Nucleosynthesis Fundamentals: Stellar Origins of Elements

[00:00:00][Music] just to tell you a few words about me I uh did my PhD a long time ago 2002 with Corin shonel who is a professor in University of Geneva and some of the ones of the exoplanet gang of Geneva might know her and uh Manuel forestini who who died just after my my PhD comp completion and I did this on a St Evolution modeling and in particular the transport processes that affect the uh Stell Evolution modeling and maybe I will tell you a bit more in between slides about this and uh then I engaged in a postdoc uh in Brussels at Institute of astronomy astrophysics of University Libra the brel where there their speciality is nuclear astrophysics so where I gained a great knowledge of uh some things that I'm going to present to you uh today and there I worked on aluminium 26 which was about to be uh observed by the integral uh telescope Satellite by Isa integral is a gamar ray uh spec uh satellite that was uh meant to do the first high resolution meaning this looking as a very Square histogram of spectroscopy G spectroscopy of radio nucleid which aluminium 26 is and uh then I moved to uh Paris uh and worked on um 3D uh simulations of stars and uh back to my place to where I'm from actually from to m to the great joy of my family and uh so today I'm here to I have about 3 hours uh to talk you about nuclear synthesis is so from the presentations I saw yesterday you have very diverse uh backgrounds and uh some of you might know much more than I do in uh well all of you or lots of you know much more than I do in chemistry the last time I did chemistry was a long long time ago uh we are going to talk about nuclear physics a bit and uh then I will uh try to answer or to give you some Clues on how when and when Nuit are produced so I use the word nucleates uh which is the word that we use in nuclear as physics or in nuclear synthesis meaning the basic name of atoms or bare bare atom without the electronic uh shells around and uh let's start we have three hours um I first I I before I start I have two apologies to make first I won't be here uh for the rest rest of the week unfortunately so if you have questions don't hesitate to ask them uh just after the lectures and uh you you have my email and don't hesitate to contact me if you want further material or whatever and uh the second is that I'm a bit tired so I hope my English won't be too the big question it's good that I do not have too many uh astronomy pictures uh the big question is uh where do we so as we I I think and I think that here everyone thinks the same living things so not only we but also plants bacteria and whatever come from so that's the the big question that we have been you as a human beings um asking and uh wondering about uh forever I think and uh another way to to put this question into perspective is the the way I'm going to address it is where do the elements that constitute that make living things come from and so that's what nucleosynthesis is about so nucleosynthesis is about uh nuclei that you synthesize so know how you syn synthesize the nuclei so most of you do uh lots of you do chemistry uh some of you uh work on biology and in all these cases you work more with molecules than than with atoms but uh these molecules are made of atoms and nucle synthesis is about finding out how when and where these atoms are synthesized and that's what we are going to address here so it's a broad topic that uh spans from Nuclear Physics to a galactic chemical Evolution and I I will try to Bro some Panorama hoping that uh it's not too low level or too high level and uh I I hope that uh it will uh it will give you some some clues or at least some reminders for those those of you who already know about it so the chemical elements you know them all uh they were uh organized in the 19th century by uh mandf and uh other people at the same time as always not only one super ID in super researcher but several people having the same ideas and converging into a something and so this uh periodic table of elements there are nowadays 103 elements and there are here it's here presented in its uh classical chem chemical form with the different families of elements and the elements were classified by Mandel at that time uh they had only 60 something elements at that time and uh it did uh they knew the the mass of the element and uh they uh they started e opposed to um to organize them uh as uh with Gathering their properties chemical and physical properties and uh the power of His finding and that's why we still associate his name with this table is that um he he saw a predictive power in this classification uh and uh foreseen that some elements could be discovered uh that were in the family of hydrogen for instance of or carbon or other and so from these uh elements we uh we know that uh the living Elements Living matter is made of some of these elements and all of these you know much better than I do uh and we have among the chemical known elements there are 25 which are essential to to life and six six major elements in living organisms which are the the chn or the schops things and uh it's 98% of the of the human uh of a human body so it's a lot and so we see that we have lots of oxygen lots of carbon and uh a bit of hydrogen and the other things are a bit Tracy but as some of you know much better than me they they are very uh important to life for instance phosphorus which is only 1% is very meaningful because uh it's the it's an atom that uh enters everything which is energy transfer in uh in the the cells and so it's something that we want to to look at so so the idea is that we have this table of chemical elements and uh we have these elements that we find in living things and we want to know uh where where do they come from so before we start on where do they come from uh I think it's good to uh to have a small uh intro Rory class crash course on nuclear processes and so just before I start on it I what I just would like to know because there are physicists among you but not that many so who has uh some background on nuclear physics nuclear reaction rates thermonuclear reactions okay so not that many okay so for those of you who know about it and uh do not hesitate to well I I was to say no do not hesitate to interrupt me but no do not interrupt me but uh just uh keep keep Corrections or or supplementary uh things in mind for for when we have questions so um I'm going to to talk about what's a nuclear reaction how it works because it will be fundamental to explain you how these atoms are synthesized so here what you see is a different way to organize elements uh compared to the to the periodic table this is the nuclei chart and this nuclei chart uh is a two-dimensional representation of nuclear and radioactive prop properties of all uh Atomic uh of all atoms and so uh it's a a chart that where you have in uh in the absis you have the number of neutrons n and uh the ordinates you have the number of protons Z so when you are here here at the bottom you have hydrogen and up there you have the the latest uh um the heaviest elements a color coding that is interesting in this chart is that everything that is black here the black dots are uh stable uh atoms and every and so this is called the value of stability and you may see that uh at some point for the very heavy ones you have no stable elements anymore and uh what does it mean that they are not stable it means that they will Decay radioactively at some point to go back to uh stable ones so everything that is on the each edges of the valley of stability as a um half life that might be very long but not always and in the end they will they can decay to the black ones each line represents isotopes of the same atom and you see also that the the heavier the atom the the more you have uh new um Isotopes expected for the very big ones here which are quite difficult to synthesize most of these very heavy ones are synthesized in human Laboratories they have not been observed in the universe and they have halflife times of very short