Transcript PHYS_3380_100714_bw - The University of Texas at Dallas

PHYS-3380 Astronomy
Angular Resolution
Resolving power: Wave nature of light =>
The telescope aperture produces
fringe rings that set a limit to the
resolution of the telescope.
Resolving power = minimum angular
distance amin between two objects that
can be separated.
amin = 1.22 (/D)
For optical wavelengths, this gives
amin = 11.6 arcsec / D[cm]
amin
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So: the angular resolution/resolving power of a reflecting telescope is
dependent on the diameter of its mirror
Mirror Angular Resolution Animation
and the wavelength of the light
Wavelength Effect on Resolution
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Light Gathering Ability: Size Does Matter
1. Light-gathering
power: Depends on
the surface area A of
the primary lens /
mirror, proportional
to diameter squared:
D
A = (D/2)2
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So: light collecting ability of a reflecting telescope is dependent on the
area of the mirror
Light Collecting Area Animation
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Magnifying Power
Magnifying Power = ability of the telescope to make the image
appear bigger.
The magnification depends on the ratio of focal lengths of
the primary mirror/lens (Fo) and the eyepiece (Fe):
M = Fo/Fe
A larger magnification does not improve the resolving
power of the telescope!
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Interferometry
Recall: Resolving power of a telescope depends on diameter D:
amin = 1.22 /D.
This holds true even if
not the entire surface is
filled out.
• Combine the signals from
several smaller telescopes
to simulate one big mirror
 Interferometry
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Uses of Telescopes
1.
Imaging
–
use a camera to take pictures (images)
2. Photometry
measure total amount of light from an object
3. Spectroscopy
–
use a spectrograph to separate the light into its different
wavelengths
4. Timing
–
measure how the amount of light changes with time
(sometimes in a fraction of a second)
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Imaging
• In astronomy, filters are
usually placed in front of
a camera to allow only
certain colors to be
imaged
• Single color images are
superimposed to form
true color images.
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Spectroscopy
• The spectrograph reflects light of
a grating: a finely ruled, smooth
surface.
• Light interferes with itself and
disperses into colors.
• This spectrum is recorded by a
digital detector called a CCD.
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Nonvisible Light
•
•
Special detectors/receivers record light invisible to the human eye - gamma
rays, x-rays, ultraviolet, infrared, radio waves.
- each type of light can provide information not available from
other types.
Digital images are reconstructed using false-color coding so that we can see
this light.
Chandra X-ray image of the Center of the Milky Way Galaxy
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The Crab Nebula
Visible
Radio Waves
Infrared
X-rays
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Atmospheric Effects
Earth’s atmosphere causes problems for astronomers on the ground:
• Bad weather makes it impossible to observe the night sky.
• Man-made light is reflected by the atmosphere, thus making the night
sky brighter.
– light pollution
• The atmosphere absorbs light - dependent on wavelength
• Air turbulence in the atmosphere distorts light.
– That is why the stars appear to “twinkle”.
– Angular resolution is degraded.
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Light Pollution
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Radio Astronomy
Recall: Radio waves of  ~ 1 cm – 1 m also penetrate the
Earth’s atmosphere and can be observed from the ground.
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Radio Telescopes
Large dish focuses the
energy of radio waves
onto a small receiver
(antenna)
Amplified signals are
stored in computers and
converted into images,
spectra, etc.
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Radio Telescopes
• The wavelengths of radio waves are long.
• So the dishes which reflect them must be very large to achieve any
reasonable angular resolution.
305-meter radio telescope at Arecibo, Puerto Rico
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Radio Interferometry
The Very
Large Array
(VLA): 27
dishes are
combined to
simulate a
large dish of
36 km in
diameter.
Even larger arrays consist of dishes spread out over the entire U.S.
(VLBA = Very Long Baseline Array) or even the whole Earth (VLBI
= Very Long Baseline Interferometry)!
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Most sensitive VLBI array in the world - European VLBI Network (EVN).
