Astrophysics

IB HL option D

Planet Definition - 4 points

• An object that orbits the sun

• is not a satellite of an object

• is massive enough that its own gravity forces it to be round

• has cleared its neighbourhood of smaller objects around it (due to its gravity) - ruled out Pluto

Moon Definition

• Natural satellite that orbits a planet - could also orbit a dwarf and minor planet (pluto has moons - dwarf)

Small Solar System Bodies Definitions

• All other objects except satellites, orbiting the sun

Asteroids / minor planets definition

• Small Solar System Bodies

• An object that orbits the sun that isn’t a planet or comet

• (e.g. Ceres and Ryugu)

Comet definition

• Small solar system bodies

• An object containing frozen gases, rock and dust;

• When a comet nears the sun heating up causing the gases to vaporise

• Produces a coma (small atmosphere) and a tail (directed away from the sun due to the solar winds)

Planetary System Definition

• A set of gravitationally bound non-stellar (not stars) objects in orbit around a star/star system

Star Definition

• A luminous Balls of gas, mostly hydrogen and helium, held together by its own gravity

Gravitational Equilibrium in Stars occurs when…

• Nuclear fusion at the star’s core creates high pressure in the gases that counteracts the forces of gravity (creating equilibrium)

Binary System Definition

• Two stars that rotate around a common centre of mass

Constellation

• A configuration of stars in the night sky (viewed from earth)

• Located close together that when joined by connecting lines form some sort of imagined picture.

Stellar Clusters Definition

• Groups of stars that are gravitationally bound together

• Two Types:

  • Globular Cluster

  • Open Cluster

Globular Clusters

• Tight Group of hundreds or thousands of very old stars

Open Clusters

• Less than a few hundred stars

• Normally very young

Nebula Definition

• Interstellar cloud of dust and gases

• All stars are formed in a nebula

Galaxy Definition

• A system of millions or billions of stars and their planetary, and dust and gas, held together by gravitational attraction

Galaxy Clusters Definition

• A structure consisting of hundreds of thousands of galaxies, bound together by gravity

Supercluster Definition

• A large group of smaller galaxy cluster;

• Among the largest structures in the universe

Light year unit

• ly

• Distance travelled by light in one year

• 1 ly = 9.46x10^15m

Astronomical Unit

• AU

• Average distance between the sun and the Earth

• 1AU = 1.50x10^11

Parsec

• pc

• Distance of which 1AU subtends an angle of 1 arc second

  • Arc second → 1/3600 of 1 degree

• 1pc = 3.26ly = 3.09x10^16

The nature of stars

Stars depend on the equilibrium between two opposing forces. The gravitational force pushing in and the radiation and gas pressure pushing out. This is gained through nuclear fusion.

Stellar Parallax

• The apparent movement of a nearby star against the distant background stars as the earth moves around the sun

• p is the parallax angle

Distance to star - equation

Parallax Limitations

• Parallax angles of less than 0.01 arc-seconds are difficult to resolve from Earth to the atmosphere

  • absorption

  • scattering of light

  • turbulence (causes to twinkle)

• This limits distance measurements to 100 pc

• Gaia - telescope orbiting the earth (outside atmosphere), can resolve angles to 10 micro arc-seconds (0.000010 arc-second), measuring stars up to 100 000pc

Luminosity

• L

• The total energy radiated by a star per second

• Measured in watts

• Can’t directly determine a star’s luminosity, can measure it’s apparent brightness

• The more Luminous the star, the apparent brightness will be greater

• b∝L

Apparent Brightness

• b

• Measured in watts per square metre (from earth)

• How bright it appears to be

• Closer = brighter

• Bigger = brighter

Black-Body Definitions

• Idealised absorbers of all electromagnetic radiation that falls on it, and then re-radiated.

• The spectrum of the radiated energy depends on the body’s temperature

• While stars aren’t perfect black-bodies, they are capable of emitting all wavelengths of EM radiation.

  • Follows the Stefan-Boltzman Law

Stefan-Boltzman Law

If we approximate stars as being spherical:

• A=4πr^2

• ∴L=σ4πr^2T^4

• Therefore Luminosity depends on size and temperature

Stellar Spectra

Blue to orange/red where blue is the hottest.

Stellar Spectra Allow us to Determine:

• Chemical composition - spikes or dips can be matched to known elements

• Density - dips in a star’s spectrum usually relate to light from the hot dense centre of the star being absorbed by cooler, lower-density gas further out in the star.

