Last time I wrote about our research on neutron stars. In that case we were concerned with the properties of neutron stars - its mass and size. But these are determined by the particles inside the star, the quarks and gluons and how they influence each other by the strong force.
However, a neutron star is much more than just quarks and gluons bound by gravity and the strong force.
Neutron stars are also affected by the weak force. This happens in a quite subtle way. The weak force can transform a neutron into a proton, an electron and an (anti)neutrino, and back. In a neutron star, this happens all the time. Still, the neutron are neutrons most of the time, hence the name neutron stars. Looking into this process more microscopically, the protons and neutrons consist out of quarks. The proton out of two up quarks and a down quark, and the neutron out of one up quark and two down quarks. Thus, what really happens is that a down quark changes into an up quark and an electron and an (anti)neutrino and back.
As noted, this does not happen too often. But this is actually only true for a neutron star just hanging around. When neutron stars are created in a supernova, this happens very often. In particular, the star which becomes a supernova is mostly protons, which have to be converted to neutrons for the neutron star. Another case is when two neutron stars collide. Then this process becomes much more important, and more rapid. The latter is quite exciting, as the consequences maybe observable in astronomy in the next few years.
So, how can the process be described? Usually, the weak force is weak, as the name says. Thus, it is usually possible to consider it a small effect. Such small effects are well described by perturbation theory. This is OK, if the neutron star just hangs around. But for collisions, or forming, the effect is no longer small. And then other methods are necessary. For the same reasons as in the case of inert neutron stars we cannot use simulations to do so. But our third possibility, the so-called equations of motion, work.
Therefore Walid Mian, a PhD student of mine, and myself used these equations to study how quarks behave, if we offer to them a background of electrons and (anti)neutrinos. We have published a paper about our results, and I would like to outline what we found.
Unfortunately, we still cannot do the calculations exactly. So, in a sense, we cannot independently vary the amount of electrons and (anti)neutrinos, and the strength of their coupling to the quarks. Thus, we can only estimate what a more intense combination of both together means. Since this is qualitatively what we expect to happen during the collision of two neutron stars, this should be a reasonable approximation.
For a very small intensity we do not see anything but what we expect in perturbation theory. But the first surprise was already when we cranked up the intensity. Much earlier than expected new effects which showed up. In fact, they started to be there at intensities some factor 10-1000 smaller than expected. Thus, the weak interaction could play a much larger role in such environments than usually assumed. That was the first insight.
The second was that the type of quarks - whether it is an up or a down quark is more relevant than expected. In particular, whether they have a different mass, like it is in nature, or the same mass makes a big difference. If the mass is different qualitatively new effects arise, which was not expected in this form.
The observed effects themselves are actually quite interesting: They make the quarks, depending on their type, either more sensitive or less sensitive to the weak force. This is important. When neutron stars are created or collide, they become very hot. The main way to get cooler is by dumping (anti)neutrinos into space. This becomes more efficient if the quarks react less to the weak force. Thus, our findings could have consequences on how quickly neutron stars could become colder.
We also saw that these effects only start to play a role if the quark can move inside the neutron star over a sufficiently large distance. Where sufficiently large is here about the size of a neutron. Thus the environment of a neutron star shows itself already when the quarks start to feel that they do not live in a single neutron, but rather in a neutron star, where there neutrons touch each other. All of the qualitative new effects then started to appear.
Unfortunately, to estimate how important these new effects for the neutron star really are, we first have to understand what it means for the neutrons. Essentially, we have to somehow pull our results on a larger scale - what does this mean for the whole neutron - before we can recreate our investigation of the full neutron star with these effects included. Not even to mention the impact for a collision, which is even more complicated.
Thus, our current next step is to understand what the weak interaction implies for hadrons, i.e. states of multiple quarks like the neutron. The first step is to understand how the hadron can decay and reform by the weak force, as I described earlier. The decay itself can be described already quite well using perturbation theory. But decay and reforming, or even an endless chain of these processes, cannot yet. To become able to do so is where we head next.
Showing posts with label Astrophysics. Show all posts
Showing posts with label Astrophysics. Show all posts
Monday, April 10, 2017
Thursday, March 30, 2017
Building a dead star
I have written previously about how we investigate QCD to learn about neutron stars. Neutron stars are the extremely dense and small objects left over after a medium-sized star became a supernova.
For that, we have decided to take a detour. To do so, we have slightly modified the strong interactions. The reason for this modification was to do numerical simulations. In the original version of the theory, this is yet impossible. Mainly, because we have not yet been able to develop an algorithm, which is fast enough to get a result within our lifetime. With the small changes we did to our theory, this changes. And therefore, we have now a (rough) idea of how this theory behaves at densities relevant for neutron stars.
Now Ouraman Hajizadeh, a PhD student of mine, and I went all the way. We used these results to construct a neutron star from it. What we found is written up in a paper. And I will describe here what we learned.
The first insight is that we needed a baseline. Of course, we could compare to what we have on neutron star from astrophysics. But we do not yet know too much about their internal structure. This may change with the newly established gravitational wave astronomy, but this will take a few years. Thus, we decided to use neutrons, which do not interact with each other, as the baseline. A neutron star of such particles is only held together by the gravitational pull and the so-called Pauli principle. This principle forbids certain types of particles, so-called fermions, to occupy the same spots. Neutrons are such fermions. Any difference from such a neutron star has therefore to be attributed to interactions.
