by johnnydeep » Fri Aug 21, 2020 9:20 pm
BDanielMayfield wrote: ↑Fri Aug 21, 2020 8:11 pm
Consensus speaks. The "whys?" have it.
FWIW, I emailed Paul Howell <
phowell@bowdoin.edu> from the
Unwinding attribution on the image and he replied as follows:
I suppose at a certain level your question would be better answered by Robert Nemiroff and Jerry Bonnell. Taking a stab at it, I would say the point is education and engagement. It looks like it worked <g>. Not just this image, but the whole idea behind APOD if I may speak for Robert and Jerry.
Sure, there is nothing in the 'unwound' image that could not be measured. In fact, that has certainly been done. But like a plot that illuminates something more intuitively than a column of numbers, this image reinforces the remarkable property that spiral arms (often) obey a log spiral.
I guess I could go a bit further and say that the image demonstrates that the end of one arm closest to NGC 5195 departs from a log spiral which tends to support the idea that there has been an interaction. This too is not something that you could not deduce through analysis but the image is more accessible to a broader group.
I only glanced quickly at the discussions (semester startup and all . . . ), but here's some feedback.
- The progressive 'fuzziness' of the image as you get closer to the bottom is a consequence of the logarithmic transformation. If you look at a plot of y=ln(x), you will see it is steep at first and then flattens. Consequently, pixels that originate close to the origin (the center of M51 e.g.) get stretched more vertically due to the transformation. Additionally, the x-axis is the phase angle of the transformation. Pixels close to the origin subtend a greater angle than those far away. That stretches those pixels along the phase axis. So pixels at a small radius (near the bottom, e.g.) are quite stretched in each direction.
- NGC 5195 comes through largely unscathed for these reasons: At large r and for relatively small changes in r, y=ln(r) is approximately linear. So the y-axis maps pretty much the same way you see it. Then, the small angle approximation gives us that theta ~ sin(theta) where theta is in radians. This means that angular displacement maps to linear displacement in proportion. So the x-axis maps to what you see as well since NGC 5195 is not close to the origin.
- I think I saw a post wondering why two arms don't end up straight but opposed (?). The reason is that each arm is displaced in phase angle by roughly pi radians.
- Not sure if this was discussed, but there is no beginning or end to the image along the x (phase) axis. It just continuously repeats since you are simply wrapping around as you go. Think of it as a picture on a coffee mug that has no start or end. Hmmmmmmm <g>.
Did this help? I'm still not really appreciating it properly I suppose, other than the log plot linear result "proving" the log nature of the spiral. Also, who are Robert Nemiroff and Jerry Bonnell?
EDIT: BDanielMayfield let me know who they are just below
[quote=BDanielMayfield post_id=305424 time=1598040709 user_id=139536]
Consensus speaks. The "whys?" have it.
[/quote]
FWIW, I emailed Paul Howell <phowell@bowdoin.edu> from the [i]Unwinding [/i]attribution on the image and he replied as follows:
[quote]I suppose at a certain level your question would be better answered by Robert Nemiroff and Jerry Bonnell. Taking a stab at it, I would say the point is education and engagement. It looks like it worked <g>. Not just this image, but the whole idea behind APOD if I may speak for Robert and Jerry.
Sure, there is nothing in the 'unwound' image that could not be measured. In fact, that has certainly been done. But like a plot that illuminates something more intuitively than a column of numbers, this image reinforces the remarkable property that spiral arms (often) obey a log spiral.
I guess I could go a bit further and say that the image demonstrates that the end of one arm closest to NGC 5195 departs from a log spiral which tends to support the idea that there has been an interaction. This too is not something that you could not deduce through analysis but the image is more accessible to a broader group.
I only glanced quickly at the discussions (semester startup and all . . . ), but here's some feedback.
- The progressive 'fuzziness' of the image as you get closer to the bottom is a consequence of the logarithmic transformation. If you look at a plot of y=ln(x), you will see it is steep at first and then flattens. Consequently, pixels that originate close to the origin (the center of M51 e.g.) get stretched more vertically due to the transformation. Additionally, the x-axis is the phase angle of the transformation. Pixels close to the origin subtend a greater angle than those far away. That stretches those pixels along the phase axis. So pixels at a small radius (near the bottom, e.g.) are quite stretched in each direction.
- NGC 5195 comes through largely unscathed for these reasons: At large r and for relatively small changes in r, y=ln(r) is approximately linear. So the y-axis maps pretty much the same way you see it. Then, the small angle approximation gives us that theta ~ sin(theta) where theta is in radians. This means that angular displacement maps to linear displacement in proportion. So the x-axis maps to what you see as well since NGC 5195 is not close to the origin.
- I think I saw a post wondering why two arms don't end up straight but opposed (?). The reason is that each arm is displaced in phase angle by roughly pi radians.
- Not sure if this was discussed, but there is no beginning or end to the image along the x (phase) axis. It just continuously repeats since you are simply wrapping around as you go. Think of it as a picture on a coffee mug that has no start or end. Hmmmmmmm <g>.
[/quote]
Did this help? I'm still not really appreciating it properly I suppose, other than the log plot linear result "proving" the log nature of the spiral. Also, who are Robert Nemiroff and Jerry Bonnell?
EDIT: BDanielMayfield let me know who they are just below :oops: