Gregory M. Green, Edward F. Schlafly, Douglas P. Finkbeiner, Hans-Walter Rix, Nicolas Martin, William Burgett, Peter W. Draper, Heather Flewelling, Klaus Hodapp… 展开作者
Gregory M. Green, Edward F. Schlafly, Douglas P. Finkbeiner, Hans-Walter Rix, Nicolas Martin, William Burgett, Peter W. Draper, Heather Flewelling, Klaus Hodapp, Nicholas Kaiser, Rolf Peter Kudritzki, Eugene Magnier, Nigel Metcalfe, Paul Price, John Tonry, Richard Wainscoat
We present a three-dimensional map of interstellar dust reddening, covering three-quarters of the sky out to a distance of several kiloparsecs, based on Pan-STARRS 1 and 2MASS photometry. The map reveals a wealth of detailed structure, from filaments to large cloud complexes. The map has a hybrid angular resolution, with most of the map at an angular resolution of 3.4' to 13.7', and a maximum distance resolution of ~25%. The three-dimensional distribution of dust is determined in a fully probabilistic framework, yielding the uncertainty in the reddening distribution along each line of sight, as well as stellar distances, reddenings and classifications for 800 million stars detected by Pan-STARRS 1. We demonstrate the consistency of our reddening estimates with those of two-dimensional emission-based maps of dust reddening. In particular, we find agreement with the Planck 353 GHz optical depth-based reddening map to within 0.05 mag in E(B-V) to a depth of 0.5 mag, and explore systematics at reddenings less than E(B-V) ~ 0.08 mag. We validate our per-star reddening estimates by comparison with reddening estimates for stars with both SDSS photometry and SEGUE spectral classifications, finding per-star agreement to within 0.1 mag out to a stellar E(B-V) of 1 mag. We compare our map to two existing three-dimensional dust maps, by Marshall et al. (2006) and Lallement et al. (2013), demonstrating our finer angular resolution, and better distance resolution compared to the former within ~3 kpc. The map can be queried or downloaded at http://argonaut.skymaps.info. We expect the three-dimensional reddening map presented here to find a wide range of uses, among them correcting for reddening and extinction for objects embedded in the plane of the Galaxy, studies of Galactic structure, calibration of future emission-based dust maps and determining distances to objects of known reddening.
Aims: We show the existence of a small family of inner-galaxy dust lanes and dust lane standing shocks beyond the two major ones that were previously known to exist Methods: We analyze images of CO emission in the inner regions of the Galaxy Results: The peculiar kinematics of the major dust lane features are repeated in several other distinct instances at l > 0deg, in one case at a contrary location 100 pc above the galactic equator at l > 3degr at the upper extremity of Clump 2. Like the previously-known dust lanes, these new examples are alsoassociated with localized, exceptionally broad li…
To a great extent, our understanding of the life cycle of dust is based on the observational and theoretical studies of the Milky Way and the Magellanic Clouds, which will be the topic of this contribution. Over past years, a large volume of observations with unprecedented spatial resolution has been accumulated for the Milky Way. It permits investigations of different stages of the life cycle of dust, from its formation in stellar sources to destruction in star-forming regions and supernovae shocks. Observations of dust emission, extinction, polarisation of light, and interstellar element dep…
We present a three-dimensional modeling of the Milky Way dust distribution by fitting the value-added star catalog of LAMOST spectral survey. The global dust distribution can be described by an exponential disk with scale-length of 3,192 pc and scale height of 103 pc. In this modeling, the Sun is located above the dust disk with a vertical distance of 23 pc. Besides the global smooth structure, two substructures around the solar position are also identified. The one located at $150^{\circ}<l<200^{\circ}$ and $-5^{\circ}<b<-30^{\circ}$ is consistent with the Gould Belt model of \citet{Gontcharo…
Large stellar surveys are sensitive to interstellar dust through the effects of reddening. Using extinctions measured from photometry and spectroscopy, together with three-dimensional (3D) positions of individual stars, it is possible to construct a three-dimensional dust map. We present the first continuous map of the dust distribution in the Galactic disk out to 7 kpc within 100 pc of the Galactic midplane, using red clump and giant stars from SDSS APOGEE DR14. We use a non-parametric method based on Gaussian Processes to map the dust density, which is the local property of the ISM rather th…