The observed neutron stars show the existence of interactions. This is exemplified by their mass. A neutron star made out of non-interacting neutrons can have only masses which are somewhat below the mass of our sun. The heaviest neutron stars we have observed so far are more than twice the mass of our sun. The heaviest possible neutron stars could be a little bit heavier than three times our sun. Everything which is heavier would collapse further, either to a different object unknown to us, or to a black hole.
Now, the theory we investigated is different from the true strong-interactions by two effects. One is that we had only one type of quarks, rather than the real number. Also, our quarks was heavier than the lightest quark in nature. Finally, we have more colors and also more gluons than in nature. Thus, our neutron has a somewhat different structure than the real one. But we used this modified version of the neutron to create our baseline, so that we can still see the effect of interactions.
Then, we cranked the machinery. This machinery is a little bit of general relativity, and thermodynamics. The prior is not modified, but our theory determines the latter. What we got was a quite interesting result. First, our heaviest neutron star was much heavier than our baseline. Roughly 20 to 50 percent heaver than our sun, depending on details and uncertainties. Also, a typical neutron star of this mass had much less variation of its size than the baseline. For non-interacting neutrons, changing the maximum mass by ten percent changes the radius by a kilometer, or so. In our case, this changed the radius almost not at all. So, our heaviest neutron stars are much more reluctant to change. So interactions indeed change the structure of a neutron star considerably.
Another long-standing question is, what the internal structure of a neutron star is. Especially, whether they are a, more or less, monolithic block, except for a a very thin layer close to the surface. Or whether they are composed of many different layers, like our earth. In our case, we find indeed a layered structure. There is an outer surface, a kilometer or so thick, and then a different state of matter down to the core. However, the change appears to be quite soft, and there is no hard distinction. Still, our results signal that there a light neutron stars, which only consist out of the 'surface' material, and only heavier neutron stars have such a core of different stuff. Thus, there could be two classes of neutron stars, with different properties. However, the single-type class is lighter than those which have been observed so far. Such light neutron stars, while apparently stable, seem not, or rarely, be formed during the supernovas giving birth to neutron stars.
Of course, the question is, to which extent such qualitative features can be translated to the real case. We can learn more about this by doing the same in other theories. If features turn out to be generic, this points at something which may also happen for the real case. But even our case, which in a certain sense is the simplest possibility, was not trivial. It may take some time to repeat it for other theories.
For that, we have decided to take a detour. To do so, we have slightly modified the strong interactions. The reason for this modification was to do numerical simulations. In the original version of the theory, this is yet impossible. Mainly, because we have not yet been able to develop an algorithm, which is fast enough to get a result within our lifetime. With the small changes we did to our theory, this changes. And therefore, we have now a (rough) idea of how this theory behaves at densities relevant for neutron stars.
Now Ouraman Hajizadeh, a PhD student of mine, and I went all the way. We used these results to construct a neutron star from it. What we found is written up in a paper. And I will describe here what we learned.
The first insight is that we needed a baseline. Of course, we could compare to what we have on neutron star from astrophysics. But we do not yet know too much about their internal structure. This may change with the newly established gravitational wave astronomy, but this will take a few years. Thus, we decided to use neutrons, which do not interact with each other, as the baseline. A neutron star of such particles is only held together by the gravitational pull and the so-called Pauli principle. This principle forbids certain types of particles, so-called fermions, to occupy the same spots. Neutrons are such fermions. Any difference from such a neutron star has therefore to be attributed to interactions.
The observed neutron stars show the existence of interactions. This is exemplified by their mass. A neutron star made out of non-interacting neutrons can have only masses which are somewhat below the mass of our sun. The heaviest neutron stars we have observed so far are more than twice the mass of our sun. The heaviest possible neutron stars could be a little bit heavier than three times our sun. Everything which is heavier would collapse further, either to a different object unknown to us, or to a black hole.
Now, the theory we investigated is different from the true strong-interactions by two effects. One is that we had only one type of quarks, rather than the real number. Also, our quarks was heavier than the lightest quark in nature. Finally, we have more colors and also more gluons than in nature. Thus, our neutron has a somewhat different structure than the real one. But we used this modified version of the neutron to create our baseline, so that we can still see the effect of interactions.
Then, we cranked the machinery. This machinery is a little bit of general relativity, and thermodynamics. The prior is not modified, but our theory determines the latter. What we got was a quite interesting result. First, our heaviest neutron star was much heavier than our baseline. Roughly 20 to 50 percent heaver than our sun, depending on details and uncertainties. Also, a typical neutron star of this mass had much less variation of its size than the baseline. For non-interacting neutrons, changing the maximum mass by ten percent changes the radius by a kilometer, or so. In our case, this changed the radius almost not at all. So, our heaviest neutron stars are much more reluctant to change. So interactions indeed change the structure of a neutron star considerably.
Another long-standing question is, what the internal structure of a neutron star is. Especially, whether they are a, more or less, monolithic block, except for a a very thin layer close to the surface. Or whether they are composed of many different layers, like our earth. In our case, we find indeed a layered structure. There is an outer surface, a kilometer or so thick, and then a different state of matter down to the core. However, the change appears to be quite soft, and there is no hard distinction. Still, our results signal that there a light neutron stars, which only consist out of the 'surface' material, and only heavier neutron stars have such a core of different stuff. Thus, there could be two classes of neutron stars, with different properties. However, the single-type class is lighter than those which have been observed so far. Such light neutron stars, while apparently stable, seem not, or rarely, be formed during the supernovas giving birth to neutron stars.
