by neufer » Sat Nov 30, 2019 8:33 pm
BDanielMayfield wrote: βFri Nov 29, 2019 9:11 pm
So then how unlikely is this "coincidental" alignment?
What are the odds of the inner ring's perfect positioning right in the dead center of Hoag's galaxy's ring gap?
I just can't buy it that this is just total chance.
Hoag's Object apparent diameter is 0.28β² and therefore
covers just
1/600,000,000th (=[1.0-cos(0.28β²)]/2) of the sky.
If there are ~
N ring galaxies within 600 Mly of the sun then there are
~30,000
N ring galaxies within 18.6 Gly (=31 x 600 Mly) of the sun and therefore
~30,000
N ring galaxies at least 1/31st the apparent diameter of Hoag's Object.
The probability that the center of one of these ring galaxies lies
within Hoag's Object is ~30,000
N/600,000,000 or
N chances in 20,000.
A partial list of known ring galaxies within 600 Mly
suggests that
N in this case is probably on the order of ~20.
Hence, the probability that Hoag's Object
coincidentally contains a distinct
though more distant "
Piglet" is certainly no more than ~1 in 1,000
(and considering "
Piglet's" large size could be more like ~1 in 30,000).
[quote=BDanielMayfield post_id=297510 time=1575061885 user_id=139536]
So then how unlikely is this "coincidental" alignment?
What are the odds of the inner ring's perfect positioning right in the dead center of Hoag's galaxy's ring gap?
I just can't buy it that this is just total chance.[/quote]Hoag's Object apparent diameter is 0.28β² and therefore
covers just [b]1/600,000,000th[/b] (=[1.0-cos(0.28β²)]/2) of the sky.
If there are ~[b][color=#FF0000]N[/color][/b] ring galaxies within 600 Mly of the sun then there are
~30,000[b][color=#FF0000]N[/color][/b] ring galaxies within 18.6 Gly (=31 x 600 Mly) of the sun and therefore
~30,000[b][color=#FF0000]N[/color][/b] ring galaxies at least 1/31st the apparent diameter of Hoag's Object.
The probability that the center of one of these ring galaxies lies
within Hoag's Object is ~30,000[b][color=#FF0000]N[/color][/b]/600,000,000 or [b][color=#FF0000]N[/color][/b] chances in 20,000.
[url=https://en.wikipedia.org/wiki/List_of_ring_galaxies]A partial list of known ring galaxies within 600 Mly[/url]
suggests that [b][color=#FF0000]N[/color][/b] in this case is probably on the order of ~20.
Hence, the probability that Hoag's Object [b][i][u]coincidentally[/u][/i][/b] contains a distinct
though more distant "[b][color=#FF0000]Piglet[/color][/b]" is certainly no more than ~1 in 1,000
(and considering "[b][color=#FF0000]Piglet's[/color][/b]" large size could be more like ~1 in 30,000).