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The Story so far.
The Nature of Astronomy—based on observation
Our information largely comes from electromagnetic radiation emitted
- EM radiation has const. vel. in vacuum c = λν
- all λ exist
- can be polarised
Black Body radiation
-Stefan-Boltzmann Law PA = σT4
-Wien’s Law λMAX.T = 2.9 x 10-3 m.K
Atoms can only exist in discrete energy levels. Consequently transitions
between levels have discrete energies. The spectrum of lines is
then characteristic of the chemical element.
Kirchhoff’s Laws:- Summary of observations about BB spectrum
and both emission and absorption spectra
Doppler shift:Z = [(c + v)/(c - v)]1/2 - 1 = / 0
If v  c then we can write
 = v/c.
Stellar spectra-4
Here we see the atomic spectra
for white light,sunlight and a
series of elements.
Note that the last spectra are for
Na in emission and absorption.
These spectra provide clear
fingerprints for the chemical
elements.
Molecular Spectra
Molecule can rotate and vibrate so in
addition to the discrete levels we have
levels built on them with energies
associated with them.
We end up with closely spaced bands
of levels built on each intrinsic level.
[Rotations and vibrations]
Vibrations:- Levels equally spaced
Rotations:- LevelsE = (h/2)2.[I(I + 1)]
2ζ
where ζ is the moment-of inertia
Information on Surface Temperature from Spectral Features.
• Stars contain 75% H and 25% He plus small amounts of other elements.
• At T = 6000K we have 3/2 kT  eVs. This is similar to the binding
energies of molecules.At this T they are broken up in collisions.As T
rises spectral features related to molecules will disappear.
• At low T atoms are neutral.As T increases collisions cause them to be
ionised.At even higher T they become doubly then triply ionised etc.
The spectra of ions differ from those of atoms.
• We get a progression as T increases.At low T we have neutral atoms
and molecules.The latter disappear and the former fade as T increases.
We then get spectra from singly charged ions. At still higher T we get
doubly charged ions.
• H line is n = 2 to n =3 absorption line. The n = 2 level is first excited
state in H.It is in middle of red part of spectrum.
At low T very few H atoms are thermally excited so H is weak.
As T increases so does occupation of n = 2 level and H becomes
stronger. This absorption line reaches a peak at 10,000K. Beyond this
many of the atoms are ionised and it fades again.
Summary of Stellar classification
[Metals?]
Temperature
Remember-each of the classes is further subdivided 0-9
In the last few years there has been an attempt to introduce two more groups on the
low temperature end. These are faint stars at low temperature, more and more of which are
being classified. They are L and T. L stars have T between 1300 and 2500K. One sees a lot
of metal hydride molecules such as CrH and FeH. T dwarves are even cooler and show a lot
of methane. They are, in general, failed stars like Jupiter.
Classification of Stellar Spectra – Harvard Scheme
TYPE Colour
O
B
A
F
G
K
M
Approx T
Blue
>25000K
Blue
11-25000K
Blue
7.5-11000K
Blue/white 6-7500K
White/yellow 5-6000K
Orange/Red 3.5-5000K
Red
<3500K
Main Characteristics
Singly ionised He in emission/absorption
Neutral He in absorption
H lines at max. strength for A0, decreasing thereafter
metallic lines become noticeable
Solar-type, Absorption lines of metallic atoms/ions grow
Metallic lines dominate
Molecular bands of TiO noticeable
Examples
10 LACERTA
RIGEL/SPICA
SIRIUS/VEGA
CANOPUS
SUN
ARCTURUS
BETELGEUSE
Temp.
Within each of these broad categories Annie Jump Cannon assigned sub-categories 0 – 9 with 0 being at the high T end.
This is known as the Harvard scheme. It was funded by the wife of a wealthy doctor-Henry Draper and was carried out
by a team composed largely of women [see photo of them in Universe, 6 th Ed. Fig 19.10]. They included Williamina
Fleming, Antonia Maury and Annie Jump Cannon.
Later Cecilia Payne and Meghnad Saha showed that the catalogue the Harvard group created and classified was an
indicator of surface temperature.
