📝 Original Info
- Title: Images of the radiatively inefficient accretion flow surrounding a Kerr black hole: application in Sgr A*
- ArXiv ID: 0904.4090
- Date: 2014-11-18
- Authors: Researchers from original ArXiv paper
📝 Abstract
In fully general relativity, we calculate the images of the radiatively inefficient accretion flow (RIAF) surrounding a Kerr black hole with arbitrary spins, inclination angles, and observational wavelengths. For the same initial conditions, such as the fixed accretion rate, it is found that the intrinsic size and radiation intensity of the images become larger, but the images become more compact in the inner region, while the size of the black hole shadow decreases with the increase of the black hole spin. With the increase of the inclination angles, the shapes of the black hole shadows change and become smaller, even disappear at all due to the obscuration by the thick disks. For median inclination angles, the radial velocity observed at infinity is larger because of both the rotation and radial motion of the fluid in the disk, which results in the luminous part of the images is much brighter. For larger inclination angles, such as the disk is edge on, the emission becomes dimmer at longer observational wavelengths (such as at 7.0mm and 3.5mm wavelengths), or brighter at shorter observational wavelengths (such as at 1.3 mm wavelength) than that of the face on case, except for the high spin and high inclination images. These complex behaviors are due to the combination of the Lorentz boosting effect and the radiative absorption in the disk. We hope our results are helpful to determine the spin parameter of the black hole in low luminosity sources, such as the Galactic center. A primary analysis by comparison with the observed sizes of Sgr A* at millimeters strongly suggests that the disk around the central black hole at Sgr A* is highly inclined or the central black hole is rotating fast.
💡 Deep Analysis
Deep Dive into Images of the radiatively inefficient accretion flow surrounding a Kerr black hole: application in Sgr A*.
In fully general relativity, we calculate the images of the radiatively inefficient accretion flow (RIAF) surrounding a Kerr black hole with arbitrary spins, inclination angles, and observational wavelengths. For the same initial conditions, such as the fixed accretion rate, it is found that the intrinsic size and radiation intensity of the images become larger, but the images become more compact in the inner region, while the size of the black hole shadow decreases with the increase of the black hole spin. With the increase of the inclination angles, the shapes of the black hole shadows change and become smaller, even disappear at all due to the obscuration by the thick disks. For median inclination angles, the radial velocity observed at infinity is larger because of both the rotation and radial motion of the fluid in the disk, which results in the luminous part of the images is much brighter. For larger inclination angles, such as the disk is edge on, the emission becomes dimmer at
📄 Full Content
More and more observations indicate that supermassive black holes reside in most local galaxies, and the coevolution of galaxies, quasars and supermassive black holes was realized in last decade (e.g., Ferrarese & Merritt 2000;Gebhardt et al. 2000;Hopkins et al. 2008). From the stellar dynamics, it is not surprising to find that the compact radio source Sagittarius (Sgr) A* at the center of our Galaxy is associated with a ∼ 4×10 6 M ⊙ massive dark object (Schödel et al. 2003;Ghez et al. 2005;Ghez et al. 2008). A natural candidate of the massive dark object is massive black hole, as emphasized by Kormendy & Richstone (1995), they argued convincingly that this object is a black hole, and the other alternatives to a black hole should be ruled out. Some of these alternatives have already been excluded. They include a cluster of dark objects, such as the stellar remnants or brown dwarfs (Maoz 1998), a binary made of point masses, self gravitationally supported Fermi ball (Miller 2006;Tsiklauri & Viollier 1998;Munyaneza et al. 1998;Yuan, Narayan, & Rees 2004). Another alternative which is still waiting for being excluded is self gravitationally supported boson ball (Torres et al. 2000;Yuan, Narayan, & Rees 2004). However, the problem of this model is that the mass of bosons is arbitrarily assumed to make a massive boson ball, and the energy dissipation between bosons may lead to the collapse of the ball (Maoz 1998).
Recent very-long baseline interferometry (VLBI) observation at the wavelength of 3.5mm shows its intrinsic size is 0.126±0.017 mas, about ∼ 1AU , and the resulting lower limit of its mass density is 6.5 × 10 21 M ⊙ pc -3 (Shen et al. 2005), and the VLBI observation at 1.3mm gives the intrinsic size 0.037 +0.016 -0.010 mas, and the resulting lower limit of its mass density is 9.3 × 10 22 M ⊙ pc -3 (Doeleman et al. 2008), which strongly supports that Sgr A* is a supermassive black hole. The millimeter VLBI observation has been used to estimate the parameters of SgrA* accretion flow (Broderick et al. 2008). In the near future, higher resolution observations of Sgr A* at infrared (Paumard et al. 2005) and sub-millimeter wavelengths will be available (Doeleman & Bower 2004;Miyoshi et al. 2004;Fish et al. 2008), which can provide a direct test of the physical processes under the strong gravity, such as the dynamics of the accreted gas, complex trajectories of photons, and so on. Therefore, it is necessary to investigate the images of the flux and polarization of realistic accretion flows (Yuan et al. 2004;Broderick & Loeb 2006a;Huang et al. 2007Huang et al. , 2008)), and the images and light curves associated with a hot spot in the accretion flow near the black hole horizon (Broderick & Loeb 2005, 2006b), the hot spot is proposed to explain the observations of near-infrared and X-ray flaring of Sgr A*.
It is generally believed that Sgr A* was a low luminosity AGN whose activity was switched off due to insufficient gas supply (Narayan 2002). Multi-wavelength observations put strict constraints on theoretical accretion models of the massive black hole at the Galactic center. Among the theoretical models, the advection-dominated accretion flow (ADAF) model, also called the radiatively inefficient accretion flow (RIAF) model is claimed to be very successful in modeling the multi-wavelength spectrum from radio to X-ray (Narayan et al. 1995(Narayan et al. , 1998;;Yuan et al. 2003Yuan et al. , 2004)).
Based on the RIAF model, the images of Sgr A* at millimeter have been calculated, the size of the images is compared with observations to put an independent constraint on the RIAF model (Yuan et al. 2006;Huang et al. 2007), and the shape of the images, especially the location of the image centroid of Sgr A* can be used to determine the black hole spin (Broderick & Loeb 2006a).
There are several shortcomings in the previous calculations: first, although the treatment of the photon trajectories is within the framework of fully general relativity by using a ray tracing method, the accretion model is Newtonian, which means the global structure of the accretion flow is based on the Newtonian dynamics. The general relativity effect for the accretion flow is mimicked with Paczynski & Wiita potential. Therefore, the radial velocity of the accretion flow very close to the black hole is larger than the speed of light and thus is unphysical. Second, the massive black hole is assumed to be a non-rotating (Schwarzschild) hole in Yuan et al. (2004).
In this paper, following Manmoto (2000), the global structure of the relativistic ADAF around a Kerr black hole is derived to calculate the images of Sgr A* surrounding a Kerr black hole with an arbitrary black hole spin and viewing angle at several millimeter wavebands. Our treatment is within the framework of fully general relativity. A brief introduction to relativistic ADAF model is given in §2. The ray tracing method and the radiation transfer in curved space-time are discus
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