Astrophysics Flashcards
What is the luminosity of a star
The total energy emitted per second
Sun abt 4e26
Apparent magnitude m
depends on luminosity and distance from Earth.
Magnitude 1 star has 100x intensity of magnitude 6 star, so a 1m was 2.51x brighter than 2m
brightest objects in the sky have negative apparent magnitudes
I2/I1 = 2.51^(m1-m2)
Hipparchus scale
Brightest stars given apparent magnitude of 1, while dimmest given apparent magnitude of 6.
Considering visible radiation emitted by object - visible luminosity - important when using optical telescopes
Parallax
Imagine ur moving - stationary objects in the foreground seem to move faster/more than objects further away. Apparent change in position is parallax. Greater the angle of parallax, closer the object is
Definition of parsec
1 Parsec is distance at which 1AU subtends an angle of 1 arcsecond
remember arcsecond is angular separation/2
What is the astronomical unit (AU)
What is a light year
The average distance from the Earth to the sun, Earth’s orbit is an ellipse
Light year - distance light (EM radiation) travels in a vacuum in one Earth year
Distance in light years tells you how long ago light left object
Defining parallax angle
Consider Earth orbiting sun. There’s a star far away enough such that its relative motion is negligible (stays stationary).
Draw right angle triangle where distance from earth to star forms hyp, radius of Earth’s orbit forms opposite. In 6 months, the Earth would have moved relative to the star, and would have swept out an angle of 2x the parallax angle.
parallax is the apparent shift of position of any nearby star against the background of distant stars- distant stars have virtually fixed position
Greater angle of parallax, closer body is
Defining parsec in terms of AU and arcseconds
1 parsec is the distance at which 1AU subtends an angle of 1 arcsecond
parsec is between sun n star
What is absolute magnitude
+eq
The apparent magnitude that an object would have if it was viewed from 10 parsecs away
m-M=5log(d/10)
doesnt depend on distance from earth
What is a standard candle
An astronomical object with a known absolute magnitude - can directly calculate luminosity
e.g. type 1a supernovae
Definition of a perfect black body
+ stuff + peak wavelength eq
A body that can absorb and emit all wavelengths of electromagnetic radiation
Black body since they don’t reflect
Graph of intensity vs wavelength varies with temperature - higher temperature, higher peak intensity at a lower wavelength, also less broad of a peak. Higher temp causes intensity to increase at every wavelength, however not an equal increase, shorter wavelengths have greater increases
λT = k where k = 2.9e-3 metre kelvins
as energy decreases becomes more red, as energy increases becomes more violet
Stefan’s law + intensity
Power output/Luminosity of a star is related to surface area and T by
P=σAT^4 where A = 4π r^2
I = P/4πd^2 inverse sq law (d is distance between Earth and star)
Assuming star is a perfect sphere
radiation spreads out and becomes “diluted” so intensity decreases
Wien’s displacement law
λmaxT = k where k = 2.9e-3 metre kelvins where λmax is the peak wavelength of a black body curve
and T is the abs temp of the outer layer (photosphere)/surface
KELVIN KELVIN KELVIN
Useless things that might be useful
There’s almost a million million stars in the milky way
light from sun takes 500s
Observable universe - region we can observe via em radiation (observed temporal edge but not spatial)
arc minute and arc second
arc minute = 1/60 a degree
ac second = 1/3600 a degree
Why would very small parallax angles be hard to measure
Smearing effect of Earth’s atmosphere - limits Earth based telescope
Method used to measure distances greater than 300 parsecs
Standard candles
Relating D, radius of Earth’s orbit and angle of parallax
D=1/theta
D in parsecs
Theta in arcSECONDS
Calculating angle subtended as viewed from Earth
Calculate normal angle subtended then x 2 since accounting for motion
Brightness is
A subjective scale of measurement
Stars are bright since they emit EM radiation
Intensity is
Effective brightness of a star, follows inverse sq law wrt star (Assuming star gives out equal amount of energy in each direction)
Luminosity vs intensity
Luminosity - power output, intensity - apparent brightness
Reasons why brightness is subjective
Air pollution, atmospheric distortion and human interpretation
Remember for apparent magnitude scale
Vega set as 0 point w m=0. However all shtick is only true for visible light, different stars have different apparent magnitudes for different parts of em spectrum
1 Parsec
= 3.26 Light years
Examples of black bodies
Stars, Stoves, furnaces, warm blooded animals
Magnitudes and power
Two stars w the same absolute magnitude have the same power output - relate w Stefan’s law
Ax:Ay = Ty:Tx = (dx/dy)^2
Assumptions when analysing stars
Assuming star is p black body, no light is absorbed/scattered by material between star and observer.