Note:- The spectra reflect the temperature and composition of the surface and essentially the composition of the Star prior
to formation since no nuclear reactions occur in the surface and there is little mixing with the interior
A full classification should include Luminosity - See YERKES or MMK classification scheme.
UV
N and O
O3
Proportion of light
which arrives at
sea level
H2O
Ionosphere
Altitude at which atmos.
reduces intensity of radn
by one-half.
• Picture shows absorption of radiation by Earth’s atmosphere.
There is strong absorption by N and O in the X-ray and gamma-ray
regions, strong absorption by ozone in the UV,absorption of H2O in
the infrared. Free electrons in the ionosphere reflect very long 
radio waves.
Telescopes
• Astronomy arose from a) curiosity about the stars, b) desire to predict
seasons and c) need to use it to navigate.
• We can see  5,000-6,000 stars by eye in a clear sky.
• There have been several “revolutions” in Astronomy.
Astronomy
1)Galileo’s and Newton’s telescopes
2)Development of Radio-Astronomy
followed by extension of observations
to all parts of the spectrum.
3)The ability to place instruments in
space to avoid the distorting effects
of the atmosphere and the strong
absorption at some wavelengths.
Sir Isaac Newton(1642-1727)
Galileo’s and Newton’s telescopes
• There are two types of telescope based on lenses(Galileo) and
mirrors(Newton).
• Light travels in straight lines.
• Stars are a long way away and so light
n1
1
arriving from them is essentially in the
form of parallel rays.
• What happens when it crosses the
n2
boundary between two media.As we see
2
in the figure its path is bent.The amount
by which it is bent is given by Snell’s Law
Snell’s Law
• If we write the index of refraction for a single medium as
n1 = c/v then we can write
n1.sin 1 = n2.sin 2
This is an empirical law that comes directly from observation.
• Galileo did not invent the refracting telescope
but he used it to great effect.[see UNIVERSE
ed.6,page 70]
• One should note that with lenses and mirrors
light follows the same path through the system
in either direction.
•
Galileo Galilei
(1564-1642)
a)With a converging lens a beam of light
parallel to the axis of symmetry(optical axis) can be brought to a focus
b)With a diverging lens the parallel beam appears to diverge from a pt.
This unique point is called the FOCAL POINT and distance from this
point to the centre of the lens is called the Focal Length(f).
Note:- f = f() for lenses.
Refracting Telescope
• If we take the positive direction as the direction of the incoming light,
then f is +ve for a converging lens,-ve for a diverging lens.
• Lensmaker’s formula:- For a thin lens,assuming the surfaces are
spheroidal, we can write
1 = ( n - 1)[ 1/ R1 - 1/ R2]
f
Where n is the index of refraction of the lens, R1 and R2
are the radii of curvature of the two surfaces. For convex
lens R is +ve, and for a concave lens R is -ve.
Objectives of Telescope Design
There are three main objectives of telescope design:a)To maximise brightness of the image-to allow us to see
faint objects.
b)To resolve objects separated by small angles.
c)To magnify the image so that objects can be seen to have
size.
Image Brightness
• The amount of light a telescope can gather is called the
LIGHT GRASP.
• For simple designs the light grasp is proportional to the
cross-section of the aperture where the light enters.
• Simple telescopes almost always have a circular aperture so
the cross-sectional area is just
( D/2 )2 = D2/4
where D is the diameter of the opening.
• Put simply LIGHT GRASP  D2
• With the naked eye on a clear night we see  5,000-6,000 stars
With a telescope( D = 20 cm ) we see  500,000 stars
Resolving Power
• How well can one separate the images of two closely spaced objects?
-It is dictated by diffraction of light at the aperture.
• Figure shows diffraction at a single slit
with a width b. Assuming a wavefront
arrives at the aperture any ray passing
through can be associated with a ray
leaving the aperture a distance b/2
away.If they are /2 out of phase then
destructive interference occurs.Then
b/2.sin1 = /2 or sin1 = /b
• If we divide the aperture into 4 parts then
b/4.sin1 = /2 or sin1 = 2/b
More generally sin1 = m/b where m = 1,2,3,4,---------Thus we get darkness on the screen at these points and we get the
diffraction pattern shown in the figure.
Rayleigh’s Criterion
• The figure shows examples of the two overlapping diffraction patterns
from two sources.