To understand how the evolution of grain size distribution in galaxies affects observed dust properties, we apply a post-processing dust evolution model to galaxy merger trees from the IllustrisTNG cosmological hydrodynamical simulation. Our dust model includes stellar dust production, sputtering in hot gas, dust growth by accretion and coagulation in the dense interstellar medium (ISM), and shattering in the diffuse ISM. We decompose the grain size distribution into different dust species depending on the elemental abundances and the dense ISM fraction given by the simulation. In our previous…
Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学前沿天文与天体物理研究所）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）；Department of Astronomy, Tsinghua University（清华大学天文系）；South-Western Institute for Astronomy Research, Yunnan University（云南大学西南天文研究所）；Key Lab of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台光学天文重点实验室）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）
We develop a cosmological model for the evolution of dust grains in galaxies with a distribution of sizes in order to understand the origin of the Milky Way dust extinction curve. Our model considers the formation of active dust in evolved stars, growth by accretion and coagulation, and destruction processes via shattering, sputtering, and astration in the ISM of galaxies over cosmic time. Our main results follow. Galaxies in our cosmological model with masses comparable to the Milky Way's at z~0 exhibit a diverse range of extinction laws, though with slopes and bump strengths comparable to th…
The mean absolute extinction towards the central parsec of the Milky Way is A_K~3 mag, including both foreground and Galactic center dust. Here we present a measurement of dust extinction within the Galactic old nuclear star cluster (NSC), based on combining differential extinctions of NSC stars with their u_l proper motions along Galactic longitude. Extinction within the NSC preferentially affects stars at its far side, and because the NSC rotates, this causes higher extinctions for NSC stars with negative u_l, as well as an asymmetry in the u_l-histograms. We model these effects using an axi…
We model dust evolution in Milky Way-like galaxies by post-processing the IllustrisTNG cosmological hydrodynamical simulations in order to predict dust-to-gas ratios and grain size distributions. We treat grain-size-dependent dust growth and destruction processes using a 64-bin discrete grain size evolution model without spatially resolving each galaxy. Our model broadly reproduces the observed dust--metallicity scaling relation in nearby galaxies. The grain size distribution is dominated by large grains at $z\gtrsim 3$ and the small-grain abundance rapidly increases by shattering and accretio…
We present a new two-component dust geometry model, the \textit{Chocolate Chip Cookie} model, where the clumpy nebular regions are embedded in a diffuse stellar/ISM disk, like chocolate chips in a cookie. By approximating the binomial distribution of the clumpy nebular regions with a continuous Gaussian distribution and omitting the dust scattering effect, our model solves the dust attenuation process for both the emission lines and stellar continua via analytical approaches. Our Chocolate Chip Cookie model successfully fits the inclination dependence of both the effective dust reddening of th…
The study of the Milky Way structure is vital importance for a better understanding of the universe. This study digs deeper into the structure of Milky Way Galaxys with emphasis to its spiral arms. Multiple data sources were sought including the NASA websites. As found out, the Milky Way is a disk shaped galaxy composed of four spiral arms, two large and the rest are smaller. The spiral arms are regions of actively forming new stars dominated by young stars, dust and gas. Dust and gas are primary materials for the formation of new stars. This dust is also responsible for the reddish appearance…
An updated catalog of 205 observed tangents to the spiral arms (in Galactic longitudes) since 1980 is presented. This represents an addition of 80 arm tangents in 6 years (since 2016). Most arm tangents are observed at telescopes in the radio regime. In this study, the separation of each arm tracer from the dust lane is analyzed to obtain the relative speed away from the dust lane (an age gradient). Each arm tracer is observed to be separated from the dust lane, showing an age gradient of about 11.3 +/- 2 Myr/kpc across the spiral arm; this gives a relative speed away from the dust lane of abo…
We constrain the light extinction properties of Milky Way dust. We investigated the correlations between dust column density as inferred from infrared data and the observed colours of celestial objects at cosmological distances with low levels of colour dispersion. Results derived using colours of quasars, brightest central galaxies, and luminous red galaxies are broadly consistent, indicating a proportionality constant between the reddening E(B-V)=A_B-A_V and the dust column density D^T (given in units of MJy/sr) of p=E(B-V)/D^T=0.02 and a reddening parameter R_V=A_V/E(B-V)=3 with fractional …
