adsabs/AstroCLIMB huggingface dataset:
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Photon shells of the Kerr BH spacetime. Black region is the central BH. Gray region is the outer ergoregion. There is ﹩r=\sqrt{{y}^{2}+{z}^{2}}﹩, and ﹩\theta =\arccos (z/r)﹩. ﹩{r}_{\epsilon }^{+}﹩ is the outer ergosurface. Spins signed on the panels are in Table 2. Orange dashed curves are the photon shells. Dashed yellow curve is radius r lim (where ℓ = 0) defined in Equation (20). Solid (dashed) curves are the curve ﹩{\ell }_{{\boldsymbol{D}}}={\ell }_{\sigma }^{\mp }=﹩ constant, connecting the extreme points of pressure and surfaces extreme points of the corotating (counterrotating) tori; see Appendix A. Radius r ( T ,Θ) (where ﹩\dot{\phi }=0﹩) is defined in Equation (25). Radii ﹩{r}_{* }^{\pm }﹩, with * = {mso, mbo, γ}, and ﹩{r}_{(* )}^{\pm }﹩ constraining the tori center location (see Table 1), coincide with the corotating and counterrotating geodesic structures' values. Notation ﹩{{\ell }}_{* }^{\pm }﹩ is for ℓevaluated at radius ﹩{r}_{* }^{\pm }﹩ respectively.
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Spherical photon orbits and inversion points. Upper left panel: radius r ( T ,Θ):ℓ   T   = ℓ Θ as function of the radius r for different BH spin values signed on the curves. Upper right panel: angle σ ( T ,Θ):ℓ   T   = ℓ Θ as function of the radius r. Each curve is for a different spin color coded according to the upper right panel. Bottom left panel: Carter constant q Θ evaluated on r ( T ,Θ) for different spins as function of the angle σ. Bottom right panel: impact parameter ℓ   T  (r ( T ,Θ)) = ℓ Θ(r (                         T                      ,Θ)) for fixed χ, where χ = a as function of the angle σ (dashed curves), and for χ = σ as function of the spin a (solid curves). Momentum ℓ Θ and Carter constant q Θ are defined in Equation (11). ℓ   T   is evaluated at the inversion surface. Radius r ( T ,Θ) is defined in Equation (25), and angle σ( T , Θ) is in Equation (24).
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Corotating and counterrotating tori in the photon shell. Yellow region is the photon shell. Right panel: black region is the central BH; gray region is the outer ergoregion. Vertical lines are spins listed in Table 2. Brown region is considered in Equation (24). Radius r lim (where ℓ = 0) is in Equation (20). Radii ﹩{r}_{* }^{\pm }﹩, with * = {mso, mbo, γ}, and ﹩{r}_{(* )}^{\pm }﹩ constraining the tori center location (see Table 1), coincide with the corotating and counterrotating geodesic structures' values. (± are for counterrotating/corotating momenta.) Left panel: radius ﹩r:{{\ell }}_{\sigma }^{\pm }({\sigma }_{\pm },a)={{\ell }}_{* }^{\pm }(a)﹩ for different momenta ﹩{{\ell }}_{* }^{\pm }﹩ is plotted as function off the BH spin a. Functions σ ± define the photon shell. Curves ﹩{\ell }_{{\boldsymbol{D}}}={\ell }_{\sigma }^{-}﹩ (﹩{\ell }_{{\boldsymbol{D}}}={\ell }_{\sigma }^{+}﹩) = constant connect the corotating (counterrotating) tori extreme points of pressure and surfaces; see Appendix A. Notation ﹩{{\ell }}_{* }^{\pm }﹩ is for ℓ evaluated at radius ﹩{r}_{* }^{\pm }﹩ respectively. Radius r ( T ,Θ) is defined in Equation (25).
