PHYS-3380 Astronomy Angular Resolution Resolving power: Wave nature of light => The telescope aperture produces fringe rings that set a limit to the resolution.

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.

amin = 1.22 (/D)

Resolving power = minimum angular distance amin between two objects that can be separated.

For optical wavelengths, this gives

amin = 11.6 arcsec / D[cm]

amin

PHYS-3380 Astronomy

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

PHYS-3380 Astronomy

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:

A = (D/2)2

D

PHYS-3380 Astronomy

So: light collecting ability of a reflecting telescope is dependent on the area of the mirror

Light Collecting Area Animation

PHYS-3380 Astronomy

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!

PHYS-3380 Astronomy

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

PHYS-3380 Astronomy

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)

Uses of Telescopes

PHYS-3380 Astronomy

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.

PHYS-3380 Astronomy Spectroscopy

• The spectrograph reflects light off 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.

PHYS-3380 Astronomy

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

PHYS-3380 Astronomy The Crab NebulaVisible Infrared

Radio Waves X-rays

PHYS-3380 Astronomy

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.

Atmospheric Effects

PHYS-3380 Astronomy

Light Pollution

PHYS-3380 Astronomy

PHYS-3380 Astronomy

Radio Astronomy

Recall: Radio waves of ~ 1 cm – 1 m also penetrate the Earth’s atmosphere and can be observed from the ground.

PHYS-3380 Astronomy

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.

PHYS-3380 Astronomy

Radio Telescopes

305-meter radio telescope at Arecibo, Puerto Rico

• The wavelengths of radio waves are long.• So the dishes which reflect them must be very large to achieve any

reasonable angular resolution.

PHYS-3380 Astronomy

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)!

PHYS 3380 - AstronomyMost 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.

PHYS-3380 Astronomy

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.

PHYS-3380 Astronomy

Atmospheric Distortion Animation

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.

PHYS-3380 Astronomy

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.

AO mirror off AO mirror on

• Angular resolution improves.

• These two stars are separated by 0.38

• Without AO, we see only one star.

PHYS-3380 Astronomy

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PHYS-3380 Astronomy

The Sun

PHYS-3380 Astronomy

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

PHYS-3380 Astronomy

Striking a BalanceThe 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

PHYS-3380 Astronomy

One second of output from the Sun (luminosity) would provide power for the human race for the next 500,000 years

PHYS-3380 Astronomy

Layers of the Sun

PHYS-3380 Astronomy

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.

PHYS-3380 Astronomy

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 E-M repulsion

- this requires high temperatures and pressures

When nuclei touch, the nuclear force binds them together

PHYS-3380 Astronomy

Energy Generation in the Sun: The Proton-Proton Chain

Basic reaction:

4 1H 4He + energy

Need large proton speed ( high temperature) to overcome Coulomb barrier (electromagnetic repulsion between protons).

Sun needs 1038 reactions, transforming 5 million tons of mass into energy every second, to resist its own gravity.

T ≥ 107 0K = 10 million 0K

PHYS-3380 Astronomy

1. 1H + 1H 2H + e+ + - two protons fuse to make deuterium- one of the protons turns into a neutron and releases energy in

the form of a positron and a neutrino - average time for this step - 1 billion years

neutrino carries up to 0.42 MeVthe 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 minutes, decaying into a proton, an electron, and an anti-neutrino.

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

p+ n + e+ + (inverse -decay)

The Three Step Process

n p+ + e- + (-decay)

PHYS-3380 Astronomy 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

PHYS-3380 Astronomy

Proton-Proton Chain Animation

PHYS-3380 AstronomyEnergy 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.

PHYS-3380 Astronomy

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

PHYS-3380 Astronomy

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):

3He + 4He 7Be + 7Be + e- 7Li + 7Li + 1H 4He + 4He

Or even the PPIII chain(rare, 0.3% of the time):

7Be + 1H 8B + 8B 8Be + e+ + 8Be 4He + 4He

Other Helium Production Paths in the Sun

PHYS-3380 AstronomyEnergy Production

Nuclear fusion can produce energy up to the production of iron.

For elements heavier than iron, energy is gained by nuclear fission.

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.