Naked Eye Limiting Magnitude: Redux

Having just tried to assess Naked Eye Limiting Magnitude from a dark site, I realised that my previous post on the subject merited some amendments.

Rather than using the whole constellation of Ursa Minor to carry out your NELM estimate, it’s much simpler to use just part of it, that part around the “body” of UMi, roughly bounded by and immediately surrounding β, γ, ζ, and η UMi. Here’s a more detailed star chart of that part of the sky, with all 34 stars brighter than magnitude 7.2 labelled.

UMi detail down to mag 7.2

And here’s a list of the magnitudes of each of these stars:

Star Number (Name)	Magnitude	Star Number (Name)	Magnitude
1 (β UMi)	2.05	18	6.55
2 (γ UMi)	3.00	19	6.60
3 (ζ UMi)	4.25	20	6.60
4 (5 UMi)	4.25	21	6.65
5 (4 UMi)	4.80	22	6.70
6 (η UMi)	4.95	23	6.80
7 (θ UMi)	5.00	24	6.85
8 (11 UMi)	5.00	25	6.85
9 (19 UMi)	5.45	26	6.85
10	5.55	27	6.85
11	5.70	28	6.85
12	6.00	29	6.90
13	6.25	30	6.95
14	6.30	31	7.00
15 (20 UMi)	6.35	32	7.10
16	6.35	33	7.20
17 (3 UMi)	6.40	34	7.20

As you can see, it’s much easier to fine-tune your NELM estimate using this chart compared to the previous one, as there are not such big jumps between brightnesses from one star to the next.

Colours in this table correspond to the Bortle Scale colour key.

Crucially, one thing I omitted to note in the previous post was that this process should be carried out when your target stars are high above the horizon. The stars of Ursa Minor, when observed from the UK, vary in altitude between 40° and 70° roughly speaking, so ideally you’d wait until they were higher than 60° above the northern horizon.

Month	Times when Kocab (β UMi) alt > 60°
mid Jan	0300 till start astronomical twilight (~0600)
mid Feb	0100 till start astronomical twilight (~0530)
mid Mar	2330 till start astronomical twilight (~0430)
mid Apr	2230 till start astronomical twilight (~0400)
mid May	end astronomical twilight till start astronomical twilight
mid Jun	no hours of darkness
mid Jul	no hours of darkness
mid Aug	never > 60° during hours of darkness
mid Sep	never > 60° during hours of darkness
mid Oct	never > 60° during hours of darkness
mid Nov	never > 60° during hours of darkness
mid Dec	0500 till start astronomical twilight (~0630)

UPDATE: Here’s the chart with the magnitudes written directly beside each star.

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Naked Eye Limiting Magnitude: Assessing Sky Brightness

There are a variety of ways of measuring your night sky quality, and one of the most effective ways is by looking for the faintest star you can find with your naked eye, and noting its brightness, or magnitude. This provides what is known as Naked Eye Limiting Magnitude, NELM.

Of course just randomly casting about the sky for faint stars can lead you on a merry chase, and so a very useful method is to use one specific constellation – one you can always see, no matter what time of year – and look only at stars within that one constellation. This narrows the field somewhat, and makes your task that much easier.

For observers in Europe and North America the constellation of Ursa Minor, the Little Bear, provides an excellent choice for estimating NELM.

The overall shape of Ursa Minor is made up of seven bright-ish stars, but around and amongst these are many more fainter stars.

Ursa Minor

Bright Star Name (Bayer Designation)	Magnitude
Polaris (α)	1.95
Kocab (β)	2.05
Phercab (γ)	3.00
Yildun (δ)	4.35
Urodelus (ε)	4.20
Ahfa al Farkadain (ζ)	4.25
Anwar al Farkadain (η)	4.95

Even some of these “brighter” stars might not be visible from city centres. For example, if you are observing from a site with Bortle Class 8 you would not see η-UMi, while those unhappy stargazers under a Bortle Class 9 sky would only be able to pick out the three brightest stars, α-, β-, and γ-UMi. Only at Bortle Class 7 and darker will you make out all seven of the main stars of Ursa Minor.

But what if you’re at a good dark sky site? Well, you’re going to need a longer list of magnitudes, and a more detailed map of Ursa Minor.

Star Number on Above Map	Star Name	Visual Magnitude	Bortle Class
1	α UMi	1.95	9
2	β UMi	2.05	9
3	γ UMi	3.00	9
4	ε UMi	4.20	8
5	5 UMi	4.25	8
6	ζ UMi	4.25	8
7	δ UMi	4.35	8
8	4 UMi	4.85	7
9	η UMi	4.96	7
10	θ UMi	5.00	7
11	11 UMi	5.02	6
12	19 UMi	5.45	6
13	24 UMi	5.75	5
14	λ UMi	6.30	4
15	20 UMi	6.35	4
16	3 UMi	6.40	4
17	π1 UMi	6.55	3
18	HIP74818	6.65	3
19	14 UMi	7.35	2

The stars in the map and table above have been numbered (by me – these aren’t official designations) from 1 to 19, with 1 (Polaris) being the brightest, and 19 (14 UMi) being the dimmest. You will only be able to see all 19 numbered stars from exceptionally dark places, virtually free of light pollution, what Bortle called “typical truly dark sky sites”. From my garden in the outskirts of a major city I can see numbers 11 and 12, but not number 13, giving me an NELM of 5.45.