Astrophysics

Ray Diagrams

1. Rays of light that pass through the middle of the lens do not reflect.

2. Rays parallel to the principle axis will refract through the focal point.

3. Rays travelling through the focal point before the lens will exit parallel to the principle axis.

Power of a lens

P = 1/ f

Refracting Telescopes

1. Comprised of two converging lenses

2. Objective lens collects light from stars and creates a real image at its focal point.

3. The eyepiece magnifies the image produced, creating a virtual image at infinity.

   

Normal Adjustment

The distance between the two lenses in a refracting telescope is the sum of their focal lengths, so their focal points are in the same place.

Magnifying Power / Angular Magnification

M = angle subtended by image / angle subtended by object

Reflecting Telescopes

1. A concave primary mirror with a long focal length focuses the light.

2. A small convex secondary mirror positioned near the focal point reflects the nearly focused light.

3. An eyepiece lens refracts the light so it enters the eye parallel and forms a virtual object at infinity.

   

Spherical Abberation

Curvature of the lens or mirror means rays to be focused on different points, causing image blurring and distortion

Chromatic aberration

Different wavelengths of light are distracted by different amounts, causing coloured fringing around the edge of the image. This can be solved using a second conclave lens to focus all the light.

Advantages + Disadvantages Refracting Telescopes

• Chromatic and spherical aberration.

• Large lenses bend and distort under their own weight.

• Large magnifications require very large diameter objective lenses with long focal length.

• Has greater angular magnification for same length.

Advantages + Disadvantages Reflecting Telescopes

• Spherical aberration.

• Mirrors are light and easy to handle.

• Large composite primary mirrors can be made from lots of smaller mirror segments.

• Easier to support as mirrors can be supported from behind.

• Have a wider field of view for the same length.

Collecting Power

Measures the amount of light energy collected per second. It is directly proportional to the square of the objective’s diameter.

Resolving Power

The smallest angular separation that an instrument can distinguish between two objects.

Rayleigh Criterion

Two sources will be just resolved if the central maximum of the diffraction pattern of one coincides with the first minimum of the other.

Charge-coupled devices

An array of light-sensitive pixels which are highly sensitive to photons. Incident photons cause electrons to be released, with the number of electrons released proportional to the intensity of incident light.

Advantages of CCDs

• Higher quantum efficiency

• Can operate over a wider range of wavelengths

• Can resolve images more clearly as have higher pixel resolution

• Images can be shared and stored

• Can be time exposed to produce brighter images

Telescopes at Ground Level

Can observe:

• Visible Light

• Some IR

• Most microwave

• Most radio waves

Radio telescopes

• Because radio wavelengths are much larger than visible, they require a much larger diameter to achieve the same resolving power.

• Wire mesh instead of mirrors.

• Study galaxies and map the milky way by studying 21cm radio waves produced by hydrogen atoms.

IR Telescopes

• Large concave mirrors focus radiation onto a detector.

• Study cooler regions in space, such as dust clouds.

• Often launched into space.

UV Telescopes

• Only found in space.

• Map star formation regions and other hot objects in space.

X-ray Telescopes

• Only found in space.

• Consist of parabolic and hyperbolic mirrors.

• Observe active galaxies, black holes and neutron stars.

Gamma Telescopes

• Only found in space.

• Observe quasars, black holes and gamma ray bursts.

Advantages of Satellite Telescopes

• No absorption of electromagnetic waves by the atmosphere.

• No light pollution or other sources of interference.

• No optical effects, such as scattering or scintillation.

Astronomical Unit

Average distance between the earth and sun.

Light Year

Distance light travels through space in a year.

Parsec

Distance at which the angel of parallax is 1 arcsond.

Parallax

The apparent change of position of a star in comparison to more distant stars as a result of the orbit of the Earth. Only works for distances of about 100pc, because beyond this angles are too small to accurately measure.

Magnitude Equation

m = M + 5log(d/10)

Black Bodies

Objects that are perfect emitters and absorbers of all possible wavelengths. Can be used to deduce Wein’s and Stephen’s Laws.

Wien’s Law

Peak wavelength of emitted radiation is inversely proportional to the absolute temperature.

Inverse Square Law

I = P / (4*pi*d²)

Hydrogen Balmer Absorption Lines

Caused by the excitation of hydrogen atoms from the n = 2 state to higher energy levels, which requires very high temperatures. Found in O, B and A stars.

