Properties of strange quark matter objects with two types of surface treatments

We study strange quark matter (SQM) objects ranging from strangelets to strange stars based on our recently proposed unified description. The important interface effects are investigated by adopting a constant surface tension as well as the multiple reflection expansion (MRE) method. It is shown that the properties of SQM objects are strongly affected by the different surface treatments. In the former case, strangelets are more compact, an electric dipole is predicted on the surface of the quark part, and a local minimum of the energy per baryon appears for unusually small values of the surface tension. In the latter case, on the other hand, an electric potential well is formed, and the energy per baryon decreases monotonically with the SQM object’s size. It is found that the MRE scenario coincides with the constant-surface-tension one if realistic values are considered. However, the effects of quark depletion on the quark-vacuum interface cannot be solely described by a constant surface tension. Thus we conclude that the MRE scenario is more reasonable.

Figure 1

The energy per baryon from strangelets to strange stars. The full lines and shaded regions correspond to the central values and uncertainty of $B^{1/4}=152\pm 7\mathrm{MeV}$; the same convention is adopted for other figures. For a given bag constant $B$, the minimum energy per baryon coincides with the maximum mass and baryon number in Figs. 2 and 3, respectively.

Figure 2

The normalized $M-R$ probability distribution of eight pulsars (Fig. 10 of Ref. [24]). As $B$ increases, the maximum mass of strange stars decreases.

Figure 3

The baryon numbers of strange stars. The dash-dotted line shows the baryon number determined by $A={(R/0.9\mathrm{fm})}^3$.

Figure 4

The energy excess per baryon of strangelets $(\frac{M}{A}-{\frac{M}{A}|}_{\mathrm{sat}})$ with ${\frac{M}{A}|}_{\mathrm{sat}}$ given in Table 1.

Figure 5

The critical surface tension as a function of strange quark masses. For the cases adopting smaller surface tension values, there exists a local minimum for the energy per baryon of strangelets at a certain size.

Figure 6

The ratio of radius to baryon number for strangelets.

Figure 7

The electric potential from the SQM core to the surface of strange stars with $R=9\mathrm{km}$. For a given bag constant, the surface profiles becomes identical for SQM objects with $R\gtrsim {10}^4\mathrm{fm}$.

Figure 8

(a) The chemical potential of electrons ${\mu }_e(R)$ on the SQM core surface. (b) The sum of the chemical potential of quarks on the SQM core surface with $\mu \equiv {\mu }_u+{\mu }_d+{\mu }_s$.

Figure 9

(a) The charge-to-mass ratio of the SQM core of strangelets, which is compared with previous findings indicated by the thick dash-dotted line (Fig. 4 of Ref. [4]) and dashed line (Fig. 2 of Ref. [60]). (b) The surface charge density ${\sigma }^{\mathrm{surf}}$ of the SQM core for strangelets, which gives $Q(R)={\sigma }^{\mathrm{surf}}{R}^2$. The values of ${\sigma }^{\mathrm{surf}}$ are much larger than the upper bound $7\times {10}^{-5}{\mathrm{fm}}^{-2}$ considering electron-positron pair creation [42].