具有排斥自相互作用的标量场暗物质的核包晕：德布罗意波长以外的流体动力学
Core-Envelope Haloes in Scalar Field Dark Matter with Repulsive Self-Interaction: Fluid Dynamics Beyond the de Broglie Wavelength
摘要：
由超轻玻色子组成的标量场暗物质（SFDM）由于其新颖的结构-形成动力学（耦合薛定谔-泊松方程）而成为标准无碰撞冷暗物质（CDM）的替代物，引起了人们极大的兴趣。在SFDM（FDM）的自由场（“模糊”）限制中，结构在德布罗意波长以下被抑制，但在更大尺度上类似于CDM。维里化晕具有半径为$\simλ_\text{deB}$的“孤波”核，被类似CDM的包络所包围。当足够强的排斥性自相互作用（SI）也存在时，结构可以被抑制到低于第二个长度尺度$λ_\text{SI}$，具有$λ_\text{SI}> λ_\text{deB}$ -被称为$λ_\text{SI}> λ_\text{deB}$ -费米（TF）制度。FDM动力学由于量子压力而不同于CDM，并且SFDM-TF通过增加SI压力而进一步不同。然而，在小的$λ_\text{deB}$极限中，我们可以通过可压缩的$γ=5/3$理想气体的流体守恒方程来模拟所有三个，其中理想气体压力来源于内部速度色散，并且对于TF状态，增加了SI压力$P_\text{SI}\propto ρ^2$。我们使用这些流体方程来模拟晕形成的引力坍缩在1D，球对称，证明了第一次，SFDM-TF晕形成的核心大小的$R_\text{TF}$，半径的SI压力支持$(n=1)$ -多面体，围绕CDM样信封。与局域宇宙中矮星系的自转曲线相比，当$R_\text{TF}\gtrsim 1$为kpc时，SFDM-TF晕通过了[“太大而不能倒”+“尖点核”]检验。
英文摘要：
Scalar Field Dark Matter (SFDM) comprised of ultralight bosons has attracted great interest as an alternative to standard, collisionless Cold Dark Matter (CDM) because of its novel structure-formation dynamics, described by the coupled Schrödinger-Poisson equations. In the free-field ("fuzzy") limit of SFDM (FDM), structure is inhibited below the de Broglie wavelength, but resembles CDM on larger scales. Virialized haloes have "solitonic" cores of radius $\simλ_\text{deB}$, surrounded by CDM-like envelopes. When a strong enough repulsive self-interaction (SI) is also present, structure can be inhibited below a second length scale, $λ_\text{SI}$, with $λ_\text{SI}> λ_\text{deB}$ -- called the Thomas-Fermi (TF) regime. FDM dynamics differs from CDM because of quantum pressure, and SFDM-TF differs further by adding SI pressure. In the small-$λ_\text{deB}$ limit, however, we can model all three by fluid conservation equations for a compressible, $γ=5/3$ ideal gas, with ideal gas pressure sourced by internal velocity dispersion and, for the TF regime, an added SI pressure, $P_\text{SI}\propto ρ^2$. We use these fluid equations to simulate halo formation from gravitational collapse in 1D, spherical symmetry, demonstrating for the first time that SFDM-TF haloes form with cores the size of $R_\text{TF}$, the radius of an SI-pressure-supported $(n=1)$-polytrope, surrounded by CDM-like envelopes. In comparison with rotation curves of dwarf galaxies in the local Universe, SFDM-TF haloes pass the ["too-big-to-fail" + "cusp-core"]-test if $R_\text{TF}\gtrsim 1$ kpc.
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