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# 2. Brightness units

There are a number of different brightness units in use in the different fields of night sky brightness with their individual traditions and advantages. Rather than trying the Sisiphus work of standardising the use of brightness units, we give here conversion tables. These should help to transform whatever was given in an original reference to the desired physical units and allow intercomparison between different sources. As a rule, we will in the quantitative information on night sky brightness stay with the units of the original papers. The units come in two groups:
(1)
physical units:
- photons/cm2 s sr Å.
- Rayleigh/Å [R/Å]. Originally a measure of the emission in a column through the atmosphere, it also may be understood as a sky brightness of 106/4 photons/cm2 s sr Å.
- in W/m2 sr as well as in W/cm2 sr and - in the cgs system - in erg/cm2 s sr Å, where
1 W/m2 sr = 10-4W/cm2 sr = 0.10 erg/cm2 s sr Å.
- in MJy/sr or Jy/sr, where 1 Jy = 10-26 W m-2Hz-1.
Note that [W/m2 sr Hz] = [W/m2 sr m] and [W/m2 sr m] = [Hz/m]10[W/m2 sr Hz].
(2)
- S10 units [tenth magnitude star per degree squared]. This is the brightness equivalent to the flux of a star of magnitude 10 (tenth magnitude in the wavelength range under consideration) distributed over one degree squared. Basically it refers to A0 stars, which essentially have the same magnitude in all wavelength bands. The S10 unit was convenient in terms of calibration by stars and in that by its use most values of the night sky brightness in the visual fall in the range 100 - 1000.
- (units of the mean brightness of the solar disk, mainly used in observations of the solar corona).
- [solar type stars of tenth magnitude per degree squared]. The unit has also been called S10 or S10(vis). This unit is a convenient measure of the zodiacal light in the visual, where its spectral energy distribution would be equal to the solar one for neutral scattering. With and the mean solid angle of the Sun of sr (Allen 1985), we have, denoting the solar irradiance at 1 AU as ,
1 /sr = 4.50 10-16 .
As representation of the solar radiation we use the solar spectral irradiance data of Neckel & Labs (1984). This understanding of the unit almost exactly agrees with the definition given by Sparrow & Weinberg (1976).

Because of the different traditions we give the conversion tables separately for the ultraviolet, the visual and the infrared. Note that the conversion factors to physical units may be slightly different for a narrow-band filter and a broad-band filter at the same wavelength. A useful quantitity to remember when working with the conversion tables is the energy of a 1 m photon: Ws.

 Wavelength 1 photon/cm2 s sr Å corresponds to Conversion factor (nm) [W/m2 sr m] [erg/cm2 s sr Å] [Jy/sr] R/Å 30 6.62 10-10 6.62 10-11 0.199 1.26 10-5 3.331 10-9 60 3.31 10-10 3.31 10-11 0.398 1.26 10-5 8.328 10-10 100 1.99 10-10 1.99 10-11 0.663 1.26 10-5 2.998 10-10 121.6a 1.63 10-10 1.63 10-11 0.856 1.26 10-5 2.027 10-10 150 1.32 10-10 1.32 10-11 0.994 1.26 10-5 1.332 10-10 200 9.93 10-11 9.93 10-12 1.325 1.26 10-5 7.495 10-11 250 7.95 10-11 7.95 10-12 1.657 1.26 10-5 4.797 10-11 300 6.62 10-11 6.62 10-12 1.988 1.26 10-5 3.331 10-11 350 5.68 10-11 5.68 10-12 2.319 1.26 10-5 2.447 10-11 400 4.97 10-11 4.97 10-12 2.650 1.26 10-5 1.874 10-11 500 3.97 10-11 3.97 10-12 2.120 1.26 10-5 1.199 10-11 656.3b 3.03 10-11 3.03 10-12 4.349 1.26 10-5 6.960 10-12 1 m 1.99 10-11 1.99 10-12 6.628 1.26 10-5 2.998 10-12 2 m 9.93 10-12 9.93 10-13 13.25 1.26 10-5 7.495 10-13 4 m 4.97 10-12 4.97 10-13 26.50 1.26 10-5 1.874 10-13

a Ly,b H.

