Atlas and Catalog of Dark Clouds Based on the 2 Micron All Sky Survey. II. Correction of the Background Using the Besançon Galaxy Model

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1 PASJ: Publ. Astron. Soc. Japan 65, 31, 2013 April 25 c Astronomical Society of Japan. Atlas and Catalog of Dark Clouds Based on the 2 Micron All Sky Survey. II. Correction of the Background Using the Besançon Galaxy Model Kazuhito DOBASHI, 1 Douglas J. MARSHALL, 2,3 Tomomi SHIMOIKURA, 1 and Jean-Philippe BERNARD 2 1 Department of Astronomy and Earth Sciences, Tokyo Gakugei University, Nukuikitamachi, Koganei, Tokyo dobashi@u-gakugei.ac.jp, ikura@u-gakugei.ac.jp 2 Université de Toulouse, Institut de Recherche en Astrophysique et Planétologie, 9av. du Colonel-Roche - BP , Toulouse Cedex 4, France douglas.marshall@cea.fr, jean-philippe.bernard@irap.omp.eu 3 Astrophysique Instrumentation Modélisation (AIM), Service d Astrophysique, Irfu, CEA Saclay, Gif sur Yvette, France (Received 2011 November 21; accepted 2012 October 23) Abstract In this paper, we give a correction to the large scale color excess maps of E(J H ) and E(H K S ) derived by Dobashi (2011, PASJ, 63, S1) based on the 2 Micron All Sky Survey Point Source Catalog (2MASS PSC). These maps were produced using a new technique named X percentile method, and they cover all of the sky at the 1 0 grid. The maps, however, suffer from an apparent error on a large scale arising from an ambiguity in determining the background star colors. The error is relatively large in the inner region of the Galaxy at jlj. 90 ı, and the maps may overestimate the true extinction by a few magnitudes in A V in this region. To improve the background determination, we performed a Monte Carlo simulation to generate a star catalog equivalent to the 2MASS PSC based on the Besançon Galaxy Model described by Robin et al. (2003, A&A, 409, 523). The simulated catalog contains stars whose apparent magnitudes in the J, H, and K S bands are calculated assuming no interstellar dust throughout the Galaxy. We applied the X percentile method to the simulated star catalog, and regarded the resulting star color maps as the background. As a result, the overestimation in the original color excess maps has been significantly improved. Extinction maps of A J, A H, and A KS made by Dobashi (2011) were also improved utilizing the resulting color excess maps. In this paper, we further investigated possible errors arising from the X percentile method itself by setting an artificial diffuse dust disk in the simulated star catalog, and found that the diffuse dust on a large scale can be underestimated by 20% for the galactic latitude range jbj > 5 ı at most, which should be noted when the color excess maps are compared with other dataset including the far-infrared dust emission detected by Planck and Herschel satellites. Key words: atlas catalog ISM: cloud ISM: dust ISM: extinction 1. Introduction The purpose of this paper is to give a correction to the all-sky color excess maps of E(J H ) and E(H K S ) generated by Dobashi (2011). 1 The maps were produced from the 2 Micron All Sky Survey Point Source Catalog (2MASS PSC: Skrutskie et al. 2006) by applying a new technique named X percentile method (Dobashi et al. 2008, 2009) to measure the color excess of stars by dust. They are drawn at the 1 0 grid with a moderate angular resolution ( ), and are useful for a wide range of research topics especially for studies of dense cores in dark clouds leading to star formation (e.g., Shimoikura & Dobashi 2011). The maps, however, suffer from a systematic offset arising from an ambiguity in determining the background star colors, i.e., the mean intrinsic star colors unreddened by dust, which is needed to determine the zero point of color excess. In general, determination of the background star color is a common problem for extinction maps derived by measuring star colors 1 The all-sky color excess and extinction maps corrected for the background are available at hhttp://darkclouds.u-gakugei.ac.jp/index.htmli or hhttp://astro.u-gakugei.ac.jp/ tenmon/atlas/index.htmli. in the sky, because there is no region without dust in the galactic plane that can be used as a reference field. This problem can be serious when producing color excess maps or extinction maps on a very large scale (Dobashi et al. 2005; Rowles & Froebrich 2009), because the intrinsic star colors and densities should vary a lot as a function of the galactic coordinates. In deriving the color excess maps, Dobashi (2011) used several sets of the threshold magnitudes as summarized in table 1, and selected the deepest Set 1 to measure the star color distributions in the sky for a better angular resolution and sensitivity. However, the background star colors at the deep threshold magnitudes are difficult to assess accurately. For this problem, Dobashi (2011) employed a simple assumption that brighter stars in the 2MASS PSC (i.e., brighter than Set 6 in the table) are dominated by nearby stars and their mean colors, expressed as C 1 in his equation (8), are constant in all of the directions in the sky. He then regarded C 1 +ΔC as the background star colors for Set 1 where ΔC is the difference between the observed star color maps drawn at the threshold magnitudes Set 1 and Set 6 (see his subsection 3.2 and our section 3).

