AST202S: Introduction to Modern Astrophysics

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AST202S Introduction to Modern Astrophysics

• Brief historic overview
• Celestial mechanics
• Our solar system
• Formation of solar systems
• Electromagnetic radiation
• Star formation
• Stellar evolution
• Our Milky Way as a galaxy
• Galaxy formation and evolution
• The Early Universe

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Electromagnetic radiation and matter (ZG Chapter
8)
Outlook characterise electromagnetic radiation,
atomic structure of matter, interactions between
matter and radiation. We conceive of an
electrically charged particle as having an
electric field, just as we conceive of a mass
having a gravitational field. The electric
field will drop off proportionally to the surface
area through which it spreads, so the electric
force has an inverse-square law, just as gravity
does. On small scales, the Coulomb force
dominates, on large scales, the
gravitational force dominates.
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• Electric charges are source of electric fields
• Electric fields accelerate electric charges
• Moving charges generate magnetic fields
• Magnetic fields accelerate moving charges
• Time-varying electric fields generate
  (perpendicular) magnetic fields
• Time-varying magnetic fields generate electric
  fields
• Light consists of a self-propagating wave of
  varying electric and magnetic fields.

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Electromagnetic waves may propagate through a
pure vacuum at speed c
If the electric field always oscillates in a
single plane, the wave is plane-polarized,
otherwise it is elliptically polarized (if d1
d2 constant). If Ex and Ey are in phase ?
plane-polarized not in phase ? elliptically
polarized 90 out of phase ? circular polarization
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The electromagnetic spectrum Wavelength Energy
or Frequency Type of Radiation 10-6 nm 1240
MeV Gamma Rays 10-5 nm 124.0 MeV Gamma
Rays 10-4 nm 12.4 MeV Gamma Rays 10-3 nm 1.24
MeV Gamma Rays 10-2 nm 124 KeV X-rays 10-1
nm 12.4 KeV X-rays 1 nm 10-9 m 1.24
KeV Ultraviolet (UV) 10 nm 124
eV Ultraviolet (UV) 100 nm 12.4
eV Ultraviolet (UV) 1000 nm 1 µm 1.24
eV Optical 10 µm 0.124 eV Infrared (IR) 100
µm 0.0124 eV Infrared (IR) 1000 µm 1
mm 0.0012 eV Infrared (IR) 10 mm 1 cm 30 000
MHz Microwave (radar) 10 cm 3000 MHz UHF 100
cm 1 m 300 MHz FM 10 m 30 MHz Short-wave
radio 100 m 3 MHz Short-wave radio 1000 m 1
km 300 kHz Long-wave radio 10 km 30
kHz Long-wave radio 100 km 3 kHz Long-wave
radio 380 nm 3800 Å Optical (Blue) 520 nm
5200 Å Optical (Green) 700 nm 7000
Å Optical (Red)
Note 1 eV 1.6021 x 10-19 J It is the energy
gained by an electron accelerating through a
potential difference of 1 Volt
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Atmospheric window optical, near-infrared, radio.
Ultraviolet, X-rays and Gamma-rays are
effectively blocked by the Ozone (O3) layer in
the Earths atmosphere. To study this part of
the electromagnetic spectrum you will need to
send a satellite in orbit.
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Reflection and refraction of light.
Angle of incidence (i) with respect to the
normal of the reflecting surface, equals the
angle of reflection (r)
When light passes from one medium into another,
it results in the refraction of light. Generally,
the speed of light v in a medium is different
from the speed of light c in a vacuum. Index of
refraction n c/v Snells law n1 sin i n2
sin r
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Diffraction and interference of light.
Diffraction
Interference
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Doppler effect.
Imagine a light source receding at speed v from
an observer while emitting radiation at
wavelength ?0 and frequency ?0. In the time t
1/v0, one wavelength (?0) emerges from the
source, but as seen by the observer, that wave
has the length because the source has
traveled the distance vt to the left. The
observed frequency is
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Doppler effect.
If ? gt ?0 and ? lt ?0, the light is redshifted
(shifted to longer wavelengths, ie. to the
red) If ? lt ?0 and ? gt ?0, the light is
blueshifted (shifted to shorter wavelengths, ie.
to the blue) ? the source is approaching the
observer.
In the case of v approaching c, Einsteins theory
of special relativity must be used. v is the
relative speed of the source and observer, and no
relative speed greater than the speed of light is
possible (v c).
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The Quantum Nature of Light Photons. Light is
neither a particle nor a wave, but it can
manifest itself as either one of the other! The
interaction of light with atoms and molecules is
understandable only if electromagnetic energy
propagates in the form of discrete bundles, which
we call photons or quanta. The energy of a light
quantum E is proportional to the frequency
characterising the light wave E h ? where h
6.626 x 10-34 Js (Plancks constant) One
