Milky Way’s Mass and Stellar Halo Velocity
Dispersion Profiles
Sarah A. Bird
Shanghai Astronomical Observatory
In collaboration with Juntai Shen, Xiang Xiang Xue,Chao Liu, Chris Flynn, Ling Zhu, Jie Wang

HaloK giants

Kinematics

Mass*Contents

1

Stellar Halos2

LAMOST K-Giant Halo Stars

3

Results: Kinematics

4

Results: Galactic Mass Estimation

5Conclusion

Milky Way Stellar HaloSarah A. Bird

HaloK giants

Kinematics

Mass

*

The Milky Way (Bland-Hawthorn & Gerhard 2016, Helmi 2008, Figure: NASA/JPL-Caltech/ESO/R. Hurt)

Mass:Dark matter mass within ∼ 250
kpc ∼ 1012 M⊙
Visible mass ∼ 1011 M⊙

Visible mass:
Disk + bulge = 99%
Stellar halo = 1%
Stellar halo = ∼ 1% globularclusters + 99% stars

Halo stars: old, metal-poor, large
random motions

Milky Way Stellar HaloSarah A. Bird

HaloK giants

Kinematics

Mass*

Milky Way stellar halo

Motivation to study the stellar
halo:
Constrain galaxy formation
Properties of the old stellar
populations
Find remnants of past mergers
Test cosmological models
Probe the dark matter halo

Milky Way Stellar HaloSarah A. Bird

HaloK giants

Kinematics

Mass*

Milky Way stellar halo properties[1,2]
Typical values for
Galactocentric radius[4]age[1]
peak metallicity [Fe/H][3,4]metallicity range [Fe/H][3]spatial distribution[4]n, density profile[4−7] ρ ∝ r −nkinematics[8,9,10,11]
Galactic radial velocity dispersion[11,12,13]

inner halo
< 20 kpc> 10 Gyr−1.6 dex−4 − 0 dex
flattened2−4

outer halo
> 20 kpc> 10 Gyr−2.2 dex−4 − 0 dex
spherical
2−4radial+wiggle

isotropic to radial

120 km/sdeclines to 50 km/s

[1]

Helmi 2008, [2] Bland-Hawthorn & Gerhard 2016, [3] Ryan & Norris 1991, [4] Carollo+07,10,12, [5] Deason+11,Gnedin+10, [7] Xu+17, [8] Sommer-Larsen+97, [9] Kafle+12,[10] Deason+13, [11] Kafle+14, [12] Battaglia+05,06,[13]
Deason+12[6]

Milky Way Stellar HaloSarah A. BirdHalo

K giants

Kinematics

Mass*

Useful tracers of halo star kinematics Figure: Sandage83

giant stars
RR Lyraeblue horizontal
branch stars

Milky Way Stellar HaloSarah A. BirdHalo

K giantsKinematics

Mass*

Stellar tracers of the halo
Tracer Star

NumberDistance Range [kpc]SurveyReference

K giant

BHB

69006036
4664
19334985
3549
666

5 − 180
5 − 125
5 − 6016 − 48
5 − 8010 − 50
20 − 100

Bird+17
Xue+14
Kafle+12
Deason+12
Xue+11
Deason+11
De Propris+10

A-type910

15 − 75

BHB

2558
1170
700

5 − 605 − 96< 45

LAMOST
SDSS/SEGUESDSS/SEGUESDSS/SEGUESDSS/SEGUESDSS/SEGUE
2QZ Redshift
SurveyHypervelocity
Star Survey
SDSS/SEGUESDSS/SEGUE
mixture of surveys

K giant
BHB[1]BHB
BHB
BHB

BHB
BHB
[1]

Brown+10

Xue+08Sirko+04
Sommer-Larsen+97

blue horizontal branch

Milky Way Stellar HaloSarah A. Bird

HaloK giants

Kinematics

Mass*Collecting more Milky Way halo stars!

LAMOST Photo Gallery

Milky Way Stellar HaloSarah A. BirdHalo

K giants

Kinematics

Mass

*

Contents

1

Stellar Halos2

LAMOST K-Giant Halo Stars

3

Results: Kinematics

4

Results: Galactic Mass Estimation

5

Conclusion

Milky Way Stellar HaloSarah A. Bird

HaloK giants

Kinematics

Mass

*

Galactic K-giant halo stars from LAMOSTSelection criteria:
LAMOST Data Release 3100

4000 < Teff /K < 5600

8060

surface gravity log g < 4 dex

distance using method of Xue+14

Z [kpc]exclusion of red clump stars based on
Mgb lines Liu+1440200-20-40-60|Z| > 5 kpc-20020406080

X [kpc][Fe/H] < −1.3 dex
total: over 6900 K-giant spectra out toRgc = 200 kpc
Milky Way Stellar HaloSarah A. BirdHalo

K giants

Kinematics

Mass*

Halo K-giant matches: LAMOST vs SEGUE (Xue+14)

Milky Way Stellar HaloSarah A. Bird

HaloK giants

Kinematics

Mass

*

Number histogram of LAMOST halo K giants
3.5log(number of stars)

32.5

2

1.5

10

Milky Way Stellar Halo

20406080100120Galactocentric radius Rgc [kpc]140160Sarah A. Bird

HaloK giants

Kinematics

Mass

*

Contents

1

Stellar Halos2

LAMOST K-Giant Halo Stars

3

Results: Kinematics

4

Results: Galactic Mass Estimation

5Conclusion

Milky Way Stellar HaloSarah A. BirdHalo

K giants

Kinematics

Mass

*

Line-of-sight velocity of LAMOST halo K giants
500

LAMOST halo K-giant stars

400300vgsr [km/s]

