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H. -B. Yuan

Publications and source records attributed to H. -B. Yuan.

At least 19 recordsLinked to original sources

Vertical Structure of Interstellar Dust in the Milky Way

Interstellar dust plays a central role in the evolution of galaxies by shaping star formation, altering observed stellar properties, and redistributing radiation across the electromagnetic spectrum. In the Milky Way, dust is concentrated in the Galactic disk and often associated with large-scale structures such as spiral arms and molecular clouds. Here we present a detailed analysis of the vertical distribution and substructure of interstellar dust using a sample of approximately 23 million stars from literature with high-precision extinction measurements. We derive three-dimensional dust density profiles along various sightlines and fit vertical dust distributions using both single and double exponential disk models across 12 Galactocentric radial bins from $\sim$6 to $\sim$12\,kpc. We show that a two-component disk model--comprising a ``thin'' and a ``thick'' dust disk--provides a better fit to the vertical dust profile than a single exponential disk, as indicated by Bayesian Information Criterion (BIC) comparisons. The thin and thick disks have average scale heights of $81.0 \pm 6.7$\,pc and $152.0 \pm 7.0$\,pc, respectively. Our results also identify significant dust substructures, which align well with known spiral arms, molecular clouds, and star-forming regions.

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The miniJPAS survey: stellar atmospheric parameters from 56 optical filters

With a unique set of 54 overlapping narrow-band and two broader filters covering the entire optical range, the incoming Javalambre-Physics of the Accelerating Universe Astrophysical Survey (J-PAS) will provide a great opportunity for stellar physics and near-field cosmology. In this work, we use the miniJPAS data in 56 J-PAS filters and 4 complementary SDSS-like filters to explore and prove the potential of the J-PAS filter system in characterizing stars and deriving their atmospheric parameters. We obtain estimates for the effective temperature with a good precision (<150 K) from spectral energy distribution fitting. We have constructed the metallicity-dependent stellar loci in 59 colours for the miniJPAS FGK dwarf stars, after correcting certain systematic errors in flat-fielding. The very blue colours, including uJAVA-r, J0378-r, J0390-r, uJPAS-r, show the strongest metallicity dependence, around 0.25 mag/dex. The sensitivities decrease to about 0.1 mag/dex for the J0400-r, J0410-r, and J0420-r colours. The locus fitting residuals show peaks at the J0390, J0430, J0510, and J0520 filters, suggesting that individual elemental abundances such as [Ca/Fe], [C/Fe], and [Mg/Fe] can also be determined from the J-PAS photometry. Via stellar loci, we have achieved a typical metallicity precision of 0.1 dex. The miniJPAS filters also demonstrate strong potential in discriminating dwarfs and giants, particularly the J0520 and J0510 filters. Our results demonstrate the power of the J-PAS filter system in stellar parameter determinations and the huge potential of the coming J-PAS survey in stellar and Galactic studies.

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Three-Dimensional Distribution of the Interstellar Dust in the Milky Way

We present a three-dimensional (3D) extinction map of the southern sky. The map covers the SkyMapper Southern Survey (SMSS) area of $\sim$ 14,000 ${\rm deg^{2}}$ and has spatial resolutions between 6.9 and 27 arcmin. Based on the multi-band photometry of SMSS, the Two Micron All Sky Survey, the Wide-Field Infrared Survey Explorer Survey and the Gaia mission, we have estimated values of the $r$-band extinction for $\sim$ 19 million stars with the spectral energy distribution (SED) analysis. Together with the distances calculated from the Gaia data release 2 (DR2) parallaxes, we have constructed a three-dimensional extinction map of the southern sky. By combining our 3D extinction map with those from the literature, we present an all-sky 3D extinction map, and use it to explore the 3D distribution of the Galactic dust grains. We use two different models, one consisting a single disk and another of two disks, to fit the 3D distribution of the Galactic dust grains. The data is better fitted by a two-disk model, yielding smaller values of the Bayesian Information Criterion (BIC). The best fit model has scale heights of 73 and 225 pc for the "thin" and "thick" dust disks, respectively.

