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Register a new userSimple and accurate modelling of the gravitational potential produced by thick and thin exponential disks
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We present accurate models of the gravitational potential produced by a radially exponential disk mass distribution. The models are produced by combining three separate Miyamoto-Nagai disks. Such models have been used previously to model the disk of the Milky Way, but here we extend this framework to allow its application to disks of any mass, scalelength, and a wide range of thickness from infinitely thin to near spherical (ellipticities from 0 to 0.9). The models have the advantage of simplicity of implementation, and we expect faster run speeds over a double exponential disk treatment. The potentials are fully analytical, and differentiable at all points. The mass distribution of our models deviates from the radial mass distribution of a pure exponential disk by <0.4% out to 4 disk scalelengths, and <1.9% out to 10 disk scalelengths. We tabulate fitting parameters which facilitate construction of exponential disks for any scalelength, and a wide range of disk thickness (a user-friendly, web-based interface is also available). Our recipe is well suited for numerical modelling of the tidal effects of a giant disk galaxy on star clusters or dwarf galaxies. We consider three worked examples; the Milky Way thin and thick disk, and a disky dwarf galaxy.
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Using N-body simulations of the Galactic disks, we qualitatively study how the metallicity distributions of the thick and thin disk stars are modified by radial mixing induced by the bar and spiral arms. We show that radial mixing drives a positive vertical metallicity gradient in the mono-age disk population whose initial scale-height is constant and initial radial metallicity gradient is tight and negative. On the other hand, if the initial disk is flaring, with scale-height increasing with galactocentric radius, radial mixing leads to a negative vertical metallicity gradient, which is consistent with the current observed trend. We also discuss impacts of radial mixing on the metallicity distribution of the thick disk stars. By matching the metallicity distribution of N-body models to the SDSS/APOGEE data, we argue that the progenitor of the Milky Ways thick disk should not have a steep negative metallicity gradient.
We analyze the Miyamoto--Nagai substitution, which was introduced over forty years ago to build models of thick disks and flattened elliptical galaxies. Through it, any spherical potential can be converted to an axisymmetric potential via the replacement of spherical polar $r^2$ with $R^2 + ( a + !sqrt{z^2+b^2} )^2$, where ($R,z$) are cylindrical coordinates and $a$ and $b$ are constants. We show that if the spherical potential has everywhere positive density, and satisfies some straightforward constraints, then the transformed model also corresponds to positive density everywhere. This is in sharp contradistinction to substitutions like $r^2 rightarrow R^2 + z^2/q^2$, which leads to simple potentials but can give negative densities. We use the Miyamoto--Nagai substitution to generate a number of new flattened models with analytic potential--density pairs. These include (i) a flattened model with an asymptotically flat rotation curve, which (unlike Binneys logarithmic model) is always non-negative for a wide-range of axis ratios, (ii) flattened generalizations of the hypervirial models which include Satohs disk as a limiting case and (iii) a flattened analogue of the Navarro--Frenk--White halo which has the cosmologically interesting density fall-off of (distance)$^{-3}$. Finally, we discuss properties of the prolate and triaxial generalizations of the Miyamoto-Nagai substitution.
We analyze the oxygen abundances of a stellar sample representative of the two major Galactic populations: the thin and thick disks. The aim is to investigate the differences between members of the Galactic disks and to contribute to the understanding on the origin of oxygen chemical enrichment in the Galaxy. The analysis is based on the [O,{sc i}]=6300.30,AA~ oxygen line in HR spectra ($Rsim$52,500) obtained from the GES Survey. By comparing the observed spectra with a theoretical dataset, computed in LTE with the SPECTRUM synthesis and ATLAS12 codes, we derive the oxygen abundances of 516 FGK dwarfs for which we have previously measured carbon abundances. Based on kinematic, chemical and dynamical considerations we identify 20 thin and 365 thick disk members. We study potential trends of both subsamples in terms of their chemistry ([O/H], [O/Fe], [O/Mg], and [C/O] versus [Fe/H] and [Mg/H]), age, and position in the Galaxy. Main results are: (a) [O/H] and [O/Fe] ratios versus [Fe/H] show systematic differences between thin and thick disk stars with enhanced O abundance of thick disk stars with respect to thin disk members and a monotonic decrement of [O/Fe] with increasing metallicity, even at metal-rich regime; (b) a smooth correlation of [O/Mg] with age in both populations, suggesting that this abundance ratio can be a good proxy of stellar ages within the Milky Way; (c) thin disk members with [Fe/H]$simeq0$ display a [C/O] ratio smaller than the solar value, suggesting a possibly outward migration of the Sun from lower Galactocentric radii.
