Chapter20 Flashcards
Why do we use different units of measurement for cosmology?
Bevause the distances are so far using it in standard form is pointless, and hard to compare
So what are the three distances?
1) the AU
- average distance from earth tk the sun
2) light hear
- distance covered by speed of light in one earth year
3) the PARSEC
Before defining the parsec, we must define the angles arcsecond and arc minutes!
In 1° there is 60 arc minutes
In 1 arc minute there is 60 arc seconds
Thus in 1\3600 degrees = 1 arc second
We use these as the angles measured are sooo small
So whats the definition of a parsec?
A parsec is the distance at which an angle of 1 arcsecond subtends a distance ( radius) 1 AU
This forms a triangle , with oppsite being AU, adjacent being parsec and angle being 1 arc second
As arcsecond is so small, what expression can we make
Therefore what can we say for the angles needed to subtend 1 AU at DIFFERENT parsecs?
Use small angle approximation
Therefore tan 1m arcsecond = roughly 1 AU/ 1 Parsec
So if we double distance away (from sun), and stil, want to subtended 1 AU, the only way this works is if the angle becomes 1/2 too (1/2 = 1/2)
Therefore theta is inversely proprtinsl to distance in parsecs! As an approximation
So what’s the formula relating theta and parsec distance ti subtend a radius of 1 au , and how
Theta inversely prop to parsec distance
Due to small angle approx. Derived from definition of parsec …
What is the stellar parallax technique used ti find?
What is stellar parallax
The distances of relatively close stars to earth , less than 100 pc
It is the APPARENT shift in positon kf a star against a FAR AWAY BACKDROP when observed fro, different places in the earths orbit
Explain how the stellar parallax works
So when we are in postion A, looking at a star we see it in a specific place relative to the backdrop
Come back to this on its OPPSITE point of orbit, we saw the star shifted to a new place relative to its back drop
In reality the star hadn’t moved at all, it’s just an illusion due ti the ANGLE WE SEE IT AT
This angle is the PARALLAX ANGLE
As the distance is always 1 AU from the sun from both OPPSITE points of orbit, if thr angle is in arc seconds then we know the distance to the sun measured in par secs is = 1 / angle !
So if we know thr paralled angle, we can roughly work out how far away
Why is the stellar parallax only used for stars less than 100pc away? Why not any more
Because the father awya you go, the less the stellar parallax is , and thus the harder it is to calculate the parallax angle
In fact it becomes impossible with current level of resolution of equipmemt on earth so far , thus we can’t
Stellar parallax summary
Used to find the distance of a nearby star to thr sun using the illusion of the apparent shift in postion of the star relative to a fixed background drop
Take two points of oppsite orbit on the earth and see the parallax angle. As the distance being subtended by this angle is 1 AU, we can use d = 1/p to find how far it is
But must be in parsecs and arcsecond, don’t lack
Parallax angle definition
This is the angle which subtends a raidus 1 au ar a certain distance away in parsecs from the sun
What is the Doppler effect
The apparent shifts in frequency / wavelength due to the relative motion between the object and the observer
Where the change in freuwney is prop to the velocity of thr object
Explain Doppler shift
As something moves further away, due to the wavelengths being more spread out from each other, the apparent wavkefnth observed at the observer is much bigger than what it was before, thus frewuency less too
As something moves closer to you, the wbakengghd catch up with each other, making the apparent wbskenght less and thus the freuwneyc increase
This effect is observed for any wave, so light as well as sound
In the context of planets?
If a planet is moving awya from us, the frequencies will be less, as a result all th spectral lines for absorption will be shifted to the red side = red shift
If comes to us then blue shift
As most of them are red shift, we can conclude in general u inverse is expanding
If you found the shifted frequency of one, how to find the shifted wl bery esislyl
Use speed of light
When doing Doppler shift for sound, or ultrasound or whatever what is the equation changed
Need to use speed of thing, so sound, ultrasound etc
That’d why when I run fast as I can I don’t become red, I do but very slightly because of speed of light fsctor
But when sound moved away we do hear it become low frequency because the speed of the object is comparable to the speed of sound .
