Week 10: Lecture 48: An introduction to Nuclear Astrophysics – Part 2

So this lecture we continue with our discussion of nuclear astrophysics. Uh so initially we will talk about the evidence for dark matter and dark energy and then we will talk about what powers the sun. What is it uh that uh leads to so much of energy production in the sun and that is the main reaction chain is the PP fusion chain. So let's first talk about dark matter. The strongest evidence for dark matter is the so-called rotation curves of stars and galaxies which show that there is a gravitating matter inside of the orbit which does not seem to be seen through electromagnetic radiation and this was therefore referred to as dark matter by Ziki in 1933 and more convincing evidence was uh found by Vera Rubin in 1970. So this is in the so Ziki's ideas and our conclusions and of course Rubin's uh you know conclusions were are all summarized in this paper of astrophysical journal in 1970. So uh the evidence is like this one example of that is the rotation curve of the so-called Nessier galaxy 33. So what you find is that if you go out from the center of the galaxy then the velocity uh increases like this but it is supposed to decrease if uh you you look at the stars that give out light and so it initially increases and then it should decrease. Whereas what has found in this Messier galaxy and this is just one of many that have been seen uh is that it goes up and where it is supposed to fall it actually keeps on rising albeit at a slower rate. Okay. So the conclusion was that uh the and of course these would be very few stars here as you go out in the galaxy but uh this rotation curve meant that there's some other kind of matter which is interacting gravitationally but we which we don't see through the electromagnetic spectrum because it doesn't interact electromagnetically. That was the belief. So the other evidences for this dark matter include gravitational lensing. That mean there is a strong source which you see in a lensed way uh in uh so the there is some matter there which is actually focusing uh light which otherwise would have gone out. Uh and uh so this lensing phenomena is what is seen. Then the structure of the galaxy clusters there is a so-called bullet cluster where you see uh two galaxies going through each other or and uh you you see that the thing which is giving out light is actually not moving in the same manner that the whole cluster as a whole is moving. So there is some dark matter in this which is causing this effect. And then of course there are anisotropies in the cosmic microwave background very tiny anisotropies at the level of one part in 10 the 3 10 the 4 and uh this can also be explained by the existence of dark matter an alternate explanation of course requires a modification of Newton's law of gravitation and uh the I mean the kind of modification that is required is that you should it should be stronger at larger distances than 1x r² if it falls off by 1x r² then you at this if it falls off slower at larger distances then you could get something like this dependence. Now what is the rationale or what the reason for this so-called modification of Newton's uh law go by the name of Mond uh that is of course not known but if you just from the data if you say that there is something like this happening stronger than the fall of like 1x r² so it is r to the power of delta where delta at large distances it is less than two then of course This can explain this rotation curve and many other phenomena. Uh the other hand there are some things that cannot be explained by the existence of dark matter but which can be explained by this and vice versa. So the field is still open. Uh so this is the same rotation curve is shown as a in a blown up way. This is observations from the 21 cm hydrogen line. This is a microwave line and this is observation from star light and this is what you I I'm repeating what is expected from a visible disc and this is what you actually observe and so this can be explained if you have dark matter or as I said a modified neutron gravity. So the next question would be what is dark matter made of? Uh so there have been several searches for uh the constituents of this dark matter uh and these uh uh range from a few GEV to hundreds of GE and uh since this dark matter doesn't interact there has to be of course some known some interaction which is just yet unknown maybe at the level of millak or super weak uh if these D0 particles are there then as we plow through this as the Earth plows through this dark matter. Uh we should see evidence of that. So these dark matter particles can scatter off nuclei in your detector and you should see a telltale signal corresponding to that. So [snorts] the searches on terrestrial searches involving light and heavy nuclei have been carried out with very low thresholds, low background. So it is placed deep underground locations and so on. But we have as yet not found any firm evidence. uh it could also be that we are looking in the wrong places. So examp for example could the dark matter just consist of black holes or axons and so this is there is a review in this Canadian journal of physics uh 2025 which you could look up for more details and in any case one of the exclusion plots in this uh paper uh rules out sigma v uh as a function of the mass of this dark matter particle. This here it's called Kai. So in Gev. So right from about 10 the minus Q * 10us 3 GV that means of the order of MEV to about 10 7 G there are bounds. So this part is ruled out by various kinds of experiments and uh it could still be that