We present the results of 0.1-pc-scale observations in 250 GHz and 350GHz towards a newly-discovered hot molecular core in a nearby low-metallicity galaxy, the Large Magellanic Cloud (LMC), with the Atacama Large Millimeter/submillimeter Array. A variety of C/N/O/Si/S-bearing molecules are detected towards the high-mass young stellar object, ST16. A rotating protostellar envelope is for the first time detected outside our Galaxy by SO2 and 34SO lines. An outflow cavity is traced by CCH and CN. The isotope abundance of sulfur in the source is estimated to be 32S/34S = 17 and 32S/33S = 53 based on SO, SO2, and CS isotopologues, suggesting that both 34S and 33S are overabundant in the LMC. Rotation diagram analyses show that the source is associated with hot gas (>100K) traced by high-excitation lines of CH3OH and SO2, as well as warm gas (~50K) traced by CH3OH, SO2, 34SO, OCS, CH3CN lines. A comparison of molecular abundances between LMC and Galactic hot cores suggests that organic molecules (e.g., CH3OH, a classical hot core tracer) show a large abundance variation in low metallicity, where the present source is classified into an organic-poor hot core. Our astrochemical simulations suggest that different grain temperature during the initial ice-forming stage would contribute to the chemical differentiation. In contrast, SO2 shows similar abundances within all the known LMC hot cores and the typical abundance roughly scales with the LMC's metallicity. Nitrogen-bearing molecules are generally less abundant in LMC hot cores, except for NO. The present results suggest that chemical compositions of hot cores do not always simply scale with the metallicity.
We have derived high spatial resolution metallicity maps covering $\sim$42 deg$^2$ across the Small Magellanic Cloud (SMC) in an attempt to understand its metallicity distribution and gradients up to a radius of $\sim$ 4$^{\circ}$. Using the near-infrared VISTA Survey of the Magellanic Clouds, our data cover a thrice larger area compared with previous studies. We identify red giant branch (RGB) stars in spatially distinct $Y, (Y-K_{\rm s})$ colour--magnitude diagrams. In any of our selected subregions, the RGB slope is used as an indicator of the average metallicity, based on calibration to me…
The Cepheid Period-Luminosity (PL) relation is the key tool for measuring astronomical distances and for establishing the extragalactic distance scale. In particular, the local value of the Hubble constant ($H_0$) strongly depends on Cepheid distance measurements. The recent Gaia Data Releases and other parallax measurements from the Hubble Space Telescope (HST) already enabled to improve the accuracy of the slope ($α$) and intercept ($β$) of the PL relation. However, the dependence of this law on metallicity is still largely debated. In this paper, we combine three samples of Cepheids in the …
We have created an estimated metallicity map of the Small Magellanic Cloud (SMC) using the Magellanic Cloud Photometric Survey (MCPS) and Optical Gravitational Lensing Experiment (OGLE III) photometric data. This is a first of its kind map of metallicity up to a radius of $\sim$ 2.5$^{\circ}$. We identify the RGB in the V, (V$-$I) colour magnitude diagrams of small subregions of varying sizes in both data sets. We use the slope of the RGB as an indicator of the average metallicity of a subregion, and calibrate the RGB slope to metallicity using available spectroscopic data for selected subregi…
We present results from the largest CaII triplet line metallicity study of Small Magellanic Cloud (SMC) field red giant stars to date, involving 3037 objects spread across approximately 37.5 sq. deg., centred on this galaxy. We find a median metallicity of [Fe/H]=-0.99+/-0.01, with clear evidence for an abundance gradient of -0.075+/-0.011 dex / deg. over the inner 5 deg. We interpret the abundance gradient to be the result of an increasing fraction of young stars with decreasing galacto-centric radius, coupled with a uniform global age-metallicity relation. We also demonstrate that the age-me…
We have derived high-spatial-resolution metallicity maps covering $\sim$105~deg$^2$ across the Large Magellanic Cloud (LMC) using near-infrared passbands from the VISTA Survey of the Magellanic Clouds. We attempt to understand the metallicity distribution and gradients of the LMC up to a radius of $\sim$ 6~kpc. We identify red giant branch (RGB) stars in spatially distinct $Y, (Y-K_{\rm s})$ colour-magnitude diagrams. In any of our selected subregions, the RGB slope is used as an indicator of the average metallicity, based on calibration to metallicity using spectroscopic data. The mean LMC me…
