Option D: Astrophysics

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1. Objects in the Universe

The solar system

Order of planets:

Sun - Mercury - Venus - Earth - Mars - Jupiter - Saturn - Uranus - Neptune

There exist dwarf planets like Pluto.

→ Order of size

Jupiter

Saturn

Uranus

Neptune

Earth

Venus

Mars

Mercury

Planets closer to the sun are rocky planets, while those further away are gas giants

Asteroids

→ a small, solid object in our solar system, orbiting the sun

→ believed to be remnants of the protoplanetary disk

Comets

→ believed to originate in the Oort cloud and consist of rock, dust and ice.

→ have higly eliptical orbits, mostly outside the furthermost planets

Stellar clusters vs constellations

→ A stellar cluster is a group of stars physically near each other and all

produced by the collapse of the same gas cloud.

→ A constellation is a group of stars in a recognizable pattern which

appear to be physically near each other, but are not necessarily.

Relative Distances and the Night Sky

light year

→ the distance that light travels in a vacuum in a year

The average distance between:

- stars in a galaxy: 1 pc

- galaxies in the same cluster: 10^2 pc

- galaxies in different clusters: 10^6 pc

Stellar constellations appear to rotate around Polaris

→ Due to the rotation of the Earth around its axis

→ Sky changes seasonally due to rotation of the Earth

around the sun

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2. Stellar radiation and stellar types

Apparent Brightness and Luminosity

luminosity

→ the energy radiated per second

→ Determined by the Stefan Boltzmann Law

apparent brightness

→ the received power per unit area (W/m^2)

→ how bright we observe a star to be from Earth

Stellar radiation

Stars behave like black bodies

→ There is a peak wavelength at which the most energy is emitted;

the higher the temperature, the lower this wavelength

→ Wien's law relates temperature to peak wavelength

Stellar Spectra and Spectral Classes

Light from stars is absorbed by their outer layer of gas, producing an

absorption spectrum

→ This allows us to identify the elements that make up outer layers

of the star

Main sequence stars are divided into 7 spectral classes based on

surface temperature.

→ O, B, A, F, G, K, M.

( Oh Be A Fine Girl Kiss Me )

→ The sun is a G class star (yellow star)

The Hertzsprung-Russell Diagram is a scattergraph of luminosity vs temperature / (spectral class vs absolute magnitude)

on which individual stars are plotted.

Star Types

Main Sequence

- Stable stars in equilibrium between radiation pressure and gravitation

- Found on the main sequence in a HR diagram, spectral type and

luminosity depend on its mass

- Fuse hydrogen to helium

Red Giants

- Large 'cool' reddish star with a large luminosity

- Fusion of elements heavier than hydrogen

White Dwarfs

- Small stars with high surface temperatures but low luminosities

- 'Dead' stars which have used all their fuel, core has no further source

energy and will gradually radiate away energy and cool down

Cepheid Variable

- A periodically variable red giant due to periodic variation in star size

Binary stars

- Two stars in orbit around their common centre of mass

Visual

- Can be seen separately

Eclipsing

- Occult one another partially or totally periodically

Spectroscopic

- Can only be detected by red or blueshift in their spectra

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3. Stellar Distances and Magnitudes

Parallax

Used to determine distances to stars closer than 100 pc away

- Otherwise, the parallax angle becomes too small to measure accurately

The parallax angle is measured by measuring the angular position of the

star relative to the background of fixed stars in 2 positions six months

apart. The parallax angle p = 1/2 of separation.

For d in pc and p in arc seconds;

d = 1/p

Absolute and Apparent Magnitudes

Apparent Magnitude, m

- Old scale of star brightness, initially going from 1 to 6

- Mag. 1 is brightest, 100x brighter than mag. 6;

increase of 1 on this scale is 2.51 times less bright

- Apparent magnitudes may be negative numbers

Absolute Magnitude, M

- Compares star brightness if they would all be placed

at 10 pc from Earth

Spectroscopic Parallax

Used for finding star distances of up to 10 Mpc

Rearranging apparent brightness equation;

- Spectrum enables its temperature to be determined (Wien's law)

- HR diagram enables luminosity to be found (assume main sq)

Cepheid Variables to find distance

The period of a Cepheid Variable's pulsation is related to its

luminosity.

