Rotating accretion flows in D dimensions: Sonic points, critical points, and photon spheres

Abstract

We give the formulation and the general analysis of the rotational accretion problem on Ddimensional spherical spacetime and investigate sonic points and critical points. First, we construct the simple two-dimensional rotating accretion flow model in general D-dimensional static spherically symmetric spacetime and formulate the problem. The flow forms a two-dimensional disk lying on the equatorial plane and the disk is assumed to be geometrically thin and has uniform distribution in the polar angle directions. Analyzing the critical point of the problem, we give the conditions for the critical point and its classification explicitly and show the coincidence with the sonic point for generic equation of state (EOS). Next, adopting the EOS of ideal photon gas to the analysis, we reveal that there always exists a correspondence between the sonic points and the photon spheres of the spacetime. Our main result is that the sonic point of the rotating accretion flow of ideal photon gas must be on (one of) the unstable photon sphere(s) of the spacetime in arbitrary spacetime dimensions. This paper extends this correspondence for spherical flows shown in the authors' previous work to rotating accretion disks.

Photon surfaces in spherically, planar, and hyperbolically symmetric spacetimes in D dimensions: Sonic point/photon sphere correspondence

“…We can easily observe that SP/PS correspondence holds in Schwarzschild (anti) de-Sitter spacetime from the work by Mach et al [7] with the knowledge that the spacetime has a photon sphere on the radius 3M . Surprisingly, it was recently found that SP/PS correspondence always holds in arbitrary static spherically symmetric spacetime of arbitrary dimensions for spherical flow [9] and rotational flow [10]. In addition to its applications to observations in astrophysics, SP/PS correspondence has interesting implications concerning fundamental mechanism of fluid dynamics on curved spacetime.…”

Spherical Accretion Flow onto General Parameterized Spherically Symmetric Black Hole Spacetimes

“…Recently, it was shown that there is a correspondence between the sonic points of ideal photon gas and the photon sphere in static spherically symmetric spacetimes [44]. This important result is valid not only for spherical accretion of the ideal photon gas, but also for rotating accretion in static spherically symmetric spacetimes [45][46][47]. In this section, we establish this correspondence in the parameterized spherically symmetric black hole.…”

“…Recently, it was shown that there is a correspondence between the sonic points of accreting ideal photon gas and the photon sphere in static spherically symmetric spacetimes [44]. This important result is valid not only for spherical accretion of the idea photon gas, but also for rotating accretion in static spherically symmetric spacetimes [46,47]. In an observational viewpoint, as mentioned in [47], this correspondence connects two independent observations, the observation of lights from sources behind a black hole and the observation of emission from accreted radiation fluid onto the black hole, because the size of the shadow of the hole is determined by the radius of the photon sphere and the accreted fluid can signal the sonic point.…”

Deflection angle of a light ray reflected by a general marginally unstable photon sphere in a strong deflection limit

“…Static, spherically symmetric spacetimes, which describe strong gravitational fields caused by compact objects, have circular photon orbits and the set of the photon orbits is called photon (antiphoton) sphere if it is unstable (stable) [4]. The property of the (anti)photon sphere such as the upper bound of the radius [5] and number [6] has been investigated since the (anti)photon sphere is related in phenomena in the strong gravitational field such as the high-frequency behavior of the photon absorption cross section [7,8], stability of thinshell wormholes [9,10], the high-frequency spectrum of quasinormal modes of compact objects [11][12][13], a centrifugal force and gyroscopic precession [14][15][16][17], Bondi's sonic horizon of a radial fluid [18][19][20][21][22][23], and an apparent shape during a collapsing star to be a black hole [24][25][26]. Extensions and alternatives of the photon sphere have been investigated [27][28][29][30][31][32][33][34][35][36][37][38][39] and instability of the compact objects caused by the slow decay of linear waves near stable photon rings has been considered [40][41][42].…”