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The Extinction and Distance of the MBM Molecular Clouds at High Galactic Latitude

The Extinction and Distance of the MBM Molecular Clouds at High Galactic Latitude Based on the accurate color excess E of more than 4 million stars and the E of more than 1 million G,G NUV,G BP RP BP stars from Sun et al., the distance and extinction of the molecular clouds (MCs) in the Magnani–Blitz–Mundy catalog at |b| > 20° are studied in combination with the distance measurement of Gaia/EDR3. The distance, as well as the color excess, is determined for 66 MCs. The color excess ratio E /E is derived for 39 of NUV,G G ,G BP BP RP them, which is obviously larger and implies more small particles at smaller extinction. In addition, the scale height of the dust disk is found to be about 100 pc and becomes large at the anticenter direction due to the disk flaring. Unified Astronomy Thesaurus concepts: Interstellar dust (836); Ultraviolet extinction (1738); High latitude field (737); Distance measure (737); Molecular clouds (1072) Supporting material: figure set, machine-readable tables 1. Introduction stars. Because MCs possess not only high-density gas but also high-density dust, their extinction significantly exceeds the The study of molecular clouds (MCs), the site of star surrounding diffuse interstellar medium. Thus, the distance to formation (Blitz & Williams 1999), is important for the MCs can be inferred from the high extinction they cause information on the initial mass function of stars and the (Goodman et al. 2009; Chen et al. 2017). Early in 1923, Wolf buildup of galaxies. Molecular clouds in the Milky Way are (1923) first effectively described Wolf diagrams based on star the nearest and most accessible star-forming sites. Carbon counts in obscured versus reference fields to determine the monoxide is the main tracer of MCs, which is much more distance to MCs, and Magnani & de Vries (1986) applied the easily excited and observed than H and is used to detect a Wolf diagrams to a small subset of Magnani–Blitz–Mundy large number of MCs in many large-scale joint observations (MBM) clouds. Using the two-dimensional (2D) Galactic of the galaxy (e.g., Magnani et al. 1985; May et al. 1997; extinction maps, Dobashi (2011) identified more than 7000 Dame et al. 2001). However, the distance as the fundamental MCs based on the idea that high extinction is caused by MCs. and key parameter for studying MCs is often difficult to As the extinction map is 2D, no distance information can be determine. Many distance measurement methods, such as obtained. With the 3D extinction maps, which are constructed stellar photometric parallax and period–luminosity relation, by comparing the observed color distributions of Galactic giant are not suitable for MCs. stars with those predicted by the Galactic model, Marshall et al. Previously, a popular method was to estimate the distance to (2009) cataloged over 1000 clouds together with their distance the clouds using Galactic kinematics, i.e., the distance at which information and determined that the errors of their distances are the radial velocity of the cloud corresponds to the rotation about 0.5–1 kpc. Comparing the stars in front of the clouds, curve of the Galactic disk (e.g., Brand et al. 1994; May et al. which have little extinction, with the predictions of the Galactic 1997; Nakagawa et al. 2005; Roman-Duval et al. 2009; García model, Lada et al. (2009) and Lombardi et al. (2011) estimated et al. 2014; Miville-Deschênes et al. 2017). This technique is the distances to many clouds. With the multiband photometry widely applied to estimate the distances to a large number of by Pan-STARRS1 (Kaiser et al. 2010) and the resultant color MCs in the inner disk of the Galaxy (e.g., Roman-Duval et al. indexes of numerous stars, Schlafly et al. (2014) derived the 2009). But the well-known problems are the large uncertainty distances to 18 well-known star-forming regions and 108 MCs induced by the presence of peculiar and noncircular motions at high Galactic latitude selected from Magnani et al. (1985) and Dame et al. (2001) according to the breakpoint of the and the ambiguity where one velocity can correspond to two extinction. distances at either side of the tangent point. Another frequently The distances obtained in these studies are not measured used method is to find the distance to the objects associated directly but with the help of some stellar or Galactic model and with a cloud and to place the cloud at the same distance; for suffer relatively large uncertainty. The Gaia mission has instance, many clouds have produced young OB associations changed this situation drastically. The Gaia/DR2 catalog of stars for which distances can be estimated. This method can (Gaia/DR2; Gaia Collaboration et al. 2018) provides the be applied to some specific cases. distances to more than a billion stars, renewing the way to Both of the above methods are applicable only to low- determine the distance to MCs by their extinction. With the latitude clouds in the disk because high-latitude clouds deviate Gaia/DR2 data, Zucker et al. (2019) present a uniform catalog a lot from the disk rotation curve and have no young massive of accurate distances to local MCs according to the breakpoint of the extinction. Yan et al. (2019) obtain the distances to MCs Original content from this work may be used under the terms at high Galactic latitudes (|b| > 10°) from the parallax of the Creative Commons Attribution 4.0 licence. Any further (Lindegren et al. 2018) and G-band extinction (A ) measure- distribution of this work must maintain attribution to the author(s) and the title G of the work, journal citation and DOI. ments of the stars at the cloud’s sight line from Gaia/DR2. 1 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Figure 1. Distribution of the MBM molecular clouds (ellipses) in the extinction map (blue background) expressed as E from Paper I, where the red and green G, BPGRP ellipses represent the molecular clouds within and outside the extinction map respectively. Based on the 3D dust reddening map and estimates of color enhanced population of very small grains. We (Paper I) also excesses and distances of over 32 million stars, Chen et al. find that there may be more small dust grains at high than at (2020) identified 567 dust/MCs within 4 kpc from the Sun at low galactic latitude, which is supported by the steeper increase low Galactic latitudes (|b| „ 10°) with a hierarchical structure of extinction toward the FUV band. identification method and obtained their distance estimates by a This paper is part of an ongoing project to study the dust model-fitting algorithm. Benefiting from the large number extinction and dust as well as the 3D distribution of MCs at of stars for the individual MCs and the robust estimates of the high latitude based on the spectroscopic and astrometric measurements of stars. This work focuses on the MBM high- stellar distances from Gaia/DR2, the errors of the distances in latitude MCs. these works are typically only about 5%. The high-latitude MCs are generally optically thin, which leads to much smaller extinction than those in the disk, and 2. Sample and Data usually very close, thus a precise measurement of extinction and distance to the stars is necessary to estimate their distance Blitz et al. (1984) started a project to conduct a systematic by the extinction method. Spectroscopy can be used to search of high-latitude MCs using the CO line observation determine the stellar intrinsic color index and thus extinction of potentially obscured regions identified from the Palomar is usually more accurate than multiband photometry. The Observatory Sky Survey prints, which was followed up general inefficiency of spectroscopy in comparison with and completed by Magnani et al. (1985)(MBM) . This photometry has recently been compensated by large-area project resulted in 124 detections of MCs with |b| > 20°.We multiobject spectroscopy such as the LAMOST survey, which adopt the center positions of the MCs from MBM, and the size has observed almost 10 million stars. Using the stellar as well if given. For the 88 MCs whose size is unavailable parameters derived from the LAMOST and GALAH surveys, in MBM, a radius of 90′ is taken as default, which is we (Sun et al. 2021, Paper I hereafter) determined the color approximately the average size of the high-latitude MCs (Dutra excess E accurate to ∼0.01 mag on average toward about G,G BP RP & Bica 2002). 4 million stars. In addition, the color excess E is NUV,G BP The tracers for the extinction and distance of high-latitude calculated for more than 1 million stars accurate to ∼0.1 mag. clouds are chosen from Paper I. Using the blue-edge method Moreover, Gaia/EDR3 was recently released with apparently (see Jian et al. 2017 and Sun et al. 2018), Paper I calculated the more precise measurements of stellar parallaxes and distances. color excess with respect to the Gaia/G , G , and GALEX/ BP RP The combination of the accurate color excess and distance NUV bands, i.e., E and E of more than 4 million G,G NUV,G BP RP BP brings about the possibility of determining the distances to the and 1 million dwarfs, respectively, which are mostly located at MCs at high latitude. In addition, the dust property in the high- high latitude. These color excesses are determined from the latitude clouds may be inferred from the color excess ratio of intrinsic and observed color indexes, in which the intrinsic E /E . Welty & Fowler (1992) studied the low- NUV,G G ,G log g BP BP RP color index is determined from the stellar parameters T , , eff resolution UV spectra of the B3 V star HD 210121 located and metal abundance Z from the LAMOST/DR7 and behind the high-latitude MC DBB 80 and obtained an GALAH/DR3 spectroscopic surveys. The average error of extinction curve with a very steep rise in the far-UV. The extremely steep far-UV extinction and the augmentation of the http://simbad.u-strasbg.fr/simbad/sim-ref?querymethod=bib&simbo=on& intensity at 12 μm are consistent with the presence of an submit=submit+bibcode&bibcode=1985ApJ...295..402M 2 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. 2 −1 2 −1 Figure 2. Linear fitting of the color excess E to the Planck/857 GHz intensity I (10 MJy sr )(top) and E to I (10 MJy sr )(bottom). The G,G 857GHz NUV,G 857GHz BP RP BP grayscale decodes the source density, the red and magenta crosses denote the median values of each bin with small and large deviations from the linear fitting line (see Section 3.1.1 for details). The inset shows the distribution of the residuals with its median and standard deviation. 