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Ringed accretion tori and photon shell. Yellow region is the photon shell. Gray region (overlapped to the photon shell) is the outer ergoregion. Central black region is the central BH. Left panel: There is ﹩r=\sqrt{{y}^{2}+{z}^{2}}﹩ and ﹩\theta =\arccos (z/r)﹩. Blue and purple curves are protojets; green, cyan, and orange surfaces are tori. Toroidal parameters ℓ   D   are signed on the panel. Radius r lim (where ℓ = 0; in right panel is green solid curve) is in Equation (20). Radius r ( T ,Θ) is defined in Equation (25). Right panel: ﹩{r}_{\times }^{-}﹩ (﹩{r}_{\mathrm{center}}^{-}﹩) are the cusp (center) of the corotating cusped torus. Radius ﹩{r}_{\mathrm{outer}}^{-}﹩ is the outer edge of the corotating torus. See Figure 12 for further details.
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Analysis of the limiting radius ﹩{r}_{\mathrm{lim}}.﹩ Radius r lim (where ℓ = 0) is defined in Equation (20). Spins (vertical lines) are listed Table 2. Black region is the central BH, gray region is the outer ergosurface, and yellow region is the photon shell. Radii ﹩{r}_{* }^{\pm }﹩, with * = {mso, mbo, γ}, and ﹩{r}_{(* )}^{\pm }﹩ constraining the tori center location (see Table 1), coincide with the corotating and counterrotating geodesic structures' values. ( ± are for counterrotating/corotating momenta.) Notation ﹩{{\ell }}_{* }^{\pm }﹩ is for ℓevaluated at radius ﹩{r}_{* }^{\pm }﹩ respectively. Bottom panels are different views of the upper right panel.
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Crossing of accretion tori and photon shell. Upper left panel: angle ﹩\sigma :{\ell }_{{\boldsymbol{D}}}^{-}={\ell }_{\sigma }^{-}({r}_{\gamma }^{+})={\ell }_{* }^{-}﹩ as function of the BH spin a. Momenta ﹩{\ell }_{{\boldsymbol{D}}}={\ell }_{\sigma }^{\pm }﹩ are defined in Appendix A, and connect the counterrotating (corotating tori) extreme points of pressure and surfaces. Radii ﹩{r}_{* }^{\pm }﹩, with * = {mso, mbo, γ} (see Table 1), coincide with the corotating and counterrotating geodesic structures' values. Notation ﹩{{\ell }}_{* }^{\pm }﹩ is for ℓ evaluated at radius ﹩{r}_{* }^{\pm }﹩ respectively. (± are for counterrotating/corotating momenta.) All the spins (vertical lines in all panels) are defined in Table 2. Upper right panel: angle ﹩\sigma :{\ell }_{{\boldsymbol{D}}}^{-}={\ell }_{\sigma }^{-}({r}_{\mathrm{lim}})={\ell }_{* }^{-}﹩ as function of the BH spin a. Radius r lim (where ℓ = 0) defined in Equation (20). Bottom left panel: angle ﹩\sigma :{\ell }_{{\boldsymbol{D}}}^{-}={\ell }_{\sigma }^{-}(a\approx 1)=﹩ constant as function of the radius r. The panel is split in the region for ﹩{\ell }_{{\boldsymbol{D}}}^{-}\lt {\ell }_{\mathrm{mso}}^{-}﹩ and ﹩{\ell }_{{\boldsymbol{D}}}^{-}\gt {\ell }_{\mathrm{mso}}^{-}﹩. Bottom right panel: yellow region is the photon shell. Gray region (overlapped to the photon shell) is the outer ergoregion. Black region is the central BH. ﹩{r}_{\times }^{-}﹩ is the cusp of the corotating cusped torus. Radius ﹩{r}_{\mathrm{outer}}^{-}﹩ is the outer edge of the corotating torus. See Figure 12 and caption Figure 13 for further details.
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Close-up views of Figure 14—upper left panel.
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Kerr BH shadow boundaries for at all observational angles σ, and for fixed impact parameter ℓ or spherical orbit radius ℓ. Celestial coordinate β as function of the coordinate α for all values of angle σ ∈ [0, 1], for fixed BH spin a and for the outer ergosurface ﹩{r}_{\epsilon }^{+}(a,\sigma )﹩ (bottom panel), radius ﹩{r}_{* }^{\pm }﹩ (i), and impact parameter ℓ (upper left panel). Radii ﹩{r}_{* }^{\pm }﹩, with * = {mso, mbo, γ} (see Table 1), coincide with the counterrotating (+) and corotating (−) geodesic structures' values. Notation ﹩{{\ell }}_{* }^{\pm }﹩ is for ℓ evaluated at radius ﹩{r}_{* }^{\pm }﹩ respectively (the momenta of the geodesic structures). Arrows indicate the increasing values of σ along each curve. Each curve is for a fixed spin; each point of a curve is for a different value of σ.
