Has the darkness of the night sky changed at your observing site? Would you like to know your naked-eye magnitude limit? Find out using both traditional and digital ways.

Finding your limit
How faint a star can you see with the naked eye? The darker the sky the more vivid the Milky Way . . . and everything else celestial!
Bob King

We all like to know how dark the sky is at our favorite observing sites. It makes it easy to compare one place to another and helps us decide how deep we might go with our telescope that night. A set of stars with stable brightnesses (no variables please!) running the gamut of magnitudes from bright to faint and positioned at a comfortable viewing angle fits the bill. The faintest one visible determines the NELM, or "naked-eye limiting magnitude," for that location.

Transparency can be highly variable, dependent on the amount of haze, smoke, and humidity in the air as well as your elevation. Long-term monitoring of limiting magnitude can reveal information about trends in local and regional light pollution or even the variability of airglow, caused by the recombination of atoms and electrons in the upper atmosphere that were ionized by the Sun's UV light earlier that day.

Determining the best part of the sky to pick a standard set of stars isn't always easy. Ideally, you should have a different set for each season. Maybe even a set for each direction since for most of us the sky is rarely uniform but instead brighter here and darker there due to variations in local light pollution levels.

Casey Reed

The object's altitude is also important so we must factor in atmospheric extinction. The closer a star is to the horizon the more air you have to look through and the more its light is dimmed or extinguished by the atmosphere and its brew of natural and synthetic aerosols.

The amount of air directly overhead is called 1 air mass. For a star 30° above the horizon, you're looking through 2 air masses. At 10°, 5.6 air masses, and for an object on the horizon, 40 air masses. A star seen 5° above the horizon will be dimmed by 3.5 magnitudes compared to the same star at the zenith assuming identical, ideal atmospheric conditions.

Box of stars!
This map of the Great Square of Pegasus, well-placed in the evening sky during fall and early winter, shows stars labeled with their visual magnitudes. Variables with a range greater than about 0.05 magnitude were left unlabeled. Maps of Octans and Ursa Minor can be found at the links below.
Stellarium with additions by the author

With this in mind, let's pick a set of stars of known magnitude at a high enough altitude (to avoid the worst of atmospheric extinction) and visible over much of the year. The celestial poles are ideal for mid-latitude observers, which is why you'll often see Ursa Minor used as an example. But to be fair to the Southern Hemisphere and with a nod to observers around Earth's middle, I've included three maps: Ursa Minor, Octans (Ursa Minor's equivalent in the Southern Hemisphere), and a familiar seasonal asterism, the Great Square of Pegasus.

I encourage you to create your own limiting magnitude maps by selecting what you feel is more appropriate for your location. Avoid the zenith, which has an unfair advantage, and areas within 40° of the horizon. At 40°, extinction amounts to about 0.2 magnitudes.

Find darkness
In this view from the Light Pollution Atlas centered on Indianapolis, sky brightness ranges from Bortle Class 9 (worst) to Class 4 (suburban / rural transition). Click the map to go to the site.
Jurij Stare, www.lightpollutionmap.info / Falchi, Fabio et al., advances.sciencemag.org/content/2/6/e1600377

A darker sky means more satisfying views of our favorite cosmic objects. If you live where light pollution gets you down, check out the interactive Light Pollution Atlas to help you find the darkest possible area in your region reachable by car. Color-coded zones of light pollution overlay detailed road maps that you can zoom into in great detail. Click anywhere and you'll get details about the site including its Bortle class — our next topic. Very handy!

Determining your NELM and including it in descriptions of what you see through your telescope provides a standard for comparing observations. A more comprehensive standard that uses limiting magnitude as its basis is the Bortle Dark-Sky Scale created by amateur astronomer and Sky & Telescope writer John Bortle. It first appeared in the February 2001 issue of Sky & Telescope magazine. Bortle considered NELM alone too dependent on individual eyesight and the variable amounts of time people put into the effort of seeing the faintest star.

Gradations of darkness
The Bortle Dark-Sky Scale visualized. skyglowproject.com

His nine-level scale bundles several factors including NELM, the appearance of the zodiacal light and Milky Way, telescope magnitude limit, and naked-eye visibility of familiar deep-sky objects like M33 and M31. Observer Nirvana is rated Class 1 with stars of magnitude 7.6–8.0 visible and M33 obvious with the naked eye. A rural sky, the best many of us who live near cities can reach, rates a Class 3. A Class 9, or inner-city sky, has a limiting magnitude of 4.0 or less.

