Cosmology | Lecture 3

[Music] this program is brought to you by Stanford University all right let's uh let's review a little bit the basic equations of cosmology and then I want to take you through a little tour of these equations and what they say about the structure of the universe and then perhaps we will get to the subject of dark matter I want to talk about dark matter a little bit also because most of the matter in the universe is dark so I will discuss that with you and I will explain to you in what way it is either mysterious or not mysterious depending on your taste all right oh we derived the Freedman robertson-walker LeMay tried on who else equation from energy conservation assuming that the universe was homogeneous incidentally in this course I never show these beautiful pictures of galaxies and everything else just because some I don't know how to run the projector up there among other things but I will draw for you the universe the way it would look in one of these gorgeous gorgeous pictures you just have to substitute black for white and white for black and then it looks like this but somehow it looks better when you invert the color and on a scale larger than the size of clusters of galaxies there are clusters of galaxies on scales larger than sizes of clusters or galaxies millions of like many millions of light years the many many millions of light years but not billions of light years smaller than billions of light years bigger than millions of light years the universe looks pretty homogeneous pretty smooth ok so assuming that it's good and smooth and concentrating on one galaxies doesn't really have to be a galaxy it could just be an imaginary particle moving along with the flow and thinking of ourselves as the center there's nothing important about where we are but just to get an orientation thinking of ourselves as the center of coordinates we studied the equations of energy conservation for this particle thought of as a Newtonian particle moving under the influence of gravity the gravity due to everything within a sphere centered on us and with radius equal to the distance of the sphere I'm just going to go through that again because it's really it's really simple if we choose let's put the part let's put the galaxies over here on the x axis and in fact let's put it at x equals 1 if it's at x equals 1 that means it's distance okay what is its distance then from us if it's a and we are of course x equals 0 its distance is then by definition the scale factor a that's the definition of the scale factor the distance at x equals 1 the distance at x equals 2 is 2a and so forth and so on so we could concentrate just on this galaxy by itself that's at the coordinate x equals 1 and we can study how it moves under the influence of everything else in there it has an energy its energy is first of all a kinetic energy of outward motion its kinetic energy of outward motion is 1/2 now its velocity squared its mass let's also let its mass be 1 let's let its mass be 1 unit then I don't have to keep writing masses which just cancel anyway 1/2 its mass times its velocity squared and what is its velocity squared if its distance is AE then its velocity squared is just a dot squared where that means time derivative that's that's its kinetic energy what about its potential energy its potential energy is minus the mass contained within here now what's the mass contained within here that's 4 PI over 3 times that's the volume of the sphere and no that's not the volume of the sphere yet we have to multiply it by a cubed that's the volume of the sphere we multiply that by the mass density and that's the mass of everything inside this shell 4/3 pi that's volume times a cubed times the density okay that's the mass in there but remember the gravitational potential energy is the mass times G divided by the distance well just distance so we have to put G in there the potential energy and then divide by the distance and the distance is just a what does Newton tell us Newton tells us that this is constant and independent of time so this is just some constant and I call that constant I think I call that constant minus K and making it minus K does not necessarily mean that it's negative K can either be positive or negative but I just called it K and that is the basic equation of cosmology to make it a little bit more familiar I don't know familiar I'm not familiar depending on your background first of all we can divide by a and make this a square here now we can divide the entire equation by a squared let's first multiply by two ah wait let's first multiply by two to get rid of the half here that makes this eight PI over three and I should have called this thing K only after multiplying by two the standard the standard notation would have this being minus K after I multiply by two but in any case it's constant so it doesn't matter whether I call it K or two K now I divide it by a squared and get a dot over a squared that's the square of the Hubble constant or the Hubble none constant let's shift this over to the right-hand side and that becomes 8 PI over 3G and I've divided by a squared so this a squared is no longer here times the mass density and then minus K divided by a squared the a squared I just divided both sides of the equation by a squared and this is the Freedman robertson-walker equation Freedman frw l and everybody else I'll tell you now although we will take us through next week next week we will discuss it in a little more detail the connection with Einstein's equations I'll just remind you that the Einstein equations in particular the time time component of the Einstein equations have the form of some tensor which is composed out of the curvature tensor what is it it's R 0 0 minus 1/2 G 0 0 times the curvature scalar is equal to what is equal to T naught naught whether with a constant in there which is related to there's also some eight pies and threes there's also some I can't remember the exact numbers but I think it has a PI over three and G in it but things of that nature the connection is simple with this equation if I transpose all the things without any energy density in them a dot over a squared plus K over a squared that's the left hand side of Einstein's equations if we plug in an expanding metric which we'll write down in greater detail next time if we plug it in and calculate the left-hand side what we get we get a dot over a squared plus K over a squared and the right hand side we just get the energy density Rho is of course the mass density but mass and energy are the same thing equals MC squared and so this equation really is nothing but the time time component of the Einstein equation I tell you that now just that for orientation sake that we have not abandoned Albert for Isaac but at this stage Isaac and Albert say the same thing so you might as well think about Newtonian mechanics to get a first orientation all right now next thing we did is we plugged in or we assumed a form for Rho for the mass density and I'll tell you from now on I'm going to call it the energy density the energy of a system at rest now why are we talking about a system at rest because our coordinates are moving with the material so the material in the coordinate frame that we're using is Everywhere's at rest relative to the coordinates and under those circumstances Rho is nothing but the mass density at rest or the energy density at rest all right so let's add let's take a little cube we take a cube which is one coordinate unit on the side that means it's length width and height are a the scale factor itself and prescribe how much mass is in there let's assume there was a mass m in there there's some value of mass in there and furthermore under the assumption of homogeneity on a large enough scale every cube of the same size has the same mass so let's just call it the mass M inside that cube then what is the density the density is M which is constant the energy in that cube it stays constant Evert the masses move but they don't go into or out of the box and so the amount of mass in there stays constant but the mass density is M divided by the volume which is a cubed and that's Rho so now we can write our frw equation as a dot over a squared Hubble constant squared is equal to 8 pi G over 3 and now M this constant M divided by a cubed this is not the mass of any specific object it's just a mess within this cube I call it M maybe I should have used another letter for it but it doesn't matter the mass in the unit cube minus K over a squared all right we decided last time and I'm going to continue for a time being imagining not imagining but using the empirical fact it is an empirical fact an observational fact that this constant K is very close to zero it's too close to zero to tell whether it's positive or negative I will tell you now it does correspond to the curvature of space but it's too small to be able to tell whether it's positive or negative and it's a very good approximation in cosmology just to ignore it and that's the simple equation which describes the expansion of the universe this is called the matter-dominated universe it's matter-dominated what that means is that this formula here corresponds to a situation where you have the energy in this box just in the form of particles at rest you count up all the masses in that box if the masses were moving with a tremendous velocity there would also be kinetic energy huge amounts of kinetic energy in the box and then we might say that we were talking about and if the kinetic energy was bigger than MC squared or bigger than just M if we set the speed of light equal to 1 that means that the particles are moving with very close to the speed of light then we would no longer say it was matter dominated when one speaks about matter dominated one is speaking about the mass distribution being made up of things which are essentially at rest moving with the flow so in that case young for the time being since these particles we can think of these particles and the particles are not moving we can for the moment just say the temperature zero and we can also say the pressure is zero if all the particles came to rest in this room the room got so cold that all