All Figures

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig1.ps}} \end{figure}$ Figure 1: Distribution of all sources listed in the catalogue as a function of magnitude ( dashed-line histogram), those with a photometric accuracy better than 10% ( dashed-filled histogram) and of selected stellar as well as probably stellar objects ( continuous histogram). $K_{\rm s}$ magnitudes are shown on the top panel and J magnitudes on the bottom one. Bins correspond to 0.1 mag and magnitudes are apparent. The vertical line at $K_{\rm s}=18.15$ indicates the position of the tip of the RGB while the continuous-filled histograms show sources with $K_{\rm s}<18.15$ , most of them are AGB stars, and their corresponding J band distribution; this is the sample used in the paper.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig2.ps}} \end{figure}$ Figure 2: Colour-magnitude diagram of the stellar sources detected in J and $K_{\rm s}$ across M 33. Dashed vertical-lines and continuous slanted-lines define regions occupied by O-rich and C-rich candidate AGB stars, respectively. These appear statistically distinct from foreground stars and super giant stars of M 33. The position of the tip of the RGB is also indicated.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig3.ps}} \end{figure}$ Figure 3: Distribution of the number of C-rich and O-rich AGB stars versus $K{_{\rm s,}}_0$ magnitude. Both the result of selecting these stars using vertical lines ( dashed-line histograms) and using slanted lines ( continuous-line histograms) are shown; bins are of 0.1 mag.
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In the text

$\begin{figure} \mbox{ \epsfxsize=4.4cm \epsfbox{9366fig4a.ps}\hspace*{-7mm} \ep... ...6fig4c.ps}\hspace*{-7mm} \epsfxsize=4.4cm \epsfbox{9366fig4d.ps} }\end{figure}$ Figure 4: (From left to right) Distribution of the number density of C stars, M stars, super giant stars and mostly foreground stars. See the text for the selection of each sample. Contours are at: 3, 9, 18, 33, 45, 55, 65 and 75 for C stars, 2, 5, 10, 15, 20, 25, 30 and 35 for M stars, 0.5, 2, 4, 6, 8 and 10 for super giant stars, and 1.4, 2 and 3 for foreground stars. Darker regions correspond to higher numbers. North is to the top and East is to the left.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig5.ps}} \end{figure}$ Figure 5: Distribution of C-rich AGB stars across M 33. Coordinates are in degrees and are centred at $(\alpha , \delta )=(23.46^{\circ }, 30.66^{\circ })$ according to van den Bergh (2000). Sectors of elliptical rings defining the regions used in this study are clearly indicated. Each ring contains an approximately equal number of stars. North is to the top and East to the left.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig6.ps}} \end{figure}$ Figure 6: Colour-magnitude diagram of the non-stellar sources detected in J and $K_{\rm s}$ across M 33. Many of these sources are blends but there are also HII regions, associations and background galaxies. Lines are like in Fig. 2.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig7.ps}} \end{figure}$ Figure 7: Distribution of the number of C-rich AGB stars within each elliptical ring. Rings are marked with the value of the semi-major axis (degrees). The selection of sources performed using slanted lines is shown by continuous-line histograms while the selection using vertical lines is shown by dashed-line histograms. Bins are of 0.2 mag.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig8.ps}} \end{figure}$ Figure 8: The same as for Fig. 7 but for O-rich AGB stars.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig9.ps}} \end{figure}$ Figure 9: Distribution of the difference between the peak of magnitudes (squares) and colours (triangles) of C stars within 8 sectors and their average of a unique ellipse with a semi-major axis of $0.7^{\circ }$ versus PA (see text for details). The best fit sinusoid has a half amplitude of $0.03\pm 0.01$ mag and corresponds to $\phi =28^{\circ }\pm 6^{\circ }$ . This angle is measured on the plane of the galaxy where $0^{\circ }$ corresponds to the NE point of the major axis and increasing to the East. Errors on each point are at most 0.02 mag and have been omitted for clarity.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig10a.ps}}\par\resizebox{8.8cm}{!}{\includegraphics{9366fig10b.ps}} \end{figure}$ Figure 10: Distribution of the C/M ratio across M33. C-rich and O-rich AGB stars above the tip of the RGB have been selected using slanted lines ( top) or using vertical lines ( bottom). Darker regions correspond to higher ratios. Contours are at: 0.2, 0.6, 1.2, 1.6, 2.0 and 2.4 in the top panel and at 0.25, 0.5, 1.0, 2.0, 3.0, 3.5 and 4.0 in the bottom panel.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig11.ps}} \end{figure}$ Figure 11: The same as the bottom panel of Fig. 10 but using bins of $2.4^{\prime }$ . Contours are at: 0.25, 0.5, 1.0, 1.5, 2.0 and 2.5.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig12a.ps}}\par\resizebox{8.8cm}{!}{\includegraphics{9366fig12b.ps}} \end{figure}$ Figure 12: Comparison between the observed $K_{\rm s}$ magnitude distribution of C and M stars (histograms) and theoretical distributions. The probability that a given model represents the observed distributions, associated to the $\chi ^2$ value, is indicated. These histograms are fitted with models corresponding to a SFR with $\alpha =5$ (or a mean age of 8.7 Gyr) and a metallicity Z =0.0005 ( top panel) or Z =0.001 ( bottom panel). In the electronic version of this figure C stars are in red, M stars in light blue, the sum of C and M stars is in black while RGB stars are in dark blue.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig13.ps}} \end{figure}$ Figure 13: Probability as a function of mean age for models of a given metallicity which represent the stellar population of M 33 in a sector of a ring. Different symbols refer to a different metallicity as follows: Z=0.0005 (filled triangles), Z=0.001 (empty triangles). Other models explored in this study give a probability much lower than the values plotted here and are not shown.
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In the text