you have uh sigma V could be in this ballpark. So the smaller the cross-section of course it becomes harder to detect. uh of course we don't know what that interaction process is as I said it could be midi or micro weak and so on level so the colored regions as I said again repeating are excluded by experiment so this is typically like any other uh plots that we have seen this is a exclusion plot for dark matter velocity product with cross-section versus mass okay now dark energy is even more difficult to probably understand but there's a Nobel Prize given to this kind of conclusion that was drawn by three physicists who got the Nobel prize here in 2011 but of course there are many other experiments also uh experimental data that has been looked at and so the expansion of the universe appears to be accelerating uh based on Hubble velocity measurements using type 1A supernova which are supposed to be standard candles in uh astrophysics. So using this data of course at that time they had a somewhat limited data set but within that by analyzing that data set they came to the conclusion that there is dark energy and this is causing an accelerated expansion. So if one examines a much larger data set which is data sets which are now available of type 1 a supernova then the conclusions seem to be different and one such paper is here it's a a 2018 paper evidence for isotropy of cosmic acceleration and they attributed not to a dark energy but just due to some attractor which is sitting at the edge of the the universe. Okay. So if you go by the paradigm that many people most people believe in most cosmologists believe in uh and this is taken from the one of the Nobel laureates lectures in 2011 then we believe that we have about 72% dark energy 24% dark matter and what we see is only 4%. Okay. So there is lot of according to this uh you know paradigm there is a lot of dark energy and dark matter that is around. Now let's come to something which is which has been measured in over the last you know 60 years or so more than that. Uh so this has to do with what powers the sun are the reactions the fusion reaction chains. uh we have evidence for those reactions going on because we have observed solar neutrinos and indeed this uh careful study of those led to a so-called solar neutrino problem and that also was sorted out that was solved by looking at reactions that don't depend on the flavor of the neutrino that you're observing and uh also we will talk a little bit about measurements of nuclear properties and reactions of astrophysical interest of course all of that will not be covered covered in this particular lecture but this is the general flow that will be there of the lectures. So these are the some of the important uh references Hans Beth's Nobel lecture in ' 67. So apart from many things that Hansbay did he also you know was the first one to say that uh to delineate how nuclear reactions actually cause energy production in the sun. Then there is a very nice uh paper in nature on by John Beall how does the sun shine also on the Nobel website Nobel prize website. Ray Davis in his 2002 Nobel lecture a half century with solar nutrinos. And then these are two reviews which summarize all the nuclear data that existed around the end of the uh 20th century. thought 26 27 years ago. So uh how did we come to this conclusion that nuclear reactions are the source of solar energy? So early on in uh you know 1854 1862 Lord Kelvin proposed that meteors falling into the sun release gravitational potential energy. The sun is of course a massive object. So there are bodies that can fall into the sun. uh they can get captured and that can release uh the gravitational potential energy. So the rate at which this happens from there you can get the estimated sun's age uh as something like 30 million years. So the sun was just born 30 million years ago. So this is basically from the potential energy of gravitation of the sun and divided by de by dt rate at which these things uh meteors or other objects fall into the earth. So of course this trashed the Darwinian theory which required at least 300 million years if not more billions of years to for life to evolve the way it is the kind of variety that we have plants and you know fish life in the sea life on land and so on. So this opposed uh this went opposite to the requirement of Darwin. Now, Rutherford using the uh law of uh uh you know radioactive decay law was able to date things on the earth and he showed that uh the life of the uh the earth the earth has lived at least a few billion years. Okay. So if the earth is so many billion years old, the sun also has to be and so this cannot be the source of energy in the sun. In 1920, Edington realized the potential of nuclear processes because by that time uh some of the nuclear reactions were known and for in I mean uh for instance Aston's mass measurements showed that you can get a huge amount of energy four protons combined to give four helium. Of course, what else uh they didn't quite know. Uh although beta decay was known, but the nutrino was not known at that time. But just the mass measurements told uh people at that time including Edington who was the first one to point out the potential that four protons can combine to give four helium and energy release. This energy release was in the region of MV and that is to be compared with the electron volt energy released in atomic chemical processes. Okay. So this was potentially a very attractive source. But it was not until the 30s that Beth was able to show that there is a series of reactions that take place that can actually give