200
1000-100-200-300-4000

Milky Way Stellar Halo

20406080
100 120 140
Galactocentric radius Rgc [kpc]160

180200Sarah A. Bird

HaloK giants

Kinematics

Mass

*

Velocity histograms with LAMOST
Use velocities to exclude
streams
Double Gaussian fit:

narrow Gaussian:stellar stream
remove streams fromfurther analysis
if amplitude of narrow
Gaussian is smaller
than 10% of thebroad Gaussian, refitwith a single Gaussian
Milky Way Stellar Haloσ = 109
σ = 20.1

25--35 kpc

10080

number of stars

broad Gaussian:smooth distributionof halo stars

12060

40200−600−400−2000vgsr

200400600

Sarah A. Bird

HaloK giants

Kinematics

Mass*

Line-of-sight velocity dispersion: observations

140

Comparison between
different tracer
samples:consistent results
flattened profile

σlos [km s-1]

120
1008060
Bird+17 LAMOST K giants
Xue+14 SEGUE K giants
Xue+08 SEGUE BHBs
Battaglia+05,06 mixed objects

402000Milky Way Stellar Halo

20406080
100 120
Galactocentric radius Rgc [kpc]140160Sarah A. Bird

HaloK giantsKinematics

Mass*

Contents

1Stellar Halos2

LAMOST K-Giant Halo Stars

3

Results: Kinematics

4

Results: Galactic Mass Estimation

5Conclusion

Milky Way Stellar HaloSarah A. Bird

HaloK giants

Kinematics

Mass*

Jeans equation and virial theorem
Jeans equation describes the motion of a collection of tracer
particles in a galactic potential dΦdr2β 2dΦd(νσr2 ) +νσr = νdrr
drσr radial and σt tangential velocity dispersion profile
anisotropy parameter β = 1 −ν density profile of particles

2σθ2 +σφσ2= 1 − σt22σr2r

Virial theorem describes the system as a whole, relating
together the average over time of the kinetic and potential
energies. For example the system here is a galaxy.

GMhv 2 i =r
Milky Way Stellar HaloSarah A. Bird

HaloK giants

Kinematics

Mass*Tracer mass estimator Evans+11Nr 0.5 (0.5 + γ − 2β) X 0.5 2Mout ≈ outri vr ,iGN
i=1

Estimates mass Mout out to the distance rout of the furthest
data point
Observations of N number of halo tracers
radial velocity vrgalactocentric distance r

Assumptions
simplest case dynamics: spherical system traced by anon-rotating relaxed population in equilibrium
Navarro-Frenk-White dark halo density profile
tracer number density ∝ r −γ with γ ≈ 4 Xu+17

velocity isotropy (β = 0)
Milky Way Stellar HaloSarah A. BirdHalo

K giants

Kinematics

Mass*

Milky Way mass profile: LAMOST + SEGUE
1.6

LAMOST+SEGUE K giants
total
Bovy & Rix (2013) baryons
NFW fit: c=23, Rvir=208 kpc

M(<Rgc) [1012 MO• ]

1.4
1.2
10.8
0.60.40.2010
Milky Way Stellar Halo100
Galactocentric radius Rgc [kpc]Sarah A. BirdHalo

K giants

Kinematics

Mass*

Milky Way mass: LAMOST + SEGUELAMOST contributes toover half our sample
5 < Rgc /kpc < 200
over 10,000 K giants
NFW fit:r200 = 210 ± 16 kpc
concentrationc = 23 ± 5
M200 =0.9 ± 0.3 × 1012 M⊙
figure: Bird+17, adapted from Wang+15

Milky Way Stellar Halo

Bird+17Huang+16
Kafle+14
Kafle+12
Watkins+10
Gnedin+10
Xue+08Battaglia+05
0.5

11.5
2
M200 [1012 MO• ]2.5

3

Sarah A. Bird

HaloK giants

Kinematics

Mass

*

Milky Way circular velocity profile
450vcirc(Rgc) [km s-1]

400
350
300
250

LAMOST+SEGUE K giant Bird+17
SDSS K giant Xue+14
SDSS BHB Xue+08
total
Bovy & Rix (2013) baryons
NFW fit: c=23, Rvir=208 kpc

200
150
100
50010

Milky Way Stellar Halo100
Galactocentric Radius Rgc [kpc]Sarah A. Bird

HaloK giants

Kinematics

Mass*Contents

1

Stellar Halos2

LAMOST K-Giant Halo Stars

3

Results: Kinematics

4

Results: Galactic Mass Estimation5Conclusion

Milky Way Stellar HaloSarah A. Bird

HaloK giants

Kinematics

Mass*Thanks!
Summary:
LAMOST contributes to overhalf our sample of > 104K-giants
140

Flattened velocity dispersionprofile

Galactic circular velocity profile
with LAMOST+SEGUE
Collect ∼ 104 halo stars withLAMOST

σlos [km s-1]

Galactic mass estimate withLAMOST+SEGUE

120
1008060
Bird+17 LAMOST K giants
Xue+14 SEGUE K giants
Xue+08 SEGUE BHBs
Battaglia+05,06 mixed objects

40200020406080100 120
Galactocentric radius Rgc [kpc]140160Combine LAMOST+Gaia tomeasure 3D velocities
email: sarahbird@shao.ac.cn
Milky Way Stellar HaloSarah A. Bird