The Milky Way
I suggest to consult the excellent lectures held at Saas-Fee by
Gilmore, King and van der Kruit in the Book “The Milky
Way as a Galaxy” edited by Buser & King and published by
the University Science Books. Indeed these lectures on the
Milky Way are simply introductory and for a deepest
understanding I suggest reading the book that is indeed a
good book to keep in your own libray.
I use these lectures as an introduction to the dynamics of
galaxies, a subject a will deal with next.
1
Scale height and Luminosity
By counting stars as a function of the
distance from the Sun I can measure
various quantities, some of these are:
D(r) The density of stars of any
spectral type.
DS(r) The density of stars for a given
spectral type.
The above are generally defined
respect the density of stars near the
sun.
We can also define a scale height
counting stars perpendicular to the
galactic plane. Obviously the density
distribution perpendicular to the
galactic plane will also depend from
the the distance on the plane from the
galactic center. For a model see for
instance Kent, Dame and Fazio 1991.
The scale height, αS is defined for the
spectral type S by the following
equation:
The step is accounted for by the life
time of main sequence stars, the age
Of the disk etc.
DS(z)=DS(0) e-(|z|/αS)
Keeping in mind that about the plane
the plane the cusp must be modified by
a Gaussian.
2
Scale Height of the Disk
Scale Height for various objects
500
Cp = Classical Cepheids
O_Cl= Open Clustres
PN = Planetary nebulae
Nae = Novae
Scale Heigt (pc)
400
300
200
100
0
O
Cp
B O_Cl D_G
A
F
PN
gK Nae dG
dK
dM
gG
Object
3
Scale Height above the disk
Old Galactic Objects
3500
WD = White Dwarfs
3000
V5_8 = Long Period Variables M5
M8
RRL< = RRLyrae P<0.5 days
RRL> = RRLyrae P<0.5 days
WV = W Virginis Variable
Scale Heught (pc)
V0_4 = Long Period Variables M0
M4
2500
2000
1500
1000
SD = Subdwarfs
GCl = Globular Clusters
500
0
dK
dM
gG
WD V5_8 RRL< V0_4 RRL> WV
SD
GCl
Object
4
The |z| density distribution of K-dwarfs
5
The Nuclear Region
The radial velocities are from
Genzel and Townes
1987. Note that the
region shown here is of
about 4.8 pc.
It seems we are looking at a
spiral arm structure.
Obviously the peculiar
structure we see must
also be inclined to the
plane
otherwise
we
would not be able to see
the pseudo arms.
Compare next with the
velocity curve and with
the HI map. It seems
clear we are witnessing
organized motion.
6
The HI distribution
At the center a schematic
representation of the expanding
3 kpc arm (Rougoor and Oort).
That is almost 1000 larger than
the size of the previous
structure.
7
Mean velocities of stars near the Galactic Center
Referred to the position of
IR16
8
Velocity Dispersion
The student estimate the Mass as a function of
the distance from the center. We will do it also
later on in the course when we study the
dynamics of Galaxies. Look also at the
rotational velocity.
Black Hole or Stellar Cluster?
9
Velocity of OH/IR stars
Galactic Longitude
10
Molecules, Radio continuum and much more
The center of our galaxy is very much
revealing about the activity observed in
other pseudo normal galaxies and in
active galaxies.
As we know the Center is very much
obscured
by
dust,
Indeed
a
concentration of stars at the very center
can be observed only if we use the K
band at 2.2 microns.
We have in the innermost 2 pc region the
emission of ionized gas and molecules.
But we also receive Gamma rays from
sources emitting at .511 MeV
positorn electron annihilation and
Gamma ray continuum. But we also
receive in line radiation, 1.8 MeV, due
to the decay of Al26 (lifetime about 106
years).
The nuclear region is rich of on going
phenomena and may make us
understand details on the physics of
external galaxies.
11
And now?
The frame covers about 50 x 50
parsecs and South is to the
right. These radio emission
carried out at 20 cm maps a
very particular structure since
the emission come from parallel
wisps and bend of about 90
degrees. In addition it has been
observed the presence of strong
polarization .
Quite likely the structure observed
is due to a strong magnetic field
of about 10-2 Gauss (the mean
field of a Galaxy is generally
10-5 Gauss).
12
The spiral arms – Open Clusters
Young Clusters and
Stellar Associations
13
Now let’s see further away from the Center
We use of the Globular Clusters as a
probe of the old population
distribution.
In the Figure I show the H R plot of a
Globular Cluster.
HB = Horizontal Branch
AGB = Asymptotic Giant Branch
RGB = Red Giant branch
SGB = Sub Giant branch
MS = Main Sequence
TO = Turn Off Point
BS = Blue Strugglers
14
A Younger Cluster M92
Globular clusters are fundamental in
the determination of the Age of the
Universe being among the oldest
objects we know.
Thanks to the theoretical knowledge
we have on the stellar evolution we
can estimate the age of these objects
quite accurately.
In this Clusters we have a very well
defined main sequence turning off at a
magnitude of about V=18.5. Here we
begin to burn hydrogen in a thick shell
which will narrow in the course of its
evolution. More massive stars are
already forming the gian sequence.
15
Turnoffs and Main Sequence for GCl.
16
The age
Stella evolution tracks allow the estimate of the age of
Globular clusters.
Uncertainties are however present both because we do not
know accurately the metal abundances and because we have
observational uncertainties on the distance, photometry and
other parameters.
The reference age is in the range of 13 – 16 Gyr with an
uncertainty of 2 – 3 Gyr.
From theoretical studies and evolutionary tracks we can
derive an equation relating the Luminosity of the turn off
point to the age of the cluster. This is equation (1).
The time spent on the main sequence, the core hydrogen
burning phase, depends on the the amount of hydrogen
available for burning and on the Luminosity of the star.
Assuming that the fraction of stellar mass which takes part
to the hydrogen burning (very dubious assumption – see
also Christensen - Dalsgaard) and the efficiency by which H
is transformed into He is not a function of the stellar mass
we derive for the duration of the Main sequence phase
equation (2).
( 1)
L 
2
log  TO  ≈ 0.019 ( log Z ) + 0.065 log Z + 0.41Y − 1.179  log ( t9 )


