Download Note: `n` - Centre for Astrophysics and Planetary Science

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Astrophysics
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Dr. Mark Price.
Centre for Astrophysics and Planetary Science,
Room 103 (Ingram, Mon. & Fri.).
E-mail: [email protected]
Lecture notes available at:
http://astro.kent.ac.uk/mds/lecnotes.htm
after each lecture.
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Lecture 1: Introduction to telescopes
Lecture Outline.
Lecture #1: Introduction to telescopes
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Basic optical principles
Refractor
Reflector
Advantages and disadvantages of each
Discussion of F-ratios/focal lengths/speed.
Lectures #2, #3: Introduction to the E-M spectrum
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General discussion of E-M spectrum from radio -> gamma rays
Heterodyne receivers
Bolometers & Golay cells
Photoconductors
Hand out assignment #7.
Lecture #4 and #5: Visible and beyond detectors.
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CCDs
Grazing incident focussing (X-rays etc.)
‘Exotic’ detectors (neutrino, gravity wave etc.).
Lecture #5: Space and ground based observatories
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Descriptions of ground based observatories and instruments (JCMT,
SCUBA2, ALMA etc.).
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Descriptions of space based observatories and instruments (SIRTF,
Spitzer, Kepler etc.).
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List of on-line resources.
Lecture #6: Revision and review lecture (as required).
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Telescopes.
There are two basic types of telescopes, refractors and reflectors. The part of the
telescope that gathers the light, called the objective, determines the type of
telescope.
A refractor telescope uses a glass lens as its objective. The glass lens is at the
front of the telescope and light is bent (refracted) as it passes through the lens.
A reflector telescope uses a mirror as its objective. The mirror is close to the rear
of the telescope and light is bounced off (reflected) as it strikes the mirror.
Refractor Telescopes
The refractor telescope uses a lens to gather and focus light. The first telescopes
built were refractors and the invention of the refracting telescope is generally
ascribed to Galileo in 1609, although it is recorded that a Dutch lens maker
called Hans Lippershey built one in 1608. The small, cheap toy telescopes sold
in shops are generally of the refractor type.
Refracting Telescopes focus light using lenses and the Principle of
Refraction.
Note: ‘n’ is a function of the wavelength of the incident radiation.
Generally, as wavelength increase, ‘n’ decreases. So shorter
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wavelength light (eg blue) is ‘bent’ more than longer wavelength
light (eg red).
The Refractive Index of Air is very nearly 1 (n air = 1.0003, depending on
Temperature & Pressure, but astronomers need to take this into account when
calculating wavelengths in the earth's atmosphere). The refractive index of
water is nH2O = 1.33 and refractive indices for various kinds of glass vary from
about n = 1.5--1.8. A diamond's luster is partially due to its high refractive index,
n = 2.4.
In order to look through a telescope you need two lenses, the objective, which is
the principal lens of the telescope, and an eyepiece. The image scale in the focal
place is determined by the focal length of the objective; if you look through the
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telescope, the magnification will be determined by the ratio of the focal lengths
of the objective and the eyepiece.
The sensitivity of the telescope is determined by the collecting area of the
objective lens (or primary mirror) which is proportional to the square of the
diameter of the primary lens or mirror:
d 
Area =    
2
2
Though excellent refractors are still made, the disadvantages of the refractor
telescope have blocked the construction of very large refractors for use in
astronomical research.
Advantages
1. The glass surface inside the tube is sealed from the atmosphere so it
rarely needs cleaning.
2. Since the tube is closed off from the outside, air currents and effects due
to changing temperatures are eliminated. This means that the images are
steadier and sharper than those from a reflector telescope of the same
size.
3. Refractor telescopes are rugged. After the initial alignment, their optical
system is more resistant to misalignment than the reflector telescopes.
4. Generally produce a sharper image than reflectors due to the lack of
secondary mirror support structure.
Disadvantages
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1. All refractors suffer from an effect called chromatic aberration (``color
deviation or distortion'') that produces a rainbow of colors around the
image. Because of the wave nature of light, the longer wavelength light
(redder colors) is bent less than the shorter wavelength light (bluer
colors) as it passes through the lens. This is used in prisms to produce
rainbows, but can it ruin an astronomical image!
There are a couple of ways to reduce chromatic aberration. One way uses
multiple compensating lenses to counteract chromatic aberration. The
other way uses a very long objective focal length (distance between the
focus and the objective) to minimize the effect. This is why the early
refracting telescopes were made very long.