The evolution of the metal content of the universe can be tracked through rest-frame UV spectroscopy of damped Ly-$α$ systems (DLAs). Gas-phase abundances in DLAs must be corrected for dust depletion effects, which can be accomplished by calibrating the relation between abundance ratios such as [Zn/Fe] and depletions (the fraction of metals in gas, as opposed to dust). Using samples of gas-phase abundances and depletions in the Milky Way (MW), LMC, and SMC, we demonstrate that the relation between [Zn/Fe] and other abundance ratios does not change significantly between these local galaxies and…
We present redshift-zero synthetic observational data considering dust attenuation and dust emission for the thirty galaxies of the Auriga project, calculated with the SKIRT radiative transfer code. The post-processing procedure includes components for star-forming regions, stellar sources, and diffuse dust taking into account stochastic heating of dust grains. This allows us to obtain realistic high-resolution broadband images and fluxes from ultraviolet to sub-millimeter wavelengths. For the diffuse dust component, we consider two mechanisms for assigning dust to gas cells in the simulation.…
We introduce a dust model for cosmological simulations implemented in the moving-mesh code AREPO and present a suite of cosmological hydrodynamical zoom-in simulations to study dust formation within galactic haloes. Our model accounts for the stellar production of dust, accretion of gas-phase metals onto existing grains, destruction of dust through local supernova activity, and dust driven by winds from star-forming regions. We find that accurate stellar and active galactic nuclei feedback is needed to reproduce the observed dust-metallicity relation and that dust growth largely dominates dust…
We use $Gaia$ eDR3 data and legacy spectroscopic surveys to map the Milky Way disc substructure towards the Galactic Anticenter at heliocentric distances $d\geq10\,\rm{kpc}$. We report the discovery of multiple previously undetected new filaments embedded in the outer disc in highly extincted regions. Stars in these over-densities have distance gradients expected for disc material and move on disc-like orbits with $v_ϕ\sim170-230\,\rm{km\,s^{-1}}$, showing small spreads in energy. Such a morphology argues against a quiescently growing Galactic thin disc. Some of these structures are interprete…
Dust properties appear to vary according to the environment in which the dust evolves. Previous observational indications of these variations in the FIR and submm spectral range are scarce and limited to specific regions of the sky. To determine whether these results can be generalised to larger scales, we study the evolution in dust emissivities from the FIR to mm wavelengths, in the atomic and molecular ISM, along the Galactic plane towards the outer Galaxy. We correlate the dust FIR to mm emission with the HI and CO emission. The study is carried out using the DIRBE data from 100 to 240 mic…
In this paper we present the CMZoom Survey's catalog of compact sources (< 10'', ~0.4pc) within the Central Molecular Zone (CMZ). CMZoom is a Submillimeter Array (SMA) large program designed to provide a complete and unbiased map of all high column density gas (N(H$_2$) $\geq$ 10$^{23}$ cm$^{-2}$) of the innermost 500pc of the Galaxy in the 1.3mm dust continuum. We generate both a robust catalog designed to reduce spurious source detections, and a second catalog with higher completeness, both generated using a pruned dendrogram. In the robust catalog, we report 285 compact sources, or 816 in t…
We observe the density wave angular pattern speed OMEGA-p to be near 12 to 17 km / s / kpc, by the separation between a typical optical HII region (from the spiral arm dust lane) and using a HII evolution time model to yield its relative speed, and independently by the separation between a typical radio maser (from the spiral arm dust lane) with a maser model.
From the Sun, a look at the edge of each spiral arm in our Milky Way (seen tangentially, along the line of sight) can yield numerous insights. Using different arm tracers (dust, masers, synchrotron emission, CO gas, open star clusters), we observe here for the first time an age gradient (about 12 +/-2 Myrs/kpc), much as predicted by the density wave theory. This implies that the arm tracers are leaving the dust lane at a relative speed of about 81 +/-10 km/s. We then compare with recent optical data obtained from the Gaia satellite, pertaining to the spiral arms.