Of course, the question is, to which extent such qualitative features can be translated to the real case. We can learn more about this by doing the same in other theories. If features turn out to be generic, this points at something which may also happen for the real case. But even our case, which in a certain sense is the simplest possibility, was not trivial. It may take some time to repeat it for other theories.
Friday, July 10, 2015
Playing indirectly
One of my research areas are neutron stars. To understand them requires to understand how the strong interactions behave when the matter is enormously densely packed. A new PhD student of mine has now started to work on this topic, and I would like to describe a little bit what we will be looking at.
I have already written in the past that this type of situation is very hard to deal with, because we cannot just do simulations. This is unfortunate, since simulations have been very successful in uncovering what happened in the early universe. In that case, the system is hot rather than dense. Though the reason for the problem is 'just' technical, chances are not too bright to resolve it in the near future.
Hence, I had already quite some time ago decided that a possibility is to play indirectly. The basic idea is that there are other methods, which would work. The price we have to pay is that we need to make approximations in these methods. But we would like to check these approximations, ideally against simulations. But we cannot, because there are no. So how to break the circle?
To escape this problem, we can again use a detour. We did this once, because we hoped that we will learn more about the qualitative features. That we can get some insight into this type of physics. Now, we have a much more quantitative approach. We use theories, which are very similar to the strong interactions (also called QCD), but are not QCD, but which can be simulated. And these we will use to break the circle.
Why is it possible to perform simulations for this type of theories? Well, the main reason is the difference between particles and anti-particles. In QCD, a quark and an anti-quark are fundamentally very different objects. Hence, a large density can mean two things. A large density could be having many more quarks than anti-quarks, but still have plenty of both. Or it could be just to have many of one type. For a neutron-star both situations are relevant. And thus, there may be actually many more particles present then we would think, just many of them anti-particles. This is at the heart of the problem, that there is so much more than just the superficial number of particles.
This problem is evaded by using a theory instead where there are no anti-quarks. To be more precise, a theory in which anti-quarks are the same as quarks. There exists a number of such theories. However, such a change is very drastic. It thus may happen that the so changed theory is so radically different from QCD that any comparison becomes meaningless. Thus, it is necessary to ensure that the theory is close enough to the original.
Two candidates for such theories have been identified so far. One is the so-called G2QCD, of which I talked about previously. Another one is very close to QCD, but instead of three color charges is has just two different ones. Both cases have their own merits. The first is closer to QCD. In this theory there are protons and neutrons. The latter does not have these, but it is very cheap to simulate. Both theories are hence quite different, but actually share both also many other traits with QCD.
It therefore stands to reason that whatever approximation describes both well will also work for QCD. Thus, we will now use the simulations of both theories to test the approximations made in the other methods. Especially, we will look at the properties of the quarks and gluons. We will then use the insights gained to improve the approximations. Until we describe both theories well enough. Then we will translate the approximations back to QCD. And if everything works out, we will have then an acceptable description of a piece of neutron star matter.
I have already written in the past that this type of situation is very hard to deal with, because we cannot just do simulations. This is unfortunate, since simulations have been very successful in uncovering what happened in the early universe. In that case, the system is hot rather than dense. Though the reason for the problem is 'just' technical, chances are not too bright to resolve it in the near future.
Hence, I had already quite some time ago decided that a possibility is to play indirectly. The basic idea is that there are other methods, which would work. The price we have to pay is that we need to make approximations in these methods. But we would like to check these approximations, ideally against simulations. But we cannot, because there are no. So how to break the circle?
To escape this problem, we can again use a detour. We did this once, because we hoped that we will learn more about the qualitative features. That we can get some insight into this type of physics. Now, we have a much more quantitative approach. We use theories, which are very similar to the strong interactions (also called QCD), but are not QCD, but which can be simulated. And these we will use to break the circle.
Why is it possible to perform simulations for this type of theories? Well, the main reason is the difference between particles and anti-particles. In QCD, a quark and an anti-quark are fundamentally very different objects. Hence, a large density can mean two things. A large density could be having many more quarks than anti-quarks, but still have plenty of both. Or it could be just to have many of one type. For a neutron-star both situations are relevant. And thus, there may be actually many more particles present then we would think, just many of them anti-particles. This is at the heart of the problem, that there is so much more than just the superficial number of particles.
This problem is evaded by using a theory instead where there are no anti-quarks. To be more precise, a theory in which anti-quarks are the same as quarks. There exists a number of such theories. However, such a change is very drastic. It thus may happen that the so changed theory is so radically different from QCD that any comparison becomes meaningless. Thus, it is necessary to ensure that the theory is close enough to the original.
Two candidates for such theories have been identified so far. One is the so-called G2QCD, of which I talked about previously. Another one is very close to QCD, but instead of three color charges is has just two different ones. Both cases have their own merits. The first is closer to QCD. In this theory there are protons and neutrons. The latter does not have these, but it is very cheap to simulate. Both theories are hence quite different, but actually share both also many other traits with QCD.
It therefore stands to reason that whatever approximation describes both well will also work for QCD. Thus, we will now use the simulations of both theories to test the approximations made in the other methods. Especially, we will look at the properties of the quarks and gluons. We will then use the insights gained to improve the approximations. Until we describe both theories well enough. Then we will translate the approximations back to QCD. And if everything works out, we will have then an acceptable description of a piece of neutron star matter.