ALSO NOTE a hotter star might not appear brighter than a cooler one as it may not emit as much visible EM radiation - important to use optical and non optical telescopes
Significance of emission and absorption spectrum
Unique for each element, can therefore be used to identify elements when unsure of contents of a substance
Each line in emission spectrum due to a photon of specific energy hf. Absorption line due to absorption
Excite sample, let sample de excite and record emission, compare w known elements. Doesn’t matter where sample is excited spectrum always the same
Can also observe redshift/blueshift
For hydrogen absorption line to occur in visible part of spectrum
Electron must be in n=2 state
Visible absorption lines caused by electrons moving from higher energy level to n=2 state
Why hydrogen atoms in n=1 state can’t absorb visible photons
Visible photons don’t have sufficient energy to cause excitation from n=1
Balmer series
Series of lines corresponding to wavelengths of visible part of hydrogen’s absorption spectrum
SPECIFICALLY seen when light from a star has been absorbed by hydrogen in atmosphere while passing through
For this to occur, electrons in H atom have to exist in n=2 state, happens at hot temperatures, where collisions between atoms give electrons more energy. If energy is too high, some electrons may reach n=3, which would result in fewer Balmer transitions. So INTENSITY of Balmer line depends on temperature
Also balmer lines only give info of surface properties, not core (core doesn’t contain electrons)
What causes absorption lines in spectrum from star
Due to “corona”/atmosphere of hot gases surrounding the star above photosphere, Photosphere emits continuous spectrum. Atoms/ions/molecules in hot gases absorb photons of diff wavelengths
How many temperatures possible for a given intensity of Balmer lines
2 due to nature of graph - curve up then peak then down. To combat use absorption lines of other atoms/molecules
Stellar class system from hottest to coldest
OBAFGKM
Spectral class O
Blue
Between 25,000 - 50000 K
He+ion,He and H
(most atoms in n=3)
Class B
Blue
between 11,000-25,000 K
He,H (balmer)
Class A
Blue-white
between 7,500-11000 K
Strong H, ionised metals
Many atoms in n=2
Class F
White
6000-7500 K
Ionised metals
Class G
Yellow white
5,000-6,000 K
Ionised metals, neutral atoms (metals)
Class K
Orange
3,500 - 5,000 K
Neutral atoms
Class M
Red
<3,500 K
neutral atoms, TiO
Star is cool enough to form molecules
Red giants have lowest surface temperature, bc their intensity of emission is so low as their surface area is so high
Explaining intensity of Balmer line for each spectral class
O - weak
B - slightly stronger - stars are too hot so more atoms likely to be ionised
A - strongest - perfect temperature for n=2
F - weak - too cool for n=2 excited state
GKM - very weak/none - too cool to excite. + very little atomic hydrogen
Dwarf star
Star much smaller in diameter than sun
Giant star
Star much larger in diameter than sun
Two stars w same surface T but unequal absolute magnitudes
One with greater power output has larger surface area - larger diameter
Two stars w same M but unequal surface temperatures
Hotter star has smaller surface area - smaller d kek
Plotting axes for H diagram
Y axis absolute magnitude
-15 at top, 10 at bottom
X axis surface temperature
50,000 K at origin, 2500 at other end
(very hot lhs very cool rhs)
Scale is non linear
can also be classes on x axis
Also HR diagram significant as it tells us there are fundamentally different types of stars -allowed discovery of life cycle of star
Each quadrant in HR diagram
Top left - bright and hot
bottom left - dim and hot
Top right - cool and bright
Bottom right - cool and dim
Groups on HR diagram
Giants in M0
Supergiants around top right from B at M=-10
White dwarfs at 10<M<15 around bottom left corner
Main sequence form approximately diagonal from O-10 to M15
SUN IS AT G5
VEGA - approx A0
BETELGEUSE - approx M-5
Approximated that all stars have same power output
At top of main sequence are hot and luminous blue, bottom are cool and dim reds
Why is more energy required to fuse larger elements together
Larger nuclei have more protons so greater electrostatic repulsion - greater force required over distance
Fusion of heavier elements occurs in the core - requires a larger gravitational pressure as nuclei have more protons, opp for lighter elements.