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Probing the galactic halo with RR Lyrae stars I: The catalog

We present a catalog of 5,290 RR Lyrae stars (RRLs) with metallicities estimated from spectra of the LAMOST Experiment for Galactic Understanding and Exploration (LEGUE) and the Sloan Extension for Galactic Understanding and Exploration (SEGUE) surveys. Nearly 70 per cent of them (3,642 objects) also have systemic radial velocities measured. Given the pulsating nature of RRLs, metallicity estimates are based on spectra of individual exposures, by matching them with the synthetic templates. The systemic radial velocities are measured by fitting the observed velocity as a function of phase assuming an empirical pulsating velocity template curve. Various tests show that our analyses yield metallicities with a typical precision of 0.20\,dex and systemic radial velocities with uncertainties ranging from 5 to 21\,km\,s$^{-1}$ (depending on the number of radial velocity measurements available for a given star). Based on the well calibrated near-infrared $PM_{W1}Z$ or $PM_{K_{\rm s}}Z$, and $M_{V}$-[Fe/H] relations, precise distances are derived for these RRLs. Finally, we include Gaia DR2 proper motions in our catalog. The catalog should be very useful for various Galactic studies, especially of the Galactic halo.

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A catalogue of H$α$ emission-line point sources in the vicinity fields of M31 and M33 from the LAMOST survey

We present a catalogue of 3,305 H$α$ emission-line point sources observed with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) in the vicinity fields of M31 and M33 during September 2011 and January 2016. The catalogue contains 1,487 emission-line stars, 532 emission-line nebulae including 377 likely planetary nebulae (PNe), 83 H~{\textsc{ii}} regions candidates and 20 possible supernovae remnants (SNRs) and 1,286 unknown objects. Among them, 24 PN candidates, 19 H~{\sc ii} region candidates, 10 SNR candidates and 1 symbiotic star candidate are new discoveries. Radial velocities and fluxes estimated from the H$α$ line and those quantities of seven other major emission lines including H$β$, [O~{\textsc{iii}}]~$λ$4959, [O~{\textsc{iii}}]~$λ$5007, [N~{\textsc{ii}}]~$λ$6548, [N~{\textsc{ii}}]~$λ$6583, [S~{\textsc{ii}}]~$λ$6717 and [S~{\textsc{ii}}]~$λ$6731 lines of all the catalogued sources yielded from the LAMOST spectra are also presented in our catalogue. Our catalogue is an ideal starting point to study the chemistry properties and kinematics of M31 and M33.

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A large catalogue of molecular clouds with accurate distances within 4 kpc of the Galactic disk

We present a large, homogeneous catalogue of molecular clouds within 4 kpc from the Sun at low Galactic latitudes ($|b|$ $<$ 10\degr) with unprecedented accurate distance determinations. Based on the three-dimensional dust reddening map and estimates of colour excesses and distances of over 32 million stars presented in Chen et al, we have identified 567 dust/molecular clouds with a hierarchical structure identification method and obtained their distance estimates by a dust model fitting algorithm. The typical distance uncertainty is less than 5 per cent. As far as we know, this is the first large catalogue of molecular clouds in the Galactic plane with distances derived in a direct manner. The clouds are seen to lie along the Sagittarius, Local and Perseus Arms. In addition to the known structures, we propose the existence of a possible {\it spur}, with a pitch angle of about 34\degr, connecting the Local and the Sagittarius Arms in the fourth quadrant. We have also derived the physical properties of those molecular clouds. The distribution of cloud properties in different parameter spaces agrees grossly with the previous results. Our cloud sample is an ideal starting point to study the concentration of dust and gas in the solar vicinity and their star formation activities.

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Mapping the Galactic disk with the LAMOST and Gaia Red clump sample. II. 3D asymmetrical kinematics of mono-age populations in the disk between 6$-14$ \,kpc

We perform analysis of the three-dimensional kinematics of Milky Way disk stars in mono-age populations. We focus on stars between Galactocentric distances of $R=6$ and 14 \,kpc, selected from the combined LAMOST DR4 red clump giant stars and Gaia DR2 proper motion catalogue. We confirm the 3D asymmetrical motions of recent works and provide time tagging of the Galactic outer disk asymmetrical motions near the anticenter direction out to Galactocentric distances of 14\,kpc. Radial Galactocentric motions reach values up to 10 km s$^{-1}$, depending on the age of the population, and present a north-south asymmetry in the region corresponding to density and velocity substructures that were sensitive to the perturbations in the early 6 \,Gyr. After that time, the disk stars in this asymmetrical structure have become kinematically hotter, and are thus not sensitive to perturbations, and we find the structure is a relatively younger population. With quantitative analysis, we find stars both above and below the plane at $R\gtrsim 9$ kpc that exhibit bending mode motions of which the sensitive duration is around 8 \,Gyr. We speculate that the in-plane asymmetries might not be mainly caused by a fast rotating bar, intrinsically elliptical outer disk, secular expansion of the disk, or streams. Spiral arm dynamics, out-of-equilibrium models, minor mergers or others are important contributors. Vertical motions might be dominated by bending and breathing modes induced by complicated inner or external perturbers. It is likely that many of these mechanisms are coupled together.

