MIDCOURSE SPACE EXPERIMENT VERSUS IRAS TWO-COLOR DIAGRAMS AND THE CIRCUMSTELLAR ENVELOPE-SEQUENCE OF OXYGEN-RICH LATE-TYPE STARS

For the cross-identification between IRAS and MSX sources we used the positions from version 2.0 of the IRAS PSC (245,889 sources) and Faint Source Catalog (FSC; 173,044 sources) and version 2.3 from the MSX(6C) PSC (440,487 sources; Beichman et al. 1988; Egan et al. 2003).

Because we were very wary of contamination with incorrect cross-identifications, but on the other hand needed a data set of cross-identification as large as possible, we compromised between mission position accuracy and search radius. That is, IRAS PSC 12 μm positions typically are accurate to ∼7–9'', within a beam (angular resolution) of ∼1 × 5', and MSX PSC 8.28 μm positions typically are accurate to ∼2'', within a beam of ∼18'' (Neugebauer et al. 1984; Hacking et al. 1985; Ojha et al. 2007; Beichman et al. 1988; Egan et al. 2003). We therefore used a search radius of 10''; the arithmetic mean of the beam and accuracy of the MSX mission, which is the more restrictive between IRAS and MSX. We used the same 10'' to cross-identify the MSX PSC with the IRAS FSC for two reasons. First, this expands the data set with more sources to compare IRAS and MSX colors. Second, it also reveals those IRAS–MSX PSC cross-identifications that could be confused with faint IRAS sources. Our data set thus excludes the MSX sources that had more than one possible IRAS counterpart within 10'', whether or not from the IRAS PSC or FSC, but also includes the (single) fainter IRAS counterparts. In total, we found 45,895 MSX sources identified with single IRAS PSC sources and 620 identified with single IRAS FSC sources (46,515 total). Multiple identifications within 10'' were found for 482 MSX sources, whereas 393,490 MSX sources had no counterpart in the IRAS PSC nor in the IRAS FSC within 10'' radius.

Two MSX sources were removed because they could be (at 664 or 554) identified with the same FSC source. Similarly, we removed another 76 MSX sources for which the identification with a unique IRAS PSC source within 10'' was ambiguous. To be consistent with the multiple identifications above, this means removing the MSX source even in the case where one possible identification was within 3'' (287) and the other was as far as (almost) 10'' (960) away. From this sub-total of 46,437 sources which match in position, we removed 26,743 cross-identifications for which the MSX sources had fewer than two reliable flux densities (i.e., "quality numbers" for the photometry which were not 3 or 4), i.e., for which not a single reliable, good quality MSX color could be calculated. Another 16,194 IRAS sources were removed for which any of the 12, 25, or 60 μm fluxes were unreliable (quality not 3) as in that case we could not place them in the IRAS 2CD diagram reliably. Finally, another 957 sources were removed as they fall outside the traditional van der Veen & Habing (1988) IRAS 2CD color magnitude range limits (their Figures 5(a) and (b): −2 < [12]-[25] < 2 and −3 < [25]-[60] < 1; see next subsection). The remaining catalog of good quality IRAS sources in the traditional van der Veen & Habing (1988) IRAS 2CD with a likely unique MSX counterpart within 10'' radius for which at least one good quality MSX color could be derived is 2543. Only two sources are from the FSC. Figure 1 shows the histogram of the difference in position between the final 2543 IRAS and MSX associations. From the peaked distribution around 25 (with ∼18'' angular resolution) we conclude that the associations are very likely proper cross-identifications. The location of these remaining cross-identified IRAS/MSX sources in the IRAS 2CD diagram is shown in Figure 2.

