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ASTC22 - Lecture 7 Milky Way's kinematics and structure. Parallax Luminosity and mass functions - a few basic facts Kinematics of the solar neighborhood Asymmetric drift Thin disk, thick disk Open and globular clusters - metallicity, age, distribution, motion Infrared view

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ASTC22 - Lecture 7

Milky Way's

kinematics and structure


Luminosity and mass functions - a few basic facts

Kinematics of the solar neighborhood

Asymmetric drift

Thin disk, thick disk

Open and globular clusters

- metallicity, age, distribution, motion

Infrared view

Galactic bulge and center

Differential rotation


Step number one:

measure the parallax (Hipparcos satellite, 1989-1993)

measure the apparent magnitude m.

This could be done for0.12 mln bright stars, with positional

accuracy ~milliarcsec (1 milliarcsec = 1/1000 seeing disk)

Step number two:

derive distance from (d/ 1pc) = (1” / parallax)

derive the absolute magnitude from distance modulus

m - M = 5 log (d/ 10pc) = 5 log (0.1” / parallax)

This gave accurate distances to ~few*100 pc.


The most numerous stars in the Galaxy are small, 0.3-0.5 Msun

M*(Salpeter IMF)



Frequency of stars with different masses = a power-law with exponent (index) -2.35


Thin and thick

disks of the Galaxy


Vertical velocity w.r.t. sun (W) as a function of stellar age:

stars are born in a thin disk with small W; old stars are in a thick disk.

-10 km/s


The Bottlinger diagram

for 200 main-sequence

star from the solar neighborhood

U = radial velocity difference

w.r.t. the sun

V = tangential velocity diff.

- pop I objects similar to the sun

U=U* - Usun

V=V* - Vsun

gc = Galactic center

in general (U,V,W)

V <0

U>0 or <0

Retrograde prograde

orbits orbits





Open clusters - e.g., Pleiades, Hyades

(Pop I)

16 Myr

100 Myr


gas nebulae


47 Tucanae is the second

brightest globular cluster.

It contains ~1 mln star.

It can only be seen from

the Southern Hemisphere.

This image is 34 arcmin

across, ~ 0.56 degrees

(comparable with Moon, Sun).

The infrared colors of all

these stars are very similar.


Globular clusters - e.g. omega Centauri, 47 Tucanae

(Pop II)

spherical system

thick disk

Connection between kinematics and geometry: thick disk of high-metallicity

globular clusters (left-hand panel) is made of objects on low-inclination, nearly-circular

orbits <=> the system has some prograde rotation.

Spherical system (right panel) has completely disorganized motions, no rotation

on average; some clusters have prograge, some retrograde motion, Orbits are highly



Age, distance, metallicity

are varied in models until

the predicted H-R diagram

(below) matches the

observations (above).

For instance,

47 Tuc has

[Fe/H] = -0.83 and age

~12 Gyr

M30 has

[Fe/H] = -2.31 and age

~14 Gyr

One also uses RR Lyr variables

(pulsating low-mass stars with

L~50 Lsun) as standard candles




(microns) (Kelvin) WHAT WE SEE

Near-Infrared 0.8 to 5 740 to 5200 Cooler red stars,

Red giants, Dust is transparent

Mid-Infrared 5 to 2590 to 750 Planets, comets, asteroids Dust warmed by starlight Protoplanetary disks

Far-Infrared 25 to 350 10 to 100 Cold dust Central regions of galaxies Very cold molecular clouds


Sub-mm and mm 850-2000 10 to 30 Larger (~mm), cold dust grains

Radio e.g., 21 cm HI line Global structure of the Galaxy,

hydrogen clouds


Infrared view of the center of the Galaxy:

optical view 2MASS (2 micron all-sky) survey

Picture made from star counts

(not a direct image)

total of 250 mln stars measured

in 2MASS.


Infrared view of

the Galaxy

hR = 2 to 4 kpc, both for the thin (hz ~ 0.3 kpc) and the thick disk (hz ~ 1.5 kpc)

Beyond R=15 kpc, the disk density is rapidly declining. The brightness distributions of

other galaxies show similar downturns.


Infrared view of the Galaxy: 2MASS (2 micron all-sky) survey

20% of Galaxy’s light from the bulge, R~1 kpc

Stars: few Gyr old, metal-rich unlike the metal-poor stars of the

galactic halo, the inner halo is also more round and does not show rotation

(bulge rotates in the prograde sense, like the sun, but slower:

<Vc> ~ 100 km/s)

A slight asymmetry of the bulge and additional kinematic data

show that the Milky Way has a central bar extending to

R=2-3 kpc. It is a Sbc galaxy or SABbc( r) - there can be no

perfect agreement when looking at multiwavelength data!

The center of the Galaxy (nucleus) is a very exotic place,

with the Sagittarius A* radio source, surrounded by a torus (R=7 pc) of molecular

gas, which flows in at a rate of 0.001-0.01 Msun/yr and formed dozens of

massive stars within the last 3-7 Myr. Nucleus (right panel, showing gas) is

much smaller than the black dot in the background picture.

A fairly dark and inactive, ‘starved’ black hole (m= 2-3e6 Msun) lurks in the center

of Galactic Nucleus (white dot).


Galactic Nucleus



Differential rotation of the Galaxy:

rotation with shear,

similar to Kepler’s laws

Differential rotation of the Galaxy was discovered by Jan Oort in 1927

using proper motions of stars at different galactic longitudes l,

because it varied as Vt ~ const + cos 2 l,

(which was actually known in 1900).


The position and velocity of the

“Local Standard of Rest” (solar neighb.)

Ro = sun-Galaxy center dist.

Ro = 8.5 kpc (IAU), 8 kpc (recent)

Vo= 220 km/s (IAU), 200 km/s (recent)

IAU=International Astron. Union

Rotation of

the Galaxy

Assuming circular motions of S and P,


Rotation of

the Galaxy

Errata (CUP,on-line)!



Jan Oort (1900-1992)


This section of the book shows you how A,B, Ro, Vo, are fitted

to the observed radial velocity it ! (other parts