Working magnitude limits

[glenc]

I have been trying to establish working magnitude limits (WML) for the southern deep sky catalogs produced by Lacaille in 1751-52, Dunlop in 1826 and John Herschel (JH) in 1834-38. I defined the WML as the magnitude where they saw half the objects in a modern catalog and missed half of them.
For example JH saw half the galaxies in the Principle Galaxy Catalog (PGC) brighter than magnitude 12.7 and he missed half the galaxies brighter than 12.7. Dunlop's WML using the PGC is 10.9. Lacaille only saw one galaxy (M83 = mag 7.1) so I used globular clusters to find his WML = 6.4.

It turns out that the WML is about 85% of their magnitude limits for stars.
Their star mag limits are L=7.6, D=13.1 and JH=15.2.

This suggests that we can comfortably (or easily) see deep sky objects to magnitude [9.1 + 5log(D)] x 85% where D is the aperture in inches.
The WML for a 12" is 12.3. We can see fainter objects but they are not obvious when sweeping.
(Some more WML are 8" = 11.6, 10" = 12.0, 16" = 12.9 and 20" = 13.3)

Does anyone have any suggests or comments on how to define or find a WML? Does the above sound reasonable?

[Ian Robinson]

In my variable star observing days - I used a trick called averted vision to "see" stars close to or just beyond my ordinary threshhold when my eyes which were young then (in my teens) were dark adapted.

Works a treat on point light sources .... not sure how good it is on extended fuzzies.

[glenc]

Averted vision works well with galaxies too. I can see mag 14.7 stars with my 12" and mag 12.0 galaxies like NGC 4387 are easy. The WML isn't the same as the faintest object we can see. Ron saw the magnitude 13.7 galaxy NGC 646 with a 16".
http://www.iceinspace.com.au/forum/showthread.php?t=22041&highlight=ngc+360

[Merlin66]

Field contrast and attention can easily get you down in visual magnitude.
I used x180 on SuperNovae search and regularly got down to 15.5mag with a 12" Newt.
Remember a lot of the time Herschel was just sweeping and recording "on the run" so I would have thought his WML would have been lower than a dedicated amateur purposely looking for/ observing a known object.

[glenc]

Yes that is the point, he was "on the run" and only had a short time to look at each object. Thanks for the mag 15.5 observation.

[Rob_K]

Hi Glen, this is excellent stuff, congratulations! :thumbsup:

However, your formula should be expessed as [9.1 + 5logD] x 85%. Took me a while to work this out, as I punched in my aperture and got a WML of mag 11.8, which was obviously too high (more like my threshhold, although I have seen some mag 12 objects). 10.5 is a better figure, but still maybe a touch high. Perhaps the formula might fall down a little with small apertures - would like to know your opinion on this. Certainly, no 2" telescope would have a WML in excess of mag 9.1, you'd think.

Cheers -

Rob

[glenc]

Thanks Rob, I have corrected the formula in post#1.
I saw a mag 10.7 star next to M83 last night with 20x80s but the WML for 20x80s is be more like 9.9.

[Ian Robinson]

I regularly observed variable stars as faint as 11.5 mag with my 20x65 binoculars and my 60mm refractor (in the 1970s). Averted vision again.

And Herchell's telescope optics weren't too flash either by modern standards. Specula mirrors - reflectivity only about 0.72 (varies from 63% at 4500 A. to 75% at 6500 A , and less if tarnished).

[glenc]

Ian, I was interested in your percentages for reflectivity. Do you have a web site for them?
Magnitude 11.5 with 65mm binoculars suggest that the formula is m = 9.5 + 5log D with D in inches.
That is the magnitude limit for stars of course not a WML for DSO.
My WML is defined as the magnitude where the observer only finds half the DSO available.
Herschel's 18.5" with no secondary mirror was about equal to a modern Newtonian 16.5" assuming 88% reflectivity for Al and 61% for speculum at 550nm.

[glenc]

Here are some curves for finding magnitude limits.
http://www.uv.es/jrtorres/tools.html#Visib

[Ian Robinson]

Here : http://www.iop.org/EJ/volume/0950-7671/24
S Tolansky et al 1947 J. Sci. Instrum. 24 248-249 .

[glenc]

Thanks Ian