认识物质的基本组成及其间的基本相互作用是物理学研究的动机之一。我们知道，日常生活中的物质由原子、分子构成，而原子核与核外电子组成了原子。虽然质子和中子是构成原子核的基本单元，但它们却是由更基本的夸克所组成的。人们现在还了解到，夸克和轻子（例如电子）之间存在四种基本相互作用：强力、弱力、电磁力和引力。这些理论框架是上世纪人类最伟大的成就。
在这四种基本相互作用中，经典引力可被爱因斯坦广义相对论精确地描述；弱力和电磁力能用弱电统一理论很好地刻画；而强力的理论框架则是量子色动力学（QCD）。类似于描述电磁相互作用的量子电动力学（QED），QCD是描述带色荷粒子（夸克和胶子）之间的基本理论。研究发现，在能标较高时，QCD具有渐近自由属性，并已被高能实验很好地检验；然而在较低能标下，如何理解QCD丰富的非微扰特性却是人们面临的严峻挑战。后者也与美国克莱数学研究所给出的“七大世纪奖金问题”之一（Yang-Mills and Mass Gap）密切相关。值得一提的是，类似于原子核，脉冲星类致密星体也是典型的低能QCD系统，相关研究无疑将有助于人们更好地理解非微扰QCD行为。
脉冲星类致密星是超新星爆发残骸，其平均密度比原子核还高。普通恒星因其中心的核聚变释放能量而发光；当核能耗尽时，大质量恒星核心的内部压力不能抵抗其自引力，最终导致星核塌缩，并表现为超新星爆发。这种宇宙中已知最致密物质的状态如何，一直以来是天文学和物理学的研究热点。尽管至今未能完全揭示这类致密星的本质，但人们还是作了如下四类推测。强子星（例如早年研究的中子星）内部基本成分是强子，不存在夸克物质（即由游离夸克组成的物质）, 而中心密度足够高时可能会形成具有夸克物质核心的混合/混杂星。几乎完全由夸克物质构成的致密星称为夸克星。而我国学者提出的夸克集团星是由夸克集团（由6个或更多夸克组成的多夸克态）构成的凝聚体，它有别于通常的中子星和夸克星。值得注意的是，强子星和混合/混杂星被引力束缚，而夸克星和夸克集团星的表面是自束缚的。那么，如何依据天文观测区分一般中子星和夸克集团星呢？一般来说包括两种方式。一是寻找大质量的致密星。例如，前几年天文学家发现了两颗约两倍太阳质量的脉冲星，从而排除了所有极限质量低于两倍太阳质量的星体模型。二是寻找较小质量致密星且限制其半径。因为自束缚星体的质量和半径都可以小，而引力束缚星体则不然：质量越低半径则越大。然而，利用天文观测同时限制致密星的质量和半径却是极其困难的。
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| 观测对双星4U 1746-37中致密星质量和半径的限制（图中深灰色区域的置信度达68%），并跟模型推测的质量半径曲线作对比。彩色实线由夸克集团星模型给出，而黑色曲线根据传统中子星模型得到。 |
最近，我系李兆升博士与其合作者利用罗西 X 射线时变望远镜的观测资料，详细分析了X 射线双星 4U 1746-37 一类特殊的X 射线暴数据，计算了其中致密星的质量和半径。结果表明，该双星中致密星的质量和半径明显比理论对强子星和混杂星的预期值小，而与夸克集团星的理论预期较一致。因此，该致密星是夸克集团星的很好候选体。未来进一步的观测研究（如30米光学望远镜TMT等）若能肯定夸克集团星的存在，将深刻地影响人们关于致密物质状态和恒星晚期演化方面的基本认识。这一结果发表在Astrophysical Journal上（798, 56, 2015; http://iopscience.iop.org/0004-637X/798/1/56/）。此工作受到“973”、自然科学基金、博士后科学基金等项目的资助。
4U 1746-37: a low-mass quark-cluster star?
Pulsar-like compact stars are 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 the Universe. The equation of state of dense matter at supra-nuclear density is 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 that hadron 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 are surely difficult.
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| The black and grey contours show the constraints on the mass and radius of compact star in 4U 1746-37. The curves are the mass-radius relations calculated from various models. It is evident that the mass-radius curves of quark-cluster stars pass the observational constraints. |
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.
