Astronomy & Astrophysics

All Figures

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0519f01.eps} \end{figure}$ Figure 1: The bias of the nearest neighbors interpolation on a model where the true extinction is $A(\vec x) = 0.1~\mbox{mag}$ for x₁ < 0 and $0.9~\mbox{mag}$ for $x_1 \ge 0$ . The solid lines show the average measured extinction of the nearest neighbours method, calculated using Eq. (9) for various numbers of neighbours N. The dashed lines show the extinction that one would measure if the density of stars were uniform in the whole field. Note that the solid lines are always below the dashed lines except at the extremes of this plot (where all estimators agree with the true value of A there). For this plot we set $\alpha = 0.34$ , k = 1.55, and $\rho _0 = 1$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0519f02.eps} \end{figure}$ Figure 2: Similarly to Fig. 1, but for the median-nearest neighbors interpolation. Again, the solid lines, representing the expected mean measurements, are always below the dashed lines, representing the same measurements in the ideal case where the density of background stars is uniform within the whole field. Note that because of the properties of the median, for large values of N the ``transition'' from $A = 0.1~\mbox{mag}$ to $A = 0.9~\mbox{mag}$ is faster than in Fig. 1.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0519f03.eps} \end{figure}$ Figure 3: Similarly to Fig. 1, but for the moving average smoothing with a Gaussian window function with different dispersion parameters $\sigma$ . As for Figs. 1 and 2, the solid lines, representing the expected mean measurements, are always below the dashed lines, representing the same measurements in the ideal case where the density of background stars is uniform within the whole field.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0519f04.eps} \end{figure}$ Figure 4: Similar to Fig. 3, but for the NICEST moving average smoothing (see Sect. 3). In this case a significant bias is observed only for $\sigma = 0.5$ , which however corresponds to a very small weight number $\mathcal{N} \simeq 2$ .
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=8cm,clip]{0519f05a.eps} \include... ...]{0519f05c.eps} \includegraphics[width=8cm,clip]{0519f05d.eps} } \end{figure}$ Figure 5: Top left: the original 2MASS/NICER map of the Pipe nebula used in the simulations. Top right: the mean reconstructed map that one would obtain if the density of background stars were uniform. This is basically a smoothed version of the original map on the left. Levels are spaced at $0.2~\mbox{mag}$ . Bottom left: the difference between the average reconstructed maps, calculated from background stars following the density of Eq. (2), and the average map at top right. Levels are spaced at $0.02~\mbox{mag}$ . Bottom right: same map as bottom left, but using the improved method presented in this paper. Levels are spaced at $0.0025~\mbox{mag}$ .
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=8cm,clip]{0519f06a.eps} \includegraphics[width=8cm,clip]{0519f06b.eps} } \end{figure}$ Figure 6: Left: average reconstructed map using a 1-star (N = 1) Voronoi method, assuming a uniform distribution of stars. Levels are spaced at $0.2~\mbox{mag}$ . Right: difference between the average reconstructed Voronoi map, obtained from background stars following the density of Eq. (2), and the average true map to the left. Levels are spaced at $0.02~\mbox{mag}$ .
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=8.8cm, bb=149 305 485 524]{0519f... ...includegraphics[width=8.8cm, bb=149 305 485 524]{0519f07b.eps} } \end{figure}$ Figure 7: Same as Fig. 5 ( bottom), but with a fraction of f = 0.05 of foreground stars. The increases of relative number of foreground stars in the denser regions of the cloud makes the bias more pronounced. Still, NICEST performs very well. Contours levels are spaced at $0.02~\mbox{mag}$ in the NICER plot ( left) and at $0.005~\mbox{mag}$ in the NICEST plot ( right); contours at $-0.1~\mbox{mag}$ or below are plotted in white.
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In the text

$\begin{figure} \par\includegraphics[width=13.5cm,clip]{0519f08.eps} \end{figure}$ Figure 8: The NICEST extinction map of the Pipe nebula, using the modified estimator (28).
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0519f09.eps} \end{figure}$ Figure 9: The difference between the modified extinction estimates (Eq. (28)) and the standard ones [Eq. (1)] around Barnard 59. The contour levels are at $A = \{ 0.5, 1.0, 1.5, 2.0 \}~\mbox{mag}$ of the map of Fig. 8.
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0519f10.eps} \end{figure}$ Figure 10: The difference between the modified extinction estimates (Eq. (28)) and the standard ones (Eq. (1)) around the peak ID 3 of Lombardi et al. (2006). The contour levels are at $A = \{ 0.5, 1.0, 1.5, 2.0 \}~\mbox{mag}$ of the map of Fig. 8.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0519f11.eps} \end{figure}$ Figure 11: The average difference $\Delta A$ between the estimators (28) and (1) as a function of the estimated column density A. The lower, solid line is relative to the Pipe nebula map at ${\it FWHM} = 1~\mbox{arcmin}$ resolution; the upper dashed line is at for a resolution ${\it FWHM} = 1.5~\mbox{ arcmin}$ . The latter plot is essentially what we would obtain at a ${\it FWHM} = 1~\mbox{arcmin}$ if the distance of the Pipe nebula increases by a factor 1.5.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0519f03.eps} \end{figure}$	Figure 3: Similarly to Fig. 1, but for the moving average smoothing with a Gaussian window function with different dispersion parameters $\sigma$ . As for Figs. 1 and 2, the solid lines, representing the expected mean measurements, are always below the dashed lines, representing the same measurements in the ideal case where the density of background stars is uniform within the whole field.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0519f04.eps} \end{figure}$	Figure 4: Similar to Fig. 3, but for the NICEST moving average smoothing (see Sect. 3). In this case a significant bias is observed only for $\sigma = 0.5$ , which however corresponds to a very small weight number $\mathcal{N} \simeq 2$ .
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$\begin{figure} \par\mbox{\includegraphics[width=8cm,clip]{0519f06a.eps} \includegraphics[width=8cm,clip]{0519f06b.eps} } \end{figure}$	Figure 6: Left: average reconstructed map using a 1-star (N = 1) Voronoi method, assuming a uniform distribution of stars. Levels are spaced at $0.2~\mbox{mag}$ . Right: difference between the average reconstructed Voronoi map, obtained from background stars following the density of Eq. (2), and the average true map to the left. Levels are spaced at $0.02~\mbox{mag}$ .
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$\begin{figure} \par\includegraphics[width=13.5cm,clip]{0519f08.eps} \end{figure}$	Figure 8: The NICEST extinction map of the Pipe nebula, using the modified estimator (28).
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$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0519f09.eps} \end{figure}$	Figure 9: The difference between the modified extinction estimates (Eq. (28)) and the standard ones [Eq. (1)] around Barnard 59. The contour levels are at $A = \{ 0.5, 1.0, 1.5, 2.0 \}~\mbox{mag}$ of the map of Fig. 8.
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$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0519f10.eps} \end{figure}$	Figure 10: The difference between the modified extinction estimates (Eq. (28)) and the standard ones (Eq. (1)) around the peak ID 3 of Lombardi et al. (2006). The contour levels are at $A = \{ 0.5, 1.0, 1.5, 2.0 \}~\mbox{mag}$ of the map of Fig. 8.
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