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Accretion tori extreme points and photon shell. Right panel: tori momenta ﹩{\ell }_{{\boldsymbol{D}}}={\ell }_{\sigma }^{\mp }({\sigma }_{\pm })﹩ = constant, connecting the extreme points of pressure, and surfaces of the corotating and counterrotating tori (solid and dashed curves respectively; see Appendix A) are shown as functions of the radius r. Each curve is for a BH spin a signed on the curves. Functions σ ±, defining the photon's shells, are in Equation (18). Left panel: solutions ﹩\sigma :{\ell }_{{\boldsymbol{D}}}={\ell }_{\sigma }^{\mp }(a,r)={\ell }_{{\rm{\Theta }}}(a,r)﹩ are shown as functions of the radius r for different a signed on the curves. Momentum ℓ Θ is defined in Equation (11).
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Kerr BH shadow boundaries. Upper panels: shadow boundaries for (a ≈ 1, σ = 0.81; upper left panel) and (a = 0.81, σ = 1; upper right panel). Points on the shadow's boundaries correspond to the orbits with a fixed impact parameter ℓ or fixed radius r as signed on the upper left panel. ﹩{r}_{\epsilon }^{+}(a,\sigma )﹩, yellow points, is the outer ergosurface. Radius ﹩{r}_{\mathrm{lim}}﹩, gray points, correspond to the impact parameter ℓ = 0 and α = 0. Radii ﹩{r}_{* }^{-}﹩, with * = {mso, mbo, γ} (see Table 1), coincide with the corotating (−) geodesic structures' values. ﹩{r}_{\gamma }^{\pm }﹩ coincide with the outer and inner white points (+ is for counterrotating photon circular orbit on the equatorial plane), where (α [0,1], α [0,2]), and there is β = 0. Notation ﹩{{\ell }}_{* }^{\pm }﹩ is for ℓ evaluated at radius ﹩{r}_{* }^{\pm }﹩ respectively (the momenta of the geodesic structures). Where ℓ   T   is the inversion surface impact parameter (where ﹩\dot{\phi }=0﹩). Bottom left (right) panel is a realization of the upper left (right) panel, in the plane (y,z). There is ﹩r=\sqrt{{y}^{2}+{z}^{2}}﹩ and ﹩\theta =\arccos (z/r)﹩. (The bottom left panel is for a = 0.9.) Central black region is the BH; gray region is the outer ergoregion. Dashed orange curves are the photon shell. The lines σ = 0.81 (purple line in the left panel) and σ = 1 the equatorial plane (right panel) show the region included in the photon shell on the upper panels, i.e., all points therefore correspond to the upper panel points on the shadow boundary. Hence, white points correspond to the coordinates (α [0,1], α [0,2]). The surface with ﹩r={r}_{\mathrm{lim}}(a)﹩, r = r ( T ,Θ)(a, σ), defined in Equation (25), r = r   T  (a, σ), and ﹩{r}_{* }^{-}﹩ are also shown. The intersection of these surfaces with the lines σ = constant, included in the photon shell, define the points on the shadow boundary of the upper panels. (For convenience curves, ﹩{\ell }_{{\boldsymbol{D}}}={\ell }_{\sigma }^{-}=﹩ constant, connecting the extreme points of pressure, and surfaces extreme points of the corotating tori are also shown—see Figure 16.)
