Radiation transfer of emission lines in curved space-time

Abstract

Abstract. We present a general formulation for ray-tracing calculations in curved space-time. The formulation takes full account of relativistic effects in the photon transport and the relative motions of the emitters and the light-of-sight absorbing material. We apply the formulation to calculate the emission from accretion disks and tori around rotating black holes. In our model the emission lines and continuum originate from an accretion disk or torus, and the motion of the emitters in the disk/torus is determined by the gravity of the black hole and the space-time structure near the black hole. The line-of-sight absorbing medium is comprised of cold absorbing cloudlets. These cloudlets are kinematically hot, with their velocity dispersion determined by the local virial temperature. The emission from the accretion disk/torus is resonantly absorbed/scattered. Our calculations demonstrate that line-of-sight absorption significantly modifies the profiles of lines from the accretion disks. It is often difficult to disentangle absorption effects from other geometrical and kinematics effects, such as the viewing inclination and the spin of the black hole. Our calculations also show that emission lines from accretion tori and from thin accretion disks differ substantially. Large geometrical obscuration could occur in tori, and as a consequence lines from tori generally have much weaker redshift wings at large viewing inclination angles. Moreover, the blue peak is truncated.

Variations in emission from episodic plasmoid ejecta around black holes

“…(see Baschek et al 1997;Fuerst & Wu 2004;Wu et al 2008), where ν is the frequency of the radiation, I is the invariant intensity, and λ is the affine parameter. The absorption coefficient χ0 and the emission coefficient η0, which are functions of frequency, are evaluated in the local fluid rest frame (hence the subscript "0").…”

Line emission from optically thick relativistic accretion tori

“…In particular the isobaric surface that describes the "surface" of the optically thick torus may be obtained by integrating away from the marginally stable orbit on its equator (Fuerst & Wu 2004). …”

“…If points beyond of 20R g are included the best fit value of n slowly decreases towards zero as the torus becomes more Keplerian in character. We use the above combined with the surface-finding method described in Fuerst & Wu (2004) and Fuerst (2005) to generate the tori in this paper. The shapes of the tori modelled in this paper are shown in Fig.…”

“…As in Fuerst & Wu (2004), the line emissivity is assumed to be a power law with I ∝ r −k . For the ray tracing, torus images of 1000 × 1000 pixels are constructed.…”

“…The method works well for 3D objects with most boundary conditions, provided that the step size in the integration is small enough (see e.g. Fuerst & Wu 2004). In practical calculations, a ray-tracing algorithm is often used.…”