arXiv subjects

Dennis Stello

Publications and source records attributed to Dennis Stello.

At least 91 records · Page 5Linked to original sources

arXiv2020

Asteroseismology of luminous red giants with Kepler. II. Dependence of mass loss on pulsations and radiation

Mass loss by red giants is an important process to understand the final stages of stellar evolution and the chemical enrichment of the interstellar medium. Mass-loss rates are thought to be controlled by pulsation-enhanced dust-driven outflows. Here we investigate the relationships between mass loss, pulsations, and radiation, using 3213 luminous Kepler red giants and 135000 ASAS-SN semiregulars and Miras. Mass-loss rates are traced by infrared colours using 2MASS and WISE and by observed-to-model WISE fluxes, and are also estimated using dust mass-loss rates from literature assuming a typical gas-to-dust mass ratio of 400. To specify the pulsations, we extract the period and height of the highest peak in the power spectrum of oscillation. Absolute magnitudes are obtained from the 2MASS Ks band and the Gaia DR2 parallaxes. Our results follow. (i) Substantial mass loss sets in at pulsation periods above ~60 and ~100 days, corresponding to Asymptotic-Giant-Branch stars at the base of the period-luminosity sequences C' and C. (ii) The mass-loss rate starts to rapidly increase in semiregulars for which the luminosity is just above the Red-Giant-Branch tip and gradually plateaus to a level similar to that of Miras. (iii) The mass-loss rates in Miras do not depend on luminosity, consistent with pulsation-enhanced dust-driven winds. (iv) The accumulated mass loss on the Red Giant Branch consistent with asteroseismic predictions reduces the masses of red-clump stars by 6.3%, less than the typical uncertainty on their asteroseismic masses. Thus mass loss is currently not a limitation of stellar age estimates for galactic archaeology studies.

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arXiv2020

Testing the intrinsic scatter of the asteroseismic scaling relations with Kepler red giants

Asteroseismic scaling relations are often used to derive stellar masses and radii, particulaly for stellar, exoplanet, and Galactic studies. It is therefore important that their precisions are known. Here we measure the intrinsic scatter of the underlying seismic scaling relations for $Δν$ and $ν_{\rm max}$, using two sharp features that are formed in the H--R diagram (or related diagrams) by the red giant populations. These features are the edge near the zero-age core-helium-burning phase, and the strong clustering of stars at the so-called red giant branch bump. The broadening of those features is determined by factors including the intrinsic scatter of the scaling relations themselves, and therefore it is capable of imposing constraints on them. We modelled Kepler stars with a Galaxia synthetic population, upon which we applied the intrinsic scatter of the scaling relations to match the degree of sharpness seen in the observation. We found that the random errors from measuring $Δν$ and $ν_{\rm max}$ provide the dominating scatter that blurs the features. As a consequence, we conclude that the scaling relations have intrinsic scatter of $\sim0.5\%$ ($Δν$), $\sim1.1\%$ ($ν_{\rm max}$), $\sim1.7\%$ ($M$) and $\sim0.4\%$ ($R$), for the SYD pipeline measured $Δν$ and $ν_{\rm max}$. This confirms that the scaling relations are very powerful tools. In addition, we show that standard evolution models fail to predict some of the structures in the observed population of both the HeB and RGB stars. Further stellar model improvements are needed to reproduce the exact distributions.

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arXiv2020

Prospects for Galactic and stellar astrophysics with asteroseismology of giant stars in the $\it{TESS}$ Continuous Viewing Zones and beyond

