LIFTING THE DUSTY VEIL WITH NEAR- AND MID-INFRARED PHOTOMETRY. I. DESCRIPTION AND APPLICATIONS OF THE RAYLEIGH–JEANS COLOR EXCESS METHOD

As the only major galaxy for which we can obtain detailed information on the chemistry, kinematics, and spatial distribution of large numbers of individual stars, the Milky Way (MW), remains a primary laboratory for understanding the structure and evolution of spiral galaxies. An important tool in the study of Galactic structure is the color–magnitude diagram (CMD). The CMD for stars along a given line of sight contains information on their distributions of spatial density, age, and metallicity. The advent of high precision, linear, wide-area photometry from electronic array detectors, aided by the interpretive insights provided by computer models to project the convolution of population age, metallicity, and density distribution into synthesized stellar color–magnitude distributions (e.g., Bahcall & Soneira 1980; Robin & Creze 1986; Yoshii et al. 1987; Reid & Majewski 1993; Ng et al. 1995; Castellani et al. 2002; Robin et al. 2003; Girardi et al. 2005), is finally allowing authentic realizations of the type of systematic surveying of MW stellar populations first attempted by Herschel (1785) and established as a formal goal of Galactic astronomers more than a century ago (Kapteyn 1906). Profound fulfillment of this long-sought goal—the production of stellar CMDs having extraordinary statistics over extensive angular coverage—is being provided by large-area surveys like the Two Micron All-Sky Survey (2MASS; Skrutskie et al. 2006), the Sloan Digital Sky Survey (SDSS; York et al. 2000), and UKIDSS (Lucas et al. 2008) and will be expected to continue with future endeavors like Pan-STARRS (Kaiser et al. 2002), the Large Synoptic Survey Telescope (Ivezic et al. 2008), and Sky-Mapper (Keller et al. 2007).

However, a fundamental and unresolved difficulty with systematic explorations of the Galaxy, despite the existence of huge databases of accurate photometry for billions of stars, is extinction by interstellar dust. This obstacle has thwarted astronomers dating back to Herschel, Struve (1847), and Kapteyn (1909), and, despite having been initially quantified by Trumpler (1930) 80 years ago, remains a roadblock to our detailed understanding of the inner MW and to the interpretation of CMDs of its stars. While the reduced effects of dust on near-infrared (NIR) photometry have allowed us to take CMD-probing of the Galaxy to dustier regions at lower latitudes, our view of the densest, but most important, parts of our Galaxy is still challenged by heavy and non-uniform reddening and extinction, which typically renders low latitude field stellar CMDs virtually uninterpretable in a stellar populations context. The problem is multi-faceted. (1) When beyond modest levels of extinction (when, e.g., E[B−V] ≳ 0.5), the dust density is generally variable on angular scales smaller than the resolution of available reddening maps. (2) Existing reddening maps (e.g., Burstein & Heiles 1982; Schlegel et al. 1998, SFD hereafter) are two-dimensional—they give only the total Galactic extinction along a line of sight, not just that which is foreground to a particular star. At optical wavelengths, star-by-star dereddening from combined UBV colors is commonly attempted, but this technique is hampered in highly extinguished regions, where (3) the "standard Galactic extinction law"¹ no longer applies (e.g., Cardelli et al. 1989), and where (4) the extinction pushes stars to substantially fainter magnitudes (exacerbated by the fact that in such regions R_V can exceed 5). Finally, (5) in many instances the process of dereddening the observed colors of a star back to their (unknown) intrinsic values is degenerate because the reddening vectors and the distribution of stars in color–color space are either parallel (see Section 2) or intersect at multiple points (e.g., as in the case of UBV dereddening).

Some of these problems are lessened by moving to near-infrared wavelengths. For example, variations in the extinction law are typically considered to be less of a problem in the NIR (Cardelli et al. 1989; Indebetouw et al. 2005; although we show elsewhere—Zasowski et al. 2009, Paper II hereafter—that variations do exist in the near- and mid-infrared extinction law that appear to be related to Galactic gradients in dust grain size or composition). On the other hand, NIR photometry is confounded by an additional problem: the reddening vector for NIR colors is almost exactly parallel to the stellar locus in color–color distributions. Figure 1(a) demonstrates the problem for NIR two-color combinations: the process of correcting the observed JHK_s colors of a star back to the intrinsic values is severely degenerate between reddening and intrinsic stellar type (particularly when both intrinsic and observational color scatter of stars along these loci is considered). The problem is the same for all permutations of broadband NIR colors.

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However, as we shall demonstrate, the combination of 2MASS and Spitzer-IRAC photometry (or any near- and mid-infrared dataset) allows a direct and reliable assessment of the line-of-sight reddening to any particular star—and across wavelengths where the reddening law is more universal (Rieke & Lebofsky 1985; Cardelli et al. 1989—although not entirely so, Paper II). Moreover, at these wavelengths, the color effects of reddening and stellar atmospheres are almost completely separable, an advantage that is the foundation of the present series of papers (see Section 1.5).

With Trumpler's (1930) determination that the observed brightnesses of stars are modulated by the presence of interstellar dust, a definitive explanation of the previously known (e.g., Öpik 1929; Gerasimovič 1929) but not understood phenomenon of stellar reddening—whereby a star has a measured color that is redder than expected for its spectral type—was at hand. Öpik (1931) explored several hypotheses for the origin of reddening (as seen in early-type stars) and concluded that absorption of light by interstellar dust clouds was the most probable explanation.²

Soon an association of at least some of this selective absorption with dark clouds (of the type photographed extensively and famously by E. E. Barnard and S. I. Bailey decades before) was made through what may be the first published color-excess (i.e., reddening) maps across an individual cloud (one associated with the open cluster NGC 663) by Carol Jane Anger (1931), and then across a general region (Cepheus) by Elvey & Mehlin (1932). These studies were soon followed by the first rudimentary large-scale maps of optical color excess as a function of longitude, latitude, and distance (e.g., Elvey 1931; Zug 1933; Stebbins 1933; Stebbins & Whitford 1936), which immediately revealed the global non-uniformity of the distribution of the reddening particles. Williams (1934) summarizes much of this early pioneering work. Nevertheless, for decades, researchers have been frequently tempted or forced to use simple assumptions about the distribution of dust—e.g., the layered models giving rise to cosecant(b) laws, and/or spatial homogeneity leading to assumed linear relations of color excess with distance.³

A correlation between the color excess and the total space absorption was subsequently identified, and soon the ratio between the selective and total extinction was quantified for different optical wavelengths (e.g., Stebbins & Whitford 1936; Greenstein & Henyey 1941), which led to the first attempts at defining the extinction law with wavelength (Stebbins et al. 1939). With a reliable extinction law, observed color excesses could be translated back into total extinctions, a necessary step in mapping the distribution of both dust and stars in the Galaxy. Although alternative methods have been developed to measure line-of-sight extinction (e.g., through counts of background galaxies, or by mapping proxies for dust obscuration, such as the intensity of radiation by associated gas or thermal emission by the dust itself), use of color excesses have always provided the most reliable means by which to measure extinction along the line of sight to a star, and, specifically, foreground to that star.

The use of infrared color excesses to calculate levels of dust extinction, taking advantage of the reduced influence of extinction at longer wavelengths, has a history primarily in the exploration and mapping of the extinction in dark (i.e., molecular) clouds. For example, Jones et al. (1980) explored the observed distribution of (J − H) and (H − K) colors of stars in the direction of a specific Bok globule in the Coalsack Nebula to estimate reddenings.

As shown in Figure 1, the problem with this sort of analysis is the degeneracy between the NIR reddening vector and the stellar locus for most spectral types, which leaves as generally inseparable the intrinsic colors of the stars versus the degree of reddening to each star. Nevertheless, with infrared spectra for only a small fraction of their 75 tracer stars available to constrain the general types of stars in their photometric survey, Jones et al. estimated the radial variation in extinction (derived through E[J − K]) in the globule after assuming all stars to be of a specific spectral type (M3 III). A similar approach was applied by Hyland (1981) to map six Bok globules, by Casali (1986) for another six, and by Smith (1987) for the Carina nebula.