Using high-quality observed period-luminosity relations in both Magellanic Clouds in VIJHKs bands and optical and near-infrared Wesenheit indices we determine the effect of metallicity on Cepheid P-L relations by comparing the relative distance between LMC and SMC as determined from the Cepheids to the distance difference between the Clouds which has been derived with very high accuracy from late-type eclipsing binary systems. Within an uncertainty of 3% which is dominated by the uncertainty on the mean metallicity difference between the Cepheid populations in LMC and SMC we find metallicity e…
Context: Analysis of ages and metallicities of star clusters in the Magellanic Clouds provide information for studies on the chemical evolution of the Clouds and other dwarf irregular galaxies. Aims: The aim is to derive ages and metallicities from integrated spectra of 14 star clusters in the Small Magellanic Cloud, including a few intermediate/old age star clusters. Methods: Making use of a full-spectrum fitting technique, we compared the integrated spectra of the sample clusters to three different sets of single stellar population models, using two fitting codes available in the literature.…
We present the first metallicity distribution functions of the old field populations in the Magellanic Clouds. Our metallicities are based on the Fourier decomposition of Type ab RR Lyrae light curves from the Optical Gravitational Lensing Experiment (OGLE-III). On the metallicity scale of Zinn & West; we find a mean metallicity of [Fe/H] = -1.50 +/- 0.24 dex based on 16776 RR Lyrae stars in the Large Magellanic Cloud (LMC). For the Small Magellanic Cloud (SMC) we obtain -1.70 +/- 0.27 dex based on 1831 RR Lyrae stars. These uncertainties represent the intrinsic spread in the population rather…
We have estimated a metallicity map of the Large Magellanic Cloud (LMC) using the Magellanic Cloud Photometric Survey (MCPS) and Optical Gravitational Lensing Experiment (OGLE III) photometric data. This is a first of its kind map of metallicity up to a radius of 4 - 5 degrees, derived using photometric data and calibrated using spectroscopic data of Red Giant Branch (RGB) stars. We identify the RGB in the V, (V$-$I) colour magnitude diagrams of small subregions of varying sizes in both data sets. We use the slope of the RGB as an indicator of the average metallicity of a subregion, and calibr…
In an era of extensive photometric observations, the catalogs of RR Lyr type variable stars number tens of thousands of objects. The relation between the iron abundance [Fe/H] and the Fourier parameters of the stars light curve allows us to investigate mean metallicities and metallicity gradients in various stellar environments, independently of time-consuming spectroscopic observations. In this paper we use almost 6500 $V$- and $I$-band light curves of fundamental mode RR Lyr stars from the OGLE-IV survey to provide a relation between the $V$- and $I$-band phase parameter $φ_{31}$ used to est…
Prompted by the ongoing interest in Spitzer Infrared Spectrometer spectra of carbon stars in the Large Magellanic Cloud, we have investigated the circumstellar chemistry of carbon stars in low-metallicity environments. Consistent with observations, our models show that acetylene is particularly abundant in the inner regions of low metallicity carbon-rich AGB stars -- more abundant than carbon monoxide. As a consequence, larger hydrocarbons have higher abundances at the metallicities of the Magellanic Clouds than in stars with solar metallicity. We also find the oxygen and nitrogen chemistry is…
We report new spectroscopic observations obtained with the Michigan/Magellan Fiber System of 308 red giants (RGs) located in two fields near the photometric center of the bar of the Large Magellanic Cloud. This sample consists of 131 stars observed in previous studies (in one field) and 177 newly-observed stars (in the second field) selected specifically to more reliably establish the metallicity and age distributions of the bar. For each star, we measure its heliocentric line-of-sight velocity, surface gravity and metallicity from its high-resolution spectrum (effective temperatures come from…
