9.2 classification of stars

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Cards (34)

Luminosity
Power output of a star
Sun’s luminosity = $4\times10^{26}W$
Rate of energy transfer
Watts
Total EM radiation emitted each second
Dependent on object only
Intensity
Observed brightness of an object
How much energy is received
Power per unit area
$Wm$
Energy per second per metre squared
$Js^{-1}m^{-2}$
dependent on the object and the distance from it
$b=$ $\frac{L}{4\pi r^2}$ the
Apparent magnitude, m
How bright objects appear from earth
Brightness depends on luminosity and distance
The Hipparchus scale
Rated stars according to brightness
1 = brightest
6 = dimmest
Magnitude 1 star has an intensity 100x greater than a magnitude 6 star
Logarithmic scale
Difference of 1 magnitude = $100^{\frac{1}{5}}$ = 2.51x brighter
Brightness (intensity) ratio $\frac{I_2}{I_1}\approx2.51^{m_1-m_2}$
Scale extended in both directions
The smaller or more negative the number, the brighter the star
Brightness is subjective
Parsec, pc
$3.08\times10^{16}m$
The distance away when the parallax angle is 1 arcsecond
Parallax angle = the angle of the apparent change in position
Closer objects appear to move faster than objects further away
Arcsecond = $\frac{1}{3600}$ °
The distance to nearby stars is calculated by how they move relative to distant stars when the Earth is in different parts of its orbit
distance to object (pc) = 1 $\div$ parallax angle (arcseconds)
$d=$ $\frac{1}{\theta}$
Lightyear, ly
$9.46\times10^{15}m$
Distance electromagnetic waves travel through a vacuum in a year
Light travels at a constant speed
1 ly = 63 000 Au
Astronomical units, Au
$1.5\times10^{11}m$
Average distance between the Sun and Earth
Average radius of Earth’s orbit
Absolute magnitude, M
The apparent magnitude if the object is 10pc away
Dependent only on luminosity
$m-M=$ $5\log\left(\frac{d}{10}\right)$
$d=$ $10\times10^{\frac{m-M}{5}}$
Useful to measure the distance of stars too big to measure the parallax angle
Standard candles = objects with a known absolute magnitude
Can calculate luminosity directly
cepheid variable star - periodic variation in luminosity that has a constant known relationship with its maximum luminosity
Stefan’s law
Luminosity is related to temperature and surface area
Power output is proportional to the fourth power of the star proportional
Directly proportional to the surface area
$P=$ $\sigma AT^4$
= $5.67\times10^{-8}Wm^{-2}K^{-4}$
Inverse square law
Intensity is the power of radiation per square metre
As radiation spreads out and dilutes, the intensity decreases
If the energy has been emitted from a point or a sphere, then it obeys the inverse square law
$I=$ $\frac{P}{4\pi d^2}$
Wein’s law
The black-body radiation curve for different temperatures peaks at a wavelength, this is inversely proportional to the temperature
$\lambda_{\max}=$ $\frac{k}{T}$
$\lambda_{\max}$ = maximum wavelength emitted by an object at the peak intensity
T = surface temperature (K)
$\lambda_{\max}T=$ $2.9\times10^{-3}mK$
The higher the temperature, the shorter the wavelength at peak intensity
The higher the temperature, the greater the intensity at each wavelength
Black-body radiators
All bodies emit a spectrum of thermal radiation in the form of electromagnetic waves
Mostly infrared part of the spectrum
Black body radiation = pure black surfaces emit well-defined, strong radiation
Ideal black-body radiator = absorbs and emits all wavelengths
A perfect black-body radiator is a theoretical object
Stars are the best approximation and produce a continuous spectrum
... black-body radiators
Radiation emitted has a characteristic spectrum determined by the temperature
Represented on the black-body radiation curve of intensity against wavelength
As temperature increases, the peak of the curve moves
This moves to a lower wavelength and a higher intensity
Measuring properties
These 3 laws were used to work out the properties of stars
Atmosphere only lets through certain wavelengths of electromagnetic radiation
Visible light, most radio waves, near-infrared, some ultraviolet