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To be consistent with the original IRAS 2CD nomenclature we follow the (uncorrected) color magnitude definition used by van der Veen & Habing (1988), i.e., color magnitude [α] − [β] = −2.5 × log₁₀(F_α/F_β), where F_χ is the measured flux density in Jansky (Jy) at waveband χ taken from the IRAS PSC/FSC version 2.0 or from the MSX PSC version 2.3 (Beichman et al. 1988; Egan et al. 2003). For IRAS wavebands we will use the numbers 12, 25, and 60 to designate the waveband; the center wavelength in μm of the filter passband. For MSX, we will use the capital letters A, C, D, and E for the wavebands centered at 8.28, 12.13, 14.65, and 21.3 μm, respectively. If we call a source "blue" or "bluer" we refer to the smaller or more negative value(s) of a color; relatively larger or more positive color values are "red" or "redder." We also use the IRAS color regions determined by van der Veen & Habing (1988). That is, statistically, the oxygen-rich stars are located in the IRAS color regions identified with capital roman numerals I, II, IIIa, IIIb, IV, and V along the CSE-sequence, and carbon-rich stars typically are located in the IRAS color regions VIa, VIb, and VII (Figure 2). Color region VIII contains a complex mixture of sources. For the remainder of this paper we will concentrate on the oxygen-rich CSE-sequence I–V, completely ignore the 88 sources in color region VIII, and only occasionally comment on the carbon-rich sources in color regions VIa, VIb, and VII. Later, we will also introduce MSX color regions with non-capitalized roman numerals (i, ii, iiia, iiib, iv, and v) (to keep them recognizable as distinct MSX, rather than IRAS color regions), but where the same type of sources can be found in the different 2CDs (Section 4).

In our analysis, we have chosen not to apply any zero-magnitude or color corrections. One of the strengths of the IRAS 2CD as defined by van der Veen & Habing (1988) is that it also did not have any of these corrections applied. The analysis of van der Veen & Habing (1988) was therefore independent of different choices of extinction curves and spectral energy distributions (SEDs) of individual objects. Only in Section 3.2, we will temporarily divert and apply a zero-magnitude correction—a simple axis shift—to compare our data with other data sets. The zero-magnitude correction is applied by, e.g., adding $2.5 \times {\log }_{10} (\frac{58.49}{18.29}) = 1.2622$ to the uncorrected [A]−[D] color and $2.5 \times {\log }_{10} (\frac{18.29}{8.80}) = 0.7943$ to the uncorrected [D]−[E] color, where 58.49, 26.51, 18.29, and 8.80 Jy are the zero-magnitude flux densities for the MSX bands A, C, D, and E, respectively.

Finally, although we made an effort to exclude data that is "confused" (i.e., where the IRAS beam would include emission from several objects as compared to emission from a single object in the smaller MSX beam), it is quite possible that a few sources are confused or misidentified. However, from the tail of Figure 1 we estimate that the number of misidentifications or confused sources is less than 10%. Since we are making a statistical comparison of the colors, we expect no major difference in our conclusions when a few misidentified objects remain in the sample.

The CSE-sequence of oxygen-rich objects in the IRAS 2CD (see Figure 2) is an exponential function of the IRAS [12]−[25] color resulting in an IRAS [25]−[60] color. With respect to the [12]−[25] color region domain the CSE-sequence overlaps in regions IIIb and IV (between 0.4 < [12]–[25] < 1.0) and in regions IV and V (between 1.0 < [12]–[25] < 1.4). However, this overlap is much less than in the [25]−[60] color region domain, where regions I–IIIb overlap between −2.4 < [25]–[60] < −1.6. It is therefore convenient to regard the CSE-sequence in terms of IRAS [12]−[25] color. Using the [12]−[25] colors at this stage does not distinguish between carbon-rich objects in regions VIa, VIb, and VII and oxygen-rich objects along the CSE-sequence for [12]−[25] < 0.4; we will discuss this further in Section 3.2.