Formation of star up till Main sequence
Dust and gas clouds in space contract under gravity becoming denser, forming a PROTOSTAR
In collapse, GPE converted to thermal as gas atoms gain Ek, interior of collapsing matter becomes hotter.
If enough matter’s there, temperature becomes high enough for nuclear fusion to occur
(If there’s not enough star doesn’t heat up enough and eventually cools when it stops contracting
Energy released from fusing H to He increases core temperature. Outer layer of protostar becomes hot and light emitting layer (photosphere) formed - now a star.
New star reaches internal equilibrium as inward gravitational force = outward radiation pressure. Star stable with constant luminosity. M depends on its mass, greater mass greater M - luminosity. Remains in main sequence for most lifetime. Emitting light due to H burning in core.
Sphere is the most stable shape in the universe
During main sequence, when fusing H, mass before>mass afterwards, energy lost to radiation
Fusion pressure from fusion products acts outwards
Larger stars need greater rate of fusion, spend less time on the main sequence
Red giant phase
Most H in core converted to He, fusion pressure decreases, core contracts, increasing temperature of core - makes star hot enough to carry out fusion of He and other elements - star increases in size as fusion pressure»gravity(larger fragments pushing outwards). Red giants fuse elements larger than H
Temperature is lower than main sequence as even though there is greater energy, there is greater area so more spread out + Stefan’s law maintaining constant power output.
Wavelength at at peak intensity increases
Red giant phase about 1/5 lifetime
Core vs Shell burning
Core - fusion in inner layer
Shell - fusion in outer layer
In red giant phase, core burning heats up outer layer allowing shell burning
White dwarf phase`
When nuclear fusion in core ceases, star cools and core contracts, ejecting outer layer which form new planetary nebulae
Mass between 4 and 8 solar masses, core heats up enough to cause energy release via fusion forming nuclei as heavy as iron. Stops when all fuel (light nuclei) is used up
After ejecting layer, star is a little bit more than core, which is white due to release of GPE. If mass is under 1.4 solar masses contraction of core stops as electrons in core can’t be forced any closer (as they must exist in shells). Star now stable and is a white dwarf - cools as it radiates thermal energy into space and eventually becomes invisible. If mass greater than 1.4 solar masses, explodes in supernova
electrons repel each other as they must exist in shells - stops atoms from contracting further. Repulsive electron force = gravitational force
White dwarf is core of carbon
must have high T according to Stefan’s law
When does fusion cease
When star runs out of fuel (light nuclei) or iron formed - more stable than other nuclei so can’t be fused to be made more stable
energetically unfavourable - highest binding energy per nucleon
Red supergiants
Occur above 8 solar masses, red giant swells into supergiant which explodes in supernova. Can fuse up to iron. Unopposed gravitational force causes star to implode into core, increases pressure and temperature causing supernova - enough energy to fuse iron + releasing elements formed in giant phase forming new nebula
Energy output of a supernova
10^44 joules
Characteristics of supernova
Rapid increase in M (between -15 and -20). Increase in luminosity occurs in abt 24 hours, then gradual decrease over time scale in order of years
Increase in luminosity usually corresponds to change of abt 20 magnitudes
Can cause intense outflow of neutrinos and gamma photons
Light curve shows sharp initial peak then gradual decrease
M on y axis days on x
Type 1a supernovae
All undergo same light curve. Show strong absorption line due to silicon. Peak luminosity abt 10^9 times the sun then decrease. (Thought to occur when white dwarf in binary system attracts matter from companion star)
Reach a KNOWN peak luminosity, known as standard candles
Peak is -20
Type I supernovae
Have no strong hydrogen lines present and divided into 1a 1b and 1c
Death of a high mass star
Core mass greater than 1.4 solar masses, electrons in core can no longer prevent further collapse as they are forced to react w protons to form neutrons. p+e—n+v
Sudden collapse makes core denser until neutrons can’t be forced any closer - core density abt same as atomic nuclei. Suddenly becomes rigid, and matter surrounding the core hits it and rebounds as a shock wave, propelling the surrounding matter outwards into space in an explosion. Releases so much energy it may outshine host galaxy. Enough energy to form elements heavier than iron
Also causes outflow of neutrinos + gamma neutrons
Neutron stars
Core of a supernova after surrounding mater has been expelled - small compared to the Sun.