can crudely picture a classical light wave of
wavelength ? and frequency v as composed of many
quanta, each with the energy given by the above
equation.
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Intensity versus Flux.
In detecting the energy (or counting the photons)
coming from a distant source, one must be
careful to distinguish between intensity and
flux. Intensity depends upon direction, in the
sense that the intensity I of a source is the
amount of energy emitted per unit time ?t, per
unit area of the source ?A, per unit frequency
interval ??, per unit solid angle ?O in a given
direction. The solid angle of the beam is
related to the area ?a intercepted by the beam at
the spherical surface of radius r by
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The dimensionless unit of the solid angle is the
steradian (sr), with the entire spherical area
subtending 4p sr. Units of intensity are
W/m2Hzsr The total energy per second from a
spherical star of surface area A, also
called luminosity L, is Flux F relates
directly to what we measure with a telescope.
The monochromatic flux of energy through a
surface (or into a detector) is the amount of
energy per unit time passing through a unit area
of the surface per unit frequency interval F(v)
energy/?A?t?v (units are W/sHz)
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Atomic Structure Scales of 10-10 m realm of
atoms and molecules (bound aggregates of
atoms) What is an atom? Consists of a small
nucleus (which contains most of the atoms mass
in a size of the order of 10-14 m) surrounded by
a diffuse cloud of electrons (extending out
to about 10-10 m) The atomic nucleus consists of
protons and neutrons, bound together by
strong interaction. Proton, neutron and electron
are the fundamental building blocks of an
atom. Name Mass (kg) Mass (electron
mass) Electric Charge Proton 1.6725 x
10-27 1836 e Neutron 1.6748 x
10-27 1838 0 Electron 9.1091 x 10-31 1 -e e
1.602 x 10-19 Coulomb (C) A neutral atom
consists of an equal amount of protons and
electrons, with approximately the same number of
protons and neutrons (for the lighter elements).
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Atomic Structure An element is determined by the
number of protons Z (called the atomic
number). A given element may exist in several
different forms, called isotopes. All isotopes
of an element has the same atomic number, but
differing numbers of neutrons (N). The different
isotopic nuclei are called nuclides. To
characterise a nuclide, the following notation is
used ZNX or AX where X is the symbol of the
element having Z protons and A Z N is the
atomic mass. For example three isotopes of
hydrogen are known, namely ordinary hydrogen
(1H), deuterium (2H) and tritium (3H). The mass
of an atom is conveniently given in terms of
atomic mass units (amu) the standard is 12C,
which has a mass of exactly 12 amu. Since 1 amu
is essentially the mass of a proton, an atoms
mass is nearly A amu.
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The Bohr atom. In 1911, Ernest Rutherford
proposed a nuclear model of the atom. Bohr first
postulated that only a discrete number of orbits
are allowed to the electron and when in those
orbits, the electron cannot radiate. The
permitted orbits are those in which the orbital
angular momentum of the electron is an integral
multiple of h/2p, where h is Plancks
constant. Consider an electron in a circular
orbit of radius r about a nucleus of charge
Ze The centripetal force (Fcen) maintaining the
orbit is provided by the coulombic attraction
between the electron and the nucleus
The permitted discrete orbits occur
at geometrically increasing (n2) distances, with
the smallest Bohr orbit occuring when the
principal quantum number n equals unity.
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The Bohr atom. The total energy (E) of these
orbits is the sum of the potential energy and the
kinetic energy, where the potential energy for an
atom is That these energies are negative,
indicates that the orbits are bound. The smallest
Bohr orbit (n1) is the most strongly bound, and
all orbit are bound until n ? 8 where E ? 0. For
E gt 0, a continuum of unbound orbits is available
to the electron.
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Quantized radiation Bohrs second postulate
concerns the absorption and emission of radiation
by an atom the fundamental interaction between
matter and radiation. It states that (a)
radiation in the form of a single discrete
quantum is emitted or absorbed as the electron
jumps from one orbit to another, (b) the
energy of this radiation equals the energy
difference between the orbits. When an
electron makes a transition from a higher orbit
(na) to a lower orbit (nb), a photon is emitted.
The energy of this process may be symbolised
by E(na) E(nb) hv (emission) where na gt
nb. For an electron to make a transition from
the lower orbit to the upper orbit, the atom must
absorb a photon of exactly the correct
energy E(nb) hv E(na) (absorption) The
frequency of the photon involved is