Light blocked by dust and man-made pollution
Observatories placed at high altitudes, away from cities, in low humidity
Measuring devices are sensitive to wavelength
Glass absorbs UV but is transparent to visible light
Spectral classes
depends on relative strength of certain absorption lines
Only Bold Americans Feel Good Kissing Minors
Spectral class O
Intrinsic colour = Blue
Temperature, K = 25 000 - 50 000
Prominent absorption lines = He+, He, H
Spectral class B
Intrinsic colour = Blue
Temperature, K = 11 000 - 25 000
Prominent absorption lines = He, H
...spectral classes
Spectral class F
Intrinsic colour = White
Temperature, K = 6 000 - 7 500
Prominent absorption lines = Ionised metals
Spectral class G
Intrinsic colour = Yellow-white
Temperature, K = 5 000 - 6 000
Prominent absorption lines = Ionised and neutral metals
Spectral class K
Intrinsic colour = Orange
Temperature, K = 3 500 - 5 000
Prominent absorption lines = Neutral metals
Spectral class M
Intrinsic colour = Red
Temperature, K = < 3 500
Prominent absorption lines = Neutral metals, TiO
Hydrogen Balmer absorption spectra
The Balmer series = set of lines in the hydrogen spectrum
Electrons only exist at certain levels of well-defined energy levels
Create lines in emission and absorption spectra
In atomic hydrogen, the electron is usually in the ground state
n = 1
An electron can move up to the excitation levels
Wavelengths corresponding to the visible part of the hydrogen spectrum caused by electrons moving from higher energy levels to the first excitation level
n = 2
Temperature spectral lines
For hydrogen absorption lines to occur in the visible part of the star’s spectrum, an electron in the hydrogen atom must already be in the n=2 state
Occurs at high temperatures where collisions between atoms, with five electrons, give extra energy
If the temperature is too high, the majority of electrons will reach n=3 or above
Won't be any Balmer transitions
Intensity of Balmer lines depends on the star temperature
For a particular intensity of the Balmer lines, two temperatures are possible
Look at absorption lines of other atoms and molecules
Hertzsprung-Russel diagram
Absolute magnitude against temperature (spectral class)
50 000K - 2 500K
+15 - -10 absolute magnitude
Main sequence
Long diagonal band
Long-lived stable phase - fusing hydrogen into helium
E.g. the sun
Red giants and red supergiants
Red giants and red supergiants
Top-right corner
Star with high luminosity and low surface temperature
Huge surface area - Stefan’s law
White dwarf
Low luminosity and high temperature
Very small - Stefan’s law
Bottom-left corner
Stars at the end of their lives, cooling down after fusion
Solar mass = mass of the sun, $2\times10^{30}kg$
Life of a star
Nebula
Protostar
Main sequence
4a. Red giant (< 3 solar mass)
5a. White dwarf (< 1.4 solar mass)
6. Black dwarf
5b. Supernova (1.4 < m < 3)
4b. Red supergiant (> 3 solar mass)
5. Supernova
6a. Neutron star (1.4 < m < 3)
6b. Black hole (> 3 solar mass)
Protostar
Nebulas have fragments of mass that are pulled together under gravity
Irregular clumps rotate and the gravity of angular momentum spins them inwards to form a dense core
Surrounded by circumstellar disc - disc of material
When it gets hot enough elements fuse producing strong stellar winds that blow away any nearby material
Main sequence
Stable star due to equilibrium of fusion and gravity
Hydrogen nuclei fused into helium nuclei
The greater the mass the shorter the main sequence star period
Uses fuel faster
Red giant
For a star < 3 solar mass
Once hydrogen runs out the temperature of the core increases
Helium nuclei fused into heavier elements
Carbon
Oxygen
Berylium
Outer layers expand and cool
White dwarf
For star < 1.4 solar mass
When the red giant has used up all its fuel fusion stops
Core contracts as gravity is greater than outward force
Outer layers are thrown off forming a planetary nebula around the remaining core
Cire becomes very dense
$10^8-10^9kgm^{-3}$
White dwarf cools to become a black dwarf
Red supergiant