the particles came to rest in the room relative to the coordinates of the room there would be no pressure pressure happens when there are particles crossing the boundaries of this box and it will see it is important we're going to come back to it but matter-dominated means the particles are at rest in the box moving together with the box as the Box flows along with the flow of galaxies then under those circumstances those are the circumstances where we should label this now matter-dominated there may be other forms of energy around so there may be other contributions but in our universe today well I was going to say I was going to say something false I was going to say our universe is matter-dominated it is actually not it is dominated by dark energy but we'll come to that in a while [Music] about all of the ordinary matter galaxies protons neutrons they all add up and this is the so called matter dominated universe the last time we solved the equations we solve the equations not by solving the equations but by guessing an answer standard honourable method to solve equations I said let's try a power law you might have tried something else you might have tried sine a cosine or hyperbolic newgy function or whatever but the but first thing I always try is a is a power law so we tried constant times time to a power we plugged it in what do we find we found first of all to match the two sides to match the two sides we had to choose P equal to two-thirds maybe I should go through that again very quickly if this is a a dot is CP T to the P minus one and a dot over a is equal to C's cancel out and we just get P over T Square it and we get P squared over T squared so the point is the left hand side is proportional to 1 over x squared the right hand side is proportional to 1 over time to the 3p a cubed goes like T to the 3p so we have to have T to the 3p being T squared that means that P has no choice but to be 2/3 so that tells us that the universe expands is the 2/3 power of the time it doesn't expand linearly a doesn't grow like time it grows like the 2/3 power of the time and we can also plug in and cat once we know that then we can plug back into the equation and compute C if we like C doesn't tell us very much it's just if you're doing the bookkeeping and you want to keep track of everything you want to keep track of everything and if you do you find that C cubed is equal the 6 pi M G it work it out this is the more interesting thing here that the universe expands is the 2/3 power of of time what does that look like if we were to plot it if we plot vertically the scale factor horizontally time then eight the two-thirds power looks something like this linear would just be a straight line this is not as strong as linear so it turns over like that okay that's the that's the matter dominated universe and it was the way the universe behaved for a rather long time that behaved this way from about a hundred thousand years in age that's pretty young the universe is ten billion years old from about a hundred thousand years in age to about a couple of billion years billion or two billion years or something like that it behaved according to this matter-dominated law now before that the universe's energy was dominated by something else it was dominated by radiation not by matter so let me explain why the universe today is filled with photons we detect those photons most of the photons are in the microwave range for the moment we're not going to discuss where they came from they are the remnants of the Big Bang but let's just take it as a observed fact that there are a large number of photons floating around in the microwave range and in fact roughly there are about 10 to the ninth photons for every atom or for every proton in the universe so the universe in terms of numbers just in terms of population is largely made of photons on the other hand the photons have very much less energy than the proton or even the electrons the protons have energy MC squared the photons have no mass but they do have energy they do have energy every photon has energy but let's talk about that energy a little bit it's deadly when one speaks about the photon having an energy MC squared we're talking about the rest energy how do we get away with saying the photon has no mass but it has an energy well we're not talking about the rest energy of the photon the photon has energy but it's moving if you try to slow it down to rest that we just disappear it would have nothing no mass no nothing so photons have energy and let's discuss the photons and why in the very early universe the universe was radiation-dominated that means dominated by the inner that means the energy density was mostly in the form of photons why that's true so let's begin with the formula for the energy of a photon again we can think of a box unit on the side it's filled up with photons now photons move that means photons can pass out through the box but on the average there are as many photons coming into the boxes out of a box and so the number of photons pretty much stays constant in the box but unlike the protons the energy of a photon depends on the size of the box so let's let's discuss that a little bit let's begin with the energy of a photon the energy of a photon standard symbol for photon is a gamma that doesn't mean it's a gamma ray gamma rays are just high-energy photons but gamma is the standard symbol for a photon the energy of a photon is equal the Planck's constant is terribly tiny constant 10 to the minus 30 or whatever it is times what times the frequency of the light that that that photon is composing let's call that new what are the units of new what over time what over time yes yes yes yes yes but this is yes certainly hurts hurts cycles per second cycles per second this is also H bar Omega but I'll just call it H nu now we have a wave going by us we have this we are necessarily because we're already we've already studied quantum mechanics and we're completely familiar with quantum mechanics completely comfortable with it we have no trouble jumping back and forth from wave to particle picture right good okay so associated with these photons is a wave and a wave moves with the speed of light C ah and if it was just an ordinary wave in this room moving past us with the speed of light it would have a wavelength lambda a wavelength lambda and the shorter the wavelength clearly the sugar clearly the biggest see you stand there with your nose watching or watching the wave you're watching the wave go past you and the electric field goes up and down up and down up and down and oscillates it oscillates for the frequency that frequency is nu it's quite clear the faster the speed of light is the larger the frequency the more cycles per second and the shorter the wavelength the larger the frequency so the frequency is equal to the speed of light divided by the wavelength so we can rewrite the photon energy as H times C over lambda the important thing here is the lambda in the denominator now what happens to a photon of a given wavelength as the universe expands and here is where we will make an assumption the assumption is very well justified by studying the dynamics of electromagnetic waves but here is the assumption that as the universe expands the photon wavelengths expand with it imagine for example a wave in a waveguide or in a box and that wave is the longest wavelength that you can have in that box it looks like that it has no nodes in other words it doesn't third doesn't oscillate this has one-half of an oscillation what happens is the Box grows as the Box grows the wavelength expands to match the box it will not jump to a wave with a node in our with our nodes in nodes mean places where it goes to zero won't do that it will just expand with a box as the universe expands it's like an expanding box and the wavelength of every photon gets stretched in proportion to the increased factor of the scale factor in other words the wavelength whatever the wavelength was if the scale factor doubles then the wavelength doubles the wavelength is proportional to the scale factor another way to say it well no that's good enough that's good enough every photon has a wavelength that is not frozen in time but grows linearly together with the scale factor that means since the wavelength is in the denominator and the wavelength is growing with a scale factor it means that the energy of the photons is decreasing as the scale factor grows and in particular the energy of any photon whatever its initial energy was it will scale like some constant divided by the scale factor as the scale factor increases the wavelength gets longer the energy decreases so we have this box of photons now there's a given number of photons in the box on the average it's true they pass in and pass out of the box but on the average is a given number of photons in the box every single photon is the Box expands its energy scales like 1 over a now that means that the total amount of energy in this box won't be a constant like m as it was when we just had nonrelativistic stationary particles there but it will scale like a constant divided by a now M here does not mean mass it's just a it's just a label it's just a parameter whatever the energy in the box as a expands the energy will decrease like a constant divided by a that's the energy per photon now how many photons are in the box let's suppose that there are in photons sorry this is I made a mistake let's just call this something over a constant of a that's perfect on but if every photon in the box has an energy that goes like 1 over a and the number of photons stays fixed that means the total energy in that box also scales like 1 over a II that's the point so the energy in this box energy in the box is some constant divided by a now what's the energy density in the box the energy density in the box you take the energy and divide it by the volume of the box so we divide by the volume and the volume is a cubed so that's another a cubed in the denominator and what we discover is the discovery that the energy of a box of photons as you expand the box goes like 1 over 8 to the 4th power instead of 1 over a cubed when all we had was particles at rest