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The Bohr model of the Hydrogen Atom Applying
Bohrs picture to the simplest atom, hydrogen
(Z1) with its single electron. The electrons
permitted orbital energies are where R' 2.18
x 10-18 J incorporates all the other
constants. The Rydberg constant R ( R'/ch)
has the value of 10.96776 µm-1 for
hydrogen. Transitions of the Lyman series all
have the ground state (nb 1) as their lowest
orbit, with na 2. (Ultraviolet) In the
optical, there is the Balmer series (nb 2, na
3). These were the first discovered and are
designated Ha (na3), Hß (na4), H? (na5), etc.
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Energy-level diagrams Bohrs simple theory is
an approximation of the actual dynamics of atomic
phenomena. When extended to atoms more
complicated than hydrogen, the theory encounters
difficulties and the full mathematics of quantum
mechanics must be employed to understand the
full details. Atoms can be represented
abstractly by means of energy-level diagrams. It
is directly related to the atomic transitions and
can be constructed for complicated
atoms. When the atom is in any level above
the ground state it is in an excited state, and
the energy of such a level is called
the excitation potential.
Hydrogen energy-level diagram
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Excitation, de-excitation, ionization An atom
can be excited to a higher energy level in two
ways radiatively or collisionally. Radiative
excitation a photon is absorbed by the atom the
photons energy must correspond exactly to the
energy difference between two energy levels of
the atom ? produces absorption lines
superimposed on a background continuous
spectrum. Collisional excitation a free
particle (an electron or another atom) colliding
with an atom, giving part of its kinetic energy
to the atom. Such inelastic collision does
not involve any photons. Energy deposited is E
m(vi2 vf2)/2, if this corresponds to the
energy of an electronic transition, the atom is
collisionally excited. Such an excited atom
returns to its ground state by emitting photons,
producing an emission line spectrum.
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Excitation, de-excitation, ionization Atoms are
always interacting with the electromagnetic field
? causes an excited atom to jump spontaneously to
a lower energy level (de-excite) in a
characteristic time of order 10-8 s. Because a
photon is emitted, this process is called
radiative de-excitation. Another form of
de-excitation is collisional de-excitation, where
the phenomenon is not announced by a photon (the
exact inverse of collisional excitation). Most
spontaneous downward transitions occur on short
time scales, however, certain transitions
because of quantum mechanical rules take
place much more slowly. These transitions are
forbidden transitions and result in forbidden
lines.
Reddish glow Ha greenish glow forbidden oxygen
lines OIII
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Excitation, de-excitation, ionization
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Excitation, de-excitation, ionization With
sufficient energy (either radiative or
collisional) to liberate an electron from
a neutral atom, the atom is ionized.
Schematically, this reaction is X energy ? X
e- where X represents the atom. E.g. neutral
hydrogen is denoted as either H or HI, where the
roman numeral I indicates the neutral state.
Similarly, for neutral helium, we can write He,
or HeI. Single ionized hydrogen is noted as H
HII (for singly ionized helium He HeII) The
energy required to ionize an atom depends upon
the ionization state of the atom, the particular
electron to be liberated, and the excitation
levels of that electron. Consider the hydrogen
atom, an electron from the ground state (n 1),
is removed from the atom when we supply it the
energy E 13.6 eV (the ionization
potential). The ionization potential for an
electron in excitation level n is The kinetic
energy available to the departing electron is the
difference between the energy provided and the
ionization potential (E IP).
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Spectral-line intensities The intensity of an
emission line is proportional to the number of
photons emitted in that transition, similarly
the strength of an absorption line relative to
the adjacent continuum depends on the number of
photons absorbed. An absorption line is never
infinitely sharp (it exhibits a profile, the
intensity of which could vary with wavelength).
The total strength of a line is proportional to
its area, which is represented by its equivalent
width (top figure). Various physical processes
result in the broadening of spectral lines (see
later)!
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Ionization equilibrium As the temperature of a
gas is increased, more and more energy (radiative
or collisional) becomes available to ionize the
atoms. The greater the electron density (Ne the
number of electrons per unit volume), the greater
the probability that an ion will capture an