$\begin{figure} \par\mbox{\epsfxsize=3.5cm \epsfbox{9366fig14a.ps}\hspace{-0.5cm}... ...g14s.ps}\hspace{-0.5cm} \epsfxsize=3.5cm \epsfbox{9366fig14t.ps} }\end{figure}$ Figure 14: Surface distribution of the most probable metallicity ( first and third rows) at a given SFR (or mean age) and the associated probability distribution ( second and fourth rows) obtained by fitting the $K_{\rm s}$ magnitude distribution of C stars. C stars have been selected from the near-infrared colour-magnitude diagram (Fig. 2) using vertical lines ( top two rows) and using slanted lines ( bottom two rows). From left to right each column refers to a mean age of 2, 3.9, 6.3, 8.7 and 10.6 Gyr, respectively. Contours for each panel in the top row are at Z = 0.00048 (panel 1); 0.00048, 0.0005, 0.0006 and 0.0007 (panels 2 and 3); 0.00048, 0.0005, 0.0006, 0.0008, 0.0012 and 0.002 (panel 4); 0.001, 0.003, 0.005 and 0.007 (panel 5). Contours for each panel in the third row are at Z = 0.00048, 0.0005, 0.0006 and 0.0007 (panels 1, 2, 3, 4); 0.00048, 0.0005 and 0.001 (panel 5). The grey scale for the probability distributions shows only values above 0.7 (contours are at 0.85, 0.95 and 0.99) and 0.95 (contours are at 0.97, 0.98 and 0.99) for the second and fourth rows respectively. Darker regions correspond to higher values.
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In the text

$\begin{figure} \par\mbox{\epsfxsize=6cm \epsfbox{9366fig15a.ps}\hspace{-1cm} \ep... ...6fig15e.ps}\hspace{-1cm} \epsfxsize=6cm \epsfbox{9366fig15f.ps} }\end{figure}$ Figure 15: Spatial distributions of the mean age of the stellar population of M 33 ( left), of the metallicity ( middle) and of the statistical probability that expresses the confidence level of the previous distribution. These distributions have been constructed from the comparison between the observed $K_{\rm s}$ magnitude distribution of C-type AGB stars with theoretical distributions. C stars have been selected from the colour-magnitude diagram (Fig. 2) using vertical lines ( top row) or slanted lines ( bottom row). Bins are of $2.4^{\prime }$ and dark regions correspond to high numbers. From left to right contours are at: 5, 6, 7, 8 ( top) and 5.5, 6.5, 8.5, 10.5 ( bottom) Gyr for age; 0.0005, 0.0006 ( top) and 0.0005, 0.0006, 0.0008, 0.004 ( bottom) for metallicity where only values above 0.0002 are displayed; 0.992, 0.994, 0.996, 0.998, 0.999 where only values above 0.98 are displayed ( top) and 0.85, 0.95, 0.98, 0.999 where only values above 0.98 are displayed ( bottom) for probability.
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In the text

$\begin{figure} \par\mbox{\epsfxsize=6cm \epsfbox{9366fig16a.ps}\hspace{-1cm} \ep... ...6fig16e.ps}\hspace{-1cm} \epsfxsize=6cm \epsfbox{9366fig16f.ps} }\end{figure}$ Figure 16: Spatial distributions of the mean age of the stellar population of M 33 ( left), of the metallicity ( middle) and of the statistical probability that expresses the confidence level of the previous distributions ( right). These maps have been constructed from the comparison between the observed $K_{\rm s}$ magnitude distribution of M-type AGB stars with theoretical distributions. M stars have been selected from the colour-magnitude diagram (Fig. 2) using vertical lines ( top row) or slanted lines ( bottom row). Bins are of $2.4^{\prime }$ and dark regions correspond to high numbers. From left to right contours are at: 1, 2, 4, 6 ( top) and 5, 6, 7, 8.5 ( bottom) for age; 0.0065, 0.008, 0.01, 0.015 ( top and bottom) for metallicity; 0.5, 0.8 ( top) and 0.8, 0.9 ( bottom) for probability.
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In the text