We analyze 494 main sequence turnoff and subgiant stars from the AMBRE:HARPS survey. These stars have accurate astrometric information from textit{Gaia}/DR1, providing reliable age estimates with relative uncertainties of $pm1-2$ Gyr and allowing precise orbital determinations. The sample is split based on chemistry into a low-[Mg/Fe] sequence, which are often identified as thin disk stellar populations, and a high-[Mg/Fe] sequence, which are often associated with the thick disk. We find that the high-[Mg/Fe] chemical sequence has extended star formation for several Gyr and is coeval with the oldest stars of the low-[Mg/Fe] chemical sequence: both the low- and high-[Mg/Fe] sequences were forming stars at the same time. The high-[Mg/Fe] stellar populations are only vertically extended for the oldest, most-metal poor and highest [Mg/Fe] stars. When comparing vertical velocity dispersion for both sequences, the high-[Mg/Fe] sequence has lower velocity dispersion than the low-[Mg/Fe] sequence for stars of similar age. Identifying either group as thin or thick disk based on chemistry is misleading. The stars belonging to the high-[Mg/Fe] sequence have perigalacticons that originate in the inner disk, while the perigalacticons of stars on the low-[Mg/Fe] sequence are generally around the solar neighborhood. From the orbital properties of the stars, the high-and low-[Mg/Fe] sequences are most likely a reflection of the chemical enrichment history of the inner and outer disk populations; radial mixing causes both populations to be observed in situ at the solar position. Based on these results, we emphasize that it is important to be clear in defining what populations are being referenced when using the terms thin and thick disk, and that ideally the term thick disk should be reserved for purely geometric definitions to avoid confusion and be consistent with definitions in external galaxies.
Since thin disc stars are younger than thick disc stars on average, the thin disc is predicted by some models to start forming after the thick disc had formed, around 10 Gyr ago. Accordingly, no significant old thin disc population should exist. Using 6-D coordinates from Gaia-DR2 and age estimates from Sanders & Das (2018), we select $sim 24000$ old stars (${tau > 10}$ Gyr, with uncertainties $lesssim 15%$) within 2 kpc from the Sun (full sample). A cross-match with APOGEE-DR16 ($sim 1000$ stars) reveals comparable fractions of old chemically defined thin/thick disc stars. We show that the full sample pericenter radius ($r_mathrm{per}$) distribution has three peaks, one associated with the stellar halo and the other two having contributions from the thin/thick discs. Using a high-resolution $N$-body+Smooth Particle Hydrodynamics simulation, we demonstrate that one peak, at $r_mathrm{per}approx 7.1$ kpc, is produced by stars from both discs which were born in the inner Galaxy and migrated to the Solar Neighbourhood. In the Solar Neighbourhood, $sim 1/2$ ($sim 1/3$) of the old thin (thick) disc stars are classified as migrators. Our results suggest that thin/thick discs are affected differently by radial migration inasmuch as they have different eccentricity distributions, regardless of vertical scale heights. We interpret the existence of a significant old thin disc population as evidence for an early co-formation of thin/thick discs, arguing that clump instabilities in the early disc offer a compelling explanation for the observed trends.
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