We aim to compare variations in the full-UV dust extinction curve (912-3000 Angstrom), with the HI/H$_2$/total H content along diffuse Milky Way sightlines, to investigate possible connections between ISM conditions and dust properties. We combine an existing sample of 75 UV extinction curves based on IUE and FUSE data, with atomic and molecular column densities measured through UV absorption. The H$_2$ column density data are based on existing Lyman-Werner absorption band models from earlier work on the extinction curves. Literature values for the HI column density were compiled, and improved…
The high cosmological precision offered by the next generation of galaxy surveys hinges on improved corrections for Galactic dust extinction. We explore the possibility of estimating both the dust extinction and large-scale structure from a single photometric galaxy survey, making use of the predictable manner in which Milky Way dust affects the measured brightness and colors of galaxies in a given sky location in several redshift bins. To test our method, we use a synthetic catalog from a cosmological simulation designed to model the Vera C. Rubin Observatory Legacy Survey of Space and Time. …
We investigate reddening by Milky Way dust in the low-extinction regime of $E_{B-V}<0.15$. Using over 50,000 QSOs at $0.5<z<2.5$ from the SDSS DR7 QSO Catalogue we probe the residual SDSS colours after dereddening and correcting for the known spectroscopic redshifts. We find that the extinction vector of Schlafly & Finkbeiner (2011) is a better fit to the data than that used by Schlegel et al. (1998, SFD). There is evidence for a non-linearity in the SFD reddening map, which is similarly present in the V1.2 map of the Planck Collaboration. This non-linearity is similarly seen when galaxies or …
(Aims) In this work, we predict the far-infrared polarisation signal emitted by non-spherical dust grains in nearby galaxies. We determine the angular resolution and sensitivity required to study the magnetic field configuration in these galaxies. (Methods) We post-process a set of Milky Way like galaxies from the Auriga project, assuming a dust mix consisting of spheroidal dust grains that are partially aligned with the model magnetic field. We constrain our dust model using Planck 353 GHz observations of the Milky Way. This model is then extrapolated to shorter wavelengths that cover the pea…
We present redshift-zero synthetic dust-aware observations for the 45 Milky Way-mass simulated galaxies of the ARTEMIS project, calculated with the SKIRT radiative transfer code. The post-processing procedure includes components for star-forming regions, stellar sources, and diffuse dust. We produce and publicly release realistic high-resolution images for 50 commonly-used broadband filters from ultraviolet to sub-millimetre wavelengths and for 18 different viewing angles. We compare the simulated ARTEMIS galaxies to observed galaxies in the DustPedia database with similar stellar mass and sta…
The Planck-HFI all-sky survey from 353 to 857GHz combined with the 100 microns IRAS show that the dust properties vary in the diffuse ISM at high Galactic latitude (1e19<NH<2.5e20 H/cm2). Our aim is to explain these variations with changes in the ISM properties and grain evolution. Our starting point is the latest core-mantle dust model. It consists of small aromatic-rich carbon grains, larger amorphous carbon grains with aliphatic-rich cores and aromatic-rich mantles, and amorphous silicates with Fe/FeS nano-inclusions covered by aromatic-rich carbon mantles. We explore whether variations in …
A first taste of MEAD (Measuring Extinction and Abundances of Dust) -- I. Diffuse Milky Way interstellar dust extinction features in JWST infrared spectra
Near-infrared spectroscopy from APOGEE and wide-field optical photometry from Pan-STARRS1 have recently made possible precise measurements of the shape of the extinction curve for tens of thousands of stars, parameterized by R(V). These measurements revealed structures in R(V) with large angular scales, which are challenging to explain in existing dust paradigms. In this work, we combine three-dimensional maps of dust column density with R(V) measurements to constrain the three-dimensional distribution of R(V) in the Milky Way. We find that variations in R(V) are correlated on kiloparsec scale…