While follow-up study of their Bok globule by Jones et al. (1984) increased to several dozen the number of available spectra (along with other data) for classifying the stars and improving the reddening estimates, this effort only highlighted the labor-intensive nature of pairing photometry with spectroscopy on a star-by-star basis to break the degeneracies between intrinsic NIR stellar colors and the reddening vectors. More recently, Arce & Goodman (1999b, p. 278) compared and summarized the quality of various techniques for mapping extinction, and asserted that the "most exact method for measuring extinction [is] using the color excesses of individual stars with measured spectral type." However, as they point out (p. 280), "the real drawback of this technique is the large amount of time required to measure each and every star's spectrum." A reliable means by which to estimate stellar type and reddening from photometry alone would clearly allow much more flexibility and improve our ability to exploit large photometric surveys.

The early dark cloud studies listed in Section 1.3, which undertook a statistical approach to deriving color excesses—i.e., basically assuming an "average" intrinsic color for sources against which to estimate color excesses—were relatively successful because of their use of infrared data in highly reddened regions: the actual range of intrinsic NIR colors of the stars was relatively narrow compared to the degree of reddening being mapped.

An important development along this path of statistical IR reddening mapping was made by Lada et al. (1994), who, in their extensive study of the molecular cloud IC5146, adopted an improved statistical approach to determining color excesses which they called the Near-Infrared Color Excess (NICE) method. By focusing solely on stellar (H − K) colors, Lada et al. (1994) were able to take advantage of the even more limited intrinsic stellar color range (assumed by them as 0 < (H − K)₀ < 0.3 for stars with spectral types from A0 to late M—see also Figure 3 below) to substantially reduce uncertainty in derived NIR reddening values for random field stars. These authors point out that even simply assuming that the average intrinsic color of field stars is (H − K)₀ = 0.15 leads to a maximum uncertainty in the ultimately derived total extinction, A_V, of less than 2.5 magnitudes. However, while residual uncertainties in the extinction at the level of 2.5 mag may be sufficiently negligible in the study of dense molecular clouds reaching extinctions of A_V = 40 mag, for mapping the more diffuse extinction of the typical interstellar medium (ISM), the large reddening-to-extinction conversion factor leads to severe fractional A_V errors for a given E(H − K) error.

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It is possible to reduce uncertainties by averaging over many stars, but this can severely limit the resolution of the final extinction map. For example, Lada et al. (1994) spend considerable effort modeling their results to account for cloud structure fluctuations on scales smaller than the resolution of their maps (which had 1.5 × 1.5 arcmin cells; see also Alves et al. 1998, Lada et al. 1999, and Arce & Goodman 1999b). Other disadvantages of the method (at least from the standpoint of understanding individual clouds) include the difficulty of understanding the relative placement of the stars along the line of sight, the potential for certain stars to suffer circumstellar extinction (e.g., dust shells), the varying density of stars on the sky, the non-constancy of stellar populations with position in the sky (see especially Arce & Goodman 1999b and Popowski et al. 2003 on this point), the dilution of high extinction peaks because of averaging, and the requirement that the dispersion in the mean colors of stars in the control fields be significantly smaller than in the target field, since the latter serves as a limit on the ultimate uncertainties. All of these affect the usefulness of applying the NICE method more broadly along the Galactic Plane (Alves et al. 1998; Froebrich & del Burgo 2006).⁴ Clearly, it would be much better to know the intrinsic color of each star to maximize the resolution of reddening maps to the scale of star-to-star spacing.

Lombardi & Alves (2001) set out to generalize the Lada et al. (1994) NICE method to take advantage of multi-band data (specifically, JHK_s data from 2MASS) and introduced the NICER (Near-Infrared Color Excess–Revisited) technique. In their specific application, Lombardi & Alves use both (J − H) and (H − K_s) colors and the NICER technique to make extinction maps over a large area (625 deg²) around the Orion and Mon R2 region. In principle, the main problem with including J-band photometry in these color-excess methods is the larger scatter in intrinsic (J − H)₀ colors for stars, which is more than three times larger than in (H − K_s)₀ (Girardi et al. 2002; see also Figures 3(b) and 5(b)). However, Lombari & Alves argue that the complication of including the larger intrinsic scatter brought by incorporating (J − H) colors in the analysis is offset by the typically smaller uncertainties one encounters in J-band photometry compared to K_s, as well as the smaller numerical ratio of A_V/E(J − H) compared to A_V/E(J − K_s) (they used 9.35 versus 15.87; Rieke & Lebofsky 1985), which diminishes the effect of color-excess uncertainties once converted to total extinctions. The NICER method seeks to balance these trade-offs between E(J − H) and E(H − K_s) derived maps with an optimization via maximum likelihood; however, the method is still intrinsically based on taking advantage of average field star colors, assuming constancy of that mean color with position in the sky, and spatially smoothing over numerous stars to create each "pixel" in a map. Thus, for example, the Lombardi & Alves map of the Orion cloud yielded some regions with "negative extinction" owing to the presence of many contaminating blue stars from the open cluster NGC 2204. Nevertheless, Lombardi & Alves show that for the same angular resolution, the NICER method yields less noisy extinction maps that are more sensitive to lower extinction than the NICE method using (H − K_s) colors alone. This group has successfully applied the same methodology to explore the Pipe Nebula (Lombardi et al. 2006) and the Ophiuchus and Lupus Cloud Complexes (Lombardi et al. 2008). More recently, Gosling et al. (2009) have updated the NICER method to include a variable extinction law; they apply their "V-NICE" method to understanding the nuclear bulge, assuming as their baseline intrinsic colors some mean (J − H) and (H − K_s) colors of G, K, and M stars.

As implied in Section 1.1, a primary motivation for our investigation of improved dereddening methods derives from an interest in stellar populations and Galactic structure, a fact that shapes our dereddening strategy and desired data products. To these ends we have developed the Rayleigh–Jeans Color Excess (RJCE⁵) method, which builds on and contrasts with previous reddening studies in the following ways.

• 1.  
  As with numerous investigations stretching back to the 1930s (Section 1.2), we use stellar color excesses to gauge the amount of foreground dust.
• 2.  
  Like NICE, NICER, V-NICE and related studies (Section 1.4), we rely on infrared colors to measure the excesses because these can be gauged more reliably due to the narrower intrinsic color range of stars at these wavelengths. This reason is of course in addition to the advantageous facts that infrared extinction is both weaker than optical extinction (which allows greater distances to be explored in dusty regions) and the extinction law is less variable with wavelength and environment than that at shorter wavelengths.
• 3.  
  Similar to the Imara & Blitz (2007), Froebrich et al. (2007), Rowles & Froebrich (2009), Dobashi et al. (2008, 2009), and Gosling et al. (2009) studies (Section 1.4), we are interested in large-scale mapping of dust (reddening) around the Galaxy—i.e., not just that around specific clouds, but also down to rather low dust column densities where a high precision method is required to assess the color excesses.
• 4.  
  However, because the stars themselves are a primary interest, we are not content with simply assuming their intrinsic photometric properties as in most of the large-scale, statistical studies; rather, we want to measure these properties. The stars are not just a means to an end (i.e., evaluating and understanding the dust) to be averaged over; rather, the distribution and properties of the stars are end goals in themselves. By accurately reproducing the intrinsic color–magnitude distributions of the stars, we can learn about the distribution of stellar populations within the Galaxy (with a particular emphasis on the much more obscured and less well-studied populations at low latitudes), as well as the density laws of the dusty inner Milky Way via photometric isolation of various "standard candles." As a bonus, with accurate knowledge of the three-dimensional distribution of stellar types, we can in turn hope to map the three-dimensional distribution of the dust itself.
• 5.  
  Because we seek an accurate means to attain accurate star-by-star foreground reddening (as opposed to statistically assessed, area-averaged, line-of-sight reddening), the desired method to deal with extinction must gauge the reddening to each star and, at the same time, recover that star's intrinsic photometric properties.
• 6.  
  The RJCE method we describe meets this requirement, and we believe it is the first technique to utilize a combination of near-infrared (NIR) and mid-infrared (MIR) photometry for dereddening on a large scale. By exploiting these combined wavelengths, the color effects of reddening and stellar atmospheres can be almost completely separated: The observed NIR–MIR colors contain information on the foreground reddening to a star explicitly, whereas the NIR-only spectral energy distributions (SEDs; especially those using the J-band filter) contain information on the stellar types. Again, previous extinction studies using solely NIR photometry cannot achieve this separability because of the degeneracy of the reddening vector and the intrinsic distribution of stellar NIR colors.
• 7.  
  Unlike previous studies, the RJCE methodology includes both an accurate, star-by-star dereddening procedure as well as a second step of recovering and exploiting the recovered intrinsic stellar spectral types for further improvements in our understanding of the distributions of both the stars and dust.