IMPORTSNT POINT
Why within a spectral line, will the indicual lines not be the EXACT same shift?
What is the same ?
As the equation shows the change in wavelength is prop to wavlength and speed
If speed is the same fro each wavelength, then the change is only proprtinsl to its CURRENT WAVELENGTH
Therefore the absolute shifts are different but percentage is the same, with ratio v/c constsnt!
Thus if something red shifts, the red ones will red shift THE MOST and the blue ones thr lesdt
But in this case the PERCENAGGE SHIFT is the same for each one, as it must be
This is why you can’t straight compare the distances first, need to reverse the shift and then compare
If further away stars have a more red shift, what does this mean fully
This means Fully that rhe stars are travelling faster (not to do with further away) as change in wavelength is proptinal to speed
As a result, if the further away stars are travelling faster than closer ones
- this means universe expanding at an ACCELERATING RATE
What were the conclusions bubble made
1) that light coming from most GALAXIES (nit stars because too close ) confirmed were red shifted
2) that the further away thr galaxy was, the MORE red shifted (and thus faster speed ) it was travelling at
What was thus HUBBLES law
After plotting receding speeds of many galaxies against distance away from earth , the trend seemed to show linear
Therefore v is prop to d
So the receding speed of a galaxy was roughly propritnsk to the distance away from earth
What is HUBBLES constsnt , why is the value not well defined
Plotting on groan showed the trend was DEFINITELY LINEAR, however the gradient was hard as the uncertainty quite big
The HUBBLES constsnt is just the gradient
What units do some astronomers like
They like km per MPC so might have ti convert, to give you s-1 especially when trying to find the age of thr universe
What does the fact further away galaxies are more red shifted mean
That they are travlling at a higher speed away, thus the universe is expanding at an ACCELERATIMG RATE,
Here it’s the space between universe that expands
What is the cosmological principle
Basically means the same everywhere
- the laws of physics are valid in all parts of the universe , any model on earth will work with sake physics over all of space time
- isotropic ( means that there is no edge or centre to the universe , and looks the same in all directions by any observer )
- homogenous (means that the density of the universe is uniform, matter is distributed evenly across universe and we see the same structures everywhere )
Again
- isotopic means to every observer in all directions the universe looks the same, no centre or edge
- homogenous means the density of the universe is uniform, mater is distributed even,y across u inverse and same structured found everywhere
- laws of physics work everywhere
Why having these assumptions can mean we are very off some prediction?
Can never know for a fact if the lhysics are the same in every part of the universe, so whatever science says might not be the
Why does bubbles law breakdown for galaxies close and very very far from us?
1) galaxies close to us could be attracted to us by gravitation pull so these actually show a blue shift, and hence don’t follow HUBBLES law. Only very immediate gs,sides are like this but k really we are expanding
2) galaxies very far have accelerated too much so have escaped the proprtinsl trend, it’s possible the trend changes too
If Doppler shift spectral line and this shows a blue and red shift happened at the same time what does this show
It’d a BINARY STAR SYSTREM
One star is coming closer to us and thus blue shift, other star will be moving away so red shift
So light will show both at same time this can only be explained by binary star
Remember binary star system the periods of roatiaon no matter mass is the same, and the centripetal force aimed at centre of mass but bravtwiknsk at centre of each planet
Big Bang
What are the two pieces of evidence that is used to prove the Big Bang?
1) HUBBLES law
2) CMBR with the TEMPERTAURE of the universe assuming it’s a black body emitter
How does HUBBLES law suggest Big Bang to be true
HUBBLES law suggests universe is expanding from each other at an accelrwtion way, such that if we turned back time thr univerde would be concentrated into one point, which is what the big bangs suggests
What is the big bangs theory
It’d thst the universe was a small dense and hot point which expanded and over time became what we are today
Why couldn’t HUBBLES law be conclusive evidence for Big Bang alone?
Other theories could explain HUBBLES law too, meaning Big Bang wasn’t necessarily true
So another piece of evidence was needed
Why did Big Bang predict CMBR ?
Big Bang stated that when universe was young unjverde was saturated with high energy gamma photons .