Monday, February 3, 2014
The trouble with new toys
You may remember that one of the projects I am working on is understanding so-called neutron stars. These are the remnants of heavy stars, which die in a gigantic explosion called a supernova. One of the main problems with understanding these neutron stars is that it is far too expensive to simulate them in detail using computers. We try in our research to circumvent this problem by using not the original theory describing neutron stars, but a slightly modified version. For this modified theory, we actually can do simulations. So is now everything shiny? No, unfortunately not. And about these problems we have published a new paper recently. Today, I will outline what we did in this paper.
So what is actually the problem? The problem is that some of our theories are not linear. What does now linear mean? Well, a theory is called linear, if we apply an external input to it, and the effect is has on theory is of (roughly) the same size as whatever we applied. In contrast, for anything which is non-linear, the response can be much larger, or much smaller, than whatever we applied. Unfortunately, the strong interactions, which is responsible for neutron stars, is non-linear. Hence, even though we modified it just a little bit, we can potentially have very strong changes. Therefore, we have to make sure that whatever we did was not having unplanned and strong effects. This task led to the mentioned paper.
The main question we have to answer is: If the theory is so sensitive to modifications, were the effects of our modifications still harmless enough? Can we still learn something?
The answer is, as always, it depends. To judge the similarities, we have looked at the hadrons, the particles build up from quarks and gluons. In the strong force, the masses of these hadrons follow a very special pattern. Especially, there are some unusually light ones, the a few intermediate ones, and then, already quite heavy, the first one which plays an important role in everyday life: The proton, the nucleus of a hydrogen atom. We found that in our modified theory this pattern repeats itself. This is already a good sign. However, we also found some indications that not all is well. Some of the lighter particles have a number of different details than in nature, especially the lightest ones.
Since we are mostly interested in neutron stars, we also did the calculations at large densities. There, we saw that indeed the slightly different properties of the lightest particles play a role. At quite small densities, we observe a behavior, which we are reasonably sure will not occur in nature. So is then all lost? It does not seem so. While at these densities the behavior is different, this will probably not play an important role for the densities we are really interested in. And indeed, at higher densities the theory behaved similar to the expectations: It seems to behave in a way which we would guess based on the observations of real neutron stars, and general arguments. This is quite encouraging. Still, we also encountered two more challenges. One is that to make a definite statement, we will need much more precision: Some of what we see is sensitive to details. We need to understand this better. And this will require much more calculations.
The other one is that we are still not quite sure if there is not some special kind of different particle playing a too important role. This special kind of particle is similar to the proton, but not present in nature. It is only a feature of the modified theory. This is a so-called hybrid. In contrast to the proton, which consist out of three quarks and no gluons, it is made out of one quark and three gluons. There are certain technical reasons, why this particle could be a problem when trying to understand neutron stars. So far, it escaped detection in our calculations. We have to find it, to make really sure what is going on. This will be a challenge.
Fortunately, still, even in the worst case scenario of both problems, what we did will not be irrelevant. On the one hand, it was a genuinely new theory we looked at, and we learned already very much about how theories in general work. And the second is - what we created will also serve as a benchmark for other methods. If someone creates a new method to get to the neutron star's core, she or he can test it again our simulations, to build confidence in it.
So what is actually the problem? The problem is that some of our theories are not linear. What does now linear mean? Well, a theory is called linear, if we apply an external input to it, and the effect is has on theory is of (roughly) the same size as whatever we applied. In contrast, for anything which is non-linear, the response can be much larger, or much smaller, than whatever we applied. Unfortunately, the strong interactions, which is responsible for neutron stars, is non-linear. Hence, even though we modified it just a little bit, we can potentially have very strong changes. Therefore, we have to make sure that whatever we did was not having unplanned and strong effects. This task led to the mentioned paper.
The main question we have to answer is: If the theory is so sensitive to modifications, were the effects of our modifications still harmless enough? Can we still learn something?
The answer is, as always, it depends. To judge the similarities, we have looked at the hadrons, the particles build up from quarks and gluons. In the strong force, the masses of these hadrons follow a very special pattern. Especially, there are some unusually light ones, the a few intermediate ones, and then, already quite heavy, the first one which plays an important role in everyday life: The proton, the nucleus of a hydrogen atom. We found that in our modified theory this pattern repeats itself. This is already a good sign. However, we also found some indications that not all is well. Some of the lighter particles have a number of different details than in nature, especially the lightest ones.
Since we are mostly interested in neutron stars, we also did the calculations at large densities. There, we saw that indeed the slightly different properties of the lightest particles play a role. At quite small densities, we observe a behavior, which we are reasonably sure will not occur in nature. So is then all lost? It does not seem so. While at these densities the behavior is different, this will probably not play an important role for the densities we are really interested in. And indeed, at higher densities the theory behaved similar to the expectations: It seems to behave in a way which we would guess based on the observations of real neutron stars, and general arguments. This is quite encouraging. Still, we also encountered two more challenges. One is that to make a definite statement, we will need much more precision: Some of what we see is sensitive to details. We need to understand this better. And this will require much more calculations.
