ , for $D=20\times 10^{14}$ (labelled "20''), $5\times 10^{14}$ cm ("5'') and $D=2\times 10^{14}$ ("2''): the intrinsic synchrotron emission i.e. no Razin or SSA (solid); only Razin effect included (dashed); only SSA included (dotted). The intrinsic synchrotron emission is shown to highlight the effect of separation on the synchrotron emission i.e. in the absence of the strong free-free absorption, as seen in Fig. 5.
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In the text

$\begin{figure} \par\vspace{17.9cm} \special{psfile=fig7a.eps vscale=41 hscale=41... ...sfile=fig7c.eps vscale=41 hscale=41 hoffset=5 voffset=-23 angle=0}\end{figure}$ Figure 9: Intensity distributions at 1.6 GHz and $0^\circ$ inclination for an orbital separation of 20 (top), 5 (middle), and $2 \times 10^{14}$ cm (bottom), corresponding to angular separations of 133, 33 and 13.3 mas respectively. The crosses denote the positions of the stars, with the WR star located at (0, 0). Each image has the same intensity scale and contours. The contours were chosen to highlight the relative brightness of the stellar wind of the WR star and the emission from the collision region. Though not shown, the emission extends to the boundaries of the panels (see also Fig. 17).
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In the text

$\begin{figure} \par\includegraphics[width=8.6cm,clip]{inc.ps}\end{figure}$ Figure 10: The effect of free-free opacity as a function of inclination angle on the synchrotron spectra of the standard model with $\zeta =10^{-4}$ . The inclination angle of the axis of symmetry to the plane of the sky for the various spectra is shown. Dashed lines indicate $i< 0^\circ$ ( i.e. WR star in front), the solid line $i = 0^\circ$ ( i.e. quadrature), and dotted lines $i > 0^\circ$ ( i.e. OB star in front).
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In the text

$\begin{figure} \par\vspace{15.6cm} \special{psfile=p60inc.2.eps vscale=45 hscale... ...e=m30inc.2.eps vscale=45 hscale=45 hoffset=-5 voffset=-43 angle=0}\end{figure}$ Figure 11: The 1.6-GHz intensity distribution for a model with $D = 5 \times 10^{14}$ cm at $+60^\circ$ (top), $+30^\circ$ (middle), and $-30^\circ$ (bottom) inclination. At positive angles the OB star is closer to the observer than the WR star. The crosses denote the position of the stars, with the WR star at (0, 0). Each image has the same intensity greyscale and contour intervals (also used in the middle panel of Fig. 9, showing the $0^\circ$ case). The optically thick part of the OB-star wind is the obvious "hole'' (top panel), below which the synchrotron emission is seen, surrounded by the free-free emission, largely from the WR wind. As inclination decreases, the hole becomes less pronounced and the synchrotron intensity increases as the line-of-sight opacity through the OB wind decreases. When the WR star is closer to the observer (i<0), the optically thick part of the WR-star wind obscures the lower part of synchrotron emission region.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{inc_ssa_int.ps} \end{figure}$ Figure 12: The effect of SSA on the spectrum of the emission emerging from the shocked region as a function of inclination angle for the standard model with $\zeta =10^{-4}$ . The inclination angle of the axis of symmetry to the plane of the sky for the various spectra is shown. Dashed lines indicate $i< 0^\circ$ ( i.e. WR star in front), the solid line $i = 0^\circ$ ( i.e. quadrature), and dotted lines $i > 0^\circ$ ( i.e. OB star in front). The dot-dashed line is the intrinsic synchrotron emission from the shocked gas, which is independent of inclination, plotted for reference.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{ff_inc.ps} \end{figure}$ Figure 13: The change in thermal flux as a function of inclination angle using the standard model with $\zeta =10^{-4}$ . Shown are curves for 1.6 (solid), 5 (dotted) and 22 GHz (dot-dashed).
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In the text

