The chemo-dynamical structure of the Milky Way Jo Bovy (Institute - PowerPoint PPT Presentation

The chemo-dynamical structure of the Milky Way Jo Bovy (Institute for Advanced Study; Hubble fellow) with Hans-Walter Rix (MPIA), Lan Zhang (NAO,MPIA), Yuan-Sen Ting (Harvard)

MASS DISTRIBUTION IN THE INNER MILKY WAY • Disk scale length is main unknown for determining the mass distribution at R <~ 10 kpc • No existing dynamical measurements of the scale length • Halo density profile largely unconstrained R d = 2 kpc R d = 3 kpc Binney & Tremaine (2008)

MASS DISTRIBUTION IN THE INNER MILKY WAY • Is the Milky Way’s disk maximal? • Is the halo contracted? • What is the total stellar mass of the Milky Way? • Is all of the dynamical mass accounted for by baryonic matter + ~spherical DM?

Terminal velocities of HI/CO CURRENT DATA E.g., McClure-Griffiths et al., • Rotation curve: M(R) but does not distinguish between spherical Clemens et al. (~halo) and flattened (~disk) components • F Z (Z;R of sun): vertical force at the sun • Want F Z (R,Z) =~ Σ (R,Z) to measure the disk scale length F Z (Z,R of sun) Stellar rotation curve Zhang et al.(2013) Bovy et al. (2012) O

BASIC IDEA OF VERTICAL MASS MEASUREMENT • Throw a ball up with a known velocity v and measure its maximum height g = v 2 h z 2 h z • For stars we can statistically measure their velocities and the heights they reach above the plane: • Velocity distribution: characterized by dispersion f ( v z | z ) σ z • Density: ~ exponential with scale height ρ ( z ) h z • Assuming that the stars are in a steady state, we can relate these to the gravitational potential K Z ≈ σ 2 Z h Z

STEADY -STATE MODELING: JEANS+POISSON EQUATIONS • Jeans Eqns.: Moments of collisionless Boltzmann equation that describes the steady state • or DF modeling (Jeans theorem)

STEADY -STATE MODELING: JEANS+POISSON EQUATIONS • Jeans Eqns.: Moments of collisionless Boltzmann equation that describes the steady state 1D Tilt =~ 0 slope of rotation curve =~ 0 • or DF modeling (Jeans theorem)

SEGUE • spectra for 240,000 stars • R ≈ 1800 Yanny et al. (2009) • 14 < r < 20 • T eff , log g, [Fe/H] (±0.15 dex), [ α /Fe] (±0.1 dex) • photometric distances ≈ 12% for main-sequence stars • δ v los ≈ 7 km/s, δμ ≈ 3.5 mas/yr ≈ 18 km/s/kpc • relatively simple selection for G & K samples

MAPS: MONO-ABUNDANCE POPULATIONS Bovy et al. (2012abc)

MAPS: MONO-ABUNDANCE POPULATIONS Bovy et al. (2012abc)

MAPS: MONO-ABUNDANCE POPULATIONS Bovy et al. (2012abc) Radial

MAPS: MONO-ABUNDANCE POPULATIONS Bovy et al. (2012abc) Vertical Radial

MAPS: MONO-ABUNDANCE POPULATIONS Bovy et al. (2012abc) Kinematics Vertical Radial

MAPS: MONO-ABUNDANCE POPULATIONS Bovy et al. (2012abc) Kinematics Vertical Radial • MAPs: simple spatial and kinematic structure: • Exponential in R and |Z| • Velocity dispersion constant with height

SEGUE ANALYSIS OF MULTIPLE POPULATIONS • The Milky Way disk has many different populations of stars • SDSS/SEGUE: 6D positions and velocities / metallicities and alpha-element abundances for 10k K-dwarf stars • Main-sequence stars with precise distances • 200 pc < |Z| < 1.5 kpc Lan Zhang, Rix, van de Ven, Bovy, et al. (2012)

DIFFERENT POPULATIONS HAVE VERY DIFFERENT SPATIAL AND KINEMATIC PROFILES These should all give the same gravitational potential Zhang, Rix, van de Ven, Bovy, et al. (2012)

RESULTS FROM JOINT FIT Zhang, Rix, van de Ven, Bovy, et al. (2012)

RESULTS FROM JOINT FIT Bovy & Tremaine (2012) Zhang et al. (2012) Garbari et al. (2012) Zhang, Rix, van de Ven, Bovy, et al. (2012) Σ ( R 0 , | Z | ≤ 1 . 1 kpc) = 69 ± 6 M � pc � 2 + measurements of DM density and disk surface density

RADIAL DISK AND HALO PROFILES • We can perform the previous analysis at R =/= R 0 => Σ (R) and ρ (R) • This will allow us to measure the disk profile (scale length) and infer the halo profile

SEGUE G DWARFS • G dwarf sample: 0.48 ≤ g-r ≤ 0.55, 14.5 ≤ r ≤ 20.2, log g > 4.2, SN > 15, — 30,000 stars • Narrow range of Teff → relative ranking of [Fe/H] and [ α /Fe] good Bovy et al. (2012b); ApJ 753 , 148