we said the total mass in the box was in we divided by the volume and we said the mass density was M over a cubed but for photons because each photons energy decreases as you expand the box it's 1 divided by 8 to the 4th okay so let's go back now now we have now imagine that the universe instead of being filled with protons neutrons electrons ordinary particles moving slowly let's imagine that the universe is filled with photons as I said photons pass through the box they come in and they go out but we'll assume that the number of photons in the box on the average as many come in as go out in that case we have to modify the equation which equation this one over here we have to modify it and instead of the right-hand side being M over a cubed it now becomes M divided by a to the fourth so this is now the radiation dominated universe [Music] it looks pretty similar a dot over a squared equals same thing 8 pi G over 3 and now the energy density which instead of being M over a cubed is a constant which I called M again different constant divided by a to the fourth it even has different units now well can we solve that equation yeah we can solve that equation we do it the same way let's plug in let's make a trial solution a equals C T to a P to the P again a dot over a is just P divided by T that's a dot over a peda vided by T we square it P squared over T squared that's the left side now let's go to the right side 8 pi G over 3m and now a to the fourth so now I'm going to have in the denominator C to the fourth that's not going to be very interesting but T to the 4 P 8 to the fourth is C to the fourth times T to the 4 P and now if I'm going to match both sides this one goes like 1 over T squared as time goes on this one goes like 1 over T to the 4 P for P had better equal to otherwise they can't match okay so for P a better equal to or P equals 1/2 so we've discovered that the radiation-dominated universe expands not like T to the 2/3 but like t to the 1/2 square root of T in other words this expand and we can also calculate the constant see I'll leave it to you to calculate the constant see it's not very interesting or I'll tell you whether C to the force is 32 PI over 3 times GM that was not very illuminating to me either but the fact that the universe expands like T to the one-half power instead of T to the 2/3 is somewhat interesting ok yeah there's always a G in this is yeah this is the gravitating effect of energy remember in Newton's theory yeah ok good it's a good question we discussed it last time but let me come back to it not last time let's quarter Newton's theory is the theory of things moving very slowly compared to the speed of light the dominant form of energy when things move was closed so it's slow compared to the speed of light is just the mass the M c-squared energy that's you may think of M as being simply the energy plus a little bit of kinetic energy may be there all right when things move near the speed of light then the energy is not proportional to the mass it's more complicated for example photons which have no mass do have energy but the right hand side or the thing which gravitates the thing which pulls the thing which causes gravity is not rest mass it is energy when the object is slow then its energy and its mass are the same a rapidly moving photon will gravitate will cause will cause things to be pulled toward it another example here's an example take a box and fill it with lots and lots of radiation radiation so so much radiation that it would melt the walls of the box but let's walls that won't get melted in our imagination and we fill this box with a huge amount of radiation that box will gravitate more than the box without the radiation in it it will have more energy Eve if the box is at rest its energy is the mass times and will gravitate they will gravitate and pull things toward it so it's energy which is the thing which gravitates when we're writing this equation here this doesn't really stand for massed rest mass it stands for energy density okay so it's energy density which gravitates and it gravitates proportional to Newton's constant G okay yep is either of these equations solvable with a decrease in some time oh yeah in fact I mean if you put back the 1 over a square the K over a squared term you'll find examples where it increases and then decreases well maybe we'll do that for the time being it's not too important because there's no I mean it's it may be important conceptually for some reasons but the universe does not appear to be doing anything like that yeah the equation well it is a socially play yeah what happens to the energy instead the energy per photon so the total energy pushed down what happened to conservation of energy no no this equations our conservation of energy this is kinetic energy let's put back let's put back the K or K and multiply by a squared these equations state conservation of energy but there's two kinds of energy one of them are the ordinary things such as photons and protons and neutrons and everything they go on the right-hand side the left hand side is the energy of expansion it's the energy of the gravitational field it's the thing which is left out until you know about general relativity okay so these are actually what is it it's really the kinetic energy of the of the outward moving things here is kinetic energy here's the energy of the object in a frame of reference in which it's at rest so in other words this is the rest energy of a box moving with the flow and this is its kinetic energy it's the sum of them which which is conserved and if you send it if you set it equal to zero in other words if you said this minus this equal to zero that's surely conserved so it's a balance between two kinds of energy kinetic and potential just the assertion that it's the energy that's doing the gravitating it's the other kinds of it yeah that is not clear until you go to general relativity yes that's right that's correct right you might have guessed it from special relativity a equals MC squared you might have guessed it in fact Einstein did guess it that's exactly how I guessed it what he did what he did was he first examined me he studied a box of photons like this and he said what's the mass of that box of photons all right so here was his thought experiment he said let's push on that box of photons when you push on the box of photons just take the box by itself it takes a certain force to accelerate the box because the box has a mass but now when you start to accelerate the box more photons hit this side of the box then hit that side of the box because you're pushing the box this wall is moving away from the photons this wall is moving toward the photons and so you actually have to push a little bit harder to push against the pressure the radiation pressure in the box that means effectively the mass of the box is a little bit bigger and Einstein worked it out and he found that the extra mass the extra inertia of the box was in fact proportional to the energy of the photons in there that was the origin of the equals MC squared now he also had rather early the idea of the equivalence principle that [Music] the gravity works the same on all objects and from that he came to the conclusion that the earth would pull on this box as if it had a mass not equal to just the mass of the original box but the mass plus the photons in there but if the earth pulls on the Box the Box pulls on the earth etc etc so rather early he had the idea that energy gravitates took them a while to get it all together and ultimately yes it's the general theory of relativity which tells us that that it's energy which goes on the side right remember last quarter we talked about having to make tensor equations and the left-hand side of Einstein's equation is a tensor the right-hand side is the energy momentum tensor compose that of energy and momentum okay so we have two kinds of cosmologies real cosmology is a combination of both of them but let's try to understand under what circumstances and when and at what times the universe might be matter dominated and when it might be radiation dominated in fact it is a question of when whether the universe is matter dominated or radiation dominated the reason is the following are I just explained to you that as the universe expands the energy density of radiation decreases but it follows that when the universe if you imagine contracting it going backward the energy density of radiation must have been much larger if you squeeze it it's larger if you let it alright so at some point when the universe was really squeezed where the wavelengths of all the photons were really small the photons had more in gee then the ordinary matter yeah as universe ages does the pee go go continuously from 1/2 to 2/3 yeah family's it not abruptly for sure but more or less in a fairly narrow range of time and it doesn't jump I was going to say it jumps it doesn't jump it goes continuously from 1/2 to 2/3 well I was about to draw a give you a rough idea but let's let's let's just plot just to get the idea up on the blackboard all right let's first plot energy density density and let's draw both cases the matter-dominated here's the matter-dominated it looks at the matter energy density and that goes it goes to zero and let's go to zero and how does it go to zero it goes to zero like 1 over 8 cubed it also becomes infinite when a goes to zero this is let's say this could be yeah this is a a on the horizontal axis scale factor when the scale factor goes to zero that's the situation where the universe is shrunk to a point the density becomes infinite right now that's the this is the matter energy density let's collect matter out here and then there's radiation the radiation is 1 over 8 to the 4th 1 over 8 to the 4th is smaller when a is big but bigger when a is small so 1 over a to the fourth looks like this and at some point they cross at some point the V matter density becomes less than the radiation density so sufficiently early if we go back far enough the universe was radiation-dominated okay what does that mean in terms of exactly what was asked before what does that mean about the growth of the universe it means it started out