electron and becomes a neutral atom. These two
competing processes, ionization (?) and
recombination (?) are written as X ? X e- A
steady state condition of ionization equilibrium
is achieved in the gas when the rate of
ionization equals the rate of recombination.
The Boltzmann equation gives the number of atoms
in an excited state relative to the number in any
other state this applies both to neutral and
ionized atoms. The Saha equation tells us the
relative populations of two adjacent stages of
ionization.
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Spectral-line broadening Spectral lines are
never perfectly sharp their profiles always have
a finite width. Quantum mechanics account for the
minimal width (natural broadening) of a
spectral feature, and various physical processes
further broaden the profile. ? by interpreting
the observed profile of a spectral line one can
deduce characteristics of the radiation from a
star or any astrophysical source. Natural
broadening Heisenberg uncertainty specifies
that An assemblage of atoms will produce an
absorption or emission line with a minimum spread
in photon frequencies the natural width of
order ?v ?E/h 1/?t Typical value 10-5 nm
(depends on the intrinsic lifetime of an
energy level) Thermal Doppler broadening Depend
s upon the temperature and composition of a gas
(remember the Maxwellian velocity
distribution). Most probable speed of particles
in such a gas is
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Thermal Doppler broadening (continued) Particles
moving towards the observer will emit
blueshifted light those moving away, redshifted.
The spectral line will thus be broadened equally
to shorter and longer wavelengths. Example
Hydrogen at 6000 K moves at the most probable
speed v 10 km/s, corresponding to a
fractional Doppler broadening of ??/? v/c 3
x 10-5 ? thermal Doppler with of Ha is
approximately 0.02 nm. Concept application What
is the magnitude of the Doppler broadening for
iron at the surface of the Sun? Collisional
broadening Energy levels of an atom are shifted
by neighbouring particles (especially
charged particles, ions and electrons called
the Stark effect). In a gas, these
perturbations are random and result in the
broadening of spectral lines. The greater the
density (hence pressure) of the gas, the greater
the width of the spectral lines. Zeeman
effect When an atom is placed in a magnetic
field, the atomic energy levels each
separate into three or more sublevels because of
the electrons magnetic dipole.
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Blackbody radiation (revisited, but now in more
detail) Where does a thermal continuous
spectrum come from? Various emission and
absorption continue can originate from individual
atoms and spectral features become more
broadened as atoms interact more strongly with
one another. When an aggregate of atoms interact
so strongly (such as in a solid, a liquid, or an
opaque gas) that all detailed spectral features
are washed out, a thermal continuum
results! Such a continuous spectrum comes from a
blackbody, whose spectrum only depends upon the
absolute temperature. (named blackbody because it
absorbs all electromagnetic energy incident upon
it it is completely black). However, thermal
equilibrium requires that the body radiates
energy at exactly the same rate that it absorbs
energy otherwise, the body will heat up or cool
down. Plancks spectral intensity relation the
Planck blackbody radiation law
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Useful approximations of Plancks blackbody
radiation law _at_low temperatures and short
wavelengths ? Wien distribution In the
opposite case, where the exponential is much
small than unity, one can use the power series
expansion for the exponential to note that ex-1
x, and therefore This is known as the
Rayleigh-Jeans distribution and is valid at high
temperatures and long wavelengths (low
frequencies).
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Wiens law A blackbody emits at a peak
intensity that shifts to shorter wavelengths as
its temperature increases (see Figure on page 30
of this weeks notes). The peak wavelength
(where dI(?)/d? 0) of the Plancks curve is
expressed by Wiens displacement law as where
?max is expressed in meters and T in
kelvins. Note (as a reminder) that the Suns
continuum spectrum peaks at 500 nm,
therefore the surface temperature is near 5800
K. Stefan-Boltzmann law The area under the
Planck curve (integrating the Planck function)
represents the total energy flux F (W/m2) emitted
by a blackbody when we sum over all wavelengths
and solid angles
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• In summary
• A blackbody radiator has a number
• of special characteristics
• a blackbody emits some energy
• at all wavelengths,
• a hotter blackbody emits more
• energy per unit area and
• time at all wavelengths
• than a cooler one does,
• a hotter blackbody emits a greater
• proportion of its radiation
• at shorter wavelengths
• than a cooler one,
• the amount of radiation emitted