2. How well the light passes through the lens varies with the wavelength of
the light. Ultraviolet light does not pass through the lens at all.
3. How well the light passes through decreases as the thickness of the lens
increases.
4. It is difficult to make a glass lens with no imperfections inside the lens
and with a perfect curvature on both sides of the lens.
5. The objective lens can be supported only at the ends. The glass lens will
sag under its own weight. Note: A 40” (~1 meter) diameter refractor lens
weighs approximately 1.5 – 2 tons!
Because of these disadvantages, the largest refractor telescope ever built is one
at the Yerkes Observatory, which was built more than 100 years ago! It has an
objective 1.02 meters (40 inches) across at one end of a 19.2-meter (63 feet) tube.
The two largest refractors are shown below. The first picture is the 40-inch
refractor at Yerkes Observatory. The second picture shows an astronomer
(Kyle Cudworth) next to the objective to give you an idea of the size of the
telescope. Notice the size of the people in the first picture! The third picture is
the 0.91-meter (36-inch) refractor at Lick Observatory. Notice the astronomer at
the lower left. The last picture is E.E. Barnard at the eyepiece of the Lick 36inch.
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.
Reflector Telescopes
The reflector telescope uses a mirror to gather and focus light. All celestial
objects (including those in our solar system) are so distant that all of the light
rays coming from them reach the Earth as parallel rays. Because the light rays
are parallel to each other, the reflector telescope's mirror has a parabolic shape.
The parabolic-shaped mirror focusses the parallel lights rays to a single point.
All modern research telescopes and large amateur ones are of the reflector type
because of its advantages over the refractor telescope.
Advantages
1. Reflector telescopes do not suffer from chromatic aberration because all
wavelengths will reflect off the mirror in the same way.
2. Support for the objective mirror is all along the back side so they can be
made very BIG! The larger reflecting telescopes have primary mirrors > 8
metres in diameter, compare that to 1 metre for refractors. This gives a
factor of 64 improvement in light gathering power.
3. Reflector telescopes are cheaper to make than refractors of the same size.
4. Because light is reflecting off the objective, rather than passing through
it, only one side of the reflector telescope's objective needs to be perfect.
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Modern reflecting telescopes use a parabolically shaped primary mirror coated
with a thin film of aluminum.
Disadvantages
1. It is easy to get the optics out of alignment.
2. A reflector telescope's tube is open to the outside thus thermal
differences in the tubes can effect the ‘seeing’. Also the optics need
frequent cleaning.
3. Often a secondary mirror is used to redirect the light into a more
convenient viewing spot. The secondary mirror and its supports can
produce diffraction effects: bright objects have spikes (the ``christmas
star effect'').
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Two famous reflector telescopes are shown below. The first picture is of the 5meter (200-inch) Hale Telescope at Palomar Observatory. The number refers to
the diameter of the objective (almost 17 feet across!). The telescope is the
vertical piece in the middle with the mirror close to the floor. The huge diagonal
piece is used to balance the telescope. Until recently it was the world's largest
optical/infrared telescope.
All modern optical/infrared telescopes are reflecting telescopes, because:
1. Reflecting telescopes do not suffer from chromatic aberration.
2. Figuring a mirror requires polishing only one precise surface rather than
two (or four for a compound lens).
3. Mirrors are easier to support because they can be supported on the sides
and the back; large lenses tend to sag because they can only be supported
on the perimeter.
Reflectors are also much more versatile than refractors because they can be used
at several different foci.
The world's largest optical/infrared telescopes are the twin 10-meter Keck
Telescopes operated by the University of California and Caltech on the 13,700ft
dormant volcano, Mauna Kea, Hawaii. These are amongst the principal
research instruments of optical and infrared astronomers.
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The Keck Telescopes employ hexagonal segmented primary mirrors, each
made out of 36 hexagonal segments, 1.8m in diameter. In order to maintain a
precise optical surface the positions of the segments are monitored by sensors
which relay signals to a computer which drives precision actuators, keeping
each segment in proper alignment.
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Mauna Kea is probably the world's best observatory site because of its stable
atmosphere, maintained by the island's marine layer, and its altitude. Over 20
astronomical telescopes from the US, Britain, Canada, France and Japan are in
operation or under construction.