• brings together the largest European radiotelescopes for typically week-long
sessions
Very Long Baseline Array (VLBA)
• uses ten dedicated, 25-meter telescopes spanning 5351 miles across the
United States
• the largest VLBI array that operates all year round as both an astronomical
and geodesy instrument.
Global VLBI
• Combination of the EVN and VLBA
Space Very Long Baseline Interferometry (SVLBI)
•dedicated VLBI placed in Earth orbit to provide greatly extended baselines.
•HALCA, an 8 meter radio telescope - launched in February 1997 - made
observations until October 2003,
•small size of the dish - only very strong radio sources could be
observed with
•Spektr-R (or RadioAstron) - launched in July 2011.
When Global VLBI combined with one or more space-based VLBI antennas gives
resolution of microarcseconds.
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Science of Radio Astronomy
Radio astronomy reveals several features, not visible at other
wavelengths:
- neutral hydrogen clouds (which don’t emit any visible light),
containing ~ 90 % of all the atoms in the Universe.
- molecules (often located in dense clouds, where visible light is
completely absorbed).
- Radio waves penetrate gas and dust clouds, so we can observe
regions from which visible light is heavily absorbed.
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Atmospheric Distortion
The turbulence (ever-changing motion) of the atmosphere causes
distortion - twinkling of starlight. Bends light in constantly shifting
patterns. Like looking down the road on a hot day and seeing distant
cars rippling and distorting. Why best viewing is when it is cold and
calm.
Atmospheric Distortion Animation
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Adaptive Optics (AO)
•
•
•
It is possible to “de-twinkle” a star.
The wavefronts of a star’s light rays are deformed by the atmosphere.
By monitoring the distortions of the light from a nearby bright star (or a laser):
– a computer can deform the secondary mirror in the opposite way.
– the wavefronts, when reflected, are restored to their original state.
• Angular resolution
improves.
• These two stars are
separated by 0.38
• Without AO, we see
only one star.
AO mirror off
AO mirror on
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The Sun
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The Sun’s Energy Source
The first scientific theories involved chemical reactions or gravitational
collapse.
- chemical burning ruled out…it can not account for the Sun’s
luminosity
- conversion of gravitational potential energy into heat as the Sun
contracts would only keep the Sun shining for 25 million years
- late 19th-century geological research indicated the Earth was older
than that
Development of nuclear physics led to the correct answer
- the Sun generates energy via nuclear fusion reactions
- Hydrogen is converted into Helium in the Sun’s core
- the mass lost in this conversion is transformed into energy
- the amount of energy is given by Einstein’s equation: E = mc2
- given the Sun’s mass, this will provide enough energy for the Sun to
shine for 10 billion years
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Striking a Balance
The Sun began as a cloud of gas undergoing gravitational collapse.
- the same heating process, once proposed to power the Sun, did cause
the core of the Sun to get hot and dense enough to start nuclear fusion
reactions
Once begun, the fusion reactions generated energy which provided an
outward pressure.
This pressure perfectly balances the
inward force of gravity.
- deep inside the Sun, the pressure is
strongest where gravity is strongest
- near the surface, the pressure is
weakest where gravity is weakest
This balance is called gravitational
equilibrium.
- it causes the Sun’s size to remain
stable
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One second of output from the Sun (luminosity) would provide power
for the human race for the next 500,000 years
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Layers of the Sun
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Core
T = 1.5 x 107 K; depth = 0 – 0.25 R
Density - up to 150,000 kg/m³ (154 times the density of water on
Earth)
Pressure 200 billion times that on the surface of Earth
This is where the Sun’s energy is generated.
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Why does fusion occur in the Sun’s core ?
Nuclear fusion
- a reaction where heavier nuclei are
created by combining (fusing) lighter
nuclei.
- all nuclei are positively charged
Electromagnetic force causes nuclei to
repel each other.
- for fusion to occur, nuclei must be
moving fast enough to overcome EM repulsion
- this requires high temperatures and
pressures
When nuclei touch, the nuclear force
binds them together
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Energy Generation in the Sun: The Proton-Proton Chain
Need large proton speed ( high
temperature) to overcome
Coulomb barrier (electromagnetic
repulsion between protons).