The dereddening step of the RJCE methodology builds upon the advances achieved with the NICE method—and, moreover, allows us to take color-excess dereddening from the realm of a statistical to a star-by-star procedure—because of two factors. First, the degeneracy between NIR stellar colors and reddening vectors is virtually eliminated as one moves to longer wavelength photometry. This is evident, for example, through comparison of the reddening vector and stellar locus for the most relevant spectral types shown in Figures 1(c) and 1(d),⁶ but a second key feature that MIR photometry—such as that afforded by IRAC on the Spitzer Space Telescope—adds to the Galactic structure toolbox is the measurement of fluxes on what is ostensibly the Rayleigh–Jeans part of the SED of most stars. In the limit that stellar atmospheres radiate as perfect blackbodies, their colors are all the same across the MIR bands for most stellar temperatures (spectral types)⁷; this means that observed departures from this standard color directly and explicitly reflect reddening by dust. We show below that even in the case of real stellar atmospheres, the flux ratios across the various MIR color combinations, even including the reddest NIR bands, are generally constant enough across stellar types (i.e., the color variations are small enough) so as to make the RJCE method remarkably robust. Figure 2 shows realistic stellar SEDs (i.e., non-blackbody models) and their uniformity of slope at MIR wavelengths, and illustrates the degree to which we can expect nearly identical colors for most normal stars with long-wavelength and long-baseline filter combinations.

Figure 1(c) demonstrates two examples of how reddenings might be measured using the power of combining NIR and MIR photometry.

(1) As has been traditionally done, combinations of measured colors can be used to determine the extinction to a star by dereddening along color-excess vectors projected back to the intrinsic stellar locus. As mentioned above, reddening vectors for NIR bands combined with MIR bands are generally not degenerate with the stellar locus for most stars typically encountered (e.g., compare reddening vectors in Figures 1(c) and 1(d) with that in 1(a)). Other combinations of NIR–MIR filters than those shown in Figure 1 also show promising degrees of orthogonality between the reddening vector and stellar locus, and, in theory, one could use the combination of many NIR–MIR color combinations to determine the reddening to a star. This procedure would be equivalent to performing, e.g., a least squares fit to the linear combination of the infrared extinction law (i.e., scaling all color excesses to a common reddening, say, E[J−K_s]) and the SED of the stellar type at the intersection of the reddening vector and the stellar locus. As demonstrated by Figure 1(c), for most typically encountered stellar types there is only a single such intersection point.

(2) As seen in the particular example in Figure 1(c), the intrinsic (H − [4.5μ])₀ variation of stellar colors is very small over a wide range of spectral types: less than 0.1 mag across F, G, and K stars (spanning a very large range of age and [Fe/H]) and only 0.4 mag across the entire range of B through M spectral type (Girardi et al. 2002), ignoring late type dwarfs in both cases. The near constancy of (H − [4.5μ])₀ colors means that the foreground interstellar reddening, E(H − [4.5μ]), can be estimated from the observed (H − [4.5μ]) alone for most typically encountered stars; conversion of this particular color excess to an extinction (we choose to use the K_s band) is possible through the adoption of an IR extinction law and intrinsic (H − [4.5μ])₀ value:

$$\begin{equation} \displaystyle A(K_s) = 0.918 (H-[4.5\mu ]-0.08). \end{equation} \tag{ 1 }$$

Obviously, when using this method, the stronger the reddening is, the less significant are the effects of the small variation in intrinsic stellar colors. Moreover, in most directions of the Galaxy, including in the Galactic midplane, the vast majority of stars seen in 2MASS CMDs (for example) are evolved F, G, and K stars with colors between those of a several-Gyr-old population's main-sequence turnoff (MSTO) and red giant branch tip. We demonstrate the efficacy of this particular, simple, single-color version of RJCE dereddening below (Figure 6), but investigation of other combinations of colors (some also explored below) show that this procedure works more or less for any combination of NIR–MIR filters sampling the Rayleigh–Jeans part of SEDs (e.g., H, K_s, [3.6μ], [4.5μ], but not J), so that it is possible to make multiple, independent measures of the reddening for each star in this way.

In future papers we plan to discuss in detail the effects of the (small) intrinsic color variations in stars, as well as to optimize methods for taking advantage of multiple color data. Here we focus on a couple of example variants of the RJCE method and compare extinction maps made with RJCE and 2MASS+GLIMPSE-detected stars to those made using other infrared excess dereddening methods (Section 3.3) and dust tracers (Section 4). In particular, we show that RJCE-generated extinction maps of the midplane bear little resemblance to those derived by SFD from 100μ emission, while, on the other hand, they do strongly resemble the distribution of ¹³CO (J = 1→0) molecular cloud emission, as well as the distribution of overall 2MASS star counts. Through demonstration of these various correlations and non-correlations among the different maps, we highlight the inadequacy of long wavelength infrared dust emission to serve as a suitable linear proxy for dust extinction.

We also explore the power of the RJCE methodology to recover stellar type information (Section 3.4), discuss several limitations of the RJCE method (Section 3.5), and show a few test applications that demonstrate the potential of the RJCE method to both overcome and explore Galactic dust (Section 5). In a companion paper (D. L. Nidever et al. 2011, in preparation Paper III hereafter) we provide high resolution, electronic versions of the new, two-dimensional extinction maps we have created across the entire GLIMPSE-I and Vela–Carina (Spitzer PID 40791) IRAC survey areas using the methods outlined in this paper. In the future we expect to improve the quality of these maps as we refine the simple version of the RJCE method used here. One ultimate goal is to apply this dereddening methodology to ascertain the three-dimensional distribution of both dust and stars within the Galactic midplane, lifting the dusty veil at low latitudes to facilitate new approaches to persistent, as well as recently recognized, problems in Galactic structure and stellar population studies.

In this subsection, we evaluate some of the NIR–MIR color combinations presently available for use with the RJCE method, with a particular focus on data from 2MASS and Spitzer-IRAC. The histograms in Figure 3 summarize the expected stellar color ranges for the filter combinations shown in Figure 1 and for main sequence (MS), red clump (RC), and red giant branch (RGB) stars separately. We have divided the evolved stars into the RC (0.55 ⩽ [J − K_s]₀ ⩽ 0.85) and RGB (0.85 ⩽ [J − K_s]₀ ⩽ 1.4) groups by color, guided by the Girardi et al. (2002) isochrones as well as TRILEGAL (Girardi et al. 2005) modeling.

In Section 2.1, we proposed that colors composed of filters falling on the Rayleigh–Jeans portion of the stellar SED would have values nearly independent of stellar type. Figure 3 further explores the degree to which this hypothesis holds true. Here, the range of intrinsic colors over all three sampled groups of stars (MS, RC, and RGB), as well as the ranges within each group, generally decrease with colors made from increasingly redder filter passbands, though there are some subtleties. For example, the (H − [4.5μ])₀ color ranges are about as narrow as those for (K_s − [3.6μ])₀, presumably because the broader wavelength baseline of the former color combination compared to the latter compensates for the slightly greater sensitivity of H to stellar SED variations than K_s. Nevertheless, in principle, either of these two color combinations offer very promising RJCE method possibilities because of the negligible range of intrinsic stellar colors. In this paper, we have generally opted for use of (H − [4.5μ])₀ as our baseline RJCE method color index. Figure 3 also demonstrates how strongly sensitive colors that include the J-band are to stellar type/temperature, with both (J − H)₀ and (J − K_s)₀ spanning more than a magnitude for normal stars. It is precisely this sensitivity that we aim to exploit after dereddening with (H − [4.5μ]) colors to separate stars by their temperature/type.

Figures 1 and 3 are slightly unphysical because each point in the Girardi et al. isochrones is given equal weight (in Figure 3 the points within each stellar group are given equal weight, but each of the histograms is normalized to peak at unity). In contrast, any particular direction in the Galaxy will be weighted toward higher representations of specific age/metallicity populations, and this will generally narrow the intrinsic color ranges of the actually sampled stars even further. To demonstrate this point Figures 4 and 5 present analogous distributions to Figures 1 and 3, respectively, but now using stellar distributions derived from a TRILEGAL model of a typical GLIMPSE-like field (simulating 4.0 deg² at (l, b) = (25, 0)° with zero extinction). In this case, the weighting in the color distributions are affected by the specific adopted age, metallicity, and luminosity function combinations of TRILEGAL at this Galactic position, but the crucial feature—the further restriction of the intrinsic NIR–MIR color distribution spreads—is clearly visible.