2 31-2 K. Dobashi et al. [Vol. 65, Fig. 1. Distributions of the simulated stars in the Galaxy brighter than the magnitude Set 1 (upper panels) and Set 6 (lower panels) in table 1. The distributions are shown as the surface densities of stars () on the XY plane, and those for the dwarfs, giants, and their sum are displayed separately in the right, middle, and left panels, respectively. Positions of the Sun (X = 0, Y = 8) and the galactic center (X = 0, Y = 0) are indicated by the cross and plus signs. Contours are drawn logarithmically from log() = 4pc 2 with a 0.25 pc 2 step. The assumption for the constant C 1 seems to work to some extent in the outer region of the Galaxy (jlj > 90 ı ), while the assumption may be inappropriate in the inner region (jlj90 ı ) because of the contamination by distant and bright giants whose intrinsic colors are redder than nearby stars containing a number of dwarfs. Compared with an extinction map derived from the far-infrared (FIR) dust emission (Schlegel et al. 1998), there is actually a bump in his color excess maps along the galactic plane in the inner region (see his figures 18b and 18c), which may represent an overestimation of the color excess due to the simple assumption for the background star colors (see his section 5). In order to better determine the background star colors and then to give a correction to the maps by Dobashi (2011), we generated a star catalog equivalent to the 2MASS PSC through a simulation based on the Besançon Galaxy Model (hereafter, BGM) described by Robin et al. (2003), which is one of the latest stellar population syntheses in the Galaxy. A comparison with such a model should provide us a more reliable estimate for the background star colors, and has been used to infer the 3 dimensional distribution of dust in the Galaxy (Marshall et al. 2006) as well as to determine the distance to dark clouds (Marshall et al. 2009; Ade et al. 2011a, 2011b) The simulated star catalog generated in this paper includes no reddening or extinction by the interstellar dust, so that we Table 1. Threshold magnitudes used by Dobashi (2011). Set of the m t J m t H m t K S magnitudes (mag) (mag) (mag) Set Set Set Set Set Set Set can measure the variation of C 1 mentioned above, which is the key of our correction. We will describe the simulated star catalog itself in section 2. In order to infer the background star colors and to give a correction to the color excess maps by Dobashi (2011), we measured the mean star color distributions all over the sky using the simulated star catalog by applying the X percentile method exactly in the same way as he did. We then compared the resulting star color maps from the simulated star catalog with those from the 2MASS PSC to derive the color excess maps corrected for the background. The method of Dobashi (2011) is summarized in section 3. We describe

3 No. 2] Correction to the Extinction Maps by Dobashi (2011) 31-3 the correction for the background in section 4, and compare the resulting maps with the dust map by Schlegel, Finkbeiner, and Davis (1998) in section 5. We further investigate possible errors to quantify diffuse extended dust by the X percentile method in section 6, and compare our maps with the dust map again taking into account the possible error in section 7. Conclusions of this paper are summarized in section 8. Other errors of the resulting maps such as the counting uncertainty as well as comparison with other large-scale extinction maps (e.g., Dobashi et al. 2005) are already described in the original paper by Dobashi (2011). In this paper, we concentrate on the determination of the background star colors based on the BGM and the newly found errors by the usage of the model. Table 2. Number of simulated stars. Magnitude set Total Giants Dwarfs Set (9.7%) (0.8%) (25.7%) Set (14.6%) (7.4%) (96.8%) Numbers in parentheses are the fraction of stars within 1 kpc from the Sun. 2. Simulated Star Catalog We produced a star catalog equivalent to the 2MASS PSC through simulations based on the BGM which was originally described by Robin et al. (2003) and further tuned by Reylé et al. (2009) and Robin et al. (2012). The model is a tool with which one can calculate the stellar content of the Milky Way in three dimensions. It is able to produce simulated catalogs in a large number of filters, while accounting for photometric noise. The model is semi-empirical, using theoretical elements such as stellar formation and evolution scenarios, as well as empirical constraints inferred from the Hipparcos mission and other large scale surveys in the optical and the near-infrared (NIR) wavelengths including 2MASS. The model separates stars of the Galaxy into four populations, i.e., the warped thin disk, the thick disk, the central bulge, and the extended halo. For details, see a series of papers related to the model (Robin et al. 2003; Marshall et al. 2006; Reyléetal. 2009; Robin et al. 2012). Based on the model, we performed a Monte Carlo simulation to generate stars in the Galaxy. In order to produce a star catalog equivalent to the 2MASS PSC, we selected stars that would be observed with apparent magnitudes brighter than the threshold magnitudes (m J, m H, m KS ) = (16.5, 16.0, 15.5) mag, assuming that the Sun is located at (X, Y, Z) = (0.000, 8.000, 0.015) kpc in the Galaxy. The threshold magnitudes are slightly deeper than Set 1 in table 1 which was employed by Dobashi (2011) to produce the color excess and extinction maps. We then recorded parameters of the selected stars such as the apparent and absolute magnitudes, spectral types, and coordinates (X, Y, Z) in the Galaxy. In total, stars are recorded in our catalog. Note that we assumed no reddening by dust in the simulation, so that we can use the star catalog to measure the background star colors in section 4. Among the cataloged stars, there are and stars brighter than the magnitudes Set 1 and Set 6, respectively, as summarized in table 2. We show their distributions in figure 1. Note that the stars are distributed asymmetrically with respect to the galactic center, because only stars with apparent magnitudes brighter than Set 1 and Set 6 are selected. As seen in the figure, dwarfs are distributed mostly around the Sun, because they are intrinsically faint. Actually, 26% and 97% of dwarfs are located within 1 kpc from the Sun for Fig. 2. Distribution of the simulated stars brighter than (a) Set 1 and (b) Set 6 shown as a function of the distance (D) from the Sun. The vertical axis is the number of stars contained in a half of the spherical shell (either at jlj90 ı or jlj < 90 ı ) with a radius of D and a thickness of 100 pc centered at the Sun. Numbers of giants, dwarfs, and their sum are shown by the broken, dotted, and thin solid lines, respectively. Set 1 and Set 6, respectively (see table 2). On the contrary, giants (including subgiants) are more widely distributed, especially toward the inner region of the Galaxy even beyond the galactic center for both Set 1 and Set 6, because they are intrinsically much brighter. This feature is clearer in figure 2 which shows the number of stars as a function of distance from the