There are also new apps for both Android and iPhone that let you use the phones' cameras to help navigate to and determine how faint a star you can see. For more information, check out the Dark Sky Meter (iPhone) and the Loss of the night (Android) on Google Play. Observers have the option with either app of sending their observations to international databases used to monitor night-sky brightness across the planet.

Any of these methods makes us more aware of what's happening to our sky, information we can use to better educate city councils on managing lighting to preserve the night or simply to inform our observing.

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Airglow

Comments


Image of Anthony Barreiro

Anthony Barreiro

October 10, 2018 at 5:26 pm

Here's a memorable scale that's useful in the city:
Magnitude 0 Vega.
Magnitude 1 Deneb.
The four stars of the head of Draco are
Magnitude 2 Eltanin / gamma Draconis.
Magnitude 3 beta Draconis.
Magnitude 4 xi Draconis.
Magnitude 5 nu Draconis.

Here's a chart for Draco: https://en.wikipedia.org/wiki/Draco_(constellation)#/media/File:Draco_IAU.svg

I happened to check from the sidewalk in front of my home the other night when the sky was clear: beta Draconis was clearly visible and xi Draconis wobbled in and out, so I called it 3.5. A few years ago the limiting magnitude was consistently closer to 4, but the installation of poorly designed LED streetlights and a boom in extravagantly illuminated skyscrapers has worsened the light pollution.

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Jakob

October 11, 2018 at 4:27 am

Same experience from my area in Sweden. It gets worse by the year )-: J

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Bob King

October 11, 2018 at 12:05 pm

Hi Anthony,
Very handy — thanks! Especially the convenience of the Draco head.

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Jakob

October 11, 2018 at 4:24 am

Just what I needed to know. Thanks for introducing this me to this site. Good wheather awaits this coming weekend so I will prepare for rural skies (-: J

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Bob King

October 11, 2018 at 12:05 pm

You're welcome, Jakob! It's an excellent resource.

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Rod

October 11, 2018 at 9:53 am

Very good report Bob. I live along the Patuxent river valley farms in Maryland, small farms, horses, alpacas, and hay growing, etc. No street lights where I am at and for quite a distance due to the fields and park areas. Sue French in the June 2018 issue of Sky & Telescope on page 54 reported about observing Nu1 and Nu2 Coronae Borealis, mv +5.4 and +5.6. I can still see these stars along with all those in Corona Borealis (7 stars). Observing to the west and northwest is worse because of lighting from DC area and towns farther away. Chesapeake Bay area viewing (east) is still very good and south and north east. I can walk out and distinctly see M31 - no problem. Portions of the Milky Way too running from Cygnus to Sagittarius in the fall - but not desert skies 🙂

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Bob King

October 11, 2018 at 12:07 pm

Hi Rod,
Similar here from my home but thankfully a 15-mile drive north brings exceptional skies in the north, east and west with NELM of ~6.3 and the gegenschein plainly visible on moonless, fall nights.

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richard szweda

October 13, 2018 at 11:16 am

I'm a little confused ....
Shouldn't
"A star seen at the zenith will be dimmed by 3.5 magnitudes compared to the same star 5° above the horizon assuming identical, ideal atmospheric conditions."
be ...
A star seen at the zenith will be brightened by 3.5 magnitudes compared to the same star 5° above the horizon assuming identical, ideal atmospheric conditions." ?
Thanks.

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goodricke1

October 13, 2018 at 5:38 pm

I suppose it could be interpreted as meaning that a star 3.5 magnitudes dimmer can be seen at the zenith compared to 5° above the horizon, but yes, the wording could be somewhat less obtuse!

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Bob King

October 14, 2018 at 11:20 am

Dear goodricke,
Sorry, I didn't mean for you to bend over backwards to make sense of it 🙂 Thanks for pointing this out. As you might have suspected I meant exactly the converse. Text now corrected. Thanks again!

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Joseph-Malet

March 5, 2019 at 9:37 pm

Is there a scale that uses the Sky Quality Meter numbers and arrive at what the Bortle Dark-Sky Scale is?
The description of each scale is too general and subjective to know which scale you are in for me. The SQM provides an accurate number on what the dark sky measurement is. Thanks, Joseph

I went to a site and measured 21.63 which is very good, but based on the description for the Bortle scale 1 & 2 I cannot tell which one to use,

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Bob King

March 6, 2019 at 3:28 pm

Hi Joseph,
Yes! Thank you for asking. There is such a scale that correlates the two measures of sky darkness at this link: http://www.cleardarksky.com/lp/ChrSprPkPAlp.html

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