We report on the spread of [Fe/H] values in the massive Large Magellanic Cloud cluster NGC1978, recently confirmed to harbor multiple populations of nearly the same age. We used accurate Stromgren photometry of carefully selected cluster red giant branch stars along with a high-dispersion spectroscopy-based calibration of the metallicity-sensitive index m1. Once accounting for the photometry quality, assessed from extensive artificial stars tests to trace the photometric uncertainties as a function of the position to the cluster's center as well as the stellar brightness, and those from the me…
X-Shooting ULLYSES: Massive stars at low metallicity XIV. Properties of SMC late-O and B supergiants reveal the metallicity dependence of winds in the Magellanic Clouds
University of Sheffield(谢菲尔德大学);KU Leuven(荷语鲁汶大学);Armagh Observatory and Planetarium(阿马赫天文台和天文馆);Zentrum für Astronomie der Universität Heidelberg, Astronomisches Rechen-Institut(海德堡大学天文学中心,天文计算研究所)
We present results from Washington CT1 photometry for eleven star fields located in the western outskirts of the Small Magellanic Cloud (SMC), which cover angular distances to its centre from 2 up to 13 degrees (~ 2.2 - 13.8 kpc). The colour- magnitude diagrams, cleaned from the unavoidable Milky Way (MW) and background galaxy signatures, reveal that the most distant dominant main sequence (MS) stellar populations from the SMC centre are located at an angular distance of ~ 5.7 deg (6.1 kpc); no sign of farther clear SMC MS is visible other than the residuals from the MW/background field contam…
NGC 796 is a massive young cluster located 59 kpc from us in the diffuse intergalactic medium of the 1/5-1/10 $Z_{\odot}$ Magellanic Bridge, allowing to probe variations in star formation and stellar evolution processes as a function of metallicity in a resolved fashion, providing a link between resolved studies of nearby solar-metallicity and unresolved distant metal-poor clusters located in high-redshift galaxies. In this paper, we present adaptive optics $gri$H$α$ imaging of NGC 796 (at 0.5", which is ~0.14 pc at the cluster distance) along with optical spectroscopy of two bright members to…
We present the results of a photometric survey for Be stars in eleven young clusters in the Large Magellanic Cloud and fourteen young clusters in the Small Magellanic Cloud. B stars with hydrogen in emission are identified on the basis of their R-Hα colour. We find that Be star fraction in clusters decreases with cluster age, and also decreases with the metallicity.
We investigate the infrared (IR) properties of cool, evolved stars in the Small Magellanic Cloud (SMC), including the red giant branch (RGB) stars and the dust-producing red supergiant (RSG) and asymptotic giant branch (AGB) stars using observations from the Spitzer Space Telescope Legacy program entitled: "Surveying the Agents of Galaxy Evolution in the Tidally-stripped, Low Metallicity SMC", or SAGE-SMC. The survey includes, for the first time, full spatial coverage of the SMC bar, wing, and tail regions at infrared (IR) wavelengths (3.6 - 160 microns). We identify evolved stars using a comb…
Period-luminosity relations (PLRs) of type II Cepheids (T2Cs) in the Small Magellanic Cloud are derived based on OGLE-III, IRSF/SIRIUS and other data, and these are compared with results for the Large Magellanic Cloud and Galactic globular clusters. Evidence is found for a change of the PLR slopes from system to system. Treating the longer period T2Cs (W Vir stars) separately gives an SMC-LMC modulus difference of 0.39+-0.05 mag without any metallicity corrections being applied. This agrees well with the difference in moduli based on different distance indicators, in particular the PLRs of cla…
The Magellanic Clouds provide the only laboratory to study the effect of metallicity and galaxy mass on molecular gas and star formation at high (~20 pc) resolution. We use the dust emission from HERITAGE Herschel data to map the molecular gas in the Magellanic Clouds, avoiding the known biases of CO emission as a tracer of H$_{2}$. Using our dust-based molecular gas estimates, we find molecular gas depletion times of ~0.4 Gyr in the LMC and ~0.6 SMC at 1 kpc scales. These depletion times fall within the range found for normal disk galaxies, but are shorter than the average value, which could …
New Optical and Mid-Infrared RR Lyrae Period-Luminosity-Metallicity Relations for Precision Distances and Metallicity Distributions in the Magellanic Clouds
NSF NOIRLab(美国国家光学红外天文研究实验室);University of North Florida(北佛罗里达大学);Vanderbilt University(范德堡大学);Florida State University(佛罗里达州立大学);Università di Roma Tor Vergata(罗马托尔维加塔大学);INAF – Osservatorio Astronomico di Roma(意大利国家天体物理研究所罗马天文台);INFN Sezione di Roma(意大利国家核物理研究所罗马分部);INAF – Osservatorio Astronomico di Abruzzo(意大利国家天体物理研究所阿布鲁佐天文台);INFN, Sezione di Pisa(意大利国家核物理研究所比萨分部);Dartmouth College(达特茅斯学院)
