Download ASTR2050 Spring 2005 •

ASTR2050 Spring 2005
Lecture 11am 22 March 2005
In this class we will cover “Clusters of Stars”:
• Types of clusters
• Distances to clusters
• Cluster dynamics: The Virial Theorem
• HR diagrams: Ages and populations
1
Types of Clusters
Assumption: All stars in a cluster are (about) the same age
• “Galactic” or “Open” clusters
• In the Galactic disk
• ≤1000 stars and ≤10pc across
• Sometimes associated with gas/dust clouds
• “Globular” clusters
• Appear grouped about the Galactic center
➽ Find center of the Galaxy at 10kpc
4 to 106 stars and 20 to 100 pc across
10
•
• No gas/dust clouds
2
Examples of Open Clusters
M6 “Butterfly Cluster”
M37
Age ≈50 Million years
Age ≈300 Million years
See Kutner Figure 13.1
3
Examples of Globular Clusters
M5
M80
Age ≈13 Billion years
Age ≈15 Billion years
See Kutner Figure 13.2
4
Distances to Clusters
• Main Sequence matching
• Recall 18 Feb studio class (“Pleiades”)
• OK for all clusters (but, later this class...)
• Cepheids and RR Lyrae stars
• Useful if you can find them
• Globular clusters have many RR Lyrae
• Star motion in “moving” clusters
• Accurate method, but...
• Clusters must be nearby
5
Distances to Moving Clusters
Kutner Fig 13.3
vr
A
)
vT
v
Distance d is determined from
proper angular motion µ which
arises from tangential speed vT :
vT (km/sec)
µ(rad/sec) =
d(km)
Li
ne
of
Sig
ht
Star
The Doppler shift is used to
measure the radial velocity vr.
A
)
Observer
2
2
2
=vr + vT
v
tan A=vT /vr
or for d(pc) and µ(arcsec/year)
d = vT /4.74µ = vr tan A/4.74µ
So how can we measure A?
6
Convergent Point
A cluster of stars will
appear to move towards
a “convergent point”.
This makes it possible to
determine the angle A.
Example: The Hyades
Identify the
“convergent
point” using a
large number of
moving stars.
A
7
Cluster Dynamics and The Virial Theorem
Consider the motion of a mass in a circular orbit:
1 2 1 mv2 1 GMm 1 GMm
1
K= mv = R
= R 2 =
=− U
2
2 R
2 R
2 R
2
So, the total energy is E = K +U = U/2 < 0
For a collection of objects (like a cluster of stars) that
are moving in equilibrium, this relationship still holds:
!K" = −!U"/2
and
E = !K" + !U" = !U"/2
This powerful result is known as “the virial theorem”.
See Kutner section 13.3.1 for the derivation
8
Example: Why don’t clusters fly apart?
See Kutner Section 13.3.2
2
3
GM
Assume the cluster is a sphere
of mass M and radius R. Then U = − 5 R
(15 Feb 10am)
If the cluster has N stars each
# of mass
$ m, then
N
K=!
i=1
!
"
1 2
1
1 N 2
m!vi = (mN)
!vi
!
2
2
N i=1
1
2
= M!v "
2
so that !v " = 2K/M = −U/M = (3/5)GM/R
But
2
1 2
GMm
GM
2
2
mvesc =
⇒ vesc = 2
> "v #
2
R
R
Also: Homework problem on “Virial Mass”. (We’ll use this later.)
9
HR Diagrams: Ages and Populations
A young cluster
An old
cluster
10
Globular clusters are different
M3
12
Horizontal
branch
14
16
V
18
RR Lyrae
Blue
stragglers
Turnoff
20
22
-0.5
0
Sun would be still on the main sequence,
but globular clusters are much older !?
11
0.5
B-V
1
1.5
☛
Stellar Populations
Globular clusters are nearly pure H and He (no “metals”)
and stellar evolution details are sensitive to composition.
Galactic clusters are more typical of stars in the galactic
disk, including “metals”. We call these Population I stars.
Low metallicity stars, like those found in globular clusters,
are called Population II stars.
We think of Population I stars as “young”, and made up of
recycled materials. Population II stars are “old”, and might
be made from primordial materials from the birth of the
universe.
12