ones so we don't know yet all these Isotopes so to understand the way you populate this chart and the way you go from uh one isotop to another or from one uh line to another line you need to to have some basics in in uh the the physics uh that are there so there are several ways to populate this some uh elements are built from Neutron capture which are everything that is blue here so the neutron Rich elements some elements are uh proton Rich everything that is uh reddish or magent here and then you have these very unstable elements up there and um there are several Pathways to explain the uh the formation of all these elements so the first pathway is uh the Decay radioactive decay and it involves uh some of the fundamental interactions in physics which I recall here so we have the strong force which is uh the one that uh keeps nuclei together and uh it's a force that is appears in nuclear fion and fusion and it determines the quar structure of the proton and neutron then you have the electromagnetic force which uh works with uh so this is the particle that is the driver of the force so you have the gluant for the strong force the photon for the electromagnetic force where you have uh the interaction of the the nucleus and the electrons because it's for charge particles then you have the weak force and this weak force is very interesting it's the one that appears in beta radioactivity I will come to it just after next slide and it's the force that is um allowing a proton and uh a neutron to convert into a proton which is not really a conversion but in in this way uh what you have to know is that Neutron and protons are made of the same quarks which are the even more fundamental particles and um quarks oscillate in nature they can change uh nature change flavor and color and um the thing is that uh in order to build up a proton you you have to exchange a boson W most of them are Z boson and um and this will uh allow you from a neutron to produce a proton and emit a anti neutrino and an electron and then you have of course gravitation which is the force with the largest uh uh scale of action and which uh which explains uh most of the architecture of our universe and the particle for gravitation is not yet found um so the nuclear processes that we have in this uh chart of nuclei so we have the stable nuclei and then outside the valley we have spontanous Decay radioactive decay and there are various uh types of radioactive decay there's the alpha decay uh which is a strong interaction meaning that your your nuclear will split and they won't split in whatever manner they will just emit an alpha particle so an alpha particle is a bare nucleus nucleus of ilium so this is the strong Decay it's alpha alpha decay then you have the weak interaction which is the beta Decay which is the normal radioactive uh reactions that you know know of in this process there's a weak interaction because you have a conversion of a neutron into a proton and an ele um uh so as you as I just show you when this uh appears this happens due to the reorganization of the quarks within the the particles you will emit a n an anti- neutrino or neutrino depending on if it's beta Plus or beta minus and an electron and so this is the weak interaction and there's another one which is the gamma Decay this will happen a bit like uh when you have uh an emission of uh in in a spectrum where you look at uh spect uh emission lines in a spectrum which correspond to a change of energy uh in uh in the electronic shells here it's uh you have a a nuclei a nucleus that is in an excited U energy level and that will Decay but the entire nuclei it's not not uh an electron changing orbit it's the nuclei that decays and it will emit a photon and this is electromagnetic interaction so now we see that in the chart that we add before which is here again we can uh read this chart in another way so here you have the line with uh equal number of protons and neutrons and you see that beta minus Decay will uh may have the the nuclei go to the value of stability with decreasing proton neutron number um beta plus Decay will uh lead you to the value of stability with uh decreasing proton number uh and alpha decay so uh this one of emitting particles is the radioactivity that involves the very heavy elements that go down move down uh in Neutron and proton numbers and so to move from one element to another yeah if you go up you capture a proton if you go left uh uh right sorry the other left if you go right you capture a neutron and if you uh follow the the diagonal the diagonal here you capture a alpha particle so now that we have an idea of these elements uh in addition to radioactivity that helps you populate this chart for the stable elements um what uh what synthesized is uh them is thermonuclear reactions so the elements can be um classified according to their binding energy so The Binding binding energy is uh the energy uh that was uh it's a negative energy because it's not an energy that the atom possess but it's the one that uh the atom uh that you need to uh bring to the atom to to cut it to break it and so it's made of uh the number the so the mass default so you recognize all the the equation of Einstein so it's the number of uh neutrons times the mass of the neutron plus the number of protons times the mass of the proton plus the mass of the entire nucleus and this means that in a in a nucleus it's not the a nucleus is its mass and energy because of this relation is not only the sum of the mass or energy of each of the constituents but it's something more this was found out by by Einstein and gave up this idea of the mass defect if you uh if you want to classify these binding energies uh depending on the mass number which is the sum of protons and neutrons inside the nucleus you can bring you have this which is an absolute value because the binding energy is negative normally and um it's given here in energies which uh is uh done a lot in astrophysics so the mass of an electron because of the equivalence between mass and energy it can be expressed in electron volts so in an energetic uh uh unit so it's 0 511 Mega electron volt and you have here The Binding energies of the nuclei so you can compare them it goes up to 8 8.8 for the for the iron and what you see is that this curve is not whatever there's a pattern in this curve you have Light Elements hydrogen here with a low binding energy and this will help uh make it quickly in history of universe then you have I uh helium which has a very high binding energy and we will come to it uh later and then you have just increasing binding energies up to the iron group uh in this uh elements you have a kind of what is uh uh you have um an equilibrium a kind of um um maximum of uh bindingness so this elements are very mostly tightly bound and the other ones are not that tightly bound because then you have uh they are too heavy and uh and it's difficult for them to to be stable and so you have a curve that divides into two parts one part which is with increasing binding energy and another one which is with decreasing binding energy in terms of nuclear thermonuclear reactions it means that to build to synthesize elements from hydrogen to iron there will be you will have to pile up uh small Elements which is called fusion and on the contrary to build these ones it will be built this part of the of the elements is built backwards meaning that you build from seeds you increase the number of neutrons in these elements but then they are not tightly bound and very easily destroyed in particular with radioactivity and you will have nuclear fishion okay and in both cases you will emit energy and that's what we we are going to to look at and how we traced them actually there will be a few slides with some uh equations but uh do not worry there are not that many and I think I I decided to show them because I think it's a bit important for you to have a good picture on how nucleosynthesis Works to have a good understanding so first of all because I know we all come from different communities and notations can be