# What's the percentage of strange matter inside a star at any time?

Is there any amount of strange matter (or "top matter"?) inside stars?

By strange matter I mean matter made out of flavours of quark other than up/down.

Zero. Normal stars are not dense enough to produce strange matter. They have regular matter only (neutrons and protons).

Strange matter has been hypothesized to form inside neutron stars, but this is highly speculative. Presently, nobody really knows what's in the nucleus of neutrons stars.

Some references:

Physics and Astrophysics of Strange Quark Matter (Madsen, 1998)

Strange Quark Matter and Compact Stars (Weber, 2004)

• Recent studies using LIGO claim to now have evidence of quark matter in large neutron stars. (Nature Physics, 2020)
– J...
Sep 8 at 16:17
• @J... thank you! Do they only talk about quark matter, or actual strange matter (with some quarks different form up and down)? Sep 8 at 16:46
• @Prallax The paper only briefly mentions strange quarks, but confines the analysis to the more general "QCD matter", so I don't think there is any evidence to allow them to say they've detected strange quark matter specifically. You can read the paper for more detail, of course.
– J...
Sep 8 at 18:31

Let me first underline two specific definitions of @Alexandre:

• We are looking for "matter", that means a finite region in space in thermal equilibrium.
• And we are looking for "strangeness", in the sense that strange quarks play a role.

That means that we are not only interested in some transient, intermediate process, and it means that we are looking for any matter with strange quarks - not only "strange matter", which is a specific term for quark matter beyond the hadronic state with strange quarks present.

The idea of @Alexandre to look for it inside stars is actually a good one. First, strange quarks are present in hyperons, so to say the next-heavier baryons beyond proton and neutron. Here on earth, they are instable and decay very fastly. Let's look for a place in the universe where they might exist in thermal equilibrium! For simplicity, we consider the hyperon of the lowest mass, the $$\Lambda$$-particle (uds), with 1116 MeV. The Fermi-Dirac distribution for the occupation number of free Lambdas reads in the non-relativistic limit as follows.

$$n = \frac{1}{\exp(\frac{-\mu+m_\Lambda c^2+E_{kin}}{kT})+1}$$

From this equation, it is obvious that one should look for hyperons (aka large values of $$n$$) at a place where you have

• high temperature $$T$$
• or very high chemical potentials $$\mu$$

While temperature in the center of stars would not reach relevant temperatures on GeV scale, the chemical potential $$\mu$$ does. Because it is more familiar, one can think instead of chemical potential in terms of pressure or density. Such a high density of more than the density of atomic nuclei exists in the core of neutron stars. Indeed, it is intuitive that, if you pack and compress neutrons and protons together, you have to increase the energy of each new particle more and more, because of the Pauli principle. At one point, it is energetically more favorable to occupy hyperon-states instead. This idea was also discussed in detail, for example here - the title directly addresses @Alexandre's question, if you wish. @Prallax is quite right to say:

nobody really knows what's in the nucleus of neutrons stars.

But the appearance of hyperons is quite expected, based on the hadronic spectrum.

For even higher densities, a transition to a quark matter phase is expected, where strange quarks would be present for sure. (The color-superconducting CFL-phase is expected to be the stable phase at high densities, and contains strange quarks.) But it is not clear if this is really occuring in compact stars.

Edit: Corrected the sign-error in the Fermi-Dirac distribution