3. Method E and E is ∼0.01 mag and 0.1 mag, respectively. G,G NUV,G BP RP BP 3.1. Selection of the Reference and Cloud Region Furthermore, the distances to those sources are obtained by the corresponding parallax in Gaia/EDR3 (Gaia Collaboration 3.1.1. The Planck 857 GHz map et al. 2021). The extinction of the cloud is the difference between the post- The cross-match between the MBM MCs and the stars in cloud and the pre-cloud extinction. Then, it is necessary to Paper I finds that there are 75 MCs for which the sight line E to 13,773 stars is available, and 47 MCs of these for delineate the region of the cloud and the background for reference G,G BP RP which the sight line E to 3614 stars is available as well. in order to determine the extinction caused by the MC. The area NUV,G BP The distributions of all the E in Paper I and MBM MCs given by MBM makes a very good initial value for the region of G,G BP RP are displayed in Figure 1, where the red and green ellipses the cloud, but no reference region is available. Though the region represent the MCs within and outside the extinction map, in front of the cloud can be taken as reference as Zhao et al. respectively. (2020, 2018) have done, the high-latitude MCs are usually close 3 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. −1 Figure 3. The studied area (top) and histogram (bottom) of I (MJy sr ) in MBM 5 (left), MBM 40 (middle), and MBM 109 (right). In the studied area, the gray 857GHz filled region bordered by a black dashed line is the background region, and the green–yellow–red region bordered by the red dashed line region inside the MBM cloud region (black solid line) is the cloud region. In the histogram, the black dashed curve is the local Gaussian fit, where the blue bars represent the noise (left) and transition (right) region, the gray bars represent the background region sources and the red bars represent the cloud region sources. and the small-range foreground stars hardly reflect the global determined according to the Planck/857 GHz intensity. At first, trend of extinction variation along the sight line with no cloud. both the reference and cloud region are searched for in a square Thus an independent region other than the cloud region is area with a side length of four times the cloud’s equivalent selected as the reference. Moreover, the cloud normally has an angular diameter (qq ´ ) centered at the cloud major minor irregular shape such that an ellipse cannot describe the true position. However, I does not decrease significantly 857GHz boundary of the cloud. We determine the precise border of the within this area in many cases. So, the region is expanded to m cloud according to the infrared emission image instead of the times of the cloud’s angular diameter until an appropriate molecular emission because infrared emission comes directly region can be found for reference. The technical route of from dust and is proportional to extinction. selecting the areas is illustrated by taking three typical cases The Planck 857 GHz image (Planck Collaboration et al. (MBM 5, MBM 109, and MBM 40) as examples in Figure 3. 2020), closely correlated with the dust emission, is used to The distribution of the small peak is fitted by a Gaussian mark the reference and MC region. The Planck 857 GHz function to determine the median (μ) and the standard deviation survey has a similar spatial resolution (5¢) to the IRAS 100 μm (σ) of I for the reference region; then, the region with 857GHz image (Schlegel et al. 1998; Miville-Deschênes & Lagache I in the range of μ − σ to μ is selected as the reference 857GHz 2005), while its sensitivity is much higher. In comparison with region, denoted by the black dashed line and gray histogram in the CO survey (Dame et al. 2001), the Planck 857 GHz survey the upper and lower panels, respectively, of Figure 3, and the is more complete at high Galactic latitude. region with I above μ + 3σ (the red dashed line and 857GHz In order to see the relation between the 857 GHz (350 μm) histogram in the upper and lower panels, respectively, of cumulative dust emission from Planck Collaboration et al. Figure 3) and inside the MBM-assigned MC area (marked by (2020) and the color excess, the sources from Paper I are the black solid-line ellipse) is selected as the cloud region. selected only when they have latitude |b| > 20° and Galactic MBM 5 is a relatively isolated object for which the reference plane distance |h| > 200 pc so that their extinction can be considered to be cumulative along the specific sight lines. The region can be found in an area four times as big as the cloud comparison of the extinction with the dust emission, as shown area. But MBM 109 is located within a large high-I area 857GHz in Figure 2, finds a very tight linear relationship between them. toward the sight line of the Tau–Per–Aur complex cloud so that The quantitative relation is obtained in the same way as in the reference area has to be found in a far area; specifically, the Paper I by iteratively clipping stars beyond 3σ of the median, area is expanded to 16 times the cloud’s angular diameter. 21 - which results in E I () 10 MJy sr = 3.95, and G ,G 857GHz BP RP MBM 40 is taken as an example because it will be shown later 21 - E I () 10 MJy sr = 12.32. NUV,G 857GHz BP that its distance is only 63 pc, which might put it inside the Local Bubble or right at the boundary of the Local Bubble. It can be seen that the values of μ and σ depend on the property 3.1.2. Selection of the Reference and Cloud Region and location of the MC. In this way, the reference and cloud The denser MCs are supposed to have higher infrared area is defined for each cloud in an area specified by the m intensity than the reference region so that the areas can be value listed in Table 1. 4 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Table 1 The Distances and Color Excesses of the Molecular Clouds a a a b c d d d d d d d d d 0 MC 0 MC ¢ ¢ Cloud l b d d d E h DE m E h DE CERs Zucker Schlafly this work G,G G,G G,G NUV,G NUV,G NUV,G BP RP BP RP BP RP BP BP BP (°)(°)(pc)(pc)(pc)(mag)(pc)(mag)(mag)(pc)(mag) (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) MBM 1 110.19 −41.229 265 228 285 ± 9.0 0.07 ± 0.0005 146 ± 8.7 0.09 ± 0.0022 8.0 0.20 ± 0.0155 296 ± 81.3 0.32 ± 0.0278 3.81 MBM 3 131.291 −45.676 314 277 309 ± 1.4 0.07 ± 0.0003 193 ± 3.8 0.11 ± 0.0010 4.0 0.20 ± 0.0036 185 ± 16.2 0.40 ± 0.0082 3.96 MBM 4 133.515 −45.303 286 269 320 ± 8.0 0.08 ± 0.0014 274 ± 14.6 0.13 ± 0.0013 4.0 0.22 ± 0.0133 104 ± 44.2 0.44 ± 0.0183 3.92 MBM 5 145.967 −49.074 279 187 297 ± 2.3 0.08 ± 0.0003 225 ± 3.1 0.14 ± 0.0012 4.0 0.23 ± 0.0051 260 ± 19.7 0.46 ± 0.0188 3.51 MBM 6 145.065 −39.349 111 151 153 ± 0.9 0.10 ± 0.0003 164 ± 2.7 0.23 ± 0.0017 8.0 0.28 ± 0.0054 179 ± 19.2 0.63 ± 0.0251 2.96 MBM 7 150.429 −38.074 171 148 213 ± 26.2 0.11 ± 0.0003 183 ± 2.1 0.20 ± 0.0026 10.0 0.31 ± 0.0039 156 ± 12.1 0.63 ± 0.0188 3.28 MBM 8 151.75 −38.669 255 199 262 ± 0.2 0.17 ± 0.0007 176 ± 3.5 0.26 ± 0.0028 12.0 0.48 ± 0.0106 108 ± 22.6 0.76 ± 0.0742 3.25 MBM 9 156.531 −44.722 262 246 248 ± 36.1 0.14 ± 0.0011 223 ± 7.7 0.08 ± 0.0034 4.0 0.38 ± 0.0282 277 ± 67.3 0.35 ± 0.0440 4.07 MBM 11 157.983 −35.06 250 185 147 ± 101.7 0.11 ± 0.0016 198 ± 14.2 0.33 ± 0.0037 16.0 MBM 12 159.351 −34.324 252 234 278 ± 61.8 0.16 ± 0.0008 155 ± 5.3 0.51 ± 0.0181 4.0 0.49 ± 0.0123 201 ± 23.5 0.99 ± 0.0451 3.56 MBM 13 161.591 −35.89 237 191 409 ± 0.5 0.17 ± 0.0011 177 ± 4.7 0.42 ± 0.0108 12.0 0.48 ± 0.0162 155 ± 23.3 0.70 ± 0.0631 3.24 MBM 14 162.458 −31.861 275 233 295 ± 0.4 0.22 ± 0.0009 212 ± 2.8 0.27 ± 0.0006 2.0 0.69 ± 0.0058 259 ± 7.6 0.99 ± 0.0168 3.61 MBM 15 191.666 −52.294 200 160 164 ± 120.7 0.07 ± 0.0009 191 ± 10.2 0.11 ± 0.0038 5.0 0.17 ± 0.0136 152 ± 72.3 0.22 ± 0.0495 1.96 MBM 16 170.603 −37.273 170 147 210 ± 28.4 0.16 ± 0.0004 233 ± 2.5 0.64 ± 0.0057 10.0 0.47 ± 0.0075 246 ± 15.8 1.45 ± 0.0442 3.15 MBM 17 167.526 −26.606 130 165 231 ± 38.6 0.22 ± 0.0012 260 ± 5.4 0.30 ± 0.0072 4.0 MBM 18 189.105 −36.016 155 166 149 ± 1.9 0.08 ± 0.0007 333 ± 8.4 0.41 ± 0.0022 12.0 0.21 ± 0.0056 336 ± 28.4 1.10 ± 0.0148 3.09 MBM 19 186.041 −29.929 143 156 293 ± 0.2 0.08 ± 0.0008 368 ± 10.3 0.34 ± 0.0075 72.0 MBM 22 208.091 −27.477 266 238 181 ± 1.2 0.06 ± 0.0114 388 ± 137.2 0.11 ± 0.0047 2.0 MBM 23 171.835 26.706 349 305 252 ± 182.1 0.10 ± 0.0008 395 ± 10.1 0.07 ± 0.0052 10.0 0.31 ± 0.0167 470 ± 70.3 0.27 ± 0.0619 5.75 MBM 24 172.272 26.965 351 279 338 ± 0.9 0.10 ± 0.0010 368 ± 13.0 0.11 ± 0.0015 4.0 0.32 ± 0.0224 490 ± 77.1 0.43 ± 0.0273 4.42 MBM 25 173.752 31.475 342 297 362 ± 2.1 0.06 ± 0.0007 317 ± 12.2 0.07 ± 0.0008 4.0 0.15 ± 0.0101 410 ± 83.5 0.28 ± 0.0106 4.06 MBM 34 2.307 35.7 117 110 178 ± 43.3 0.06 ± 0.0004 107 ± 8.2 0.14 ± 0.0022 14.0 0.14 ± 0.0092 174 ± 69.1 0.37 ± 0.0283 2.76 MBM 35 6.571 38.128 86 89 296 ± 10.4 0.19 ± 0.0016 150 ± 9.5 0.23 ± 0.0066 4.0 MBM 36 4.229 35.792 107 105 99 ± 10.6 0.10 ± 0.0006 176 ± 5.8 0.42 ± 0.0013 8.0 0.34 ± 0.0139 234 ± 38.0 0.94 ± 0.0356 3.05 MBM 37 6.067 36.757 115 121 143 ± 0.4 0.11 ± 0.0013 83 ± 13.7 0.32 ± 0.0011 4.0 0.34 ± 0.0290 107 ± 41.5 0.80 ± 0.0649 2.60 MBM 38 8.222 36.338 92 77 286 ± 14.2 0.13 ± 0.0009 142 ± 7.6 0.52 ± 0.0399 12.0 0.40 ± 0.0186 108 ± 50.2 1.51 ± 0.0675 2.98 MBM 40 37.57 44.667 93 64 63 ± 51.3 0.06 ± 0.0003 122 ± 6.4 0.14 ± 0.0013 8.0 0.17 ± 0.0046 217 ± 26.1 0.39 ± 0.0123 2.92 MBM 49 64.496 −26.539 212 204 330 ± 2.1 0.09 ± 0.0006 172 ± 10.0 0.13 ± 0.0014 2.0 0.24 ± 0.0112 179 ± 55.3 0.29 ± 0.0258 3.09 MBM 51 73.313 −51.526 190 ± 9.2 0.07 ± 0.0007 100 ± 9.0 0.06 ± 0.1058 12.0 0.25 ± 0.0233 272 ± 94.6 0.14 ± 0.0825 1.64 MBM 53 93.965 −34.058 259 253 266 ± 0.7 0.07 ± 0.0003 204 ± 6.3 0.18 ± 0.0013 8.0 0.20 ± 0.0071 285 ± 36.9 0.85 ± 0.0154 4.21 MBM 54 91.624 −38.103 245 231 238 ± 18.5 0.06 ± 0.0005 159 ± 7.2 0.15 ± 0.0028 10.0 0.14 ± 0.0044 163 ± 35.6 0.53 ± 0.0137 4.03 MBM 55 89.19 −40.936 245 206 266 ± 1.5 0.06 ± 0.0004 152 ± 6.9 0.15 ± 0.0007 4.0 0.15 ± 0.0069 244 ± 54.2 0.22 ± 0.0207 3.88 MBM 56 103.075 −26.06 265 227 271 ± 46.4 0.11 ± 0.0006 173 ± 6.5 0.19 ± 0.0024 4.0 0.33 ± 0.0098 163 ± 40.1 0.58 ± 0.0714 2.52 MBM 101 158.191 −21.412 289 283 288 ± 0.2 0.26 ± 0.0004 194 ± 1.8 0.60 ± 0.0012 8.0 0.81 ± 0.0043 245 ± 5.3 1.36 ± 0.0738 2.54 MBM 102 158.561 −21.154 289 275 289 ± 0.1 0.25 ± 0.0004 201 ± 1.6 0.59 ± 0.0010 8.0 0.79 ± 0.0040 248 ± 6.0 1.19 ± 0.0480 2.56 MBM 103 158.885 −21.552 279 269 285 ± 0.1 0.25 ± 0.0006 196 ± 3.3 0.49 ± 0.0009 8.0 0.78 ± 0.0041 235 ± 5.5 1.18 ± 0.0368 3.13 MBM 104 158.405 −20.436 281 262 291 ± 0.1 0.28 ± 0.0007 194 ± 3.4 0.69 ± 0.0007 5.0 0.95 ± 0.0110 243 ± 11.4 1.09 ± 0.0628 2.11 MBM 105 169.52 −20.126 127 139 142 ± 0.4 0.20 ± 0.0003 178 ± 1.6 0.27 ± 0.0005 5.0 0.61 ± 0.0073 192 ± 13.3 0.62 ± 0.0134 2.52 MBM 106 176.334 −20.781 158 190 179 ± 0.1 0.23 ± 0.0006 213 ± 2.4 0.40 ± 0.0005 16.0 MBM 107 177.654 −20.343 141 197 142 ± 0.3 0.24 ± 0.0009 213 ± 3.5 0.48 ± 0.0007 16.0 MBM 108 178.238 −20.342 143 168 139 ± 0.4 0.24 ± 0.0009 213 ± 2.8 0.48 ± 0.0014 16.0 MBM 109 178.93 −20.1 155 160 176 ± 8.5 0.23 ± 0.0005 209 ± 2.1 0.38 ± 0.0012 16.0 0.72 ± 0.0038 241 ± 4.9 0.82 ± 0.0367 3.27 MBM 110 207.598 −22.944 356 313 300 ± 1.4 0.13 ± 0.0025 464 ± 19.5 0.12 ± 0.0009 4.0 MBM 111 208.547 −20.222 400 366 403 ± 0.3 0.13 ± 0.0025 468 ± 21.2 0.30 ± 0.0011 4.0 MBM 115 342.331 24.146 141 137 126 ± 46.4 0.13 ± 0.0006 52 ± 2.4 0.28 ± 0.0015 8.0 0.37 ± 0.0143 76 ± 22.1 0.79 ± 0.0362 3.23 MBM 116 342.715 24.506 137 134 158 ± 29.6 0.14 ± 0.0006 51 ± 1.6 0.29 ± 0.0015 8.0 0.39 ± 0.0134 70 ± 17.8 0.83 ± 0.0383 3.20 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Table 1 (Continued) a a a b c d d d d d d d d d 0 MC 0 MC ¢ ¢ Cloud l b d d d E h DE m E h DE CERs Zucker Schlafly this work G,G G,G G,G NUV,G NUV,G NUV,G BP RP BP RP BP RP BP BP BP (°)(°)(pc)(pc)(pc)(mag)(pc)(mag)(mag)(pc)(mag) (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) MBM 117 343.001 24.085 138 140 141 ± 2.1 0.13 ± 0.0006 51 ± 1.3 0.23 ± 0.0014 8.0 0.40 ± 0.0164 86 ± 25.6 1.01 ± 0.0832 3.21 MBM 118 344.018 24.758 140 56 146 ± 10.3 0.13 ± 0.0007 51 ± 1.9 0.27 ± 0.0021 8.0 MBM 119 341.613 21.396 169 150 111 ± 84.2 0.12 ± 0.0009 51 ± 1.0 0.11 ± 0.0024 8.0 MBM 120 344.231 24.188 135 59 145 ± 0.7 0.12 ± 0.0007 52 ± 2.1 0.28 ± 0.0022 8.0 MBM 123 343.281 22.121 143 101 75 ± 63.9 0.13 ± 0.0008 51 ± 1.0 0.22 ± 0.0035 8.0 0.50 ± 0.0592 197 ± 81.9 0.24 ± 0.0562 2.83 MBM 124 343.966 22.725 145 89 147 ± 122.3 0.13 ± 0.0006 51 ± 0.9 0.14 ± 0.0098 8.0 MBM 125 355.536 22.541 129 115 131 ± 1.1 0.14 ± 0.0004 51 ± 1.6 0.30 ± 0.0026 21.0 MBM 127 355.409 20.877 146 147 150 ± 0.2 0.14 ± 0.0003 51 ± 1.3 0.89 ± 0.0070 21.0 MBM 128 355.562 20.592 136 134 150 ± 0.2 0.14 ± 0.0003 51 ± 1.4 0.89 ± 0.0067 21.0 MBM 129 356.155 20.761 139 141 145 ± 0.7 0.14 ± 0.0004 51 ± 47.5 0.52 ± 0.0033 21.0 MBM 130 356.805 20.265 129 109 150 ± 0.1 0.14 ± 0.0004 51 ± 1.3 0.60 ± 0.0042 21.0 MBM 131 359.156 21.787 158 106 161 ± 0.3 0.14 ± 0.0004 51 ± 1.2 0.48 ± 0.0027 21.0 MBM 133 359.176 21.37 161 98 240 ± 0.6 0.14 ± 0.0004 51 ± 1.2 0.57 ± 0.0052 21.0 MBM 134 0.132 21.782 158 121 285 ± 0.7 0.07 ± 0.0003 73 ± 8.1 0.46 ± 0.0062 24.0 MBM 136 1.271 20.992 139 120 110 ± 20.2 0.09 ± 0.0004 101 ± 4.6 0.42 ± 0.0027 21.0 MBM 145 8.482 21.842 108 152 185 ± 0.6 0.07 ± 0.0005 71 ± 12.6 0.49 ± 0.0024 16.0 MBM 146 8.784 22.035 116 179 197 ± 0.4 0.07 ± 0.0005 63 ± 8.6 0.46 ± 0.0058 16.0 MBM 148 7.543 21.066 156 116 186 ± 0.4 0.07 ± 0.0007 80 ± 14.4 0.55 ± 0.0023 16.0 MBM 151 21.533 20.93 138 122 145 ± 0.2 0.18 ± 0.0003 100 ± 1.9 0.31 ± 0.0006 8.0 0.53 ± 0.0042 107 ± 9.6 0.83 ± 0.0135 3.07 MBM 152 359.48 −20.474 86 ± 65.8 0.10 ± 0.0021 134 ± 16.0 0.15 ± 0.0024 4.0 Notes. The molecular cloud’s series number (Column 1) and Galactic coordinates (Columns 2 and 3) retrieved from Magnani et al. (1985). The distance and the error (Column 4) from Zucker et al. (2019). The distance and the error (Column 5) from Schlafly et al. (2014). The distance and the errors (Column 6), the foreground fitting parameters (Columns 7 and 8), and the color excess jump in the optical (Column 9), the multiples of the cloud’s angular diameter (Column 10), the foreground fitting parameters (Columns 11 and 12), and the color excess jump (Column 13) in the optical-ultraviolet bands, and the color excess ratio of molecular clouds (Column 14) from this work. (This table is available in machine-readable form.) The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Figure 4. The fitting to the color excess, E , variation with the distance to the stars in the reference (green dots) and the cloud (red dots) region for the three G,G BP RP typical clouds MBM 5, MBM 40, and MBM 109 with the extinction−distance model (Equations (1), (2), and (3). The parameters derived are shown in the upper-left MC 0 corner, where “d” is the distance, “ΔE” is the color excess jump (DE ), and E and h¢ are the foreground parameters of the molecular cloud (E and G, BPGRP G, BPGRP h ). (An extended version of this figure for all the studied clouds is available online). G,G BP RP (The complete figure set (11 images) is available.) 