early we'll try to estimate in a moment where this happens when that happened a little while right if I plot now I plot something different I plot the scale factor versus time okay the scale factor versus time here was energy versus the scale factor here is the scale factor versus time the scale factor for radiation-dominated goes like the square root of time T to the one-half and that looks like this and let's extrapolate it but at some point where this crossover happens it's a bad approximation beyond that to say that the universe is mainly radiation the energy it becomes mainly matter at that point and not it's not a sharp point there's a region in here it makes a transition from t to the 1/2 from square root of T to T to the 2/3 D to the 2/3 is bigger than T to the one-half and so that's what the universe looked like for a fairly long amount of time the interesting question is where did that point happen okay so we can talk about that a little bit now oh no before we talk about that let's talk about temperature let's talk about temperature I want to talk about the various interesting things which happened one of the things which happened was this transition from matter from radiation-dominated to matter-dominated that happened after about 10,000 years roughly speaking something like about 10,000 maybe a little more than 10,000 years 10,000 years after the Big Bang okay something else happened which is actually observational II more dramatic what happened to the photons if you run the universe backward to early times if you run it forward their wavelength grows if you run it backward their wavelength shrinks what happens to the energy of the photon as you run it backward increases what does that mean about the temperature of the universe goes up it goes up in fact to a good approximation the temperature of a black body of the temperature of a box of radiation is basically just the energy of a single photon it differs by some numerical factor so apart from some trivial numerical factor the temperature of the radiation this is the temperature of the photons which are moving around through the universe they have a temperature and their temperature changes with time it goes like 1 over a now when I say close is 1 over a I mean I just mean it's proportional to 1 over a e if a doubles the temperature becomes half as big if a quadruples the temperature is 1/4 is big and so forth so the bigger a the smaller the temperature the smaller a the bigger the temperature and just proportional to 1 over a ok now that means as we trace backward there was a time when the temperature was much hotter in fact there was a time the temperature was as hot as the surface of the Sun the surface of the Sun is rather different visually than the space around it in particular the Sun is opaque you cannot see this myth it's not because the Sun is too bright to see the stars behind it that's not why you can't see the stars behind it you can't see the stars behind it because the star light hits the Sun hits the material of the Sun and gets absorbed into the Sun and gets rattled around and just gets absorbed by the Sun rather than transmitted through the Sun the Sun is opaque why is it opaque it's opaque because it's ionized ionized means that the atoms have been separated into positive and negative charges an ordinary atom is electrically neutral because an ordinary atom is electrically neutral it means that an electric field doesn't accelerate it a vibrating electric field doesn't doesn't do much to the atom it may cause the atom to change size and shape a little bit but it doesn't it doesn't accelerate the atom because the atom is neutral but if the atom were replaced by a proton and an electron let's say a hydrogen atom if the atom was replaced by a electron and a proton freely moving not bound to each other the electric field would slosh the electrons back and forth it wouldn't slosh the protons as much because the protons are heavier so when an electric field passes through an ionized material it sloshes the electric charge back and forth and when it sloshes the electric charge back and forth the electric charge behaves as an electric conductor and electric conductors are opaque it's the reason that a mirror is opaque why can't like go through a mirror why does it bounce off because the light hitting the mirror drives electric currents and the electric currents radiate the signal back so a ionized material is very opaque if you heat up hydrogen in fact we haven't discussed it very much yet what was the universe made out of what is the universe made out of mostly hydrogen universes largely hydrogen it was even more hydrogen in the past hydrogen and some helium but if you go back early enough the temperature was high enough that the helium and hydrogen were ionized electrons were pulled off the I atoms and it was opaque it was hot and opaque in fact it looked it was about like the surface of the Sun let's ask when that happened see if we can figure out when that happened well there's a particular temperature what's the temperature of the photons today three degrees today's temperature temperature today is very cold three degrees absolute zero above absolute zero okay what is the temperature near the surface of the Sun anybody know 3,000 degrees something like that 3,000 degrees about a thousand times larger about a thousand times larger so the temperature at which the gas ionizes let's call that the ionizing temperature and it's also more or less the surface of the Sun that's about 3,000 degrees well if the temperature varies like one over a as they get smaller and smaller the temperature goes up that means that at a time of ionization the universe must have been the scale factor it must have been a thousand times smaller than it is today the temperature scales together with the scale factor as one over a if the temperature today is a thousand times colder than it was at a an that means the universe must be a thousand times bigger let's see if we can figure out when that was at what time that was let's define a time let's remember the following now the scale factor grows like T to the 2/3 today T to the 2/3 during the matter dominated era the late times were matter dominated after the universe cooled down a bit all right so a grows as 2/3 what this tells us is that the time to the 2/3 today divided by the time at which ionization happened to the 2/3 must be about a factor of a thousand the scale factor today is a thousand times bigger than it was at ionization the scale factor is proportional to the T to the 2/3 and so this tells us that the scale factor today to the 2/3 power divided by the scale factor at ionization to the 2/3 power must be about a thousand all right we know what the time today is what's the time today this is today 1550 point seven fifteen something about thirteen point five billion years it's about 13 point that we measure by measuring the Hubble constant that tells us how fast the galaxies are moving apart if we run it backwards it tells us how long it was since the galaxies were sitting on top of each other thirteen point five billion years let's call it ten billion years this is ten billion so this is 10 to the 10th to the 2/3 well let's let's let's see what should we do if we take if we take the three halves power of both sides it becomes T today divided by T at iron ization is equal to one thousand to the three halves I've taken the three half side of both equations the three half side of something to the two thirds to just cancel out what's a thousand to the three halves what's it with square root of a thousand is about 30 so that's about thirty thousand right yes hmm thirty thousand isn't yeah yeah it's - it's a thousand to the one plus one half a thousand to the one is a thousand a thousand to the one half is thirty thirty thousand okay so that's thirty thousand three times ten to the fourth in years now sorry just it's not years three times ten to the fourth okay so that tells us the T ionisation let's just solve them fifty ionization T ion time when ionization happened if we run it backwards is equal to T today that is ten billion years ten to the tenth divided by three times ten to the fourth right go do it right actually thirteen twelve thirteen and a half at the top forty nine million instead of two and a half on the bathroom are you rounding it down to ten most doing order a marriage okay okay thirteen scan okay thirteen is ten well we we we can adjust it later alright so ten to the tenth divided by ten to the fourth is ten to the sixth this is ten to the six that's ten to the fifth times 10 divided by three 10 divided by 3 is 3 so that's 300,000 years after three hundred thousand years before three hundred thousand years the universe was completely ionized it was completely opaque why could not travel very far there was a dense plasma of torn apart atoms the nuclei were mostly hydrogen with a bit of helium and main thing is it was hot and opaque as hot as the Sun as the surface of the Sun and oh and opaque like the Sun now let's let's so let's think about what that means to an astronomer an astronomer with very good telescope here's the astronomer at the center of the universe and the astronomer looks out and as he looks out he looks into the past alright so if he looks to UM to the next galaxy the Andromeda he's looking about two million years into the past that's not much if he looks out some distant galaxy out here he's looking further into the past and the shells are both distance as well as time backward in time as you go further and further out well as you go further and further out the temperature of the photons is increasing the temperature locally out here to a traveller who is traveling with them is higher than over here because he's looking back into the past and as you look back into the past the temperature was higher eventually at some distance namely about thirteen or ten thirteen thirteen point five billion light years he sees back to the point where the universe is ionized so an out beyond that the universe is completely ionized and light cannot penetrate it it just scatters around light just scatters around in here and then at some point as you move in it becomes cool enough for atoms to recombine for atoms to recombine and become uh ngayon eyes for the electrons they get trapped by the protons and form atomic hydrogen and atomic helium at that point the universe becomes pretty transparent why is it transparent because it's not a plasma anymore so way out far it's a plasma out to some place now of course it's a fuzzy place it's not a sharp place it's a fuzzy place where the universe goes from being a plasma to being a time at which the universe went from being a plasma to being a clear system was just some neutral atoms at that point light can travel through the universe without scattering very much this surface where you go from plasma to ordinary gas is called the surface of last scattering that's the surface of last scattering a photon rattling around there will come to that surface of last scattering and then pretty much be able to freely move through the universe so when we look out all the things that we normally see are on the inside of the surface of last scattering and we can't really look out beyond the surface of last scattering not with electromagnetic waves anyway yeah so that's a so basically what you're saying is our limitation with our telescopes radio etc they cannot look young for top 300 thousand years but that's it yeah not three hundred thousand years ago but they can't look back right earlier than 300 thousand now are there other things that can look back yes neutrinos are electrically uncharged they don't get scattered by the by the ions in there the tree nose just passed through an ionized gas eventually it gets hot enough that even neutrinos interact with each other strongly so there's some other shell out here that's the surface of last scattering for neutrinos but with the neutrino telescope which doesn't exist of course such a thing doesn't exist but with the neutrino telescope if you could see the very low energy neutrinos then you would be able to see deeper into the past a graviton telescope could see even deeper into the past but why when we look out in the sky and we look up here don't we see the surface of the Sun in every direction this is a modern form of Olbers paradox if it's true that out here everything is as hot as the surface of the Sun why don't we look out at the night sky and see the bright glare pressure this is not standing still relative to us it is moving away from us with very close to the speed of light and that means that every photon and its way in here has been red shifted by a factor of a thousand that's what made the temperature go from 3,000 degrees the three degrees so what we look out and we see is microwaves of temperature three degrees that's not much of a signal a three degree blackbody you don't see it 3,000 degrees if you looked out in every direction you'd burn your eyeballs so that neutrons protons weights it again when moment of last scattering from the tree knows when the neutrons and electrons shooting with Thompson electric no I think it was earlier than that it was at the time when the weak interaction was as strong as the electromagnetic interaction which was a good deal more energetic you know I don't think that that's yeah and right and the graviton is even further back but they're even harder to see and what I mean what makes them hard to see is the same thing which allows them to get through this junk the reason they get through the junk is because they're so weakly interacting you can't see that sphere that is what you see the cosmic background radiation you see the sphere but I'm talking about the retreat oh honey that's our key we do in fact see this oh yes yes yes yes that is what you see when you see the cosmic microwave background absolutely yeah yeah yeah yeah time's going to begin what does that take that rather cons why would why would there be a shelf or rabbit on board but what the ocean takes a graviton oh gravitons become strongly interacting with each other when the energy gets high enough and when the temperature gets high enough and what would be the distance from the long distance the Planck distance 10 to the minus 33 centimeters all right 10 to the minus 42 seconds so well the point at the point that I was raising though was it's the same thing which makes them be able to get through this junk which makes them hard to detect they're hard to detect because everything is transparent to them including the detectors all right if I understand correctly that the surface of the Sun is where it seems to be because that's the temperature at which light would be kind of opaque to light so that's why it's not as the size it appears to be that's that's the temperature at which there which the ionization which it's called recombination where the atoms recombine now why is it as sharp as it is the Sun has a fairly sharp edge when you when you look at it and the answer happens to be the exponential behavior of the Boltzmann distribution I didn't want to get into that today but but that seems like when you talk about the temperature for photos you're talking about the temperature a blackbody is central great news P creation is that temperature okay yeah but that is not the temperature the temperature is essentially the energy of the average photon okay the average energy the photon has an energy which is 1 over its wavelength so yes the temperature is 1 over the wavelength of the radiation no no no that's energy density that's not the energy of a single photon T to the 4th is either the energy density or the or the energy flux the luminosity yeah yeah the 8 to the 4th is as a combination of the energy per photon and the number of photons per unit volume okay so in order to find the energy density of a blackbody you have to know the energy per photon and the number of photons per watt per unit volume the number of photons per unit volume goes like T cubed and the energy of a photon goes as T and that's what gives you t to the fourth or whatever yeah yeah how about the neutrinos don't have any intrinsic motion I mean that with the big move is very close to so your lunch on the photons you can't stop them so they're always going but but aren't the neutrinos that are aren't they sort of attack just go to had a box full of neutrinos doesn't that thing why are they moving my mad was not moving relative to the boxes that are that are growing with this with a ray of the universe photons move yes the full town red bar neutrinos mmm tight on neutrino why doughnut reno's move well the first approximation they're massless are the very much like photons they have a teeny teeny teeny tiny mass so they happen so they're very nice so to say you can't treat their energy is much larger than a mass you can't treat them like as it's not relative particles they have to be created separately for practical purposes you can treat them as being like photons yeah yeah a neutrino would have to have a very very very low energy in order for it to be moving much slower than the speed of light so you know it's only recently it's only in the last several years that people have really been able to measure the mass of the neutrino because it's so small and for all practical purposes not all practical purposes but for many practical purposes neutrinos just move with the speed of light so these original neutrino is also very cold no they were hot they were hot no now now think now they're probably about a little bit colder than the photons maybe two degrees but similar to the photons you know what what time after the Big Bang these gathering for the adrenals yeah I would have to say but it's it's it's microscopically small it's much smaller yeah yeah we'd have to do we'd have to do some work mmm why is that services well the surface is no it's it's cooler yeah decoupled earlier and yeah then stuff happened that was out of equilibrium and heated the photons it didn't heat the neutrinos so so I know buddy of course has ever measured the neutrinos people I believe estimates something like two degrees but it would be a little bit colder okay now we want to talk about dark matter now let's talk about dark matter our dark matter was not discovered by studying cosmology where cosmology means you know the universe as a as a whole cosmology means the study of things bigger than a few billion light years anything smaller than that is astronomy and then they did invented this this word if it's ugly astronomy ugly difficult astronomy meaning to say that it's not neat and elegant and they call it gastronomy that's not my word yeah all right so the dark matter which certainly has an important cosmological consequence very important it was not discovered by cosmologists looking at cosmology it was discovered by by astronomers looking at galaxies and so galaxies is a small object on the scale of the whole universe and measuring what I call the rotation curves of the other galaxies the rotation curves are simply the rate at which things move around the orbital velocity of stars at different distances from the center so let's start with orbital velocity and let's go all the ways back to the solar system just to get a handle on orbital velocities the solar system or any system which is composed of a central mass and orbiting one or more orbiting planets let's call them all right now what I'm interested in the mass of the central object is M the things orbiting around that are considered to be lighter and I want to know the velocity of an orbiting object as a function of its radius as a function of its distance from the center the orbiting object let's say the orbiting object has a mass little m okay let's see if we can work it out what we use is Newton's equations F equals MA what is the animal applying it to the planet alright what is the force on the planet the force is due to the Sun at the center it doesn't have to be the Sun just some central object and some orbiting planetary system the force is M mg divided by R squared right where R is the radius of the orbit that's the force and it's directed radially inward that's equal to the mass times the acceleration so we have to know is the acceleration of an object moving in a circular orbit I'm going to write down the answer the acceleration of a circular orbit is toward the center it involves the velocity and the radius anybody know the formula V squared over R I am NOT going to prove that we're just going to check its dimensions what's the dimensions of acceleration dimensions of acceleration are length per unit time per unit time length per unit time squared velocity per unit time is acceleration velocity is length over time per unit time let's just check that velocity squared over R has the same units velocity squared has length squared over x squared and R has length so hopefully these have the same units they do okay it's a true fact that the acceleration of a circular orbit is toward the center same direction as the as the force and it's proportional to the velocity square equal to the velocity squared divided by the radius of the orbit okay so let's do some cancellation the little M's cancel out which means that the acceleration doesn't depend on the mass of this object we can multiply both sides by R and then we find that the velocity is equal to the square root of Mg over R in particular the velocity of a distant planet is smaller than the velocity of a centrally located velocity of Neptune or Pluto is much smaller than the velocity not just E and that's just the angular frequency but the actual velocity falls off as 1 over the square root of R now if you look at galaxies through a telescope what you see of course is light and I was always believed that the amount of light coming from a region was proportional to the number of stars in that region and so forth so will be proportional to the amount of mass in that region and galaxies are mostly cores the center and then there are these some galaxies are spiral arm galaxies if you look at them from the edge they look like that but most of the light and most of the material the observable material the light matter a light matter means the matter that you can see because it glows because it gives off light most of it is in the core of the galaxy so if you were to just take literally that mass follows light that the mass distribution is comparable to the light distribution and look at gal and look at stars at different distances out here they would mostly be moving in the field of a central object similar to the similar to the center of a solar system if that were the case now we can also look down on this from above that's a car very diffuse bunch of stuff out here that doesn't how much light coming out of it and we can everything moves around we can measure we can measure the velocity of stars in such galaxies or we can measure the relative velocity we can measure the overall velocity of the receding galaxy is a relatively nearby galaxies we measure the overall recessional velocity and then we measure the difference between the velocity of this point and that point we discover that this point is moving toward us this point is moving away from us and in that way compare it with the overall velocity we can pretty well calculate the velocity of orbiting the orbital velocity not calculon measure the orbital velocity of stars as a function of the distance from the center and what do we find not me but what do the people who do this kind of work find they find that the velocity does not fall off like 1 over the square root of R instead it's pretty constant the velocity of that the angular var takes longer to go around far away but that's because it's along a distance but the velocity of a star over here is about the same as the velocity of a star over here is about the same as the velocity of a star near the outer edge of the of the galaxy so there's something wrong with this picture of a galaxy that it's mostly composed of matter near the center all right so you can do something else and say wait a minute now let's let's see if we can figure out where the matter really is maybe maybe mass doesn't follow light maybe the light distribution is not a good sampling of the mass so let's use what we do know about these velocities to see what we can say about how the mass is distributed ok now think of let's suppose now that the mass is not concentrated at the center but it's distributed in some way it's distributed in some way and from simplicity let's say it's distributed nice and symmetrically then what mass should we be using in here for a planet or not a planet for a star at distance R from the center what mass should we be using well we should be using all of the mass out to a distance R remember a planet or a star moving at a certain radius feels all the mass inside that shell so we can correct this formula and we can say let's correct this formula and say the right formula is M of R times G M of R times G the meaning of this M of R is it's the amount of mass in a sphere of radius R so far we've not assumed anything particular about that distribution of mass we've just assumed that there's an ocean a functional motion of the mass within a sphere of radius R this formula is very general because it also doesn't say anything at the you don't know what M of R is but you measure V but V you discover is constant you discover that all of these velocities are the same so what does that say about M of R it grows linearly with r the amount of mass out the distance R is proportional to R so the amount of mass and a sphere of radius R apparently grows like R what about the density of mass does that grow now we have to divide by R cubed if we want the debt if we want the average density of mass the average density of mass we would want to divide by R cubed and no it doesn't mean that the density that it gets denser and denser as you go out but it does mean that there's a halo of mass out there which is more pronounced that that most of the mass of the galaxy is out farm out near the edges and maybe even beyond the visible galaxies now I say okay we can use the velocity to actually tell us what M of R is we can figure out using the velocities we can tell what the mass out to a given distance R is and we can compare it take the whole galaxy out oh it's very extremities we know what the mass distribution is just from these from the rotational speed of the stars and we can say how much mass is there altogether how much mass is there in this hidden unobserved mass in the hidden unobserved mass that does not follow light it is not proportional to the light there's about 10 times the mass that would that we would normally associate with stars and luminous objects that produce the light of the galaxy in other words the estimate of just saying that the galaxy is made up of stars or luminous matter like stars captures only about a tenth of the mass of the galaxy the galaxy is at least ten times heavier yeah so that's that's correct so you can still be more dark Nana yeah I think that that's true that's that is true I may be I think what's true is the total mass that's expected to be in a galaxy is about ten times the the mass of the luminous matter it does of course fall off when you go far enough away but you're right out to the out of the boundaries it it follows this Dark Matter curve and I believe the total mass of a galaxy is roughly about ten times what you would you what you see with light this is that right um I think it's yeah what no dark energy is about thirty percent dark and dark and what I get is four percent are girls there's your oh yeah so protective 1001 1001 symmetric right dark dark matter like luminous matter is what about 4% of the whole and and the dark matter is probably another thirty percent so it's something like a fact of ten or seven or something like that 4 times 7 is 28 yeah for some galaxies that is that a lot of the dark matter is beyond the last yeah yeah but I think that I think the total amount of it is about 10 times the mass of a galaxy total amount but some of it extends out beyond the galaxies I'm not an expert at this incidentally but how the density looks like the daddy over R squared well yeah you can um reason for let's see no no by I don't this is not something that that's subject to anything except the simulations and simulations account for some of it but I don't know all galaxies and galaxies no structures so you get variation with Sun Sun Sun Sun yeah I think for all big galaxies yeah yeah it's pretty much the same we can calculate what the density is let's say the density is such is the you have Rho which is the density stood a little bit better Rho of R now if you integrate Rho of R now what do we have to integrate it with to find the mass within a shell for PI R squared in particular R squared V R right and you're right for pi and then okay about the 4 pi this is the thing which is equal to 1/2 you integrate it from 0 the capital R and this is the total matter the total mass within radius R and this is the thing which grows as R ok so how would you solve this equation well we can differentiate but we can differentiate both sides of it with respect to our what happens when we differentiate an integral with respect to our you just get the integrand right so we get Rho of R R squared is equal to 1 Rho of R looks like 1 over R squared Rho of R is one of our squared but there's a lot of matter out there and about 10 times what's in the galaxies what do we know about it it doesn't shine so that's one thing it doesn't produce light another thing we know about it is it didn't contract it's it's it's much bigger halo than the size of the galaxy the galaxy is a fairly small thing embedded in a big halo of this dark matter the dark matter is in a form of a spherical halo even if the galaxy is in the form of a of a disk galaxy of some sort at least that's expected and it's I think even observed that so it's a big globular blob of mass that has not contracted together with the with the with the luminous matter to form a smaller more concentrated thing what is it that causes the contraction of a bunch of gas to go smaller lower the temperature no no it shrinks it shrinks when it shrinks the temperature goes up that's why stars form when it shrinks the star it goes up it's a good friction dissipation of some thought or another some form of dissipation some sort of collisions some sort of friction is the thing which which causes if you just started with a ball of gas and the gas is going back and