The NASA-$\it{TESS}$ mission presents a treasure trove for understanding the stars it observes and the Milky Way, in which they reside. We present a first look at the prospects for Galactic and stellar astrophysics by performing initial asteroseismic analyses of bright ($G < 11$) red giant stars in the $\it{TESS}$ Southern Continuous Viewing Zone (SCVZ). Using three independent pipelines, we detect $ν_{\mathrm{max}}$ and $Δν$ in 41% of the 15,405 star parent sample (6,388 stars), with consistency at a level of $\sim 2\%$ in $ν_{\mathrm{max}}$ and $\sim 5\%$ in $Δν$. Based on this, we predict that seismology will be attainable for $\sim 3\times10^{5}$ giants across the whole sky, subject to improvements in analysis and data reduction techniques. The best quality $\it{TESS}$-CVZ data, for 5,574 stars where pipelines returned consistent results, provide high quality power spectra across a number of stellar evolutionary states. This makes possible studies of, for example, the Asymptotic Giant Branch bump (AGBb). We demonstrate that mixed $\ell=1$ modes and rotational splitting are cleanly observed in the 1-year data set. By combining $\it{TESS}$-CVZ data with $\it{TESS}$-HERMES, $\it{SkyMapper}$, APOGEE and $\it{Gaia}$ we demonstrate the potential for Galactic archaeology studies using the data, which provides good age precision and accuracy that reproduces the age of high $\mathrm{[α/Fe]}$ stars and relationships between mass and kinematics from studies based on $\it{Kepler}$. Better quality astrometry and simpler target selection than the $\it{Kepler}$ sample makes this data ideal for studies of the local star formation history and evolution of the Galactic disc. These results provide a strong case for detailed spectroscopic follow-up in the CVZs to complement that which has been (or will be) collected by current surveys. [Abridged]

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arXiv2020

The K2 Galactic Archaeology Program Data Release 2: Asteroseismic results from campaigns 4, 6, & 7

Studies of Galactic structure and evolution have benefitted enormously from Gaia kinematic information, though additional, intrinsic stellar parameters like age are required to best constrain Galactic models. Asteroseismology is the most precise method of providing such information for field star populations $\textit{en masse}$, but existing samples for the most part have been limited to a few narrow fields of view by the CoRoT and Kepler missions. In an effort to provide well-characterized stellar parameters across a wide range in Galactic position, we present the second data release of red giant asteroseismic parameters for the K2 Galactic Archaeology Program (GAP). We provide $ν_{\mathrm{max}}$ and $Δν$ based on six independent pipeline analyses; first-ascent red giant branch (RGB) and red clump (RC) evolutionary state classifications from machine learning; and ready-to-use radius & mass coefficients, $κ_R$ & $κ_M$, which, when appropriately multiplied by a solar-scaled effective temperature factor, yield physical stellar radii and masses. In total, we report 4395 radius and mass coefficients, with typical uncertainties of $3.3\% \mathrm{\ (stat.)} \pm 1\% \mathrm{\ (syst.)}$ for $κ_R$ and $7.7\% \mathrm{\ (stat.)} \pm 2\% \mathrm{\ (syst.)}$ for $κ_M$ among RGB stars, and $5.0\% \mathrm{\ (stat.)} \pm 1\% \mathrm{\ (syst.)}$ for $κ_R$ and $10.5\% \mathrm{\ (stat.)} \pm 2\% \mathrm{\ (syst.)}$ for $κ_M$ among RC stars. We verify that the sample is nearly complete -- except for a dearth of stars with $ν_{\mathrm{max}} \lesssim 10-20μ$Hz -- by comparing to Galactic models and visual inspection. Our asteroseismic radii agree with radii derived from Gaia Data Release 2 parallaxes to within $2.2 \pm 0.3\%$ for RGB stars and $2.0 \pm 0.6\%$ for RC stars.

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arXiv2020

The GALAH Survey: Dependence of elemental abundances on age and metallicity for stars in the Galactic disc

Using data from the GALAH survey, we explore the dependence of elemental abundances on stellar age and metallicity among Galactic disc stars. We find that the abundance of most elements can be predicted from age and [Fe/H] with an intrinsic scatter of about 0.03 dex. We discuss the possible causes for the existence of the abundance-age-metallicity relations. Using a stochastic chemical enrichment scheme based on the size of Supernovae remnants, we show the intrinsic scatter is expected to be small, about 0.05 dex or even smaller if there is additional mixing in the ISM. Elemental abundances show trends with both age and metallicity and the relationship is well described by a simple model in which the dependence of abundance ([X/Fe]) on age and [Fe/H] are additively separable. Elements can be grouped based on the direction of their abundance gradient in the (age,[Fe/H]) plane and different groups can be roughly associated with three distinct nucleosynthetic production sites, the exploding massive stars, the exploding white dwarfs and the AGB stars. However, the abundances of some elements, like Co, La, and Li, show large scatter for a given age and metallicity, suggesting processes other than simple Galactic chemical evolution are at play. We also compare the abundance trends of main-sequence turn-off stars against that of giants, whose ages were estimated using asteroseismic information from the K2 mission. For most elements, the trends of main-sequence turn-off stars are similar to that of giants. The existence of abundance relations implies that we can estimate the age and birth radius of disc stars, which is important for studying the dynamic and chemical evolution of the Galaxy.