• In two dimensions situation is more complicated.We get a bright, central
spot called an AIREY disc. The eqns. for location of maxima and
minima are the same but m is no longer a simple integer. The first two
minima have m = 1.22 and 2.233.
• Many possible criteria for resolution but most common is
RAYLEIGH’S CRITERION = Two objects can be resolved if first
minimum of one coincides
with the centre of the Airey
disc of the other.Assuming
that sinm = m where m is
the angular separation,then
m = 1.22/b
• In figure right and left are
cases well resolved and unresolved.In the centre Rayleigh’s criterion.
Resolving Power
•From Rayleigh’s Criterion m = 1.22/b and resolving power increases
with increasing b, decreasing . In other words good resolution is
achieved when  is much smaller than the aperture so that light is not
affected by it.
• m does not improve without limit as we increase b -this is because of
turbulence in the atmosphere. The local changes in atmospheric density
cause refraction in many different directions. This causes stars to appear
to twinkle. Since angular sizes of planets are much larger than scale of
turbulence the distortions average out and they do not twinkle.
Atmosphere
Eye
Attempt to show how the Earth’s
atmosphere behaves like a continuously
varying,thick,weak lens. As a result the
light from a star appears to enter the eye
from different directions. It is grossly
exaggerated here.
Magnification
• We only benefit from resolving power if the telescope has sufficient
magnification as well.
• Although we see a star as a point source it subtends a definite angle in
the sky.Our design must make it appear to subtend a larger angle.
• We define ANGULAR MAGNIFICATION = Apparent angle
Actual angle
• The picture compares the angular sizes of Venus, Moon and Sun.
By chance the Sun and Moon both subtend 0.50 although the Sun is
400 times farther away.Venus subtends 0.0170 so to see Venus the
same size as we see the Moon we need Ang.Magn.= 0.5/0.017  30
Refracting Telescope
• Stars have a small angular size (exaggerated here). The converging lens
forms an image at focal length f0. It would appear on a screen at this pt.
• This image is the object for the second lens and is at the focal pt.
Now the light will emerge as almost parallel rays but at a much larger
angle( ) to each other.[Note:-The image at the end is inverted]
• Simple geometry suggests that Angular Magnification = / = f0/fe
• If we relax the condition that  is small then eqn. is not strictly valid but
if we adjust the lens separation a little we can get a focus and it remains
a good approximation.
Difficulties with lenses and refraction
• It is relatively easy to make a small refracting telescope. If f0/fe is large
then we have good ang.magn.The sum of ( f0 + fe ) should equal the lens
separation with a control to allow length variation to correct the focus.
• However a large telescope of this type is difficult to make.
- You need a large aperture to get the Light Grasp but it is very difficult
to make large,high quality lenses. Even if you can there are problems
supporting them within the telescope so that light passes through but
the device does not sag.
• In addition the focal length varies with
wavelength although not a strong function.
This is CHROMATIC ABERRATION.
• It is negligible in a small telescope with thin
lenses but becomes unacceptable in a large
telescope.One possible cure is a compound
lens which together give no variation with .
This is impractical for a large objective lens.
The Reflecting Telescope
• Here the concave mirror replaces the objective
lens - to collect light and form first image.
Light is reflected down the telescope back
towards the object being viewed.A small flat
mirror is placed inside the telescope to deflect
the light to where it can be viewed.A flat mirror
does not affect the image but does cut out some
light and the image is a bit fainter.
• Mirrors reflect light in same way independent of  so
problem of chromatic aberration is overcome.
• Separation of mirror and lens remains the same,equal to ( f0 + fe ), but
since the light is reflected back on itself the telescope is shorter, thus
improving the mechanical stability. Mirrors can also be supported from
behind.They can also be produced on a large scale with great accuracy.
The surface is usually coated with Al-this can be removed and recoated.
Problems with Reflecting Telescopes
• First main problem is choosing the shape of the mirror
• Different mirror shapes give different
problems depending on the task in
hand.
As we see on right of figure a
spherical mirror suffers from
SPHERICAL ABERRATION
• As we see on the right the solution
lies in the use of a PARABOLIC
mirror.
However this only works for axial rays and this limits the field of view.
