玻色-爱因斯坦凝聚冷暗物质晕中的Angular Momentum和涡旋形成
Angular Momentum and Vortex Formation in Bose-Einstein-Condensed Cold Dark Matter Haloes
摘要：
粒子物理学标准模型的扩展预测了非常轻的玻色子，范围从QCD轴子的10 ^{-5} eV到超轻粒子的10 ^{-33} eV，这可能是宇宙中的冷暗物质（CDM）。如果是这样，它们的相空间密度必须足够高，以形成玻色-爱因斯坦凝聚体（BEC）。BEC-CDM动力学的流体性质不同于标准的无碰撞CDM（sCDM），因此星系晕的观测可能会区分它们。sCDM在小尺度上的星系观测中存在问题，BEC-CDM可以在大范围的粒子质量m和自相互作用强度g下克服这些问题。对于半径为R、质量为M的星系尺度上的量子相干性，德布罗意波长λ_deB <~R，要求m>~m_H \cong 10 ^{-25}（R/100千秒差距）^{-1/2}（M/10 ^{1/2} M_solar）^{-1/2} eV，否则lambda_deB <<R，但自相互作用平衡重力，要求m>> m_H和g>> g_H \cong 2 x 10 ^{-64}（R/100 kpc）（M/10 ^{12} M_solar）^{-1} eV cm ^3。在这里，我们研究的角动量的影响，很大程度上被忽视。自旋参数λ \cong 0.05是由大尺度结构的潮汐扭矩，就像sCDM。由于实验室BEC如果旋转得足够快，就会产生量子涡旋，因此我们要问，这种角动量是否足以在BEC晕中形成涡旋，从而影响它们的结构，并产生潜在的可观察到的后果。最小角动量L_{QM} = $\hbar M/m$，需要m ≥ 9.5 m_H（λ = 0.05），接近影响星系尺度结构所需的粒子质量。我们研究平衡的自引力，旋转BEC晕满足Gross-Pitaevskii-Poisson方程，计算是否和当涡是积极的青睐。旋涡的形式，只要自相互作用是足够强的，其中包括一大部分的范围内的m和g的BEC-CDM晕的兴趣。
英文摘要：
(Abridged) Extensions of the standard model of particle physics predict very light bosons, ranging from about 10^{-5} eV for the QCD axion to 10^{-33} eV for ultra-light particles, which could be the cold dark matter (CDM) in the Universe. If so, their phase-space density must be high enough to form a Bose-Einstein condensate (BEC). The fluid-like nature of BEC-CDM dynamics differs from that of standard collisionless CDM (sCDM), so observations of galactic haloes may distinguish them. sCDM has problems with galaxy observations on small scales, which BEC-CDM may overcome for a large range of particle mass m and self-interaction strength g. For quantum-coherence on galactic scales of radius R and mass M, either the de-Broglie wavelength lambda_deB <~ R, requiring m >~ m_H \cong 10^{-25}(R/100 kpc)^{-1/2}(M/10^{12} M_solar)^{-1/2} eV, or else lambda_deB << R but self-interaction balances gravity, requiring m >> m_H and g >> g_H \cong 2 x 10^{-64} (R/100 kpc)(M/10^{12} M_solar)^{-1} eV cm^3. Here we study the largely-neglected effects of angular momentum. Spin parameters lambda \cong 0.05 are expected from tidal-torquing by large-scale structure, just as for sCDM. Since lab BECs develop quantum vortices if rotated rapidly enough, we ask if this angular momentum is sufficient to form vortices in BEC haloes, affecting their structure with potentially observable consequences. The minimum angular momentum for this, L_{QM} = $\hbar M/m$, requires m >= 9.5 m_H for lambda = 0.05, close to the particle mass required to influence structure on galactic scales. We study the equilibrium of self-gravitating, rotating BEC haloes which satisfy the Gross-Pitaevskii-Poisson equations, to calculate if and when vortices are energetically favoured. Vortices form as long as self-interaction is strong enough, which includes a large part of the range of m and g of interest for BEC-CDM haloes.
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