3.2. The Extinction-jump Model improved by Zhao et al. (2020) and used to determine the Under the assumption that interstellar extinction increases distance and the extinction of Galactic supernova remnants smoothly with distance in the absence of any MCs, the (SNRs). A similar model is used by Chen et al. (2017) and Yu extinction will make an upward jump at the distance of the et al. (2019) for other SNRs as well as MCs. The MCs cause cloud in the presence of an MC. In order to obtain accurate the same effect as SNRs on the extinction and thus the distance to and extinction of MCs, we take the extinction-jump extinction-jump model is applicable. In detail, the total model in Zhao et al. (2020), which is insensitive to the outliers. extinction in terms of color excess E(d) toward the sight line This model was designed originally by Zhao et al. (2018) and of the MC is composed of two parts: the color excess of the 7 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Figure 5. The same as Figure 4, but for E . NUV,G BP MC cloud E (d), which dominates the total extinction, and the to the center, and δd is the radius of the cloud calculated from DISM color excess of the diffuse interstellar medium E (d), d × θ with θ being the cloud’s angular diameter. c c c However, unlike Chen et al. (2017), Yu et al. (2019), and DISM MC Ed ()=+ E ()d E ()d.1 ( ) Zhao et al. (2020) which use a two-order polynomial function or root function, we use an exponential law to fit the color MC Moreover, E (d) is described by an erf function, excess caused by the diffuse interstellar dust, -d dd - c DISM 0 MC MC ⎡ ⎛ ⎞⎤ Ed ()=´E (13 -e h¢ ) ( ) Ed ()=DE ´ 1e + rf⎜⎟,2 ( ) ⎢ ⎥ 2dd ⎝ ⎠ ⎣ ⎦ The function is modified to be in line with the high-latitude MC where ΔE is the amplitude of the color excess jump, i.e., location of the MCs, in the sight line of which the material MC MC DE orDE caused by the cloud, d is the distance (including the interstellar dust) density falls exponentially with G,G NUV,G c BP RP BP 8 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Figure 6. The distribution of the distances (d) and their uncertainties (σ ). the vertical distance from the Galactic plane. Under this form, Similar to step (2), but replacing the optical parameters by 0 0 the parameter E reflects the cumulative color excess, and ultraviolet values, i.e., E by E and E and G,G NUV,G BP RP BP G,G BP RP hs ¢´ in()b with b being the latitude of the cloud is the scale ¢ ¢ h by E and h . In addition, the value of d G,G NUV,G NUV,G c BP RP BP BP height (h) of the dust disk in the sight line. resulting from the optical color excess is adopted rather than fitted because the number of measurements in the UV band is only about a quarter in the visual, thus only the jump MC 3.3. The Model Fitting DE is derived in this step. NUV, G BP The model fitting for MBM 5, MBM 40, and MBM 109 with The model fitting is performed with the Markov Chain the reference and cloud sources are displayed as the example in Monte Carlo procedure (Foreman-Mackey et al. 2013). In order MC MC Figures 4 and 5 for DE and DE , respectively. G,G NUV,G to set the initial parameters very reasonably, a Markov chain is BP RP BP The green dots denote the sources in the reference region used first run with 100 walkers and 250 steps. Then, the final chain to determine the variation of extinction with distance in the uses the initial parameters with 100 walkers and 2000 steps, diffuse medium, and the red dots denote the sources in the and we choose the last 1750 steps from each walker to sample cloud region used to determine the distance and extinction of the final posterior. The best estimates are the median values the cloud. The key parameters with the uncertainty derived (50th percentile) of the posterior distribution and the from modeling are shown in the upper-left corner of the figures uncertainties are derived from the 16th and 84th percentile (an extended version of Figure 4 is available for all the sample values. clouds). The variation of stellar extinction with distance is fitted separately for the reference region and the cloud region. Because the sample becomes more and more incomplete with 4. Results and Discussions distance, only the objects closer than 2000 pc with relative 4.1. The Distance distance uncertainty <30% are taken into account. The fitting steps are in the following order: (1) fitting the optical The distance is derived for 66 of the 75 MBM clouds toward extinction–distance measurements, i.e., the E versus d G,G BP RP whose sight line more than three stars are present with an points of the reference region, by Equation (3) to obtain the optical color excess measurement and lying behind the MC. parameters E and h to describe the change of G,G G,G BP RP BP RP The derived parameters are tabulated in Table 1. The E with d in the reference region. (2) Fitting the optical G,G BP RP distribution of the distances and their uncertainties is shown in extinction–distance measurements of the cloud region by Figure 6 where the symbols follow the convention in Figure 4. Equations (1) and (2) after substituting the above values of A simple visual inspection would conclude that the fitting E and h into Equation (1), which yields the G,G G,G BP RP BP RP agrees very well with the measurements in most cases. MC distance d and the optical jump of the MC. (3) The DE c Meanwhile, the distances to G37.57−35.06 (MBM 11), G,G BP RP same as step (1) but replacing E by the E of the G,G NUV,G G157.98+44.67 (MBM 40), G341.61+21.40 (MBM 119), BP RP BP reference region sources to obtain E and h . (4) G343.28+22.12 (MBM 123), and G359.48−20.47 (MBM NUV,G NUV,G BP BP 9 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Figure 7. The distance d (upper panel) and the Galactic disk distance |z| (lower panel) versus the Galactic latitude |b|. 152) seem to be underestimated because there are few sources For MBM 40, more objects in front of the cloud should be at a very close distance. As mentioned earlier, MBM 40 is the measured to confirm its close distance. nearest with a distance of only 63 ± 51 pc, which puts it inside Figure 7 shows the distance d and the vertical distance to the the Local Bubble or right at the boundary of the Local Bubble, Galactic plane |z| versus the Galactic latitude |b|. There is no if true. Though the uncertainty is large, the best value is systematic trend of d with |b| expected as these clouds are consistent with that of Schlafly et al. (2014). On the other hand, local, while |z| increases with the Galactic latitude |b|. this value is smaller than the 93 pc obtained by Zucker et al. The distances to 9 of the 66 MCs were measured by Yan (2019). Indeed, Figures 4 and 5 indicate that the first stars that et al. (2019) and to 64 of them by Schlafly et al. (2014) and show a marked increase in color excess have a distance of Zucker et al. (2019); these are compared with ours in Figure 8. about 125 pc, apparently much larger, though still within the It can be seen that the distances are more or less identical range of the uncertainty. These cases indicate that a precise between the works at d < 200 pc. When d > 200 pc, this work distance from our method needs a continuous distribution of yields a systematically larger distance than the others to a the distance of the tracers, in particular around the jump point. different extent in that the difference with Schlafly et al. (2014) 10 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Figure 8. The comparison of the distances to molecular clouds with those obtained by Schlafly et al. (2014), Yan et al. (2019), and Zucker et al. (2019). The inset is the distribution of the differences with their results. is the largest and the difference with the other two works are various MBM clouds. Such confusion implies that the mostly within the uncertainties. Comparing with these works, boundary of a cloud needs to be redefined and will be this work differs in a few aspects: (1) the intrinsic color indexes considered in our next work. Figure 10 shows the maximum max are derived from spectroscopy rather than photometry, (2) the stellar E , i.e., E behind each MBM cloud G,G G,G BP RP BP RP stellar distance comes from the Gaia/EDR3 catalog instead of identifiable in the Lynds dark clouds catalog in comparison the DR2 catalog, (3) the model considers the thickness of the with all the other clouds, where the blue asterisks denote the MC, and (4) the rise of the color excess of the foreground MBM MC containing some Lynds dark cloud(s). It can be seen max sources with distance is considered separately, which prevents that the majority of these clouds have E > 1.0, i.e., G,G BP RP the premature occurrence of jumps in some MCs. The first two A > 2.0 mag. Because dark clouds are normally defined to factors improve the accuracy but should have no systematic have A > 5 mag, this is not consistent with the expectation for influence on the distance. a dark cloud. It is likely that an interstellar cloud might have an average extinction of 2 mag with small patches having extinctions of 5 mag or more and so, on the basis of these 4.2. The Extinction small patches, the cloud is defined as a dark cloud while its 4.2.1. The Cloud average extinction is more like that of a translucent cloud. Meanwhile, a few clouds have A ∼ 1.0–2.0 mag, smaller than The extinction is determined for 66 MCs expressed by the V MC the extinction that a dark cloud should have. One possible optical color excess DE and for 39 MCs by the UV- G,G BP RP MC reason is that the stars that suffer serious extinction may optical color excess DE . Their distribution along the NUV,G BP become too faint to be observable by the LAMOST or GALAH latitude is shown in Figure 9 where the increase at low latitudes spectroscopy survey. This also shows that the method in this is visible as expected from their smaller vertical distance to the work derives the median rather than the highest extinction of a Galactic plane as evident in the lower panel of Figure 7. cloud so that it is more appropriate for relatively large clouds Meanwhile, it should be noted that the extinction appears large MC than smaller dense clouds. Additionally, several MBM clouds around |b| ∼ 35°−40°. The majority ofDE is not bigger G,G max BP RP have no associated Lynds dark clouds but with E > 1.0, G,G BP RP than 0.4 mag, i.e., A ∼ 0.8 mag, and some clouds cause a large A < 3.0 mag is still an acceptable extinction for a translucent extinction but still smaller than A ∼ 3 mag. Therefore, most of cloud though we cannot exclude the possibility of the presence the clouds may be classified as translucent, and some of them of some dark nebula. as diffuse MCs. It should be noted that there are some stars with a large color excess, which is not reflected in the fitting parameters. The 4.2.2. The Reference Region cross-identification with the Lynds dark clouds (Lynds 1962) finds that 24 MBM clouds contain 20 Lynds dark clouds, The reference region is selected from the low-intensity noise- which are listed in Table 2. Some MBM clouds cover multiple like emission at Planck/857 GHz, representative of the diffuse Lynds clouds while some Lynds clouds repetitively appear in interstellar medium. Our model for the reference extinction by 11 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. MC MC Figure 9. The change of DE and DE with the Galactic latitude |b|. G, BPGRP NUV,GBP ¢ ¢ Equation (3) assumes an exponential disk with vertical height. After multiplying h and h by sin() b , the dust G,G NUV,G BP RP BP The parameter E in Equation (3) is the cumulative extinction disk scale height h and h in the sight line is G,G NUV,G BP RP BP andhb ¢ sin() is the scale height of the extinction/dust disk obtained. Figure 11 (b) presents the relation between h G,G BP RP toward the specific high-latitude sight line. and h , which are basically distributed near the equal line NUV,G BP The relationship between the parameters from fitting E while some points deviate. Because the parameter h¢ is very G,G BP RP sensitive to the data size, h should be more reliable due and E for the reference regions is shown in Figure 11. G,G BP RP NUV,G BP to its much smaller error and more data points in the Gaia/ As shown in Figure 11(a), there is a good linear relationship 0 0 EDR3 catalog. The change of E and∣∣ h with between E and E . The slope of the fitting line is G,G G,G BP RP G,G NUV,G BP RP BP RP BP Galactic longitude is displayed in Figures 11(c) and 11(d). The 3.27, which reflects the ratio of the accumulated color excess of the diffuse interstellar medium in the UV and optical bands. scale height varies from about 50 to 250 pc, with an obvious increase toward the anticenter direction consistent with a flaring This ratio is very close to the all-sky color excess ratio of 3.25 in Paper I. dust disk. This median thickness of about 100 pc indicates that 12 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Table 2 MBM Molecular Clouds Associated with Lynds Dark Cloud a a MBMb b max c max c LDN MBM LDN Area Area E MBM LDN 2 2 (deg)(deg)(mag)(mag) MBM 12 LDN 1453 1.767 0.066 1.84 1.528 MBM 12 LDN 1454 1.767 0.86 1.84 1.84 MBM 12 LDN 1457 1.767 0.262 1.84 1.786 MBM 12 LDN1458 1.767 0.056 1.84 1.113 MBM 18 LDN 1569 2.836 0.631 1.009 0.855 MBM 36 LDN 134 1.767 0.22 1.183 1.109 MBM 37 LDN 169 1.227 0.86 1.612 1.612 MBM 37 LDN 183 1.227 0.24 1.612 1.612 MBM 101 LDN 1452 1.767 1.66 1.945 1.945 MBM 101 LDN 1448 1.767 0.053 1.945 1.296 MBM 101 LDN 1451 1.767 0.14 1.945 1.569 MBM 102 LDN 1448 1.767 0.053 1.945 1.296 MBM 102 LDN 1451 1.767 0.14 1.945 1.569 MBM 102 LDN 1452 1.767 1.66 1.945 1.945 MBM 103 LDN 1451 1.767 0.14 1.885 1.569 MBM 103 LDN 1448 1.767 0.053 1.885 1.296 MBM 103 LDN 1452 1.767 1.66 1.885 1.945 MBM 104 LDN 1452 1.767 1.66 2.387 1.945 MBM 107 LDN 1543 1.767 0.09 1.732 1.732 MBM 107 LDN 1546 1.767 0.37 1.732 1.842 MBM 108 LDN 1543 1.767 0.09 2.018 1.732 MBM 108 LDN 1546 1.767 0.37 2.018 1.842 MBM 109 LDN 1546 1.767 0.37 2.018 1.842 MBM 110 LDN 1634 1.767 0.492 0.773 0.466 MBM 111 LDN 1640 1.767 0.018 1.379 0.005 MBM 125 LDN 1721 1.767 0.287 0.769 0.424 MBM 126 LDN 1719 1.767 0.61 1.218 1.218 MBM 127 LDN 1719 1.767 0.61 1.218 1.218 MBM 128 LDN 1719 1.767 0.61 1.218 1.218 MBM 129 LDN 1719 1.767 0.61 1.218 1.218 MBM 130 LDN 1752 1.767 1.78 0.979 1.421 MBM 131 LDN 1781 1.767 1.19 0.778 0.778 MBM 133 LDN 1781 1.767 1.19 0.778 0.778 MBM 134 LDN 1781 1.767 1.19 0.559 0.778 MBM 145 LDN 234 1.767 1.41 0.648 0.802 MBM 148 LDN 234 1.767 1.41 0.802 0.802 Notes. The molecular cloud’s series number (Columns 1 and 2) from Magnani et al. (1985)(MBM) and Lynds (1962)(LDN). The cloud area (Columns 3 and 4) from MBM and LDN. The maximum color excess E in the cloud region (Columns 5 and 6) from MBM and LDN. G,G BP RP (This table is available in machine-readable form.) MC MC the dust disk agrees with the thin gaseous disk of the Milky cloud. However, the ratio DEE D of the cloud NUV,G G,G BP BP RP Way whose scale height ranges around 100–300 pc (e.g., has great uncertainty, perhaps due to the very large dispersion Ferguson et al. 2017; Ma et al. 2017). in the extinction. Instead, the sources behind the cloud are all The resultant E is compared with Schlegel et al. (1998, taken into consideration to determine the color excess ratio G,G BP RP E /E and then the dust property of an MC. By SFD98) for the reference region because E is supposed NUV,G G,G BP BP RP G,G BP RP subtracting the color excess of the diffuse interstellar medium to be the cumulative extinction along the sight line. The value SFD SFD at equal distances from the color excess of these sources, the of E is first converted to E for comparison (Niu et al. B,V G,G BP RP corresponding color excess of the MC in the sight line is 2021). Figure 12 shows the linear fitting between E and G,G BP RP obtained. Requiring the number of selected sources to be SFD the median value of E in each studied reference area. The G,G BP RP N … 3, the color excess ratios of 39 MCs are calculated by slope is 0.95 and the intercept is −0.005, which means our linear fitting through iterative 3σ clipping (Paper I). The results result is very consistent with that of SFD98. of MBM 5, MBM 40, and MBM 109 are displayed in Figure 13, where E and E have a good linear NUV,G G,G BP BP RP 4.3. Dust Property of High-latitude Molecular Clouds relationship. Because the extinction of an MC changes across the cloud, The change of the color excess ratios (E E ) NUV,G G ,G BP BP RP MC MC the overall average color excess of the cloud, i.e., DE G,G with DE of these MCs is shown in the lower panel of BP RP G,G BP RP MC andDE , should be an extinction indicator of the overall Figure 14. Obviously, the color excess ratio of the MCs (red NUV,G BP 13 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. max Figure 10. The change of maximum extinction E in the sight line of molecular clouds with the Galactic latitude |b|. The blue and red asterisks are the result of G,G BP RP MBM clouds with or without Lynds dark cloud. MC asterisks) increases atDE < 0.3. As Paper I pointed out, whole high-latitude sky in Paper I and now confirmed by G,G BP RP there exists a systematic variation in both T and E with this work. eff G,G BP RP the Galactic location for the tracing stars, which can shift the effective wavelength of the filters and then the color excess ratio E E in a complicated way (see Figure 10 of 5. Summary NUV,G G ,G BP BP RP Paper I). In brief, E E generally decreases with NUV,G G ,G BP BP RP This work uses the color excesses of more than 4 million E when T > 6500 K, while increases with E G,G eff G,G BP RP BP RP stars in the visual and 1 million stars in the ultraviolet to when T < 6500 K. On average, this color excess ratio is eff explore the high-latitude MCs cataloged by Magnani et al. bigger for higher T . The upper panel of Figure 14 confirms eff (1985). The cloud and reference region are selected from the MC that T changes with DE . In order to see the change of eff G,G BP RP Planck/857 GHz image in order to clarify the extinction caused MC dust property, the effects of T and DE on the color eff G,G by the cloud. The distances to 66 clouds are determined by the BP RP excess ratio should be stripped off in advance. For this purpose, extinction jump along the sight line caused by the cloud denser the color excess ratio of each is calculated assuming that only than the diffuse area. MC T and DE play a role, i.e., convolving the stellar eff G,G The major results of this paper are as follows: BP RP emergent spectrum with the response curve of the filter and the 1. The cumulative color excess E of the diffuse ISM G,G BP RP F99 extinction curve at R = 3.1 (Fitzpatrick 1999) to get the and scale height h of the dust disk is derived for 66 visible color excess ratio at the corresponding effective wavelength. areas, while the cumulative color excess E of the The derived color excess ratio is represented by blue asterisks NUV,G BP diffuse ISM is obtained for 39 areas. The calculated scale in Figure 14, which agrees with the expectation from Paper I height is around 50–250 pc, which agrees with the thin that the lower T around 6000 K in combination with the eff MC gaseous disk of the Milky. smaller DE should lead to a smaller E E . NUV,G G ,G G,G BP RP BP BP RP MC 2. The distances and color excess DE is determined G,G The observed trend that the color excess ratio of the MCs BP RP MC for 66 MCs, and the extinction jump DE is increases at smaller E is thus in the opposite direction. It G,G NUV,G BP RP BP seems that this trend can only be explained by the change of determined for 39 MCs. The distances of this work are dust property at small extinction. In principle, the color excess slightly larger than the results of Schlafly et al. (2014) and ratio is sensitive to the composition and size distribution of the closer to that of Zucker et al. (2019). dust particles (Draine 2011). Larson & Whittet (2005) conclude 3. The color excess ratio E /E of 39 MCs is NUV,G G ,G BP BP RP calculated and found to be obviously larger at lower that many high-latitude clouds have enhanced abundances of relatively small grains based on the near-infrared extinction extinction, which cannot be interpreted as the shift of the effective wavelength because of the variation in T and curves. The enhanced proportion of small grains can also eff explain the observed ratio variation of the near-ultraviolet-to- E . This indicates that the MCs with lower G,G BP RP extinction have more small dust particles. visual extinction here. Indeed, this trend is already found in the 14 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. 0 0 0 Figure 11. The relationship of E and E (top, left) and h and h (top, right) as well as the distribution of E (bottom, left) and ∣h ∣(bottom, NUV,G G ,G NUV,G G ,G G ,G G,G BP BP RP BP RP BP BP RP BP RP 0 0 right). Red asterisks are the parameters of foreground and black line is the fitting line of E and E (top, left) and h = h line (top, right). NUV,G G,G NUV,GBP G, BPGRP BP BP RP 0 SFD Figure 12. Comparison between E and E in the background region. G,G G,G BP RP BP RP 15 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Figure 14. The change of T (upper panel) and color excess ratios eff MC E /E (lower panel) withDE . Red asterisks are the results NUV,G G,G BP BP RP G, BPGRP of the studied molecular clouds, while the blue asterisks are the simulation results considering the effective wavelength shift because of T and eff MC DE (see Paper I for details). G,G BP RP He Zhao (赵赫) https://orcid.org/0000-0003-2645-6869 Yi Ren (任逸) https://orcid.org/0000-0003-1218-8699 References Blitz, L., Magnani, L., & Mundy, L. 1984, ApJL, 282, L9 Blitz, L., & Williams, J. P. 1999, in NATO ASIC Proc. 540, The Origin of Stars and Planetary Systems, ed. C. Lada & N. Kylafis (Dordrecht: Kluwer), 3 Figure 13. Linear fitting of the color excess E to E in MBM 5, NUV,G G,G BP BP RP Brand, J., Cesaroni, R., Caselli, P., et al. 1994, A&AS, 103, 541 MBM 40, and MBM 109. Red and magenta dots are sources in and out of the Chen, B. Q., Li, G. X., Yuan, H. B., et al. 2020, MNRAS, 493, 351 95% confidence interval, the black line is the fitting curve, and the purple Chen, B. Q., Liu, X. W., Ren, J. 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The Extinction and Distance of the MBM Molecular Clouds at High Galactic Latitude

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IOP Publishing
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© 2021. The Author(s). Published by the American Astronomical Society.