something quite tricky as vocabulary not using the same words to talk about the same things uh it even happens within astrophysics classical astrophysics so a nuclear reaction can be noted as a a chemical reaction this way and so these are this is the target nucleus this is the projectiles this is the door water nuclear and these are the particle the um additional particle that that are emitted in the process and it can also be noted this way so x a yielding Y and B okay uh and this notation you will see in other slides so when you have a thermonuclear reaction you must uh comply to the lws of physics and in particular you will have conservation of charge and barion number numers and so charge is noted Z so the sum of the charge of the two elements uh implied in the involved in the nuclear reaction is the same before and after the reaction and it's the same for the barion numbers and you also have conservation of energy and here you have the energy a bit like we talked about before you have the energy of uh each of the of the elements in the nuclear reaction and you also have these additional energies which are the energies in the center of mass of kinetic energy because as you have um moving particles you have to find um a framework within uh which you can describe the movements and so this is the center of mass uh framework that we use in in nuclear physics the energy that is produced by a nuclear reaction be it fion or Fusion is called the the Q value and the Q value is the difference between the masses of the mass energy of the uh particles that interact in first and with the mass energies of the particles that are formed that are synthesized and you see that this Q value as you have a sum here uh with uh something uh and something substracted might be positive or negative so so when the Q value is negative this happens for nuclei that are heavier than iron so the ones here you it means that instead of producing energy you have a negative production so you consume energy this is called endothermic reactions and this explains why you cannot fuse elements because each time you want to combine them instead of making energy you consume energy so in this part for this nuclei you will only have fishion on the other part here which is the one that uh we are will be more interested in because this is the way we build up these elements you have exothermic reactions meaning that when you have a thermonuclear reaction between two elements that have a a mass comprised between hydrogen and iron it will release energy and uh this is very important for Stellar physics and in general because this is why and I will go back to it uh later this is how Stars uh make energies and radiate now that we have these Clues the thing is that what we want to know is uh how uh elements are built and to build an element you need to uh have both of them so the projectile and the target to collide at some point okay so we can do this in coll ERS but it also we can also look theoretically how it works when you Collide this um these elements in a reaction that involves a a particle a and a Target nucleus X you will produce an amount of energy uh and this amount of energy is equal to uh the the amount of energy that you that you liberate the nuclear reaction rate meaning the number of reactions per second and per per unit volume that happens divided because this is a specific uh energy production rate by the density of the medium okay uh as you will see I will drop the the product of the nuclear reaction because normally if you have two particles interacting a proton and a carbon 12 for instance you can only make one the outcome is just one one specific nuclei so we normally drop the Y that's why it's here and so the reaction rate depends on the number density of course of particles a and X their relative velocity and the cross-section of the reaction which is called Sigma and this is a nuclear reaction rate and this is what we try to understand and characterize and what explains the synthesis of all the elements in the mandal of table and so the reaction rate is the number of reactions per nucleus per Target nucleus per unit time divided by the number of incident particles so particles a per surface unit and time unit and this reaction rate is often refer to as the mean value of the Velocity so the sigma V here uh times the avagadro number and so this is what we in nuclear astrophysics call a nuclear reaction rate so what we want to do is how this behaves in terms of energies temperatures and uh nuclei why do we care about this because this will uh tell us how we can build up the different elements so in a classical framework when you want to do a nuclear reaction to occur the energy of the projectile must exit the barrier which is uh due to the Electro magnetic force in order for the projectile to fall into The Well of the strong interaction within the new the the the target nucleus in order to make a new nucleus and so this was uh known early in early 20th century but there was a problem and the problem was that for a proton proton reaction which you could say it should be the easiest one because you just have two protons that need to be put together uh we we realize that due to the high colum barrier of the protons uh it would require temperatures that are above uh a billion uh Kelvin and billion Kelvin is very difficult to to attain and so if this would be the only way to synthesize uh elements uh we won't have any elements complex elements in the universe because this is very there are very few environments in the universe that attain such high temperatures so there's something else and this something else was understood quite rapidly uh with quantum mechanics and this something else was first hypothesized by gamov in 1928 and gamov said that um according to uh to quantum mechanics and to the wave form of the atoms of the particles uh there's a non-null probability that the projectile actually tunnels through the colum barrier to interact with the nucleus and so it will tunnel make a composite nucleus and then the the daughter nuclear of the nuclear reaction and so it's kind of the Magics of uh of nature that to build everything that we are here we need to have these very very tiny probabilities to happen and this is Possible only because we have so many uh particles in the universe and some places where there are very high temperatures that give uh enough energy for for the tunneling to upen to happen so the energy that maximizes the probability for this intera for the tunnel effect is called the gam of window and the gam of window I will show you here in this plot that shows you energy uh probability of interaction as a function of energy and you see that the gam of window is uh the interaction between the distribution of particles energy distribution of normal matter particles which is the max well boltman uh distribution which goes as energy uh divided by kinetic thermal energy KT and here the colum barrier which has this uh form and the way the place where both uh tails of distributions interact is the energy that maximizes the probability of a nuclear reaction and uh another way to show it here is just for carbon uh involving uh nuclear reactions and we will come to it later do not worry if you don't understand this graph now uh if you plot the density uh and temperature in this view graph you can uh you can locate the the places where you the gamma of range is uh is reached for proton capture on carbon 12 proton capture on carbon 13 uh alpha particle capture on carbon 12 and two carbon 12 nuclei interacting and what we see is that you it requires higher and higher energies for this to happen because the colum barrier are higher and higher and uh so this means that it cannot happen everywhere at once and uh we can identify the locations the where these kind of nuclear nuclear reactions happen so to finish and wrap up on thermonuclear reactions uh I have a last thing to talk about which is non-resonant and resonant reactions so nuclear reaction can be a non-resonant one meaning that you you have a Target