forth and back and forth oscillating some of its going around in a circle nothing much happens to it it just stays about that size it shrinks because of collisions and because of radiation it radiates away energy it shrinks and you know interesting kinds of collisions and processes have to happen in order to cause it to shrink well ordinary matter has plenty of different kinds of processes in particular radiates light and the radiation of light causes it to collapse and other kinds of processes collisions between atoms and so forth whatever this stuff is out there it's very collisionless and it doesn't radiate light so it's very weakly interacting somehow it doesn't do very much other than gravitate stable unstable structure no because it would gravity reinforce it to that hole keeps it kinetic energy okay what keeps what keeps the what keeps some the earth going around the Sun why doesn't the earth fall into the Sun no friction right there's a little bit of friction so the earth is slowly falling into the Sun and at one time there was more friction which caused the primordial gas cloud to coalesce and condense into things so whatever this stuff is out there it has a lot less friction than other matter yeah just is it what spiracle shell no it's not a shell it's it's a sphere but whose density goes down like one over R squared this fear not a torus not a Taurus Taurus be very hard to see no idea it's not a Taurus it's a sphere large spherical blob yeah possibility of intergalactic dark matter or dark galaxies dark galaxies you mean just a blob of dark matter yeah I mean we gravitate so yeah yeah neutrinos just wouldn't behave that way they're moving too fast yeah they're moving too fast they are these are slow this is the ball a ball well it's not it's not a uniform ball this is a ball yeah yeah a ball which is more dense in the center but the density doesn't suddenly fall off like the light does it gradually falls off how do you how do we know that there's dark matter outside the luminous stars you see going around as you can measure the velocity of the other different arms that galaxies and and say how much matters inside that but you can yeah you can tell you can you can roughly estimate the mass of a galaxy by looking at the motion of other galaxies in the vicinity of the galaxy so what's that colliding galaxies but just just the motion of the animal I suppose the motion of the Magellanic Clouds and things like that they tell you something about the total mass or the auto so it must be the motion the relative motion of nearby galaxies which give you some hint at what the total mass of the galaxy is the black hole would not be coming no no no no dogma is very definitely collapsed you mean could it be a bunch of black holes people have talked about that and I think the general conclusion is no but I'm not really sure exactly why would they be living for a massive thing he has to be lensing they'd be lensing but also if those black holes originated from ordinary matter it would say that in the primordial universe before those black holes formed there was a lot lot more ordinary matter out there and that would be deadly for nucleosynthesis and and the the origin of the elements so the best bet I think I think the best bet by far is is that they're elementary particles which are very weakly interacting or absolutely but they're not as flat or they're not the the dark matter is not as flattened as as the Galactic plane would indicate presumably they have the same net angular Melissa Sara Lee not necessarily no I don't think so I don't think that where is the angular velocity come from well I mean you know the angular the angular velocity of the solar system is not the same as the angular velocity of the Sun in fact the angular velocity the solar system is not exactly well defined not exactly oh oh um yeah good yeah I would say that the angular I don't know you know I don't know what's known about the rotational motion of the halo I don't know the dark matter dark matter halo it's a great I don't know the answer whether anything is known about the rotational motion of the halo increasing energy what's that is the dark metal decreasing energy decreasing energy once I'm eating enough metal the energy decreasing decreasing with respect to what time function time are why would it be decreasing it's pretty much staying the same it's not changing very much doesn't interact with anything it doesn't lose kinetic energy really that's another question we haven't come to that we can when you're estimating the ordinary matter in a galaxy if you add up all the planets and the Oort cloud and creeper belt and all that stuff in a solar system how big a fraction of that is the to of the total mass of a solar system yeah go to school yeah solar system essentially the Sun yeah conservative conservation of angular momentum from the Big Bang it seems like if there wasn't any net angular momentum of that initial mass and you have different galaxies they would net out to have to not have a greater angular momentum so does that come into play with with also the angular momentum of rewarding whether the angular momenta of galaxies show some alignment well that I mean they all couldn't be spinning clockwise from look for it one girl I would have been that was noticing but from that point of view that would that what can you conclude anything about the angular momentum of these starts matter clouds that they would also have to balance to them well I think you product I think it's pretty pretty darn certain that they average out on the average but whether the angular velocity of weather I think the question was is there some locking which locks the the visible galaxies to the halo I think that was the question I don't know I will try to find out I don't know the angular velocity of the galaxies came from something I hadn't you would think at least at least a pilot reported to the same same direction along spin up the but even that I don't know and I don't know if it's measured it's a good question I really don't know the answer never what's that or well it seems like the dark matter is more the primordial thing that coalesced it was probably the first thing to start coalescing into well-defined structures and the ordinary matter probably followed it got trapped by it but then the friction of the ordinary matter and collisions caused it to sort of continue to shrink while the dark matter being largely transparent to itself didn't shrink except the only thing that affects the dark matter is gravity gravity is enough to cause it the convention start to shrink and start folding common denominator is gravity what's that it's only common denominator is being away yeah yeah that's the only that's the only serious interaction between them we relegated energy come from achieving it from collapsing doesn't interact accepted rather said collapsing where did that energy come from from potential energy originally started originally started with a pretty uniform distribution but don't think of his uniform distributions this thing that is very large diffuse blobs of gas very very large and very diffuse and they did gravity pull them together gravity caused them to contract and they contracted some and the process of contracting potential energy got converted to I just had a question here about the mechanics is it the case if you have a particles that don't interact except gravitationally and they're in a disk it's unstable and it must II think I suspect the disk is unstable so it has to evolve to it a a fall really varying but other than that No yeah now how did this how the globe the globular structure manages to stabilize the disk-like structure in it that I don't know maybe related to polarity to work to the polarity what was the polarity mean oh it doesn't have to do with magnetic fields it doesn't have to do with magnetic fields I don't think I don't think so even that I don't know for sure this is this is really the subject of people who do large-scale simulations less pressure than it is and there isn't more and more random orbits because if they're rotating at this they run into each other much less often than they do if they're if all the orbits are going or why are we haywire every which way you know I'm sure so we seem to be that some through some chance that anticipated process would lead lead to a dislike structure no it certainly did the solar system and around Saturn and so I don't know yeah I'm beyond my paygrade now I'm not enough I'm not enough of a gastro physicist to know the answer to these questions you know how many good an estimate for the amount of dark matter between the galaxies well I think from the more relative motion of galaxies the relative motion of the galaxies themselves is sensitive to the material between them most of Dark Matters right around the galaxy's there wasn't much well let's spread out something like like this and how far that goes out does it continue like that until you get to the next galaxy sort of or does it or does it tail off and then a flat region in between I don't know the answer the question let's see a galaxy is how big is the galaxy a hundred thousand light-years right something like a hundred thousand light-years and the distance to the next galaxy is about a million light-years two million light-years something like that so I've seen basically the dark matter within the clusters of galaxies has no uniform distribution it's like clouds in the sky there's more dance and less dance reason yeah it's it's okay there's like the progression of the gallon we the point being what well they mapped out you know dark rabbit their density the relative density of the dark matter right in the clusters and they show these plows super cogs and in the nature which says that the galaxies what fit and it goes vertically one over R squared but that either increase in there decreases when they pass through each other oh that's for sure but they're you know how its distributed in the region you know halfway between the galaxies I don't know came back to the single galaxy model which you have up there in most galaxies have a supermassive black hole or a black hole but that's a very small fraction