Spectral Classes

Spectral Class	Colour	Temperature (K)
O	Blue	25,000 – 50,000
B	Blue	11,000 – 25,000
A	Blue / White	7,500 – 11,000
F	White	6,000 – 7,500
G	Yellow / White	5,000 – 6,000
K	Orange	3,500 – 5,000
M	Red	< 3,500

Hertzsprung-Russel Diagram

• Plots temperature against magnitude.

• Logarithmic temperature scale from 50,000 to 2,500.

• Absolute magnitude scale from +15 to -10.

Protostars

• Clouds of gas and dust.

• Contract under gravitational attraction.

• As they rotate, they spin inward to form a denser centre so temperature increases.

• Eventually nuclear fusion occurs.

• Outer layer of protostar becomes hot and a photosphere is formed.

Main Sequence

• Helium fused into hydrogen.

• Gravity balanced by radiation pressure.

Red giant and Supergiant

• Under 3 solar masses: red giant.

• All hydrogen has been fused.

• Core collapses and outer layers expand.

• When the core is dense enough, helium fusion begins to occur.

White Dwarf

• Under 1.4 solar masses

• When helium used up, core contracts.

• Electron pressure balances gravitational pressure.

• Planetary nebula.

Supernova

• Above 1.4 solar masses.

• Star collapses until it has the density of atomic nuclei.

• Core suddenly becomes rigid.

• Collapsing matter rebounds, releasing so much energy that elements heavier than iron can be fused.

Neutron Star

• Between 1.4 and 3 solar masses.

• Protons and electrons become neutrons.

• Density of nuclear matter.

• Pulsars are spinning neutron stars that emit beams of radiation from their magnetic poles.

Black Hole

• Greater than 3 solar masses.

• Neutron pressure isn’t strong enough to withstand gravitational force.

• Escape velocity greater than the speed of light.

• Event horizon = point at which escape velocity is greater than the speed of light.

Supermassive Black Holes

Formed by

• The collapse of massive gas clouds as the universe was forming.

• A normal black hole that accumulated huge amounts of matter over millions of years.

• Several black holes merging together.

Type I Supernovae

No strong hydrogen lines, occur when a star accumulates matter from its companion star and explodes after reaching critical mass.

Type II Supernovae

Occur at the death of a high mass star.

Type 1a Supernova

White dwarf star begins to accumulate the mass of a companion giant star. When the white dwarf reaches critical mass, fusion begins and becomes unstoppable, causing the white dwarf to explode. Can be used as standard candles.

Eclipsing Binaries

1. Stars are beside one another.

2. Smaller star eclipses the larger one, brightness at a minimum.

3. Larger star eclipses the smaller one, brightness decreases to a lesser degree.

Hubble Law

The further away a galaxy is from us, the greater the redshift of stars within it. This can be found using the equation v = Hd, where H, the Hubble Constant, is measured in km s^-1 Mpc^-1

Age of the Universe

1 / H = d / v = t

Proof for the Big Bang

• CMBR: Remaining high-energy radiation from the Big Bang, which has redshifted over time.

• Relative abundances of hydrogen and helium.

Dark Energy

The rate at which the universe is expanding is accelerating, so scientists have theorised the existence of dark energy.

Quasars

• Oldest and most distant objects in the known universe.

• Active galactic nuclei.

• Only found at great distances, suggesting they existed in the early universe and confirming its evolutionary nature.

• They have extremely large optical redshifts, very powerful light output and a relatively small size.

Transit Method

• Measure the light intensity of a star.

• A regular dip in intensity can be observed when the planet transits the star.

• Size and orbital period of the planet can be determined by amount of intensity drop and its duration.

Radial Velocity

• Measure the Doppler shift in light received by a star as it orbits around a barycentre.

• Time period of Doppler shift cycle equal to time period of planets rotation.

• Only works for high mass planets orbiting near their star.

Spectroscopic Binaries

• Binary star system in which the stars are too close to be resolved by a telescope.

• When the stars eclipse one another, they travel perpendicular to the line of sight, so there is no Doppler shift in emitted radiation.

• When the stars are travelling in opposite direction, the spectral lines split into two, with one red-shifted and one blue-shifted.