With the development of the observing technology,scientists commenced research of observing and computing exoplanets' oblateness and apsidal precession now.Exoplanet's density profile and rotation period determine its oblateness.Its Love number k2 has an obvious negative correlation with its core size.So oblateness and k2 can well constrain its interior structure.The polytropic models based on different polytropic indices are built from the Lane-Emden equation.Then flattening numbers are solved by the Wavre's integral-differential equation.Flattening numbers of 469 selected exoplanets from NASA (National Aeronautics and Space Administration) Exoplanet Archive which have estimated values of radius,mass,and orbit period at the same time are computed under 2 assumptions:tidal locking and fixed rotation period of 10.55hours.The result shows that flattening numbers are too small to be detected under the tidal locking assumption,and 28％ of exoplanets have the flattening numbers larger than 0.1 using fixed rotation period of 10.55 hours.The Love numbers are solved by the Zharkov's approach,and k2 has an obvious negative correlation with its core size comparing with the core-size reference index.%随着观测技术不断进步,已经有了很多对系外行星扁率和拱点进动的观测进展.行星的扁率是由行星的内部密度剖面与其自转决定的,勒夫数k2与其核的大小存在明显的负相关.故扁率与k2可以很好地限定系外行星的内部结构.从Lane-Emden方程出发,构建了不同多方指数下的行星模型.继而通过解算Wavre的积分微分方程得到其扁率,结果表明:多方指数越小,自转越快,扁率越大.从NASA(美国国家航空航天局)系外行星表中,挑选了469个同时具有质量、半径和轨道周期观测或估算值的系外行星,在两种不同自转周期假设下,计算了它们的扁率.结果表明:如果采用潮汐锁定假设,绝大多数系外行星的扁率非常小,约97％的行星小于0.01,难以被观测到;而在固定的10.55 h自转周期假设下,有28％的行星扁率大于0.1.通过解算Zharkov简化的2阶微分方程,得到了不同多方模型下的勒夫数,并讨论了k2与核大小的关系.
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