The second picture shows the path light travels in the 10-meter Keck Telescope
at the W.M. Keck Observatory. The objective is composed of 36 hexagonal
mirrors put together to act as one large mirror 10 meters across. The small
image next to it shows the 10-meter objective. The person in the red clothing at
the center gives you a sense of scale.
In both the reflector and refractor telescopes, the focus is before the eyepiece, so
the image in astronomical telescopes is upside down. Telescopes used to look at
things on the Earth's surface use another lens to re-invert the image right-side
up. Most reflector telescopes will use a smaller secondary mirror in front of the
large primary mirror to reflect the light to a more convenient viewing spot.
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Isaac Newton used a flat secondary mirror at a 45° angle to reflect the light to
an eyepiece at the side of the telescope tube near the top. Such an arrangement,
called a newtonian design is used by many amateur telescopes.
Many reflector telescope use another light path design called the cassegrain
design to reflect the light back through a hole in the primary mirror, so that
detectors or the eyepiece can be conveniently placed behind the telescope. Most
of the large telescopes used for research, including the Hubble Space Telescope,
are of this design. Some of the largest telescopes like the Hale Telescope and the
Keck Telescope have places to put detectors at the prime focus, where the light
from the primary mirror first comes to a focus. The images in reflector
telescopes do not have holes or shadows in them because the light rays from the
unblocked parts of the primary mirror are all added together when they are
focussed together. Even though part of the primary mirror is blocked or
missing, there is still plenty of usable primary mirror space to gather the light.
Both types of telescope can suffer from a defect called spherical aberration so
that not all of the light is focused to the same point. This can happen if the
mirror is not curved enough (shaped like part of a sphere instead of a
paraboloid) or the glass lens is not shaped correctly.
Hubble Space Telescope: a classic case of spherical aberration.
The Hubble Space Telescope objective suffered from this (it was too flat by 2
microns, about 1/50 the width of a human hair) so it used corrective optics to
compensate. The corrective optics intercept the light beams from the secondary
mirror before they reach the cameras and spectrographs. Fortunately, the
Hubble Space Telescope's spherical aberration was so perfect, that it was easy to
correct for!
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Even before the servicing mission that installed the corrective optics 2.5 years
after the Hubble Space Telescope was put in orbit, astronomers were able to get
significant results from the telescope. The images were computer-enhanced to
correct for the spherical aberration to produce sharper images than from any
ground-based telescope. Also, astronomers were able to observe ultraviolet
light from celestial objects and fainter objects than could be seen from the
ground. However, the computer processing took a long time and the aberration
prevented the focusing of most of the light. This meant that astronomers could
not see the very faint (and distant) objects they were looking for.
M 100 a few days before (left) and after (right) the corrective optics (COSTAR)
were installed in December 1993.
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Summary of optical telescopes.
The principle part of the telescope is called the collecting aperture, acting as a
means to focus light and to produce a primary image.
Note that the arriving light comes into the front of the telescope as parallel rays.
This is generally true for all astronomical objects as they can be considered to be
at infinity in comparison to the dimensions of any telescope.
As all the objects to be investigated are effectively at infinity, the distance of the
primary images from the collecting aperture is defined as the focal length, F, of
the telescope. A plane through this point, and at right angles to the optic axis is
defined as the focal plane. It is often convenient to describe a telescope in terms
of its focal length, f, which is the ratio of the focal length of the collector to its
diameter, D:
f 
F
D
This definition is synonymous with the ‘speed’ of an optical system when
applied to general photography.
The quantity of energy which is collected per unit time by the telescope is
proportional to the collecting area.
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When a telescope is directed at the sky, an image of part of the celestial sphere
is produced in the focal plane. The relationship between the size of this image
and the angular field which is represented by it is governed by the focal length
of the telescope. In the lower of the pictures above, rays are drawn for two stars
separated by an angle . For convenience, one star has been placed on the optic
axis of the telescope. Rays which pass through the centre of the system are not
deviated, thus the separation, s, of the two images in the focal plane is given by:
s = F tan 
As is  is normally very small, this can be re-written as:
s=F
where  is normally expressed in radians.
The correspondence between an angle and its representation in the focal plane
is known as the plate scale of the telescope, which can be seen to be given by:
d 1

ds F
Normally this is expressed in arc seconds per mm, and in this case the plate
scale is given by:
d 206265

ds
F
where F and s are expressed in mm and in seconds of arc respectively, with the
numerical term (206265) referring to the number of arc seconds in a radian.