Strictly speaking, in terms of the center wavelength of the wavebands, the IRAS [12]−[25] color would correspond roughly to the MSX [C]−[E] color, with no corresponding color in the Spitzer (GLIMPSE+MIPS) nor in the ISOGAL surveys. However, as readily explained in Ortiz et al. (2005), the MSX A filter covers the 9.7 μm silicate feature, whereas the 11.3 μm SiC feature would appear in the MSX C filter; the IRAS 12 μm band filter includes both features.⁴ As the silicate feature is typically the most prominent in the IRAS LRS, the IRAS [12]−[25] color may also, or better, correspond to the MSX [A]−[E] color. Figures 3 and 4 and Table 1 compare the IRAS colors to the MSX colors that could be derived from the cross-identifications. This comparison shows that the IRAS [12]−[25] color can generally be converted to MSX colors, most notably in the MSX [A]−[E] and [C]−[E] colors, but also with a reasonable color range in the MSX [A]−[D] color (Table 2). We note that there is no dependence on total flux density at any waveband (Figure 4). Except for the [C]−[E] color, the dispersion and deviation from the trend is in general larger for very red sources, where [12]−[25] > 1, but overall the agreement is well within a third of a magnitude. We note that most of these sources are intrinsically variable evolved stars for which a difference in color due to non-simultaneous observations within a mission, or observing different stellar phases between the IRAS and MSX missions is reflected in this dispersion (Robitaille et al. 2007). No conversion can be made for the IRAS [25]−[60] color. This is not surprising as all MSX colors are determined for the SED shortward of 25 μm, and are largely insensitive to the SED and IRAS color longward of 25 μm wavelength.

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For the oxygen-rich sources along the CSE-sequence, this close correspondence to the IRAS [12]−[25] color to three MSX colors is fortunate, as the CSE-sequence thus can be represented by the IRAS [12]−[25] color, and also by the MSX [A]−[E], [C]−[E], and [A]−[D] colors. We will thus assume that the small inaccuracies of converting IRAS colors using the linear relations in Table 1 remain within the noise of the whole sample of derived MSX colors. Then the IRAS CSE-sequence can be described as MSX CSE-sequences by substituting the IRAS [12]−[25] color with two different MSX colors in Equation (2) of van der Veen & Habing (1988) for the range of valid IRAS [12]−[25] colors (−1.5 < [12]−[25] <+1.3). It follows that the IRAS [25]−[60] color can be eliminated by equating the right hand sides of the two equations obtained above. Rearrangement of the resulting equation yields the MSX CSE-sequences given in Table 3 (Section 4.1).

In a statistical sense, IRAS colors can be used to separate the carbon-rich sources from the oxygen-rich sources, as the carbon-rich CSEs typically reside in IRAS regions VIa, VIb, and VII. However, when only MSX colors are available the separation of carbon-rich from oxygen-rich envelopes becomes more of a problem. Although other information is sometimes available upon which a clearer distinction between carbon-rich and oxygen-rich CSEs can be made, (e.g. J, K, or L band 2MASS or DENIS flux densities, Suh et al. 2001; Lumsden et al. 2002; Suh 2007), the challenge is to make such a distinction using only the data available within the MSX catalog (e.g., Lumsden et al. 2002; Sevenster 2002; Ortiz et al. 2005). In our view, the most promising case is the data in Figure 3 of Ortiz et al. (2005) which implicitly suggest that a first separation can be made. Ortiz et al. (2005) show that discriminating between C and O rich stars is better done using K − [A] versus [A]−[D] colors (their Figure 2), but here we only use MSX colors and turn to their analysis of the zero-magnitude-corrected MSX [D]−[E] versus MSX [A]−[D] color (their Figure 3). The samples in Ortiz et al. (2005) are well defined as the data from Loup et al. (1993) that they use are identified as carbon-rich stars and indeed typically, but not uniquely, populate IRAS color regions VIa, VIb, and VII (Loup et al. 1993, their Figure 3). Similarly, but vice versa for oxygen-rich stars in regions I–V, this reminds one that the IRAS boundary between carbon-rich and oxygen-rich color regions is not strict.

In Figure 3 of Ortiz et al. (2005) the carbon-rich stars (filled squares) are mostly separated from the oxygen-rich OH/IR objects by the line [A] − [D] = −2 · ([D] − [E]) + 2.5 using zero-magnitude-corrected colors. This separator is the dotted line in our Figure 5 and labeled "C vs O".⁵ Is it possible to use this empirical line to generally make the division between carbon-rich and oxygen-rich objects when the composition of the envelope is not known a priori, e.g., such as in samples used in Ojha et al. (2007) and here?

