Light echos and coherent autocorrelations in a black hole spacetime
Light echos and coherent autocorrelations in a black hole spacetime
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DOI：
10.1088/1361-6382/abeae4
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发表时间：
2020-12
影响因子：
3.5
通讯作者：
P. Chesler;L. Blackburn;S. Doeleman;Michael D. Johnson;J. Moran;R. Narayan;M. Wielgus
中科院分区：
文献类型：
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作者：
P. Chesler;L. Blackburn;S. Doeleman;Michael D. Johnson;J. Moran;R. Narayan;M. Wielgus
事件视界望远镜最近拍摄到了第一批黑洞图像。这些图像是通过测量位于地球各地的望远镜测量的复杂电场的相干关联函数来合成的。该关联函数对应于假设源发射空间非相干辐射的图像的傅里叶变换。然而，黑洞不同于标准的天体物理物体：在没有吸收和散射的情况下，观察者会在每个发射位置看到一系列日益减弱的回波。这些回波对应于在到达观测者之前环绕黑洞一次或多次的射线。这种多路径传播将空间和时间相关性引入到电场中，这些电场编码了黑洞的属性，而不考虑内在的可变性。我们研究了在单筒望远镜上测量的相干时间自相关函数。具体地说，我们研究了由Schwarzschild黑洞附近的起伏物质引起的标量场关联函数⟨Ψ(T)Ψ(0)⟩的简化玩具问题。我们发现关联函数在等于光子轨道周期的整数倍的时间处达到峰值，相应的功率谱密度像λ/rg一样消失，其中rg=Gm/c2是黑洞的引力半径，λ是观测到的辐射波长。对于在毫米波段观测到的超大质量黑洞，相对于∼10−13λmm/M6的直接发射，回波中的能量被抑制，其中λmm=λ/(1 Mm)和M6=M/(106M⊙)。因此，利用相干电场自相关来探测黑洞附近的多径传播，在现有技术下是不可行的。
The Event Horizon Telescope recently produced the first images of a black hole. These images were synthesized by measuring the coherent correlation function of the complex electric field measured at telescopes located across the Earth. This correlation function corresponds to the Fourier transform of the image under the assumption that the source emits spatially incoherent radiation. However, black holes differ from standard astrophysical objects: in the absence of absorption and scattering, an observer sees a series of increasingly demagnified echos of each emitting location. These echos correspond to rays that orbit the black hole one or more times before reaching the observer. This multi-path propagation introduces spatial and temporal correlations into the electric field that encode properties of the black hole, irrespective of intrinsic variability. We explore the coherent temporal autocorrelation function measured at a single telescope. Specifically, we study the simplified toy problem of scalar field correlation functions ⟨Ψ(t)Ψ(0)⟩ sourced by fluctuating matter located near a Schwarzschild black hole. We find that the correlation function is peaked at times equal to integer multiples of the photon orbit period; the corresponding power spectral density vanishes like λ/r g where r g = GM/c 2 is the gravitational radius of the black hole and λ is the wavelength of radiation observed. For supermassive black holes observed at millimeter wavelengths, the power in echos is suppressed relative to direct emission by ∼10−13 λ mm/M 6, where λ mm = λ/(1 mm) and M 6 = M/(106 M ⊙). Consequently, detecting multi-path propagation near a black hole using the coherent electric field autocorrelation is infeasible with current technology.