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0067-0049
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1538-4365
DOI
10.3847/1538-4365/ac1601
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Abstract

Based on the accurate color excess E of more than 4 million stars and the E of more than 1 million G,G NUV,G BP RP BP stars from Sun et al., the distance and extinction of the molecular clouds (MCs) in the Magnani–Blitz–Mundy catalog at |b| > 20° are studied in combination with the distance measurement of Gaia/EDR3. The distance, as well as the color excess, is determined for 66 MCs. The color excess ratio E /E is derived for 39 of NUV,G G ,G BP BP RP them, which is obviously larger and implies more small particles at smaller extinction. In addition, the scale height of the dust disk is found to be about 100 pc and becomes large at the anticenter direction due to the disk flaring. Unified Astronomy Thesaurus concepts: Interstellar dust (836); Ultraviolet extinction (1738); High latitude field (737); Distance measure (737); Molecular clouds (1072) Supporting material: figure set, machine-readable tables 1. Introduction stars. Because MCs possess not only high-density gas but also high-density dust, their extinction significantly exceeds the The study of molecular clouds (MCs), the site of star surrounding diffuse interstellar medium. Thus, the distance to formation (Blitz & Williams 1999), is important for the MCs can be inferred from the high extinction they cause information on the initial mass function of stars and the (Goodman et al. 2009; Chen et al. 2017). Early in 1923, Wolf buildup of galaxies. Molecular clouds in the Milky Way are (1923) first effectively described Wolf diagrams based on star the nearest and most accessible star-forming sites. Carbon counts in obscured versus reference fields to determine the monoxide is the main tracer of MCs, which is much more distance to MCs, and Magnani & de Vries (1986) applied the easily excited and observed than H and is used to detect a Wolf diagrams to a small subset of Magnani–Blitz–Mundy large number of MCs in many large-scale joint observations (MBM) clouds. Using the two-dimensional (2D) Galactic of the galaxy (e.g., Magnani et al. 1985; May et al. 1997; extinction maps, Dobashi (2011) identified more than 7000 Dame et al. 2001). However, the distance as the fundamental MCs based on the idea that high extinction is caused by MCs. and key parameter for studying MCs is often difficult to As the extinction map is 2D, no distance information can be determine. Many distance measurement methods, such as obtained. With the 3D extinction maps, which are constructed stellar photometric parallax and period–luminosity relation, by comparing the observed color distributions of Galactic giant are not suitable for MCs. stars with those predicted by the Galactic model, Marshall et al. Previously, a popular method was to estimate the distance to (2009) cataloged over 1000 clouds together with their distance the clouds using Galactic kinematics, i.e., the distance at which information and determined that the errors of their distances are the radial velocity of the cloud corresponds to the rotation about 0.5–1 kpc. Comparing the stars in front of the clouds, curve of the Galactic disk (e.g., Brand et al. 1994; May et al. which have little extinction, with the predictions of the Galactic 1997; Nakagawa et al. 2005; Roman-Duval et al. 2009; García model, Lada et al. (2009) and Lombardi et al. (2011) estimated et al. 2014; Miville-Deschênes et al. 2017). This technique is the distances to many clouds. With the multiband photometry widely applied to estimate the distances to a large number of by Pan-STARRS1 (Kaiser et al. 2010) and the resultant color MCs in the inner disk of the Galaxy (e.g., Roman-Duval et al. indexes of numerous stars, Schlafly et al. (2014) derived the 2009). But the well-known problems are the large uncertainty distances to 18 well-known star-forming regions and 108 MCs induced by the presence of peculiar and noncircular motions at high Galactic latitude selected from Magnani et al. (1985) and Dame et al. (2001) according to the breakpoint of the and the ambiguity where one velocity can correspond to two extinction. distances at either side of the tangent point. Another frequently The distances obtained in these studies are not measured used method is to find the distance to the objects associated directly but with the help of some stellar or Galactic model and with a cloud and to place the cloud at the same distance; for suffer relatively large uncertainty. The Gaia mission has instance, many clouds have produced young OB associations changed this situation drastically. The Gaia/DR2 catalog of stars for which distances can be estimated. This method can (Gaia/DR2; Gaia Collaboration et al. 2018) provides the be applied to some specific cases. distances to more than a billion stars, renewing the way to Both of the above methods are applicable only to low- determine the distance to MCs by their extinction. With the latitude clouds in the disk because high-latitude clouds deviate Gaia/DR2 data, Zucker et al. (2019) present a uniform catalog a lot from the disk rotation curve and have no young massive of accurate distances to local MCs according to the breakpoint of the extinction. Yan et al. (2019) obtain the distances to MCs Original content from this work may be used under the terms at high Galactic latitudes (|b| > 10°) from the parallax of the Creative Commons Attribution 4.0 licence. Any further (Lindegren et al. 2018) and G-band extinction (A ) measure- distribution of this work must maintain attribution to the author(s) and the title G of the work, journal citation and DOI. ments of the stars at the cloud’s sight line from Gaia/DR2. 1 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Figure 1. Distribution of the MBM molecular clouds (ellipses) in the extinction map (blue background) expressed as E from Paper I, where the red and green G, BPGRP ellipses represent the molecular clouds within and outside the extinction map respectively. Based on the 3D dust reddening map and estimates of color enhanced population of very small grains. We (Paper I) also excesses and distances of over 32 million stars, Chen et al. find that there may be more small dust grains at high than at (2020) identified 567 dust/MCs within 4 kpc from the Sun at low galactic latitude, which is supported by the steeper increase low Galactic latitudes (|b| „ 10°) with a hierarchical structure of extinction toward the FUV band. identification method and obtained their distance estimates by a This paper is part of an ongoing project to study the dust model-fitting algorithm. Benefiting from the large number extinction and dust as well as the 3D distribution of MCs at of stars for the individual MCs and the robust estimates of the high latitude based on the spectroscopic and astrometric measurements of stars. This work focuses on the MBM high- stellar distances from Gaia/DR2, the errors of the distances in latitude MCs. these works are typically only about 5%. The high-latitude MCs are generally optically thin, which leads to much smaller extinction than those in the disk, and 2. Sample and Data usually very close, thus a precise measurement of extinction and distance to the stars is necessary to estimate their distance Blitz et al. (1984) started a project to conduct a systematic by the extinction method. Spectroscopy can be used to search of high-latitude MCs using the CO line observation determine the stellar intrinsic color index and thus extinction of potentially obscured regions identified from the Palomar is usually more accurate than multiband photometry. The Observatory Sky Survey prints, which was followed up general inefficiency of spectroscopy in comparison with and completed by Magnani et al. (1985)(MBM) . This photometry has recently been compensated by large-area project resulted in 124 detections of MCs with |b| > 20°.We multiobject spectroscopy such as the LAMOST survey, which adopt the center positions of the MCs from MBM, and the size has observed almost 10 million stars. Using the stellar as well if given. For the 88 MCs whose size is unavailable parameters derived from the LAMOST and GALAH surveys, in MBM, a radius of 90′ is taken as default, which is we (Sun et al. 2021, Paper I hereafter) determined the color approximately the average size of the high-latitude MCs (Dutra excess E accurate to ∼0.01 mag on average toward about G,G BP RP & Bica 2002). 4 million stars. In addition, the color excess E is NUV,G BP The tracers for the extinction and distance of high-latitude calculated for more than 1 million stars accurate to ∼0.1 mag. clouds are chosen from Paper I. Using the blue-edge method Moreover, Gaia/EDR3 was recently released with apparently (see Jian et al. 2017 and Sun et al. 2018), Paper I calculated the more precise measurements of stellar parallaxes and distances. color excess with respect to the Gaia/G , G , and GALEX/ BP RP The combination of the accurate color excess and distance NUV bands, i.e., E and E of more than 4 million G,G NUV,G BP RP BP brings about the possibility of determining the distances to the and 1 million dwarfs, respectively, which are mostly located at MCs at high latitude. In addition, the dust property in the high- high latitude. These color excesses are determined from the latitude clouds may be inferred from the color excess ratio of intrinsic and observed color indexes, in which the intrinsic E /E . Welty & Fowler (1992) studied the low- NUV,G G ,G log g BP BP RP color index is determined from the stellar parameters T , , eff resolution UV spectra of the B3 V star HD 210121 located and metal abundance Z from the LAMOST/DR7 and behind the high-latitude MC DBB 80 and obtained an GALAH/DR3 spectroscopic surveys. The average error of extinction curve with a very steep rise in the far-UV. The extremely steep far-UV extinction and the augmentation of the http://simbad.u-strasbg.fr/simbad/sim-ref?querymethod=bib&simbo=on& intensity at 12 μm are consistent with the presence of an submit=submit+bibcode&bibcode=1985ApJ...295..402M 2 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. 2 −1 2 −1 Figure 2. Linear fitting of the color excess E to the Planck/857 GHz intensity I (10 MJy sr )(top) and E to I (10 MJy sr )(bottom). The G,G 857GHz NUV,G 857GHz BP RP BP grayscale decodes the source density, the red and magenta crosses denote the median values of each bin with small and large deviations from the linear fitting line (see Section 3.1.1 for details). The inset shows the distribution of the residuals with its median and standard deviation. 