nuclear nuclear so a projectile and the projectile will uh be uh will enter the colum barrier directly and uh fits directly within the lower energy level of the target nucleus so this is a direct capter capture and it leads when you when you want to uh plot the cross-section of the reaction in terms of energy it leads to this kind of of me of uh of curve here so and uh which is uh which scales something like a square root of energy and uh what is shown in this uh image is that you have several orders of magnitudes in energy and that in nuclear physics Laboratories experiments accelerators you can directly measure these kind of reactions but it's very difficult to go to the energies that are the ones that have the gam of energy and so there's a a great work to do to extrapolate so you need measurements theoretical computations of quantum physics to extrapolate on the nuclear reaction rates that are actually meaningful for astrophysics and then you see that in this curve you also have these kind of spiky things and these spikes are due to non to resonant nuclear reactions and you will you will understand in a in a few minutes uh why I talk about this this even though it might seem very technical to you it's it's a bit important because it's due to a resonance that uh we understand the formation of uh heavy elements so these resonant reactions they happen when the energy of the incident particle corresponds to a difference between two levels of energy in the Target nucleus so the probability is not that big but then in this in the the way it's schematized here you have the projectile on the target Target and it makes a comp compound nucleus which is unstable and uh this you will have the uh gamma gamma Decay that I talked about before you you make this element normally the notation is for instance if it's carbon 12 it will be carbon 12 with a star meaning that it's excited and then it will Decay to a final state which is the compound nucleus and so in this way in this uh place as you see you have the spikes here meaning that the when you have a resonance the you have a magnification uh by several orders of magnitude of the probability of interaction between these two species a and x and so this when you have a resonance the non-resonant uh reaction rate is uh is really uh orders of magnitude below so resonances are very important because they can change completely the yield of your nuclear reactions you may have a nuclear reactions that in normal nonresonant uh conditions appears to be uh to be very um how would you would we say not very efficient but then if you have a resonance at a certain energy the the target nuclear and projectile nuclear at certain energies you may amplify uh the the reaction rate you have understood that uh we to do to build up the stable nuclei we go through thero thermonuclear reactions there are two ways to do it fusion and fishion and uh in Fusion reactions uh we build these uh cross-sections that I talked about these cross-sections depend on energy they have a specific form mathematical form that I didn't show and uh what you might expect from what I uh told you about the tunel effect and everything is that this um nuclear reaction rate drops enormously when your colum barrier increases because it's very difficult to overcome the colum barrier and so the probability that you actually tunnel is very low so the reaction rates they are very different comparing to the coolum barrier and so comparing to to the initial mass of the nuclear the other thing that I uh that is important is that the the nuclear reactions crosssections they depend very uh highly on temperature and this is very important because this means that thermonuclear Fusion reactions of hydrogen and carbon for instance they will occur at very different temperature why why is it so so this is related to overcome the barer you need more energy for the particle and to have more energy you need a hotter medium normally it also depends on density of the medium but in a much less uh uh important way so that's why normally it's overlooked the density uh dependence even though in proper thermonuclear fusion reaction computations you include of course the the dependence on on density and the thing is that as they occur at very different temperature these nuclear reactions do not occur at the same time and this is very important because as you will see later uh this morning um this explains Stellar Evolution actually only this purely Nuclear Physics facts here you have some uh uh values of uh the the the types of types of nuclear fusion reactions so proton proton proton capture on nitrogen 14 alpha particle Capt capture on uh carbon 12 and uh uh an interaction between two nuclear of oxygen and uh what you see here is that the dependence in temperature is the highest when you go to heavier elements you see that it's to the power 182 depending on the temperature and here you have the the height of the colum colum barrier that you have to overcome of course for proton proton the colum barrier you have to overcome is the mass of the electron is the one shielding uh but if you have heavy nuclear you have lots of electrons and so you have to overcome a larger barrier even though within Stars I talk about the electrons but as you all know uh when the when the gas is very hot it becomes a plasma and you all know very well about it and so in the plasma the electrons are not around the nuclei anymore so that's what we have Stars we have this these plasmas but the electrons are here around the the electrons and they contribute to the nuclear reactions through something that we called shielding and so they also act as if they were around the nuclear even though they are not around their proper nuclear anymore let so now back to these elements so now uh what if we go back to these elements we have uh talked about basic of of nuclear physics so we know that the Light Elements up to iron everything here is built by Fusion that everything here is built by fishion and that uh considering the different isotopes they are built by uh beta Decay or alpha decay okay so now you know how they are organized everything so this is the origin but now we want to know how and where we know how it happens we want to know when and where it happens now and there's a color code in this uh in this uh periodic table and we will come to it later for you to you will have the color code later uh but it corresponds actually to when and where this happens so to to address these questions of where and where this happens the first thing that we have to do is to measure the abundances of all these elements and uh we can measure them in the Earth crust we can measure them in whatever actually if we have a spec spectroscop spectroscopy you can do it with all kind of things and um to to know the origin of elements what we want to know is how these elements now that we have identified them how they uh distribute in the universe and so it's a big task to know how they distribute in the universe as a whole so to as a starter we will look at how they distribute in the sun it's the first thing or in the solar system and um and then there will be an hypothesis to uh go from this to what we call the cosmic abundances so the cosmic abundances uh they refer to the chemical composition of the Sun and solar neighborhood and this chemical composition of the sun it is um determined through uh two ways spectroscopy um uh so Inu spectroscopy or in analysis chemical analysis of the contes uh which you have here and here you have a a small uh cartoon of the Proto PL Proto Sun Proto solar nebula I think we you all more or less all know about it uh so and there that's so I'm sorry I'm very bad that name so I don't remember but I know that there's someone working two at least two or three people working on the Jets and on uh looking at uh the elements that you can find in protoplanetary discs as so you might have uh remembered better than me who I'm talking about and so you you can go to them for more information but here what you have is a cartoon of what should have