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

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

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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

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SLIDE 1

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)

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SLIDE 2
  • 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

MASS DISTRIBUTION IN THE INNER MILKY WAY

Binney & Tremaine (2008)

Rd = 2 kpc Rd = 3 kpc

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SLIDE 3

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?

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SLIDE 4
  • Rotation curve: M(R) but does not

distinguish between spherical (~halo) and flattened (~disk) components

  • FZ(Z;R of sun): vertical force at the

sun

  • Want FZ(R,Z) =~ Σ(R,Z) to

measure the disk scale length

CURRENT DATA

Terminal velocities of HI/CO Stellar rotation curve O FZ(Z,R of sun)

Zhang et al.(2013) Bovy et al. (2012) E.g., McClure-Griffiths et al., Clemens et al.

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SLIDE 5

BASIC IDEA OF VERTICAL MASS MEASUREMENT

  • Throw a ball up with a known velocity v and measure its maximum height

hz

  • For stars we can statistically measure their velocities and the heights they

reach above the plane:

  • Velocity distribution: characterized by dispersion
  • Density: ~ exponential with scale height
  • Assuming that the stars are in a steady state, we can relate these to the

gravitational potential

g = v2 2 hz

f(vz|z) ρ(z) σz hz KZ ≈ σ2

Z

hZ

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SLIDE 6
  • Jeans Eqns.: Moments of collisionless Boltzmann equation that describes

the steady state

  • or DF modeling (Jeans theorem)

STEADY

  • STATE MODELING: JEANS+POISSON

EQUATIONS

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SLIDE 7
  • Jeans Eqns.: Moments of collisionless Boltzmann equation that describes

the steady state

  • or DF modeling (Jeans theorem)

STEADY

  • STATE MODELING: JEANS+POISSON

EQUATIONS

1D Tilt =~ 0 slope of rotation curve =~ 0

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SLIDE 8

SEGUE

  • spectra for 240,000 stars
  • R ≈ 1800
  • 14 < r < 20
  • Teff, log g, [Fe/H] (±0.15 dex), [α/Fe] (±0.1 dex)
  • photometric distances ≈ 12% for main-sequence stars
  • δvlos ≈ 7 km/s, δμ ≈ 3.5 mas/yr ≈ 18 km/s/kpc
  • relatively simple selection for G & K samples

Yanny et al. (2009)

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SLIDE 9

MAPS: MONO-ABUNDANCE POPULATIONS

Bovy et al. (2012abc)

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SLIDE 10

MAPS: MONO-ABUNDANCE POPULATIONS

Bovy et al. (2012abc)

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SLIDE 11

MAPS: MONO-ABUNDANCE POPULATIONS

Radial

Bovy et al. (2012abc)

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SLIDE 12

MAPS: MONO-ABUNDANCE POPULATIONS

Radial Vertical

Bovy et al. (2012abc)

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SLIDE 13

MAPS: MONO-ABUNDANCE POPULATIONS

Radial Vertical Kinematics

Bovy et al. (2012abc)

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SLIDE 14

MAPS: MONO-ABUNDANCE POPULATIONS

  • MAPs: simple spatial and kinematic structure:
  • Exponential in R and |Z|
  • Velocity dispersion constant with height

Radial Vertical Kinematics

Bovy et al. (2012abc)

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SLIDE 15

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)

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SLIDE 16

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)

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SLIDE 17

RESULTS FROM JOINT FIT

Zhang, Rix, van de Ven, Bovy, et al. (2012)

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SLIDE 18

RESULTS FROM JOINT FIT

Garbari et al. (2012) Bovy & Tremaine (2012) Zhang et al. (2012) Zhang, Rix, van de Ven, Bovy, et al. (2012)

Σ(R0, |Z| ≤ 1.1 kpc) = 69 ± 6 M pc2

+ measurements of DM density and disk surface density

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SLIDE 19

RADIAL DISK AND HALO PROFILES

  • We can perform the previous analysis at R =/= R0 => Σ(R) and ρ(R)
  • This will allow us to measure the disk profile (scale length) and infer the

halo profile

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SLIDE 20

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

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SLIDE 21

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

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SLIDE 22
  • Model the distribution function of stars in x,v as being in a

steady state:

DISTRIBUTION FUNCTION MODELING

p(x, v|model) = DF(x, v) R dxdvDF(x, v) p(x, v|model) = DF(J(x, v)) R dxdvDF(J(x, v))

  • With selection function:

p(x, v|model) = DF(J(x, v)) R dxdvDF(J(x, v))S(x)