3. Method E and E is ∼0.01 mag and 0.1 mag, respectively. G,G NUV,G BP RP BP 3.1. Selection of the Reference and Cloud Region Furthermore, the distances to those sources are obtained by the corresponding parallax in Gaia/EDR3 (Gaia Collaboration 3.1.1. The Planck 857 GHz map et al. 2021). The extinction of the cloud is the difference between the post- The cross-match between the MBM MCs and the stars in cloud and the pre-cloud extinction. Then, it is necessary to Paper I finds that there are 75 MCs for which the sight line E to 13,773 stars is available, and 47 MCs of these for delineate the region of the cloud and the background for reference G,G BP RP which the sight line E to 3614 stars is available as well. in order to determine the extinction caused by the MC. The area NUV,G BP The distributions of all the E in Paper I and MBM MCs given by MBM makes a very good initial value for the region of G,G BP RP are displayed in Figure 1, where the red and green ellipses the cloud, but no reference region is available. Though the region represent the MCs within and outside the extinction map, in front of the cloud can be taken as reference as Zhao et al. respectively. (2020, 2018) have done, the high-latitude MCs are usually close 3 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. −1 Figure 3. The studied area (top) and histogram (bottom) of I (MJy sr ) in MBM 5 (left), MBM 40 (middle), and MBM 109 (right). In the studied area, the gray 857GHz filled region bordered by a black dashed line is the background region, and the green–yellow–red region bordered by the red dashed line region inside the MBM cloud region (black solid line) is the cloud region. In the histogram, the black dashed curve is the local Gaussian fit, where the blue bars represent the noise (left) and transition (right) region, the gray bars represent the background region sources and the red bars represent the cloud region sources. and the small-range foreground stars hardly reflect the global determined according to the Planck/857 GHz intensity. At first, trend of extinction variation along the sight line with no cloud. both the reference and cloud region are searched for in a square Thus an independent region other than the cloud region is area with a side length of four times the cloud’s equivalent selected as the reference. Moreover, the cloud normally has an angular diameter (qq ´ ) centered at the cloud major minor irregular shape such that an ellipse cannot describe the true position. However, I does not decrease significantly 857GHz boundary of the cloud. We determine the precise border of the within this area in many cases. So, the region is expanded to m cloud according to the infrared emission image instead of the times of the cloud’s angular diameter until an appropriate molecular emission because infrared emission comes directly region can be found for reference. The technical route of from dust and is proportional to extinction. selecting the areas is illustrated by taking three typical cases The Planck 857 GHz image (Planck Collaboration et al. (MBM 5, MBM 109, and MBM 40) as examples in Figure 3. 2020), closely correlated with the dust emission, is used to The distribution of the small peak is fitted by a Gaussian mark the reference and MC region. The Planck 857 GHz function to determine the median (μ) and the standard deviation survey has a similar spatial resolution (5¢) to the IRAS 100 μm (σ) of I for the reference region; then, the region with 857GHz image (Schlegel et al. 1998; Miville-Deschênes & Lagache I in the range of μ − σ to μ is selected as the reference 857GHz 2005), while its sensitivity is much higher. In comparison with region, denoted by the black dashed line and gray histogram in the CO survey (Dame et al. 2001), the Planck 857 GHz survey the upper and lower panels, respectively, of Figure 3, and the is more complete at high Galactic latitude. region with I above μ + 3σ (the red dashed line and 857GHz In order to see the relation between the 857 GHz (350 μm) histogram in the upper and lower panels, respectively, of cumulative dust emission from Planck Collaboration et al. Figure 3) and inside the MBM-assigned MC area (marked by (2020) and the color excess, the sources from Paper I are the black solid-line ellipse) is selected as the cloud region. selected only when they have latitude |b| > 20° and Galactic MBM 5 is a relatively isolated object for which the reference plane distance |h| > 200 pc so that their extinction can be considered to be cumulative along the specific sight lines. The region can be found in an area four times as big as the cloud comparison of the extinction with the dust emission, as shown area. But MBM 109 is located within a large high-I area 857GHz in Figure 2, finds a very tight linear relationship between them. toward the sight line of the Tau–Per–Aur complex cloud so that The quantitative relation is obtained in the same way as in the reference area has to be found in a far area; specifically, the Paper I by iteratively clipping stars beyond 3σ of the median, area is expanded to 16 times the cloud’s angular diameter. 21 - which results in E I () 10 MJy sr = 3.95, and G ,G 857GHz BP RP MBM 40 is taken as an example because it will be shown later 21 - E I () 10 MJy sr = 12.32. NUV,G 857GHz BP that its distance is only 63 pc, which might put it inside the Local Bubble or right at the boundary of the Local Bubble. It can be seen that the values of μ and σ depend on the property 3.1.2. Selection of the Reference and Cloud Region and location of the MC. In this way, the reference and cloud The denser MCs are supposed to have higher infrared area is defined for each cloud in an area specified by the m intensity than the reference region so that the areas can be value listed in Table 1. 4 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Table 1 The Distances and Color Excesses of the Molecular Clouds a a a b c d d d d d d d d d 0 MC 0 MC ¢ ¢ Cloud l b d d d E h DE m E h DE CERs Zucker Schlafly this work G,G G,G G,G NUV,G NUV,G NUV,G BP RP BP RP BP RP BP BP BP (°)(°)(pc)(pc)(pc)(mag)(pc)(mag)(mag)(pc)(mag) (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) MBM 1 110.19 −41.229 265 228 285 ± 9.0 0.07 ± 0.0005 146 ± 8.7 0.09 ± 0.0022 8.0 0.20 ± 0.0155 296 ± 81.3 0.32 ± 0.0278 3.81 MBM 3 131.291 −45.676 314 277 309 ± 1.4 0.07 ± 0.0003 193 ± 3.8 0.11 ± 0.0010 4.0 0.20 ± 0.0036 185 ± 16.2 0.40 ± 0.0082 3.96 MBM 4 133.515 −45.303 286 269 320 ± 8.0 0.08 ± 0.0014 274 ± 14.6 0.13 ± 0.0013 4.0 0.22 ± 0.0133 104 ± 44.2 0.44 ± 0.0183 3.92 MBM 5 145.967 −49.074 279 187 297 ± 2.3 0.08 ± 0.0003 225 ± 3.1 0.14 ± 0.0012 4.0 0.23 ± 0.0051 260 ± 19.7 0.46 ± 0.0188 3.51 MBM 6 145.065 −39.349 111 151 153 ± 0.9 0.10 ± 0.0003 164 ± 2.7 0.23 ± 0.0017 8.0 0.28 ± 0.0054 179 ± 19.2 0.63 ± 0.0251 2.96 MBM 7 150.429 −38.074 171 148 213 ± 26.2 0.11 ± 0.0003 183 ± 2.1 0.20 ± 0.0026 10.0 0.31 ± 0.0039 156 ± 12.1 0.63 ± 0.0188 3.28 MBM 8 151.75 −38.669 255 199 262 ± 0.2 0.17 ± 0.0007 176 ± 3.5 0.26 ± 0.0028 12.0 0.48 ± 0.0106 108 ± 22.6 0.76 ± 0.0742 3.25 MBM 9 156.531 −44.722 262 246 248 ± 36.1 0.14 ± 0.0011 223 ± 7.7 0.08 ± 0.0034 4.0 0.38 ± 0.0282 277 ± 67.3 0.35 ± 0.0440 4.07 MBM 11 157.983 −35.06 250 185 147 ± 101.7 0.11 ± 0.0016 198 ± 14.2 0.33 ± 0.0037 16.0 MBM 12 159.351 −34.324 252 234 278 ± 61.8 0.16 ± 0.0008 155 ± 5.3 0.51 ± 0.0181 4.0 0.49 ± 0.0123 201 ± 23.5 0.99 ± 0.0451 3.56 MBM 13 161.591 −35.89 237 191 409 ± 0.5 0.17 ± 0.0011 177 ± 4.7 0.42 ± 0.0108 12.0 0.48 ± 0.0162 155 ± 23.3 0.70 ± 0.0631 3.24 MBM 14 162.458 −31.861 275 233 295 ± 0.4 0.22 ± 0.0009 212 ± 2.8 0.27 ± 0.0006 2.0 0.69 ± 0.0058 259 ± 7.6 0.99 ± 0.0168 3.61 MBM 15 191.666 −52.294 200 160 164 ± 120.7 0.07 ± 0.0009 191 ± 10.2 0.11 ± 0.0038 5.0 0.17 ± 0.0136 152 ± 72.3 0.22 ± 0.0495 1.96 MBM 16 170.603 −37.273 170 147 210 ± 28.4 0.16 ± 0.0004 233 ± 2.5 0.64 ± 0.0057 10.0 0.47 ± 0.0075 246 ± 15.8 1.45 ± 0.0442 3.15 MBM 17 167.526 −26.606 130 165 231 ± 38.6 0.22 ± 0.0012 260 ± 5.4 0.30 ± 0.0072 4.0 MBM 18 189.105 −36.016 155 166 149 ± 1.9 0.08 ± 0.0007 333 ± 8.4 0.41 ± 0.0022 12.0 0.21 ± 0.0056 336 ± 28.4 1.10 ± 0.0148 3.09 MBM 19 186.041 −29.929 143 156 293 ± 0.2 0.08 ± 0.0008 368 ± 10.3 0.34 ± 0.0075 72.0 MBM 22 208.091 −27.477 266 238 181 ± 1.2 0.06 ± 0.0114 388 ± 137.2 0.11 ± 0.0047 2.0 MBM 23 171.835 26.706 349 305 252 ± 182.1 0.10 ± 0.0008 395 ± 10.1 0.07 ± 0.0052 10.0 0.31 ± 0.0167 470 ± 70.3 0.27 ± 0.0619 5.75 MBM 24 172.272 26.965 351 279 338 ± 0.9 0.10 ± 0.0010 368 ± 13.0 0.11 ± 0.0015 4.0 0.32 ± 0.0224 490 ± 77.1 0.43 ± 0.0273 4.42 MBM 25 173.752 31.475 342 297 362 ± 2.1 0.06 ± 0.0007 317 ± 12.2 0.07 ± 0.0008 4.0 0.15 ± 0.0101 410 ± 83.5 0.28 ± 0.0106 4.06 MBM 34 2.307 35.7 117 110 178 ± 43.3 0.06 ± 0.0004 107 ± 8.2 0.14 ± 0.0022 14.0 0.14 ± 0.0092 174 ± 69.1 0.37 ± 0.0283 2.76 MBM 35 6.571 38.128 86 89 296 ± 10.4 0.19 ± 0.0016 150 ± 9.5 0.23 ± 0.0066 4.0 MBM 36 4.229 35.792 107 105 99 ± 10.6 0.10 ± 0.0006 176 ± 5.8 0.42 ± 0.0013 8.0 0.34 ± 0.0139 234 ± 38.0 0.94 ± 0.0356 3.05 MBM 37 6.067 36.757 115 121 143 ± 0.4 0.11 ± 0.0013 83 ± 13.7 0.32 ± 0.0011 4.0 0.34 ± 0.0290 107 ± 41.5 0.80 ± 0.0649 2.60 MBM 38 8.222 36.338 92 77 286 ± 14.2 0.13 ± 0.0009 142 ± 7.6 0.52 ± 0.0399 12.0 0.40 ± 0.0186 108 ± 50.2 1.51 ± 0.0675 2.98 MBM 40 37.57 44.667 93 64 63 ± 51.3 0.06 ± 0.0003 122 ± 6.4 0.14 ± 0.0013 8.0 0.17 ± 0.0046 217 ± 26.1 0.39 ± 0.0123 2.92 MBM 49 64.496 −26.539 212 204 330 ± 2.1 0.09 ± 0.0006 172 ± 10.0 0.13 ± 0.0014 2.0 0.24 ± 0.0112 179 ± 55.3 0.29 ± 0.0258 3.09 MBM 51 73.313 −51.526 190 ± 9.2 0.07 ± 0.0007 100 ± 9.0 0.06 ± 0.1058 12.0 0.25 ± 0.0233 272 ± 94.6 0.14 ± 0.0825 1.64 MBM 53 93.965 −34.058 259 253 266 ± 0.7 0.07 ± 0.0003 204 ± 6.3 0.18 ± 0.0013 8.0 0.20 ± 0.0071 285 ± 36.9 0.85 ± 0.0154 4.21 MBM 54 91.624 −38.103 245 231 238 ± 18.5 0.06 ± 0.0005 159 ± 7.2 0.15 ± 0.0028 10.0 0.14 ± 0.0044 163 ± 35.6 0.53 ± 0.0137 4.03 MBM 55 89.19 −40.936 245 206 266 ± 1.5 0.06 ± 0.0004 152 ± 6.9 0.15 ± 0.0007 4.0 0.15 ± 0.0069 244 ± 54.2 0.22 ± 0.0207 3.88 MBM 56 103.075 −26.06 265 227 271 ± 46.4 0.11 ± 0.0006 173 ± 6.5 0.19 ± 0.0024 4.0 0.33 ± 0.0098 163 ± 40.1 0.58 ± 0.0714 2.52 MBM 101 158.191 −21.412 289 283 288 ± 0.2 0.26 ± 0.0004 194 ± 1.8 0.60 ± 0.0012 8.0 0.81 ± 0.0043 245 ± 5.3 1.36 ± 0.0738 2.54 MBM 102 158.561 −21.154 289 275 289 ± 0.1 0.25 ± 0.0004 201 ± 1.6 0.59 ± 0.0010 8.0 0.79 ± 0.0040 248 ± 6.0 1.19 ± 0.0480 2.56 MBM 103 158.885 −21.552 279 269 285 ± 0.1 0.25 ± 0.0006 196 ± 3.3 0.49 ± 0.0009 8.0 0.78 ± 0.0041 235 ± 5.5 1.18 ± 0.0368 3.13 MBM 104 158.405 −20.436 281 262 291 ± 0.1 0.28 ± 0.0007 194 ± 3.4 0.69 ± 0.0007 5.0 0.95 ± 0.0110 243 ± 11.4 1.09 ± 0.0628 2.11 MBM 105 169.52 −20.126 127 139 142 ± 0.4 0.20 ± 0.0003 178 ± 1.6 0.27 ± 0.0005 5.0 0.61 ± 0.0073 192 ± 13.3 0.62 ± 0.0134 2.52 MBM 106 176.334 −20.781 158 190 179 ± 0.1 0.23 ± 0.0006 213 ± 2.4 0.40 ± 0.0005 16.0 MBM 107 177.654 −20.343 141 197 142 ± 0.3 0.24 ± 0.0009 213 ± 3.5 0.48 ± 0.0007 16.0 MBM 108 178.238 −20.342 143 168 139 ± 0.4 0.24 ± 0.0009 213 ± 2.8 0.48 ± 0.0014 16.0 MBM 109 178.93 −20.1 155 160 176 ± 8.5 0.23 ± 0.0005 209 ± 2.1 0.38 ± 0.0012 16.0 0.72 ± 0.0038 241 ± 4.9 0.82 ± 0.0367 3.27 MBM 110 207.598 −22.944 356 313 300 ± 1.4 0.13 ± 0.0025 464 ± 19.5 0.12 ± 0.0009 4.0 MBM 111 208.547 −20.222 400 366 403 ± 0.3 0.13 ± 0.0025 468 ± 21.2 0.30 ± 0.0011 4.0 MBM 115 342.331 24.146 141 137 126 ± 46.4 0.13 ± 0.0006 52 ± 2.4 0.28 ± 0.0015 8.0 0.37 ± 0.0143 76 ± 22.1 0.79 ± 0.0362 3.23 MBM 116 342.715 24.506 137 134 158 ± 29.6 0.14 ± 0.0006 51 ± 1.6 0.29 ± 0.0015 8.0 0.39 ± 0.0134 70 ± 17.8 0.83 ± 0.0383 3.20 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Table 1 (Continued) a a a b c d d d d d d d d d 0 MC 0 MC ¢ ¢ Cloud l b d d d E h DE m E h DE CERs Zucker Schlafly this work G,G G,G G,G NUV,G NUV,G NUV,G BP RP BP RP BP RP BP BP BP (°)(°)(pc)(pc)(pc)(mag)(pc)(mag)(mag)(pc)(mag) (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) MBM 117 343.001 24.085 138 140 141 ± 2.1 0.13 ± 0.0006 51 ± 1.3 0.23 ± 0.0014 8.0 0.40 ± 0.0164 86 ± 25.6 1.01 ± 0.0832 3.21 MBM 118 344.018 24.758 140 56 146 ± 10.3 0.13 ± 0.0007 51 ± 1.9 0.27 ± 0.0021 8.0 MBM 119 341.613 21.396 169 150 111 ± 84.2 0.12 ± 0.0009 51 ± 1.0 0.11 ± 0.0024 8.0 MBM 120 344.231 24.188 135 59 145 ± 0.7 0.12 ± 0.0007 52 ± 2.1 0.28 ± 0.0022 8.0 MBM 123 343.281 22.121 143 101 75 ± 63.9 0.13 ± 0.0008 51 ± 1.0 0.22 ± 0.0035 8.0 0.50 ± 0.0592 197 ± 81.9 0.24 ± 0.0562 2.83 MBM 124 343.966 22.725 145 89 147 ± 122.3 0.13 ± 0.0006 51 ± 0.9 0.14 ± 0.0098 8.0 MBM 125 355.536 22.541 129 115 131 ± 1.1 0.14 ± 0.0004 51 ± 1.6 0.30 ± 0.0026 21.0 MBM 127 355.409 20.877 146 147 150 ± 0.2 0.14 ± 0.0003 51 ± 1.3 0.89 ± 0.0070 21.0 MBM 128 355.562 20.592 136 134 150 ± 0.2 0.14 ± 0.0003 51 ± 1.4 0.89 ± 0.0067 21.0 MBM 129 356.155 20.761 139 141 145 ± 0.7 0.14 ± 0.0004 51 ± 47.5 0.52 ± 0.0033 21.0 MBM 130 356.805 20.265 129 109 150 ± 0.1 0.14 ± 0.0004 51 ± 1.3 0.60 ± 0.0042 21.0 