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Mapping the Galactic disk with the LAMOST and Gaia Red clump sample: III: A new velocity substructure and time stamps of the Galactic disk asymmetry in the disk between 12$-$15 \,kpc

We investigate the three-dimensional asymmetrical kinematics and present time stamps of the Milky Way disk between Galactocentric distances of $R=12$ and 15 \,kpc, using red clump stars selected from the LAMOST Galactic survey, also with proper motion measurements provided by the Gaia DR2. We discover velocity substructure above the Galactic plane corresponding to a density dip found recently ("south-middle opposite" density structure[R $\sim$ 12-15 \,kpc, Z $\sim$ 1.5 \,kpc] discovered in \citet{Wang2018b, Wang2018c}) in the radial and azimuthal velocity. For the vertical velocity, we detect clear vertical bulk motions or bending mode motions, which has no clear north-south asymmetry corresponding to the in-plane asymmetrical features. In the subsample of stars with different ages, we find that there is little temporal evolution of the in-plane asymmetry from 0$-$14 \,Gyr, which means the structure is sensitive to the perturbations in almost cosmic time possibly. We propose that the possible scenario of this asymmetric velocity structure is caused by the mechanisms generated in-plane, rather than vertical perturbations.

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Milky Way tomography with the SkyMapper Southern Survey: I: Atmospheric parameters and distances of one million red giants

Accurate determinations of atmospheric parameters (effective temperature $T_{\rm eff}$, surface gravity log $g$ and metallicity [Fe/H]) and distances for large complete samples are of vital importance for various Galactic studies. We have developed a photometric method to select red giant stars and estimate their atmospheric parameters from the photometric colors provided by the SkyMapper Southern Survey (SMSS) data release (DR) 1.1, using stars in common with the LAMOST Galactic spectroscopic surveys as a training set. Distances are estimated with two different approaches: one based on the Gaia DR2 parallaxes for nearby ($d \leq 4.5$ kpc) bright stars and another based on the absolute magnitudes predicted by intrinsic color $(g-i)_0$ and photometric metallicity [Fe/H] for distant ($d > 4.5$ kpc) faint stars. Various tests show that our method is capable of delivering atmospheric parameters with a precision of $\sim$80 K for $T_{\rm eff}$, $\sim$0.18 dex for [Fe/H] and $\sim$0.35 dex for log $g$, but with a significant systematic error at log $g \sim$ 2.3. For distances delivered from $(g-i)_0$ and photometric [Fe/H], our test with the member stars of globular clusters show a median uncertainty of 16 per cent with a negligible zero-point offset. Using this method, atmospheric parameters and distances of nearly one million red giant stars are derived from SMSS DR1.1. Proper motion measurements from Gaia DR2 are available for almost all of the red giant stars, and radial velocity measurements from several large spectroscopic surveys are available for 44 per cent of these. This sample will be accessible online at https://yanghuang0.wixsite.com/yangh/research .

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The Galactic disc phase spirals at different Galactic positions revealed by Gaia and LAMOST data

We have investigated the distributions of stellar azimuthal and radial velocity components $V_Φ$ and $V_{R}$ in the vertical position-velocity plane $Z$-$V_{Z}$ across the Galactic disc of $6.34 \lesssim R \lesssim 12.34$\,kpc and $|Φ| \lesssim 7.5^{\circ}$ using a Gaia and Gaia-LAMOST sample of stars. As found in previous works, the distributions exhibit significant spiral patterns. The $V_{R}$ distributions also show clear quadrupole patterns, which are the consequence of the well-known tilt of the velocity ellipsoid. The observed spiral and quadrupole patterns in the phase space plane vary strongly with radial and azimuthal positions. The phase spirals of $V_Φ$ become more and more relaxed as $R$ increases. The spiral patterns of $V_Φ$ and $V_{R}$ and the quadrupole patterns of $V_{R}$ are strongest at $-2^{\circ} < Φ< 2^{\circ}$ but negligible at $4^{\circ} < Φ< 6^{\circ}$ and $-6^{\circ} < Φ< -4^{\circ}$. Our results suggest an external origin of the phase spirals. In this scenario, the intruder, most likely the previously well-known Sagittarius dwarf galaxy, passed through the Galactic plane in the direction towards either Galactic center or anti-center. The azimuthal variations of the phase spirals also help us constrain the passage duration of the intruder. A detailed model is required to reproduce the observed radial and azimuthal variations of the phase spirals of $V_Φ$ and $V_{R}$.