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One of the most extensive databases of NIR–MIR photometry comes from combining 2MASS with the various GLIMPSE surveys of the Galactic midplane (see references in Churchwell et al. 2009). We will depend on the data in the GLIMPSE-I and Vela–Carina surveys for the remainder of this paper; additional large sky surveys with the Spitzer-IRAC instrument afford the opportunity to apply the RJCE method to a large fraction of the dustiest directions in the Milky Way, but this we leave to future work.

Figure 6 demonstrates the application of the simple, single color version of the RJCE method via estimation of E(H − [4.5μ]), after assuming that the intrinsic SEDs of all stars have (H − [4.5μ])₀ = 0.08; for now we adopt this color—typical for the evolved F, G, and K stars that dominate at GLIMPSE magnitudes (Figure 1)—as the baseline (H − [4.5μ])₀ color index for most stars. To demonstrate how effectively the method works, we have selected an extremely reddened demonstration field from the GLIMPSE program (at [l, b]=[307, 0]°) that has a mean and maximum E(B − V) given by SFD as 7.7 and 13.0 mag, respectively. More significantly, as shown by the distribution of stellar colors in Figure 6(d), this field has extremely variable differential infrared reddening with 0 ≲ E(J − [4.5μ]) ≲ 7 mag; this translates to a range of total extinctions spanning roughly 0 ≲ A_V ≲ 30 mag.

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Figure 6(a) shows the raw 2MASS ([J − K_s], K_s) CMD for this demonstration field. Two of the three nominally vertical "fingers" one sees in a typical 2MASS CMD of Galactic field stars—one due to MSTO stars and the other due to RC stars—are discernible in Figure 6(a) as sequences arcing to redder colors with increasing magnitude as both distance and the amount of cumulative foreground dust increase. At the faintest magnitudes shown, the RC sequence broadens considerably due to highly variable, patchy reddening. The third stellar population sequence typically seen in the 2MASS CMD, that of more distant RGB stars, is completely smeared out in Figure 6(a), because these stars typically suffer the most total and differential reddening along the line of sight.

In general, the effectiveness of any dereddening attempt can be gauged by the resulting color–magnitude coherence of typically well-defined stellar population features like the RC, as well as the dereddened colors of the nominal stellar sequences. Figure 6(b) shows what happens to the raw CMD when it is dereddened using the SFD extinction maps: The CMD actually looks worse, in that (1) the primary CMD loci are greatly smeared out, even more so than in the uncorrected CMD, and (2) the bulk of the stars have had their reddening grossly overcorrected, as evidenced by the extraordinarily blue and obviously incorrect colors for a large fraction of the stars. In addition, (3) the overall spread in colors in the SFD-corrected CMD is significantly larger than for the uncorrected CMD. That the SFD extinction maps tend to lead to overcorrections of colors in heavily extinguished Galactic midplane fields has been noted previously by a number of studies (see discussion in Section 4.4). These studies typically have found that the SFD maps were off by a simple scale factor; however, were this the only problem with the SFD maps, the coherence of the discernible CMD fingers in the raw CMD—like that of the RC—should be maintained when corrected for reddening by these maps, even if these sequences were shifted in color and orientation in the CMD. The significantly smeared-out CMDs that result from dereddening with the SFD maps show that these maps are not just off by a scale factor, but problematic in more nettlesome ways. We will show the extent of these issues with the SFD maps in highly extinguished regions in more detail in Section 4.4.

In contrast to the broadening of the distribution of stars in the SFD-corrected CMD in Figure 6(b), dereddening with the simple RJCE algorithm described above—using the Indebetouw et al. (2005) reddening law and assuming (H − [4.5μ])₀ = 0.08 for all stars—yields far superior results (Figure 6(c)), as evidenced by a much narrower overall distribution of stars, with coherent MSTO, RC, and RGB stellar sequences corrected to their proper colors. For example, the RC is centered at a color of (J − K_s)₀ ∼ 0.7 mag, appropriate to disk metallicity RC stars (e.g., Salaris & Girardi 2002). Figure 6(e) is a close-up of the restored CMD to show more clearly the RJCE-dereddened colors of the distinct stellar population sequences. Figures 6(c) and 6(e) demonstrate that the primary stellar population sequences are not only clearly visible and restored to their proper colors, but in the case of the MSTO and RC they are each appropriately vertical and significantly narrower (as seen in Figure 6(c)).

The line drawn in Figure 6(e) is the isochrone for a solar metallicity RGB (from Ivanov & Borissova 2002), shifted to a distance of 16 kpc. This line skirts below the concentration of RC and RGB stars in this field and suggests not only that a solar metallicity RGB is a reasonable match to the metallicity of these evolved disk stars, but also that a true, sudden decrease in stellar density occurs near this distance at about this longitude (that is, the sudden drop in the number of stars near the line is not due to sample incompleteness, but rather to a real drop in stellar density at the edge of the MW disk for this line of sight; see discussion in Section 5.2).

The sources of uncertainty in extinction values derived with RJCE are (1) intrinsic scatter in the stellar color(s) used to estimate reddening, (2) uncertainty in the stellar photometric measurements, and (3) variations and uncertainties in the extinction law used for reddening/extinction conversion. The first of these is assessed from the suite of Padova isochrones spanning the full available range of metallicity and age (i.e., those used in Figures 1 and 4), yielding a maximum σ(H − [4.5μ])₀ ∼ 0.04.⁸ The photometric uncertainties of stars with both 2MASS H and IRAC [4.5μ] detections typically range from 0.02–0.12 mag in H and 0.02–0.21 mag in [4.5μ], with an average uncertainty of σ_H ∼ 0.05 and σ_[4.5μ] ∼ 0.1, over the entire range of available magnitudes. (Unlike the [5.8μ] and [8.0μ] IRAC bands, [4.5μ]-band photometry is largely unaffected by dust continuum emission; Churchwell et al. 2009). We find these uncertainties to be uncorrelated with reddening, and these ranges describe even the more heavily reddened and crowded inner Galaxy.

Infrared extinction law variations, such as those assessed in Paper II and Indebetouw et al. (2005), may cause small systematic underestimates or overestimates of the extinction in particularly dense or diffuse ISM, respectively; however, the variation in A(K_s)/E(H − [4.5μ]) measured in Paper II produces a ≲7% possible error in the final A(K_s) values (i.e., ±∼3.5%). We note that this does not include a possible systematic error due to the assumption of a constant A_H/A_[4.5μ], but work targeting the non-bulge NIR extinction law (e.g., Stead & Hoare 2009) has shown this variation to be small compared to those at longer wavelengths. For very dense interstellar clouds (explicitly excluded from Paper II but studied in, e.g., Chapman et al. 2009), which have the "flattest" (i.e., grayest) MIR extinction curves, the reddening-to-extinction ratio is only 7% greater than the value we have adopted here. And as we discuss in Section 3.5, these densest regions tend to suffer from far more significant problems that overwhelm this potential systematic error.

In summary, by combining the above sources of uncertainty, we estimate an approximate RJCE extinction uncertainty (in the K_s band) of ≲0.11 mag for a typical individual star. This total RJCE uncertainty is comparable to the contribution of the intrinsic spread in the (J − H) and (H − K_s) colors alone in NIR–only color-excess studies such as NICE, and as we show below (and has been described in, e.g., Dobashi et al. 2008), the application of "Nth percentile" extinction mapping to large sets of stars significantly reduces the uncertainty of total extinction maps and rejects influence by statistical or genuine outliers.

As discussed in Section 1.4, the development of NICE, NICER, and related methods has yielded variously effective means for taking advantage of large area photometric surveys to make extinction maps in a variety of Galactic contexts. These maps are limited in their resolution by the density of available stars and the level of smoothing over stars—the more stars averaged over, the lower are the influence of random errors from, e.g., limitations in the precision of the photometry, as well as the innate dispersion and variation in intrinsic stellar colors. In the limit of large numbers of stars averaged over, these color-excess methods are effective tools for creating relatively reliable two-dimensional extinction maps. The RJCE method is intended to improve on these other methods by making more accurate estimates of reddening for each star; this enables one to make extinction maps with arbitrarily small resolution, limited only by the areal density of stars. Nevertheless, it is useful and important to check the results of the various methods at a fixed resolution, one appropriate for all surveys.