Low- and intermediate-mass stars are one of the important dust sources in the interstellar medium (ISM) of galaxies. The compositions of dust ejected from these stars are likely to affect those in the ISM. We investigate dust in post-Asymptotic Giant Branch (AGB) stars, which are in a late evolutionary phase for low- and intermediate-mass stars, and which produce a wide variety of dust grains. We are particularly targeting post-AGB stars in the Large Magellanic Cloud (LMC), which has about half of the solar metallicity, to investigate the effects of sub-solar metallicity on dust compositions. …
In this work we study 35 stellar clusters in the Small Magellanic Cloud (SMC) in order to provide their mean metallicities and ages. We also provide mean metallicities of the fields surrounding the clusters. We used Strömgren photometry obtained with the 4.1 m SOAR telescope and take advantage of $(b - y)$ and $m1$ colors for which there is a metallicity calibration presented in the literature. The spatial metallicity and age distributions of clusters across the SMC are investigated using the results obtained by Strömgren photometry. We confirm earlier observations that younger, more metal-ric…
The zero point of the reddening toward the Large Magellanic Cloud (LMC) has been the subject of some dispute. Its uncertainty propagates as a systematic error for methods which measure the extragalactic distance scale through knowledge of the absolute extinction of LMC stars. In an effort to resolve this issue, we used three different methods to calibrate the most widely-used metric to predict LMC extinction, the intrinsic color of the red clump, $(V-I)_{RC,0}$, for the inner $\sim$3 degrees of that galaxy. The first approach was to empirically calibrate the color zeropoints of the BaSTI isoch…
We analyze ages and metallicities for some 5.5 million stars distributed throughout the Large Magellanic Cloud (LMC) main body, obtained from CCD Washington CT1 photometry. We produce a comprehensive field star Age-Metallicity Relationship (AMR) from the earliest epoch until ~1 Gyr ago. This AMR reveals that the LMC has not evolved chemically as either a closed-box or bursting system, exclusively, but as a combination of both scenarios that have varied in relative strength over the lifetime of the galaxy, although the bursting model falls closer to the data in general. Furthermore, while old a…
We present results obtained from Stromgren photometry of 13 young (~30-220 Myr) Magellanic Cloud (MC) clusters, most of them lacking in the literature from direct metallicity measurements. We derived for them [Fe/H] values from a high-dispersion spectroscopy-based empirical calibration of the Stromgren metallicity sensitive index m1 for yellow and red supergiants (SGs). Particular care was given while estimating their respective uncertainties. In order to obtain the mean cluster metallicities, we used [Fe/H] values of selected SGs for which we required to be located within the cluster radii, p…
We assemble a catalogue of Magellanic Cloud red giants from Data Release 2 of the $Gaia$ mission and, utilising machine learning methods, obtain photometric metallicity estimates for them. In doing so, we are able to chemically map the entirety of the Magellanic System at once. Our high resolution maps reveal a plethora of substructure, with the Large Magellanic Cloud (LMC) bar and spiral arm being readily apparent. We uncover a curious spiral-like feature in the southern portion of the LMC disc, hosting relatively metal-rich giants and likely a by-product of historic encounter with the Small …
The Large and Small Magellanic Clouds (LMC and SMC), gas-rich dwarf companions of the Milky Way, are the nearest laboratories for detailed studies on the formation and survival of complex organic molecules (COMs) under metal poor conditions. To date, only methanol, methyl formate, and dimethyl ether have been detected in these galaxies - all three toward two hot cores in the N113 star-forming region in the LMC, the only extragalactic sources exhibiting complex hot core chemistry. We describe a small and diverse sample of the LMC and SMC sources associated with COMs or hot core chemistry, and c…
We present results from the analysis of 2997 fundamental mode RR Lyrae variables located in the Small Magellanic Cloud (SMC). For these objects near-infrared time-series photometry from the VISTA survey of the Magellanic Clouds system (VMC) and visual light curves from the OGLE IV survey are available. In this study the multi-epoch $K_{\rm s}$-band VMC photometry was used for the first time to derive intensity-averaged magnitudes of the SMC RR Lyrae stars. We determined individual distances to the RR Lyrae stars from the near-infrared period-absolute magnitude-metallicity ($PM_{K_{\rm s}}Z$) r…