• Velocity - Using the Doppler shift/effect of the spikes in the star’s spectrum can be used to determine how fast the star is moving.

• Temperature - Treating stars as Black bodies, Wein’s law can be used to relate a star’s surface temperature to the wavelength of maximum intensity in the star’s blank body radiated curve

  • λmax * T = 2.9x10^-3 mK → Data booklet

Cepheid Variables

• Extremely luminous stars that have a periodic variation of luminosity

Relationship between the luminosity and the period of the cepheid

• Linear relationship between the relative luminosity and the period of the cepheid.

• This allowed measurement of the period allowed the luminosity to be determined

• By measuring the apparent brightness, the distance to the cepheid variable to be determined using the equation.

Cycle of a cepheid variable star

1. Loss of Hydrostatic Equilibrium - the pressure inside the star is no longer able to overcome the gravitational forces leading to the outer layers of gas collapsing inwards

2. The layer of gas becomes compressed - less transparent (more dense) meaning the EM radiation that’s being radiated from inside the star isn’t able to escape

3. Temperature in the Gas layer increases - causes build-up of pressure *Intensity decreases here (you see it not as bright)

4. The Gas layer is pushed outwards -

5. The layer cools as it expands - becoming less dense

6. The decrease in density - radiation can now escape again as the pressure decreases *Intensity increases here (you see it brighter)

Hertzprung - Russel (HR) Diagram corner characteristics

• Top right - cool & bright

• Top left - Hot & bright

• Bottom left - Hot & dim

• Bottom Right - Cool & dim

Mass-Luminosity relation for main sequence stars

The luminosity increases with the mass

a=3.5 is commonly used for main sequence stars and doesn’t apply to red giants or white dwarfs

Main Sequence

• Produce energy from fusion of hydrogen and other light elements

• 90% of stars are here

Red giants

• Cooler than the sun;

• Much more luminous - larger than the sun

• Only 1% of stars are giants / super giants

Supergiants

• Very large and very bright

• Only 1% of stars are giants / super giants

White Dwarfs

• White-ish colour

• Remnants of old stars

• Dead stars

• Stars that have used up their fuel source so no-longer radiate their heat source

• Low Luminosity - small surface area

• Takes billions of years to cool down

• 9% of all stars

Define cosmology

The study of the universe. How it began, how it developed, and what will happen to it in the future

Olber’s Paradox

If the universe is infinite and has an infiinite number of stars then there should be no dark sky at night

Big Bang Model

Solved the Olber’s paradox. The Universe was “created” at a point about 13.8 billion years ago. It was dense and hot but is now expanding and cooling down. This is the “creation” of everything in the universe (matter, space, and time)

The everything expansion

How do we know the universe is expanding?

We know the universe is expanding because of the doppler effect on EM waves

Red shift

When the wavelength increases and the frequency decreases. The source (star) is moving away from the observer (earth). Most galaxies are seen to be moving away from the earth and away from each other. (raisin toast when baking where the raisins are the galaxies)

Blue Shift

When the wavelength decreases and the frequency increases. The source (star) is moving towards the observer (earth)

Recession Speed

A graph os a galaxy vs the distance the galaxy is from earth from cepheid variable stars. There are significant uncertainties in this data. The further away a galaxy is the faster it is receding

Hubbles Law

The current Velocity of recession, v, of a galaxy is proportional its distance d from Earth. This law can be written as:

v=H_od

Hubble’s constant, H_o

H_o = (70km) / (s x Mpc).

It is believed that this constant has changed over billions of years but is now constant

Occam’s Razor

If you need to choose between two or more possible theories then choose the one with the least amount of assumptions

Hubble Time

T ~ 1/H_o T is the age of the universe and is approximately 1.4 × 10¹⁰

Cosmic Microwave Background (CMB) radiation

Low level microwave radiation can be detected coming almost equally from all directions (it is isotropic) rather than from a specific source. The average temperature of the universe is about 2.76K

Observable / visible Universe

The universe we can observe from earth is a sphere around us of radius 4.6 × 10¹⁰ ly

Rate of expansion of universe

It’s increasing. we know this because of red-shift from type 1a supernova

Dark Energy

A form of energy of low density but present throughout the universe

The Cosmic Scale Factor, R

Represents the size of the universe by comparing the distance between any two specified places (like two galaxies) at different times. These distances and the cosmic scale factor increase with time because the universe is expanding.

