1' INTRODUCTION TO STELLAR OBSERVATIONS

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1. INTRODUCTION TO STELLAR OBSERVATIONS
1.1 BRIGHTNESS, LUMINOSITY AND MAGNITUDES
LUMINOSITY Units of power i.e...... J
s-1 APPARENT LUMINOSITY l J m-2 s-1 as
measured by a telescope at Earth ABSOLUTE
LUMINOSITY Energy loss from a star
Earth
surface area 4pr2
r
star
DISTANCE MEASUREMENT Trigonometric parallax A
stars parallax is 1/2 the angle subtended at the
star by the diameter of the earths orbit around
the sun.
In practice the star appears to move throughout
the year against the positions of distant
stars. d R/Tan a A star at a distance of 1
parsec has a parallax of 1 arc second . (1 pc
1016 m 3 light years) Limit of utility 1/50²

• Other Techniques for Distance Measurement
• Cepheid variables (See later)
• A variety of techniques based on known
  properties of stars
• Red shifts for extragalactic distances
• NOTE the distance measurement process is
  pyramidal with increasing distance.
• Thus the measurement errors are compounded for
  objects at increasing distances.

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STELLAR MAGNITUDE The measurement of the
brightness (i.e..... amount of light received at
the earth in photons m-2 s-1) is logarithmic with
negative scale factor -2.515. (the 5th root of
100). Apparent Magnitude
Absolute Magnitude
Sun
-20 -15 -10 -5 0 5 10 15 20 25
Moon
Venus
Sirius
BRIGHTNESS
With the absolute magnitude set at 10pc. k1
-5 log1010
Eye
Pluto
1.2 SPECTRA OF STARS
Big Telescope
This classification is based upon the Black Body
radiation colour O stars are the
hottest M stars are the coolest
Luminosity
l
NOTE Knowledge of L and the surface temperature
of the star enables the radius of the star to be
estimated
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Black-body Spectra
The spectral shape is derived from the Planck
expression
1.3 HERTZSPRUNG-RUSSEL DIAGRAMME
The various measurable parameters (M,T,L)
associated with stars are not independent of one
another. The common physics for the various
classes results in a functional relationship and
consequent well defined positions on the H-R
diagramme. e.g. The main sequence represents the
HèHe burning phase. It appears as a line on the
H-R diagramme because the stellar mass is a free
parameter.
Log L
Supergiants
Blue Giants
Red Giants
Sun

Mass
Main Sequence
White Dwarfs
O B A F G K M
Log T
Much of this course work is related to the
identification of the physical processes
associated with the various star classifications.
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1.4 THE H-R DIAGRAMME FOR INDIVIDUAL
CLUSTERS The H-R diagrammes of individual
galactic clusters are of special interest. Since
the stars are physically bound together, all the
members of a single cluster will have been formed
from the same dust cloud at the same time - they
are all, therefore, of roughly the same age.
Furthermore, since all are effectively at the
same distance, there is no need to use the
absolute magnitude and the H-R diagrammes can be
prepared using the apparent magnitudes. Let us
look at some specific examples.
YOUNG OPEN CLUSTER - THE PLEIADES
m
T

• The stars are newly formed 106 years
• All stars lie along the main sequence from M to O

OLD OPEN STAR CLUSTER e.g. M36
m
O M
T

• The higher temperature (mass) stars disappear
• RED GIANTS appear

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VERY OLD CLUSTERS - GLOBULAR CLUSTER
L
O M
M5
T

• The stars turn off towards the Red Giants at
  lower temperatures
• The age of the Globular Cluster is gt109 years

• In General
• Stars do not live forever, presumably due to
  limited H to He conversion.
• Red (less massive) stars live longer

H-R DIAGRAMME FOR SELECTED GALACTIC CLUSTERS
Since all the stars in a cluster were formed at
roughly the same time, we see it frozen at some
point in its evolutionary history. The stars
greater than some transitional mass will have
evolved off the main sequence. If the lifetime of
a star on the main sequence is related to its
mass then the age of a cluster can be readily
estimated from the position of the main sequence
turn-off point. Clearly complications arise due
to interstellar reddening, distance measurement
etc....
m
Apart from understanding the relationship between
mass and main sequence lifetime, it is also
possible to evaluate the lifetimes of the stars
in phases other than the main sequence.
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1.5 STELLAR POPULATIONS AND GALACTIC STRUCTURE
POPULATION I STARS

• These are the youngest objects and must have been
  formed recently out of the interstellar dust.
  They have the following characteristics
• They are very rich (2-3) in heavy elements
  (metal rich)
• Recognised by O-B star types in young clusters,
  includes T-Tauri, d Cepheids
• Only exist in (lt200pc) the Galactic disk, and
  primarily in the spiral arms
• Low (lt10 km/s) velocities perpendicular to
  Galactic plane

POPULATION II STARS

• These represent the older and oldest stars in the
  Galaxy, many are as old as the Galaxy itself.
  They have the following characteristics
• They are very poor (lt1) in heavy elements
  (metal poor)
• They exist in the older clusters
• The oldest (extreme Pop II) exist in Globular
  clusters
• Pronounced motions (gt20 km/s) wrt the Galactic
  Plane

GLOBULAR CLUSTERS
Globular clusters represent the oldest stars in
the Galaxy and are characterised as follows