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Three-dimensional interstellar dust reddening maps of the Galactic plane

We present new three-dimensional (3D) interstellar dust reddening maps of the Galactic plane in three colours, E(G-Ks), E(Bp-Rp) and E(H-Ks). The maps have a spatial angular resolution of 6 arcmin and covers over 7000 deg$^2$ of the Galactic plane for Galactic longitude 0 deg $<$ $l$ $<$ 360 deg and latitude $|b|$ $<$ $10$ deg. The maps are constructed from robust parallax estimates from the Gaia Data Release 2 (Gaia DR2) combined with the high-quality optical photometry from the Gaia DR2 and the infrared photometry from the 2MASS and WISE surveys. We estimate the colour excesses, E(G-Ks), E(Bp-Rp) and E(H-Ks), of over 56 million stars with the machine learning algorithm Random Forest regression, using a training data set constructed from the large-scale spectroscopic surveys LAMOST, SEGUE and APOGEE. The results reveal the large-scale dust distribution in the Galactic disk, showing a number of features consistent with the earlier studies. The Galactic dust disk is clearly warped and show complex structures possibly spatially associated with the Sagittarius, Local and Perseus arms. We also provide the empirical extinction coefficients for the Gaia photometry that can be used to convert the colour excesses presented here to the line-of-sight extinction values in the Gaia photometric bands.

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Metallicity distributions of mono-age stellar populations of the Galactic disc from the LAMOST Galactic spectroscopic surveys

We have investigated the metallicity distributions of mono-age stellar populations across the disc of $6 \lesssim R \lesssim 12$\,kpc and $|Z| \lesssim 2$\,kpc using samples selected from the main-sequence turn-off and sub-giant (MSTO-SG) stars targeted by the LAMOST Galactic Spectroscopic surveys. Both the mean values and the profiles of the distributions exhibit significant variations with age and position. We confirm that the oldest ($>11$\,Gyr) stars have nearly flat radial [Fe/H] gradients at all heights above the disc but show negative vertical [Fe/H] gradients. For stars younger than 11\,Gyr, the radial [Fe/H] gradients flatten with $|Z|$, while the vertical [Fe/H] gradients flatten with $R$. Stars of 4--6\,Gyr exhibit steeper negative radial [Fe/H] gradients than those of either younger or older ages. Values of [$α$/Fe] of mono-age stellar populations also show significant radial and vertical gradients, with patterns varying with age. The [Fe/H] distribution profiles of old ($>8$\,Gyr) stars vary little with $R$, while those of younger stars exhibit strong radial variations, probably a consequence of significant radial migration. The [$α$/Fe] radial distribution profiles show opposite patterns of variations with age compared to those of [Fe/H]. We have also explored the impacts of stellar mixing by epicycle motions (blurring) on the [Fe/H] and [$α$/Fe] distributions, and found that blurring mainly change the widths of the distribution profiles. Our results suggest that the disc may have experienced a complex assemblage history, in which both the "inside-out" and "upside-down" formation processes may have played an important role.

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The selection function of the LAMOST Spectroscopic Survey of the Galactic Anticentre

We present a detailed analysis of the selection function of the LAMOST Spectroscopic Survey of the Galactic Anti-centre (LSS-GAC). LSS-GAC was designed to obtain low resolution optical spectra for a sample of more than 3 million stars in the Galactic anti-centre. The second release of value-added catalogues of the LSS-GAC (LSS-GAC DR2) contains stellar parameters, including radial velocity, atmospheric parameters, elemental abundances and absolute magnitudes deduced from 1.8 million spectra of 1.4 million unique stars targeted by the LSS-GAC between 2011 and 2014. For many studies using this database, such as those investigating the chemodynamical structure of the Milky Way, a detailed understanding of the selection function of the survey is indispensable. In this paper, we describe how the selection function of the LSS-GAC can be evaluated to sufficient detail and provide selection function corrections for all spectroscopic measurements with reliable parameters released in LSS-GAC DR2. The results, to be released as new entries in the LSS-GAC value-added catalogues, can be used to correct the selection effects of the catalogue for scientific studies of various purposes.