The other one is that we are still not quite sure if there is not some special kind of different particle playing a too important role. This special kind of particle is similar to the proton, but not present in nature. It is only a feature of the modified theory. This is a so-called hybrid. In contrast to the proton, which consist out of three quarks and no gluons, it is made out of one quark and three gluons. There are certain technical reasons, why this particle could be a problem when trying to understand neutron stars. So far, it escaped detection in our calculations. We have to find it, to make really sure what is going on. This will be a challenge.
Fortunately, still, even in the worst case scenario of both problems, what we did will not be irrelevant. On the one hand, it was a genuinely new theory we looked at, and we learned already very much about how theories in general work. And the second is - what we created will also serve as a benchmark for other methods. If someone creates a new method to get to the neutron star's core, she or he can test it again our simulations, to build confidence in it.
Friday, March 22, 2013
(Un-)Dead stars and particles
I have already written about some aspects of my research on neutron stars. But what is the problem with them? And what do I want to understand?
First: What are they? If you have a sufficiently massive star, it will not die in a fizzle, like our sun, but it will end violently. It will explode in a supernova. In this process, a lot of its mass gets compressed at its core. If this core is not too heavy, a remainder, a corpse of the star, will remain: A neutron star. If it is too heavy, the remainder will, however, collapse further into a black hole. But this is not the interesting case for me.
Such a neutron star is actually far from dead. It continues its life after its death. But it no longer emits light and warmth, but usually x-rays, neutrinos, and occasionally so-called gravitational waves.
Second: What do I want to understand about them? Neutron stars are enigmatic objects. Their size is about ten kilometers, not more than a larger city. At the same time they have about one to two times the mass of our sun. Thus, they are incredible dense. In fact, they are so dense that there is no place for atoms, but they consist out of the atomic nuclei. That is the case in the outer layers of the neutron star, perhaps the first kilometer or so. Going further inward, the density increases. Then everything gets so tight, that it is no longer possible to separate the nuclei, and they start to overlap. In addition, whatever electrons there still were have already after the first few meters been soaked up to change almost all of the protons into neutrons. In a certain sense, it is just one big atomic nucleus.
And even further in? Well, nobody knows. However, there are many speculations. Do we have there a different kind of matter, so-called strange matter? Such matter is obtained when one starts to replace the up and down quarks in the neutrons with strange quarks. Or does also the neutrons dissolve, and we just have a bunch of quarks? And if yes, how would such quark matter behave? Would it be a fluid, a superconducting metal, or possibly even a crystal?
And that is, where my research starts. What I want to understand is, which form this matter takes. And I am not alone with this. I have just organized a workshop, which partly focused on this subject, and we have worked hard on getting a better understanding, of what goes on in there. That becomes even more interesting as more and more results come in from astronomical observations on neutron stars. They provide us with a lot of indirect evidence on how the matter inside the neutron star's core must behave. But if we understand the strong force correctly, we should be able to calculate this.
The central problem involved in these calculations is the density. The standard approach to particle physics (and to physics in general) is to attempt to simplify the problem, and study its parts in isolation. That is quite well working for many cases, like the Higgs. However, the properties of the neutron star is determined not by the individual neutrons, but in how they interact with each other when there are many of them. Thus, by breaking the system apart you destroy what you want to study. Thus, you have to study the neutrons - or more appropriately the quarks - all together. This enlarges the complexity severely, and it is what stops us in our tracks. Particularly, because it is hard to find efficient ways to calculate anything for a real neutron star.
One way around this is to attempt to indirectly understand it, by studying a simpler system. The alternative is to simplify the system itself. This can be done by making things a bit more fuzzy. This fuzziness is achieved by not tracking each and every quark and what it precisely does. Instead, groups of quarks are tracked, and their activities is averaged. This can be a very simple step. For example, one can treat a neutron instead of being made from three quarks as made from one quark and the rest. And then approximate the rest by a single particle with simple properties. Such an approximation already gives a rough estimate of how things work. Of course, if one wants to get the last bit of precision out of the theory, then one has to return to the original three quarks.
But the problem is complicated, and thus one follows this strategy: Creating less and simpler objects first, an then refine them again. This simpler objects are often called 'effective degrees of freedom', because they effectively mimic many complicated objects. And then we solve the simpler theory describing them, the so-called effective theory. Afterwards, we go back. We refine the effective theory and the simple particles again, introducing the problems bit by bit. And solving them on the way. And that is, where we are currently. Still far away from understanding a neutron stars as a set of elementary particles, as quarks and gluons, but closing in, step by step.
First: What are they? If you have a sufficiently massive star, it will not die in a fizzle, like our sun, but it will end violently. It will explode in a supernova. In this process, a lot of its mass gets compressed at its core. If this core is not too heavy, a remainder, a corpse of the star, will remain: A neutron star. If it is too heavy, the remainder will, however, collapse further into a black hole. But this is not the interesting case for me.
Such a neutron star is actually far from dead. It continues its life after its death. But it no longer emits light and warmth, but usually x-rays, neutrinos, and occasionally so-called gravitational waves.
Second: What do I want to understand about them? Neutron stars are enigmatic objects. Their size is about ten kilometers, not more than a larger city. At the same time they have about one to two times the mass of our sun. Thus, they are incredible dense. In fact, they are so dense that there is no place for atoms, but they consist out of the atomic nuclei. That is the case in the outer layers of the neutron star, perhaps the first kilometer or so. Going further inward, the density increases. Then everything gets so tight, that it is no longer possible to separate the nuclei, and they start to overlap. In addition, whatever electrons there still were have already after the first few meters been soaked up to change almost all of the protons into neutrons. In a certain sense, it is just one big atomic nucleus.
