Limiting Magnitude

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==Limiting Magnitude and City Skies==
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Limiting magnitude is the [[magnitude]] of the dimmest object that can be seen with a particular optical system be it unaided eye's binoculars or a [[telescope]]. Several factors can affect what the actual limiting magnitude will be.
Of course the problem with observing from within a city is that the sky itself has a visual magnitude. This limits what can be observed, though with larger instruments, you can see fainter objects. For example, from my light polluted back yard within the city of Calgary (or as we like to call it, light pollution central), my unaided eye, on a good night can see down to 4th magnitude which is much brighter than the 6th to 7th magnitude that you could see at a good dark site. At this magnitude, most constellations are missing stars and other than the moon and planets, there's not a heck of a lot to look at. Even so the Pleiades and the Hyades, for example, are visible in the winter time, albeit missing stars.
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If I move up to my 10x50 binoculars, my limiting magnitude moves to around 7. This of course brings many more items into visibility, at least in theory. There are at least 50 deep sky objects that would fit into this category, that are visible from Calgary's, and hence Canada's, latitude. Now this is a theoretical 50, as for many objects, the actual surface brightness will be less than what the magnitude suggests. This is because for extended objects, i.e. non-stars, the magnitude is the aggregate of the total brightness of the object. The more spread out an object is, the dimmer it actually appears for a given magnitude. So two objects can have the same magnitude, but if one is spread out more, it would appear dimmer. This is one reason why this list won't be simply generated from a planetarium program as the magnitudes listed won't necessarily translate into observability at a given limiting magnitude.
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==Theoretical Limiting Magnitude==
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All other factors equal, the limiting magnitude of an optical system is based solely on the aperture of the objective lens. This can be worked out with the following formula:
  
I will also include objects visible with a small telescope. My 127mm (5 inch) Maksutov has a theoretical limiting magnitude of about 13. However due to light pollution within the city this becomes something around 9 to 10. Again with surface brightness differing from magnitude, it's unlikely there will be many 9th mangitude galaxies on the list, but what I can see through my scope will be.
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<math>m_v\approx2.7+5\log_{10} d</math>
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where d is the diameter of the objective lens/mirror of the optical system in mm. This formula makes the assumption that the magnification used is greater than the diameter of the objective in mm, so telescope with a 70mm objective needs an eyepiece that gives at least 70x of magnification for this formula to be accurate. It also assumes clear and dark skies <ref name="birney">Birney, D.S., Gonzales, G., Oesper, D., 2008, Observational Astronomy, 2nd ed, (Cambridge)</ref>
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So for example, a dark adapted human eye with an aperture of about 7mm has a limiting magnitude of about 6.7 at a dark site. A 50mm set of binoculars has a limiting magnitude of 11.0 and a 127mm telescope has a limiting magnitude of about 13.0.
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These magnitudes are limits for the human eye at the telescope, modern image sensors such as CCD's can push a telescope 4-6 magnitudes fainter<ref name="birney"> </ref>.
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==Factors Affecting Limiting Magnitude==
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Now the theoretical limiting magnitude calculated with the formula above  is the limiting magnitude under ideal conditions. As conditions are never ideal, the value may be less than that calculated. The atmosphere above the observing site has an effect. The closer to sea level a site is, the more atmosphere one has to look through and this has a negative effect on limiting magnitude. The weather has another effect, on how transparent the air is due to water and dust in the atmosphere. Turbulence causes stars to be smeared making them seem dimmer.
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The telescope optics also have an effect on the limiting magnitude beyond the diameter of the objective. Poorly produced or aligned optics will spread the light of an object out and make it seem dimmer. Dirt and dust on the optics will also absorb and diffract light, again making the object seem dimmer than it really is. Higher magnification can, to a point, improve contrast by making the sky appear blacker. This works especially well on stars as their light doesn't get spread out as much under magnification as does that of extended objects.
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The age and skill of the observer is also a factor. As we age, our pupils don't dilate as much as they did when we were younger, limiting how much light gets into our eye. This is less a factor with a telescope as carefully selected telescope-eyepiece combinations can compensate for this somewhat but still something to consider. Further skilled observers can generally see dimmer objects than novice observers once they learn and master techniques such as averted vision.
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Finally the sky itself has a magnitude. Even at the darkest site, there is a faint glow to the sky called air glow caused by starlight being scattered by the atmosphere. Other natural phenomenon such as the Zodiacal light and aurora also cause the sky to be less dark than it could be. Beyond natural phenomenon, the light pollution from city lights causes an incredible degradation to the brightness of the night sky. Human light pollution can push limiting magnitudes to values around 4 or higher, so only the brightest stars can be seen with the unaided eye. Binoculars and telescopes also see a corresponding reduction in their limiting magnitues such that 50mm binoculars can only see around magnitude 7 or so and a 127mm telescope is limited to around 10th magnitude.  
  