rise to these uh the power production in the sun. Now as far as the age of the earth and the sun goes, uh Rutherford through his exponential decay law which is uh which uh led to dating of the earth through uranium and thorium measurements. Uranium for instance the ratio of the 235 to 238 that already gives a clue as to the you know the time scale on which these are produced because U235 decays much faster than U238 and so although initially it might have produced been produced in roughly equal numbers the present abundance of U235 is about only about 7%. So you require uh about four or five billion years u time so that this ratio gets reduced. So uh Rutherford this is a quote from Rutherford's Royal Institution lecture in 1904. I came into the room which was half dark and presently spotted Lord Kelvin. The audience realized that I was in trouble because I wanted to talk about the age of the earth which was billions of years and these views conflicted with his. To my relief, Kelvin fell fast asleep. But as I came to the important point, I saw the old bird which is referring to Kelvin sit up open an eye and a baleful glance at me. Then a sudden inspiration came and I said Lord Kelvin had limited the age of the earth provided no new source of energy was found. That prophetic utterance referred to what we uh now considering tonight radium because of course radium releases a lot of energy in alpha decay me energy. And behold the old boy beamed on me. Okay. So it was uh so anyway this refers to the source of energy not still to the uh lifetime of the earth but this is just the uh age of the earth based on uh you know the production of energy the source of energy and if radioactivity or indeed nuclear reactions as we came to know later is the source then of course uh this conclusion is has to be changed. So Edington as I said in 1920 realized that if indeed the subatomic energizing the stars is being free freely used to maintain their great furnaces it seems to bring a little it seems to bring a little nearer to fulfillment our dream of controlling this latent power for the well-being of the human race or for its suicide sort of precient statement by Edington because of course if you go the wrong way you can use nuclear bombs to kill everybody in this on this planet. So this is the same statement here. So I think I should cut that out. I should remove this. This is the same thing and how it got duplicated here. Okay. Uh I should say here duplicate duplicate. Okay, so this the basis on which of course Edington said that you can power the sun this way or stars indeed is that you have this binding energy curve which came about as a result of Aston's mass measurements. So if you have hydrogen and uh you know with the which combines to form helium then the binding energy goes up and that energy can be then released. So in fact four protons combining to give helium actually give rise to about 28 me and u so so helium should be somewhere here at about 7 7 m per nucleon binding energy. Okay so if you have protons four protons combining you had seven into four and you have 28 m roughly released. Okay, so we go back uh a bit of history of how the nuclear reactions were discovered to power the sun. Weisacer proposed the PP and CNO reactions in two papers in 37 and 38 but without any details of energy production in stars of the sun. Beth and Critfield used this reaction and they estimated the rate at which it occurs in the sun and therefore the uh the powering of the sun through this reaction. But however in the first 1939 paper of Beth uh he actually used the CNO cycle uh which was the main uh he proposed to be the main source of energy production in the star in the sun. In the second paper he mentioned this and worked out some details and uh so subsequent reactions were given equal importance at the CNO cycle. However the nutrino was absent in this reaction if you notice uh so though it is talked about later in the paper. These are the two papers these are the the two seinal papers of methane and uh uh they eventually led to a Nobel Prize for me in 1967. So the source of these uh this CNO cycle or the reactions that place in the CNO cycle are given here. Carbon interacts with hydrogen to give you nitrogen 13. Then you have uh nitrogen 13 decaying. Carbon 13 plus hydrogen giving you nitrogen 14. Nitrogen 14 plus hydrogen giving you oxygen 15. Oxygen 15 going to nitrogen 15 through beta decay. And finally nitrogen 15 going to carbon 12 plus alpha. So these are the reactions mentioned in that paper and uh here is a portrait of painting of Hansb and this is him receiving the Nobel Prize in 67. Okay. So the other reaction that was considered by him in the subsequent paper was this H+ H going to D plus E+ and the neutrino was not mentioned in that. Of course later as I said later part of that paper does mention the neutrino uh because at that time it looked as though the nutrino is not going to be detected. So perhaps he thought what the point of putting it here. Uh also if you notice the angular momentum is not conserved because this is half and half and this is one and half. So this is half integral this is integral. But anyway this is how the paper was. So the paper goes on to say that if the star core temperature is about 16 million kelvin then the PP dominates while if it is greater then the CNO cycle dominates. Uh so as we now know the stellar interior I mean this core temperature of the sun is more in this region than in the higher region. So we and also it's a early sort of generations star so that we don't have enough of CN produced. So if uh if the sun evolves it'll