And even further in? Well, nobody knows. However, there are many speculations. Do we have there a different kind of matter, so-called strange matter? Such matter is obtained when one starts to replace the up and down quarks in the neutrons with strange quarks. Or does also the neutrons dissolve, and we just have a bunch of quarks? And if yes, how would such quark matter behave? Would it be a fluid, a superconducting metal, or possibly even a crystal?
And that is, where my research starts. What I want to understand is, which form this matter takes. And I am not alone with this. I have just organized a workshop, which partly focused on this subject, and we have worked hard on getting a better understanding, of what goes on in there. That becomes even more interesting as more and more results come in from astronomical observations on neutron stars. They provide us with a lot of indirect evidence on how the matter inside the neutron star's core must behave. But if we understand the strong force correctly, we should be able to calculate this.
The central problem involved in these calculations is the density. The standard approach to particle physics (and to physics in general) is to attempt to simplify the problem, and study its parts in isolation. That is quite well working for many cases, like the Higgs. However, the properties of the neutron star is determined not by the individual neutrons, but in how they interact with each other when there are many of them. Thus, by breaking the system apart you destroy what you want to study. Thus, you have to study the neutrons - or more appropriately the quarks - all together. This enlarges the complexity severely, and it is what stops us in our tracks. Particularly, because it is hard to find efficient ways to calculate anything for a real neutron star.
One way around this is to attempt to indirectly understand it, by studying a simpler system. The alternative is to simplify the system itself. This can be done by making things a bit more fuzzy. This fuzziness is achieved by not tracking each and every quark and what it precisely does. Instead, groups of quarks are tracked, and their activities is averaged. This can be a very simple step. For example, one can treat a neutron instead of being made from three quarks as made from one quark and the rest. And then approximate the rest by a single particle with simple properties. Such an approximation already gives a rough estimate of how things work. Of course, if one wants to get the last bit of precision out of the theory, then one has to return to the original three quarks.
But the problem is complicated, and thus one follows this strategy: Creating less and simpler objects first, an then refine them again. This simpler objects are often called 'effective degrees of freedom', because they effectively mimic many complicated objects. And then we solve the simpler theory describing them, the so-called effective theory. Afterwards, we go back. We refine the effective theory and the simple particles again, introducing the problems bit by bit. And solving them on the way. And that is, where we are currently. Still far away from understanding a neutron stars as a set of elementary particles, as quarks and gluons, but closing in, step by step.
Wednesday, January 9, 2013
Taking a detour helps
Almost all relevant physical systems are pretty complicated. One I am working on is how the interior of so-called neutron stars look like. Neutron stars is what is left of stars somewhat heavier than our sun, but not too heavy, after they became a supernova. In a neutron star the atoms collapse due to the strong gravitation. Only the atomic nuclei remain, and are packed very densely. Neutron stars have roughly one to two times the mass of our sun, but have a radius of only about ten kilometers, barely larger than a small city. These star remnants are very interesting for astronomy and astrophysics. But I am more interested what happens in their most inner core.
Deep inside the neutron star, everything is even more packed. In fact, even the atomic nuclei are no longer separated, but are mashed into a big mess. Because their are so densely packed, even the nucleons are overlapping. Thus, the substructure of them, the quarks may become the most important players.
But this nobody knows yet for sure. It has been a challenge to understand such matter since more than thirty years. It is a joint effort of theoreticians, like me, people smashing atoms on each other in accelerators, so-called heavy-ion experiments, and people observing actual neutron stars with telescopes of many kinds.
In general, if quarks come into play, very often simulations have been very helpful. But it turns out that we are not (yet) clever enough to simulate a neutron star's interior. The algorithms, which we have developed to deal with single nuclei are just too inefficient to deal with so many nuclei. For technical reasons, this is called the sign problem, denoting the particular technical problem involved. This obstruction is also known since decades, without us being able so far to remove it.
An alternative have been other methods and models, but we would like to have a combination, to be more sure of our results.
One possibility has been to circumvent the problem. We have looked at theories which are similar to the strong nuclear force, but slightly modified. The modification were such that numerical simulations were possible. We made this detour for two reasons. We hoped that we could learn something in general. And we wanted to use these results to provide us with tests for our models and other methods. In a way we cheated: We evaded the problem by doing a simpler problem. And hoped that we would learn enough by this to solve the original problem or get a new insight.
However, so far our detours had serious drawbacks. The replacement theories were only able to solve some problems, but never all at the same time. Some had the problem that the mass creation by the strong force did not work in the right way. This would yield wrong answers for size and mass of a neutron stars. Or the nucleons were not repellent enough, so that all neutron stars would collapse further to so-called quark stars, much smaller than neutron stars and made from quarks.
And here comes my own research into play. Just recently we found another theory, which we call G2-QCD for very technical reasons. Irrespective of the name, it has neither of these problems. However, it is still not QCD. E. g., it has besides the nucleons further exotic objects flying around. But it is anyway the theory closest to the original one so far investigated. And we can actually simulate it. That is something we just done very recently. The results are very encouraging, though we are yet far from a final answer for neutron stars. Nonetheless, we have now an even stronger test for all the models and results from other methods available. This should provide even more constraints on our understanding of neutron stars, though still an enormous amount of work has to be done. But this is research: Mostly progress by small steps. And we thus continue on with this theory.