4 31-4 K. Dobashi et al. [Vol. 65, Fig. 3. Comparison of the 2MASS point sources and the stars generated following the Besançon Galaxy Model with no dust. Examples of the color magnitude diagrams (the top row), the color color diagrams (the second row), and the histograms of star colors J H (the third row) as well as H K S (the bottom row) are shown. The data are sampled within four circular areas with a radius of 2 ı,2 ı,0 ị 25, and 0 ị 5 centered at the galactic coordinates (l, b) = (0 ı,60 ı ), (180 ı,60 ı ), (0 ı, 6 ı ), and (92 ı,4 ı ), respectively, as indicated above the top row. The leftmost column is to show examples for regions with almost no extinction (A V ' 0 mag), the third column is for faint extinction (A V. 2 mag), and the fourth column is for high extinction (A V & 10 mag). Sun. As seen in the figure, a large fraction of nearby stars are dwarfs, but further stars are mostly giants in our star catalog. Stars in the 2MASS PSC should be distributed in a similar way in the Galaxy. Finally, we compared the simulated stars with the 2MASS PSC in order to check the legitimacy and limitations of determining the background star colors using the BGM. The comparison is made for stars satisfying the magnitude Set 6 which was the set used to decide the background. We compared the stars at high galactic latitudes (jbj & 60 ı ) where the consistencies and differences of the two datasets can be found through a direct comparison because of no or very little extinction/reddening by dust at these latitudes. Some results are shown in figures 3a and 3b for stars sampled at (l, b) = (0 ı,60 ı ) and (180 ı,60 ı ), respectively. As seen in the color magnitude diagrams (CMDs) and the color color diagrams (CCDs) in the first two rows of the figures, the two datasets are apparently very well consistent with each at high latitudes in terms of the distributions of stars in the diagrams. The other panels of the figures 3a and 3b show histograms of the

5 No. 2] Correction to the Extinction Maps by Dobashi (2011) 31-5 star colors J H and H K S. The color distributions are also very similar, and their mean colors are consistent within an uncertainty of 0.03 mag and 0.01 mag in J H and H K S, respectively, everywhere at high latitudes, indicating that the background of the star colors can be well determined by the BGM within an error of this order. For comparison, we show the same plots in figures 3c and 3d for regions with faint extinction (A V 2 mag) and high extinction (A V 10 mag) at low galactic latitudes, respectively. As expected, the 2MASS stars are reddened in the CMDs and CCDs compared to the simulated stars. The same reddening can be seen in the histograms of J H and H K S, which is the quantity that we measure in this paper. 3. Method of Dobashi (2011) Derivation of the color excess and extinction maps from the 2MASS PSC are fully described by Dobashi (2011, see section 3). He first derived color excess maps of E(J H ) and E(H K S ) using the X percentile method, and then derived extinction maps of A J, A H, and A KS via the star count method while utilizing the color excess maps to predict the background star densities. We briefly explain his procedure in the following. The X percentile method is an extension of the near infrared color excess (NICE) method introduced by Lada et al. (1994), and it is characterized of being robust against contamination by foreground stars. The method was first used to probe dark clouds in the Magellanic Clouds (Dobashi et al. 2008, 2009). The method utilizes the color of the X percentile reddest stars found in a given cell set in the sky (X = 100% is the reddest). Taking the color of the ith reddest star as c(i) among N stars found in the cell, we measure the following two colors as a typical star color of the cell, C X0 = c.n 0 / (1) and 1 XN 1 C Xm = c.i/ (2) N 1 N i=n 0 where N i for i = 0 or 1 are N i = N 100 X i for 0 X 0 <X 1 100%. In short, C X0 is the color of the X 0 percentile star, and C Xm is the mean color of stars in the range X 0 <X<X 1 %. Given the background star colors C X0 and C Xm (i.e., the intrinsic star colors unreddened by dust), the color excesses E X0 and E Xm can be calculated as E X0 = C X0 C X0 (3) and E Xm = C Xm C Xm ; (4) respectively. For the seven sets of the threshold magnitudes listed in table 1 (Sets 1 7), Dobashi (2011) derived color excess maps of E(J H ) and E(H K S ) at every 5% for X 0 in the range 5% X 0 90% with a common X 1 of 95% based on the equations (1) (4) at the 15 0 grid with the 1 ı Fig. 4. Explanatory illustration for the method to derive the color excess maps. resolution, and further derived high resolution maps at the 1 0 grid with a changing resolution employing a technique called adaptive grid (Cambrésy 1999) with the deepest threshold magnitude Set 1. Here, we should note that it is virtually impossible to determine the background star colors C X0 and C Xm only with the 2MASS PSC, because there is no region without dust along the galactic plane, and also because the star colors should vary on a large scale. For this problem, Dobashi (2011) employed the following two assumptions: (1) Bright stars are mainly nearby stars and fainter stars are more distant stars, and (2) the mean intrinsic color of the nearby stars (designated as C 1 in the following) are constant in all of the directions. As illustrated in figure 4, the mean observed color of the bright stars O 1 within a distance of D 1 is the sum of their intrinsic color C 1 and the reddening by dust E 1, i.e., O 1 = C 1 + E 1 ; (5) and that for the fainter stars O 2 can be expressed as, O 2 = C 2 + E 2 =.C 1 +ΔC/+.E 1 +ΔE/ (6) where C 2 and E 2 are the mean intrinsic star color and the reddening by dust within D 2, and ΔC and ΔE are the differences compared to those within D 1. The difference of O 1 and O 2 is then expressed as, S = O 2 O 1 =ΔC +ΔE : (7) Note that it is possible to separate ΔC and ΔE from a given image of S (e.g., see figure 5). The total amount of the reddening by dust within D 2 can be then expressed as, E 2 = O 2.C 1 +ΔC/ : (8) Dobashi (2011) took the bright stars as those brighter than the threshold magnitude Set 6, and regarded their mean intrinsic color to be C 1 assuming it to be constant and equal to the color in the polar regions (at jbj >80 ı ). He then derived ΔC by comparing the colors with those for the other sets of the threshold magnitude (e.g., Set 1) to derive the color excess maps. For detail, see his subsection 3.2. Extinction maps of A ( = J, H, and K S ) were derived using the following equation,

6 31-6 K. Dobashi et al. [Vol. 65, Fig. 5. Maps of (a) O 2 the observed star color distribution for Set 1, (b) O 1 the observed star color distribution for Set 6, (c) S the difference calculated as O 2 O 1, (d) ΔE the distant clouds, (e) ΔC the difference of the intrinsic star colors, (f) C 2 the intrinsic star color for Set 1, (g) C 1 the intrinsic star color for Set 6, (h) C 1 +ΔC the background star color for Set 1, and (i) E 1 +ΔE the color excess derived as O 1 (C 1 +ΔC ). All of the maps are for the color J H calculated based on equation (4) for (X 0, X 1 ) = (50%, 90%). The colors C 1 and C 2 are calculated from the simulated star catalog. A = 1 n log a 10 n 0 (9) where a is the observed slope of the Wolf diagram and n is the observed star density at the threshold magnitude Set 1. It is virtually impossible to measure the background star density directly for the same reason as the color excess maps. n 0