- Observation of period gives luminosity

- Can be used to determine distance to stars and galaxies

up to 15 Mpc away

- Known as 'standard candles'

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4. Cosmology

Olbers' Paradox

Newton assumed an infinite and static universe, leading to Olbers' paradox.

- If the universe is infinite, containing an infinite number of uniformly distributed

stars, then every line of sight should eventually end on the surface of a star, and

the sky would look like the surface of a star.

- When we look out in space the brightness decreases by 1/d^2, but the area

increases proportional to d^2, hence it should be constant

Things to keep in mind:

1. Some starlight is absorbed by dust and gas etc.

2. The universe is not infinitely old and not all light has reached us yet

3. Many galaxies are moving away from us and the resulting red shift

diminishes their brightness

The Big Bang Model

In the 1920s, Hubble discovered that nearly all galaxies studied had red shifted light

and hence are moving away from us at incredible speeds.

Physicist developed the theory that space and time began with a big bang

- Currently the most widely accepted theory of the origin of the Universe

Supporting evidence: Cosmic Microwave Background Radiation

- The big bang theory predicted that as plasma from the big bang combined into

neutral atoms, photons would spread out across the universe.

- Cosmic Microwave Background Radiation provided substantial confirmation

of the general big bang theory predictions.

- Radiation was found to be isotropic and wavelength consistent with a blackbody spectrum

of about 3K

- Red shift is present due to expansion of universe, is now microwave radiation

We have assumed the universe is isotropic (see The Cosmological Principle), yet

CMB provides a different image; matter is clearly not evenly distributed.

The Cosmological Principle

Rests on two fundamental simplifying assumptions:

1. The universe is homogeneous (the same everywhere)

2. The universe is isotropic (it looks the same in every direction)

Einstein expressed in the general theory of relativity that matter

in the universe can distort space-time.

The Fate of The Universe

The fate of the universe depends on the density of matter within it.

We assign a density parameter, Ω = density / critical density.

Closed universe: Ω > 1, p > pc, universe collapses

Flat universe: Ω = 1, p = pc, universe expands forever but expansion slows

Open universe: Ω < 1, p < pc, universe expands forever

We have found that the expansion of the universe actually accelerates;

this can only be explained by the presence of dark energy

Critical density

- Derivation for simplified expression of formula for critical density;

v = H r where H is the Hubble constant

M = 4/3 π r^3 p

E = 1/2 mv^2 - (GMm)/r (= 0 for flat universe)

Dark Matter and Energy

Dark matter

- Matter that is not luminous in any part of the EM spectrum and

therefore cannot be detected

Evidence; star orbit velocities in galaxies

Close to the 'central bulge', star velocity v is proportional to r;

- M is distributed in a sphere (assuming bulge is spherical)

= 4/3 pi * r^3 p

- (GMm)/r^2 = (mv^2) / r

At the edge of the galaxy, star velocity v is proportional to 1/√r

- M acts as point mass instead as distribution through sphere;

- v^2 = GM/r

There must be a spherical distribution of matter that we cannot

observe

Potential types of dark matter:

- MACHOS (Massive Compact Halo Objects), black and brown dwarfs

- WIMPS (Weakly Interacting Massive Particles), neutrinos

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5. Stellar Evolution

Stellar evolution

- The sequence of changes that a star undergoes during its lifetime.

Stellar Life Cycle

1. Protostars

Stars are formed from a giant cloud of gas. Regions of the cloud collapse due

to gravity and the energy released heats it up until hydrogen fusion starts at

a temperature of 10 MK.

Jeans criterion:

A gas cloud will only collapse if its mass exceeds the Jeans mass;

- Most likely in a cold dense cloud

- Jeans mass varies for clouds of different temperatures

2. Core hydrogen runs out

Depending on its initial mass, after a certain amount of time the star will run

out of hydrogen in the core, stopping nuclear processes.

