Distribution functions for the Milky Way

By J. Binney. 2009

146 citations recorded by the source corpus.

Analytic distribution functions (DFs) for the Galactic disc are discussed. The DFs depend on action variables and their predictions for observable quantities are explored under the assumption that the motion perpendicular to the Galactic plane is adiabatically invariant during motion within the plane. A promising family of DFs is defined that has several adjustable parameters. A standard DF is identified by adjusting these parameters to optimize fits to the stellar density in the column above the Sun, and to the velocity distribution of nearby stars and stars ~ 1 kpc above the Sun. The optimum parameters imply a radial structure for the disc which is consistent with photometric studies of the Milky Way and similar galaxies, and that 20 per cent of the disc's luminosity comes from thick disc. The fits suggest that the value of the V component of the Sun's peculiar velocity should be revised upwards from 5.2 to ~ 11 kms⁻¹. It is argued that the standard DF provides a significantly more reliable way to divide solar-neighbourhood stars into members of the thin and thick discs than is currently used. The standard DF provides predictions for surveys of stars observed at any distance from the Sun. It is anticipated that DFs of the type discussed here will provide useful starting points for much more sophisticated chemo-dynamical models of the Milky Way.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/417e8e89e9a99dbfea72307bfb45de66cddf2a5d

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Citations in the corpus

Mass models of the Milky Way (2011, methodology): “However the analysis in this study differs from that of McMillan & Binney (2010) in that (a) the rotation curve, including v0, is defined by the mass model; (b) the value of v⊙ is assumed to be that in eq.”
Local stellar kinematics from RAVE data - I. Local standard of rest (2010, methodology): “Binney (2010) fitted distribution function models to two sets of velocity distributions and obtained a difference of about 6 km s−1 compared to the value of DB98.”
The Bar and Spiral Structure Legacy (BeSSeL) Survey: Mapping the Milky Way with VLBI Astrometry† (2011, methodology): “Note that the same data set has been also analyzed by Bovy et al. (2009), McMillan & Binney (2010), and Bobylev & Bajkova (2010).”
Galaxy Masses: A Review (2013, methodology): “Current Milky Way models may lack the richness and sophistication worthy of the data; several groups have indeed begun laying the groundwork for accurate Milky Way mass models in the era of Gaia and LSST (Binney 2010b; Sharma et al. 2011; An et al. 2012; McMillan & Binney 2013; Magorrian 2013, and t”
A DIRECT DYNAMICAL MEASUREMENT OF THE MILKY WAY'S DISK SURFACE DENSITY PROFILE, DISK SCALE LENGTH, AND DARK MATTER PROFILE AT 4 kpc ≲ R ≲ 9 kpc (2013, methodology): “Distribution function model We use the quasi-isothermal DF first proposed by Binney (2010) and later refined by Binney & McMillan (2011) to fit the dynamics of a single MAP.”
The Milky Way’s stellar disk (2013, background): “…an empirical description of the Milky Way disk, and compared to a series of papers by Binney and collaborators on dynamical modeling of the Galaxy (Binney 2010; Binney & McMillan 2011; Binney 2012; McMillan & Binney 2012), we place more emphasis two aspects that we deem crucial in Galactic disk…”
galpy: A python LIBRARY FOR GALACTIC DYNAMICS (2014, methodology): “For example, one action-based DF that is included in galpy is the quasiisothermal DF (Binney 2010; Binney & McMillan 2011), which can be used as follows: where the output is the value of the DF for this orbit.”
Dynamical modelling of the galactic bulge and bar: the Milky Way's pattern speed, stellar and dark matter mass distribution (2016, methodology): “…et al. 1990; Cappellari et al. 2009), classical distribution function-based methods (Dejonghe 1984; Qian et al. 1995), actions-based methods (Binney 2010; Sanders & Binney 2013), orbit-based methods (Schwarzschild 1979; Thomas et al. 2009) or with the Made-to-Measure (M2M) method (Syer &…”
Actions for axisymmetric potentials (2012, methodology): “To date we have used two techniques for evaluating actions: (i) torus construction (Kaasalainen & Binney 1994; Binney & McMillan 2011) and (ii) the adiabatic approximation (Binney 2010; Binney & McMillan 2011; Schönrich & Binney 2012).”
Dynamics for galactic archaeology (2013, methodology): “Binney (2010, 2012b) showed that data for the solar neighbourhood can be largely accounted for by models synthesised from quasi-isothermal dfs. Specifically, we write f(Jr, Jz, Lz) = fσr(Jr, Lz)fσz(Jz, Lz), (12) where fσr and fσz are defined to be fσr(Jr, Lz) ≡ ΩΣ 2πMσ2rκ [1 +…”
THE LONG-TERM EVOLUTION OF THE GALACTIC DISK TRACED BY DISSOLVING STAR CLUSTERS (2010, methodology): “(11) We use updated values for the coefficients (Binney 2010) where the age of the disk is tD = 10 Gyr and for which t1 = 0.1 Gyr.”
The dynamics of stars around spiral arms (2011, background): “This is slightly lower than fR ∼ 2 that is the observed ratio for the Milky Way (e.g. Holmberg et al. 2009; Binney 2010).”
THE GENESIS OF THE MILKY WAY'S THICK DISK VIA STELLAR MIGRATION (2010, background): “These authors concluded that Vφ is also well characterized by a non-Gaussian distribution (see Binney 2010, for the implied distribution function).”
Mass and shape of the Milky Way’s dark matter halo with globular clusters from Gaia and Hubble (2018, unknown): “For the disc component, we use the ‘quasi-isothermal’ DF, introduced by Binney (2010), as implemented in Vasiliev (2018): fdisc(J) = ΣνΩ 2π2κσ2Rσ 2 z exp −κJR σ2R − κJz σ2z f±,d, (3) where Ω, κ and ν are the circular, radial and vertical epicycle frequencies evaluated at the radius of the circular…”
Exploring the Milky Way stellar disk - A detailed elemental abundance study of 714 F and G dwarf stars in the solar neighbourhood (2013, background): “A better understanding of the distribution functions may lead to a better decomposition of the stellar disk into sub-components (Binney 2010).”
The Galaxy in Context: Structural, Kinematic, and Integrated Properties (2016, background): “Binney (2010, 2012) has argued that action integrals ( J) are ideal for building dynamical models because they are adiabatic invariants.”