7 No. 2] Correction to the Extinction Maps by Dobashi (2011) 31-7 Fig. 6. Color excess of E(J H ) (left panels) and E(H K S ) (right panels) shown as a function of the galactic latitude measured at the galactic longitude l = 0 ı,90 ı, 180 ı, and 270 ı. The two color excesses are E Xm in equation (4) for X 0 = 20% (thick broken lines), 50% (thin solid lines), and 80% (thin broken lines). Color excesses converted from the E(B V ) map derived by Schlegel, Finkbeiner, and Davis (1998) are also shown by gray lines (labelled FIR ) for comparison, assuming the reddening law suggested by Cardelli, Clayton, and Mathis (1989) for R V = 3.1. Thus, Dobashi (2011) attempted to reproduce n 0 from the color excess map as, n 0 = n 10 a b ˇ12 E. 1 2 / (10) where b and ˇ12 are constants related to the employed reddening law (Cardelli et al. 1989). E( 1 2 ) is the color excess map either of E(J H )ore(h K S ) derived from equation (4) for X 0 = 90%, but is smoothed to the 1 ı resolution (for detail, see his section 4). In short, the extinction maps are equivalent to the color excess maps at X 0 = 90% on a large scale, but it is noteworthy that there are significant differences among the resulting A maps on a smaller scale depending on

8 31-8 K. Dobashi et al. [Vol. 65, Fig. 7. Fraction of stars contained within D kpc from the Sun to the total number of the simulated stars. The fractions for stars brighter than the magnitude Set 1 and Set 6 are shown by the solid and broken lines, respectively. the wavelengths (see his figure 16). To summarize, the validity of his method to derive the color excess and extinction maps mainly depends on the assumption for the constant C 1 in equation (8) for the threshold magnitude Set 6. The point of this paper is to discuss and give necessary correction to this assumption. 4. Correction of the Background Star Colors and Star Densities We applied the X percentile method to the simulated star catalog to measure C X0 and C Xm in equations (1) and (2) exactly in the same way as Dobashi (2011) did to the 2MASS PSC, and derived star color maps at the 15 0 grid with the 1 ı resolution for all of the threshold magnitude sets in table 1 in the range 5% X 0 90% with X 1 = 95%. We will regard the resulting star colors as the background colors C X0 and C Xm in equations (3) and (4). In the following, we show an example of the resulting star color maps, taking the stars for the magnitude Set 6 as the bright stars, and those for Set 1 as the faint stars. Panels (a) and (b) of figure 5 show the observed star colors measured using the 2MASS PSC for Set 1 and Set 6 which are taken to be O 2 and O 1 in equations (5) and (6), respectively. Panel (c) displays their difference S = O 2 O 1 which splits into ΔE and ΔC shown in panels (d) and (e). The panels (a) (e) are taken from figure 7 of Dobashi (2011) who took the image in panel (e) to be C 1 +ΔC 1, because he assumed a constant C 1. Panels (f) and (g) in the figure show the star colors measured using the simulated star catalog which we regard as C 2 and C 1, and panel (h) show the sum of C 1 in panel (g) and ΔC in panel (e), which is equivalent to the data in panel (f) and should give the background star color for Set 1. The total Fig. 8. Example of the star density and extinction maps using stars brighter than Set 1 in table 1. (a) The observed J band star density measured using the 2MASS PSC, (b) the background star density inferred from the simulated star catalog and the color excess map of E(J H ) using equation (10), and (c) the extinction map of A J corrected for the background star density. color excess E 2 = E 1 +ΔE calculated following equation (8) is shown in panel (i), which is the final color excess map corrected for the background star color. In figure 5, we show only the color (or color excess) of J H in equations (2) and (4) for (X 0, X 1 ) = (50%, 95%), but results for the other percentiles as well as for the other color (i.e., H K S ) are similar to those shown in the figure. We show some examples of the two color excesses measured at a constant longitude for different X 0 values in figure 6. As seen in panel (g) of figure 5, it is now clear that the assumption of the constant C 1 for the magnitude Set 6 is not very appropriate especially toward the inner region of the Galaxy (jlj < 90 ı ). This is mainly because the fraction of giants among the observable stars increases toward the inner region, as expected from figure 1. It is also noteworthy that the other assumption that brighter stars are closer to us may not be very plausible either, because stars for Set 6 are mostly giants, and they can be observed even if they are located at a very large distance. Actually, as shown in figure 7, the difference between the fractions of stars contained within D kpc from the Sun to the total number of stars is small for Set 1 and Set 6, except for nearby dwarfs at D. 2 kpc. This suggests that star color maps