Figure 7 compares extinction maps of a segment of the GLIMPSE survey region made with the NICE (using [H − K_s] colors), NICER (using [J − H] and [H − K_s] colors), and RJCE methods, with the latter making use of (H − [4.5μ]) colors. For each map, we use all stars with uncertainties less than 0.5 mag in the set of photometric bands required for each method (e.g., σ_H and σ_Ks ⩽ 0.5 for NICE). In all cases we plot for each 2' × 2' cell the median A(K_s) extinction derived from color excess of all stars in the cell. We adopt the following extinction relationships for the NIR-only maps, based on the Indebetouw et al. (2005) extinction law and the mean stellar colors for giant stars (the dominant stellar type in the disk in surveys such as 2MASS and GLIMPSE) from the Girardi et al. (2002) isochrones:

$$\begin{equation} \begin{array}{cc} \displaystyle A(K_s) = 1.05 (J-H-0.76) & {\rm NICER} \\ \displaystyle A(K_s) = 1.82 (H-K_s - 0.13) & {\rm NICE(R).} \end{array} \end{equation} \tag{ 2 }$$

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Visually, the maps created by the various color-excess methods strongly resemble each other. To assess better their correspondence, we show in Figure 8 the pixel values of A(K_s) calculated from the NICE, NICER, and RJCE methods (Figure 7) plotted against one another. A strong correspondence is found at most A(K_s) levels, although there is a trend at higher extinction for the NICER (and to a lesser extent, the NICE) A(K_s) values to be larger than those from the RJCE map. This result may be attributed to NICER's systematic overestimation of A(K_s) toward red giant stars (explained more fully in Section 3.4), which would overestimate the measured extinction in each pixel by an amount proportional to the quantity of extinction. A corresponding underestimation of extinction toward foreground dwarf stars by NICE and especially NICER would explain the difference in A(K_s) pixel values at low extinction (A[K_s] ≲ 0.8).

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Another possible explanation for the non-unity correlation slope in Figure 8 is a problem with the adopted extinction law, and it is conceivable to get closer to a one-to-one correspondence if one were to adopt a modified extinction law (e.g., if the equation A(K_s) = 1.59([H − K_s] − 0.05) were used for the NICE-calculated extinctions). Note that it is not obvious a priori which total-to-selective extinction ratios to modify to achieve this correspondence, and all three of the E(J − H), E(H − K_s) and E(H − [4.5μ]) conversions to A(K_s) could need modification depending on the actual extinction law. In principle, one could use distributions like that shown in Figure 8 to rederive the relative color extinction ratios for any particular line of sight; this is the essence of the work presented in Paper II. It should be noted that without consistency in these reddening-to-extinction conversions, color-excess dereddening methods relying on multiple colors, such as NICER, may have additional systematic errors introduced.

The relative reliability of color-excess maps is commonly assessed by plotting the dispersion in extinction values for stars within a map pixel as a function of the derived extinction in that pixel (e.g., Lada et al. 1994; Lombardi et al. 2008). In part, this type of analysis has been used to ascertain the degree to which there is structure in the dust distribution on angular scales smaller than the pixel size. We note that previous authors have used the visual extinction, A(V) as the reference, though A(K_s) is just as useful for this purpose, and more naturally and reliably determined from infrared colors. In Figure 9 we compare the dispersion in A(K_s) as a function of A(K_s) itself for the maps shown in Figure 7. The solid line is an approximate match to the bottom envelope of the RJCE relationship and is included in all three plots to guide the eye in comparison.

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Two features of this comparison are evident: (1) the slope of the RJCE dispersion plot is lower than that of the NICE and NICER dispersion plots, and (2) the spread in the dispersion at each A(K_s) is lower in the RJCE case than in the others. Both features can be attributed to the greater fidelity of the derived color excesses in the case of RJCE, due to the lower dispersion in intrinsic (H − [4.5μ])₀ stellar colors compared to that for intrinsic NIR colors (see Figures 1 and 4). However, all of the dispersions are much greater than the expected extinction uncertainty (Section 3.2), which suggests that at this map resolution, the dispersion is dominated by sub-pixel-scale extinction variations (see Section 5.1 and Figure 15 for an example of how RJCE can greatly ameliorate this problem by restricting the spatial extent of the stars tracing the extinction).

As described in Section 1, until now, color-excess techniques have been primarily focused on creating extinction maps, whereas we are also interested in CMDs. These can be used not only to interpret the stellar populations along a line of sight, but also to improve our detailed understanding of the distribution of dust by placing reddened and dust-extinguished stars at specific and accurate photometric parallax distances. In this context, the NICE/NICER family of methods are less useful approaches than the RJCE method because of their less accurate assumptions about intrinsic stellar colors, their averaging of reddenings over many stars, and their inclusion of photometric bands—particularly the NIR J-band or bluer bands—that are highly sensitive not only to reddening by dust but also the intrinsic SEDs of the stars themselves.

These limitations are demonstrated in Figure 10, which compares CMDs dereddened by these various infrared excess techniques. Figure 10(a) shows a raw 2MASS, ([J − K_s], K_s) CMD for a field of area 4.0 deg² at (l, b) = (42, 0)° and having strong and variable extinction, with 0 < A(K_s) < 4. As in Figure 6(a), the CMD shows arcing trends toward redder colors at fainter magnitudes as a result of increased dust reddening along the line of sight. Figure 10(e) shows the expected CMD for the same field without reddening effects, as predicted by the TRILEGAL stellar populations model⁹ (ver. 1.4; Girardi et al. 2005). We have added photometric errors in accordance with those expected from the m–σ_m relationship of the 2MASS data. (Note that these errors have been applied to the intrinsic stellar colors and magnitudes; thus the amount of induced scatter in the colors is slightly less than would be the case for stars with fainter, extinguished magnitudes.) The TRILEGAL model shows the three principal stellar population loci discussed in Section 3.1 and seen in Figures 6(c) and 6(e): MS, RC, and RGB stars (from blue to red, respectively). The point of this model comparison is to examine the variously dereddened 2MASS CMDs for the correctness of the color distributions of the primary stellar populations and to see how the techniques affect the overall CMD appearance.

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In Figure 10(b) we show a ([J − K_s]₀, [K_s]₀) CMD derived using the NICE method, applied to the observed (H − K_s) colors of each star. As in the studies described in Section 1.4, we adopt a mean intrinsic color of (H − K_s)₀ = 0.13 for each star; this assumption has the effect of strongly compressing the derived (J − K_s)₀ colors. In particular, the reddest, brightest giants are "overdereddened" because these stars are intrinsically redder than the adopted mean color, and the NICE method attributes the observed redder colors for these stars entirely to reddening. The opposite happens for the MS stars, which have intrinsic colors bluer than (H − K_s)₀ = 0.13 and are therefore insufficiently dereddened by NICE.

This color compression is even more pronounced with a NICER dereddening; the latter technique uses both (J − H) and (H − K_s) colors to deredden, which results in an even greater homogeneity in the derived (J − K_s)₀ colors (Figure 10(c)). Thus, the three major stellar populations (MS, RC, and RGB) have been unrealistically compressed to essentially a single color (effectively representing the SED corresponding to the adopted "mean" intrinsic colors), removing any chance of recovering a star's stellar type or luminosity class information.

Figure 10(d) applies the RJCE method using the (H − [4.5μ]) color assumption (e.g., as in Figures 6(c) and 6(e)). Of the various dereddening methods, the RJCE method, which makes no assumptions about the stellar type in its application but uses only the homogeneity of (H − [4.5μ])₀ colors for all stellar types, produces the most sensibly dereddened NIR CMD, as seen by comparison of Figure 10(d) to Figure 10(e). In this panel, all of the primary loci have the same shape and color distribution as the corresponding loci in the TRILEGAL zero-extinction CMD.

One advantage of a relatively cleanly dereddened CMD is that one can select, with relatively high purity, specific stellar types to serve as tracers of the dust. For example, one could select RGB stars—the vast majority of stars redward of (J − K_s)₀ ∼ 0.85 in the CMD of Figure 10(d)—as the most distant stars at any particular magnitude, and thus those most useful for total extinction maps. Or, one could focus on RC stars (the dominant stellar type at (J − K_s)₀ ∼ 0.55–0.8), which are not intrinsically as bright as RGB stars but which make good standard candles with very little dependence of the intrinsic luminosity on metallicity (e.g., Salaris & Girardi 2002). See an initial exploration of this method in Section 5.1.