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arXiv2020

The GALAH Survey: Chemical Clocks

Previous studies have found that the elemental abundances of a star correlate directly with its age and metallicity. Using this knowledge, we derive ages for a sample of 250,000 stars taken from GALAH DR3 using only their overall metallicity and chemical abundances. Stellar ages are estimated via the machine learning algorithm $XGBoost$, using main sequence turnoff stars with precise ages as our input training set. We find that the stellar ages for the bulk of the GALAH DR3 sample are accurate to 1-2 Gyr using this method. With these ages, we replicate many recent results on the age-kinematic trends of the nearby disk, including the age-velocity dispersion relationship of the solar neighborhood and the larger global velocity dispersion relations of the disk found using $Gaia$ and GALAH. The fact that chemical abundances alone can be used to determine a reliable age for a star have profound implications for the future study of the Galaxy as well as upcoming spectroscopic surveys. These results show that the chemical abundance variation at a given birth radius is quite small, and imply that strong chemical tagging of stars directly to birth clusters may prove difficult with our current elemental abundance precision. Our results highlight the need of spectroscopic surveys to deliver precision abundances for as many nucleosynthetic production sites as possible in order to estimate reliable ages for stars directly from their chemical abundances. Applying the methods outlined in this paper opens a new door into studies of the kinematic structure and evolution of the disk, as ages may potentially be estimated for a large fraction of stars in existing spectroscopic surveys. This would yield a sample of millions of stars with reliable age determinations, and allow precise constraints to be put on various kinematic processes in the disk, such as the efficiency and timescales of radial migration.

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arXiv2020

The K2 M67 Study: Precise Mass for a Turnoff Star in the Old Open Cluster M67

We present a study of the bright detached eclipsing main sequence binary WOCS 11028 (Sanders 617) in the open cluster M67. Although the binary has only one eclipse per orbital cycle, we show that the masses of the stars can be derived very precisely thanks to a strong constraint on the orbital inclination: $M_A = 1.222\pm0.006 M_\odot$ and $M_B = 0.909\pm0.004 M_\odot$. We use a spectral energy distribution fitting method to derive characteristics of the component stars in lieu of the precise radii that would normally be derived from a doubly-eclipsing binary. The deconvolution of the SEDs reveals that the brighter component of the binary is at the faint turnoff point for the cluster -- a distinct evolutionary point that occurs after the convective core has been established and while the star is in the middle of its movement toward lower surface temperature, before the so-called hook at the end of main sequence. The measurements are in distinct disagreement with evolution models at solar metallicity: higher metal abundances are needed to reproduce the characteristics of WOCS 11028 A. We discuss the changes to model physics that are likely to be needed to address the discrepancies. The clearest conclusions are that diffusion is probably necessary to reconcile spectroscopic abundances of M67 stars with the need for higher metallicity models, and that reduced strength convective overshooting is occurring for stars at the turnoff. At super-solar bulk metallicity, various indicators agree on a cluster age between about 3.5 and 4.0 Gyr.

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arXiv2020

Milky Way Tomography with the SkyMapper Southern Survey. II. Photometric Re-calibration of SMSS DR2

We apply the spectroscopy-based stellar-color regression (SCR) method to perform an accurate photometric re-calibration of the second data release from the SkyMapper Southern Survey (SMSS DR2). From comparison with a sample of over 200,000 dwarf stars with stellar atmospheric parameters taken from GALAH+ DR3 and with accurate, homogeneous photometry from $Gaia$ DR2, zero-point offsets are detected in the original photometric catalog of SMSS DR2, in particular for the gravity- and metallicity-sensitive $uv$ bands. For $uv$ bands, the zero-point offsets are close to zero at very low extinction, and then steadily increase with $E (B - V)$, reaching as large as 0.174 and 0.134 mag respectively, at $E (B - V) \sim 0.5$ mag. These offsets largely arise from the adopted dust term in the transformations used by SMSS DR2 to construct photometric calibrators from the ATLAS reference catalog. For the $gr$ bands, the zero-point offsets exhibit negligible variations with SFD $E(B - V )$, due to their tiny coefficients on the dust term in the transformation. Our study also reveals small, but significant, spatial variations of the zero-point offsets in all $uvgr$ bands. External checks using Strömgren photometry, WD loci and the SDSS Stripe 82 standard-star catalog independently confirm the zero-points found by our revised SCR method.