Same density of nucleus - virtually no space between - neutrons can’t be completely compressed as strong force is repulsive at 0.5fm
Produced in supernova - cons of momentum may cause it to rotate
very quick - emits radio waves in narrow beams due to charged particles spiralling in intense mg field around poles of star. Mg and rotational axis are different. Radio waves sweep past Earth like lighthouse
Diameter abt 20km, very large gravitational field, high escape velocity. Form as neutrons are the most stable particle in a large system
What would happen is a GRB occurred close to the Earth
Would destroy ozone layer - mass extinction
Pulsars
Pulsating neutron stars emitting beams of radio radiation
Black holes
If core of neutron star becomes so dense that not even light can escape - black hole, can’t continue to absorb mass from its surroundings. Doesn’t emit photons, absorbs all incident photons. Event horizon is sphere surrounding black hole from which nothing can escape.
Attracts and traps surrounding matter, drawn towards a singularity at centre. May be charged, may be rotating, any property carried by in falling matter is lost. Information lost
Calculating Schwarzchild radius
R=2GM/c^2
Distance between event horizon and singularity
Also defined as the distance at which escape velocity = speed of light
Supermassive black holes
Thought to exist at centres of many galaxies. As at centres, stars are much closer together than they are at the edges. Supermassive black holes can pull in millions of stars, can therefore gain enormous amounts of matter
Gamma ray bursts
Short lived - 0.01 to 1s from black holes, due to merger of neutron stars or neutron star falling into one
Long lived - 10s to 1000s from collapse of massive star in supernova
total energy from typical GRB about the same as total energy of sun over entire lifetime
Doppler effect caveat
Observational effect - no change in actual properties of wave, only observed wave
Doppler effect example
Ambulance moving towards you, wavelength decreases f increases
Moving away opposite
Doppler effect
When wavelength/frequency of a wave is altered by relative motion between source and observer - can be experienced by any wave
Red shift
Doppler effect with light
How to determine if a star is red/blueshifting
Compare spectral lines to known spectrum. Can be done as spectral lines for element are the same regardless of motion, location,temperature or anything
Eq for amount of redshift Z
Z = Δλ/λ Δf/f or v/c
only works when v«<c
CONSIDERED TO BE ABSOLUTE CHANGE IN WAVELENGTH, BUT APPROXIMATE CHANGE IN FREQUENCY DUE TO RELATIVISTIC EFFECTS
positive z means redshift, negative means blue
Can also give time light takes to reach us. Z=0 present
Cosmological redshift
Detected from all distant galaxies except andromeda. Proof of expansion of universe + hot big bang model
Not andromeda as it’s gravitationally bound to milky way
Stellar redshift
Detected from nearby stars, pairs of stars called binary stars, allowing to determine properties
Binary star system
Two stars orbiting a common centre of mass
Light curve for eclipsing binary
M on y, time on x
highest luminosity when both are visible, higher dip when hotter is in front of cooler, lower dip when cooler is in front of hotter
Graph of changing wavelength for one star in binary
Sinusoidal - peak when star is receding with max radial/recessional velocity
(two stars next to each other)
Redshift to determine rotational motion
Consider a rotating star, part moving towards us blueshifted, part moving away redshifted
Evidence for HBB model
CMBR + abundance of H and He
Hubble’s Law
Recessional velocity of a distant galaxy is proportional to its distance from Earth
v=Hd v is recessional velocity, H Hubble’s constant, D distance from Earth
also as graph is a straight line, assumes that rate of expansion is constant - now thought not to be true
H = 65Km/s per Mpc
Kilos per second per Megaparsec
Controversy around H
I shld assume H is constant, however astronomers disagree on value since value has changed over last 60 years
Cosmological redshift
Space in between galaxies expanding, effect is that both galaxies observe the other to be moving away
Greater space in between them, greater rate of expansion
Calculating age of universe with H
v=Hd T=d/v = 1/m
Convert H from Km/s to m/s and d from Mpc to m
Assumed universe has expanded constantly, believed not to be true
Also H not assumed to be constant, which leads to an overestimate of age of universe. As we think expansion has been increasing
Dark energy
Unknown form of energy theorised to be responsible for increasing expansion of universe
Why aren’t the solar system or milky way expanding
Due to gravitational forces of sun/planets/stars opposing expansion
Also it’s possible for a galaxy to be receding from us so fast that their light never reaches us. c>v
Observable universe
Part of universe in which we can detect objects via em radiation
Radius of observable universe
Maximum distance that light can travel in age of universe
diameter about 46billion light years, however age only 13.7billion years. This is because the expansion of the universe increasing the size of the observable universe.