The observant reader may have noticed suspiciously sharp "holes" in the color-excess extinction maps (Figure 7) at the center of the highest extinction regions. Such holes are artifacts created by magnitude limits in the adopted photometric catalog (as this section will demonstrate, the limitation is generally the 2MASS contribution to the GLIMPSE catalog, so that all three of the maps shown are affected similarly). Obviously, if the dust in a particular cloud is dense enough, the total extinction can be sufficient to increase the magnitudes of any tracers behind the cloud beyond the magnitude limit of the catalog. In the event that no stars beyond the cloud are visible, the dense region of the cloud cannot be detected by any color-excess method, and that region of a two-dimensional map is either devoid of stars (if the cloud is close enough) or dominated by the lower extinction measured along the line of sight to stars foreground to the cloud. The only remedies to this sort of problem are to (1) ignore the data given in such areas (with these regions identified and flagged in some way), (2) obtain deeper photometry, or (3) use photometric bands with a lower sensitivity to dust with which stars beyond the cloud may be seen.

So far in this paper we have focused primarily on extinction maps and dereddening based on band-merged 2MASS+Spitzer-IRAC data. We have generally applied selection limits to this catalog based on choosing stars with photometric uncertainties smaller than 0.5 mag in the bands required for each particular method being used. This translates to a primary limitation being placed by the 2MASS data, as demonstrated in Figure 11. There we present for those stellar data mapped in Figure 7 the amount of extinction measured foreground to each star in each of the H, K_s, and [4.5μ] bands as a function of the RJCE-corrected H, K_s, and [4.5μ] magnitudes of that star, respectively. The extinctions in each panel were actually measured via the color excess in (H − [4.5μ]), but translated from the selective to total extinction in the photometric band shown on the abscissa using the Indebetouw et al. (2005) extinction law. In Figure 11, the catalog's intrinsic magnitude limit expected from the apparent magnitude limit of the filter explored in each panel is linear and shown by the diagonal line with a slope of −1. So, for example, it may be seen in Figure 11(a) that no star with H₀ + A(H) ≳ 15 is contributing to the maps in Figure 7. This appears to be the dominant limitation in the Figure 7 maps, because Figures 11(b) and 11(c) show that, for the most part, stars with (K_s)₀ + A(K_s) ≲ 14.3 or [4.5μ]₀ + A([4.5μ]) ≲ 14.1 would be detected were they not already excluded by the H-band magnitude limit. However, closer inspection reveals that it is actually the K_s-band photometry that seems to be the primary catalog limitation at low (A[K_s] ≲ 2) levels. Figure 11 demonstrates that color-excess maps made using 2MASS data, either entirely or partly, will have trouble probing the highest extinction regions, with an extinction limit dependent on the distance of the tracer (indirectly, via its unextinguished apparent magnitude).

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On the other hand, as suggested by the severe difference between the potential and actual limits of the [4.5μ] data shown in Figure 11(c), use of IRAC data alone holds great promise for probing these highly extinguished regions. This is highlighted vividly by the RJCE-generated maps shown in Figure 12 made using 2MASS and GLIMPSE data for (a) (H − [4.5μ]) colors and (b) ([3.6μ] − [4.5μ]) colors. Again, we have used catalogs restricted only by the photometric uncertainty limits of the relevant filters; the greater depth of the IRAC photometry, as well as the lower total-to-selective extinction ratio at these wavelengths, enables much greater sensitivity to dense clouds using only MIR filters. As the difference map (Figure 12(c)) makes especially clear, the IRAC-only map is capable of probing the dense cores of cloud complexes that appear only as artificial "holes" in the (H − [4.5μ]) extinction map due to stars behind the dense clouds being extinguished out of the 2MASS catalog. It is also obvious that greater overall extinction levels are detected in the more deeply probing ([3.6μ] − [4.5μ]) map.

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While the example shown in Figure 12 might suggest exclusive use of MIR (e.g., IRAC) photometry as the ideal solution to creating extinction maps, there are several mitigating factors that need to be considered. (1) As shown in Figures 3 and 5, the intrinsic ([3.6μ] − [4.5μ])₀ color range of stars is apparently wider than, say, that of longer wavelength baseline NIR–MIR colors, like (H − [4.5μ])₀ and (K_s − [4.5μ])₀. Of course, this might be overcome by the use of longer wavelength combinations of MIR filters. However, the GLIMPSE photometric uncertainties at 5.8μm and 8μm (IRAC channels 3 and 4) are greater than at 3.6μm and 4.5μm, the contribution from dust continuum emission is more significant, and the extinction law (A_λ/A_Ks) at these wavelengths is significantly more variable throughout the Galactic disk (Paper II). (2) Because of the still relatively narrow intrinsic color spread for stars in MIR colors, like ([3.6μ] − [4.5μ]), there is virtually no stellar type information that can be gleaned for normal stars using MIR colors only. Thus, one loses almost all stellar population information (i.e., there is no useful CMD in these filters) that one could use to prune one's tracer sample to specific tracers (e.g., the intrinsically brightest, farthest stars at each magnitude). (3) Being more weakly affected by dust means that the MIR has less sensitivity to low levels of extinction, where it will generally be less reliable at deriving A(K_s) for a given precision in the photometry. All of these suggest that hybrid schemes, whereby NIR+MIR (e.g., 2MASS+GLIMPSE) photometry is used for low extinction regions and MIR photometry alone is used in higher extinction regions (where the NIR photometry is limited in reach), might be the most optimal way to utilize color-excess extinction mapping when depending on databases like 2MASS and GLIMPSE. Obviously, with the advent of deeper, publicly available NIR surveys in the future (such as UKIDSS), the limitations of the NIR photometry seen here can be mitigated; given the limited sky coverage for high-resolution MIR photometry, such deeper NIR surveys have the capability of improving the extinction reach of NICE-like mapping, which can be used outside of the regions probed by IRAC. Of course, as discussed at length in Section 3.4, higher precision color-excess dereddening will always be obtained by combining NIR and MIR photometry. The recent and future releases of the WISE all-sky MIR photometry (Wright et al. 2010) will provide an opportunity to apply reliable RJCE extinction mapping and CMD corrections across the entire sky, particularly in out-of-plane, high-reddening regions not observed with Spitzer-IRAC.

Figure 13(c) shows the integrated ¹³CO (J = 0→1) emission in this region of the Galactic midplane, with data taken from the FCRAO Galactic Ring Survey (Jackson et al. 2006). Visually, the similarity between the RJCE extinction and ¹³CO emission maps is striking. Even small-scale and filamentary features such as the structured cloud between 25 ≲ l ≲ 27° and above b ∼ 05, or the smaller knot at (l, b) ∼ (20.8, 0.5)°, are prominent in both. The most significant differences between the maps are where, near the ¹³CO peak intensities, the RJCE extinction map appears to have "holes;" this is precisely the problem discussed in Section 3.5, and one which can be ameliorated by the strategic use of IRAC-only maps, at least for these high extinction regions.

The close correspondence between ¹³CO emission and high dust extinction is not surprising. Both common isotopologues of carbon monoxide, ¹²CO and ¹³CO, form in dusty environments, where they are shielded by the dust from dissociation in the interstellar radiation field. The relatively low abundance and higher excitation threshold of ¹³CO make this molecule optically thin even in dense molecular clouds, and hence more effective at tracing the total cloud mass (e.g., Pineda et al. 2008). Thus CO emission, particularly ¹³CO, is often used as a proxy for dust extinction, provided a dust-to-gas ratio can be assumed (see work and discussions by, e.g., Bok 1977, Frerking et al. 1982, Langer et al. 1989, and Dobashi et al. 2008; Dickman 1975).

The relation between dust extinction in the atomic and molecular phases of the ISM can be used to derive the useful but elusive conversion factor between CO and H₂ emission (X_CO; e.g., Lombardi et al. 2006, Dobashi et al. 2008; Pineda et al. 2008). We will not undertake this analysis here, but future work may enable us to use our new extinction maps (which in many lines of sight are able to probe to the edge of the Galactic disk) to directly explore the relationships among dust, H₂, and CO. Finally, CO emission observations provide useful velocity information that can be combined with extinction measures to gauge kinematical distances to dust clouds.

In Figure 13(d), we show the IRAC [8.0μ] image taken as part of the GLIMPSE-I survey (Benjamin et al. 2003). This IRAC band contains emission from hot dust and polycyclic aromatic hydrocarbons, heated by UV radiation in star-forming regions, supernova remnants, or other excited H ii regions. As such, it is not expected to be a particularly effective tracer of the majority of the dust responsible for interstellar extinction, so the clear lack of strong correspondence with the RJCE extinction map is not worrisome. We include this panel primarily to help explain discrepancies with the SFD extinction map (Section 4.4 below) and to demonstrate how observations of dust at different wavelengths can reveal quite different and complex behaviors.