been the Proto Sun here surrounded by a surrounded by a dis of of uh gas and uh dust within which these uh cones uh were formed and they've been preserved since then not completely preserved because they are since then been exposed to uh radiation of the Sun and part cosmic ray particles attacks and things so it's not that easy to to say that what you measure on this uh on this uh cont is exactly what was the when the sun formed 4.6 billion years ago but it's it's a good match and the contes are very interesting because from them you can have isotopic uh abundances which is not the case uh directly from the spectroscopy and the spectroscopy is the one of the analyzis of the Photosphere of the Sun so the Photosphere is the the part that gives you uh from which light escapes and here you have um a FR Alpha uh spectrum of the Sun from dating back to 1840 uh and you see here the plank function of energy distribution and here you see the Spectrum and the elements that have been identified so each of these uh lines correspond to a transition into uh the um for atoms energy levels and uh you see that you have absorptions lines which is the parts where you have less like light coming and so we do spectroscopy of the Photosphere to determine most of the elements some of the elements are difficult to catch in the in the Photosphere and so we measure them like neon in the corona of the sun uh but more or less with both techniques uh we are able to uh put up something that is uh called Cosmic abundances so we have the for the sun we do like this for stars other than the sun we will do chemical analysis mainly through spec exclusively I would say uh but not not not that much but through spectroscopy or spectr photometry of all the stars but also nebula and external galaxies and for the neor stars and the interstellar medium uh we see that we have a similar abundance distribution and than the solar system uh even the it's a relative distribution but that's a solar scaling to be to be applied meaning that so let me introduce because here uh I I have this notation for the first time and uh I didn't uh specify so if I go back sorry I do a small parenthesis but it's for you to understand if I go back here this is a chemist or normal uh periodic table an astrophysics astrophysicist table uh would be uh hydrogen would be named X ilium would be named Y and everything else is named z so X and X+ y + z equals 1 so x y and z are mass fractions of the total mass of the bionic matter and uh X is the mass fraction of hydrogen Y is the mass fraction of helium and Z is was what we call the mass fraction of metals so you for sure all of these are have not do not have chemical properties of or physical properties of metals but in astrophysics that's how we call them so Z is what we also called the metallicity which is the amount of heavy elements okay why do we do this uh you will see it in two slides so we have variations of the amount of heavy elements compared to the amount of hydrogen in all the stars uh and uh but but we have something which is a relative distribution which is the same which brings us to this assumption that the local abundances something is happening in the bird's world uh that the local abundances are referred to as Cosmic abundances you know so we we went we moved from a earth Centric system of philosopical view of the universe but uh but not always and sometimes it's it's still a it's still a useful to to bring everything back to us and to the Sun and uh so that's what what we get for the Sun and what you would get with amounts that are different but the relative uh abundances are like this so here you have the relative abundances in a very strange scale that only astrophysicists use uh which is uh we we use a scaling uh of an amount of a million atoms of silicon this is the zero of the scale and so it's here and uh and then you compare everything else to the amounts of atoms of silicon and so you see that hydrogen is up there at 12 in log scale so it's a six orders of magnitudes more abundant than silicon and you see a very specific pattern in these Cosmic abundances which is what we want to explain with what we call the nucleosynthesis meaning why do we have so much hydrogen why do we have so few lithium berilian and Boron uh why do we have a peak here this you know already these are the more tightly bound uh nuclei and so we have a nuclear statistic equilibrium that favors the the accumulation of this uh these uh these elements because they are the end point of both thermonuclear fusion and ficient okay so you have an accumulation here and you see you have other accumulations here around strum and another one around uh around lead which are the end products the mean end products of very heavy elements fishion when we compare the abundances of all these elements found in the Solar Photosphere compared to what is found in conres it's very satisfactory it's very nice to see that you have a beautiful Feit of one to one you can forget about these ones we don't forget about these ones because this as you see these are the the ones that you are interested in in asob exobiology astrobiology carbon nitrogen oxygen hydrogen they are all here but for all the other ones we have a very nice uh line so the the discrepancies between both are interpreted in terms of the evolution of the solar system and of the sun itself so lithium is lower in the sun because it is destroyed in the Sun by nuclear reactions captures of protons on lithium 7 which is the most abundant but even though it's the most abundant look at here the lithium is 10 orders of magnitude less abundant than hydrogen and for the other ones we see that they are uh more abundant in uh in the Solar Photosphere and it's because uh in the sun environment these are Vol volatiles and so they were lost from meteorites when when the meteorit formed so that's how we explain the discrepancies but they are very informative actually these discrepancies are very informative of the physical conditions that rained when the star when the sun and the planetesimal and and dust were formed in the early history of the solar system so what we see is that in the end in the sun we have this and uh in the early days of uh of uh of the universe and I will come to it uh ear uh just in a few seconds we had we came from abundances that can be estimated uh through uh the study of uh the the further oldest light in the universe which is the one of the cosmic wave Cosmic microwave background and models uh we have 75% of hydrogen 25% of ilium and no Metals so now you know what Z is so nothing heavier actually there are traces of heavier things but there are really traces and uh when we look at the solar system meaning at something that was built uh so 9 uh 9.4 9.4 yeah something like this a billion years after the the beginning of the clock after we we start the clock which is the model of the Big Bang we have much more elements even though all these elements they only constitute something that less than 2% of the of the matter so it's very very very small but it's a very small part that is very important of of UT utmost importance for us so there's been something here and there something between the early universe and now is stars stars have happened stars have lived and died so stars because there are biologists here stars do not live and die as you may know they're not living things but we always use these words as we use uh hydrogen burning instead of hydrogen Fusion even though there's no burning it's actual thermonuclear Fusion so just to make clear so what we call a life of a star is the part of the star uh the part of its uh lifetime when uh the energy is uh produced by nuclear reactor ctions okay and what we call the death of a star is then either you do not have any Star left anymore the star is not left anymore is destroyed or the star is maintained but not by nuclear reactions something else maintains the star and these are dead stars not Death Star but dead stars and so we are going to see now what uh how we go from one to uh the other so now I show you