• Non-parallel rays are focused by
curved mirrors in different positions.
COMATIC ABERRATION
Problems with Reflecting Telescopes
We looked earlier at the distortion of the image due to atmospheric turbulence.
Variations in air temperature also have another effect
- the mirror will distort a little due to variations in atmospheric temperature
- the mounting of the mirror may also flex mechanically due to such variations.
Active Optics – Every few seconds the mirror’s shape is adjusted to help keep the
telescope at optimum focus and also aimed at the object of interest.
Another limitation :- Clearly from what we saw about Light Grasp and angular resolution
we would like to expand the filed of view i.e. make the entrance aperture larger
However if we have a larger mirror it gets harder to cope with spherical aberration.
One solution is a CATADIOPTRIC system. Note: A reflecting system is catoptric and
a refracting systems is dioptric. This is a combination of the two.
Schmidt Camera
• A CATADIOPTRIC system must be used to increase the field of
view without the image suffering from spherical aberration.
• SCHMIDT camera shown below uses a spherically shaped film
plate placed inside and concentric with a spherical mirror.
• A thin glass correction plate is placed over the front of the telescope.
Refraction as the rays pass
through the plate corrects
spherical aberration but does
not decrease the field of view
available.
• This instrument is able to take
single focus photographs of
the sky over several degrees.
After
Before
SN1987A- This picture was taken with a Schmidt camera. It shows
a part of the sky in October 1987 before and after a supernova.
Adaptive Optics
• Variations in atmospheric density cause the blurring of images by
scintillation.
• Here the light is directed into a feedback system in which a computer
controls a small flexible mirror so that the image of a chosen bright
star always appears as a point source.
• The detector retains an image
that is corrected for the effects
of disturbances in the
atmosphere for objects close
to the chosen bright star in the
field of view.
Problems with Reflecting Telescopes
Atmospheric effects
- Turbulence causes “twinkling”
Solution – active optics
- adaptive optics
- variations in mirror or mirror mounting
light pollution
- more and more street lights, disco lasers etc
Solution-remote location
Atmospheric absorption
- solution-remote location on a mountain top well away
from sources of light pollution.
- dry to limit rain and clouds
- calm
- as high as possible
UV
N and O
O3
Proportion of light
which arrives at
sea level
H2O
Ionosphere
Altitude at which atmos.
reduces intensity of radn
by one-half.
• Picture shows absorption of radiation by Earth’s atmosphere.
There is strong absorption by N and O in the X-ray and gamma-ray
regions, strong absorption by ozone in the UV,absorption of H2O in
the infrared. Free electrons in the ionosphere reflect very long 
radio waves.
Problems with Reflecting Telescopes
Atmospheric effects
- Turbulence causes “twinkling”
Solution – active optics
- adaptive optics
- variations in mirror or mirror mounting
light pollution
- more and more street lights, disco lasers etc
Solution-remote location
Atmospheric absorption
- solution-remote location on a mountain top well away
from sources of light pollution.
- dry to limit rain and clouds
- calm
- as high as possible e.g Mauna Kea in Hawaii
Telescope in orbit or on Moon/Mars etc in future
Astronomy beyond the visible
• Observations are now possible at all
wavelengths. Radio spectrum is not absorbed
Incoming Radiation
by the atmosphere.
Receiver
• Two ways of mapping the sky.
-Move disk across the sky
-Keep receiver fixed and scan reception freq.
• m = 1.22 
D
Here D  102 m
and   104 - 106VISIBLE
So m is much poorer than for a
telescope in the visible.
Parabolic Metal dish
• Solution lies in Interferometry.
Astronomy beyond the visible - 2
• Radio-Interferometry- - long baseline = many kilometres.
Single  so receivers have to lock into single phase co-ordinated
with an atomic clock.Roughly aperture in a linear array is equal
IR
Radio waves
to length of the array.
• Atmospheric absorption is the
problem in many parts of the
spectrum.There are some windows
in IR which allows observation in
some elevated places with a warm
dry climate.
• Note that the eye is not the detector in any of the detectors we have
looked at.Real detectors include a) Film, b) Photomultiplier tubes,
c)Charged Coupled Devices = An array of small detectors on a Si
chip. Electrical charge is proportional to light arriving.