The telescope and the collected energy.
The apparent brightness of an astronomical object is increased as the square of
the diameter of the collector. Stellar brightness is normally term Flux, F, which
is the energy received per unit area per unit wavelength interval per unit time,
and often expressed in units of W m-2 Å-1.
The number of photons arriving at the telescope aperture can be written as:
NT 

4
1
D 2  t  
2
F
d
hc
Where 1 and 2 are the cut-on and cut-off wavelengths defined by the filter
that is used, and t is the integration time.
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The arrival of photons is a statistical process. When the arriving flux is low,
fluctuations are clearly seen on any recorded signal, and the measurements are
said to suffer from photon shot noise. If no other sources of error are present, the
uncertainty in any measurement is given by N T . Hence any record and its
error may be represented by N T  N T . In these circumstances, the signal-tonoise ratio (S/N) of the observation is given by:
NT
NT
 N T  D 2 t  D t
Example: At 6300Å (630nm) the flux from a source is 10-18 W m-2 Å-1. Determine
the photon rate passing through a telescope with a diameter, D = 2.2 metres
over a wavelength interval of 100 Å. Calculate the best S/N ratio of a
measurement with an integration time of 30 seconds.
NT 

4
2.2 2  30 
630  10 9
 10 18  100  36121
6.63  10 34  3  10 8
and if the noise is purely limited by shot noise, the S/N ratio is simply
782. Therefore the accuracy is about a part in 782, or about 0.1%
NT =
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Chromatic aberration.
Chromatic aberration corrected using a doublet of 2 differing refractive index
glasses.
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Spherical aberration.
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The Newtonian and Schmitt-Cassegrain optical system.
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1) “Celestron” 8-inchNewtonian reflector (~£1200)
2) “Meade” 10-inch Schmidt-Cassegrain (~£3000)
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3) “Skywatcher” 6-inch refractor (~£700)
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Radio Telescopes
Radio astronomy has its roots back in the 1930's when Karl Jansky accidentally
detected radio emission from the center of the Milky Way as part of his research
on the interference on transatlantic phone lines. The British advanced radio
antenna technology in their development of radar technology to fight the
German warplanes in World War II. After the war, astronomers adapted the
technology to detect radio waves coming from space.
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A radio telescope uses a large
metal dish or wire mesh, usually
parabolic-shaped, to reflect the
radio waves to an antenna above
the dish. An example of a mesh
is shown at left. This was the
mesh of the parabolic dish for
the former 100-meter radio
telescope at Green Bank, West
Virginia (photos courtesy of
National Radio Astronomy
Observatory). Looking from
underneath the radio telescope, a
person could see the clouds in the sky overhead but to the much longer
wavelength radio waves, the metal mesh was an excellent reflector.
The signal from the antenna is sent to an amplifier to magnify the very faint
signals. At the last step, the amplified signal is processed by a computer to turn
the radio signals into an image that follows the shape of the radio emission.
False colors are used to indicate the intensity of the radio emission at different
locations. An example is shown below for Jupiter. Charged particles in its
magnetic field produce a large amount of radio energy in doughnut-shaped
regions around its center. A visible band image of Jupiter is shown below the
radio image.
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Radio telescopes may be made much larger than optical/infrared telescopes
because the wavelengths of radio waves are much longer than wavelengths of
optical light. A rule of thumb is that the reflecting surface must not have
irregularities larger than about 1/5 the wavelength of light that is being
focused. By that criterion a radio telescope is several hundred thousand times
easier to figure than an optical telescope of the same size.
The Arecibo Observatory radio telescope (below) is a 305 meter reflecting
surface in a natural limestone sinkhole in NW Puerto Rico. Because the
telescope cannot be pointed independently the telescope is "steered" by tilting
the instrument housing supported over the telescope.
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Interferometry and aperture synthesis.
(Aperture synthesis: making a very large telescope out of lots of smaller ones).
Because radio signals are detected as waves, signals from different telescopes
can be added to simulate or synthesize the resolving or pin-pointing capability
of a much larger telescope. The National Radio Astronomy Observatory's Very
Large Array (VLA) near Socorro, NM, consists of 27 radio telescopes, each 25
meters in diameter which are deployed on a Y-shaped track which may be
extended up to 36km. The VLA has the resolving power of a 36km telescope
(but only the collecting-area and sensitivity of a 130m telescope).