  • With errors/missing data:

p(xobs, vobs|model) = Z dx0dv0 p(xobs, vobs|x0, v0)p(x0, v0|model)

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SLIDE 23
  • 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)

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SLIDE 24
  • 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)

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SLIDE 25
  • 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)

1 2 3 4 5

Z (kpc)

10−2 10−1 100

ν∗(R0, Z)/ν∗(R0, 0) St¨ ackel actions Adiabatic actions

R = 5 kpc R = 8 kpc R = 11 kpc

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SLIDE 26
  • 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)

1 2 3 4 5

Z (kpc)

10−2 10−1 100

ν∗(R0, Z)/ν∗(R0, 0) St¨ ackel actions Adiabatic actions

R = 5 kpc R = 8 kpc R = 11 kpc

R (kpc)

1 2 3 4 5

Z (kpc)

10 20 30 40 50 60

σZ(Z) (km s−1)

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SLIDE 27
  • 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)

1 2 3 4 5

Z (kpc)

10−2 10−1 100

ν∗(R0, Z)/ν∗(R0, 0) St¨ ackel actions Adiabatic actions

R = 5 kpc R = 8 kpc R = 11 kpc

R (kpc)

1 2 3 4 5

Z (kpc)

10 20 30 40 50 60

σZ(Z) (km s−1) Z (kpc)

1 2 3 4 5

Z (kpc)

−5 5 10 15 20 25 30

tilt of the velocity ellipsoid (deg)

S08

St¨ ackel actions Adiabatic actions

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SLIDE 28

2 4 6 8 10 12 14 16

Lz (220 km s−1 kpc)

0.0 0.5 1.0 1.5 2.0

JR (220 km s−1 kpc)

0.0 0.5 1.0 1.5 2.0

JR (220 km s−1 kpc)

0.0 0.2 0.4 0.6 0.8 1.0

JZ (220 km s−1 kpc)

SELECTION EFFECTS: FULL DF

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SLIDE 29

SELECTION EFFECTS: DISTRIBUTION OF DATA IN ACTION SPACE

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SLIDE 30

SPATIAL FITS USING DYNAMICAL MODEL

Data distribution in distance from plane small ΔR

Bovy & Rix (2013), ApJ, in press

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SLIDE 31

SPATIAL FITS USING DYNAMICAL MODEL

Data distribution in vertical velocity small ΔZ

Bovy & Rix (2013), ApJ, in press

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SLIDE 32

EXAMPLE PDF FOR 1 MAP

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SLIDE 33

EXAMPLE PDF FOR 1 MAP

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SLIDE 34

SURFACE-DENSITY PROFILE

Bovy & Rix (2013), ApJ, in press

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SLIDE 35

SURFACE-DENSITY PROFILE

Bovy & Rix (2013), ApJ, in press

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SLIDE 36

SURFACE-DENSITY PROFILE

  • ld MAPs

young MAPs

Bovy & Rix (2013), ApJ, in press

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SLIDE 37

SURFACE-DENSITY PROFILE

K dwarfs (Zhang et al. )

Bovy & Rix (2013), ApJ, in press

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SLIDE 38

SURFACE-DENSITY PROFILE

K dwarfs (Zhang et al. )

Σ(R, |Z| ≤ 1.1 kpc) = 69 M pc2 exp  −R − R0 2.5 kpc

  • Bovy & Rix (2013), ApJ, in press
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SLIDE 39

TABLE 3 Measured surface density and vertical force at different Galactocentric radii [Fe/H] [α/Fe] R Σ1.1(R) δΣ1.1(R) R0 − R KZ,1.1(R) δKZ,1.1(R) (dex) (dex) (kpc) (M pc−2) (M pc−2) (kpc) (2πG M pc−2) (2πG M pc−2)