SEGUE G DWARFS • G dwarf sample: 0.48 ≤ g-r ≤ 0.55, 14.5 ≤ r ≤ 20.2, log g > 4.2, SN > 15, — 30,000 stars • Narrow range of Teff → relative ranking of [Fe/H] and [ α /Fe] good Bovy et al. (2012b); ApJ 753 , 148

DISTRIBUTION FUNCTION MODELING DF ( x , v ) p ( x , v | model) = R d x d v DF ( x , v ) • Model the distribution function of stars in x,v as being in a steady state: DF ( J ( x , v )) p ( x , v | model) = R d x d v DF ( J ( x , v )) • With selection function: DF ( J ( x , v )) p ( x , v | model) = R d x d v DF ( J ( x , v )) S ( x ) • With errors/missing data: Z d x 0 d v 0 p ( x obs , v obs | x 0 , v 0 ) p ( x 0 , v 0 | model) p ( x obs , v obs | model) =

DISK DISTRIBUTION FUNCTION MODELING Binney (2010), Binney & McMillan (2011) • Actions calculated using Staeckel fudge (Binney 2012) in four component model for Milky Way potential (2 exponential disks, bulge, halo) • Properties of DF:

DISK DISTRIBUTION FUNCTION MODELING Binney (2010), Binney & McMillan (2011) • Actions calculated using Staeckel fudge (Binney 2012) in four component model for Milky Way potential (2 exponential disks, bulge, halo) • Properties of DF:

DISK DISTRIBUTION FUNCTION MODELING Binney (2010), Binney & McMillan (2011) 10 0 St¨ ackel actions • Actions calculated using Adiabatic actions Staeckel fudge (Binney 2012) ν ∗ ( R 0 , Z ) / ν ∗ ( R 0 , 0) in four component model for 10 − 1 Milky Way potential (2 exponential disks, bulge, halo) R = 5 kpc • Properties of DF: R = 8 kpc 10 − 2 R = 11 kpc 0 1 2 3 4 5 Z (kpc)

DISK DISTRIBUTION FUNCTION MODELING Binney (2010), Binney & McMillan (2011) R (kpc) 60 10 0 St¨ ackel actions • Actions calculated using Adiabatic actions 50 Staeckel fudge (Binney 2012) ν ∗ ( R 0 , Z ) / ν ∗ ( R 0 , 0) σ Z ( Z ) (km s − 1 ) 40 in four component model for 10 − 1 Milky Way potential (2 30 exponential disks, bulge, halo) 20 R = 5 kpc 10 • Properties of DF: R = 8 kpc 10 − 2 R = 11 kpc 0 1 2 3 4 5 0 0 1 2 3 4 5 Z (kpc) Z (kpc)

DISK DISTRIBUTION FUNCTION MODELING Binney (2010), Binney & McMillan (2011) Z (kpc) R (kpc) 30 60 10 0 St¨ ackel actions St¨ ackel actions tilt of the velocity ellipsoid (deg) Adiabatic actions 25 • Actions calculated using Adiabatic actions 50 Staeckel fudge (Binney 2012) 20 ν ∗ ( R 0 , Z ) / ν ∗ ( R 0 , 0) σ Z ( Z ) (km s − 1 ) 40 in four component model for 15 10 − 1 Milky Way potential (2 30 10 S08 exponential disks, bulge, halo) 20 5 R = 5 kpc 10 • Properties of DF: R = 8 kpc 0 10 − 2 R = 11 kpc 0 1 2 3 4 5 − 5 0 0 1 2 3 4 5 0 1 2 3 4 5 Z (kpc) Z (kpc) Z (kpc)

SELECTION EFFECTS: FULL DF 1 . 0 2 . 0 J R (220 km s − 1 kpc) J Z (220 km s − 1 kpc) 0 . 8 1 . 5 0 . 6 1 . 0 0 . 4 0 . 5 0 . 2 0 . 0 0 . 0 0 2 4 6 8 10 12 14 16 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 L z (220 km s − 1 kpc) J R (220 km s − 1 kpc)

SELECTION EFFECTS: DISTRIBUTION OF DATA IN ACTION SPACE

SPATIAL FITS USING DYNAMICAL MODEL small Δ R Data distribution in distance from plane Bovy & Rix (2013), ApJ, in press

SPATIAL FITS USING DYNAMICAL MODEL small Δ Z Data distribution in vertical velocity Bovy & Rix (2013), ApJ, in press

EXAMPLE PDF FOR 1 MAP

EXAMPLE PDF FOR 1 MAP

SURFACE-DENSITY PROFILE Bovy & Rix (2013), ApJ, in press

SURFACE-DENSITY PROFILE Bovy & Rix (2013), ApJ, in press

SURFACE-DENSITY PROFILE old MAPs young MAPs Bovy & Rix (2013), ApJ, in press

SURFACE-DENSITY PROFILE K dwarfs (Zhang et al. ) Bovy & Rix (2013), ApJ, in press

SURFACE-DENSITY PROFILE  � − R − R 0 Σ ( R, | Z | ≤ 1 . 1 kpc) = 69 M � pc � 2 exp 2 . 5 kpc K dwarfs (Zhang et al. ) Bovy & Rix (2013), ApJ, in press