Interstellar Medium

Interstellar medium (ISM) is about is about 99% gas (mostly H and He) and 1% dust. It has a low temperature and low density. ISM is not uniform (Homogenous).

it is the region between the stars that contains vast, diffuse clouds of gases and minute solid particles

Jeans Criterion and Jeans Mass, M_j

If the gravitational potential energy of a mass of gas is higher than the kinetic energy of its molecules then it will tend to collapse.

A star cannot be formed unless the mass of the gas is greater than the critical value which is Jeans mass. M_j depends on the temperature. If the ISM is warmer that the mass necessary for the formation of a star will be higher. The collapse of an interstellar cloud to form a star can only begin if it’s mass is M.M_j

Proton-Proton cycle

This is a three step cycle for fusion in a star

Occurs to main sequence stars

CNO Cycle

Example: the sun

Efficient at higher temperatures and becomes the dominant fusion process in stars where the core temp is above 17 × 10⁶ K

Also in stars on the main sequence

Triple-Alpha process

Occurs in the core of stars which have left the main sequence. It is the final fusion reaction for those main sequence stars with a mass smaller than eight solar masses, which end up as white dwarfs surrounded by a planetary nebula.

Time for a main sequence star

If the H in a star becomes depleted then the star will no longer be in equilibrium. This occurs when about 12% of the original mass of H has been fused.

The lifetime of a main sequence star depends on the original mass of H and the rate of nuclear fusion. More massive stars have more concentrated core at higher temps and deplete their hydrogen quicker.

More massive stars have shorter main sequence lifetimes. The time as a main sequence star T is proportional to the inverse of its mass m to the 2.5 power.

Lifetime of the sun

About 10¹⁰ years

Nucleosynthesis

The creation of nuclei of heavier elements by fusion

In general the contraction of the corse of main sequence stars of greater mass will result in higher temperatures, which means that the nuclei then have higher kinetic energies, so that they can overcome the larger electric repulsive forces involved in the fusion of heavier elements

Binding Energy

Amount of energy required to separate a particle from a system of particles or to disperse all the particles of the system.

Neutron Capture

Elements heavier than iron can be formed by neutron capture. Neutrons are produced in some nuclear fusion reactions within a star. The neutrons are not charged so they can get close enough to the nuclei

After neutrons capture the new elements, the nucleus can decay by beta-negative decay.

S-Process

Slow Neutron capture occurs in red giants. This occurs over a long period of time when there is low neutron density and intermediate stellar temps. Heavier elements can be created over a long period of time. Beta decay is more likely than neutron capture.

R- Process

Rapid Neutron Capture Process occurs in supernovae over a short period of time when there is a high neutron density and high stellar temperatures. Neutron capture is more likely than beta decay. More neutrons in a nucleus will lead to more beta decay and more heavier elements

Supernovae

Sudden, unpredictable and very luminous stellar explosions

Type Ia Supernovae

In a binary star system one of the stars has evolved to become a white dwarf. It’s gravitational field is now strong enough to attract matter from its neighboring star.

There is a sudden rise in mass of the white dwarf. The electron degeneracy pressure is not high enough to resist the collapse.

Type Ia supernovae can act as standard candles by using the equation

• b = (L)/(4πd²)

Type II Supernovae

When nuclear reactions in a red supergiant finish, the star collapses but the mass and energy involved are so huge that the nuclei in the core get deconstructed to protons, neutrons, electrons, photons and neutrinos. The outer layer of the star is stripped. Rapid neutron capture occurs so heavier elements are created. The core becomes a neutron star or black hole

Lifetime of stars

Starts off as a stellar nebula

Then there is two paths

Path 1:

• Average star

• Red Giant

• Planetary Nebula

• White dwarf

Path 2:

• Massive star

• Red super giant

• Supernova

• Black hole or neutron star

The Cosmological Principle

1. The universe is homogenous - everywhere looks the same

2. The universe is Isotropic - no identifiable edge, everywhere the length is the same

Fluctuations in the CMB

The differences in the temperature map correspond to areas of varying density fluctuations in the early universe. Eventually, gravity would draw the high-density fluctuations into even denser and more pronounced ones. After billions of years, these little ripples in the early universe evolved, through gravitational attraction, into the planets, stars, galaxies, and clusters of galaxies that we see today.

Critical density

The 'critical density' is the average density of matter required for the Universe to just halt its expansion, but only after an infinite time.