For a star > 3 solar mass
When a high-mass star runs out of hydrogen nuclei the same process for a red giant occurs on a larger scale
Hydrogen runs out and the temperature of the core increases
Helium nuclei fuse into heavier elements
Outer layers expand and cool
The collapse of red supergiants in a supernova causes gamma ray bursts
Can fuse elements up to iron
Supernova
For star > 1.4 solar mass
When fuel runs out fusion stops and core collapses inwards suddenly becoming rigid
Outer layers fall inwards and rebound off core launching into space in shockwave
As shockwave passes through surrounding material, elements heavier than iron fused and flung into space
Remaining core depends on mass of star
Rapidly increasing absolute magnitude
Defining feature
Release $10^{44}$ J of energy
equals energy the sun outputs in 10 billion year lifetime
Collapse of red supergiants in supernova causes gamma ray bursts
Can fuse elements upto iron
Neutron star
For a star 1.4 < m < 3 solar mass
When the core of a large star collapses gravity is so strong that it forces protons and electrons together to form neutrons
Incredibly dense
$10^{17}kgm^{-3}$
Density of nuclear matter
Pulsars = spinning neutron stars that emit beams of radiation from the magnetic poles as they spin
Up to 600 times per second
Blackhole
For a star > 3 solar mass
When the core of a giant star collapses the neutrons are unable to withstand gravity forcing them together
The gravitational pull of a black hole is so strong that light cannot escape
Event horizon = point at which escape velocity is greater than the speed of light
Schwarzchild radius = radius of the event horizon
Schwarzchild radius
Radius of event horizon
Inside the boundary the escape velocity from the black hole is fgreater than the speed of light
Nothing can escape
$\frac{1}{2}mv^2\ge\frac{GMm}{r}$
$\frac{1}{2}mv^2=$ $\frac{GMm}{R_s}$
$\frac{1}{2}c^2=$ $\frac{GM}{R_s}$
$R_s=$ $\frac{2GM}{c^2}$
Types of supernovae
Type 1 = when a star accumulates matter from its companion star in a binary system and explodes after reaching a critical mass
Type 2 = death of a high-mass star after it runs out of fuel
All types occur at the same critical mass
Have a similar peak absolute magnitude (-19.3)
Produce consistent light curves
Used as standard candles to calculate distances to far-off galaxies
Can be seen up to 1Gpc away
Type 1a supernovae
Type 1 supernova with a white dwarf
When a companion star in a binary system runs out of hydrogen, it expands allowing the white dwarf to accumulate its mass
When a white dwarf reaches critical mass fusion begins and becomes unstoppable
The white dwarf explodes in a supernova
Supermassive black holes
Believed to be at the centre of every galaxy
Stars and gas near the centre of galaxies appear to be orbiting very quickly
Concluded there must be a supermassive object at the centre with a very strong gravitational field attracting them
Formed from:
Collapse of massive gas clouds while the galaxy was forming
Normal black holes accumulated huge amounts of matter over millions of years
Several normal black holes merging together
Accelerating universe
If the expansion of the universe was decelerating more distant objects would be observed to be receding faster as expansion was faster in the past
Light from more distant objects would take longer to reach earth so would appear to be in the past
Objects would appear brighter than predicted as they would be closer than expected
Type 1a supernovae have been seen as dimmer than expected
More distant than hubble’s law predicted
Suggests expansion of the universe is accelerating and is older than hubble’s law estimates
Dark matter
Dark energy is thought to be the reason behind universe acceleration
Described as having an overall repulsive effect throughout the whole unviers
Gravity follows the inverse square law ao it decreases with distance
Dark energy remains constant so has a greater effect than gravity
Causes expansion to accelerate
Controversial because there is evidence for existence but no one knows what it is oe what is causing it