Astrophysical imaging of Kerr black holes with scalar hair

We address the astrophysical imaging of a family of deformed Kerr black holes (BHs). These are stationary, asymptotically flat BH spacetimes that are solutions of general relativity minimally coupled to a massive, complex scalar field: Kerr BHs with scalar hair (KBHsSH). Such BHs bifurcate from the vacuum Kerr solution and can be regarded as a horizon within a rotating boson star. In a recent letter [P. V. P. Cunha, C. A. R. Herdeiro, E. Radu, and H. F. Rúnarsson, Phys. Rev. Lett. 115, 211102 (2015).], it was shown that KBHsSH can exhibit very distinct shadows from the ones of their vacuum counterparts. The setup therein, however, considers the light source to be a celestial sphere sufficiently far away from the BH. Here, we analyze KBHsSH surrounded by an emitting torus of matter simulating a more realistic astrophysical environment, and study the corresponding lensing of light as seen by a very faraway observer, to appropriately model ground-based observations of Sgr ${\mathrm{A}}^{*}$. We find that the differences in imaging between KBHsSH and comparable vacuum Kerr BHs remain, albeit less dramatic than those observed for the corresponding shadows in the previous setup. In particular, we highlight two observables that might allow differentiating KBHsSH and Kerr BHs. The first is the angular size of the photon ring (in a Kerr spacetime) or lensing ring (in a KBHSH spacetime), the latter being significantly smaller for sufficiently non-Kerr-like spacetimes. The second is the existence of an edge in the intensity distribution (the photon ring in Kerr spacetime). This edge can disappear for very non-Kerr-like KBHsSH. It is plausible, therefore, that sufficiently precise very long baseline interferometric observations of BH candidates can constrain this model.

Figure 1

Left: Shadow of the KBHSH of configuration I (field of view $300\mu \mathrm{as}$). Right: The same for the comparable Kerr BH ($j_{\mathrm{ADM}}=0.999$).

Figure 2

Left: Shadow of the KBHSH of configuration II (field of view $300\mu \mathrm{as}$). Right: The same for the comparable Kerr BH ($j_{\mathrm{ADM}}=0.85$).

Figure 3

Left: Shadow of the KBHSH of configuration III (field of view $300\mu \mathrm{as}$). Right: The same for the comparable Kerr BH ($j_{\mathrm{ADM}}=0.894$).

Figure 4

Left: Shadow of the KBHSH of configuration III from an inclination of $\theta =90°$ (field of view $150\mu \mathrm{as}$). Right: Same computation, changing only the coordinate radius of the observer which is taken the same as in [26] (field of view $\pi /2$). Observe that the shadow’s topology depends on the observer’s distance.

Figure 5

Configuration I images. Upper panel: Image at 230 GHz of the torus model surrounding the Kerr BH of configuration I, computed with an analytical BL metric. All images in this article are represented in inverse colors: high intensity is in dark blue; low intensity is in yellow/orange. The dotted circles show the $1\sigma$ upper and lower confidence limits for the intrinsic angular size of the emitting zone [42]. The solid black contour encompasses the region of the accretion flow emitting 50% of the total flux: it is considered as an order-zero approximation of the size of the emitting region. The image has thus a reasonable angular size provided that the solid contour approximately lies within the dotted circles, which is the case here and in all other figures of the article. Lower left: The corresponding KBHSH setup (same ADM mass and same angular momentum). Lower right: The same image as in the upper panel, but using a numerical Kerr spacetime described with SP coordinates.

Figure 6

Configuration II images. Same as in Fig. 5. Left: Image of an accretion torus surrounding the KBHSH of configuration II. Right: Same image for the comparable Kerr case.

Figure 7

Illustration of the various interesting regions in the image: The lensing ring is the outermost ring; it is the outer boundary of the hyperlensed region. The left part of the lensing ring is visibly distorted with respect to a Kerr photon ring. The inner ring is the photon ring. It is both the inner boundary of the hyperlensed region and the outer boundary of the shadow.

Figure 8

Configuration III images. Same as in Fig. 5. Left: Image of an accretion torus surrounding the KBHSH of configuration III. Note that the outer boundary of the central “noisy” region is not a photon ring, it is a lensing ring (see text for details). Right: Same image for the comparable Kerr case. The Kerr photon ring is very similar to the KBHSH lensing ring.