Pulsar-like compact starsare created in the aftermath of the gravitational collapse of the core of a massive star at the end of its life, which triggers a supernova explosion. They are the densest forms of matter known to exist in theUniverse. The equation of state of dense matter at supra-nuclear densityis one of the key questions in astronomy and physics, which is essentially of non-perturbative quantum chromo-dynamics in the regime of low-energy scale. Pulsar observation could open a unique window for us to understand the properties of this superdense matter.

Due to the lack of full understanding of strong interaction at low-energy scale, the inner structure of pulsar is very controversial. Four kinds of inner structure models were proposed. Hadron stars, such as classical neutron star models, contain confined quarks in hadrons. If the central density could be high enough to make quarks de-confined, free quark matter would exist in the core of so-called hybrid/mixed stars. Quark stars are composed of quark matter.A quark-cluster star is condensed matter composed of quark clusters, which distinguishes from both neutron star and quark star.It is worth noting thathadron stars and hybrid/mixed stars are gravity-bound, while quark stars and quark-cluster stars are self-bound on the surface due to strong interaction. They have distinct mass-radius relations. Only quark star and quark-cluster star models predicted the existence of small radius for low-mass compact star. However, the measurements of the radius and mass of compact stars aresurely difficult.

Recently, Dr. Zhaosheng Li, a postdoc at Department of Astronomy Peking University, and his collaborators analyzed the type I X-ray burst observations collected by the RXTE, and constrained the mass and radius of compact star in 4U 1746-37. They found that an extreme low-mass and small radius of neutron star may exist in 4U 1746-37, which could be reproduced by quark-cluster star. This work was published in the Astrophysical Journal (ApJ, 798, 56, 2015).This work is supported by the 973 program, the National Natural Science Foundation of China and the China Postdoctoral Science Foundation.