9 No. 2] Correction to the Extinction Maps by Dobashi (2011) 31-9 Fig. 9. (a) An AV map taken from figure 8 of Sumi (2004), which was produced from the optical data of OGLE-II. The map covers small patchy regions with low extinction (mostly AV. 3 mag, 11 deg2 in total) around the direction of the galactic center. (b) An AV map converted from our E(H KS ) map measured in the range (X0, X1 ) = (70%, 95%) as AV = 13.2 E(H KS ). The regions investigated by Sumi are indicated by the thin solid lines. Some white parts in the map at b 0ı are the defects due to contamination by foreground stars (see subsection 6.6 of Dobashi 2011). for Set 1 and Set 6 may trace mostly the same dark clouds at a similar distance, and this may be why their difference, i.e., S in panel (c) of figure 5, is very smooth. We should note that we could derive the color excess map for Set 1 as E2 = O2 C2 using directly the simulated background color C2 in panel (f) of figure 5, rather than using C1 for Set 6. We actually attempted to use C2, but the resulting E2 map suffers from slight negative holes in some directions along the galactic plane in the outer galaxy (jlj > 90ı ) especially around the warp, suggesting that the warp parameters of the galactic model (Reyle et al. 2009) might not be precise enough at the very deep threshold magnitudes like Set 1. We therefore decided to stick to the method of Dobashi (2011) expressed in equation (8). We regarded the resulting color excesses E(J H ) and E(H KS ) in equation (4) for the range (X0, X1 ) = (90%, 95%) as E( 1 2 ) in equation (10) to improve the background star density n0, and then derived A following equation (9). We show an example of the resulting background star density and the extinction maps in figure 8. Finally, in order to check our background color subtraction, we compared the resulting maps with an AV map produced by Sumi (2004) who used red clump giant stars detected by the Optical Gravitational Lensing Experiment (OGLE). We show his map in figure 9. Sumi produced the AV map directly in the optical bands (V and I ) in limited areas with low extinction around the galactic center by measuring the total extinction toward the individual stars based on the CMDs and CCDs. Though his mapped area ( 11 deg2 in total) and the dynamical range of the measured AV values (mostly less than 3 mag) are rather limited, his map should provide an accurate value of the total AV toward the individual stars he used, and it Fig. 10. AV values measured by Sumi (2004) versus those converted from our E(H KS ) map shown in figure 9. The broken line represents their equality. Contours represent the plot density; the lowest contour is drawn at mag 2, and the others are drawn at every mag 2 from up to mag 2. 1 noise level of the Sumi s data is mostly in the range ΔAV = mag, and that of our data is ΔAV 0.3 mag. should be useful to check the zero point of the extinction in our maps. We show an example of the comparison in figure 10. As seen in the figure, AV values in our maps corrected for the background are proportional to and consistent with the Sumi s

10 31-10 K. Dobashi et al. [Vol. 65, Fig. 11. Panel (a) shows the extinction map of A V converted from E(B V ) data produced by Schlegel, Finkbeiner, and Davis (1998). Panels (b) and (b ) show the difference between the A V map converted from E(J H ) data based on equation (4) for X 0 = 50% and that shown in panel (a). Panels (c) and (c ) are the same as panels (b) and (b ), but for the E(H K S ) data. The difference maps shown in panels (b) and (c) are taken from figure 18 of Dobashi (2011), and those in panels (b ) and (c ) are from the new maps corrected for the background star colors in this work. data within an error mostly arising from the counting uncertainty of stars in our map, indicating that our correction of the background works properly. 5. Comparison with the Dust Map of Schlegel, Finkbeiner, and Davis (1998) 5.1. Origin of the Excess in the Maps of Dobashi (2011) The color excess and extinction maps derived by Dobashi (2011) show a good correlation with the map of Schlegel, Finkbeiner, and Davis (1998) derived from the FIR dust emission for individual clouds. However, on a large scale, there is an apprent excess in the Dobashi s maps in the inner region of the Galaxy (jlj < 90 ı ) when compared to their map. As he discussed in his section 5, the excess may be caused by the assumption for the constant C 1 in equation (8), or by the real change of dust properties on a large scale, but its true origin was unclear (see his section 5). Figure 11a shows an A V map converted from Schlegel s E(B V ) data as, A V (SFD) = R V E.B V/ (11) for R V = 3.1, and figures 11b and 11c show the differences compared to the 2MASS-based A V maps converted from the color excess maps derived by Dobashi (2011) as, A V.J H/= ˇJH E.J H/ (12) and A V.H K S / = ˇHKS E.H K S / (13) where ˇJH and ˇHKS are assumed to be 10.9 and 13.2 following the reddening law by Cardelli, Clayton, and Mathis (1989). The excess can be identified as a bump in the figures along the galactic plane at jbj < 90 ı. Figures 11b 0 and 11c 0 are the same difference maps, but with the data corrected for the background in this work. As seen in the figures, the excesses are much lower in the new maps, suggesting that the excess in the maps by Dobashi (2011) is very likely to be caused by

11 No. 2] Correction to the Extinction Maps by Dobashi (2011) the assumption for the constant C 1. Increase of the fraction of giants toward the inner region of the Galaxy (figures 1 and 2) should be the main cause of the excess in his maps, though contribution of the global change of dust properties may still be at play as discussed in section 7. Note that the excess is still evident even in the new difference maps in figures 11b 0 and 11c 0 around the galactic center (l 0 ı and b 0 ı ). This is probably because of the detection limits in the 2MASS PSC around the galactic center where the detection limits are slightly higher than those for Set 1 (see figure 2 of Dobashi 2011), or might be due to a missing stellar population in the galactic model. It is also possible that the excess can be due to an error of A V (SFD) because of the assumption of a constant emissivity and dust temperature along each line of sight, which is used when converting the FIR dust emission to A V (Schlegel et al. 1998) Relationships of A V (J H ), A V (H K S ), and A V (SFD) Relationships of the three A V values in equations (11) (13) are rather complicated. As detailed in section 5 of Dobashi (2011), A V (J H ) and A V (H K S ) are almost perfectly proportional to each other, but A V (J H ) is systematically larger than A V (H K S ) by a factor of The mismatch is apparently due to the inappropriate conversion factors ˇJH = 10.9 and ˇHKS = 13.2 we employed. Relative scaling factors to make A V (J H ) and A V (H K S ) consistent are given in table 7 of Dobashi (2011). Absolute scaling factors to convert the color excesses to the true A V are difficult to determine precisely, not only because they depend on the reddening law which should vary from region to region in the sky, but also because the true A V measured directly in the V band tends to be saturated in dense regions and it is often difficult to compare with the NIR color excesses directly over a wide range of A V. However, among ˇJH = 10.9 and ˇHKS = 13.2, we believe that ˇHKS = 13:2 is more appropriate than ˇJH = 10.9, because A(H K S ) with this ˇHKS is much closer to the A V values measured in the optical wavelengths by starcounts (Dobashi et al. 2005). The extinction deduced from the FIR dust emission, A V (SFD), is proportional to both of A V (J H ) and A V (H K S ), but their ratios are apparently varying on a large scale as a function of galactic longitude. For instance, as seen in figure 6, Schlegel s E(B V ) is consistent with our E(H K S )atjlj = 0 ı (the top-right panel) except for the regions close to b = 0 ı, but it is about a factor of two higher at jlj = 180 ı. The same trend is seen for the case of E(J H ), if we take into account the problem of the conversion factors ˇJH and ˇHKS. As discussed in the following sections, this is partially due to an underestimation caused by the X percentile method itself, but the main cause is likely to be the change of dust properties (i.e., the emissivity in the FIR wavelengths) in the inner and outer regions of the Galaxy. This issue will be discussed in section Underestimation of Diffuse Dust by the X Percentile Method It is known that the standard starcount and NICE method Fig. 12. Example of the simulations to estimate how much the color excess should be missed by the X percentile method. (a) Total color excess by the model disk of dust, (b) observed color excess measured by the X percentile method based on equation (4) for X 0 = 50% using the simulated stars brighter than Set 1, and (c) ratio of the observed to the total color excess. Contours represent the ratio of 1. The color excesses shown in panels (a) and (b) are E(J H ). tend to underestimate the true extinction or color excess by dust, mainly because of contamination by stars located in the foreground of dark clouds. As discussed in separate papers (Dobashi et al. 2008, 2009; Dobashi 2011), the X percentile method should be robust against such contamination to quantify individual dark clouds at high X percentiles. However, in the case of diffuse dust extending over a galactic scale, the method may also underestimate the total amount of dust severely. In the following, we will estimate how much dust we should miss by using the X percentile method. This is important especially when we compare our maps with other data derived from the FIR dust emission including that produced by