again this periodic table you will see it again twice or I guess so I guess by the end of of the morning you will you will have it imprinted in your mind if you do not sleep and so uh the colors correspond to the nuclear nucleosynthesis sites so the origin of the elements and let's let's start going into what what we I was meant to explain to you but I think uh all the introductory part will help you understand what we are going to discuss now they have different sources and um how we know this is that the abundances uh allow us to infer the physical conditions of the Productions of the nuclei because we know nuclear physics and so we know that for the synthesis to happen we need temperature in particular temperature and density conditions that are specific and so to this we are able to trace the places where these physical conditions are met and so there are not that many places there's the big bang nucleosynthesis and we will come to it so this is what we call the primordial nucleosynthesis or BBN for Big B nucle synthesis uh this uh is responsible for the majority of bionic matter meaning hydrogen and helium and a bit of lith then you have Stellar nucleosynthesis which is everything which is uh here around the green the green things and the yeah the green things let's say and uh you also have explosive nule nucleosynthesis where you have Neutron captures and beta disintegration for the verye heavy elements and you see that you have different ways of for a Star to die and uh as the star dies you may have very energetic uh events and these events will uh bring very heavy elements so Stars can explode uh different living stars or dead stars can explode and they can also merge and um and this is new science uh that is very active field these days and so you see that in the end uh if we refer to uh what Carl Sagen say in his uh in in his program I don't know if it was radio or TV program when he first said the word that we were Stardust it's actually true we are mostly Stardust Stardust and uh a bit of even big Bish dust for the hydrogen so all the elements that make everything we see here uh came from a star or from the from the early universe so now in the following I will uh just uh show you what are the reactions and what happens in these different uh sites so the Big Bang Theory is the current theory uh that we have to explain the evolution of universe it's a theory that goes backround that allows us to go backr in time go back in time so the modern cosmology uh was founded in the early in the yeah first part of the 20th century and it realized on two main principles the first one is general relativity that was proposed by Einstein in uh in uh the early uh 19 uh 20 something uh after the the first uh of not 20 maybe 1913 uh the specific relativity was published in 1905 and uh and then from this spe special relativity out of which the uh the equation of equivalence between matter energy came out he uh just uh dug more into this uh this um physical uh lows and came out with a general relativity and what what does general relativity tell us it tells us that space and time are intertwined as energy and matter are intertwined they are related to each other and both of them are related so space and time and energy matter are related and uh this makes general relativity a general generalization of the theory of gravitation so we you you have a Newtonian uh Newtonian gravitation is em embedded within the general relativity and then as you go to high energy you you come up and so to uh to the universe as a whole you come up with this kind of relations the other principle that we have uh for cosm for The Big Bang Theory is the cosmological principle uh stating that uh the distribution of matter energy in the universe is homogeneous and isotropic and uh leading to something which is this hypothesis saying that matter is uniformly distributed at large scales I think it's a sdss survey or I don't remember which survey so it's a deep survey what we call Deep survey so we look at uh the univer at the sky uh with a very long poses and we try to make a cartography of uh of the matter Galaxy clusters of galaxies in very deep uh deep observations and what you don't see is that it's more or less uniform you have fluctuations and there are some voids some Cosmic voids they exist but there are not that many and uh the um the cosmological principle is seems to be uh more or less okay so considering or considering both of these hypothesis and in particular if you apply the theory of gravitation as described by general relativity to a universe that obeys the cosmological principle so that is homogeneous and isotropic distribution of matter and energy this yields to a nonstatic geometry G Tre sorry so geometry for space time and uh this nonstatic geometry for SpaceTime um tells us that there's a scaling factor that affects this distances between fixed points meaning that when you go back in time all the all the points were closer together and uh in a in a universe that was denser and that's how you come out with a Big Bang Theory so nothing exploded at no moment but it's just that uh if you look at the conditions of the universe now days and you apply this you can just uh go back in time in your movie movie and it means that at some point the universe was very small very dense and very hot okay uh this Theory uh is is not the only Theory and it's important for you as a young scientists I think you are all convinced but uh these are only theories uh that are right until they are proven to be wrong uh as it has been the case for many theories um uh sometimes they are not fully wrong they are just uh wrong changing perspectives uh and still work as newtonan gravity still works for our nowadays life uh everyday life but still um The Big Bang Theory is with um some additions which are inflation times which is a a moment in in the universe in the very early Universe where the universe must have expanded very quickly in order to explain the structures and temperatures that we observe it's the theory that is validated by most of observables almost all observables uh there are other alternative theories uh which imply uh uh cords uh and uh these strings cosmic strings and things like this but uh they are not today uh valid ated by as many observables as The Big Bang Theory is okay um within this Big Bang Theory the mattera density determines the geometry of the universe and it controls its time Evolution and um a point important point also uh of this is that uh of course this allows us to check the temperature and matter density in the early Universe uh last thing to say The Big Bang Theory is our best Theory to understand how the universe evolved and where we come from if we have the big question of where we come from not as living things but as a as an environment it's the Big Bang Theory but yet this Big Bang Theory as a something which is it's not a failure but a weakness or not a weakness but yeah more or less is that it explains very well uh only 0.4% of our universe which is is bionic matter and all the rest is what we called Dark Matter or dark energy and dark energy which are things we don't know what they are actually and uh it's the the work of particle physicists uh that to to to understand this but uh just for you to it's always quite amazing to to know that we have a perfect Theory to understand the matter as we know it the bionic matter but this bionic matter and what we know and what we are made of is a very tiny little super tiny little bit of the entire universe and uh most of the universe which is dark energy we do not understand how it works or what it is even so it's it it's still a very big question so within this Big Bang Theory uh it was proposed uh in the early uh 19th uh 20th century and uh then validated and so this is what I was talking about this theory is the the one that we have adopted because it's validated it made lots of predictions and these predictions have been validated and the last validation was in 2015 wasn't it yes with the gravitational waves uh measurement events that we