of the mass of the quarry is in a way we can we can analyze the dark matter within that perspective in terms of the black hole I think the dark matter is rather Univ is so diffused and spread out over such a large distance that I don't think it not black hole is a tiny little thing at the core so I don't think so I was uh I'm black on dark matter well there are limits there are various kinds of limits on the nature of the particles which might be the dark matter particles motion of the bodies I don't know how accurately measuring the motion of the planets but oh we can see general relativity but iPhone as you can see there you mean is the dark matter appreciably affecting the gravity of the solar system I don't think so you know so they are the I mean haven't if they don't Iraq it's at the gravity what sort of experiments are good enough to try to detect well when you say they've done interact I mean you know or maybe they just interact very weakly yeah I mean if an electron passes through a lump of lead it will interact with the lump of lead every single time if a dark matter particle passes through a lump of lead and may interact with the lump of lead one out of 10 to the 13 times or something I just look 10 to the 13th dark matter particles pass through and you'll discover one of them so you just use the statistics of large numbers and you know there are lots of detection schemes that are out in place they're searching for dark matter thus far they're always out of the range of detectability will there be a signature of dark matter and falling towards let's to defuse it's very diffuse very reason to believe that dark matter is essentially in circular orbits I mean again you have to get notice and I think there's any reason to believe it's a circular is probably not a circle probably not in circular orbit I don't think so that could be some very very yet highly elliptical orbits yeah it's probably things like that so they would infer something some of the Dark Matter could in fact just by accident run into the shirt the black hole sugar sure it's very confused serene and this is also extremely elliptic orbits are eliminated by the way black hole of the center but the black hole is a tiny tiny tiny little geometric object at the center of the other galaxies so you're eliminating very very little bit that way yeah no I I think there's no reason to believe that the orbits are circular the orbits the orbits are probably all over the place some circular some elliptical some very elongated some of them just going back and forth except they're not hitting the enemy deflected by neutron star in every other's mess it was record by everybody yeah just stirred up and passed through the pass through the planet sister than this bastarz and presumably episode yeah it pass pass through most things in an awful attach to a neutron star but they probably pass through the earth very easily right if you have some sort of sadistic allah populous distribution on the types of orbits then you could probably get the rollbar as one of our square no I know I don't think there's any easy way to get the one over R squared don't believe there is for that that's equivalent to knowledge of the distribution of energies and it doesn't fit anything simple it's not a Boltzmann distribution so I don't think there's any simple way as far as I know it is not known exactly why the distribution is what it is now there's lots and lots and lots of simulations and I don't know what the state of the art is the gravitational lensing in it was the piece you can try and measure it that way if it's a significant portion of the mass you have like twice the lensing effect when you what kind of like image you know galaxies behind it or around it or something like that oh yeah you can you can yes the lensing do two galaxies sensitive to them is that we saying it's sensitive for the mess absolutely you have like a relative effect that you sugar will give it the optical nasty or radiation and then you would be significantly more so dark matter causes lensing yeah oh yeah dark matter is part of the mass which causes lensing so it's is there something to suggested in observation that by way of lensing and discern the distribution of dark I'm sure there is but I'm not an expert at it but I'm sure there is I mean that's that's a very obvious thing to try to do is to map out map out the dark matter by lensing where they looked at galaxies that were colliding and base because the visible matter interacts with those stars populations of stars in Iraq you get basically two hypotheses about how they the lensing and the evidence seems to be that there's I think it's a different different lensing effect because the the Dark Matter doesn't interact in the same way they told your motherboard galaxy yeah the bullet cluster is okay is a pair of galactic clusters that are interacting of it right the gas on one side which is regular matter or not and seen in x-rays and then you can measure the distribution of the total matter by looking at gravitational lensing so you get a distribution of total manner and ago in a distribution of normal matter and what's left over what is assumed to be dark man point is that when the two car galaxies collided the ordinary material interacted in a significant way the dark matter clouds just interacted gravitationally and was not such a significant interaction and the result was a separation of dark matter from from the other matter and so there's an example the controversy had to do with whether there really was dark matter or whether Newton's or Einstein's gravitational theory had to be modified you could try to fit the rotation curves of galaxies by modifying Newton's force law we got it from Newton's four slow where is it over here my modifying Newton's force law and in that picture they really wouldn't be dark matter or the the gravitating effect would be modified but it would still be attached to the same masses it would be quite clear that that would not be a good description if it was possible to separate dark matter from the ordinary matter okay and apparently in these bullet clusters this is bullet cluster two galaxies collided and the effect was a separation of the dark matter from the luminous matter and so that kind of settled the controversy of whether of whether there is dark matter or whether it's a simply a modification of Newton's law only refer to be VC perspective no no anyway that you can see it anyway you can see it optically by any way that you can see it electromagnetically but yeah I think in first approximation yes it was the visible the visible light the visible light for the most part yeah but the original hypothesis was that light the mass followed light that that the luminosity was a good measure of the abundance of mass well I think we would have noticed if it admitted any appreciable amount of radiation into other now it's possible that dark matter for example annihilates and creates gamma rays right sure sure but that you wouldn't see through ordinary telescope you see in particle detectors and right good okay must be able to use between the Miller continuity well the two they seem to be two very different things they don't seem to be but then very little is known what I would say about dark matter is very little is known in detail about what it is but it's entirely consistent it doesn't require any radical modifications of the rules that there are more particles than have yet been discovered I think we all believe we've probably just touched the surface of all of the particles that exist and that there are particles which can be very weakly interacting we already know there are the tree knows as as we've mentioned and so without doing any radical damage to any of the principles of physics we can easily accommodate dark matter by just saying it's particles that we haven't discovered yet [Music] well that sounds funny but it's probably what it is it's probably what it is that ever it gives every indication of not being anything radically different and since everybody and his brother has postulated a particle for one reason or another and both often for very very good reasons there are probably more particles many of them weaken and weakly interacting and it's probably what they are if not not but the was there thought that there's a lot of hydrogen you can't see an ionized hydrogen kind of made up this masa seems to me that was that there was a time when people thought that it might be just hydrogen there was a time nobody thinks that anymore and I think at least one of the reasons is because the amount of it is so large that it would have radically affected the creation of helium and then the early universe and radically affected in nuclear physics of the first three minutes and some really awkward way so that's there's just too much of it to fit into any when we talk about nucleosynthesis we'll talk about that a little bit there's too much of it and is there or not any evidence that dark matter has either electrical or magnetic properties well the evidence is it doesn't have very much that they're not yeah they're probably neutral lists they certainly don't have any significant electric charge the standard model has note doesn't talk to you to any pops car model does not have particles of this type the supersymmetric standard model has a thousand of them and all over the place and so sometimes people regard this as evidence or weak evidence of supersymmetry that's a that's a bit of a stretch but it could be but there's a lot of there's a lot of good reasons you know it's really sensible reasons for thinking that there are more particles and so the dark matter could be any one of them it could be a combination of them I think we'll find out I think that's not not out of the question to find out in the next 10 years [Music]

Channel: Stanford

Views: 100,041

Rating: 4.8274508 out of 5

Keywords: Science, physics, cosmology, equation, universe, expansion, dark, matter, photons, scale, factor, Newtonian, mechanics, galaxy, kinetic, energy, potential, Hubble, constant, Einstein, equations, time-time, component, cur

Id: rYQTAJ50A44

Length: 120min 27sec (7227 seconds)

Published: Fri Jun 12 2009