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In Figure 5, the sources of our sample in IRAS color regions VIa, VIb, and VII (filled squares) and the other regions (open circles) excluding region VIII (88 sources) seem to overlap in the densely populated part of the figure around the "C vs O" line. Note that only 1911 of the original 2455 sources could be plotted in this figure, as 544 sources are missing at least one good quality A, D, or E flux measurement. Figure 6 separates the two samples to show that supposed carbon-rich sources from IRAS region VIa, VIb and VII do appear in the oxygen-rich (top right) side of the "C vs O" dotted line. Supposed oxygen-rich sources also appear on the carbon-rich (bottom left) side. The IRAS color regions VIb and VII as described by van der Veen & Habing (1988) may still contain a large fraction of oxygen-rich stars based on the percentage of LRS classes 21–29 and 14–16 (Olnon et al. 1986) reported in the samples (van der Veen & Habing 1988). There is also some fraction of supposed oxygen-rich stars in regions II–IV which have LRS classes consistent with carbon-rich stars. This may also be seen, e.g., in Suh et al. (2001) where evolutionary models of carbon-rich stars do traverse oxygen-rich IRAS regions IIIa and IIIb, and models for oxygen-rich stars border region VII.

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Not surprisingly, this means that the IRAS region division between oxygen-rich and carbon-rich stars is not perfect. We therefore investigated whether a better separation between carbon-rich and oxygen-rich objects can be made using the MSX [D]−[E] versus [A]−[D] colors dividing at the "C vs O" line, with the understanding that the MSX separation may also not be perfect. We define the MSX "OC-index" for sources with good quality MSX A, D, and E flux densities:

$$\begin{equation} {\rm OC-index} = ([A]-[D]) + 2\cdot ([D]-[E]) + \zeta \end{equation} \tag{ 1 }$$

with ζ = −2.5 for zero-magnitude-corrected MSX colors and ζ = +0.35 for uncorrected MSX colors. The OC-index is thus negative if the source is on the supposedly carbon-rich side of the "C vs O" line and positive on the supposedly oxygen-rich side.

Figure 7 shows the IRAS 2CD for the sample, divided according to the OC-index separately. Although the OC-index seems to generally divide the carbon-rich from the oxygen-rich objects, it mistakenly identifies potential oxygen-rich sources in IRAS regions I and II as carbon rich. It does select the cooler and thicker CSEs in IRAS color regions IIIa–V, but since we are interested in the full CSE-sequence, (including IRAS color regions I and II), using this division does not suit our needs in this context. We conclude that regardless of the potential to increase the fraction of carbon-rich sources in samples of hot objects (T > 400 K, left of the border between region VII and IIIa), the OC-index is more a measure of temperature than CSE chemistry (Figure 7).

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The main interest in the present study is in the oxygen-rich sources along the CSE-sequence. As none of the MSX colors relates closely to the IRAS [25]−[60] color, it is expected that the carbon-rich and oxygen-rich sources overlap in MSX colors where the uncorrected IRAS [12]−[25] color is less than ∼ +0.4, the farthest extent of IRAS color region VIb. To eliminate the pollution of an oxygen-rich sample along the CSE-sequence with likely carbon-rich sources in the MSX color samples, we therefore removed from our sample all sources from the carbon-rich IRAS color regions VIa, VIb, and VII (and VIII). However, we did not remove the 388 sources with OC-index < 0 from the sample as this would eliminate all hot (T > 400 K) oxygen-rich objects as well. Thus, a reduced sample of 1489 sources with good MSX colors in the oxygen-rich IRAS regions was used in the remainder of this paper. Note that we chose to eliminate the likely carbon-rich sources. An option to introduce different symbol colors (see Figure 8) would not add to clarity in the figures later on, whereas opting for symbol colors according to their IRAS [12]−[25] color, and thus mislabeling them as oxygen-rich sources, would just plot them on top of the distribution of oxygen-rich sources with the same symbol color. That is, leaving them out from the comparison of infrared colors of oxygen-rich sources seems proper and does not alter our conclusions.