And this is just one example in my research where it is worthwhile to take a detour, and this is true for physics in general: Often the study of a simpler problem helps to reveal the solution of the original one. Even if we did not (again yet) succeeded, we made progress.
Deep inside the neutron star, everything is even more packed. In fact, even the atomic nuclei are no longer separated, but are mashed into a big mess. Because their are so densely packed, even the nucleons are overlapping. Thus, the substructure of them, the quarks may become the most important players.
But this nobody knows yet for sure. It has been a challenge to understand such matter since more than thirty years. It is a joint effort of theoreticians, like me, people smashing atoms on each other in accelerators, so-called heavy-ion experiments, and people observing actual neutron stars with telescopes of many kinds.
In general, if quarks come into play, very often simulations have been very helpful. But it turns out that we are not (yet) clever enough to simulate a neutron star's interior. The algorithms, which we have developed to deal with single nuclei are just too inefficient to deal with so many nuclei. For technical reasons, this is called the sign problem, denoting the particular technical problem involved. This obstruction is also known since decades, without us being able so far to remove it.
An alternative have been other methods and models, but we would like to have a combination, to be more sure of our results.
One possibility has been to circumvent the problem. We have looked at theories which are similar to the strong nuclear force, but slightly modified. The modification were such that numerical simulations were possible. We made this detour for two reasons. We hoped that we could learn something in general. And we wanted to use these results to provide us with tests for our models and other methods. In a way we cheated: We evaded the problem by doing a simpler problem. And hoped that we would learn enough by this to solve the original problem or get a new insight.
However, so far our detours had serious drawbacks. The replacement theories were only able to solve some problems, but never all at the same time. Some had the problem that the mass creation by the strong force did not work in the right way. This would yield wrong answers for size and mass of a neutron stars. Or the nucleons were not repellent enough, so that all neutron stars would collapse further to so-called quark stars, much smaller than neutron stars and made from quarks.
And here comes my own research into play. Just recently we found another theory, which we call G2-QCD for very technical reasons. Irrespective of the name, it has neither of these problems. However, it is still not QCD. E. g., it has besides the nucleons further exotic objects flying around. But it is anyway the theory closest to the original one so far investigated. And we can actually simulate it. That is something we just done very recently. The results are very encouraging, though we are yet far from a final answer for neutron stars. Nonetheless, we have now an even stronger test for all the models and results from other methods available. This should provide even more constraints on our understanding of neutron stars, though still an enormous amount of work has to be done. But this is research: Mostly progress by small steps. And we thus continue on with this theory.
And this is just one example in my research where it is worthwhile to take a detour, and this is true for physics in general: Often the study of a simpler problem helps to reveal the solution of the original one. Even if we did not (again yet) succeeded, we made progress.
Monday, April 23, 2012
What the strong interactions, temperature, and density have to do with each other
After the preparation with the last entry, I can now move forward to my next research topic.
Let me just collect what we had so far about the strong interactions, QCD. QCD is the theory that describes the interaction between quarks and gluons. It tells you how these make up the hadrons, like the proton and the neutron. It also describes how these combine to the atomic nuclei. The quarks and gluons cannot be seen alone: The strong force confines them. At the same time, the strong force makes the quarks condense, and thereby creates the illusion of mass. Well, this is what one can call a complicated theory.
Now imagine for a while what happens, if you heat up matter. Really make it hot, much hotter than in the interior of stars. Heat is something like energy. You can imagine that the hotter something is, the faster the movement of particles. The faster they go, he hotter they are. But the higher the energy, the smaller the things are which get involved. Hence, if things get very hot, the quarks and gluons are the one to really feel it.
When this happens, two things occur. One is that the condensate of quarks melts. As a consequence, the quarks can move much more freely. The other is that you can convert some of the energy from the heat to particles. I will come back to the mechanism behind this later. For now, it is enough that this is possible. It is nothing special to the heat case. Anyway, you can convert a small fraction of the heat to particles. If things get hot enough, a small fraction is actually quite a large number. And if things are really hot, you have created so many particles that they do not fit anymore in the space you have available. Then they start to overlap. At that point, even if you have confinement, you can no longer tell the hadrons apart. The things just overlap and you can start to swap quarks and gluons from one to another. You see, when you put enough heat into matter, things start to look very different.
Why is this interesting? I said it must be much hotter than in a star, and actually much hotter even than in a supernova. It does not appear that there is anything in nature being so hot. However, we can create tiny amounts of matter in experiments which is so hot. And also, very far in the past, such super-hot matter existed. Right after the big bang, the whole universe was very densely packed, and the temperature was so high. This was only a fraction of a second after the big bang. So, is this relevant? Well, yes. If we want to look back even further, we have to understand what happened in the transition of the strong force at that time. Since we cannot create universes to study it, we need to extrapolate back in time. And for this, we need to understand each step of going back in time. And hence, we need to understand how QCD works at very high temperatures.
This is not the only case where we need to understand QCD in extreme conditions. The other case is the interior of neutron stars. In these stars, matter is packed incredibly densely. It is very cold there, at least when comparing to the early universe. But it is so dense that hadrons again begin to overlap. Thus, you would expect that you can again exchange quarks and gluons freely between hadrons. But because it is cold, you will keep your quark condensate. In fact, there are quite a lot of speculation, whether you can create also condensates of quarks with different properties than the one usually known. To really understand how neutron stars work, and eventually also how black holes form, we have to understand how QCD works when things become dense.