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Analysis of tori crossing the photon shell boundary. Upper left panel: radius r solution of ﹩r:{V}_{\mathrm{eff}}^{2}\left({\ell }_{{\boldsymbol{D}}}^{-}({r}_{\times }),{\sigma }_{\pm }(r)\right)={K}^{2}({\ell }_{{\boldsymbol{D}}}^{-}({r}_{\times }))﹩ as function of the tori cusps ﹩{r}_{\times }\in \left[{r}_{\mathrm{mbo}}^{-},{r}_{\mathrm{mso}}^{-}\right]﹩ for different BH spins, as signed on the panel. Radii ﹩\{{r}_{\mathrm{mbo}}^{\mp },{r}_{\mathrm{mso}}^{\mp }\}﹩ coincide with the corotating/counterrotating marginally bounded and marginally stable orbits values. Function V eff is the tori effective potential; K is the function defining the tori topology (see Appendix A). ℓ   D   = ℓ ± are the counterrotating and corotating fluid specific angular momentum respectively. Functions σ ±(a, r) (photon shell boundaries) are defined in Equation (18). Dashed curve is radius ﹩{r}_{\mathrm{mbo}}^{-}(a)﹩, evaluated on the spin function ﹩{a}_{\mathrm{mso}}^{-}({r}_{\times }):{r}_{\times }={r}_{\mathrm{mso}}^{-}(a)﹩. Other panels are the solutions of ﹩\sigma :{V}_{\mathrm{eff}}^{2}\left({\ell }_{{\boldsymbol{D}}}^{\pm }({r}_{\times }),{r}_{\lambda }(\ell )\right)={K}^{2}({\ell }_{{\boldsymbol{D}}}^{\pm }({r}_{\times }),{r}_{\times })﹩ as function of the impact parameter ℓ, for counterrotating (upper right panel) and corotating (bottom panels) cusped tori. Each curve is for a different spin signed on the panels. Bottom right panel is a close-up view of the bottom left panel. The cusp r × has been fixed as in the panel. Radius r  λ  is in Equation (14).
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Inversion surfaces and photon shell (yellow region) of the Kerr BH. Gray region is the outer ergoregion. Black region is the central BH, where ﹩r=\sqrt{{y}^{2}+{z}^{2}}﹩, and ﹩\theta =\arccos (z/r)﹩. Inversion radius r   T   of the counterrotating flows (orange curves), for different fluid specific angular momenta, are represented (dotted–dashed for ﹩{{\ell }}_{\gamma }^{+}﹩, dashed for ﹩{{\ell }}_{\mathrm{mbo}}^{+}﹩ solid for ﹩{{\ell }}_{\mathrm{mso}}^{+}﹩). Radius r lim (dotted–dashed black curve) is defined in Equation (20). Radius r ( T ,Θ) is defined in Equations (25). The blue lines, z  x , mark the minimum vertical coordinate for the existence of the double inversion point (see text). There is no double inversion point for small BH spin (see right panel).
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Inversion radii r   T   of the counterrotating flows for different fluid specific angular momenta, as signed on the upper left panel, are shown as function of the BH spin a for different angle ﹩\sigma ={\sin }^{2}\theta ﹩ signed on each panel. Gray region is the outer ergoregion. Black region is the central BH. Radius r lim (dotted–dashed black curve) is defined in Equation (20). Radius r ( T ,Θ) is defined in Equations (25). Yellow curves are the photon shell boundaries. ﹩{r}_{\gamma }^{\pm }﹩ are the photon circular orbits on the equatorial plane. r + is the BH horizon. ﹩{r}_{\epsilon }^{+}﹩ is the outer ergosurface. Spins {a = 0.3, a = 0.5, a = 0.7, a = 0.9} are colored dashed vertical lines.
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Kerr BH shadow boundaries for all spins and observational angles. Right (left) panel: celestial coordinate β as function of the coordinate α for all values of angle σ ∈ [0, 1] (BH spin a ∈ [0, 1]). Each curve is for a fixed spin (angle) and a fixed radius as signed on the panel. Each point of each curve is for a fixed σ (spin a; red point is a for minimum σ, spin a; blue point for maximum σ (a)). ﹩{r}_{\epsilon }^{+}(a,\sigma )﹩ is the outer ergosurface. Radii ﹩{r}_{* }^{\pm }﹩, with * = {mso, mbo, γ}, coincide with the counterrotating (+) and corotating (−) geodesic structures' values. r   T   is the inversion radius where ﹩\dot{\phi }=0﹩.