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Figure 8 shows that sources from a particular IRAS region (a specific color) generally populate a confined region in the MSX 2CD diagrams. We therefore determined MSX 2CD color regions for sources with IRAS colors of color regions I, II, etc. We will name the MSX region with sources from IRAS color region I, MSX color region i and similarly, e.g., sources from IRAS color region IIIb, MSX color region iiib, etc. Using our limited sample of 1489 sources total, we empirically determined approximate MSX color region boundaries as follows (Figures 8 and 9):

$$\begin{equation*} \mbox{\textit {MSX}\;{\emph{i$\phantom{iib}$}}\,{:}\ } \left\{ \begin{array}{@{}ll} -2.0 \le \mbox{[A]$-$[D]} < -0.9 & {\rm or} \\ \\ -3.0 \le \mbox{[A]$-$[E]} < -1.5 & {\rm or} \\ \\ -2.0 \le \mbox{[C]$-$[E]} < -1.1& \end{array} \right. \end{equation*}$$

$$\begin{equation*} \mbox{\textit {MSX}\;{\emph{ii$\phantom{ib}$}}\,{:}\ } \left\{ \begin{array}{@{}ll} -0.9 \le \mbox{[A]$-$[D]} < -0.6 & {\rm or} \\ \\ -1.5 \le \mbox{[A]$-$[E]} < -0.7 & {\rm or} \\ \\ -1.1 \le \mbox{[C]$-$[E]} < -0.75 \end{array} \right. \end{equation*}$$

$$\begin{equation*} \mbox{\textit {MSX}\;{\emph{iiia}}\,{:}\ } \left\{ \begin{array}{@{}ll} -0.6 \le \mbox{[A]$-$[D]} < +0.4 & {\rm or} \\ \\ -0.7 \le \mbox{[A]$-$[E]} < +0.4 & {\rm or} \\ \\ -0.75 \le \mbox{[C]$-$[E]} < +0.1 \end{array} \right. \end{equation*}$$

$$\begin{equation*} \mbox{\textit {MSX}\;{\emph{iiib}}\,{:}\ } \left\{ \begin{array}{@{}ll} +0.4 \le \mbox{[A]$-$[D]} < +5.0 & {\rm and} \\ +0.1 \le \mbox{[C]$-$[E]} < +0.55 & {\rm or} \\ \\ {\mbox{1.4$\cdot$([A]$-$[E]) $-$ ([A]$-$[D])} < +0.8} & {\rm and} \\ +0.4 \le \mbox{[A]$-$[E]} < +1.1 & {\rm or} \\ \\ +0.1 \le \mbox{[C]$-$[E]} < +0.55& \end{array} \right. \end{equation*}$$

$$\begin{equation*} {\textit {MSX}\;{{{i\! v}\phantom{i}}}{:}\ }\!\! \left\{ \begin{array}{@{}ll} {+0.8 \le \mbox{1.4$\cdot$([A]$-$[E]) $-$ ([A]$-$[D])} < +1.3} & {\rm and} \\ +0.4 \le \mbox{[A]$-$[E]} < +7.0 & {\rm or} \\ \\ +0.55 \le \mbox{[C]$-$[E]} < +1.0& \end{array} \right. \end{equation*}$$

$$\begin{equation*} {\textit {MSX}\;{{v\phantom{iii}}}{:}} \left\{ \begin{array}{@{}ll} {\mbox{1.4$\cdot$([A]$-$[E]) $-$ ([A]$-$[D])} \ge +1.3 } & {\rm and} \\ +1.1 \le \mbox{[A]$-$[E]} < +7.0 & {\rm or} \\ \\ +1.0 \le \mbox{[C]$-$[E]} < +5.0{.} & \end{array} \right. \end{equation*}$$

Two regions in the [A]−[E] versus [A]−[D] diagram (upper left panel in Figure 8) are not accounted for in the above determination due to the lack of sources. The first region is for 1.1 < [A]−[E] < 7.0 and with 1.4·([A]−[E]) − ([A]−[D]) < +0.8, where sources from either IRAS region IIIb and IV can be expected. Sources from either IRAS region IV and V can be expected between +0.4 ⩽ [A]−[E] < 1.1 and with 1.4·([A]−[E]) − ([A]−[D]) > +1.3.