 Wavelength 1 MJy/sr corresponds to [Jy]a 1 S10 unitb corresponds to 1 unitc corresponds to (m) [W/m2 sr m] R/Å for 0 mag [W/m2 sr m] [Jy/sr] [W/m2 sr m] S10 units [Jy/sr] 0.36 (U) 2.31 10-5 5.27 1810 1.37 10-8 590 6.70 10-9 0.488 290 0.44 (B) 1.55 10-5 4.31 4260 2.17 10-8 1400 1.19 10-8 0.550 770 0.502 12 nm 1.19 10-5 3.78 3960 1.55 10-8 1300 1.28 10-8 0.825 1070 0.530 3.5 nm 1.07 10-5 3.58 3790 1.33 10-8 1240 1.24 10-8 0.935 1160 0.55 (V) 9.91 10-6 3.45 3640 1.18 10-8 1200 1.18 10-8 1.0 1200 0.64 () 7.32 10-6 2.96 3080 7.40 10-9 1010 1.05 10-8 1.42 1440 0.70 () 6.12 10-6 2.71 2840 5.70 10-9 930 9.21 10-9 1.61 1510 0.79 () 4.80 10-6 2.34 2550 4.02 10-9 840 7.80 10-9 1.94 1620 0.90 () 3.70 10-6 2.11 2250 2.73 10-9 740 5.76 10-9 2.11 1560 1.25 (J) 1.92 10-6 1.52 1570 -10 515 2.93 10-9 2.97 1530 1.65 (H) 1.10 10-6 1.15 1020 -10 335 1.41 10-9 3.84 1290 2.2 (K) 6.19 10-7 0.862 636 -10 210 -10 4.06 850

aReferences: for U, B, V, , Bessell (1979); for , Allen (1985); for J, H, K Bessell & Brett (1988); for 502 nm and 530 nm Hayes (1985). The references give or for a star of magnitude zero, with uncertainties of about . They are transformed to S10 units by: 1 zeroth magnitude star/sr = 3.046 S10 units.
bBy definition 1 S10 unit corresponds to 27.78 mag/'', while 22 mag'' = 205 S10.
cThe definition of this unit depends on the solar UBVRIJHK values, which are uncertain by several % beyond 1.0 m and below 400 nm. References: for U, B, V, , Allen (1985); for , Bessell & Brett (1988), Taylor (1992); for J, H, K Alonso et al. (1995); for 502 nm and 530 nm Neckel & Labs (1984).

 Wavelength 1 MJy/sr corresponds to [Jy] for star 1 S10 unit corresponds to (m) [W/m2 sr m] [cgsa] of 0 mag Ref. [W/m2 sr m] [cgsa] [Jy/sr] 1.25 (J) 1.92 10-6 1.92 10-7 1570 1 9.89 10-10 9.89 10-11 515 1.65 (H) 1.10 10-6 1.10 10-7 1020 1 3.69 10-10 3.69 10-11 335 2.2 (K) 6.19 10-7 6.19 10-8 636 1 1.29 10-10 1.29 10-11 209 3.5 (L) 2.45 10-7 2.45 10-8 281 1 2.26 10-11 2.26 10-12 92.3 3.8 (L') 2.08 10-7 2.08 10-8 235 1 1.60 10-11 1.60 10-12 77.2 4.8 (M) 1.30 10-7 1.30 10-8 152 1 6.50 10-12 6.50 10-13 49.9 8.4 4.25 10-8 4.25 10-9 58 2 8.09 10-13 8.09 10-14 19.0 10 3.00 10-8 3.00 10-9 40 3 3.94 10-13 3.94 10-14 13.1 10.6 (N) 2.67 10-8 2.67 10-9 36 3 3.15 10-13 3.15 10-14 11.8 12 2.08 10-8 2.08 10-9 28 4 1.91 10-13 1.91 10-14 9.19 20 7.50 10-9 -10 10.4 3 2.56 10-14 2.56 10-15 3.41 21 (Q) 6.80 10-9 -10 9.4 3 2.10 10-14 2.10 10-15 3.09 25 4.80 10-9 -10 6.7 4 1.06 10-14 1.06 10-15 2.20 60 -10 -11 1.19 4 90 -10 -11 100 -10 -11 135 -10 -11 175 -10 -12 200 -11 -12 240 -11 -12

aunit is [erg/cm2 s sr Å].
1Bessell & Brett (1988) 2Gillett & Stein (1971) 3Rieke et al. (1985) 4Neugebauer et al. (1988). The above references give or for a star of magnitude zero, with uncertainties of about . These values are transformed to S10 units by: 1 zeroth magnitude star/sr = 3.046 S10 units.

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