and Cosmology

2. The Milky Way as a Galaxy
46
A schematic depiction of our Galaxy is shown in
Fig. 1.3. Its most important structural parameters are
listed in Table 2.1.
2.3.1 The Galactic Disk: Distribution of Stars
By measuring the distances of stars in the Solar neighborhood
one can determine the three-dimensional stellar
distribution. From these investigations, one finds that
there are different stellar components, as we will discuss
below. For each of them, the number density in the direction
perpendicular to the Galactic disk is approximately
described by an exponential law,
(
n(z) ∝ exp − |z| )
, (2.31)
h
where the scale-height h specifies the thickness of the
respective component. One finds that h varies between
different populations of stars, motivating the definition
of different components of the Galactic disk. In principle,
three components need to be distinguished: (1) The
young thin disk contains the largest fraction of gas and
dust in the Galaxy, and in this region star formation is
still taking place today. The youngest stars are found in
the young thin disk, which has a scale-height of about
h ytd ∼ 100 pc. (2) The old thin disk is thicker and has
a scale-height of about h otd ∼ 325 pc. (3) The thick disk
has a scale-height of h thick ∼ 1.5 kpc. The thick disk
contributes only about 2% to the total mass density in the
Galactic plane at z = 0. This separation into three disk
components is rather coarse and can be further refined
if one uses a finer classification of stellar populations.
Table 2.1. Parameters and characteristic values for the components
of the Milky Way. The scale-height denotes the distance
from the Galactic plane at which the density has decreased
Molecular gas, out of which new stars are born, has
the smallest scale-height, h mol ∼ 65 pc, followed by the
atomic gas. This can be clearly seen by comparing
the distributions of atomic and molecular hydrogen in
Fig. 1.5. The younger a stellar population is, the smaller
its scale-height. Another characterization of the different
stellar populations can be made with respect to the
velocity dispersion of the stars, i.e., the amplitude of
the components of their random motions. As a first
approximation, the stars in the disk move around the
Galactic center on circular orbits. However, these orbits
are not perfectly circular: besides the orbital velocity
(which is about 220 km/s in the Solar vicinity), they
have additional random velocity components.
The formal definition of the components of the velocity
dispersion is as follows: let f(v)d 3 v be the number
density of stars (of a given population) at a fixed location,
with velocities in a volume element d 3 v around v
in the vector space of velocities. If we use Cartesian coordinates,
for example v = (v 1 ,v 2 ,v 3 ), then f(v)d 3 v is
the number of stars with the i-th velocity component
in the interval [v i ,v i + dv i ],andd 3 v = dv 1 dv 2 dv 3 . The
mean velocity 〈v〉 of the population then follows from
this distribution via
∫
∫
〈v〉 = n −1 d 3 v f(v) v , where n = d 3 v f(v)
R 3 R 3
(2.32)
denotes the total number density of stars in the population.
The velocity dispersion σ then describes the
mean squared deviations of the velocities from 〈v〉.For
to 1/e of its central value. σ z is the velocity dispersion in the
direction perpendicular to the disk
Neutral Thin Thick Stellar Dm
gas disk disk bulge halo halo
M (10 10 M ⊙ ) 0.5 6 0.2 to 0.4 1 0.1 55
L B (10 10 L ⊙ ) – 1.8 0.02 0.3 0.1 0
M/L B (M ⊙ /L ⊙ ) – 3 – 3 ∼ 1 –
diam. (kpc) 50 50 50 2 100 > 200
form e −hz /z e −hz /z e −hz /z bar? r −3.5 (a 2 +r 2 ) −1
scale-height (kpc) 0.13 0.325 1.5 0.4 3 2.8
σ z (km s −1 ) 7 20 40 120 100 –
[Fe/H] > 0.1 −0.5 to +0.3 −1.6 to −0.4 −1 to +1 −4.5 to −0.5 –