Research ArticleASTRONOMY

Universal interferometric signatures of a black hole’s photon ring

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Science Advances  18 Mar 2020:
Vol. 6, no. 12, eaaz1310
DOI: 10.1126/sciadv.aaz1310
  • Fig. 1 Time-averaged image of a GRMHD simulation of M87.

    This model has parameters chosen to be consistent with the 2017 EHT data and corresponds to the high magnetic flux “magnetically arrested disk” accretion state. It has M = 6.2 × 109M, a/M = 0.94, θobs = 163°, rhigh = 10, and mass accretion rate matching the 1.3-mm flux density (5). The spin axis points left when projected onto the image. The time average was performed over 100 snapshots produced from uniformly spaced GRMHD fluid samples over a time range of 1000M (approximately 1 year). Although visually prominent, the thin, bright ring contains only ~20% of the total image flux density.

  • Fig. 2 Photon shell and photon ring of a Kerr black hole.

    (A) Cross section of the photon shell in the (r, θ) plane in Boyer-Lindquist coordinates. The black hole spin is a/M = 0.94, directed vertically, and the color varies with r. The intersection of an observer’s line of sight with the photon shell boundaries at r=r±γ determines the visible subregion of the photon shell. (B to D) Photon ring on the screen of an observer at varying inclinations θobs relative to the spin axis, whose projection onto the plane perpendicular to the line of sight is depicted by the (left-pointing) arrow. The center of the photon ring has a displacement from the origin that increases with spin. The color coding on the ring denotes the matching radius on the shell from which the photon emanated. The photon shell rγrr+γ is only visible in its entirety to the edge-on (θobs = 90) observer. The face-on (θobs = 0) observer only receives photons from the white r=r0γ orbit. The θobs = 17 observer sees the portion of the shell delineated by the dashed lines.

  • Fig. 3 Image cross sections of a photon ring and its subrings.

    (A) Brightness cross sections for the time-averaged GRMHD image shown in Fig. 1. The blue/red curves show cross sections perpendicular/parallel to the projected spin axis. (B and C) Decomposition of the left perpendicular peak and the right parallel peak into subrings indexed by the number n of photon half-orbits executed between turning points (Eq. 3) in the polar motion. Similar results are also seen in image cross sections of simple geometrical models (10).

  • Fig. 4 Universal interferometric signatures of a photon ring.

    (A to D) Visibility amplitudes of (A and B) the time-averaged GRMHD simulation shown in Fig. 1 and (C and D) a GRMHD snapshot (see the Supplementary Materials). Amplitudes are shown for baselines perpendicular (red) and parallel (blue) to the black hole spin axis. While short baselines (left of the vertical dotted lines) display complex structure reflecting astrophysical features of the image such as emission from the disk and jet, longer baselines are dominated by the universal interferometric signatures of the photon ring. A simple model ∣V(u)∣ = ∣α+ cos (πdu) + α sin (πdu)∣(du)−1/2e−(wu)ζ is overplotted (black dashed curves), with parameters determined independently along the two axes. The periodicities encode the ring diameters along each axis and hence M/D for the black hole; their difference provides an estimate of the black hole spin and inclination. The parameters α± carry information about the angular brightness distribution (and hence spin and inclination). The dashed green curve u−1/2 shows the expected envelope for an infinitesimally thin ring, while the solid green curve u−1/2e−(wu)ζ shows the fitted envelope that carries information about the ring thickness. On even longer baselines (B and D), the dominant visibility contributions arise from subrings with increasingly higher n. The universal features are more prominent in the time-averaged image, whose ring is dominated by smaller mode numbers m and which has less small-scale power outside the photon ring.

  • Fig. 5 Prospects for observing a photon ring.

    (A) Schematic showing visibility amplitude as a function of baseline length for a photon ring with d = 40 μas and flux density comparable to M87. The black, cyan, and magenta visibilities correspond to photons with half-orbit numbers n = 1, 2, and 3. (B) Frequency-dependent range of Earth baselines and representative Earth-space baselines. Earth-space baselines shown are the longest baselines for an orbiter in low Earth orbit (LEO), in medium Earth orbit (MEO), in geostationary orbit (GEO), on the Moon, and at the second Sun-Earth Lagrange point (L2).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/12/eaaz1310/DC1

    Supplementary Materials and Methods

    Fig. S1. Lyapunov exponent as a function of image angle.

    Fig. S2. Black hole shadow diameter and asymmetry as a function of spin and inclination.

    Fig. S3. Snapshot images and visibilities.

    References (2534)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Materials and Methods
    • Fig. S1. Lyapunov exponent as a function of image angle.
    • Fig. S2. Black hole shadow diameter and asymmetry as a function of spin and inclination.
    • Fig. S3. Snapshot images and visibilities.
    • References (2534)

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