actually measured and that were also a prediction of the general relativity and the Big Bang Theory so there are three confirmation observational confirmations of the model the first first one is uh was made by Edwin oble in 1929 when uh at mont mont Wilson Observatory he was observing uh galaxies distant galaxies which were not actually known as to be distant galaxies but there were distant structures and uh looking at them uh measuring uh with with spectroscopy and measuring velocities dispersion velocities and he found out that the further objects were at greater velocities and that the Universe was expanding as was predicted by The Big Bang Theory so this was the first observational proof of Big Bang Theory then came the second one and we will come back to it just after uh but let's go chronologically in 1948 these three guys so uh Alpha Beta and G you I already talked about gamov in for for the for the nuclear reactions so this guy this guys will show up in many uh many other papers fundamental papers they uh came up with this letter to the editor which I cropped here but it's not it's just one page it's very short paper it's a bit like the Einstein's paper it's four pages and it changes physics and here it's one page and it changes to understanding or of uh of nuclear synthesis and they uh proposed uh that um various nuclear species must have uh originated not as a result of an equilibrium corresponding to a certain temperature and density but rather as a consequence of continuous building up process arrested by a rapid expansion and cooling of the primordial matter okay so they refer to this big Bank Theory where the universe is very dense and hot and there a moment where it evolves to less dense and cooler it cools down and they find that there's a tiny bit of window where you can build up the first elements the lighter elements and then the third and so I I I should now ask add the 2015 uh measurement of gravitational wave signal but the third historical uh observational confirmation to the big theory is the discovery of the cosmic macrowave background uh which has a temperature of 2.73 Kelvin by penas and Wilson they um they were using these telescopes you know the the radio telescopes that are a bit like a I don't know doesn't look like a telescope at all it looks like just tiny bits of uh of of of uh I don't know how to say it actually in English it's my sorry antennas big yeah no there were not big antennas if you look at it it's just like the things you used you used to to put your your your clothes to to dry you know your hanging strings it's something like this and actually they didn't believe the their their measurement what they found is that they were doing observations and there was a signal they couldn't get rid of and and uh every measurement they did there was always this signal pointing to this specific temperatures please comment and um and they checked on birds nests and everything and finally they they came out with abet maybe it's something related to the big buang and uh it's actually the the oldest light that we can measure it's so this Cosmic microwave background for those of you who don't know is um the light that was emitted and that confirms the cosmological principle so the universe is dense and hot and as the universe is very dense at this moment um nuclei and photons are intertwined meaning that the universe is fully opaque photons cannot Escape matter and at some point because the universe is expanding and cooling uh that's the decoupling between matter and light and so the first light is emitted this is also by the way our kind of our Horizon we will not be able to observe Beyond this because there's no observable to us um and then this light emitted just uh kept on propagating and we still observe it and we see the cooling down of the universe and now it's it's not that that far away from the absolute zero so it's 2.73 and when you trace the the curve of energy has a function of um of uh wavelength so the the plank radiation uh it's a perfect black body it's the best black body we have we we are not able to build black bodies that are as good as this one and where the the the the weight of the the line weight is uh is uh even larger of the order of the arrow bar that we have on on the measurement so it's a very beautiful physical experiment with this CMB and so this CMB shows that the Universe was dense and hot once everything shows that the Universe was dense and hot once and then came the Big Bang nuclear synthesis so let's go to it to show you the uh thermal history of the universe here I took this uh this view graph from an old paper by pel uh which is a who who is or was maybe maybe it was um a specialist of um galacy Galaxy Evolution also cosmology did lots of things as many of the astrophysicists in back in the 1950s and here you have the time after the big bang so uh do not pay attention to the linear scale it's not linear at all as you may see 10 to Theus 40 second this is the plank era so the plank era is the time at which we are able to start counting time as you know because of uh the Eisenberg uh uh principle we not measure we cannot we are not able to go past this uh this barrier and to measure times before so there's no before but uh here we start counting the counting the time and uh it's 10 Theus 40 seconds the inflation uh that I talked you uh talked about which is uh something that was added to the first Big Bang model uh happens very quickly here and um you see that in these very early days you are able to uh to build the first forces fundamental forces the electro week and you build quarks also and the nucleosynthesis uh so the moment when you have all the building blocks for matter uh only happens only happens one second after the Big B B after we start the clock and so 1 second after the big bang the temperature is of about 10 10 billion kin so very high and at such temperatures dyum nuclei can be formed by a combination of a proton and a neutron because here we are already in the phase where quarks uh combined together into protons and neutrons uh but it cannot survive because the energy of the medium is larger than the binding energy of the theum so you form it and you destroy it you form it and you destroy it and you can note it as a as a as as this you have kind of an equilibrium proton and neutrons uh give uh birth to uh dyum and Photon uh which uh the duum immediately is split into proton and Newtons and this Ts for this uh goes on for 2 seconds and uh in these two seconds the temperature as you see here has dropped quite dramatically one order of magnitude in 2 seconds which is quite a lot because the universe is expanding very fast and then as you go to 1 billion K which is you remember the the the temperature that I talked about to uh to overcome the to have a classical nuclear reaction so if you want to build a hydrogen without having to to build buil at duum without having to Tunnel okay without tunneling this happened in the early universe and then the synthesis of dyum becomes efficient meaning that when you build a dyum it's not split again because the binding energy of the medium is The Binding energy of uh dyum is now higher than the energy available in the medium and so this is the starting point of the Big Bang nucleo synthesis so the Big Bang nucleos synthesis is building protons and putting a proton and a neutron together to build so the Isotopes of hydrogen other reactions so you are here you have a a neutron that is um put together with a proton first you have neutrons neutrons uh uh they have this beta Decay that I talked about earlier so beta plus decay and so they uh they Decay emitting electrons and anti-inos and you start to have protons once you have these protons they are still still embedded in a soup of neutrons they are also capable of capturing neutrons which makes dyum this dyum is now embedded in a soup where there's dyum but also protons and neutrons and so there are several way Pathways for it to to evolve the duum can capture a proton which will uh yield ilium 3 and uh a gamma and a