We present C and O abundances in the Magellanic Clouds derived from deep spectra of HII regions. The data have been taken with the Ultraviolet-Visual Echelle Spectrograph at the 8.2-m VLT. The sample comprises 5 HII regions in the Large Magellanic Cloud (LMC) and 4 in the Small Magellanic Cloud (SMC). We measure pure recombination lines (RLs) of CII and OII in all the objects, permitting to derive the abundance discrepancy factors (ADFs) for O^2+, as well as their O/H, C/H and C/O ratios. We compare the ADFs with those of other HII regions in different galaxies. The results suggest a possible …
We present a study of the composition of gas and dust in the Large and Small Magellanic Clouds (LMC and SMC, together -- the MCs) as measured by UV absorption spectroscopy. We have measured P II and Fe II along 85 sightlines toward the MCs using archival FUSE observations. For 16 of those sightlines, we have measured Si II, Cr II, and Zn II from new HST COS observations. We have combined these measurements with H I and H$_2$ column densities and reference stellar abundances from the literature to derive gas-phase abundances, depletions, and gas-to-dust ratios (GDRs). 80 of our 84 P measurement…
We present spectroscopic observations of a sample of 15 embedded young stellar objects (YSOs) in the Large Magellanic Cloud (LMC). These observations were obtained with the Spitzer Infrared Spectrograph (IRS) as part of the SAGE-Spec Legacy program. We analyze the two prominent ice bands in the IRS spectral range: the bending mode of CO_2 ice at 15.2 micron and the ice band between 5 and 7 micron that includes contributions from the bending mode of water ice at 6 micron amongst other ice species. The 5-7 micron band is difficult to identify in our LMC sample due to the conspicuous presence of …
We report for the first time on the magnitude of the intrinsic [Fe/H] spread among ten old globular clusters (GCs) of the Large Magellanic Cloud (LMC). Such spreads are merely observed in approximately five per cent of the Milky Way GCs and recently gained more attention in theoretical models of GC evolution. We derived metallicities with a typical precision of 0.05 dex < sigma[Fe/H] < 0.20 dex for an average of 14 red giant branch stars per GC from Strömgren photometry. The respective, metallicity-sensitive indices have been calibrated to precise and accurate high-dispersion spectroscopy. For…
MAGellanic Outflow and chemistry Survey (MAGOS): Hot cores in the LMC
Institute of Science and Technology, Niigata University(新潟大学科学技术研究院);Institute of Science Tokyo(东京科学研究所);School of Physics and Astronomy, Shanghai Jiao Tong University(上海交通大学物理与天文学院);State Key Laboratory of Dark Matter Physics(暗物质物理全国重点实验室);Key Laboratory for Particle Astrophysics and Cosmology (MOE)(粒子天体物理与宇宙学教育部重点实验室);Shanghai Key Laboratory for Particle Physics and Cosmology(上海粒子物理与宇宙学重点实验室);RIKEN Pioneering Research Institute(理化学研究所前沿研究中心)
The Magellanic Stream (MS) is a well-resolved gaseous tail originating from the Magellanic Clouds. Studies of its physical properties and chemical composition are needed to understand its role in Galactic evolution. We investigate the properties of a compact HVC (CHVC 224.0-83.4-197) lying close on the sky to the MS to determine whether it is physically connected to the Stream and to examine its internal structure. Our study is based on analysis of HST/COS spectra of three QSOs (Ton S210, B0120-28, and B0117-2837) all of which pass through this single cloud at small angular separation (\lessim…
The extragalactic distance scale builds on the Cepheid period-luminosity (PL) relation. In this paper, we want to carry out a strictly differential comparison of the absolute PL relations obeyed by classical Cepheids in the Milky Way (MW), LMC and SMC galaxies. Taking advantage of the substantial metallicity difference among the Cepheid populations in these three galaxies, we want to establish a possible systematic trend of the PL relation absolute zero point as a function of metallicity, and determine the size of such an effect in optical and near-infrared photometric bands. We are using the …