12 31-12 K. Dobashi et al. [Vol. 65, Fig. 13. Distributions of the total color excess of E(J H ) and E(H K S ) by the model disk (gray lines) measured at a certain galactic longitude. Color excesses observed by the X percentile method are shown by the thick broken, thin solid, and dotted lines for X 0 = 20%, 50%, and 80%, respectively. The observed color excesses are calculated following equation (4) using the simulated stars brighter than Set 1.

13 No. 2] Correction to the Extinction Maps by Dobashi (2011) Schlegel, Finkbeiner, and Davis (1998), because the FIR dust emission is expected to trace the total amount of dust. In order to evaluate the possible underestimation, we set a diffuse dust disk at the galactic scale in the BGM, and recalculate the apparent magnitudes of the simulated stars in the presence of the disk. We then applied the X percentile method to measure the color excess for the threshold magnitudes Set 1, taking star colors without dust (as shown in figure 5f) to be the background. The ratio of the dust detected by the X percentile method to the total dust contained in the model disk should allow us to quantify the amount that our method underestimates extinction. In the evaluation, we used a simple model disk described by Robin et al. (2003) which follows an Einasto law (Einasto 1979). The density of the model disk, in units of A V kpc 1, can be expressed by the following formulae as a function of the XYZ coordinates of the Galaxy,. / = exp d 0 h 2 exp 1 h 2 (14) 2 q = X 2 + Y 2 + Z 2 =h 2 3 (15) R 2 d 0 = exp 0 R 2 exp 0 (16) h 2 1 h 2 2 where the constants are set to be 0 = 1 mag kpc 1 and (h 1, h 2, h 3, R 0 ) = (7.222, 5.777, 0.015, 8.000) kpc. Figure 12a shows the distribution of the total dust of the model disk integrated along the line of sight, which is expressed in units of E(J H ) converted from the integrated A V using equation (12). An example of the detected dust and its ratio to the total dust are displayed in figures 12b and 12c, respectively, and a change of the detected dust measured at some galactic longitudes for different X values are shown in figure 13 as a function of the galactic latitudes. As seen in these figures, the X percentile method higly underestimates the total dust in the galactic plane at jbj. 5 ı, because the dust disk extends beyond many of the simulated stars. The degree of the underestimation depends on the X percentile used, and the disk is better detected at higher X values, which is a characteristic feature of the X percentile method. On the contrary, the method slightly overestimates the total dust by 10% in the inner galactic plane (jlj. 70 ı ). This is probably because of the difference in star samples actually used to measure the reddening by the dust disk and to measure the background star colors without dust; we set the same threshold magnitudes (Set 1) for both of the measurements, while some stars used to measure the background should become fainter when we measure the dust disk, and they should escape our selection criteria for stars to use. The model disk is well detected in the rest of the regions at jbj > 5 ı. In general, it is better detected in the color excess E(H K S ) than E(J H ), and there is no strong dependence of the detection rate on the X percentiles used for the mapping. In addition, the disk is better detected in the inner region of the Galaxy (jlj. 90 ı ) than in the outer region. For example, in the case of E(H K S ), 100% and & 90% of the total dust is detected on the average in the inner and outer regions, respectively. In the case of E(J H ), the fraction of Table 3. Detection rate of the model disk at jbj > 5 ı. Color excess jlj. 90 ı jlj & 90 ı (%) (%) E(J H ) & 90 & 80 E(H K S ) 100 & 90 the detected dust is lower by 10% compared to E(H K S ). We summarized these detection rates at jbj > 5 ı in table 3. The above estimates using the model disk imply that our color excess maps based on the 2MASS PSC should underestimate the diffuse dust by a similar amount. As far as we know, this is the first quantitative estimate for the underestimation of diffuse dust detected in a large-scale color excess map derived using a similar method (e.g., NICE), which should be important especially when we compare the maps with other data tracing the total column densities along the line of sight, such as the FIR dust emission detected by Planck and Herschel as well as the all-sky data of the CO and H I 21 cm emission lines (Dame et al. 2001; Kalberla et al. 2005; Paradis et al. 2012). Such an estimate for the underestimation is possible only with an extensive simulated star catalog like the one used in the present work. 7. Discussion Here, we will compare our color excess maps again with that of Schlegel, Finkbeiner, and Davis (1998), taking into account the large-scale underestimation of diffuse dust estimated in the previous section. In order to give a correction for the underestimation, we divided our color excess maps corrected for the background by the ratio obtained through the simulation with the dust disk model. We then further divided the maps by the color excess maps converted from their E(B V ) data. An example of the resulting ratio maps is shown in figure 14 for the case of E(H K S ). If dust properties are constant throughtout the Galaxy, the ratio map derived here should be constant in all of the directions in the sky. However, the ratio is apparently not uniform, and is changing by a factor of a few as seen in the figure, suggesting a variation of the dust properties on a large scale. In terms of the ratio, the dust seen in the figure can be categorized into 2 types: One is the dust with higher ratios close to 1 (black regions in the figure), and the other is the dust with lower ratios of 0.5 (gray regions). The former is found only in the inner region at jlj. 90 ı, while the latter is largely seen in the outer region at jlj & 90 ı as well as around nearby clouds at jlj. 90 ı such as in Serpens and Lupus. This trend is obvious also in the other color excess E(J H )as well as at the other percentiles, indicating that the difference of the two types of dust is likely to be real. Although we cannot entirely rule out the possibility that the trend might be caused by an error in our correction of the background star colors, we suggest that it represents the real change of dust properties in the inner and outer regions of the Galaxy. Such a change of dust properties on a large scale would not be surprising, because there is also a clear change of gas phases in the inner and outer regions. The inner region of the Galaxy is dominated by molecular gas, while the outer