- Core collapses under gravity due to lack of outward pressure

- Outer layers expand

3. Helium burning in Red (Super)Giant

The temperature and pressure increase until helium fusion begins at core

temperature of 100 million K

- Outer layer hydrogen undergoes fusion as it heats up again

- Star expands until 100x original main sequence size

- Helium fuses into carbon using the triple-alpha process

THE NEXT STEPS DEPEND ON THE MASS OF THE STAR

4. Evolution into White Dwarf

Helium burning leads to instability and pulsations

- Outer layers gain enough KE to be ejected as a planetary nebula

- Core becomes small but dense white dwarf

- Core radiates remaining energy until it becomes a black dwarf

5. Type II Supernova (M > 5 solar masses)

Outer layers have swollen into a red supergiant

- Core begins to yield gravity and shrinks

- Grows hotter and denser and fusion of heavier elements takes

place

- Stops at iron-56; fusion takes energy instead of releasing

Star collapses nearly instantly and produce a supernova

- Outer layers flung away leaving core to collapse further

Chandrasekhar limit

White dwarf mass > 1.4 solar masses becomes neutron star

- Stars of initial 8 times solar mass

6. Neutron stars

If the chandrasekhar limit for white dwarf mass is exceeded,

electron degeneracy fails and the star will collapse into a

neutron star.

- Electrons are forced into the nuclei, where they combine

with protons to form neutrons.

- Some are called pulsars, send pulses of radiation to Earth

from their north/south poles

Oppenheimer-Volkoff limit

Neutron star > 3 solar masses becomes black hole

7. Black Holes

If Oppenheimer-Volkoff limit is exceeded, neutron

degeneracy fails and star collapses into a black hole

- Predicted by general theory of relativity

- Radius smaller than Schwarzschild radius

8. Quasar

A quasar (Quasi-stellar radio source) is an astronomical

source of electromagnetic energy, including light, that

shows a very high redshift.

- Quasars must be very distant and luminous

- Release energy equal to output of hundreds of average

galaxies combined.

- Are possibly powered by accreation of materials onto

supermassive black holes

The Mass-Luminosity Relation

For main sequence stars, the following applies:

- L is proportional to m^n , where n is between 3 and 4.

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6. Galaxies and the Expanding Universe

Galaxy

- A huge gravitationally bound system of stars, interstellar gas and dust,

plasma and (possibly) unseen dark matters.

Typical galaxies

... contain 10^10 stars

... are 10^5 ly across

... usually separated from one another in the order of millions of ly

... there are more than 10^11 galaxies in our observable universe

Three main types

1. Elliptical

2. Spiral

3. Irregular

Larger Scale Structures

Most galaxies are gravitationally bound to a number of galaxies;

- Up to 50 galaxies: group

- Thousands of galaxies: cluster

Dominated by single elliptical galaxy that destroys satellite

galaxies and adds their mass to its own

- Tens of thousands of galaxies: supercluster

The Milkyway

... is part of the Local Group (Together with Andromeda)

which contains approx. 30 galaxies and is 1 Mpc across

... is part of the Virgo Supercluster, which is dominated by

the Virgo Cluster

Red Shift of Galaxies

Results from expansion of space

Hubble's law is the relation between the distance between

us and a galaxy and how fast it is receding, v = Hd

Nearby galaxies do not conform to Hubble's law due to

low recession speed which is masked by random or peculiar

motions.

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7. Stellar processes

Fusion Processes

Proton-Proton fusion

- Occurs in main sequence stars such as the Sun

- Three stages

The CNO Process

- Occurs in stars greater than 4 solar masses

- Core temperatures above 2 x 10^7 K and has six stages

Helium Fusion

- When star moves off the main sequence

- Heavier elements are produced until Fe-56

In a massive star, heavier nuclei are produced with the

s-process of slow neutron capture

- A neutron is captured by a nucleus and beta decay

occurs, increasing proton number by 1

R-process

- Rapid neutron capture

- High neutron density so great that beta decay does not

happen before next neutron is captured.

- Creates heavy isotopes

Lifetime of Stars

The more massive a star, the shorter time it spends on the

main sequence.

- The rate of energy production needs to be greater in the

core to prevent collapse under gravity

- Sun: 10^10 billion yrs on main sequence