重力磁場在緻密雙星系統演化上的效應

Gravitomagnetic Field Effects on the Evolution of Compact Binary Systems

陳偉家(Wei-Chia Chen)

指導教授 ： 洪在明

國立清華大學/理學院/物理學系/碩士(2007年)

https://doi.org/10.6843/NTHU.2007.00511

摘要

在這個研究裡我們探討重力與超流體的交互作用。我們所選擇的系統是由一個中子星以及一個黑洞所構成的緻密雙星系統。在這裡中子星被簡化成是一大團的超流中子，而黑洞則被視為一個理想的點質量，用來產生我們想要探討的場。
然而，廣義相對論裡用來描述質能與時空之間的作用的愛因斯坦方程式，是一個高度非線性的二階張量微分方程式，只有在少數特殊的情況下才有可能求出解析解。為了避免由時空的非線性效應所造成的複雜，我們考慮的是其在弱場近似之下的形式。在這個近似之下，愛因斯坦方程式可以被寫成一組線性方程，其形式和電動力學裡的麥斯威爾方程式幾乎完全一致。然而，兩者本質上的差異還是存在。在重力裡，這套線性方程所描述的是一般牛頓的重力場以及其所相應的重力磁場。此時的場源自然也就是物質的質量以及移動的物質所構成的質量流，而不再是電動力學裡的電荷與電流。
在重力與電磁的許多對應裡，特別顯著的是重力磁場在超流體裡的反Meissner效應，亦即，在超流體內部的重力磁場並不會被排斥到超流體外，而是在其內部作震盪的行為(我們知道磁場在type-I的超導體裡頭會很迅速得被表面的感應電流抵銷，所以磁場無法進入到超導體內部，看起來像是被排出超導體外。此即Meissner效應。)。即使如此，我們發現在中子星與黑洞因為重力輻射而逐漸靠近的過程中，因為重力磁力線的壓縮、扭曲造成系統場能的改變，仍會有類似超導磁浮的現象發生。但是因為重力輻射的存在，使得這兩個星體間的重力磁浮只能是半穩定的，無法持續下去。兩種效應競爭的結果，會在平滑遞減的雙星系統軌道週期上顯現出微小的變化。最終，無可避免地，中子星仍會和黑洞碰撞。
此外，在黑洞逐漸靠近中子星的過程中，中子星內部的超流中子渦流會被慢慢地感應、誘導到較高的態。然而，超流渦流在比較高的態並不穩定，而會傾向於分解成較多、較低態的渦流。這些過程會造成中子星的自轉速率變慢，並且偶而在穩定增大的週期上出現自轉週期突變的現象，即所謂的glitch。不過這裡所說的glitch有別於一般的說法，至少兩者的形成機制是全然不同的。
必須注意的是，我們整個討論都建立在弱重力場的前提下。在雙星系統裡意指這兩個星體之間的距離有一個下限，超過這個距離，則時空的非線性性質會逐漸變得重要並且主導整個系統的演化。幸運的是，上面所提到的機制與現象皆發生在這個極限之前。

關鍵字

重力磁場 ； 緻密雙星系統 ； 超流體

並列摘要

This work discusses about the interplay of gravitation and superfluids. We focus our attention on the specific type of compact binary systems consisting of one neutron star and one black hole. Here the neutron star is regarded as a huge block of superfluid neutrons while the black hole is to provide the desired gravitational fields.
To avoid complexity of the highly nonlinear Einstein field equation, we reformulate it in weak-field approximation in which the Einstein equation reduces to a set of four equations similar to that of Maxwell in electrodynamics. In this simplification, in addition to the usual Newtonian gravitational field, we also have its dual field, the so-called gravitomagnetic field whose role in gravity is much like to magnetic field in electrodynamics. Even so, there exist many essential differences between these two dynamics, among which the most interesting is the anti-Meissner effect, contrary to that in type-I superconductor.
We found that even the gravitomagnetic field oscillates, rather than exponentially decays, inside superfluids, the compression of gravitomagnetic field lines also provides a repulsive force similar to superconducting levitation. But the situations are different from and more complicated than those in superconductivity. This gravitational levitation combined with the effect due to gravitational radiation results in quasi-stable balance states of the two stars and small variations appear on the orbital period of the binary system.
Furthermore, the left-handed nature of gravitomagnetic induction together with the instability of high-level superfluid vortices inside the neutron star causes the star rotation to decelerate and occasionally show mini-glitches during the binary evolution. However, these phenomena are extremely tiny and may not be easily discovered by astronomical observations.
It should be noticed that the consideration and calculation in this work are based on the weak-field approximation for Einstein equation, beyond which the nonlinearity of spacetime is supposed to govern the whole scenario of binary evolution. Fortunately, it can be seen that the obtained results all happen and therefore behave well within the limits.

並列關鍵字

gravitomagnetic field ； compact binary system ； superfluids

參考文獻

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