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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Sark: Night 1

Just walked east to west across Sark taking SQM measurements, from La Valette to La Fregondee, around 2km worth of data in more or less a straight line. Readings every 100m or so means that there isn’t much variation, with the darkest reading being 21.53 magnitudes per square arcsecond just west of the mill on the highest point of the island, and the brightest reading being 21.27 magnitudes per square arcsecond outside the brightly lit Mermaid Pub. To all intents and purposes though the readings were the same across the island, and it confirms what we suspected; that Sark is dark, but not as dark is it would be were it not next to Guernsey and Jersey, both of which contributed visibly towards skyglow. The best observing site so far is next to the old mill, the highest point on Sark, and indeed in all the Channel Islands. This tall tower would make an ideal observatory, but that might go against local conservation issues…

Dark skies of Sark:

Skies over Sark

Canon 5D with Sigma 8mm 180° EX DG fisheye lens f3.5, 120 seconds, ISO1000

In the above image you can see the glow from Guernsey (WNW, top right), Jersey (SSE, bottom left), and France (NE, top right). Despite the glow you can see many hundreds, indeed thousands of stars. Remember, this image was deliberately exposed to reveal light pollution, and so the sky looks more light polluted than in reality it is. This is in order to identify the worst culprits for light pollution. You can still make out the familiar shapes of the Plough, Orion the Hunter, Mars, Saturn and the Milky Way (just). For a high-res version visit my Flickr page

Now, to bed.

The Magnitude Scale in Astronomy

Astronomers describe how bright an object is using something called the magnitude scale. They might describe a bright star as being “first magnitude”, or the limit of human naked-eye observing as being “around 6.5 mag”. But what exactly do they mean?

The Greek astronomer Hipparcus, in the second century BCE, developed an early magnitude scale in which he grouped the stars in the night sky into six magnitude classes; the twenty brightest stars were given magnitude class of 1, the next brightest group a magnitude class of 2, all the way down to the faintest stars, at the limit of the human detection, which were given a magnitude class of 6.

This system is similar to that used today, except we have expanded the scale in both directions: for fainter objects, as our use of telescopes allows us to explore beyond the limit of the human eye; and for brighter objects such as the Moon and the Sun.

The faintest object detectable by the Hubble Space Telescope has a magnitude of around 32, whereas the Sun has a magnitude of around -27.

Our modern magnitude scale is logarithmic, meaning that for each unit you go up the scale, you get dimmer by a factor of 2.512 (this seemingly arbitrary number is chosen so that objects separated by 5 magnitudes – such as the brightest star in the night sky compared with the dimmest star visible to the naked eye – differ in brightness by a factor of 100, i.e. 2.512 to the power of 5).

So how much brighter is the Sun than the faintest star visible to the Hubble Space Telescope? The answer is 2.512 to the power of 60, or 10 million million million million times brighter. Those kind of astronomical numbers are impossible to visualise, and difficult to deal with, never mind to write out, and so astronomers opt for the much more manageable, if no more intuitive, magnitude scale.

Examples of magnitudes of astronomical objects

Full Moon: -12.6
Venus at its brightest: -4.6 (brightest planet)
Sirius -1.5 (brightest star in the night sky)
Vega 0 (Vega is part of the constellation Lyra the Harp, in the Summer Triangle)
Limit of an urban sky: 3 to 4
Limit of the human eye: 6.5 (depending on your eyesite of course

All of these numbers are apparent magnitude, that is the brightness as seen from Earth, and not a measure of an object’s intrinsic brightness.