Expansion of space meant these gamma photons over time was stretched in wbakenght to become microwaves, which we find today
- this means they would’ve been stretched through visible light too and now at microwaves
- the stretch itself is both the stretch and a sort of red shift
However what else backs that CMBR makes sense
If model the universe as a black body emitter, we can measure the background TEMPERTAURE and correspond thst to a peak wavelength using wiens constsnt
This gives you order microwave radiation , which checks out with CMBR
How does CMBR thus prove big biang
As only Big Bang could prove CMBR , which is backed up by TEMPERTAURE, and that as the universe cooled down the wbakenggh would’ve increased, this means Big Bang was true
The only theory that could prove both HUBBLES law and CMBR
How to estimate the age of thr universe
What assumption
If we assume that the expansion of the universe happened at a CONSTSNT SPEED ( which It didn’t because it’s accelerating) (this makes it a very crude assumption , but atleast its 14 billion years )
Then time = d/ V
And this = 1 /H0 in s-1
Which gives 14 billion years
Big Bang theory summarised
Everything was fine treated in an infinty hot and dense singularity , which after the bug bangs space time expanded and what came after is what we are today
Some key points of evolution about the Big Bang
1s , 380k
1) after 1s all the matter created in the universe stopped
2) 380k years the first atoms are made as the universe is cool enough . At this point it’s cold enough for CMBR to be present
3) 14 billion hears the humans eveokve
How is thr mass made
First the fundamental lerticles, leptons And quarks are made and they Gain mass
Then hadrons are made
Then nuclei, then nuclei capture electrins and become atoms
What is dark energy and what is it an explanation for?
Dark energy is an explanation for the accelerating universe, says that the accelrwtion needs some source of energy, which CANT BE DETECTED, and thus must be dark energy then
Features of dark energy!
Dark energy permeates throughout all of space, and is the reason why universe addelrwtedn
Acts as the fuel
In a general galaxy, where most of thr mass is concentrated in the centre, what would you expect the velocity to do as distance from centre increases?
As it increases, would expect the velocity to decrease using Kepler third law thing
So what do we expect the velocities ti be if every galaxy as distance from centre increases, and why?
However Whars happenign and why?
We expect it to decrease, as we observe same effect for smaller mass systems like solar system and Jupiter and moons
However for entire GALAXIES, the effect observed is different
Why is the effect not observed in entire galaxies?
Becaus we assume that all mass is concentrated in the centre, if it was it would work
Therefore all the mass IS NOT CONCENTRATED AT THE CENTRE
Therefore if the mass of a galaxy is nkt cintrrsted in the centre, what and where is ti?
This is DARK matter
As the velocity of the planters / stars doesn’t decrease the fur here away from the galaxy it is, there must be another type of matter that we CANT SEE THATS MAKING THE SPEEDS HIGHER
this is dark matter
So what is dark matter and it’s prorptied
Is matter that’s present in galaxies, and thought to be conetrsted at extremities which allows the stars furthered away to still rotate at same speed as the ones closest to the centre
- does not emit or absorb light
- does not interact with matter, thus is not antimatter
What does expected vs observed VELOCOTY for stars in galaxies away from the centr?
Expected is the VELOCOTY goes up as it’s close to centre, then goes down
Observed is it goes up, then stays up
Okay let’s summarise dark energy and dark matter then
1) dark energy is thought to be the energy that propels the universe into acceleration
2) dark matter is though ti be matter that is spread around the universe
- this is because if the galaxy followed systems where mass was concentrated in the centre, like solar system, then further away from centre with distance, you’d get less VELOCOTY of orbit ( y Kepler 3rd law)
- as this doesn’t acc happen and velocities are maintained there’s thought to be dark matter which we can’t see which is cinctrsted throughout universe that caused these the move fast.
- does not emit or absorb em radiator , interact with matter thud is not anti Matter either
Proper good explanation for CMBR microwaves and why they are here
When the universe was though to have been a dense concentrated area of high gamma photons, since then it’s expanded, where the universe cooled, and gamma photons have red shifted to become microwaves
