Cluster Cluster Burning Bright.... How to Determine your Limiting Magnitude

Pretty soon I’m going to be making my yearly observation of Pluto. It’s not situated well along my horizon yet, so I’m getting ready. I have seen it in the past with my eVscope, but this year I’m going after it with a Vespera and next year probably with a SeeStar. I’ll describe the procedure for hunting down the dwarf planet in the coming weeks.

To prepare I went out a couple nights ago to just see how easy it is for me to get to 14th magnitude, which is about how bright Pluto shines. (I know I’ve seen down to 17th with my eVscope 1 when I recorded the JWST on its way to orbit from my Chicago, Bortle 9, alleyway. And my image below also goes down far fainter than 14.)

So, considering Vespera is 1/2 the aperture diameter of the eVscope, I expect for the same amount of stacking time, for point sources at least, that the Vespera will see 1/4 the amount of light. I believe this then would be ~15.5th magnitude. This is close enough for me to want to test. These scopes all use very similar chip technologies, so the only really difference in sensitivity for the same amount of time should be the aperture.

(For those of you with the wonderful Dwarf II, this analysis holds pretty well too, though your aperture is a bit smaller, 24 mm, so it will probably consistently be only about 0.8 magnitude behind the Vespera for the same amount of stacking time.)

CALIBRATED OPEN CLUSTERS

The only convenient way I know to “measure” faint magnitudes is to use calibrated open clusters. NGC 6494 (M23) is one. I’m sure one can get better charts than I have below, but here is what I use for M23. Another cluster I like is M67, but it’s not convenient this time of the year.

The charts I use for M23 are from: Roger Clarks’s amazing book entitled, “Visual Astronomy of the Deep Sky,” Cambridge U. Press, 1990. Here they are:

For comparison, below is a 4 minute eVscope 1 image I captured just over two years ago and oriented to be close to matching the charts. The arrow points to a star that is easily 14th magnitude. I can see stars in the image that go at least two magnitudes fainter, though they aren't in Clark's charts.

For M67, the Royal Astronomical Society of Canada’s, “Observer’s Handbook 202X” always has a very useful chart that goes even deeper — down to 21st magnitude. Its article, “Limiting Magnitudes” by Douglas Pitcairn is the one to read and has a couple charts.

"IF THE SUN AND MOON SHOULD EVER DOUBT...." Wm. Blake.

This week I decided to try and at least satisfy myself that I wouldn’t have trouble imaging Pluto. I also decided to go out and try when the Moon was only 8 degrees away from M23 to push my background even higher than normal. The Vespera warned me that I was maybe too close for a good image. But, ever brave and always interested in taking some data, pressed go.

The next image is what I got after 10 minutes with the “light pollution” CLS filter in. I didn’t do any post processing on this image. It’s not as great as what others from better locations can do, but it gave me the data I needed.

I can clearly see that I’ve gotten down to some of Clark’s tiniest M23 spots, which are around 14th, including the one marked in the deeper eVscope image. In a larger image I can see I'm even going a bit fainter. So, I’m good to go for Pluto once the Moon starts to get out of the way. ;-)

PLAYING LIKE BIG BOYS

I love taking performance data and some future blog entries will probably bore you to tears. Calibrating and understanding how things are working is just interesting to me. One of the take aways I like from magnitude tests like this is to use them to help me think about how these scopes really hit far above their aperture when going faint. Here’s why.

For regular “live” viewing, with your eye through an amateur telescope, the limiting magnitude you will see is approximately: m~2.7+5logD, where D is the telescope's aperture in mm*. So, for my Vespera’s aperture of 50mm, if I were to just use it as one half of a pair of binoculars, I could expect to see down to about magnitude 11. Check the image and charts above and you can see the stacked image goes far fainter.

This is no surprise, but what is interesting is that — to me at least — the experience of watching my image develop on my phone is not that different than looking through an eyepiece. Which means that my sensitivity with the Vespera, even in a light polluted sky is similar to at least an 8 inch or ~200 mm scope. When I go to 17th magnitude, the equivalent live eyeball scope would have to be 724 mm or 28 inches! I’m sure some eVscope or eQuinox users have even gone down to about 18th magnitude, which is pushing the sensitivity of a 1 meter Dobsonian!

Smart scopes "sip" rather than "gulp" light.

This equivalent luminous “gain” is one thing that’s quite amazing to me. In a sky where I can barely see 3rd magnitude with my eyes alone, I can easily see stars or planets that I would need to take a telescope pushing 1 meter in aperture out to the country skies.

Another feature we’ll rely upon to find Pluto is that these scopes point where you ask them to point. This finding the planetary needle, in the stellar haystack will be much easier.

INFRARED CALIBRATION CAUTION?

There is one slight caveat to my measurements here, however. The chips in the smart scopes are all relatively sensitive in the near infrared. So, we have to be careful getting precise numbers out of them directly, even with this scheme I’ve presented. But, at least in my case, I’m not trying to produce data that can be analyzed carefully. I’m just testing my limits.

Also, the spectrum of Pluto has a lot of near infrared in it, which should help. After all, Pluto shines at the “pleasure” of the Sun, which, as we know this summer, produces plenty of heat-light, AKA infrared.

APERTURE ENVY BEATERS

Smart scopes IMHO are a cure for aperture envy. Resolution, of course, is a different matter, but if you want to see the faint sky from convenient locations, then they're great.

But, there is a tight relationship between resolution, aperture, pixel size and FOV. While still waiting for Pluto, I'll be addressing the connections between these factors next week.

Speaking of silicon chips, which are after all just large, organized sand grains, brings to mind some other words of Blake:

"To see a World in a Grain of Sand

....

Hold Infinity in the palm of your hand...."

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*Observer’s Handbook 2023,” Royal Astronomical Society of Canada, pg. 49.

Header image by Wm Blake's with apologies to the Tate Britain.... Newton (1795–1805) 460 x 600 mm.