probably become a white dwarf when the nuclear fusion will stop and then the gravitational contraction is halted by the electron degeneracy pressure. It's a fermy dra statistics that is involved here and since it's relatively small uh it will be halted by this degeneracy. Of course, if you have heavier stars then they would uh contract till you get a neutron core. Okay. So these are the PP fusion reactions that take place. So this is so-called PP1, PP2, PP3 cycles and there is also a PP4 chain. So the PP1 chain is P plus P. This is dominant reaction that occurs. This is P plus P going to dutarium plus positron plus electron type of neutrino. Now it is indeed fortunate that this is the first reaction in this PP chain and it's uh the interaction responsible for this reaction is of course the weak interaction and since it is weak these reactions will continue to go on for a few more billion years. Had this not been the case, had this been some strong or electromagnetic interaction process such that nutrino was not there. So for instance, if the two protons actually had a bound state, two hydrogen uh two helium state, then this reaction would have proceeded very rapidly and uh you would have this star uh you could have this you know the sun die in just uh less than a day rather than so many billions of years. uh the energy release is small 420 keV. Uh the next steps are of course given here P plus D going to helium 3 plus gamma. Then the helium 3 helium 3 goes to four helium plus 2 proton. Notice that this is a reaction in which all charged particles four helium and two protons. This is a electromagnetic uh process involved here. It's radiative capture of a proton and a neutron. Uh then there is berillium 7 plus electron. This is a radiative uh so sorry this is electron capture in the nucleus which produces seven lithium and a neutrino. This is a monergetic nutrino. Um then of course you can have lithium 7 plus p going to two alpha particles. Uh this is a very high energy release. uh but then you can also have a radiative capture of on berillium 7 that can produce this uh the uh berillium 7 plus proton is an important reaction it's often referred to as the 17 reaction uh it gives rise to boron 8 and a gamma ray and then the boron 8 in turn decays to two berilmate which decays to two alphas posetron and a neutrino and the q value for this reaction is very large of the order of 18 so this produces the highest energy neutral knows in this whole process. Okay. Uh berilium 8 of course decays to dual for particles. The PP4 chain is at a 2 ppm level. Helium 3 plus proton and this is also a weak interaction process. It gives rise to a neutrino spectrum which goes all the way up to 18.8 me. There is another reaction that takes place uh in the sun which is two protons and electrons. So this is a three-body initial state but that goes to a duterron plus a neutrino and that gives rise to a monetic neutrino. So which is a 1.44 me nutrino and uh this has also probably not been observed uh because it's a very weak uh process and also it gives rise to a neutrino which is only 2% 24% of the total reactions. So this has not yet been seen. Okay. So uh the as I said the PP chain leads to uh neutrinos which are monetic 1.44 me but they have not yet been detected. Okay. So this is again the PP chain with all the percentages and so on given. uh you have this uh PP this is the dominating one that decides actually how fast the protons uh burn so to speak and uh then of course you go all the way up to uh 7 capture and then this uh reaction which is only.12%. So uh and then the boron goes into this uh so this is the PP3 PP1 PP2 PP3 chain and the PB4 is one which is very small tries to a continuum but all the way up to high energies of okay so the other the cycle that was considered by Beth initially was this so-called CNO cycle which didn't of course which he gave up in the context of the sun but it still occurs at a at a low level and indeed As we saw earlier, the borax detector has found evidence for the CNO cycle in the sun, but at a level of about 1% of the PP chain. So here you start out with uh carbon 12. Then you go to to the radiative capture by radiative capture of a proton. Go to 13 nitrogen. 13 carbon by decay and then to P gamma through 14 nitrogen. P gamma to 15 oxygen. Then again to 15 nitrogen. Of course in between you have also P gamma going to oxygen 14 and beta decaying here. So there's an alternate way of getting nitrogen 14. Then there's a beta DK which goes takes you to 15 nitrogen. Then a capture process which takes you to oxygen 16. But there are also alternative ways in which you can get there and all the way up to 18 and even 19 florine when you go to neon 20 as well. Okay. So this is uh taken from these two references uh review articles there there. Okay. So in summary, we have uh mentioned briefly our current understanding of the composition of matter and energy in the universe and we believe that we only understand really 4% of uh the total matter energy content and uh the dominant components as per our present day understanding seems to be that we don't know anything about dark matter and dark energy. there's something going on which there's more definitive evidence for dark matter as compared to dark energy. Of course, there are alternate explanations of this dark energy as well uh and also dark matter which we have just mentioned. We discuss also the need for fusion reactions to power the sun and uh we will discuss more of it in a subsequent uh couple of lectures how you measure these fusion reactions and so on. Thank you. >> [music and bell] [music]