MBM 131 359.156 21.787 158 106 161 ± 0.3 0.14 ± 0.0004 51 ± 1.2 0.48 ± 0.0027 21.0 MBM 133 359.176 21.37 161 98 240 ± 0.6 0.14 ± 0.0004 51 ± 1.2 0.57 ± 0.0052 21.0 MBM 134 0.132 21.782 158 121 285 ± 0.7 0.07 ± 0.0003 73 ± 8.1 0.46 ± 0.0062 24.0 MBM 136 1.271 20.992 139 120 110 ± 20.2 0.09 ± 0.0004 101 ± 4.6 0.42 ± 0.0027 21.0 MBM 145 8.482 21.842 108 152 185 ± 0.6 0.07 ± 0.0005 71 ± 12.6 0.49 ± 0.0024 16.0 MBM 146 8.784 22.035 116 179 197 ± 0.4 0.07 ± 0.0005 63 ± 8.6 0.46 ± 0.0058 16.0 MBM 148 7.543 21.066 156 116 186 ± 0.4 0.07 ± 0.0007 80 ± 14.4 0.55 ± 0.0023 16.0 MBM 151 21.533 20.93 138 122 145 ± 0.2 0.18 ± 0.0003 100 ± 1.9 0.31 ± 0.0006 8.0 0.53 ± 0.0042 107 ± 9.6 0.83 ± 0.0135 3.07 MBM 152 359.48 −20.474 86 ± 65.8 0.10 ± 0.0021 134 ± 16.0 0.15 ± 0.0024 4.0 Notes. The molecular cloud’s series number (Column 1) and Galactic coordinates (Columns 2 and 3) retrieved from Magnani et al. (1985). The distance and the error (Column 4) from Zucker et al. (2019). The distance and the error (Column 5) from Schlafly et al. (2014). The distance and the errors (Column 6), the foreground fitting parameters (Columns 7 and 8), and the color excess jump in the optical (Column 9), the multiples of the cloud’s angular diameter (Column 10), the foreground fitting parameters (Columns 11 and 12), and the color excess jump (Column 13) in the optical-ultraviolet bands, and the color excess ratio of molecular clouds (Column 14) from this work. (This table is available in machine-readable form.) The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Figure 4. The fitting to the color excess, E , variation with the distance to the stars in the reference (green dots) and the cloud (red dots) region for the three G,G BP RP typical clouds MBM 5, MBM 40, and MBM 109 with the extinction−distance model (Equations (1), (2), and (3). The parameters derived are shown in the upper-left MC 0 corner, where “d” is the distance, “ΔE” is the color excess jump (DE ), and E and h¢ are the foreground parameters of the molecular cloud (E and G, BPGRP G, BPGRP h ). (An extended version of this figure for all the studied clouds is available online). G,G BP RP (The complete figure set (11 images) is available.) 3.2. The Extinction-jump Model improved by Zhao et al. (2020) and used to determine the Under the assumption that interstellar extinction increases distance and the extinction of Galactic supernova remnants smoothly with distance in the absence of any MCs, the (SNRs). A similar model is used by Chen et al. (2017) and Yu extinction will make an upward jump at the distance of the et al. (2019) for other SNRs as well as MCs. The MCs cause cloud in the presence of an MC. In order to obtain accurate the same effect as SNRs on the extinction and thus the distance to and extinction of MCs, we take the extinction-jump extinction-jump model is applicable. In detail, the total model in Zhao et al. (2020), which is insensitive to the outliers. extinction in terms of color excess E(d) toward the sight line This model was designed originally by Zhao et al. (2018) and of the MC is composed of two parts: the color excess of the 7 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Figure 5. The same as Figure 4, but for E . NUV,G BP MC cloud E (d), which dominates the total extinction, and the to the center, and δd is the radius of the cloud calculated from DISM color excess of the diffuse interstellar medium E (d), d × θ with θ being the cloud’s angular diameter. c c c However, unlike Chen et al. (2017), Yu et al. (2019), and DISM MC Ed ()=+ E ()d E ()d.1 ( ) Zhao et al. (2020) which use a two-order polynomial function or root function, we use an exponential law to fit the color MC Moreover, E (d) is described by an erf function, excess caused by the diffuse interstellar dust, -d dd - c DISM 0 MC MC ⎡ ⎛ ⎞⎤ Ed ()=´E (13 -e h¢ ) ( ) Ed ()=DE ´ 1e + rf⎜⎟,2 ( ) ⎢ ⎥ 2dd ⎝ ⎠ ⎣ ⎦ The function is modified to be in line with the high-latitude MC where ΔE is the amplitude of the color excess jump, i.e., location of the MCs, in the sight line of which the material MC MC DE orDE caused by the cloud, d is the distance (including the interstellar dust) density falls exponentially with G,G NUV,G c BP RP BP 8 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Figure 6. The distribution of the distances (d) and their uncertainties (σ ). the vertical distance from the Galactic plane. Under this form, Similar to step (2), but replacing the optical parameters by 0 0 the parameter E reflects the cumulative color excess, and ultraviolet values, i.e., E by E and E and G,G NUV,G BP RP BP G,G BP RP hs ¢´ in()b with b being the latitude of the cloud is the scale ¢ ¢ h by E and h . In addition, the value of d G,G NUV,G NUV,G c BP RP BP BP height (h) of the dust disk in the sight line. resulting from the optical color excess is adopted rather than fitted because the number of measurements in the UV band is only about a quarter in the visual, thus only the jump MC 3.3. The Model Fitting DE is derived in this step. NUV, G BP The model fitting for MBM 5, MBM 40, and MBM 109 with The model fitting is performed with the Markov Chain the reference and cloud sources are displayed as the example in Monte Carlo procedure (Foreman-Mackey et al. 2013). In order MC MC Figures 4 and 5 for DE and DE , respectively. G,G NUV,G to set the initial parameters very reasonably, a Markov chain is BP RP BP The green dots denote the sources in the reference region used first run with 100 walkers and 250 steps. Then, the final chain to determine the variation of extinction with distance in the uses the initial parameters with 100 walkers and 2000 steps, diffuse medium, and the red dots denote the sources in the and we choose the last 1750 steps from each walker to sample cloud region used to determine the distance and extinction of the final posterior. The best estimates are the median values the cloud. The key parameters with the uncertainty derived (50th percentile) of the posterior distribution and the from modeling are shown in the upper-left corner of the figures uncertainties are derived from the 16th and 84th percentile (an extended version of Figure 4 is available for all the sample values. clouds). The variation of stellar extinction with distance is fitted separately for the reference region and the cloud region. Because the sample becomes more and more incomplete with 4. Results and Discussions distance, only the objects closer than 2000 pc with relative 4.1. The Distance distance uncertainty <30% are taken into account. The fitting steps are in the following order: (1) fitting the optical The distance is derived for 66 of the 75 MBM clouds toward extinction–distance measurements, i.e., the E versus d G,G BP RP whose sight line more than three stars are present with an points of the reference region, by Equation (3) to obtain the optical color excess measurement and lying behind the MC. parameters E and h to describe the change of G,G G,G BP RP BP RP The derived parameters are tabulated in Table 1. The E with d in the reference region. (2) Fitting the optical G,G BP RP distribution of the distances and their uncertainties is shown in extinction–distance measurements of the cloud region by Figure 6 where the symbols follow the convention in Figure 4. Equations (1) and (2) after substituting the above values of A simple visual inspection would conclude that the fitting E and h into Equation (1), which yields the G,G G,G BP RP BP RP agrees very well with the measurements in most cases. MC distance d and the optical jump of the MC. (3) The DE c Meanwhile, the distances to G37.57−35.06 (MBM 11), G,G BP RP same as step (1) but replacing E by the E of the G,G NUV,G G157.98+44.67 (MBM 40), G341.61+21.40 (MBM 119), BP RP BP reference region sources to obtain E and h . (4) G343.28+22.12 (MBM 123), and G359.48−20.47 (MBM NUV,G NUV,G BP BP 9 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Figure 7. The distance d (upper panel) and the Galactic disk distance |z| (lower panel) versus the Galactic latitude |b|. 152) seem to be underestimated because there are few sources For MBM 40, more objects in front of the cloud should be at a very close distance. As mentioned earlier, MBM 40 is the measured to confirm its close distance. nearest with a distance of only 63 ± 51 pc, which puts it inside Figure 7 shows the distance d and the vertical distance to the the Local Bubble or right at the boundary of the Local Bubble, Galactic plane |z| versus the Galactic latitude |b|. There is no if true. Though the uncertainty is large, the best value is systematic trend of d with |b| expected as these clouds are consistent with that of Schlafly et al. (2014). On the other hand, local, while |z| increases with the Galactic latitude |b|. this value is smaller than the 93 pc obtained by Zucker et al. The distances to 9 of the 66 MCs were measured by Yan (2019). Indeed, Figures 4 and 5 indicate that the first stars that et al. (2019) and to 64 of them by Schlafly et al. (2014) and show a marked increase in color excess have a distance of Zucker et al. (2019); these are compared with ours in Figure 8. about 125 pc, apparently much larger, though still within the It can be seen that the distances are more or less identical range of the uncertainty. These cases indicate that a precise between the works at d < 200 pc. When d > 200 pc, this work distance from our method needs a continuous distribution of yields a systematically larger distance than the others to a the distance of the tracers, in particular around the jump point. different extent in that the difference with Schlafly et al. (2014) 10 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Figure 8. The comparison of the distances to molecular clouds with those obtained by Schlafly et al. (2014), Yan et al. (2019), and Zucker et al. (2019). The inset is the distribution of the differences with their results. is the largest and the difference with the other two works are various MBM clouds. Such confusion implies that the mostly within the uncertainties. Comparing with these works, boundary of a cloud needs to be redefined and will be this work differs in a few aspects: (1) the intrinsic color indexes considered in our next work. Figure 10 shows the maximum max are derived from spectroscopy rather than photometry, (2) the stellar E , i.e., E behind each MBM cloud G,G G,G BP RP BP RP stellar distance comes from the Gaia/EDR3 catalog instead of identifiable in the Lynds dark clouds catalog in comparison the DR2 catalog, (3) the model considers the thickness of the with all the other clouds, where the blue asterisks denote the MC, and (4) the rise of the color excess of the foreground MBM MC containing some Lynds dark cloud(s). It can be seen max sources with distance is considered separately, which prevents that the majority of these clouds have E > 1.0, i.e., G,G BP RP the premature occurrence of jumps in some MCs. The first two A > 2.0 mag. Because dark clouds are normally defined to factors improve the accuracy but should have no systematic have A > 5 mag, this is not consistent with the expectation for influence on the distance. a dark cloud. It is likely that an interstellar cloud might have an average extinction of 2 mag with small patches having extinctions of 5 mag or more and so, on the basis of these 4.2. The Extinction small patches, the cloud is defined as a dark cloud while its 4.2.1. The Cloud average extinction is more like that of a translucent cloud. Meanwhile, a few clouds have A ∼ 1.0–2.0 mag, smaller than The extinction is determined for 66 MCs expressed by the V MC the extinction that a dark cloud should have. One possible optical color excess DE and for 39 MCs by the UV- G,G BP RP MC reason is that the stars that suffer serious extinction may