  • 1.25

0.425 4.63 256.0 50.4 3.37 217.6 41.5

  • 1.15

0.425 4.68 270.9 44.3 3.32 230.6 36.8

  • 1.05

0.375 6.71 89.7 20.3 1.29 84.2 18.5

  • 1.05

0.425 4.77 244.2 40.1 3.23 209.0 33.2

  • 0.95

0.325 4.59 228.4 48.3 3.41 194.7 38.6

  • 0.95

0.375 5.04 207.6 34.9 2.96 180.5 29.2

  • 0.95

0.425 5.22 204.3 30.1 2.78 179.0 25.6

  • 0.95

0.475 4.68 247.9 41.3 3.32 211.4 33.7

  • 0.85

0.275 7.38 65.0 11.9 0.62 62.2 11.2

  • 0.85

0.325 6.53 104.9 19.8 1.47 97.5 18.0

  • 0.85

0.375 6.62 118.1 14.0 1.38 109.8 12.9

  • 0.85

0.425 6.66 127.6 14.0 1.34 119.0 12.9

  • 0.85

0.475 5.08 202.8 35.9 2.92 176.8 30.1

  • 0.75

0.275 7.42 64.4 11.6 0.58 61.7 11.0

  • 0.75

0.325 6.53 125.0 16.2 1.47 115.9 14.8

  • 0.75

0.375 7.11 97.3 8.0 0.89 92.0 7.5

  • 0.75

0.425 6.71 130.6 11.8 1.29 121.9 10.9

  • 0.75

0.475 6.53 103.3 19.8 1.47 96.1 18.0

  • 0.65

0.275 7.20 81.4 12.6 0.80 77.3 11.8

  • 0.65

0.325 7.20 100.2 9.9 0.80 95.2 9.3

  • 0.65

0.375 6.34 159.2 12.7 1.66 146.3 11.5

  • 0.65

0.425 6.79 108.0 14.5 1.21 101.2 13.4

  • 0.55

0.275 7.29 89.2 9.6 0.71 84.9 9.1

  • 0.55

0.325 7.29 93.1 7.8 0.71 88.5 7.4

  • 0.55

0.375 7.02 104.7 8.7 0.98 98.7 8.2

43 MEASUREMENTS OF VERTICAL FORCE THAT CAN BE USED FOR CONSTRAINING THE MASS DISTRIBUTION

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SLIDE 40
  • 1.05

0.375 6.71 89.7 20.3 1.29 84.2 18.5

  • 1.05

0.425 4.77 244.2 40.1 3.23 209.0 33.2

  • 0.95

0.325 4.59 228.4 48.3 3.41 194.7 38.6

  • 0.95

0.375 5.04 207.6 34.9 2.96 180.5 29.2

  • 0.95

0.425 5.22 204.3 30.1 2.78 179.0 25.6

  • 0.95

0.475 4.68 247.9 41.3 3.32 211.4 33.7

  • 0.85

0.275 7.38 65.0 11.9 0.62 62.2 11.2

  • 0.85

0.325 6.53 104.9 19.8 1.47 97.5 18.0

  • 0.85

0.375 6.62 118.1 14.0 1.38 109.8 12.9

  • 0.85

0.425 6.66 127.6 14.0 1.34 119.0 12.9

  • 0.85

0.475 5.08 202.8 35.9 2.92 176.8 30.1

  • 0.75

0.275 7.42 64.4 11.6 0.58 61.7 11.0

  • 0.75

0.325 6.53 125.0 16.2 1.47 115.9 14.8

  • 0.75

0.375 7.11 97.3 8.0 0.89 92.0 7.5

  • 0.75

0.425 6.71 130.6 11.8 1.29 121.9 10.9

  • 0.75

0.475 6.53 103.3 19.8 1.47 96.1 18.0

  • 0.65

0.275 7.20 81.4 12.6 0.80 77.3 11.8

  • 0.65

0.325 7.20 100.2 9.9 0.80 95.2 9.3

  • 0.65

0.375 6.34 159.2 12.7 1.66 146.3 11.5

  • 0.65

0.425 6.79 108.0 14.5 1.21 101.2 13.4

  • 0.55

0.275 7.29 89.2 9.6 0.71 84.9 9.1

  • 0.55

0.325 7.29 93.1 7.8 0.71 88.5 7.4

  • 0.55

0.375 7.02 104.7 8.7 0.98 98.7 8.2

  • 0.55

0.425 6.57 108.3 18.7 1.43 100.8 17.1

  • 0.45

0.225 7.56 77.6 8.5 0.44 74.5 8.1

  • 0.45

0.275 6.75 122.4 12.6 1.25 114.3 11.7

  • 0.45

0.325 6.84 115.7 10.1 1.16 108.4 9.4

  • 0.45

0.375 5.54 189.6 24.1 2.46 168.6 20.9

  • 0.35

0.225 7.29 91.5 10.2 0.71 87.2 9.6

  • 0.35

0.275 6.57 150.9 13.5 1.43 140.1 12.4

  • 0.35

0.325 5.67 190.6 22.3 2.33 170.6 19.5

  • 0.25

0.175 7.70 75.6 8.4 0.30 72.8 8.0

  • 0.25

0.225 7.88 64.6 8.5 0.12 62.4 8.2

  • 0.15

0.125 7.70 76.7 8.1 0.30 73.9 7.8

  • 0.15

0.175 6.08 161.8 19.8 1.92 147.4 17.7

  • 0.05

0.025 6.57 121.9 16.4 1.43 113.2 14.9

  • 0.05

0.075 7.92 71.4 7.0 0.08 69.2 6.8 0.05 0.025 8.55 54.7 4.9

  • 0.55

53.4 4.7 0.05 0.075 7.20 106.8 10.0 0.80 101.3 9.4 0.15 0.025 6.03 145.4 20.9 1.97 132.4 18.8 0.25 0.025 4.82 240.3 42.9 3.18 206.2 35.7