• Dense spherical clusters (about 100 in the
  Galaxy)
• Each cluster comprises 105 stars
• The composition is extremely metal poor, formed
  from nearly pure hydrogen
• They have a spherical distribution bout the
  centre of the Galaxy
• They move in eccentric orbits within the
  spherical halo with periods 108 y

Globular clusters appear to represent the
earliest stars formed in the Galaxy at a time
when the Galaxy had not yet collapsed to a
flattened disk-like structure.
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SCHEMATIC EDGE-ON VIEW OF THE GALAXY
Position of the Sun
10 kpc
15 kpc
NOTE the distribution of globular clusters, the
size scale, and the position of the Sun about 10
kpc left of the centre. There are about 1011
stars in the Galaxy. The central nuclear bulge is
clearly seen.
SCHEMATIC TOP VIEW OF THE GALAXY (Actually M51)
SUN
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1.6 THE MASSES OF STARS
The mass of a star is perhaps the most important
single physical parameter in terms of the
eventual fate of a star, but is extremely
difficult to measure. The most reliable methods
of the mass determination are when the star
situated is in a binary system.
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STELLAR BINARY SYSTEMS
10²
Ä 2030
Visual Binaries For the case of visual binaries
the separation of the stars is sufficiently large
and the system sufficiently close to the earth
that the motions of the stars across the sky is
detectable. The proper motions are, however,
somewhat more complex. For example the proper
motions of Sirius revealed the existence of a
faint white dwarf companion.
Ä 2020
270
90
l
Ä 2010
a Centauri
Ä 2000
Ä 1980
180
Sirius A and B
Spectroscopic Binaries
Transverse
Blue shift
Red shift
Transverse
If a binary system is situated at a larger
distance then the individual stars will not be
resolved within an image. However their periodic
rotation results in the periodic blue and red
Doppler shifts of spectroscopic lines as the star
periodically approaches and recedes from the
earth.
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Spectroscopic Binaries continued.

• Note
• The period of the sinusoidal Doppler shift is a
  direct measure of the period of the binary
  motion. However the amplitude of the velocity
  curve calculated from the maximum Doppler shift
  only represents the projected stellar velocity in
  the direction of the earth and not its orbital
  velocity within the binary system. Note also
  that, due to the different masses of the two
  stars, their projected velocities are different.
• If both stars emit a specific line then they will
  follow two separate sine curves 180 out of
  phase. Two emission line wavelengths will thus
  generally appear.

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Eclipsing Binaries
If the two stars in a binary system are
sufficiently close to one another and the
inclination angle i of the orbit is close to 90
then one star may pass behind the other. This is
an eclipsing binary. Note that, due to the low
separation of the stars they are unlikely to be
visual binaries, but will automatically be
spectroscopic binaries.
Total Eclipse
Partial Eclipse
Tidal Distortion
Hot-spot reflection
Note (i) Some possible complications may
occur in the light curves above (ii) When the
stars are close it is clear that the radiation
from one star effects the other. We cannot
assume that a free star of a given mass
will have the same colour and luminosity!
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THE APPLICATION OF KEPLERS LAWS
Typically 50 of all stars are found in binary
systems, which can be defined as two stars
gravitationally bound in orbits about a common
centre of mass. Observations of the dynamics of
the system can yield information about the masses
of the stars concerned. Since the masses are
generally comparable, each star will follow an
elliptical orbit around the common centre of mass
with the same period. For close binaries the
orbits usually approximate circles.
v2
a2
a1
M1
M2
v1
Period P
Barycentre
The centre of gravity is defined by
and
However, due to the inclination of the orbit, i,
(see previous page) we actually see
determines the Doppler shifts from M1
and
Keplers third Law states
and since
It readily follows that a mass function can be
defined as
NOTE
i) There are many forms of the mass function
possible. The equation can be arranged to include
only the observables. Above, spectroscopic Dlmax
measures v1sin i so that M1 can be estimated from
knowledge of P and M2 ii) The measurement of the
angle i is generally not possible, this is a
major problem. iii) For eclipsing binaries i 90
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1.7 STELLAR RADII
The radius of a star is an extremely important
parameter since it sets the surface gravity and
mean density for a given mass, and for a given
luminosity it determines the effective
temperature. A number of methods are available to
estimate the radii of stars.
Blackbody Radiation
Stefans law can be used to estimate stellar
radii, if we know the stars luminosity and its
effective temperature. However, stars are not
true blackbodies and the emission generally
deviates strongly from the blackbody curve.
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Lunar Occultations
The Fresnel diffraction pattern which is produced
as the moon passes in front of a star can be used
to measure the stellar diameter. The observed
pattern will differ slightly from a point
source, the more point-like the star the more
pronounced the oscillations. This method works
down to about 0.002².
(a) Large star
(b) Small star
(c) Point source
Time
Interferometric Measurement
A number of interferometric techniques have been
developed. Ground based phase interferometry can
reach about 0.01², and is essentially restricted
to large nearby stars.
Eclipsing Binaries
The accurate measurement of the intensity
profiles of the light curves associated with the
primary and secondary eclipses can be used to
evaluate the diameters of the stars concerned.
The complete orbital parameters of the system are
required for the best analysis. However as shown
above the analysis is difficult because the
relationships between the stellar and orbital
parameters and the properties of the light curve
are complex.