The Story so far.

1
The Story so far.

• The Nature of Astronomybased on observation
• Our information largely comes from
  electromagnetic radiation emitted
• - EM radiation has const. vel.
  in vacuum c ??
• - all ? exist
• - can be polarised
• ?Black Body radiation
• -Stefan-Boltzmann Law PA sT4
• -Wiens Law ?MAX.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.

?Kirchhoffs 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.?

2
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.
3
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-
Levels- E (h/2?)2.I(I 1)
2 ? where ? is the moment-of
inertia
4
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.
5
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.
6
Classification of Stellar Spectra Harvard Scheme
TYPE Colour Approx T
Main Characteristics
Examples O
Blue gt25000K Singly
ionised He in emission/absorption
10 LACERTA B
Blue 11-25000K Neutral He
in absorption
RIGEL/SPICA A
Blue 7.5-11000K H lines at
max. strength for A0, decreasing thereafter
SIRIUS/VEGA F Blue/white
6-7500K metallic lines become noticeable

CANOPUS G White/yellow 5-6000K
Solar-type, Absorption lines of metallic
atoms/ions grow SUN K
Orange/Red 3.5-5000K Metallic lines
dominate
ARCTURUS M
Red lt3500K Molecular
bands of TiO noticeable
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,
6th 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.
7
UV
N and O
H2O
Ionosphere
O3
Altitude at which atmos. reduces intensity of
radn by one-half.
Proportion of light which arrives at sea level
Picture shows absorption of radiation by
Earths 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.
8
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)Galileos and Newtons
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)
9
Galileos and Newtons 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 arriving from them
is essentially in the form of parallel rays.
What happens when it crosses the boundary
between two media.As we see in the figure its
path is bent.The amount by which it is bent is
given by Snells Law
?1
n1?
n2?
?2
Snells 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.
10
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.






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.
Galileo Galilei (1564-1642)
11
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.
Lensmakers 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.
12
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.
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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
14
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.
15
Rayleighs 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 RAYLEIGHS 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 Rayleighs
criterion.
16
Resolving Power
From Rayleighs 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.
Attempt to show how the Earths 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.
Atmosphere
Eye
17
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
18
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.
19
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.
20
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.
21
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
22
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 mirrors 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.
23
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.
24
Before
After
SN1987A- This picture was taken with a Schmidt
camera. It shows a part of the sky in October
1987 before and after a supernova.
25
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.
26
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27
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

28
UV
N and O
H2O
Ionosphere
O3
Altitude at which atmos. reduces intensity of
radn by one-half.
Proportion of light which arrives at sea level
Picture shows absorption of radiation by
Earths 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.
29
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
30
Astronomy beyond the visible
Observations are now possible at all
wavelengths. Radio spectrum is not absorbed by
the atmosphere.
Incoming Radiation
Two ways of mapping the sky. -Move disk
across the sky -Keep receiver fixed and scan
reception freq.
Receiver
?m 1.22 ? Here D ? 102 m
and ? ? 104 - 106?VISIBLE

So ?m is much poorer than for
a telescope in the visible.
D
Parabolic Metal dish
Solution lies in Interferometry.
31
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 to length of the array.
IR Radio waves
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.