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Mapping the three-dimensional dust extinction toward the supernova remnant S147 - the S147 dust cloud

We present a three dimensional (3D) extinction analysis in the region toward the supernova remnant (SNR) S147 (G180.0-1.7) using multi-band photometric data from the Xuyi Schmidt Telescope Photometric Survey of the Galactic Anticentre (XSTPS-GAC), 2MASS and WISE. We isolate a previously unrecognised dust structure likely to be associated with SNR S147. The structure, which we term as "S147 dust cloud", is estimated to have a distance $d$ = 1.22 $\pm$ 0.21 kpc, consistent with the conjecture that S147 is associated with pulsar PSR J0538 + 2817. The cloud includes several dense clumps of relatively high extinction that locate on the radio shell of S147 and coincide spatially with the CO and gamma-ray emission features. We conclude that the usage of CO measurements to trace the SNR associated MCs is unavoidably limited by the detection threshold, dust depletion, and the difficulty of distance estimates in the outer Galaxy. 3D dust extinction mapping may provide a better way to identify and study SNR-MC interactions.

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The LAMOST Spectroscopic Survey of Globular Clusters in M 31 and M 33. I. Catalog and new identifications

We present a catalog of 908 objects observed with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) in the vicinity fields of M31 and M33, targeted as globular clusters (GCs) and candidates. The targets include known GCs and candidates selected from the literature, as well as new candidates selected from the Sloan Digital Sky Survey (SDSS). Analysis shows that 356 of them are likely GCs of various degree of confidence, while the remaining ones turn out to be background galaxies and quasars, stars and HII regions in M31 or foreground Galactic stars. The 356 likely GCs include 298 bona fide GCs and 26 candidates known in the literature. Three candidates selected from the Revised Bologna Catalog of M31 GCs and candidates (RBC) and one possible cluster from Johnson et al. are confirmed to be bona fide clusters. We search for new GCs in the halo of the M31 amongst the new candidates selected from the SDSS photometry. Based on radial velocities yielded by LAMSOT spectra and visual examination of the SDSS images, we find 28 objects, 5 bona fide and 23 likely GCs. Amongst the five bona fide GCs, three have been recently discovered independently by others, the remaining 25 are our new identifications, including two bona fide ones. The new identified objects fall at projected distances ranging from 13 to 265 kpc from M31. Of the two newly discovered bona fide GCs, one is located near M33, probably a GC belonging to M33. The other bona fide GC falls on the Giant Stream with a projected distance of 78 kpc from M31. Of the 23 newly identified likely GCs, one has a projected distance of about 265 kpc from M31 and could be an intergalactic cluster.

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The evolution of stellar metallicity gradients of the Milky Way disk from LSS-GAC main sequence turn-off stars: a two-phase disk formation history?

We use 297 042 main sequence turn-off stars selected from the LSS-GAC to determine the radial and vertical gradients of stellar metallicity of the Galactic disk in the anti-center direction. We determine ages of those turn-off stars by isochrone fitting and measure the temporal variations of metallicity gradients. Our results show that the gradients, both in the radial and vertical directions, exhibit significant spatial and temporal variations. The radial gradients yielded by stars of oldest ages (>11 Gyr) are essentially zero at all heights from the disk midplane, while those given by younger stars are always negative. The vertical gradients deduced from stars of oldest ages (>11Gyr) are negative and show only very weak variations with the Galactocentric distance in the disk plane, $R$, while those yielded by younger stars show strong variations with $R$. After being essentially flat at the earliest epochs of disk formation, the radial gradients steepen as age decreases, reaching a maxima (steepest) at age 7-8 Gyr, and then they flatten again. Similar temporal trends are also found for the vertical gradients. We infer that the assemblage of the Milky Way disk may have experienced at least two distinct phases. The earlier phase is probably related to a slow, pressure-supported collapse of gas, when the gas settles down to the disk mainly in the vertical direction. In the later phase, there are significant radial flows of gas in the disk, and the rate of gas inflow near the solar neighborhood reaches a maximum around a lookback time of 7-8 Gyr. The transition of the two phases occurs around a lookback time between 8 and 11 Gyr. The two phases may be responsible for the formation of the Milky Way thick and thin disks, respectively. And, as a consequence, we recommend that stellar age is a natural, physical criterion to distinguish thin and thick disk stars. ... (abridged)

