Sky pollution, Bortle, and sky magnitude

Sky pollution, Bortle, and why dark skies massively cut integration time

Bortle vs “sky brightness”

• Bortle is a descriptive class (1–9) based on what you can see visually.

• Sky brightness is a measurable number in mag/arcsec² (SQM). This is what your exposure math actually uses.
  
  

Typical rough mapping (varies a lot with direction, altitude, humidity, moon, etc.):

• Bortle 2: ~21.6–22.0 mag/arcsec²

• Bortle 4: ~20.8–21.3

• Bortle 6: ~19.5–20.3

• Bortle 8/9: ~18–19
  
  

1) How sky mag shortens total integration time

If you’re sky-limited (which wide-field usually is), then the SNR improves like:

• SNR ∝ √(total integration / sky flux)

So to get the same final SNR, required integration time scales directly with sky brightness (flux):

Convert sky mag difference to flux ratio

A difference in sky brightness of Δm mag/arcsec² changes sky flux by:

• Sky flux ratio = 10^(0.4 × Δm)

And therefore:

• Required integration time ratio ≈ 10^(0.4 × Δm) (to reach the same depth/SNR)

Concrete examples

• Bortle 6 (20.0) → Bortle 3 (21.5):
  Δm = 1.5 → time ratio = 10^(0.6) ≈ 4× less time at 21.5.

• 20.0 → 22.0:
  Δm = 2.0 → time ratio = 10^(0.8) ≈ 6.3× less time at 22.0.

So if you needed 10 hours from a ~20.0 sky, you might need only:

• ~2.5 hours at 21.5

• ~1.6 hours at 22.0

That’s why dark-site trips are “integration multipliers”.

2) Why darker skies allow longer subs (wide-field) before sky-fog blows out the frame

For very wide field (fast lenses, big pixels, bright sky background), your sub length often hits a practical ceiling because the background climbs into:

• clipped highlights,

• lost dynamic range,

• ugly gradients,

• reduced star colour (stars saturate sooner as the background rises).

A simple rule:

• Background ADU increases linearly with exposure time and linearly with sky flux.

So the maximum sub length before “sky fog too bright” scales like:

• t_max ∝ 1 / sky flux

Meaning if you darken the sky by Δm:

• t_max ratio ≈ 10^(0.4 × Δm)

Examples

• Going from 20.0 → 21.5 (Δm=1.5):
  t_max becomes ~4× longer
  
  

• Going from 20.0 → 22.0 (Δm=2.0):
  t_max becomes ~6.3× longer

So if your wide-field setup is limited to 15s before the background gets gross at ~20.0, then at:

• 21.5 you may manage ~60s

• 22.0 you may manage ~95s

(Exact numbers depend on f/ratio, pixel size, gain/ISO, full well, and how much headroom you leave for gradients and star saturation — but the scaling holds.)

Practical takeaway for wide-field rigs

• Dark skies don’t just reduce noise — they let you run fewer, longer subs:

  • fewer files,

  • less stacking overhead,

  • less read-noise penalty,

  • easier gradients,

  • cleaner colour.

A good rule of thumb to use: A sky mag increase of 0.3 = 25% less total integration time needed!