The mass fraction of dense gas within giant molecular clouds (GMCs) of the Milky Way is investigated using 13CO data from the FCRAO Galactic Plane Surveys and the Bolocam Galactic Plane Survey (BGPS) of 1.1 mm dust continuum emission. A sample of 860 compact dust sources are selected from the BGPS catalog and kinematically linked to 344 clouds of extended (>3') 13CO J=1-0 emission. Gas masses are tabulated for the full dust source and subregions within the dust sources with mass surface densities greater than 200 M_solar/pc^2, which are assumed to be regions of enhanced volume density. Masses …
We use SDSS photometry of 73 million stars to simultaneously obtain best-fit main-sequence stellar energy distribution (SED) and amount of dust extinction along the line of sight towards each star. Using a subsample of 23 million stars with 2MASS photometry, whose addition enables more robust results, we show that SDSS photometry alone is sufficient to break degeneracies between intrinsic stellar color and dust amount when the shape of extinction curve is fixed. When using both SDSS and 2MASS photometry, the ratio of the total to selective absorption, $R_V$, can be determined with an uncertain…
We investigate the metallicity distribution function (MDF) in the Galactic halo and the relative fraction of Carbon-normal and Carbon-rich stars. To this aim, we use an improved version of the semi-analytical code GAlaxy MErger Tree and Evolution (GAMETE), that reconstructs the hierarchical merger tree of the MW, following the star formation history and the metal and dust evolution in individual progenitors. The predicted scaling relations between the dust, metal and gas masses for MW progenitors show a good agreement with observational data of local galaxies and of Gamma Ray Burst (GRB) host …
Some important predictions from 4 main models of spiral arm formation are tested here, using observational data acquired for the Milky Way galaxy. Many spiral arm models (density wave, tidal wave, nuclear Lyapunov tube, or dynamic transient wave) have some consistencies with some of the observations, and some inconsistencies. Our 4 tests consist of the relative locations and relative speeds of different arm tracers away from the dust lane, and the global arm pitch angle as obtained over two Galactic quadrants and several Galactic radii, as well as the arm's continuity of shape from Galactic qu…
Here we investigate the origin of the dust mass (Mdust) observed in the Milky Way (MW) and of dust scaling relations found in a sample of local galaxies from the DGS and KINGFISH surveys. To this aim, we model dust production from Asymptotic Giant Branch (AGB) stars and supernovae (SNe) in simulated galaxies forming along the assembly of a Milky Way-like halo in a well resolved cosmic volume of 4cMpc using the GAMESH pipeline. We explore the impact of different sets of metallicity and mass-dependent AGB and SN dust yields on the predicted Mdust. Our results show that models accounting for grai…
We compute the evolution of the grain size distribution (GSD) in a suite of numerical simulations of an isolated Milky-Way-like galaxy using the $N$-body/smoothed-particle-hydrodynamics code {\sc Gadget-4}. The full GSD is sampled on a logarithmically spaced grid with 30 bins, and its evolution is calculated self-consistently with the hydrodynamical and chemical evolution of the galaxy using a state-of-the-art star formation and feedback model. In previous versions of this model, the GSD tended to be slightly biased towards larger grains and the extinction curve had a tendency to be flatter th…
Stellar feedback created by radiation and winds from massive stars plays a significant role in both physical and chemical evolution of molecular clouds. This energy and momentum leaves an identifiable signature ("bubbles") that affect the dynamics and structure of the cloud. Most bubble searches are performed "by-eye", which are usually time-consuming, subjective and difficult to calibrate. Automatic classifications based on machine learning make it possible to perform systematic, quantifiable and repeatable searches for bubbles. We employ a previously developed machine learning algorithm, Bru…
Large fractions of metals are missing from the observable gas-phase in the interstellar medium (ISM) because they are incorporated into dust grains, a phenomenon called dust depletion. The study of dust depletion in the ISM is important to investigate the origin and evolution of metals and cosmic dust. Here we aim at characterizing the dust depletion of several metals from the Milky Way to distant galaxies. We collect ISM metal column densities from absorption-line spectroscopy in the literature, and in addition, we determine Ti and Ni column densities from a sample of 70 damped Lyman-$α$ abso…