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Kerr BH shadow boundaries; variation of the β coordinate for spin and observational angle. Celestial coordinate β > 0 for different values of the impact parameter ℓ signed on the curves as function of the BH spin a and fixed angle σ (left panel) and as function of the angle at fixed spins (right panel). Notation ﹩{{\ell }}_{* }^{\pm }﹩ is for the ℓ ±(r) evaluated at radius ﹩{r}_{* }^{\pm }﹩ respectively (the momenta of the geodesic structures), where radii ﹩{r}_{* }^{\pm }﹩, with * = {mso, mbo, γ} (see Table 1), coincide with the counterrotating (+) and corotating (−) geodesic structures' values; see Appendix A.
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Inversion impact parameter ℓ   T   on the equatorial plane σ = 1, as function of the BH spin a ∈ ]0, 1], for selected values of the inversion radii r   T   signed on the curves. Dotted vertical lines are selected spins considered in the analysis of Appendix B.
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Same as Figure B2 for angle σ = 0.51. Right panel is a close-up view of the left panel.
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Inversion radii r   T   of the counterrotating flows for different fluid specific angular momenta, as function of angle ﹩\sigma ={\sin }^{2}\theta ﹩ for fixed BH spin a signed on each panel. See Figure B2's caption for further details.
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Images of thin accretion disks around the Kerr black hole with spin a as seen by a distant observer at the different inclination angle ﹩\sigma \equiv {\sin }^{2}\theta ﹩. Each panel is for a different σ. Colored lines are isoradial curves representing rays emitted at constant radius r from the BH, as seen by an observer. (The black strips, breaking the rings, in this case are a numerical artifact.) The correspondent thin disk models are described in Figure C7 for the thin disk orbiting a BH with spin a = 0.3 (upper line, first left and second panels). There is (r outer = 14.266, r center = 7, ℓ = 3.51123). In Figure C10, for a = 0.6 (second line, third and right panels). There is (r inner = 3, r outer = 9.64867, r center = 5.19296, ℓ = 3.12238). For a = 0.81 (bottom line first left and second panels), there is (r inner = 2.3, r outer = 6.60679, r center = 3.75097, ℓ = 2.75836; see Figure C12). For a BH with spin a = 0.999 (bottom line third and right panels), class (5)(iv), torus model (c) has r inner = 1.07, r outer = 6.81754, ℓ = 2.05818 (see Figure C21).
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: BH shadow boundary (right panel), and BH photon shell and torus (left panel) for a Kerr BH with spin a = 0.3 for class (1) (﹩a\in [0,{a}_{(\gamma ,b)}^{\pm }[﹩ see Table 2) of Section 4. Left panel: yellow region is the BH photon shell. Black region is the central BH. Gray region is the outer ergoregion. (There is ﹩r=\sqrt{{y}^{2}+{z}^{2}}﹩ and ﹩\theta =\arccos (z/r)﹩.) Light blue region is the torus with parameter ℓ signed on the panel. (Note the torus is external to the photon shell.) Dotted–dashed pink line is the angle ﹩\sigma \equiv {\sin }^{2}\theta ﹩ as signed on the panel. Dashed green curve is radius r lim (where ℓ = 0) defined in Equation (20). Dashed purple curve is radius r ( T ,Θ) (where ﹩\dot{\phi }=0﹩) is defined in Equation (25). (For a = 0.3, radii r (                            T                         ,Θ) and r lim are very close in the photon shell.) Solid red (blue) curve is the curve ﹩{\ell }_{{\boldsymbol{D}}}={\ell }_{\sigma }^{-}={\ell }_{\mathrm{mso}}^{-}({\ell }_{\mathrm{mbo}}^{-})﹩. Shadow boundary at fixed σ is on the right panel in celestial coordinates (α, β).
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Left and center panels: 3D paths from a lamppost coronal model for a = 0.9 (left, class (4) for ﹩a\in [{a}_{({\ell },\gamma ,b)}^{\mp },{a}_{({\ell },\gamma ,\gamma )}^{\mp }[﹩—see Section 4) and a = 0.999 (center panel, class (5)(iv) for ﹩[{a}_{({\ell },\gamma ,\epsilon )}^{-},1]﹩). Black central region is the black hole. Right panel: photon trajectories for different impact parameter on the equatorial plane (θ = π/2) of a Kerr BH with spin a = 0.9. Central black region is the BH; gray region is the outer ergoregion. Yellow region is the photon shell. Dashed darker-blue (green) circle is the counterrotating (corotating) photon circular orbit (﹩{r}_{\gamma }^{\pm }﹩ respectively.) Dotted–dashed red (dashed black) circle is the radius r ( T ,Θ) (r lim). Each curve is for a fixed impact parameter ℓ signed on the curve. There is ﹩{{\ell }}_{\gamma }^{\pm }\equiv {\ell }({r}_{\gamma }^{\pm })﹩ respectively. (See also Figure C2.)
