All Figures

$\begin{figure} \par\resizebox{\hsize}{!}{\includegraphics[clip]{H4329F1.eps}} \end{figure}$ Figure 1: a) Individual realizations of the one-dimensional velocity field, and b) the corresponding distribution function $P\left (v\right )$ for the microturbulent (l=0, dashed histogram) and a mesoturbulent (l/L=0.1, solid histogram) model.
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In the text

$\begin{figure} \par\resizebox{\hsize}{!}{\includegraphics[clip]{H4329F2.eps}} \end{figure}$ Figure 2: Upper panels: line profiles for two individual realizations of the velocity field (solid curve) for the parameter set $l/L=0.1, \sigma _{\rm t} / v_{\rm th} = 10$ , and $\tau _0=-110$ . For comparison also the spectrum of the intensity expectation value is shown (dashed curve). Lower panels: the optical depth of the random spectra.
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In the text

$\begin{figure} \par\resizebox{\hsize}{!}{\includegraphics[clip]{H4329F3.eps}} \end{figure}$ Figure 3: Convergence of the ensemble average of N random profiles (solid line) to its expectation value (dashed line). The parameter configuration is the same as in Fig. 2.
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In the text

$\begin{figure} \par\resizebox{18cm}{!}{\includegraphics[clip]{H4329F4.eps}} \end{figure}$ Figure 4: Simulated spectra of an extended maser region. Each spectrum is composed of one hundred single realizations. In the upper ten panels we show the model calculations with a parameter set of l/L=0.1, $\sigma _{\rm t} / v_{\rm th} = 10$ , $\tau _0=-110$ and in the lower ten panels the parameter set is l/L=0.1, $\sigma _{\rm t} / v_{\rm th} = 50$ , $\tau _0=-400$ . The spectrum marked by an asterisk is used in Fig. 8.
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In the text

$\begin{figure} \par\resizebox{\hsize}{!}{\includegraphics[clip]{H4329F5.eps}} \end{figure}$ Figure 5: A sample of selected OH (left column) and CH₃OH (right column) maser spectra observed by J. Caswell. All sources are associated with star forming regions or ultra compact $\rm H {\sc ii}$ regions. Methanol masers are in general negligibly polarized which makes them particularly suitable for a comparison with our synthetic spectra. Except of the two spectra of the source 309.921+0.479 which are lefthanded polarized the polarization of all other OH sources is unknown.
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In the text

$\begin{figure} \par\resizebox{\hsize}{!}{\includegraphics[clip]{H4329F6.eps}} \end{figure}$ Figure 6: Expectation values of the intensity calculated for an expanding plane parallel slap with a constant velocity gradient of ${\rm d}v_{\rm sys}/{\rm d}s = 0, 5, 10, 15, 20, 25, 30~ v_{\rm th}/L$ (in decreasing order). All other parameters are the same as in Fig. 2.
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In the text

$\begin{figure} \par\resizebox{\hsize}{!}{\includegraphics[clip]{H4329F7.eps}} \end{figure}$ Figure 7: As in Fig. 4 the spectra model the emission of an extended maser region with the parameter configuration: l/L=0.1, $\sigma _{\rm t} / v_{\rm th} = 10$ , $\tau _0=-110$ . For all calculations the same turbulent velocity field was used. Additionally we consider along the line of sights a systematic velocity component with a constant velocity gradient ${\rm d}v_{\rm sys}/{\rm d}s$ . The values used in each calculation are shown in the upper left corner of the panels.
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In the text

$\begin{figure} \par\resizebox{\hsize}{!}{\includegraphics[clip]{H4329F8.eps}} \end{figure}$ Figure 8: Spatial intensity distribution of the spectrum in Fig. 4 marked with an asterisk. Black circles indicate a maximum intensity of a single realization greater than ten times the expectation value in the line center. Grey and white circles show maximum intensities in the range between $10\left< I_{\nu~=~0}\right>\geq I_{\rm\nu ,max} \geq \left<I_{\nu~=~0}\right>$ and $\left<I_{\nu~=~0}\right>\geq I_{\rm\nu ,max} \geq 0.1\left<I_{\nu~=~0}\right>$ respectively. The intensity in the blank boxes is below one tenth of the mean intensity in the line center
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In the text

$\begin{figure} \par\resizebox{\hsize}{!}{\includegraphics[clip]{H4329F1.eps}} \end{figure}$	Figure 1: a) Individual realizations of the one-dimensional velocity field, and b) the corresponding distribution function $P\left (v\right )$ for the microturbulent (l=0, dashed histogram) and a mesoturbulent (l/L=0.1, solid histogram) model.
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$\begin{figure} \par\resizebox{\hsize}{!}{\includegraphics[clip]{H4329F2.eps}} \end{figure}$	Figure 2: Upper panels: line profiles for two individual realizations of the velocity field (solid curve) for the parameter set $l/L=0.1, \sigma _{\rm t} / v_{\rm th} = 10$ , and $\tau _0=-110$ . For comparison also the spectrum of the intensity expectation value is shown (dashed curve). Lower panels: the optical depth of the random spectra.
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$\begin{figure} \par\resizebox{\hsize}{!}{\includegraphics[clip]{H4329F3.eps}} \end{figure}$	Figure 3: Convergence of the ensemble average of N random profiles (solid line) to its expectation value (dashed line). The parameter configuration is the same as in Fig. 2.
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$\begin{figure} \par\resizebox{\hsize}{!}{\includegraphics[clip]{H4329F6.eps}} \end{figure}$	Figure 6: Expectation values of the intensity calculated for an expanding plane parallel slap with a constant velocity gradient of ${\rm d}v_{\rm sys}/{\rm d}s = 0, 5, 10, 15, 20, 25, 30~ v_{\rm th}/L$ (in decreasing order). All other parameters are the same as in Fig. 2.
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