Hiding behind a curtain of dust: Gas and dust properties of an ultra-luminous strongly-lensed z = 3.75 galaxy behind the Milky Way disk
ESO（欧洲南方天文台）；SKA Observatory（平方公里阵列望远镜观测站）；Joint ALMA Observatory（阿塔卡马大型毫米波/亚毫米波阵列联合观测站）；National Astronomical Observatory of Japan（日本国立天文台）；Durham University（杜伦大学）；University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校）
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…
Models of chemical evolution of galaxies including the dust are nowadays required to decipher the high-z universe. In a series of three papers we have tackled the problem and set a modern chemical evolution model. In the first paper (Piovan et al., 2011a) we revised the condensation coefficients for the elements that typically are present in the dust. In the second paper (Piovan et al., 2011b) we have implemented the dust into the Padova chemical model and tested it against the observational data for the Solar Neighbourhood. In this paper we extend it to the whole Disk of the Milky Way (MW). T…
Interstellar dust extinction curves provide valuable information about dust properties, including the composition and size of the dust grains, and are essential to correct observations for the effects of interstellar dust. In this work, we measure a representative sample of near-infrared (NIR; 0.8-5.5 $μ$m) spectroscopic extinction curves for the first time, enabling us to investigate the extinction at wavelengths where it is usually only measured in broad photometric bands. We use IRTF/SpeX spectra of a sample of reddened and comparison stars to measure 15 extinction curves with the pair meth…
Milky Way Atlas: A radial-velocity-resolved, three-dimensional map of H I within 1.25 kpc
RWTH Aachen University（亚琛工业大学）；Max Planck Institute for Astrophysics（马克斯·普朗克天体物理研究所）；Max Planck Computing and Data Facility（马克斯·普朗克计算与数据中心）；University of Vienna（维也纳大学）；Deutsches Zentrum für Astrophysik（德国天体物理学中心）；Ludwig-Maximilians-Universität München（慕尼黑大学）
In this work, we derive a spatially resolved map of the line-of-sight velocity of the interstellar medium and use it, along with a second map of line-of-sight velocity from Paper I of this series, to determine the nature of gaseous spiral structure in the Milky Way. This map is derived from measurements of the 1.527 $μ$m diffuse interstellar band (DIB) in stellar spectra from the APOGEE survey and covers the nearest 4-5 kpc of the Northern Galactic plane. We cross-check this new DIB-based line-of-sight velocity map with the map derived in Paper I and find that they agree. We then compare these…
The Galactic bar plays a critical role in the evolution of the Milky Way's Central Molecular Zone (CMZ), driving mass inward toward the Galactic Center via gas flows known as dust lanes. To explore the interaction between the CMZ and the dust lanes, we run hydrodynamic simulations in AREPO, modeling the potential of the Milky Way's bar in the absence of gas self-gravity and star formation physics, and we study the flows of mass using Monte Carlo tracer particles. We estimate the efficiency of the inflow via the dust lanes, finding that only about a third (30$\pm$12%) of the dust lanes' mass in…
Three dimensional interstellar extinction maps provide a powerful tool for stellar population analysis. We use data from the VISTA Variables in the Via Lactea survey together with the Besançon stellar population synthesis model of the Galaxy to determine interstellar extinction as a function of distance in the Galactic bulge covering $ -10 < l < 10$ and $-10 < b <5$. We adopted a recently developed method to calculate the colour excess. First we constructed the H-Ks vs. Ks and J-Ks vs. Ks colour-magnitude diagrams based on the VVV catalogues that matched 2MASS. Then, based on the temperature-c…
We measure the optical spectrum of the Diffuse Galactic Light (DGL) -- the local Milky Way in reflection -- using 92,000 blank-sky spectra from the Sloan Digital Sky Survey (SDSS). We correlate the SDSS optical intensity in regions of blank sky against 100 micron intensity independently measured by the COsmic Background Explorer (COBE) and InfraRed Astronomy Satellite (IRAS) satellites, which provides a measure of the dust column density times the intensity of illuminating starlight. The spectrum of scattered light is very blue and shows a clear 4000 Angstrom break and broad Mg b absorption. T…