Basic reaction:
T ≥ 107 0K =
10 million 0K
4 1H  4He + energy
Sun needs 1038 reactions, transforming 5 million tons of mass into energy
every second, to resist its own gravity.
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The Three Step Process
1. 1H + 1H  2H + e+ + 
- two protons fuse to make deuterium
- one of the protons turns into a neutron and releases energy in
a positron and a neutrino
- average time for this step - 1 billion years
p+
n + e+ + 
the form of
(inverse -decay)
neutrino carries up to 0.42 MeV
the positron annihilates with an electron, creating two gamma rays
- 1.02 MeV
Note: In a free state the neutron is unstable with a half-life of about 12
decaying into a proton, an electron, and an anti-neutrino.
n
p+ + e- + 
minutes,
(-decay)
2. 2H + 1H  3He + 
- the deuterium then combines with another proton, releasing a
gamma ray and giving a nucleus of helium-3 - 5.49 MeV
- average time for this step - 1 second
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The Three Step Process
3. 3He + 3He  4He + 1H + 1H
- the helium-3 nucleus fuses with another helium-3 to form
normal helium - 12.86 MeV
- sets free two protons to start the whole process again.
- average time for this step - 1 million years
Total energy  26.7 MeV
Mproton = 1.67 X 10-27 kg
MHe4(nucleus)= 6.6326 X 10-27 kg
4(Mproton) - MHe4(nucleus) = 4.74 X 10-29 kg
E = mc2 = (4.74 X 10-29 kg)(2.9979 X 108 m/s)2 = 4.26 X 10-12 J
(4.26 X 10-12 J)(1 eV/ 1.602 X 10-19 J)=26.7 MeV
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Proton-Proton Chain Animation
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Energy in form of:
Gamma rays
- take one to 10 million years to work their way out from the star's
core
- scattered numerous times - lose energy as they go, heating the
gas
-eventually emerge from the surface as rays of light and heat.
Positrons
- annihilate with free electrons - produce gamma rays
Energy of motion of particles
- raises temperature of gas
Neutrinos
- almost never interact - escape
- do not contribute to heating
Inside the Sun, about 655 million tons of hydrogen are converted into 650 million tons of
helium every second.
In stars heavier than about 2 solar masses, in which the core temperature is more than
about 18 million K, the dominant process in which energy is produced by the fusion of
hydrogen into helium is a different reaction chain known as the carbon-nitrogen cycle.
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The Solar Luminosity
The Sun’s luminosity is stable over the short-term.
However, as more Hydrogen fuses into Helium:
- four H nuclei convert into one He nucleus
- the number of particles in Sun’s core decreases with time
- the Sun’s core will contract, causing it to heat up
- the fusion rate will increase to balance higher gravity
- a new equilibrium is reached for stability at a higher energy output
- the Sun’s luminosity increases with time over the long-term
Models indicate the Sun’s luminosity has increased 30% since it formed 4.6 billion
years ago.
- it has gone from 2.9 x 1026 watts to today’s 3.8 x 1026 watts
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Other Helium Production Paths in the Sun
The proton-proton chain is common path to making helium in the Sun,
but not the only one. After Step 2 is complete, other reactions can take
place -- the PPII chain (31% of the time):
+ 4He  7Be + 
7Be + e-  7Li + 
7Li + 1H  4He + 4He
3He
Or even the PPIII chain(rare, 0.3% of the time):
+ 1H  8B + 
8B  8Be + e+ + 
8Be  4He + 4He
7Be
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Energy Production
Binding energy
due to strong
force = on short
range, strongest
of the 4 known
forces:
electromagnetic,
weak, strong,
gravitational
Nuclei are made up of protons and
neutrons, but the mass of a nucleus is
always less than the sum of the
individual masses of the protons and
neutrons which constitute it. The
difference is a measure of the nuclear
binding energy which holds the nucleus
together.
Nuclear fusion can produce
energy up to the production
of iron.
For elements heavier than iron,
energy is gained by nuclear
fission.