Figure 13(e) shows the merged 2MASS+GLIMPSE stellar density in the same region of the Galactic midplane. Star counts are often used to estimate extinction in regions where the stellar populations are roughly spatially homogeneous, and where one can depend on a nearby reference field that is assumed to be relatively reddening-free (e.g., Wolf 1923; Bok 1956; Froebrich et al. 2005). However, neither of these conditions is generally applicable to the Galactic midplane, particularly toward the inner Galaxy. Nevertheless, we do see reasonable (inverse) correlation between star counts and RJCE-derived extinction, particularly in regions of high extinction, because of the increasing loss of stars behind the denser dust complexes (as in Section 3.5).

This correspondence offers reassurance that our maps are not significantly affected by foreground (low-reddening) dwarf contaminants, and that even a small number of stars behind a cloud is sufficient to make a reasonable estimate of the line-of-sight extinction through the cloud (e.g., [l, b] ∼ [20.8, 0.5]°). A close comparison of Figures 13(b) and 13(e) also allows one to see where the RJCE extinction map is limited due to a lack of background stars—these "emptier" patches of sky (e.g., near [l, b] ∼ [23.3, −0.3]° or [28.3, 0.1]°) show the location of particularly dense cores.

The currently most commonly used global reddening maps are those made by SFD from COBE/DIRBE and IRAS/ISSA data. These replaced the previously popular Burstein & Heiles (1978, 1982) maps made using the variation of galaxy counts with position in the sky. Low resolution is a primary shortcoming of either survey, particularly at low Galactic latitudes where the spatial reddening variations can be steep. The SFD maps have a 6' resolution and are now well established to become less reliable with increasing extinction, both at low latitudes and elsewhere.

For example, in a study toward the Taurus dark cloud, Arce & Goodman (1999a) found that the SFD maps overestimate reddening by 30%–50% when A(V) > 0.5, but tend to underestimate E(B−V) in regions with steep extinction gradients. Chen et al. (1999); Stanek (1998a, 1998b); Ivans et al. (1999), and von Braun & Mateo (2001) tested the SFD maps with open and globular clusters and found a range of SFD overestimates for A(V) by factors of 1.16–1.5. Contemporary and subsequent studies using a wide variety of tracers have also derived significant V-band overestimates using the SFD maps: see Cambrésy et al. (2005), Choloniewski & Valentijn (2003), Rocha-Pinto et al. (2004), Dutra et al. (2003a, 2003b), Yasuda et al. (2007), and Amôres & Lépine (2005, 2007) for examples. Even SFD themselves noted that a slight trend of residuals existed between their maps and reddenings derived from the Mg₂–(B − V) relation, suggesting that the DIRBE/IRAS maps overestimate the highest reddening values. Chen et al. (1999) stressed that there were two crucial simplifications assumed for the SFD maps: (1) that all of the dust mapped is at a single temperature, and (2) that the 40 arcmin beam of DIRBE accurately measured that temperature. Although these assumptions are applicable to the low-opacity, translucent cirrus that dominates at high Galactic latitudes, they are not true for midplane latitudes. Here, the dust emission is not well reproduced by a single temperature model, and it contains significant contributions from small-scale, clumpy molecular gas clouds (e.g., Reach et al. 1995; Lagache et al. 1998; Bernard et al. 2010; Planck Collaboration et al. 2011).

The SFD map was created assuming a standard extinction law, though it is well known that the interstellar extinction curve is variable in the optical, with A(V)/E(B − V) ranging from 2.6 to 6 for a variety of dust environments (Cardelli et al. 1989); thus it is possible to understand some of the shortcomings of the SFD map given in terms of E(B − V). In the map shown in Figure 13(a), we chose not to convert the reddening to extinction to avoid adding further uncertainties from the dispersion in A(V)/E(B − V) and A(K_s)/A(V). We have, however, adopted the prescription of Bonifacio et al. (2000) for regions with E(B − V) > 0.1:

$$\begin{equation} E(B-V) ({>}0.1) = 0.1+0.65(E[B-V]_{\rm SFD}-0.1). \end{equation} \tag{ 3 }$$

The result, shown in Figure 13(a), can be compared to the RJCE-derived map (based on (H − [4.5μ]) colors) in Figure 13(b). Of course, the immediately evident difference is that of resolution, which is much coarser in the SFD map. A second striking difference is that the very brightest "knots" of extinction in the SFD extinction map correspond in some cases to extinction "holes" in the RJCE map. (We note, however, that the extinction "hole" near (l, b) ∼ (28.3, 0.1)° also appears dark even in the IRAC [8.0μ] image (Section 4.2); this region is spatially associated with several known dark clouds (e.g., Carey et al. 1998), and the hole at 8μm indicates the presence of dust blanketing so opaque that even IRAC-only data (as in Section 3.5) are too shallow to pierce it.)

Beyond these two differences, comparison of the extinction values of the two maps reveals a broad correspondence to one another but also notable areas of significant discrepancies. For example, there are prominent features in the RJCE map that do not appear in the SFD map, and their absence is not simply due to being blurred out by the lower resolution. The patchy feature at (l, b) ∼ (26.6, −0.75)°, the small but distinct cloud at (l, b) ∼ (20.8, 0.5)°, and the large swathe of extinction from 25 ≲ l ≲ 27° and above b ∼ 05 are examples of the variety of features plainly seen in the RJCE map (Figure 13(b)) but missing in the SFD map (Figure 13(a)), whereas these same features are clearly visible in the completely independent ¹³CO map shown in Figure 13(c) (Section 4.1), demonstrating that these structures are real. On the other hand, several bright knots in the SFD map not appearing in the RJCE map—e.g., those at (l, b) = (25.4, −0.2)° and (20.7, −0.1)°—also do not stand out strongly in the ¹³CO map, supporting the notion that their non-appearance in the RJCE map is not just a result of stars being extinguished out of these maps. That the star count map in Figure 13(e) (Section 4.3) shows no special depression in counts at these positions is further support of this assertion.

Many of the differences between the SFD and RJCE maps may be readily explained by comparing Figure 13(a) to Figure 13(d), which is the IRAC [8μ] image of this GLIMPSE region (Section 4.2) and which bears a striking resemblance to the SFD map. The MIR image shows clearly that many of the high extinction knots appearing in the SFD map are due to the presence of supernova remnants, star-forming regions, and other knots of H ii, which are strongly affecting the far-infrared (FIR) emission in the DIRBE maps at these localized positions. On the other hand, features that are missing from the SFD map but found in the RJCE maps (e.g., those mentioned above) as well as the CO maps (which are good proxies for the presence of colder dust) clearly demonstrate that there are strongly light-extinguishing dust clouds sufficiently cold to have only faint FIR emission, or none at all.

In summary, very close correlations are found among the RJCE extinction map, the ¹³CO emission map, and the 2MASS stellar density map, the latter two of which are expected to be reasonable tracers of extinction by cold dust (for stellar density, only in fairly crowded regions). In contrast, significant differences are seen between the quantity and distribution of RJCE extinction and the reddening derived from 100 μm dust emission, the latter of which is much more closely correlated with the 8 μm hot dust emission, such as that from supernova remnants and H ii regions. From these comparisons, we conclude that RJCE directly and reliably traces interstellar extinction on fine scales. We also emphasize the complexity of dust behavior, and the need for studies to consider the suitability of available extinction corrections to the observations being corrected.

While the comparisons in Section 3.3 suggest that the RJCE methodology performs slightly better than that of the NICE family for two-dimensional dust mapping, the real advantages of RJCE accrue when one considers that this latter method retains sensitivity to stellar type information and luminosity class (Section 3.4). The ability to sort stars as, say, MS versus RC versus RGB type (via their position in the RJCE-dereddened CMD) allows one to key in on stars probing a wide range of different distances. As a demonstration of the potential distance sensitivity and the hope for mapping the three-dimensional distribution of dust in the Galaxy; Figure 14 shows RJCE-derived extinction maps spanning 50° ⩽ l ⩽ 60° for RGB stars (panel a), less distant RC stars (panel b), and even less distant MS stars (panel c). To make these maps, all stars in this region (with JHK_s and [4.5μ] photometric uncertainty ⩽ 0.5 mag) were first dereddened using the RJCE method applied to (H − [4.5μ]) colors, and then the ([J − K_s]₀, [K_s]₀) CMD was partitioned into "MS," "RC," and "RGB" divisions by appropriate (J − K_s)₀ colors. Comparison of the three maps reveals a variety of cloud structures that lie between the typical distances of the RGB stars (∼18-20 kpc), the RC stars (∼8 kpc), and the MS stars (∼3 kpc) used in these maps. For example, the cloud clearly visible in the RGB map at (l, b) ∼ (54.6, 0.8)° does not appear in the MS map or even the RC map, which indicates that it is a distant feature beyond the extent of the RC stellar sample. Likewise, the filamentary structure centered on (l, b) ∼ (59.0, 0.5)° apparent in both the RC and RGB maps but not the MS one traces an intermediate-distance (3–8 kpc) cloud. An even closer structure appears at (l, b) ∼ (53.7, 0.5)°, easily visible in the relatively nearby MS extinction map in addition to the two more distant ones. We note that this approach to making three-dimensional dust maps does not rely on assumed Galactic models, as has been done in previous approaches to this problem (e.g., Marshall et al. 2006).