When you take both cases together, and permit for good measure to also include all possible combinations of dense and hot, you end up with the QCD phase diagram. This phase diagram answers the question: When I have this temperature and that density, how does QCD behave? Determining this phase diagram has been a topic of research ever since these questions were first posed in the 1970s. Very important for this task have been numerical simulations of matter at high temperatures. With them, we have become confident that we start to understand what happens at very small densities and rather high temperature. We understood from this that the universe has undergone a non-violent transition when QCD changed. We can therefore now extrapolate further back in the history of the universe. But we are not yet finished for this case. Right now, we leaned what happens when we are at fixed temperature and density. But these two quantities changed, and we have not yet fully understood how this proceeds.
Things are a lot worse when we turn to the neutron stars. We have not been able to develop efficient programs to simulate the interior of a neutron star. We even suspect that it is not possible at all, for rather fundamental reasons concerning conventional computers. Progress has therefore been mainly made in two ways. One was to rely heavily on (very) simplified models, and more recently using functional methods. Another one was to study artificial theories, which are similar to QCD, but for which efficient programs can be written. From the experience with them we try to indirectly infer what happens really in QCD.
I am involved in the determination of this QCD phase diagram with two angles. One is to develop the functional methods further, such that they become a powerful tool to address these questions. Another one is to learn something from the stand-in theories. Especially in the latter case we just made a breakthrough, on which I will comment in a later entry.
Let me just collect what we had so far about the strong interactions, QCD. QCD is the theory that describes the interaction between quarks and gluons. It tells you how these make up the hadrons, like the proton and the neutron. It also describes how these combine to the atomic nuclei. The quarks and gluons cannot be seen alone: The strong force confines them. At the same time, the strong force makes the quarks condense, and thereby creates the illusion of mass. Well, this is what one can call a complicated theory.
Now imagine for a while what happens, if you heat up matter. Really make it hot, much hotter than in the interior of stars. Heat is something like energy. You can imagine that the hotter something is, the faster the movement of particles. The faster they go, he hotter they are. But the higher the energy, the smaller the things are which get involved. Hence, if things get very hot, the quarks and gluons are the one to really feel it.
When this happens, two things occur. One is that the condensate of quarks melts. As a consequence, the quarks can move much more freely. The other is that you can convert some of the energy from the heat to particles. I will come back to the mechanism behind this later. For now, it is enough that this is possible. It is nothing special to the heat case. Anyway, you can convert a small fraction of the heat to particles. If things get hot enough, a small fraction is actually quite a large number. And if things are really hot, you have created so many particles that they do not fit anymore in the space you have available. Then they start to overlap. At that point, even if you have confinement, you can no longer tell the hadrons apart. The things just overlap and you can start to swap quarks and gluons from one to another. You see, when you put enough heat into matter, things start to look very different.
Why is this interesting? I said it must be much hotter than in a star, and actually much hotter even than in a supernova. It does not appear that there is anything in nature being so hot. However, we can create tiny amounts of matter in experiments which is so hot. And also, very far in the past, such super-hot matter existed. Right after the big bang, the whole universe was very densely packed, and the temperature was so high. This was only a fraction of a second after the big bang. So, is this relevant? Well, yes. If we want to look back even further, we have to understand what happened in the transition of the strong force at that time. Since we cannot create universes to study it, we need to extrapolate back in time. And for this, we need to understand each step of going back in time. And hence, we need to understand how QCD works at very high temperatures.
This is not the only case where we need to understand QCD in extreme conditions. The other case is the interior of neutron stars. In these stars, matter is packed incredibly densely. It is very cold there, at least when comparing to the early universe. But it is so dense that hadrons again begin to overlap. Thus, you would expect that you can again exchange quarks and gluons freely between hadrons. But because it is cold, you will keep your quark condensate. In fact, there are quite a lot of speculation, whether you can create also condensates of quarks with different properties than the one usually known. To really understand how neutron stars work, and eventually also how black holes form, we have to understand how QCD works when things become dense.
When you take both cases together, and permit for good measure to also include all possible combinations of dense and hot, you end up with the QCD phase diagram. This phase diagram answers the question: When I have this temperature and that density, how does QCD behave? Determining this phase diagram has been a topic of research ever since these questions were first posed in the 1970s. Very important for this task have been numerical simulations of matter at high temperatures. With them, we have become confident that we start to understand what happens at very small densities and rather high temperature. We understood from this that the universe has undergone a non-violent transition when QCD changed. We can therefore now extrapolate further back in the history of the universe. But we are not yet finished for this case. Right now, we leaned what happens when we are at fixed temperature and density. But these two quantities changed, and we have not yet fully understood how this proceeds.
Things are a lot worse when we turn to the neutron stars. We have not been able to develop efficient programs to simulate the interior of a neutron star. We even suspect that it is not possible at all, for rather fundamental reasons concerning conventional computers. Progress has therefore been mainly made in two ways. One was to rely heavily on (very) simplified models, and more recently using functional methods. Another one was to study artificial theories, which are similar to QCD, but for which efficient programs can be written. From the experience with them we try to indirectly infer what happens really in QCD.
I am involved in the determination of this QCD phase diagram with two angles. One is to develop the functional methods further, such that they become a powerful tool to address these questions. Another one is to learn something from the stand-in theories. Especially in the latter case we just made a breakthrough, on which I will comment in a later entry.
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