14 31-14 K. Dobashi et al. [Vol. 65, Fig. 14. Distribution of the ratio of the observed color excess of E(H K S )atx 0 = 50% to that converted from the FIR data by Schlegel, Finkbeiner, and Davis (1998). The color excess map is corrected for the large-scale underestimation by the ratio map shown in figure 12c. We show only the region where the FIR data are detected significantly. Filled circles represent the positions of SNRs cataloged by D. A. Green (1998). 2 region is dominated by atomic gas (Nakanishi & Sofue 2003, 2006). If this is the case, the trend seen in figure 14 could be naturally accounted for if a great fraction of dust in the outer region (including nearby clouds around the Sun) consists of fluffy aggregates which are more emissive in the FIR by a factor of a few than normal dust grains, while they have almost the same properties in the absorption in the visual (VIS) to the NIR wavelengths (e.g., Stepnik et al. 2003). A question which immediately arises is how the aggregates could be abundant in the diffuse interstellar medium (ISM), because they should be produced through coagulation of dust grains in a very dense region such as the dense cores in molecular clouds where the collision rate is high enough. Actually, such aggregates have been identified only in dense cores in Taurus (Stepnik et al. 2003) as well as in Polaris (Bernard et al. 1999), which can be traced by molecular emission lines regarded as a high density tracer (e.g., CS: Heithausen 1999; Shimoikura et al. 2012). We suggest that the aggregates are formed in dense regions in molecular clouds, and they largely spread out into the diffuse ISM along with the dispersion of the parent cloud, e.g., after forming stars. The aggregates should survive for a long time even in the diffuse ISM, unless they are destroyed by, e.g., shock fronts of supernova remnants (SNRs), strong UV radiation, or stellar winds from nearby OB stars. In the inner region of the Galaxy, such energetic phenomena occur frequently, and the aggregates should be soon destroyed into normal grains. On the other hand, SNRs and OB stars are much fewer in the outer region, and so they can remain as aggregates there. Although it is very difficult to confirm the above speculation quantitatively, we attempt to estimate the timescales of formation and destruction of aggregates in the following. We first estimate the formation timescale of aggregates T F. Stepnik et al. (2003) estimated the grain grain coagulation timescale to form aggregates from constituent grains. Their minimum estimate is coa = yr (for coagulation of very small grains onto big grains) at the density of the core they observed (n H cm 3 ). This is much shorter than the core lifetime taken to be its free-fall time ( 10 6 yr), suggesting that aggregates can form soon after the formation of dense cores. They suggested that aggregates can be generally abundant in molecular clouds with a density of n H > 10 3 cm 3. More recently, Paradis, Bernard, and Meny (2009) investigated the FIR dust emissivity in 88 molecular clouds traced in CO. They categorized the clouds in terms of the dust temperature, and found that the dust is systematically more emissive in colder clouds than in warmer clouds by a factor of 3, indicating formation of aggregates in the colder clouds because aggregates are more sufficient coolants than normal dust grains. Such molecular clouds probably containing aggregates occupy as much as 50% of their cloud sample, supporting the prediction of Stepnik et al. (2003). Based on our color excess maps derived from the 2MASS PSC, we investigated the fraction of dust contained in molecular clouds in some nearby star forming regions such as the Ori A and Cyg OB 7 complexes. We found that roughly 20% of dust on the average is confined in regions with A V & 1 mag which trace similar regions detected in CO. If we assume that the same fraction of dust as found by Paradis et al. (2012) ( 50%) is converted to aggregates in these regions, about 10% of the total dust should be converted to aggregates for one generation of molecular clouds. The timescale of formation and destruction of molecular clouds should depend on various factors, but it may be an order of the galactic rotation ( 10 8 yr). Thus, the timescale to convert most of the dust grains in the ISM to aggregates may be an order of T F yr. For the destruction of the aggregates, we estimate the contribution of SNRs in the following. If we assume that an SNR with radius R S is expanding at the velocity V S, a volume of v = 4RS 2V S is swept up by its shock front within a unit time. Thus, if there are N S SNRs with the same radius and the same expanding velocity in the volume of the inner region of the Galaxy V 0 defined as a disk with the radius R 0 = 8 kpc and the thickness H = 0.2 kpc (i.e., V 0 = R0 2 H ), the volume should be swept up by their shock fronts within a time of T D = V 0 = R2 0 H vn s 4RS 2V : (17) sn S Because aggregates can be very easily disintegrated into constituent grains by shocks (Dominik et al. 1995), we regard this timescale as the destruction timescale of aggregates. According to the catalog of SNRs compiled by D. A. Green (1998), 2 there are 220 SNRs distributed along the galactic plane as displayed in figure 14. Among these, 187 SNRs are located at jlj < 90 ı, and 33 SNRs are located at jlj > 90 ı.if we take the radius of the Galaxy to be 20 kpc as traced in H I (Nakanishi & Sofue 2003), these numbers infer that N S ' 100 SNRs are located in the inner region of the Galaxy. Unfortunately, for most of the SNRs, the distances have not been well established, and only their angular sizes are given by D. A. Green (1998). 2 Assuming that all of the 187 SNRs are located at the distance of the galactic center, i.e., 8 kpc away from us, we estimate their mean radius to be R S ' 20 pc, 2 A Catalogue of Galactic Supernova Remnants hhttp://vizier.cfa.harvard. edu/viz-bin/cat?vii/211i.