$\begin{figure} \par\includegraphics[width=8.7cm,clip]{figure14.eps} \end{figure}$ Figure 14: The synchrotron spectrum of WR 147 as deduced by several authors - solid squares (two separate estimates from the same observational data by Skinner et al. 1999), solid pentagons (Setia Gunawan et al. 2001), open circles (fluxes from Churchwell et al. 1992 and Contreras & Rodríguez 1999). The flux at both 22 and 43 GHz is highly uncertain, with the latter estimated from a long extrapolation of a power-law fit to the lower frequency "thermal'' data points to be $\approx$ 2 mJy (Setia Gunawan et al. 2001; Skinner et al. 1999). Both high frequency points suggest a high frequency turn down. The lines are theoretical spectra from models where only free-free absorption in the circum-binary stellar wind envelope is attenuating the synchrotron emission. Models for various inclination angles are shown: 0, -30, -60 and $-85^\circ$ (corresponding to $\zeta =6.92, 7.23, 8.08$ , and $13.44\times 10^{-3}$ respectively). The $0^\circ$ model is denoted by the solid line.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{razssav2_10.ps} \end{figure}$ Figure 15: Model synchrotron spectra when SSA, the Razin effect and free-free absorption in the circum-binary stellar wind envelope are included, for various inclination angles: 0 (solid), $\pm$ 30 (dotted), and $\pm$ 60 (dashed), with corresponding values of $\zeta = (7.03, 7.32, 8.12)\times 10^{-3}$ . The data points are those shown in Fig. 14.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{figure16.ps} \end{figure}$ Figure 16: The spectrum of WR 147. The synchrotron data are those shown in Figs. 14 and 15 and represented by solid data points. The total flux as deduced by the same authors are represented by the hollow data points. The lines are the total (solid), thermal (dotted) and synchrotron (dot-dashed) spectra of the $i = 0^\circ$ models with $\zeta =7.03\times 10^{-3}$ , where SSA, Razin and free-free absorption are included in the radiative transfer calculations. The volume-filling factor f=0.134. Models at $+30^\circ$ and $-30^\circ$ are also consistent with the data.
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In the text

$\begin{figure} \par\vspace{16.7cm} \special{psfile=5ghz_greys.ps vscale=44 hscal... ...ghz_merlin.ps vscale=45 hscale=45 hoffset=240 voffset=-60 angle=0}\end{figure}$ Figure 17: Intensity distributions at 4.8 (left) and 1.6 GHz (right) of our WR 147 model at $0^\circ$ inclination. The top panels are the model intensity distributions at each frequency. The greyscale and contour range are the same in both images. The stellar wind of the OB-star companion is visible, particularly at 5 GHz, along with the WR star wind and the wind-wind collision region. The large contour range was used to show that the stellar wind of both stars extends far beyond the greyscale range. The lower images are simulated MERLIN observations generated using the model intensity distributions shown at the top, and the same u-v distribution and beam sizes as Williams et al. (1997). The beams are circular, of diameter 57 and 175 mas at 5 and 1.6 GHz respectively. The contour levels at the two frequencies are also the same as those in Williams et al. (1997). The similarities to the observations of Williams et al. (1997) is striking, most particularly the emission from the wind-collision region.
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In the text

$\begin{figure} \par\includegraphics[width=8cm]{geom.eps}\par\includegraphics[width=8cm]{geom2.eps} \end{figure}$ Figure A.1: Geometry for solving a line of sight through a grid in cylindrical polar coordinates.

In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{ffsep3.eps} \end{figure}$	Figure 5: The effect of separation on synchrotron spectra using the standard model at $0^\circ$ inclination and $\zeta =10^{-4}$ , for D=2, 5, 20, and $80\times 10^{14}$ cm. Only the effect of free-free opacity is included.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{lum_sep1.eps} \end{figure}$	Figure 6: The effect of separation on the synchrotron luminosity for a power-law electron energy distribution in the optically thin regime. Shown are the data points at four frequencies: 1.6 (solid), 5.0 (dotted), 8.3 (dashed), 14.6 GHz (dot-dashed). The slope of this log-log plot is -1/2, as expected.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{wwcff.eps} \end{figure}$	Figure 7: The effect of separation on the free-free opacity within the wind-wind collision region, using the standard model at $0^\circ$ inclination and $\zeta =10^{-4}$ , for D=2, 5, and $20\times 10^{14}$ cm. The intrinsic synchrotron emission is shown (solid) along with the spectra of the synchrotron emission emerging from the collision zone (dotted).
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{ff_inc.ps} \end{figure}$	Figure 13: The change in thermal flux as a function of inclination angle using the standard model with $\zeta =10^{-4}$ . Shown are curves for 1.6 (solid), 5 (dotted) and 22 GHz (dot-dashed).
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{razssav2_10.ps} \end{figure}$	Figure 15: Model synchrotron spectra when SSA, the Razin effect and free-free absorption in the circum-binary stellar wind envelope are included, for various inclination angles: 0 (solid), $\pm$ 30 (dotted), and $\pm$ 60 (dashed), with corresponding values of $\zeta = (7.03, 7.32, 8.12)\times 10^{-3}$ . The data points are those shown in Fig. 14.
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