optical color excess DE . Their distribution along the NUV,G BP become too faint to be observable by the LAMOST or GALAH latitude is shown in Figure 9 where the increase at low latitudes spectroscopy survey. This also shows that the method in this is visible as expected from their smaller vertical distance to the work derives the median rather than the highest extinction of a Galactic plane as evident in the lower panel of Figure 7. cloud so that it is more appropriate for relatively large clouds Meanwhile, it should be noted that the extinction appears large MC than smaller dense clouds. Additionally, several MBM clouds around |b| ∼ 35°−40°. The majority ofDE is not bigger G,G max BP RP have no associated Lynds dark clouds but with E > 1.0, G,G BP RP than 0.4 mag, i.e., A ∼ 0.8 mag, and some clouds cause a large A < 3.0 mag is still an acceptable extinction for a translucent extinction but still smaller than A ∼ 3 mag. Therefore, most of cloud though we cannot exclude the possibility of the presence the clouds may be classified as translucent, and some of them of some dark nebula. as diffuse MCs. It should be noted that there are some stars with a large color excess, which is not reflected in the fitting parameters. The 4.2.2. The Reference Region cross-identification with the Lynds dark clouds (Lynds 1962) finds that 24 MBM clouds contain 20 Lynds dark clouds, The reference region is selected from the low-intensity noise- which are listed in Table 2. Some MBM clouds cover multiple like emission at Planck/857 GHz, representative of the diffuse Lynds clouds while some Lynds clouds repetitively appear in interstellar medium. Our model for the reference extinction by 11 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. MC MC Figure 9. The change of DE and DE with the Galactic latitude |b|. G, BPGRP NUV,GBP ¢ ¢ Equation (3) assumes an exponential disk with vertical height. After multiplying h and h by sin() b , the dust G,G NUV,G BP RP BP The parameter E in Equation (3) is the cumulative extinction disk scale height h and h in the sight line is G,G NUV,G BP RP BP andhb ¢ sin() is the scale height of the extinction/dust disk obtained. Figure 11 (b) presents the relation between h G,G BP RP toward the specific high-latitude sight line. and h , which are basically distributed near the equal line NUV,G BP The relationship between the parameters from fitting E while some points deviate. Because the parameter h¢ is very G,G BP RP sensitive to the data size, h should be more reliable due and E for the reference regions is shown in Figure 11. G,G BP RP NUV,G BP to its much smaller error and more data points in the Gaia/ As shown in Figure 11(a), there is a good linear relationship 0 0 EDR3 catalog. The change of E and∣∣ h with between E and E . The slope of the fitting line is G,G G,G BP RP G,G NUV,G BP RP BP RP BP Galactic longitude is displayed in Figures 11(c) and 11(d). The 3.27, which reflects the ratio of the accumulated color excess of the diffuse interstellar medium in the UV and optical bands. scale height varies from about 50 to 250 pc, with an obvious increase toward the anticenter direction consistent with a flaring This ratio is very close to the all-sky color excess ratio of 3.25 in Paper I. dust disk. This median thickness of about 100 pc indicates that 12 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Table 2 MBM Molecular Clouds Associated with Lynds Dark Cloud a a MBMb b max c max c LDN MBM LDN Area Area E MBM LDN 2 2 (deg)(deg)(mag)(mag) MBM 12 LDN 1453 1.767 0.066 1.84 1.528 MBM 12 LDN 1454 1.767 0.86 1.84 1.84 MBM 12 LDN 1457 1.767 0.262 1.84 1.786 MBM 12 LDN1458 1.767 0.056 1.84 1.113 MBM 18 LDN 1569 2.836 0.631 1.009 0.855 MBM 36 LDN 134 1.767 0.22 1.183 1.109 MBM 37 LDN 169 1.227 0.86 1.612 1.612 MBM 37 LDN 183 1.227 0.24 1.612 1.612 MBM 101 LDN 1452 1.767 1.66 1.945 1.945 MBM 101 LDN 1448 1.767 0.053 1.945 1.296 MBM 101 LDN 1451 1.767 0.14 1.945 1.569 MBM 102 LDN 1448 1.767 0.053 1.945 1.296 MBM 102 LDN 1451 1.767 0.14 1.945 1.569 MBM 102 LDN 1452 1.767 1.66 1.945 1.945 MBM 103 LDN 1451 1.767 0.14 1.885 1.569 MBM 103 LDN 1448 1.767 0.053 1.885 1.296 MBM 103 LDN 1452 1.767 1.66 1.885 1.945 MBM 104 LDN 1452 1.767 1.66 2.387 1.945 MBM 107 LDN 1543 1.767 0.09 1.732 1.732 MBM 107 LDN 1546 1.767 0.37 1.732 1.842 MBM 108 LDN 1543 1.767 0.09 2.018 1.732 MBM 108 LDN 1546 1.767 0.37 2.018 1.842 MBM 109 LDN 1546 1.767 0.37 2.018 1.842 MBM 110 LDN 1634 1.767 0.492 0.773 0.466 MBM 111 LDN 1640 1.767 0.018 1.379 0.005 MBM 125 LDN 1721 1.767 0.287 0.769 0.424 MBM 126 LDN 1719 1.767 0.61 1.218 1.218 MBM 127 LDN 1719 1.767 0.61 1.218 1.218 MBM 128 LDN 1719 1.767 0.61 1.218 1.218 MBM 129 LDN 1719 1.767 0.61 1.218 1.218 MBM 130 LDN 1752 1.767 1.78 0.979 1.421 MBM 131 LDN 1781 1.767 1.19 0.778 0.778 MBM 133 LDN 1781 1.767 1.19 0.778 0.778 MBM 134 LDN 1781 1.767 1.19 0.559 0.778 MBM 145 LDN 234 1.767 1.41 0.648 0.802 MBM 148 LDN 234 1.767 1.41 0.802 0.802 Notes. The molecular cloud’s series number (Columns 1 and 2) from Magnani et al. (1985)(MBM) and Lynds (1962)(LDN). The cloud area (Columns 3 and 4) from MBM and LDN. The maximum color excess E in the cloud region (Columns 5 and 6) from MBM and LDN. G,G BP RP (This table is available in machine-readable form.) MC MC the dust disk agrees with the thin gaseous disk of the Milky cloud. However, the ratio DEE D of the cloud NUV,G G,G BP BP RP Way whose scale height ranges around 100–300 pc (e.g., has great uncertainty, perhaps due to the very large dispersion Ferguson et al. 2017; Ma et al. 2017). in the extinction. Instead, the sources behind the cloud are all The resultant E is compared with Schlegel et al. (1998, taken into consideration to determine the color excess ratio G,G BP RP E /E and then the dust property of an MC. By SFD98) for the reference region because E is supposed NUV,G G,G BP BP RP G,G BP RP subtracting the color excess of the diffuse interstellar medium to be the cumulative extinction along the sight line. The value SFD SFD at equal distances from the color excess of these sources, the of E is first converted to E for comparison (Niu et al. B,V G,G BP RP corresponding color excess of the MC in the sight line is 2021). Figure 12 shows the linear fitting between E and G,G BP RP obtained. Requiring the number of selected sources to be SFD the median value of E in each studied reference area. The G,G BP RP N … 3, the color excess ratios of 39 MCs are calculated by slope is 0.95 and the intercept is −0.005, which means our linear fitting through iterative 3σ clipping (Paper I). The results result is very consistent with that of SFD98. of MBM 5, MBM 40, and MBM 109 are displayed in Figure 13, where E and E have a good linear NUV,G G,G BP BP RP 4.3. Dust Property of High-latitude Molecular Clouds relationship. Because the extinction of an MC changes across the cloud, The change of the color excess ratios (E E ) NUV,G G ,G BP BP RP MC MC the overall average color excess of the cloud, i.e., DE G,G with DE of these MCs is shown in the lower panel of BP RP G,G BP RP MC andDE , should be an extinction indicator of the overall Figure 14. Obviously, the color excess ratio of the MCs (red NUV,G BP 13 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. max Figure 10. The change of maximum extinction E in the sight line of molecular clouds with the Galactic latitude |b|. The blue and red asterisks are the result of G,G BP RP MBM clouds with or without Lynds dark cloud. MC asterisks) increases atDE < 0.3. As Paper I pointed out, whole high-latitude sky in Paper I and now confirmed by G,G BP RP there exists a systematic variation in both T and E with this work. eff G,G BP RP the Galactic location for the tracing stars, which can shift the effective wavelength of the filters and then the color excess ratio E E in a complicated way (see Figure 10 of 5. Summary NUV,G G ,G BP BP RP Paper I). In brief, E E generally decreases with NUV,G G ,G BP BP RP This work uses the color excesses of more than 4 million E when T > 6500 K, while increases with E G,G eff G,G BP RP BP RP stars in the visual and 1 million stars in the ultraviolet to when T < 6500 K. On average, this color excess ratio is eff explore the high-latitude MCs cataloged by Magnani et al. bigger for higher T . The upper panel of Figure 14 confirms eff (1985). The cloud and reference region are selected from the MC that T changes with DE . In order to see the change of eff G,G BP RP Planck/857 GHz image in order to clarify the extinction caused MC dust property, the effects of T and DE on the color eff G,G by the cloud. The distances to 66 clouds are determined by the BP RP excess ratio should be stripped off in advance. For this purpose, extinction jump along the sight line caused by the cloud denser the color excess ratio of each is calculated assuming that only than the diffuse area. MC T and DE play a role, i.e., convolving the stellar eff G,G The major results of this paper are as follows: BP RP emergent spectrum with the response curve of the filter and the 1. The cumulative color excess E of the diffuse ISM G,G BP RP F99 extinction curve at R = 3.1 (Fitzpatrick 1999) to get the and scale height h of the dust disk is derived for 66 visible color excess ratio at the corresponding effective wavelength. areas, while the cumulative color excess E of the The derived color excess ratio is represented by blue asterisks NUV,G BP diffuse ISM is obtained for 39 areas. The calculated scale in Figure 14, which agrees with the expectation from Paper I height is around 50–250 pc, which agrees with the thin that the lower T around 6000 K in combination with the eff MC gaseous disk of the Milky. smaller DE should lead to a smaller E E . NUV,G G ,G G,G BP RP BP BP RP MC 2. The distances and color excess DE is determined G,G The observed trend that the color excess ratio of the MCs BP RP MC for 66 MCs, and the extinction jump DE is increases at smaller E is thus in the opposite direction. It G,G NUV,G BP RP BP seems that this trend can only be explained by the change of determined for 39 MCs. The distances of this work are dust property at small extinction. In principle, the color excess slightly larger than the results of Schlafly et al. (2014) and ratio is sensitive to the composition and size distribution of the closer to that of Zucker et al. (2019). dust particles (Draine 2011). Larson & Whittet (2005) conclude 3. The color excess ratio E /E of 39 MCs is NUV,G G ,G BP BP RP calculated and found to be obviously larger at lower that many high-latitude clouds have enhanced abundances of relatively small grains based on the near-infrared extinction extinction, which cannot be interpreted as the shift of the effective wavelength because of the variation in T and curves. The enhanced proportion of small grains can also eff explain the observed ratio variation of the near-ultraviolet-to- E . This indicates that the MCs with lower G,G BP RP extinction have more small dust particles. visual extinction here. Indeed, this trend is already found in the 14 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. 0 0 0 Figure 11. The relationship of E and E (top, left) and h and h (top, right) as well as the distribution of E (bottom, left) and ∣h ∣(bottom, NUV,G G ,G NUV,G G ,G G ,G G,G BP BP RP BP RP BP BP RP BP RP 0 0 right). Red asterisks are the parameters of foreground and black line is the fitting line of E and E (top, left) and h = h line (top, right). NUV,G G,G NUV,GBP G, BPGRP BP BP RP 0 SFD Figure 12. Comparison between E and E in the background region. G,G G,G BP RP BP RP 15 The Astrophysical Journal Supplement Series, 256:46 (17pp), 2021 October Sun et al. Figure 14. The change of T (upper panel) and color excess ratios eff MC E /E (lower panel) withDE . 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