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arXiv2020

Asteroseismic Inference of Subgiant Evolutionary Parameters with Deep Learning

With the observations of an unprecedented number of oscillating subgiant stars expected from NASA's TESS mission, the asteroseismic characterization of subgiant stars will be a vital task for stellar population studies and for testing our theories of stellar evolution. To determine the fundamental properties of a large sample of subgiant stars efficiently, we developed a deep learning method that estimates distributions of fundamental parameters like age and mass over a wide range of input physics by learning from a grid of stellar models varied in eight physical parameters. We applied our method to four Kepler subgiant stars and compare our results with previously determined estimates. Our results show good agreement with previous estimates for three of them (KIC 11026764, KIC 10920273, KIC 11395018). With the ability to explore a vast range of stellar parameters, we determine that the remaining star, KIC 10005473, is likely to have an age 1 Gyr younger than its previously determined estimate. Our method also estimates the efficiency of overshooting, undershooting, and microscopic diffusion processes, from which we determined that the parameters governing such processes are generally poorly-constrained in subgiant models. We further demonstrate our method's utility for ensemble asteroseismology by characterizing a sample of 30 Kepler subgiant stars, where we find a majority of our age, mass, and radius estimates agree within uncertainties from more computationally expensive grid-based modelling techniques.

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arXiv2020

Asteroseismic masses of four evolved planet-hosting stars using SONG and TESS: resolving the retired A-star mass controversy

The study of planet occurrence as a function of stellar mass is important for a better understanding of planet formation. Estimating stellar mass, especially in the red giant regime, is difficult. In particular, stellar masses of a sample of evolved planet-hosting stars based on spectroscopy and grid-based modelling have been put to question over the past decade with claims they were overestimated. Although efforts have been made in the past to reconcile this dispute using asteroseismology, results were inconclusive. In an attempt to resolve this controversy, we study four more evolved planet-hosting stars in this paper using asteroseismology, and we revisit previous results to make an informed study of the whole ensemble in a self-consistent way. For the four new stars, we measure their masses by locating their characteristic oscillation frequency, $\mathrmν_{\mathrm{max}}$, from their radial velocity time series observed by SONG. For two stars, we are also able to measure the large frequency separation, $\mathrm{Δν}$, helped by extended SONG single-site and dual-site observations and new TESS observations. We establish the robustness of the $\mathrmν_{\mathrm{max}}$-only-based results by determining the stellar mass from $\mathrm{Δν}$, and from both $\mathrm{Δν}$ and $\mathrmν_{\mathrm{max}}$. We then compare the seismic masses of the full ensemble of 16 stars with the spectroscopic masses from three different literature sources. We find an offset between the seismic and spectroscopic mass scales that is mass-dependent, suggesting that the previously claimed overestimation of spectroscopic masses only affects stars more massive than about 1.6 M$_\mathrm{\odot}$.

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arXiv2020

The GALAH Survey: A new constraint on cosmological lithium and Galactic lithium evolution from warm dwarf stars

Lithium depletion and enrichment in the cosmos is not yet well understood. To help tighten constraints on stellar and Galactic evolution models, we present the largest high-resolution analysis of Li abundances A(Li) to date, with results for over 100 000 GALAH field stars spanning effective temperatures $5900\,\mathrm{K} \lesssim \rm{T_{eff}} \lesssim7000\,\mathrm{K}$ and metallicities $-3 \lesssim \rm[Fe/H] \lesssim +0.5$. We separated these stars into two groups, on the warm and cool side of the so-called Li-dip, a localised region of the Kiel diagram wherein lithium is severely depleted. We discovered that stars in these two groups show similar trends in the A(Li)-[Fe/H] plane, but with a roughly constant offset in A(Li) of 0.4 dex, the warm group having higher Li abundances. At $\rm[Fe/H]\gtrsim-0.5$, a significant increasing in Li abundance with increasing metallicity is evident in both groups, signalling the onset of significant Galactic production. At lower metallicity, stars in the cool group sit on the Spite plateau, showing a reduced lithium of around 0.4 dex relative to the primordial value predicted from Big Bang nucleosynthesis (BBN). However, stars in the warm group between [Fe/H] = -1.0 and -0.5, form an elevated plateau that is largely consistent with the BBN prediction. This may indicate that these stars in fact preserve the primordial Li produced in the early Universe.