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DA white dwarfs from the LSS-GAC survey DR1: the preliminary luminosity and mass functions and formation rate

Modern large-scale surveys have allowed the identification of large numbers of white dwarfs. However, these surveys are subject to complicated target selection algorithms, which make it almost impossible to quantify to what extent the observational biases affect the observed populations. The LAMOST (Large Sky Area Multi-Object Fiber Spectroscopic Telescope) Spectroscopic Survey of the Galactic anti-center (LSS-GAC) follows a well-defined set of criteria for selecting targets for observations. This advantage over previous surveys has been fully exploited here to identify a small yet well-characterised magnitude-limited sample of hydrogen-rich (DA) white dwarfs. We derive preliminary LSS-GAC DA white dwarf luminosity and mass functions. The space density and average formation rate of DA white dwarfs we derive are 0.83+/-0.16 x 10^{-3} pc^{-3} and 5.42 +/- 0.08 x 10^{-13} pc^{-3} yr^{-1}, respectively. Additionally, using an existing Monte Carlo population synthesis code we simulate the population of single DA white dwarfs in the Galactic anti-center, under various assumptions. The synthetic populations are passed through the LSS-GAC selection criteria, taking into account all possible observational biases. This allows us to perform a meaningful comparison of the observed and simulated distributions. We find that the LSS-GAC set of criteria is highly efficient in selecting white dwarfs for spectroscopic observations (80-85 per cent) and that, overall, our simulations reproduce well the observed luminosity function. However, they fail at reproducing an excess of massive white dwarfs present in the observed mass function. A plausible explanation for this is that a sizable fraction of massive white dwarfs in the Galaxy are the product of white dwarf-white dwarf mergers.

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Dust-to-gas ratio, $X_{\rm CO}$ factor and CO-dark gas in the Galactic anticentre: an observational study

We investigate the correlation between extinction and H~{\sc i} and CO emission at intermediate and high Galactic latitudes ($|b|>10\degr$) within the footprint of the Xuyi Schmidt Telescope Photometric Survey of the Galactic anticentre (XSTPS-GAC) on small and large scales. In Paper I (Chen et al. 2014), we present a three-dimensional dust extinction map within the footprint of XSTPS-GAC, covering a sky area of over 6,000\,deg$^2$ at a spatial angular resolution of 6\,arcmin. In the current work, the map is combined with data from gas tracers, including H~{\sc i} data from the Galactic Arecibo L-band Feed Array H~{\sc i} survey and CO data from the Planck mission, to constrain the values of dust-to-gas ratio $DGR=A_V/N({\rm H})$ and CO-to-$\rm H_2$ conversion factor $X_{\rm CO}=N({\rm H_2})/W_{\rm CO}$ for the entire GAC footprint excluding the Galactic plane, as well as for selected star-forming regions (such as the Orion, Taurus and Perseus clouds) and a region of diffuse gas in the northern Galactic hemisphere. For the whole GAC footprint, we find $DGR=(4.15\pm0.01) \times 10^{-22}$\,$\rm mag\,cm^{2}$ and $X_{\rm CO}=(1.72 \pm 0.03) \times 10^{20}$\,$\rm cm^{-2}\,(K\,km\,s^{-1})^{-1}$. We have also investigated the distribution of "CO-dark" gas (DG) within the footprint of GAC and found a linear correlation between the DG column density and the $V$-band extinction: $N({\rm DG}) \simeq 2.2 \times 10^{21} (A_V - A^{c}_{V})\,\rm cm^{-2}$. The mass fraction of DG is found to be $f_{\rm DG}\sim 0.55$ toward the Galactic anticentre, which is respectively about 23 and 124 per cent of the atomic and CO-traced molecular gas in the same region. This result is consistent with the theoretical work of Papadopoulos et al. but much larger than that expected in the $\rm H_2$ cloud models by Wolfire et al.

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