To test the theoretical understanding that finding bright CO emission depends primarily on dust shielding, we investigate the relationship between CO emission ($I_{\rm CO}$) and the amount of dust (estimated from IR emission and expressed as "$A_V$") across the Large Magellanic Cloud, the Small Magellanic Cloud, and the Milky Way. We show that at our common resolution of 10 pc scales, $I_{\rm CO}$ given a fixed line-of-sight $A_V$ is similar across all three systems despite the difference in metallicity. We find some evidence for a secondary dependence of $I_{\rm CO}$ on radiation field; in th…
We report the results of subparsec-scale submillimeter observations towards an embedded high-mass young stellar object in the Small Magellanic Cloud (SMC) with ALMA. Complementary infrared data obtained with the AKARI satellite and the Gemini South telescope are also presented. The target infrared point source is spatially resolved into two dense molecular cloud cores; one is associated with a high-mass young stellar object (YSO core), while another is not associated with an infrared source (East core). The two cores are dynamically associated but show different chemical characteristics. Emiss…
(abridged) The aim of this paper is to investigate the metallicity dependence of the PL relation in V and K, based on a sample of 128 Galactic, 36 LMC, and 6 SMC Cepheids with individual Baade-Wesselink (BW) distances and individually determined metallicities from high-resolution spectroscopy. The p-relation finally adopted is 1.50 -0.24log P. The slope of this relation is based on the condition that the distance to the LMC does not depend on period or (V-K) colour and that the slope of the PL relation based on the BW distances agrees with that based on apparent magnitude. The zero point of th…
The nearby dwarf irregular galaxies the Large and Small Magellanic Clouds have metallicities of about half and a fifth solar, respectively, which offers the unique opportunity to study astrophysical processes as a function of metallicity. Masers in the outflows from evolved stars allow to measure the wind speed, vital to derive mass-loss rates and test wind driving mechanisms. The metallicity dependence of the wind speed in particular allows us to make inferences about dust formation and mass loss in the early Universe. I will review past surveys for circumstellar OH, water, and SiO masers in …
We present 52-93 micron spectra, obtained with the Spitzer Space Telescope, of luminous compact far-IR sources in the SMC. These comprise 9 Young Stellar Objects (YSOs), the compact HII region N81 and a similar object within N84, and two red supergiants (RSGs). The spectra of the sources in N81 (of which we also show the ISO-LWS spectrum between 50-170 micron) and N84 both display strong [OI] 63-micron and [OIII] 88-micron fine-structure line emission. We attribute these lines to strong shocks and photo-ionized gas, respectively, in a ``champagne flow'' scenario. The nitrogen content of these …
The temperatures of red supergiants (RSGs) are expected to depend on metallicity (Z) in such a way that lower-Z RSGs are warmer. In this work, we investigate the Z-dependence of the Hayashi limit by analysing RSGs in the low-Z galaxy Wolf-Lundmark-Mellote (WLM), and compare with the RSGs in the higher-Z environments of the Small Magellanic Cloud (SMC) and Large Magellanic Cloud (LMC). We determine the effective temperature ($T_{\textrm{eff}}$) of each star by fitting their spectral energy distributions, as observed by VLT+SHOOTER, with MARCS model atmospheres. We find average temperatures of $…
The Magellanic Stream (MS) is a massive and extended tail of multi-phase gas stripped out of the Magellanic Clouds and interacting with the Galactic halo. In this first paper of an ongoing program to study the Stream in absorption, we present a chemical abundance analysis based on HST/COS and VLT/UVES spectra of four AGN (RBS 144, NGC 7714, PHL 2525, and HE 0056-3622) lying behind the MS. Two of these sightlines yield good MS metallicity measurements: toward RBS 144 we measure a low MS metallicity of [S/H]=[S II/H I]=-1.13+/-0.16 while toward NGC 7714 we measure [O/H]=[O I/H I]=-1.24+/-0.20. T…
Cold atomic hydrogen clouds are the precursors of molecular clouds. Due to self-absorption, the opacity of cold atomic hydrogen may be high, and this gas may constitute an important mass component of the interstellar medium (ISM). Atomic hydrogen gas can be cooled to temperatures much lower than found in the cold neutral medium (CNM) through collisions with molecular hydrogen. In this paper, we search for HI Narrow Self-Absorption (HINSA) features in the Large Magellanic Cloud (LMC) as an indicator of such cold HI clouds, and use the results to quantify atomic masses and atomic-to-molecular ga…