$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics{9366fig17.ps}} \end{figure}$ Figure 17: Distribution of the difference between the individual distance moduli derived by Kim et al. (2002; filled circles) and other authors (see text; empty circles) and their mean versus position angle. Note that the point corresponding to McConnachie (2005) measurement is outside the range shown of this figure. The continuous sinusoid is the same as in Fig. 9 while the dashed sinusoid is the best fit to Kim et al. (2002) data only; the zero line is also indicated ( dotted). Error bars correspond to the random error for Kim et al. (2002) measurements, sytematic errors amount to +0.15 and-0.11, and the global error quoted by the authors for the other points.
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In the text

$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics{9366fig18.ps}} \end{figure}$ Figure 18: Colour-magnitude diagram of the near-infrared sources matched with the LPVs (crosses) from Hartman et al. (2006) and the variable stars detected by Spitzer (squares) from McQuinn et al. (2007). A colour version of this figure is available in the electronic version of the paper.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig2.ps}} \end{figure}$	Figure 2: Colour-magnitude diagram of the stellar sources detected in J and $K_{\rm s}$ across M 33. Dashed vertical-lines and continuous slanted-lines define regions occupied by O-rich and C-rich candidate AGB stars, respectively. These appear statistically distinct from foreground stars and super giant stars of M 33. The position of the tip of the RGB is also indicated.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig3.ps}} \end{figure}$	Figure 3: Distribution of the number of C-rich and O-rich AGB stars versus $K{_{\rm s,}}_0$ magnitude. Both the result of selecting these stars using vertical lines ( dashed-line histograms) and using slanted lines ( continuous-line histograms) are shown; bins are of 0.1 mag.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig5.ps}} \end{figure}$	Figure 5: Distribution of C-rich AGB stars across M 33. Coordinates are in degrees and are centred at $(\alpha , \delta )=(23.46^{\circ }, 30.66^{\circ })$ according to van den Bergh (2000). Sectors of elliptical rings defining the regions used in this study are clearly indicated. Each ring contains an approximately equal number of stars. North is to the top and East to the left.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig6.ps}} \end{figure}$	Figure 6: Colour-magnitude diagram of the non-stellar sources detected in J and $K_{\rm s}$ across M 33. Many of these sources are blends but there are also HII regions, associations and background galaxies. Lines are like in Fig. 2.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig7.ps}} \end{figure}$	Figure 7: Distribution of the number of C-rich AGB stars within each elliptical ring. Rings are marked with the value of the semi-major axis (degrees). The selection of sources performed using slanted lines is shown by continuous-line histograms while the selection using vertical lines is shown by dashed-line histograms. Bins are of 0.2 mag.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig8.ps}} \end{figure}$	Figure 8: The same as for Fig. 7 but for O-rich AGB stars.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig10a.ps}}\par\resizebox{8.8cm}{!}{\includegraphics{9366fig10b.ps}} \end{figure}$	Figure 10: Distribution of the C/M ratio across M33. C-rich and O-rich AGB stars above the tip of the RGB have been selected using slanted lines ( top) or using vertical lines ( bottom). Darker regions correspond to higher ratios. Contours are at: 0.2, 0.6, 1.2, 1.6, 2.0 and 2.4 in the top panel and at 0.25, 0.5, 1.0, 2.0, 3.0, 3.5 and 4.0 in the bottom panel.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig11.ps}} \end{figure}$	Figure 11: The same as the bottom panel of Fig. 10 but using bins of $2.4^{\prime }$ . Contours are at: 0.25, 0.5, 1.0, 1.5, 2.0 and 2.5.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics{9366fig13.ps}} \end{figure}$	Figure 13: Probability as a function of mean age for models of a given metallicity which represent the stellar population of M 33 in a sector of a ring. Different symbols refer to a different metallicity as follows: Z=0.0005 (filled triangles), Z=0.001 (empty triangles). Other models explored in this study give a probability much lower than the values plotted here and are not shown.
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$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics{9366fig18.ps}} \end{figure}$	Figure 18: Colour-magnitude diagram of the near-infrared sources matched with the LPVs (crosses) from Hartman et al. (2006) and the variable stars detected by Spitzer (squares) from McQuinn et al. (2007). A colour version of this figure is available in the electronic version of the paper.
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