L 
+ 1.246 − 0.028 ( log Z ) − 0.272 log Z − 1.073Y
2
( 2)
tMS ∝ M −(ν −1)
∼ 3 ≺ ν ≺ 5 ⇔ M = 15M
tMS ∼ 107 (TBC )
17
Distribution and Abundance
Given the distribution of Globular Clusters it is fairly easy to estimate
the centroid of the distribution and assume that coincide with the Center
of the Galaxy. By definition then we have the distance of the Sun from
the Center of the Galaxy.
The observations could be RA and D with the determination of the
distance via the RR Lyrae stars (or better Main Sequence fitting),
estimate of the interstellar absorption and transformation of coordinates
in order to have (x,y,z) with the x axis pointing to the Galactic Center
and the y in the direction rotation (l = 90, b = 0). The North Galactic
pole is the direction of z (b = 90).
The values <x> <y> <z> give the distance from the Galactic Plane and
from the Sun (a lower limit since, due to obscuration, we can not
observe very many distant clusters. From the List of Clusters give in
Cox Astrophysical Quantities the students estimate these parameters.
z
b
l
x
y
18
Globular Clusters respect to the Sun
40
Z
20
0
-20
-40
20
Y
0
-20
-40
-20
-40
0
20
40
X
19
Plane Y_Z Globular Clusters
40
Z
20
0
-20
-40
-40
-20
0
20
40
Y
20
GCl Plane X_Z
40
Z
20
0
-20
Distance of the Solar System
From the Center of the Galaxy ~ 8.8 kpc
-40
-40
-20
0
X
20
40
21
Distribution of Clusters
Globular Clusters are the brightest objects located in
the halo of a galaxy. They seem to cover a region of
about 30 – 40 kpc delimiting in this way the Halo of
the Galaxy ( see Zinn, 1985, Ap.J. 293, 424). Those
clusters that are more thn 40 kpc above the galactic
plane may not belong to the Galaxy.
Many are located near the galactic plane and the metal
abundance, [Fe/H], is much smaller than solar. A fact
that is relevant when considering the formation of the
Galaxy.
22
Number of Clusters per
kpc3
Number Density of Globular Clusters
Distance from the
Galactic Center
23
Abundances
The estimate of the abundances of
the heavy elements is of
fundamental importance because it
reflects the result of previous
evolution of the stellar content.
The
determination
of
the
abundances is accurate for those
elements for which it is possible to
observe many spectroscopic lines
and when the physical parameters
of
the
emitting
regions,
Temperature and Pressure, are
accurately known.
The metals are more abundant
near the Galactic Center.
24
Abundances in Astronomy
Wi = N A * mi grams N A Number of Avogadro; mi ≡ mass of nucleus i
WHe = 4.0026; ρ m = ∑ N i ( Number density )* mi
i
12
W
C) 1
(
1
12
12
Atomic weight W ( C ) = A ( C ) = 12 ⇒ Unit of A ≡
=
=
12
N A 12 N A
m12 C
B


m j ( A,Z ) =  Z j mH + ( Aj − Z j ) mn − j 2  ; mH = m p + me ; B j = nuclear binding energy
c 

Z ≡ Ch arg e Number; A ≡ Mass Number
WH = 1.007825;Wn = 1.008665
ρ m = ∑ N i * mi =
i
∑ N *W
i
i
NA
i
~ρ=
∑N * A
i
i
NA
i
; Nucleon Fraction ≡ X i =
N i * Ai
ρ NA
Xj
Nj
N i * Ai
Nucleon of species j
X
1;
Y
=
=
=
=
=
∑i i ∑ i ρ N
j
Aj ρ N A
Total # Nucleons
A
25
Continue – Convention
n = ∑ j N j Aj Total Number of Nucleons; ∑ j Y j
∑
=
j
Nj
n
≠ 1 generally
in Astronomy
By definition the# of Hydrogen atoms equals 10 12
log y j = log f H + log Y j or
 N


N
j
 i  ≡ log 
i
− log 

 j 
( N j )
 ( N i ) 

Ni

Nj
 = log
( Ni )


(Nj )
A 
Half solar Abundance of ratio Ai to Aj ⇒  i  = log ( 0.5 ) = −0.3
 Aj 
26
They coexist
27
Distribution of Dark nebulae
28
HI and Absorption Lines, NaI & CaII
29
Some details
The observations have been carried out
in the I Persei association. The *
marks the radial velocity of the Stars.
The 21 cm profiles have been obtained
at separation of about 1 degree in
order to scan a reasonable region of
the sky in that direction.
There is strong coincidence in velocity
of the two components HD 14542
l=135.0 b=-3.3 with two well marked
maxima in the 21 cm profile l=135.2
b=-3.6
Same for HD 14143 l=134.6 b=-3.7
with 21 cm l=134.2 b=-3.6
30