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SLIDE 41
  • Use new KZ constraints together with:
  • Σdisk(R0) from Zhang et al. (2013)
  • Terminal velocities (marginalized over

‘wiggles’ and solar motion terms)

  • constraint on local slope of rotation

curve

  • Fit 4 component potential model with

fixed bulge, ISM and stellar disk layers, and spherical power-law halo

POTENTIAL FITS

E.g., McClure-Griffiths et al., Clemens et al. Bovy & Rix (2013), ApJ, in press

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SLIDE 42

CONSTRAINTS ON THE DISK

stellar disk scale length = 2.15 ± 0.14 kpc , Σ∗(R0) = 38 ± 4 M pc−2 , Σdisk(R0) = 51 ± 4 M pc−2 , M∗ = 4.6 ± 0.3 × 1010 M , Mdisk = 5.3 ± 0.3 × 1010 M , Mbaryonic = 6.3 ± 0.3 × 1010 M .

Vc,∗ Vc

  • 2.2 Rd

= 0.83 ± 0.04

Bovy & Rix (2013), ApJ, in press

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SLIDE 43

CONSTRAINTS ON THE DISK

stellar disk scale length = 2.15 ± 0.14 kpc , Σ∗(R0) = 38 ± 4 M pc−2 , Σdisk(R0) = 51 ± 4 M pc−2 , M∗ = 4.6 ± 0.3 × 1010 M , Mdisk = 5.3 ± 0.3 × 1010 M , Mbaryonic = 6.3 ± 0.3 × 1010 M .

Vc,∗ Vc

  • 2.2 Rd

= 0.83 ± 0.04

Bovy & Rix (2013), ApJ, in press

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SLIDE 44
  • Halo contributes little to

rotation curve and surface density at R < 10 kpc

  • CONSTRAINTS ON THE HALO

α ≤ 1.53 (95 % confidence)

Bovy & Rix (2013), ApJ, in press

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SLIDE 45
  • Halo contributes little to

rotation curve and surface density at R < 10 kpc

  • CONSTRAINTS ON THE HALO

α ≤ 1.53 (95 % confidence)

Bovy & Rix (2013), ApJ, in press

ρ ∝ r-2 ρ ∝ r-1 ρ ∝constant Disk Halo

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SLIDE 46
  • Vc(R0) = 218 ± 10 km/s
  • Consistent with APOGEE

measurement (Vc(R0) = 218 ± 6 km/s)

  • Rotation curve close to flat
  • Dynamically decomposed into

disk and halo

  • These constraints do not

depend on the Sun’s motion wrt the LSR

CONSTRAINTS ON THE ROTATION CURVE

Bovy & Rix (2013), ApJ, in press

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SLIDE 47
  • Vc(R0) = 218 ± 10 km/s
  • Consistent with APOGEE

measurement (Vc(R0) = 218 ± 6 km/s)

  • Rotation curve close to flat
  • Dynamically decomposed into

disk and halo

  • These constraints do not

depend on the Sun’s motion wrt the LSR

CONSTRAINTS ON THE ROTATION CURVE

Bovy & Rix (2013), ApJ, in press

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SLIDE 48
  • MAP decomposition allows one to predict the scale length as

a function of radius

COMPARISON WITH STAR COUNTS

+

Bovy & Rix (2013), ApJ, in press

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SLIDE 49
  • MAP decomposition allows one to predict the scale length as

a function of radius

COMPARISON WITH STAR COUNTS

  • Similar results for the mass scale height vs. stellar scale height
  • We understand the stellar disk incredibly well!

Bovy & Rix (2013), ApJ, in press

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SLIDE 50

CONCLUSIONS

  • SEGUE G and K dwarf samples allow unprecedented

measurements of the vertical dynamics

  • Best dynamical measurement of local vertical mass

distribution

  • First dynamical measurement of surface density as a function
  • f R
  • We measure the scale length to be 2.15 ± 0.14 kpc ; MW

disk is maximal

  • First constraint on DM radial density profile near the Sun:

must be shallower than r^-1.5