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• Temperature
• A word of caution concerning temperatures!
• In general one cannot define temperature uniquely
  it depends on the process
• under consideration.
• For radiation, if we are dealing with a true
  blackbody emitter, one may establish the
• temperature using
• the shape of the Planck curve, at one or more
  points on the curve
• Wiens law and the wavelength of peak emission
• Stefan-Boltzmann law and the total power.
• Because no astrophysical object is a perfect
  blackbody, the temperatures obtained
• might be slightly different from each of these
  three methods.
• Temperatures can also be assigned to matter,
  based on the velocity distribution of its
• particles (a kinetic temperature), the degree of
  excitation, and the degree of ionization.
• Temperature Basic Law/Equation Observations
• Brightness Planck curve Intensity at one
  wavelength

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• Kirchhoffs Rules
• A hot and opaque solid, liquid, or highly
  compressed gas emits a continuous spectrum
• A hot, transparent gas produces a spectrum of
  emission lines. The number and position
• of these lines in the spectrum depend on which
  elements are present in the gas.
• If light with a continuous spectrum passes
  through a transparent gas at a lower
• temperature, the cooler gas causes the
  appearance of absorption lines. Their
• position in the spectrum, their strength, and
  their number depend on the
• elements in the cooler gas.

The second and third rule tells us that whether
the atoms in the gas emit or absorb depends on
the physical conditions in the gas. Emission
requires high temperatures in a transparent
(optically thin) gas absorption occurs when a
continuous spectrum from a hot object passes
through a cooler, transparent (optically thin)
gas. If the two gases have the same chemical
composition the pattern of emission lines and
absorption lines is the same.
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TELESCOPES AND DETECTORS Opening the window to
the Universe!
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Optical telescopes.. light buckets for
collecting photons! Reflecting telescopes versus
refracting telescopes!
Optical components are used to control the path
of light rays and bright light to a focus. This
is done either by a curved mirror (reflection) or
a lens (refraction)
The distance to bring the light into focus is
called the focal length the focus of a
primary reflecting mirror is called prime
focus. For either a lens or a mirror, the ratio
of focal length to diameter is called the f
ratio f ratio f/d where f is the focal length
and d the diameter.
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A convex lens will make an image of an extended
object that is smaller than the object and
inverted.
The plate scale of a telescope relates to the
focal length via s 0.01745 f (units
f/degree) e.g. the 1-m telescope at the SAAO has
Cassegrain focus with an f-ratio of f/16. The
focal length is therefore f/d 16 ? f 16100
cm 1600 cm, and the plate scale is 27.92 cm/
or 12.9 arcseconds/mm A telescopes
light-gathering power is directly proportional
to the square of its diameter. SALT has 120
times the light-gathering power (LGP) compared to
the 1-m SAAO telescope.
Various focii Prime focus, Newtonian
focus Cassegrain focus, Coude focus.
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• The resolving power of a telescope is defined as
• RP 1/?min, where ?min 206 265 ?/d
• and ?min is the minimum resolvable angle, or
  resolution in seconds of arc (206 265
• is the number of arcseconds in 1 radian). ? is
  the wavelength and d is the diameter of the
• objective in the same length units.
• Example A 1-m telescope working at a wavelength
  of 500 nm has a resolution angle of
• 1.22 ?min (1.22) (206 265) (5 x 10-7 / 1)
  0.125 arcsec
• This means that on a perfectly stable night,
  such a telescope would be able
• to see two separate stars if they are more than
  0.125 arcsec apart on the sky!
• However, remember the turbulence of the
  atmosphere
• Ground-based observations are rarely better than
  0.3 arcsec.
• Note the additional factor of 1.22 is needed to
  take diffraction into account
• (at visible wavelengths)
• Magnifying power of a telescope MP F/f
• where F is the focal length of the objective,
  and f is the focal length of the

