Messier-1 – Another way to cook a crab

OTA:………….CDK17 f/6/8

Camera:……….FLI Proline 16803, 9 micron pixels, 0.64 arcsec/pxl

Observatory:…. Rodeo, NM (Data collected by Bernard Miller)



EXPOSURES:

…R……10 x 900 sec.

…B…...11 x 900

…G….....8 x 900

…L…...22 x 1200 (not used)

…O.….13 x 1800

…H.….10 x 1800

…S.…..12 x 1800

Total exposure 32.3 hours

Processed by Alex Woronow (2021) using PixInsight, Topaz, LuminarAI, SWT

There's nothing new I could say about Messier 1, so I'll relate a bit about the processing I used on this image and on most images where I have both broadband and narrowband data.

If a target's structural features primarily result from H/S/O radiation, most image processors relegate RGB to the walk-on role of providing color to the stars. But it can play a role that I think is much more interesting and important. It can give us information about the pure emission-line signal in the images, free from the inevitable background radiation softening both the broadband and narrowband image stacks. The motivation to isolate the emission line from the background should be obvious: The emission lines delineate where the action is—where atoms are excited, where processes occur most violently, where the gasses are most dense, where hypervelocity winds sculpt and compress the cloud, where shock fronts form and clouds collide. These are the areas where the structures in the cloud arise and predominate. Often these locations signal new-star formation (although no so in M-1). But for me, these are the areas that, when revealed, make the most interesting images.

Pretend you did not read the above paragraph, then you might ask, "why not just add the Ha and R in some arbitrary proportion? after all, that's what the scripts available in PI do. Surely, this would then include all that information from the pure line radiation automatically." True, but not optimal. Such a simple mixing approach is a zero-order approach; it dilutes the pure line radiation spatially diffuse background radiation. (The background radiation arises from free-free transitions, molecular transitions, etc.).

A better approach uses a first-order extraction of the pure signal from Ha line radiation, free from the background (and the same for SII and OIII lines) "USING…MATH!!!!", as Bender said. This first-order approach offers a definite improvement over the zero-order approach of simply tossing the broadband together with the narrowband. It gives us access to an estimate of the pure emission line and the features described in the first paragraph.

Let consider a simple case where we have Green broadband and OIII narrowband images. We can write two equations:

G = OL + B

OIII = c(OL) + kB

OL is the pure OIII line radiation, and B is the background radiation that accompanies it. The k and c are scaling factorw between the broadband, G, and narrowband OIII images, depending on their relative acquisition parameters. We solve these two simultaneous equations for OL, the pure OIII line, free from its background. (We can do the same for Blue and OIII radiation lines.)

Suppose we have two narrowband contributions to the same broadband image (e.g., SII and HII). In that case, we write three simultaneous equations and solve for the two emission lines free of the background (again, to a first-order approximation). Then, with the line contributions isolated and in hand, we can mix (or not) those lines back into the broadband image, use them in the luminosity to accentuate the structures delineating levels of emission-line activity, etc.

Here, the pure-emission-line data played two roles in this image: mixed (2::1) with the corresponding broadband filter data and used to form the luminosity component, which was processed separately before being introduced into the now modified SHORGB image.

If you are interested in this approach, I have written a PixInsight script that does the math of extracting estimates of each emission line (HII, SII, OIII). I'd be glad to share it with anyone who requests it; just contact me through the "Send private message" page of Astrobin.

Futurama Fact off the Internet:

The Futurama theorem is a real-life mathematical theorem invented by Futurama writer Ken Keeler (who holds a Ph.D. in applied mathematics), purely for use in the Season 6 episode "The Prisoner of Benda." (I believe this is where Bender says the above-quoted statement.)

It is the first known theorem to be created for the sole purpose of entertainment in a TV show and, according to Keeler, was included to popularize math among young people.

The theorem proves that, regardless of how many mind switches between two bodies have been made, they can still all be restored to their original bodies using only two extra people, provided these two people have not had any mind switches prior (assuming two people cannot switch minds back with each other after their original switch).