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arXiv2020

The GALAH survey: Characterization of emission-line stars with spectral modelling using autoencoders

We present a neural network autoencoder structure that is able to extract essential latent spectral features from observed spectra and then reconstruct a spectrum from those features. Because of the training with a set of unpeculiar spectra, the network is able to reproduce a spectrum of high signal-to-noise ratio that does not show any spectral peculiarities even if they are present in an observed spectrum. Spectra generated in this manner were used to identify various emission features among spectra acquired by multiple surveys using the HERMES spectrograph at the Anglo-Australian telescope. Emission features were identified by a direct comparison of the observed and generated spectra. Using the described comparison procedure, we discovered 10,364 candidate spectra with a varying degree of H$α$/H$β$ emission component produced by different physical mechanisms. A fraction of those spectra belongs to the repeated observation that shows temporal variability in their emission profile. Among emission spectra, we find objects that feature contributions of a nearby rarefied gas (identified through the emission of [NII] and [SII] lines) that was identified in 4004 spectra, which were not all identified as having H$α$ emission. Positions of identified emission-line objects coincide with multiple known regions that harbour young stars. Similarly, detected nebular emission spectra coincide with visually-prominent nebular clouds observable in the red all-sky photographic composites.

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arXiv2020

Asteroseismology of 36 Kepler subgiants -- II: Determining ages from detailed modelling

Detailed modelling of stellar oscillations is able to give precise estimates for stellar ages, but the inferred results typically depend on the adopted model parameters used for the age inference. High-quality asteroseismic data with precise measurements of mixed modes are available for 36 Kepler subgiants. To obtain a handle on the robustness of the ages for these stars, we first study the dependencies of seismic ages on three model input parameters. We find that inferred ages do not change systematically with the helium fraction (Y) or the mixing-length parameter but depend strongly on the metallicity ([M/H]) of the model. The results indicate that age estimates of subgiants have less model dependence and hence are more reliable than those of main-sequence stars or red giants. We then model individual oscillation frequencies of the same 36 Kepler subgiants, using observed metallicities, and obtain their ages with an average precision of ~15%. The comparison with previous age estimates with different stellar codes or input physics shows good agreement (mostly within 2#). We hence suggest that seismology-determined ages of subgiants are not greatly model-dependent.

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arXiv2020

K2-HERMES II. Planet-candidate properties from K2 Campaigns 1-13

Accurate and precise radius estimates of transiting exoplanets are critical for understanding their compositions and formation mechanisms. To know the planet, we must know the host star in as much detail as possible. We present complete results for planet-candidate hosts from the K2-HERMES survey, which uses the HERMES multi-object spectrograph on the Anglo-Australian Telescope to obtain R$\sim$28,000 spectra for more than 30,000 K2 stars. We present complete host-star parameters and planet-candidate radii for 224 K2 candidate planets from C1-C13. Our results cast severe doubt on 30 K2 candidates, as we derive unphysically large radii, larger than 2 $R_{Jup}$. This work highlights the importance of obtaining accurate, precise, and self-consistent stellar parameters for ongoing large planet search programs - something that will only become more important in the coming years, as TESS begins to deliver its own harvest of exoplanets.

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arXiv2020

Very regular high-frequency pulsation modes in young intermediate-mass stars

Asteroseismology is a powerful tool for probing the internal structures of stars by using their natural pulsation frequencies. It relies on identifying sequences of pulsation modes that can be compared with theoretical models, which has been done successfully for many classes of pulsators, including low-mass solar-type stars, red giants, high-mass stars and white dwarfs. However, a large group of pulsating stars of intermediate mass--the so-called delta Scuti stars--have rich pulsation spectra for which systematic mode identification has not hitherto been possible. This arises because only a seemingly random subset of possible modes are excited, and because rapid rotation tends to spoil the regular patterns. Here we report the detection of remarkably regular sequences of high-frequency pulsation modes in 60 intermediate-mass main-sequence stars, allowing definitive mode identification. Some of these stars have space motions that indicate they are members of known associations of young stars, and modelling of their pulsation spectra confirms that these stars are indeed young.

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arXiv2020

Asteroseismology of 36 \emph{Kepler} subgiants -- I. Oscillation frequencies, linewidths and amplitudes

The presence of mixed modes makes subgiants excellent targets for asteroseismology, providing a probe for the internal structure of stars. Here we study 36 \emph{Kepler} subgiants with solar-like oscillations and report their oscillation mode parameters. We performed a so-called peakbagging exercise, i.e. estimating oscillation mode frequencies, linewidths, and amplitudes with a power spectrum model, fitted in the Bayesian framework and sampled with a Markov Chain Monte Carlo algorithm. The uncertainties of the mode frequencies have a median value of 0.180 $μ$Hz. We obtained seismic parameters from the peakbagging, analysed their correlation with stellar parameters, and examined against scaling relations. The behaviour of seismic parameters (e.g. $Δν$, $ν_{\rm max}$, $ε_p$) is in general consistent with theoretical predictions. We presented the observational p--g diagrams: $γ_1$--$Δν$ for early subgiants and $ΔΠ_1$--$Δν$ for late subgiants, and demonstrate their capability to estimate stellar mass. We also found a $\log g$ dependence on the linewidths and a mass dependence on the oscillation amplitudes and the widths of oscillation excess. This sample will be valuable constraints for modelling stars and studying mode physics such as excitation and damping.

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arXiv2020

Beyond Gaia: Asteroseismic Distances of M giants using Ground-Based Transient Surveys

Evolved stars near the tip of the red giant branch (TRGB) show solar-like oscillations with periods spanning hours to months and amplitudes ranging from $\sim$1 mmag to $\sim$100 mmag. The systematic detection of the resulting photometric variations with ground-based telescopes would enable the application of asteroseismology to a much larger and more distant sample of stars than is currently accessible with space-based telescopes such as \textit{Kepler} or the ongoing Transiting Exoplanet Survey Satellite (\textit{TESS}) mission. We present an asteroseismic analysis of 493 M giants using data from two ground-based surveys: the Asteroid Terrestrial-impact Last Alert System (ATLAS) and the All-Sky Automated Survey for Supernovae (ASAS-SN). By comparing the extracted frequencies with constraints from \textit{Kepler}, the Sloan Digital Sky Survey Apache Point Observatory Galaxy Evolution Experiment (APOGEE), and Gaia we demonstrate that ground-based transient surveys allow accurate distance measurements to oscillating M giants with a precision of $\sim$15$\%$. Using stellar population synthesis models we predict that ATLAS and ASAS-SN can provide asteroseismic distances to $\sim$2$\times$10$^{6}$ galactic M giants out to typical distances of $20-50 \; \rm{kpc}$, vastly improving the reach of Gaia and providing critical constraints for Galactic archaeology and galactic dynamics.

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arXiv2020

Fundamental relations for the velocity dispersion of stars in the Milky Way

We explore the fundamental relations governing the radial and vertical velocity dispersions of stars in the Milky Way, from combined studies of complementary surveys including GALAH, LAMOST, APOGEE, the NASA $Kepler$ and K2 missions, and $Gaia$ DR2. We find that different stellar samples, even though they target different tracer populations and employ a variety of age estimation techniques, follow the same set of fundamental relations. We provide the clearest evidence to date that, in addition to the well-known dependence on stellar age, the velocity dispersions of stars depend on orbital angular momentum $L_z$, metallicity and height above the plane $|z|$, and are well described by a multiplicatively separable functional form. The dispersions have a power-law dependence on age with exponents of 0.441$\pm 0.007$ and 0.251$\pm 0.006$ for $σ_z$ and $σ_R$ respectively, and the power law is valid even for the oldest stars. For the solar neighborhood stars, the apparent break in the power law for older stars, as seen in previous studies, is due to the anti-correlation of $L_z$ with age. The dispersions decrease with increasing $L_z$ until we reach the Sun's orbital angular momentum, after which $σ_z$ increases (implying flaring in the outer disc) while $σ_R$ flattens. The dispersions increase with decreasing metallicity, suggesting that the dispersions increase with birth radius. The dispersions also increase linearly with $|z|$. The same set of relations that work in the solar neighborhood also work for stars between $3<R/{\rm kpc}<20$. Finally, the high-[$α$/Fe] stars follow the same relations as the low-[$α$/Fe] stars.

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