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Obviously, being able to separate stars by their type also enables us to focus on the most distant, red giant stars, facilitating more reliable maps of integrated extinction along a line of sight. As discussed above (Section 3.3), one of the hindrances to previous attempts to map thick dust clouds is the difficulty of ensuring that the stars tracing the cloud are truly behind it. The usefulness of relying on the most distant possible tracers is demonstrated in Figure 14 by the fact that the map generated from giant stars highlights much deeper regions of extinction (higher A[K_s]) than the dwarf-star-generated map.

In addition, if one adopts stellar tracers of only one type, the intrinsic colors are not only more homogeneous, but also the range of stellar distances probed by stars of this type are more confined. We can demonstrate the impact of these increased homogeneities via the extinction dispersion plots shown in Figure 15, shown separately for each stellar type used in Figure 14 (MS, RC, and RGB). The net slopes for each of these dispersion trends are equal to or lower than in the case of using all stars (compare to Figure 9), and we see that the slope of the trends drops as we proceed from MS and RC star tracers (slope of 0.34) to RGB stars (slope of 0.28). This trend of decreasing slope reflects the increasing distances of the dust tracers and therefore the greater likelihood that any particular tracer will be beyond most of the dust along this line of sight.

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Furthermore, the spread of dispersion for each tracer is decreased in comparison to that of the all-star sample of Figure 15(c), because the distance probed by each stellar tracer becomes more uniform. In addition, we note a trend between the spread of dispersion and approximate distance of the stellar tracers—for example, the relatively close-by MS stars have the tightest spread, because for a fixed angular pixel size, the spatial volume probed is smaller and therefore less likely to be impacted by sub-pixel-scale dust structures. Figure 15 demonstrates once more that use of predominantly RGB tracers appears to be the most effective way to improve the reliability of two-dimensional extinction maps in the Galactic Plane.

In the previous section we showed, as an example, a general statistical method for gauging the rough distances to large dust features by taking advantage of the varying typical distances of stars in maps made by different types of stellar dust tracers. Finer detail in all three dimensions requires greater precision in the stellar distances, which is possible by estimating photometric parallaxes for individual stars. The latter is also needed if one wants an accurate assessment of the distributions of the stars themselves. Precise photometric parallaxes depend on accurately dereddened colors and having a good sense of the type of star (i.e., luminosity class) one is dealing with. It has been shown repeatedly here (e.g., Sections 3.4 and 5.1, and Figure 14) how properly dereddened CMDs allow one to discriminate several stellar types that can serve as very useful standard candles for mapping stellar density distributions. In Paper III, we will discuss the specific challenges and solutions involved in photometric parallax determinations for the different types of stellar tracers, but here we address the more general issue of RJCE map distance limits.

For a certain span of Galactic longitude, GLIMPSE and other similar Spitzer-IRAC surveys contain photometry for RGB stars all the way to the edge of the MW disk, so this population has the potential to provide very useful constraints on not only the size and shape of the disk but also the total integrated extinction through the midplane. Figure 6(e) demonstrates how we know that GLIMPSE probes to the edge of the disk along some lines of sight (in that case, at l = 307°) by virtue of the "edge" of RGB stars in the CMD (illustrated by the diagonal line in that panel). The sudden decline of stars with magnitude at each color is not due to survey incompleteness, which happens at much fainter magnitudes. This RGB edge in the CMD has a slope similar to that of an RGB from a solar metallicity isochrone, which is precisely the line shown in Figure 6(e) (from Ivanov & Borissova 2002), but shifted to an apparent magnitude corresponding to a 16 kpc distance. At this Galactic longitude, and assuming the Sun is 8.0 kpc from the Galactic center, the line corresponds to a radius for the Galactic disk of 12.8 kpc—i.e., close to the 4 scalelengths one expects for the MW disk.

We have undertaken a more systematic and careful analysis of the density drop of the RGB stars in the CMD across all of the GLIMPSE fields. For this exercise, we extend the GLIMPSE longitude coverage with an additional ∼40° of outer Galaxy Spitzer-IRAC data (proposal IDs 40719 and 20499; PI: S. Majewski). All midplane (|b| < 15) stars were dereddened using the RJCE method and then sorted into longitude bins of Δl = 2°. In each bin's CMD, we determined the K_s magnitude of the faint "edge" of the RGB by splitting the RGB into color bins of Δ(J − K_s)₀ = 0.025, fitting a Gaussian to the K_s distribution in each color bin, and then adopting as a standard "limit" to the disk's extent the K_s mag that is 1.5σ fainter than the distribution's peak.¹⁰ The array of color bin centers and RGB edges in each field's CMD were compared to the Padova suite of RGB isochrones (Girardi et al. 2002), leaving distance as a free parameter and using χ²-minimization to select the best-fitting isochrone/distance combination. This method yields an estimated age, metallicity, and distance for the stars at the faint edge of the RGB (presumably, the most distant stars) for each longitude bin's CMD. The age/metallicity grid spanned by the isochrones is relatively coarse, but we do find subsolar metallicities and ages between ∼7–10 Gyr to be the most commonly fit. Figure 16 shows the derived Galactic positions of these most distant stars, for fields fit reasonably well with isochrones (i.e., with χ² < 3, a quality limit established by visual inspection of the isochrone fits). One can see that over a large range of longitude (45° ≲ l ≲ 315°), a common Galactocentric distance of the disk "edge" is found.

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Unfortunately, Figure 16 also clearly demonstrates that even when well fit by an isochrone, the faint edge of an RGB may not actually trace a true physical drop-off in stellar density. The vertical "wall" due to near-constant derived heliocentric distance on the far side of the Galactic center emphasizes that for −45° ≲ 1 ≲ +45°, the distance range spanned by the RGBs in our CMDs is restricted by the magnitude limits (and possibly crowding effects) of the 2MASS photometry. One way to identify the longitudes at which these limits are the dominant factor, without relying on an assumed Galactic disk model, is to measure how closely the stars at the measured faint edge of the dereddened RGB actually lie to the nominal magnitude limit of the survey. Figure 17 illustrates this point. In the top row of panels, with midplane stars at l ∼ 340°, the lower edge of the stellar distribution in the left-hand panel follows closely the dashed line indicating the approximate survey detection limits.¹¹ (The limits shown here are for ideal, unconfused fields; the source confusion present in low latitude fields may account for the actually observed, brighter limit, but note that the slope of the limit is identical to the apparent cutoff slope of the data.) When the CMD is dereddened and an isochrone fitted, the stars being fit at the edge of the RGB are largely those lying near the detection limit (denoted by dark blue colors in the right-hand panel); this indicates that while the isochrone may in fact provide a reasonable estimate of the age/metallicity/distance of the stars, those stars are not probing the physical edge of the Galactic disk. As a contrast, we show in the bottom panels the same CMDs for a midplane field at l = 260°; even in the uncorrected CMD, it is clear that the majority of RGB stars at the faintest magnitudes for each color do not have apparent brightnesses approaching the survey limit (confirmed by the colors of those stars in the lower right panel), so we may be confident that in this field, the fitted isochrone is actually measuring stars at the outermost extent of the disk.

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The most important implications of this simple isochrone fitting procedure are twofold. First, we are able to indicate at which longitudes our integrated extinction maps likely explore the actual total Galactic extinction (from Figure 16, we assess this to be 45° ≲ 1 ≲ 315°), as well as the approximate distances probed by the inner Galaxy maps. Second, the isochrones fitting those RGBs that do sample the edge of the Galactic disk can provide a measurement of the stellar characteristics and distances of the edge of the Galaxy. We will explore and refine this method in future work, but even this simple interpretation of the CMD in terms of the Galactic distribution of disk stars demonstrates the potential of systematically exploring properly dereddened CMDs for a better understanding of the Galactic midplane's stellar populations.