 
==Determining Limiting Magnitude==
 
==Determining Limiting Magnitude==
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==Maps==
 
==Maps==
 
===Limiting Magnitude Maps===
 
===Limiting Magnitude Maps===
The limiting magnitude maps are .pdf and .ps files. They are held in the file repository on my blog. The links below provide access to the files:
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The limiting magnitude maps are .pdf and .ps files. They are held in the file repository on the blog evilscientist.ca. The links below provide access to the files:
  
 
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M67
 
M67
[[Image:m67.png | thumb | 640px]]
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[[Image:m67_map.png | thumb | 640px]]
  
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| [[Category:Information]]
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<References/>
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[[Category:Observing Concepts]]

Latest revision as of 09:40, 1 June 2018

Limiting magnitude is the magnitude of the dimmest object that can be seen with a particular optical system be it unaided eye's binoculars or a telescope. Several factors can affect what the actual limiting magnitude will be.

Contents

[edit] Theoretical Limiting Magnitude

All other factors equal, the limiting magnitude of an optical system is based solely on the aperture of the objective lens. This can be worked out with the following formula:

m_v\approx2.7+5\log_{10} d

where d is the diameter of the objective lens/mirror of the optical system in mm. This formula makes the assumption that the magnification used is greater than the diameter of the objective in mm, so telescope with a 70mm objective needs an eyepiece that gives at least 70x of magnification for this formula to be accurate. It also assumes clear and dark skies [1]

So for example, a dark adapted human eye with an aperture of about 7mm has a limiting magnitude of about 6.7 at a dark site. A 50mm set of binoculars has a limiting magnitude of 11.0 and a 127mm telescope has a limiting magnitude of about 13.0.

These magnitudes are limits for the human eye at the telescope, modern image sensors such as CCD's can push a telescope 4-6 magnitudes fainter[1].

[edit] Factors Affecting Limiting Magnitude

Now the theoretical limiting magnitude calculated with the formula above is the limiting magnitude under ideal conditions. As conditions are never ideal, the value may be less than that calculated. The atmosphere above the observing site has an effect. The closer to sea level a site is, the more atmosphere one has to look through and this has a negative effect on limiting magnitude. The weather has another effect, on how transparent the air is due to water and dust in the atmosphere. Turbulence causes stars to be smeared making them seem dimmer.

The telescope optics also have an effect on the limiting magnitude beyond the diameter of the objective. Poorly produced or aligned optics will spread the light of an object out and make it seem dimmer. Dirt and dust on the optics will also absorb and diffract light, again making the object seem dimmer than it really is. Higher magnification can, to a point, improve contrast by making the sky appear blacker. This works especially well on stars as their light doesn't get spread out as much under magnification as does that of extended objects.

The age and skill of the observer is also a factor. As we age, our pupils don't dilate as much as they did when we were younger, limiting how much light gets into our eye. This is less a factor with a telescope as carefully selected telescope-eyepiece combinations can compensate for this somewhat but still something to consider. Further skilled observers can generally see dimmer objects than novice observers once they learn and master techniques such as averted vision.

Finally the sky itself has a magnitude. Even at the darkest site, there is a faint glow to the sky called air glow caused by starlight being scattered by the atmosphere. Other natural phenomenon such as the Zodiacal light and aurora also cause the sky to be less dark than it could be. Beyond natural phenomenon, the light pollution from city lights causes an incredible degradation to the brightness of the night sky. Human light pollution can push limiting magnitudes to values around 4 or higher, so only the brightest stars can be seen with the unaided eye. Binoculars and telescopes also see a corresponding reduction in their limiting magnitues such that 50mm binoculars can only see around magnitude 7 or so and a 127mm telescope is limited to around 10th magnitude.

[edit] Determining Limiting Magnitude

First determine if you're using your unaided eye, binoculars or telescope. You will then need to download the appropriate map from here. If you have a postscript printer, download the .ps postscript files as they will print cleaner than the .pdf files.

Once you have your file(s), on a dark moonless night go out into your back yard with a printout of the appropriate map and locate the appropriate object – Ursa Minor (Little Dipper) for the unaided eye, the "bowl" of Ursa minor for binoculars or M67 for a telescope.

Look at the object and circle the stars you see in the sky on the map. Use a red filtered flashlight if you need it to see the map. Once you've circled the stars you can see you can go indoors and work out your limiting magnitude.

Many of the stars on the map have numbers beside them. These numbers are the magnitudes of the stars they are beside, without decimal points. The decimal points have been omitted so they don't confuse you by looking like stars. This means that a star that is magnitude 5.3 is marked as 53, 10.2 as 102 and so on. Just assume there's a decimal point before the last digit.

Find the three stars you saw with the largest numbers. These will be the dimmest ones you saw. The average of these three stars will give you a good idea what your limiting magnitude will be.

[edit] Maps

[edit] Limiting Magnitude Maps

The limiting magnitude maps are .pdf and .ps files. They are held in the file repository on the blog evilscientist.ca. The links below provide access to the files:

File File Type Contents
umivis.pdf PDF Naked eye map in PDF format
umvis.ps PS Naked eye map in postscript format
umibino.pdf PDF Binocular map in PDF format
umibino.ps PS Binocular map in postscript format
M67lim.pdf PDF Telescope map in PDF format
M67lim.ps PS Telescope map in postscript format

[edit] Locator Maps

Here are locator maps for Ursa Minor and M67

Ursa Minor

Umi.png

M67

M67 map.png


  1. 1.0 1.1 Birney, D.S., Gonzales, G., Oesper, D., 2008, Observational Astronomy, 2nd ed, (Cambridge)
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