小尺度剪切：用引力波剥离弥散的晕
Small-scale shear: Peeling off diffuse subhalos with gravitational waves
摘要：
亚星系尺度的暗晕（$M\lesssim 10^7 M_\odot$或$k\gtrsim 10^3 \,{\rm Mpc}^{-1}$）是暗物质（DM）的原始试验床。然而，它们太小，分散和黑暗，在任何现有的观测中都无法看到。在本文中，我们开发了一个完整的形式主义弱和强衍射透镜，它可以用来探测这样的subhalos与啁啾引力波（GWs）。此外，我们表明，纳瓦罗-弗伦克-怀特（NFW）subhalos在这个质量范围内确实可以单独检测，虽然在${\cal O}(10)$或更少的速度，每年在BBO和其他有限的小合并率和大所需的SNR $\gtrsim 1/γ(r_0) \sim 10^3$。这是可能的，因为NFW尺度半径$r_0$的大小与GW菲涅尔长度$r_F$相当，并且与所有现有的探测器不同，它们的透镜对较轻的subhalos更敏感。值得注意的是，我们的形式主义进一步揭示了弱透镜效应的频率依赖性（这实际上是可检测的效应）是由于在$r_F$的剪切$γ$。它不仅与近似的标度不变性相一致，而且提供了一种新的方法来测量质量分布在一个连续的更小的尺度的啁啾$r_F \propto f^{-1/2}$。同时，产生模糊爱因斯坦环的强衍射具有普遍的频率依赖性，只允许检测。这些都进一步证明了通过半解析讨论幂律配置文件。我们的发展，一个单一的透镜可以推广，并将促进衍射透镜探测DM和小规模的结构，以一个更具体和有前途的物理。
英文摘要：
Subhalos at subgalactic scales ($M\lesssim 10^7 M_\odot$ or $k\gtrsim 10^3 \,{\rm Mpc}^{-1}$) are pristine test beds of dark matter (DM). However, they are too small, diffuse and dark to be visible, in any existing observations. In this paper, we develop a complete formalism for weak and strong diffractive lensing, which can be used to probe such subhalos with chirping gravitational waves (GWs). Also, we show that Navarro-Frenk-White(NFW) subhalos in this mass range can indeed be detected individually, albeit at a rate of ${\cal O}(10)$ or less per year at BBO and others limited by small merger rates and large required SNR $\gtrsim 1/γ(r_0) \sim 10^3$. It becomes possible as NFW scale radii $r_0$ are of the right size comparable to the GW Fresnel length $r_F$, and unlike all existing probes, their lensing is more sensitive to lighter subhalos. Remarkably, our formalism further reveals that the frequency dependence of weak lensing (which is actually the detectable effect) is due to shear $γ$ at $r_F$. Not only is it consistent with an approximate scaling invariance, but it also offers a new way to measure the mass profile at a successively smaller scale of chirping $r_F \propto f^{-1/2}$. Meanwhile, strong diffraction that produces a blurred Einstein ring has a universal frequency dependence, allowing only detections. These are further demonstrated through semianalytic discussions of power-law profiles. Our developments for a single lens can be generalized and will promote diffractive lensing to a more concrete and promising physics in probing DM and small-scale structures.
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