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Apparent image of an equatorial thick disk (Polish Doughnut) in the Kerr BH spacetime with a = 0.3 (class (1) for (﹩a\in [0,{a}_{(\gamma ,b)}^{\pm }[﹩) as seen by a distant observer at different inclination angle σ signed on the panels. Each panel is for a different view angle ﹩\sigma \equiv {\sin }^{2}\theta ﹩. It refers to the analysis of Figure C5. There is (r outer = 14.266, r center = 7), and ℓ = 3.51123.
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Photon paths in the Kerr BH with spin a = 0.9 (class (4), correspondent to ﹩a\in [{a}_{({\ell },\gamma ,b)}^{\mp },{a}_{({\ell },\gamma ,\gamma )}^{\mp }[﹩—described in Section 4), for selected angles θ, signed on the panel. Center black region is the Kerr BH, gray region is the outer ergoregion, yellow circle is the inner radius of the photon shell, blue circle is the outer radius of the photon shell, red dotted–dashed circle is radius r ( T ,Θ), dashed black circle is r lim, and axis α = 0 and β = 0 are also shown. In bottom line are close-up views of the upper line. (See also Figure C1.)
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Apparent image of an equatorial thick disk (Polish Doughnut) in the Kerr BH spacetime with a = 0.6. It refers to the analysis of Figure C8. There is (r inner = 3, r outer = 9.64867, r center = 5.19296, ℓ = 3.12238).
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Apparent (redshift) image of an equatorial thin disk in the Kerr BH spacetime with a = 0.3. It refers to the analysis of Figure C5. There is (r outer = 14.266, r center = 7, ℓ = 3.51123). Each panel is for a different view angle ﹩\sigma \equiv {\sin }^{2}\theta ﹩. The observer is placed at asymptotic infinity (the radial coordinate is set at r = 1000M).
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Analysis of the photon shell “obscuration” by an internal torus. BH shadow boundary (right panel); BH photon shell and torus (left panel) for a Kerr BH with spin a = 0.6 of Section 4 (class (2) for ﹩a\in [{a}_{(\gamma ,b)}^{\pm },{a}_{(\gamma ,s)}^{\pm }[﹩—see Table 2). The gray region on the right panel is the shadow region correspondent, in the left panel, to the photon shell section occupied by the torus. For further details, see description in Figure C5.
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Photon paths in the Kerr BH spacetime with spin a = 0.999 (class (5)(iv) for ﹩[{a}_{({\ell },\gamma ,\epsilon )}^{-},1]﹩). See, for further details, the caption of Figure C2.
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Apparent image of an equatorial thin disk in the Kerr BH spacetime with a = 0.81. It refers to the analysis of Figure C11. Each panel is for a different view angle ﹩\sigma \equiv {\sin }^{2}\theta ﹩. There is (r inner = 2.3, r outer = 6.60679, r center = 3.75097, ℓ = 2.75836).
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Apparent image of an equatorial thin disk in the Kerr BH spacetime with a = 0.6. It refers to the analysis of Figure C8. Each panel is for a different view angle ﹩\sigma \equiv {\sin }^{2}\theta ﹩. There is (r inner = 3, r outer = 9.64867, r center = 5.19296, ℓ = 3.12238).
Paper: Photon Shells, Black Hole Shadows, and Accretion Toroids
Authors: D. Pugliese, Z. Stuchlík
Figure caption: Analysis of Figure C8 for a BH with spin a = 0.999 (class (5)(iv) for ﹩[{a}_{({\ell },\gamma ,\epsilon )}^{-},1]﹩—see Table 2). Disk model (a) in left panel has r inner = 1.0933999, with r outer = 2.00809 and parameter ℓ = 2.04484. Angle views σ = 0.99 (pink line central panel) and σ = 0.95 (cyan line and right panel) are shown.