Big bang model
Universe had a beginning
Started off very hot and dense and has been expanding ever since. All matter was created at the start, and matter density of universe has been decreasing over time
at start all matter concentrated into size smaller than an atom
CMBR as evidence for HBB
HBB predicts that lots of EM radiation produced in early stages of universe, which should still be observable today - As wavelengths have been stretched out this cosmic background radiation is in microwave region.
radiation is largely isotropic and homogeneous, which confirms the cosmological principle (same in all directions)
The background radiation also shows a Doppler shift
There are very tiny fluctuations in temperature,due to
tiny energy-density variations in the early universe, and are needed for the initial ‘seeding’ of galaxy formation.
Amount of He as evidence for HBB theory
The early universe had been very hot, so at some point it must have been hot enough for hydrogen
fusion to happen. By studying how much helium there is compared to hydrogen, we can
work out a time frame for this fusion. Together with the theory of the synthesis of the heavier
elements in stars, the relative abundances of all of the elements can be accounted for
Universe is 74% H and 24%He
Cosmological principle
Universe is homogenous (every part looks like the other part), and isotropic (the same in all directions) so it doesn’t have a centre
Quasars
Most distant measurable objects
Powerful galactic nucleus containing a supermassive active black hole (taking in matter around it) at the centre of a galaxy. Black hole surrounded by mass of whirling gas which produces the
light in the same way as a pulsar, magnetic fields produce jets of radiation streaming out from poles
As matter accelerated towards blackhole, causes gamma rays to be emitted
Detecting Quasars
Shot out jets of material, and were active radio sources (also show large optical redshift)
produced a continuous spectrum that was nothing like a black body radiation curve and instead
of absorption lines, there were emission lines of elements that astronomers had not seen before. But ended up being the Balmer series redshifted crazily
Exoplanets
Planets not in the solar system
Orbiting stars other than them much brighter than them so outshone. Too small to distinguish from nearby stars (angular separation between planet and star smaller than min, if not then too far away so dim)
helps if planet orbits a brown dwarf
Only a few rlly large and hot ones, far away from stars can be seen using special telescopes
Detecting exoplanets using Doppler shift
Planet and star orbit common centre of mass. As star>planet com is close to star, causes tiny variations in star’s orbit.
Causes very small red/blueshifts which can be detected and hint at exoplanet. Minimum mass of exoplanet can also be calculated.
movement
needs to be aligned with the observer’s line of sight — if the planet orbits
the star perpendicular to the line of sight then there won’t be any
detectable shift in the light from the star
Also exoplanet mass needs to be close to that of star
Detecting exoplanets using transit method
As the exoplanet crosses in front of the star, some of
the light from the star is blocked from Earth’s view.This leads to a dip in the light curve observed on Earth. From this, the radius of the exoplanet can be found.
Chances of the planet’s path being perfectly lined up so that it crosses the line of sight between the
star and the Earth is incredibly low.
This means you can only confirm observed exoplanets,
not rule out the locations of any.
Also need periodic dips to confirm existence of exoplanet, as dips can be caused by other things e.g. sun spots. Also period may be so long
Comological redshift as proof of big bang
Due to space between galaxies expanding
Extrapolating backwards, mechanism is the big bang
Production of all matter and energy produced expansion force
Why is space not at absolute 0
Heated by CMBR, which will eventually become cosmic radio wave background radiation due to expansion.
CMBR started off as gamma at beginning