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We also included the beginning, zero, and end points of the CSE-sequence in the MSX 2CDs. These are the locations of the crosses in the MSX 2CDs (Figure 8) where IRAS [12]−[25] equals to −1.5 (labeled C), zero (labeled S) and +1.3 (labeled E). The full CSE-sequence is a straight line between these points and can be obtained by eliminating the [25]−[60] color from the CSE-sequence equation in van der Veen & Habing (1988, their Equation (2)), or simply by equating the expressions for [12]−[25] from Table 1 for different MSX colors over the [12]−[25] range in MSX colors where the CSE-sequence is defined. The expressions and color ranges for the CSE-sequence in MSX colors adapted here are given in Table 3. It can be seen that indeed the CSE-sequence starts in MSX color region i, has its zero point close to the border between regions iiia and iiib,⁶ and ends in region iv. It does not enter the region (v) with the reddest sources, which are mostly (proto-)planetary nebulae.

To obtain a subsample of sources that is characterized by colors of a certain IRAS color region, the selection criteria for the same (lower case) MSX color region can be directly applied if the parent sample contains uncorrected MSX colors. For example, a subsample of sources with CSEs resembling the IRAS IIIa region colors (blue in Figure 8) can be drawn directly from the MSX catalog by applying one or more of the three equations for MSX region iiia. On the other hand, to obtain such a subsample from a parent sample that contains zero-magnitude corrected MSX colors, one would have to subtract the zero-flux magnitude fractions from Section 2.2 from the MSX source colors first.⁷ As a reminder, we emphasize that carbon-rich sources in IRAS regions VIa, VIb, and VII will overlap with MSX color regions i, ii, and iiia, with a small tail in iiib–v. Using only MSX colors it is impossible to make an accurate estimate of the fraction of contamination with carbon-rich sources in a sample. However, to get an indication, in Table 4 we show the number of sources from the cross-identified IRAS/MSX data base (2543 sources; Section 2) in each IRAS color region, when sources are selected using any of the MSX selection rules above. It is apparent from this table that selecting a sample using the MSX color relations in general selects the sources with similar IRAS colors (e.g., MSX iiia and IRAS IIIa), but that also sources from nearby IRAS regions may fulfill the MSX selection rule. This, in a statistical approach, is not worrisome; e.g., using the MSX [A]−[D] color to select MSX iiia sources will yield 82% (816/995) of IRAS IIIa sources, provided that the sample is known to be mostly oxygen-rich along the CSE-sequence. Because of the degeneracy in the vertical axis of the IRAS 2CD when only MSX colors (or IRAS [12]−[25] colors) are available, the carbon-rich objects in IRAS regions VIa, VIb, and VII also fulfill the MSX selection rules. The approximate number of sources in these IRAS regions (according to increasing [12]−[25] color) is also given in Table 4 per MSX selection rule. If the degeneracy between oxygen-rich and carbon-rich cannot be resolved, e.g., with the IRAS [25]−[60] color, then the pure fraction of IRAS region IIIa sources of the MSX iiia sources using the [A]−[D] color selection degrades to 50% (816/1624). Nevertheless, selecting on e.g., MSX iiia will thus indeed mostly yield IRAS IIIa sources, partly because some of the IRAS VIa, VIb and VII sources may be actually oxygen-rich since the IRAS boundaries also do not exactly separate the two populations. Because the density of carbon-rich sources is highest for [12]−[25] < 0, the highest contamination (cq. overlap) is in MSX color regions i, ii, and iiia. For these regions other selection criteria to increase the oxygen-rich fraction are advisable (e.g. Messineo et al. 2002; Section 5). Again, the oxygen-rich and carbon-rich objects overlap around the dividing regions in the IRAS 2CD, in particular near IRAS region VII, so the numbers in Table 4 are indicative values only for any sample other than this IRAS/MSX cross correlated data set. For the particular example above, selecting MSX iiia sources using the [A]−[D] color, the fraction of oxygen-rich objects is 61% (995/1624). That is, for such a sample the remainder, 39%, may be carbon-rich and thus will not harbor SiO masers to begin with (Section 5).

4.1.1. Possible Error in MSX PSC 2.3?