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.