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Difference in light-gathering power! Same
exposure time, but double the size of
the telescope (lower image).
Difference in angular resolution (a factor
600!), from 10 arcminutes (a), to 1 arcminute
(b), 5 arseconds (c), to 1 arcsecond (d).
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Equatorially-mounted telescopes
74-inch telescope at Sutherland ?
Alt-azimuth mounted telescope Japanese
1.4-m telescope in Sutherland ?
? 200-inch telescope at Mt. Palomar
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The SALT-design

• Various unique aspects
• multiple mirror (91)
• spherical mirrors (instead of
• parabolic) Needs spherical
• abberation corrector
• edge sensors
• moving tracker to allow tracking of
• the star as it moves through
• the field of view
• one axis of rotation (constant gravity
• vector on the mirrors)
• Future generation extremely large
• telescopes will follow this design.

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Chromatic aberration
Spherical aberration
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• Detectors
• Photographic plates.
• not much used anymore
• special photographic emulsions coated on a glass
  plate
• large collecting area ()
• very inefficient (-) compared to modern
  detectors, ie. low Quantum Efficiency ( few )
• Quantum efficiency QE(?) photon detected /
  photons incident
• A perfect detector would have QE(?) 1.0 or
  100.
• Human eye QE (550 nm) 1
• Photograph QE(400-650 nm) 1

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• Photo(multiplier) tubes.
• Not much used anymore (although some telescopes
  in Sutherland still have
• such detectors in use, e.g. 20-inch and 30-inch
  telescopes)
• Light striking the surfaces of certain materials
  can be absorbed and an electron
• dislodged (photoelectric effect).
• Displaced electrons can be individually
  counted!
• A phototube that can transform one electron in
  many (105) for ease of detection
• are called photomultiplier tubes
• Better quantum efficiency than photographic
  plates (10-20)
• Linear response (great accuracy)
• Charged-Coupled Devices
• 2-dimensional information (unlike the phototube)
• Highly efficient (QE 70-80) over a large
• wavelength range
• Large areas (mosaics of CCDs used to cover
• large areas on the sky (0.5 x 0.5 degrees)
• All modern telescopes equipped with CCDs

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Signal-to-noise All observations contain noise,
even if the instruments are perfect, because of
the statistical fluctuations in a beam of
photons acting as particles. Consider sm as the
standard deviation from the mean in a series of
measurements, for example the counting of
photons. Then if ltNgt is the mean number of
photons counted, the signal-to-noise ratio
is S/N ltNgt/sm A high signal-to-noise
indicates a high quality of observations. Photons
obey a Poisson probability distribution, so that
if these fluctuations are the only source of
noise, then sm ltNgt1/2, and hence S/N
ltNgt1/2 Therefore, if we count 104 photons, the
S/N 100. Consider a detector on which falls a
photon flux fp (measured in photons per
second). The total number of photons detected
then depends on the quantum efficiency,
the photon flux and the duration of the
observation. ltNgt QE x fp x t and so S/N (QE
x fp x t)1/2