photon uh it can also uh capture another D another dyum atom and this will also this will lead to trium or to ilium 3 depending on what particle is emitted also with the daughter so either it's a neutron or a proton so you build up ilium 3 and trium and again capturing dyum particles will yield ilium 4 um and this ilium 4 will be captured on ilium 3 which will make berum 7 which is unstable it will Decay into um it will capture a neutron and go into lithium 7 and the lithium 7 will capture a proton and go back to ilium 4 so what you see is that you build hydrogen these are the main products the different isotopes of hydrogen and you also built essentially ilium for because the other forms that you build in in particular ilium 3 is destroyed by duum capture to make ilium 4 so these are the main products of the big bang nucleosynthesis and so this is important because if we look at if we look at this we we only have a solution for what how we build the X and Y blocks that I talked about on the astrophysical periodic table you know and we don't have the Z and so now you understand why we don't have the Z actually very new computations show that you have a bit of you have tiny bits of lithium just 10 orders of magnitude less than the the other ones and you have even tinier tinier bits of carbon some isotopes of carbon that can also be built in these conditions these are the latest results but still it's 20 or 30 orders of magnitude less than hydrogen and helium so that's why we say that uh big bang nucleos synthesis is all about the X and Y so what's the problem of this big bang nucleosynthesis it's exactly that it stops at Helium essentially and you don't build something else so why does it stop at ilium and why is it the main product it's the main product because according to everything I said earlier this morning and what we know about nuclei it's Bing energy you see it here is the largest among the lightest element the Light Elements which are here everything that is lighter than carbon ilium is by far the the most bound and also as you see it's in a peak so it's not the higher because it's uh it's in a Mon Mon Mon tally okay well it's increasing all just in a row but it also decreases again before it increases so it's also the nule the the nuclei around which are lithium and uh ilium 3 and hydrogen they have lower banding energy meaning that it's easier to uh for them to capture particles and make ilium for so helium for will be the end product of this nuclear synthesis the other point which was a a problem for a while until the 50s and we will come to it later is that when you go to the nuclear chart here that I put so here it's the bottom of the nuclear chart you have all the Isotopes of hydrogen helium lithium burum Boron and carbon and if you go to the the value of stability here you see that you have um stable isotopes with uh Mass uh atomic number one 2 3 4 but there's nothing at five the lithium 5 is unstable it doesn't remain and uh again you have something at uh six but nothing at eight so you have here kind of nuclear barriers that uh that uh yield the the the following thing is that if you have processes that build up new nuclei with atomic masses uh five and8 they won't stay here so you have kind of a barrier if you cannot go past eight how can you go to uh the heavy elements that's the problem okay because it nothing is stable here so and we will come to it later and it's a stellar nucleosynthesis uh that that can uh can explain this and how we build this ones despite the fact that there's a a huge bar barrier here that explains that during the big Bank there was no heavier element built and so so this I will just finish on the Big Bang uh nuclear synthesis so the AA element are also produced but in small amounts due to their higher column barrier so here are some view graphs there are lots of uh curves uh do not worry if you can't read everything but as you see there are some carbon here and nitrogen so here are the all the isotopes of carbon and nitrogen uh that can be produced according to models of big bang nucleosynthesis uh in a few minutes you see here the time in terms of seconds but here you have the mass fraction of these elements and you see that it's lower it's 10us 15 to 10us 30 so there there are really more than traces and they are included but uh in fact they do do not really play a big role the ones that the main outcomes of nucleo St Big Bang nucleos synthesis are hydrogen here in red uh and uh the its uh its Isotopes the dyum and Trum and ilium ilium 3 and ilium 4 and some traces of the lithium ones and you see that everything happens within uh some minutes because you have this Peck and then as you see all the curves get flat and why do they get flat it's because now the universe has cooled down a lot and uh you cannot you do not have stable elements heavier elements so it's very difficult to overcome the the the colon barriers and uh and the density has dropped a lot also and so nothing moves anymore and so you have to wait for stars to happen to go beyond uh this so we will uh finish with this and have a small break um so this is the result of big bang nucleosynthesis and so it's uh this is the validation of the of the Big Bang nucleosynthesis or the way the Big Bang nucleosynthesis validates the Big Bang model so what you see here in this plots uh here what is uh shown is the number of barant per photo which is called ITA in uh in cosmology so it's a fraction of number of varant depending on the number of functions and the bionic density of the universe which is here noted uh Omega beta H2 uh which corresponds to 10 to the 7 something like this uh of this uh EA value this value can be measured uh with uh studying the fluctuations of the cosmic microwave background which was done by the plank satellite and you get this value so this is the density of Barons and the of the universe as constrained by the best measurements that we have which is Plank and now uh you also have the results of big bang nucleosynthesis computations which are the blue lines here for ilium 4 dyum ilium 3 and lithium and in green these are measurements so how do you measure primordial abundances since we are in our neighborhood we don't have Prim primordial matter anymore but we can uh go to high red shift galaxies we can also uh spot in high red shift galaxies uh some uh some gas content and uh we can have an estimate of this abundances in some very old Stars also and what you see is that the measure there's a concordance the everything coincides everything just uh crosses at the same point for helium 4 for dyum for helium 3 not for lithium uh so that's a small problem with lithium but if you forget about lithium because lithium you build very few this is very important for Stellar people but for for for the matter people what you is that great big bang works we predicted something and everything aligns so it's this is a validation of the big bank for lithium um it's been a problem for a long time and I think it's a more or less solved problem because lithium can be U either built but uh destroyed but also built in stars and so the lithium the problem is that it's not primordial anymore lithium has been contaminated at it with uh Stellar Evolution and with a cosmic ray spalation which is um very uh rapid uh neutrons and particles bombarding uh heavy seeds and making uh lithium buron and Boron uh in the proportions that we observe now because if we would look at only big buug nucleosynthesis we would have much less lithium burlion and Boron that what we observe in the cosmic abundances and to understand this it was the work of uber Rives before being known as the classical astrophysicist with a white bird and a Canadian accent is the father is the one with jeaner who uh who understood what was the lithium burlion and Boron nuclear synthesis through this pation Cosmic race pation in the early 17 1973 the paper so this not an issue and now you know the three the first boxes of our periodic table where they come from they come from big bang and it seems to [Applause] [Music] hold