15 No. 2] Correction to the Extinction Maps by Dobashi (2011) which should be statistically plausible if they are distributed randomly in the inner region. Expansion velocity should largely vary depending on the SNRs. If we assume V S ' 350 km s 1 as their mean velocity, which is the expansion velocity of the Cygnus Loop (Ghavamian et al. 2001; Raymond et al. 2003) having a radius similar to the estimated mean radius ( 20 pc) at its assumed distance 540 pc (Blair et al. 2005), equation (17) yields T D yr. It is noteworthy that this timescale is in the same order as the destruction timescale of dust grains (not necessarily aggregates) by SNRs in the Galaxy estimated theoretically by Jones et al. (1994) and Jones (1997: yr). Our estimation in the above infers that the destruction timescale of aggregates T D yr is shorter than the formation timescale T F yr in the inner region of the Galaxy, suggesting that SNRs are populous enough to destroy aggregates in the inner region. If we estimate T D in the outer region in the same way, we obtain T D yr which is comparable to T F. However, note that our estimates for T F and T D suffer from some very ambiguous parameters such as the formation timescale of molecular clouds and the total number (or density distributions) of SNRs which should vary as a function of positions in the Galaxy. These unknown parameters may change T F and T D by a factor of a few, and the condition T D >T F necessary for aggregates to survive could be easily satisfied in the outer region. It should be noted that the interaction between molecular clouds and SNRs has been long suggested to date (e.g., Tatematsu et al. 1990; Tian et al. 2010), and destruction of dust by SNRs has been actually observed (e.g., Sankrit et al. 2010; Arendt et al. 2010). Although our current estimates for the timescales are rather coarse, we suggest that aggregates are formed in molecular clouds and spread largely into the ISM, and that they are destroyed by SNRs in the inner region of the Galaxy while they survive as aggregates in the outer region. More precise estimation of the timescales for the destruction and formation of aggregates, including other possible sources of destruction such as the strong UV radiation, stellar winds, and expansion of H II regions by OB stars, is needed to confirm our hypothesis. 8. Conclusions We have given a correction to the color excess and extinction maps produced by Dobashi (2011) for the background star colors and densities. Main results of this paper are summarized in the following: (1) We have carried out a detailed stellar population synthesis simulation to generate a star catalog equivalent to the 2 Micron All Sky Survey Point Source Catalog (2MASS PSC) based on the Besançon Galaxy Model described by Robin et al. (2003). In total, stars were produced through the simulation, and we recorded their parameters such as the coordinates, apparent and absolute magnitudes in the JHK S bands, and spectral types. (2) We applied the X percentile method to the simulated star catalog in order to estimate the distributions of the mean intrinsic star colors with no interstellar dust. Regarding the resulting maps as the background star colors, we gave a correction to the color excess maps of E(J H ) and E(H K S ) produced by Dobashi (2011). Compared to the dust map derived by Schlegel, Finkbeiner, and Davis (1998), there is a large-scale excess in the color excess maps before our correction of the background. The excess becomes much smaller after the correction, indicating that the excess in his maps arose from an inappropriate assumption for the background star color. We also redetermined the background star density utilizing the resulting E(J H ) and E(H K S ) maps to improve A J, A H, and A KS maps produced by Dobashi (2011). (3) In order to evaluate an error arising from the X percentile method, we recalculated the apparent magnitudes of the simulated stars for the case when there is a diffuse dust disk on the galactic scale, and we applied the X percentile to the modified star catalog to detect the model dust disk. Comparison of the total dust in the disk and that detected by the X percentile method indicates that 80% 100% of the disk is detected at jbj > 5 ı. In general, dust in the inner regions of the Galaxy at jlj. 90 ı are better detected than in the outer region by 10%, and it is also better detected in E.H K S / than in E(J H )by10%. The 2MASS-based color excess and extinction maps corrected for the background in this paper may suffer from an underestimation by a similar factor for the diffuse extended dust components on the galactic scale. We are grateful to Dr. A. C. Robin for her providing us with the codes to generate the star catalog and the dust disk used in this paper. This work was financially supported by Grant-in-Aid for Scientific Research (nos , , and ) of Japan Society for the Promotion of Science (JSPS). References Ade, P. A. R., et al. 2011a, A&A, 536, A23 Ade, P. A. R., et al. 2011b, A&A, 536, A22 Arendt, R. G., et al. 2010, ApJ, 725, 585 Bernard, J.-P., et al. 1999, A&A, 347, 640 Blair, W. P., Sankrit, R., & Raymond, J. C. 2005, AJ, 129, 2268 Cambrésy, L. 1999, A&A, 345, 965 Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345, 245 Dame, T. M., Hartmann, D., & Thaddeus, P. 2001, ApJ, 547, 792 Dobashi, K. 2011, PASJ, 63, S1 Dobashi, K., Bernard, J.-P., Hughes, A., Paradis, D., Reach, W. T., & Kawamura, A. 2008, A&A, 484, 205 Dobashi, K., Bernard, J.-P., Kawamura, A., Egusa, F., Hughes, A., Paradis, D., Bot, C., & Reach, W. T. 2009, AJ, 137, 5099 Dobashi, K., Uehara, H., Kandori, R., Sakurai, T., Kaiden, M., Umemoto, T., & Sato, F. 2005, PASJ, 57, S1 Dominik, C., Jones, A. P., & Tielens, A. G. G. M. 1995, Ap&SS, 233, 155 Einasto, J. 1979, in IAU Symp. 84, The Large-Scale Characteristics of the Galaxy, ed. W. B. Burton (Dordrecht: D. Reidel Publishing Co.), 451 Ghavamian, P., Raymond, J., Smith, R. C., & Hartigan, P. 2001, ApJ, 547, 995