After some thought, I decided that some might be interested a graphic showing surface visibility evaluation details.
Art - I pursued a hybrid empirical evaluation using both the YouTube wireframe and an accurate, family of ray-trajectories. The two approaches agreed very well, only because the wireframe has a 1.3M
☉ example and the actual mass is estimated at 1.35M
☉.
- Fraction of surface area visible = 68% to 70%
The left panel shows a large collection of parallel light-ray trajectories originating at right from infinity interacting with a Schwarzschild black hole. The right panel a screenshot from the video showing the actual and apparent size of a 1.3M
☉ NS. The two panels are scaled so that the NS actual sizes are equal.
→ The blue rays show a family of "plunge orbits", i.e. all rays that are captured by the black hole.
→ The red rays show trajectories that aren't captured
→ The smaller black circle is the BH event horizon of mass M, and
radius = 1 Schwarzschild radius,
RS
→ The larger green circle represents the
NS actual size = 3.25
RS
→ Green shaded area represents visible NS surface.
→ The 2 black trajectory rays leave the NS from their tangent point
(furthest visible point on surface) and propagate to infinity
Note:The X and Y distance units in the left pane Are normalized by the quantity G/c
2 . The Schwarzschild radius = 2M in GR-convenient units.
- The indicator lines connecting the two panels show the very good agreement for the predicted apparent NS sizes.
The apparent size difference between and 1.3M☉ and1.35☉are within the accuracy of the evaluation techniques. (I was pleasantly surprised the agreement as this good)
[u][/u]After some thought, I decided that some might be interested a graphic showing surface visibility evaluation details.
[i]Art[/i] - I pursued a hybrid empirical evaluation using both the YouTube wireframe and an accurate, family of ray-trajectories. The two approaches agreed very well, only because the wireframe has a 1.3M[sub][size=150]☉[/size][/sub] example and the actual mass is estimated at 1.35M[sub][size=150]☉[/size][/sub].
[b][color=#0000FF][list]Fraction of surface area visible = 68% to 70%[/list][/color][/b] The left panel shows a large collection of parallel light-ray trajectories originating at right from infinity interacting with a Schwarzschild black hole. The right panel a screenshot from the video showing the actual and apparent size of a 1.3M[sub][size=150]☉[/size][/sub] NS. The two panels are scaled so that the NS actual sizes are equal.
[float=left][attachment=0]Visible Surface Fraction Evaluation_2.JPG[/attachment][/float]
→ The blue rays show a family of "plunge orbits", i.e. all rays that are captured by the black hole.
→ The red rays show trajectories that aren't captured
→ The smaller black circle is the BH event horizon of mass M, and
radius = 1 Schwarzschild radius, [i]R[sub]S[/sub][/i]
→ The larger green circle represents the [u]NS actual size [/u]= 3.25 [i]R[sub]S[/sub][/i]
→ Green shaded area represents visible NS surface.
→ The 2 black trajectory rays leave the NS from their tangent point
(furthest visible point on surface) and propagate to infinity
[b]Note:[/b]The X and Y distance units in the left pane Are normalized by the quantity G/c[sup][size=140]2[/size][/sup] . The Schwarzschild radius = 2M in GR-convenient units.
[list]The indicator lines connecting the two panels show the [u]very good agreement for the predicted apparent NS sizes.
[/u]The apparent size difference between and 1.3M[sub][size=150]☉[/size][/sub] and1.35[sub][size=150]☉[/size][/sub]are within the accuracy of the evaluation techniques. (I was pleasantly surprised the agreement as this good)[/list]