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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 106/4tex2html_wrap_inline11533 photons/cm2 s sr Å.
- tex2html_wrap_inline11281 in W/m2 sr tex2html_wrap_inline10901 as well as in W/cm2 sr tex2html_wrap_inline10901 and - in the cgs system - in erg/cm2 s sr Å, where
1 W/m2 sr tex2html_wrap_inline10901 = 10-4W/cm2 sr tex2html_wrap_inline10901 = 0.10 erg/cm2 s sr Å.
- tex2html_wrap_inline11123 in MJy/sr or Jy/sr, where 1 Jy = 10-26 W m-2Hz-1.
Note that tex2html_wrap_inline11569[W/m2 sr Hz] = tex2html_wrap_inline11573 [W/m2 sr tex2html_wrap_inline10901m] and tex2html_wrap_inline11281[W/m2 sr tex2html_wrap_inline10901m] = tex2html_wrap_inline11585[Hz/m]tex2html_wrap_inline1158710tex2html_wrap_inline11589[W/m2 sr Hz].
(2)
Traditional units:
- 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.
- tex2html_wrap_inline11599 (units of the mean brightness of the solar disk, mainly used in observations of the solar corona).
- tex2html_wrap_inline11131 [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 tex2html_wrap_inline11607 and the mean solid angle of the Sun of tex2html_wrap_inline11609 sr (Allen 1985), we have, denoting the solar irradiance at 1 AU as tex2html_wrap_inline11611,
1 tex2html_wrap_inline11613 tex2html_wrap_inline11611/sr = 4.50 10-16 tex2html_wrap_inline11599.
As representation of the solar radiation we use the solar spectral irradiance data of Neckel & Labs (1984). This understanding of the tex2html_wrap_inline11131 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 tex2html_wrap_inline10901m photon: tex2html_wrap_inline11625 Ws.

   

Wavelength 1 photon/cm2 s sr Å corresponds toConversion factor
(nm) tex2html_wrap_inline10971 [W/m2 sr tex2html_wrap_inline10901m] tex2html_wrap_inline10971 [erg/cm2 s sr Å] tex2html_wrap_inline10981 [Jy/sr] R/Å tex2html_wrap_inline10983
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 tex2html_wrap_inline10901m 1.99 10-11 1.99 10-12 6.628 1.26 10-5 2.998 10-12
2 tex2html_wrap_inline10901m 9.93 10-12 9.93 10-13 13.25 1.26 10-5 7.495 10-13
4 tex2html_wrap_inline10901m 4.97 10-12 4.97 10-13 26.50 1.26 10-5 1.874 10-13
Table 1: Conversion factors for ultraviolet brightness units

a Lytex2html_wrap_inline10825,b Htex2html_wrap_inline10825.

   

Wavelength 1 MJy/sr corresponds to tex2html_wrap_inline11123[Jy]a 1 S10 unitb corresponds to 1 tex2html_wrap_inline11131 unitc corresponds to
(tex2html_wrap_inline10901m) tex2html_wrap_inline10971 [W/m2 sr tex2html_wrap_inline10901m] R/Å for 0 mag tex2html_wrap_inline10971 [W/m2 sr tex2html_wrap_inline10901m] tex2html_wrap_inline10981 [Jy/sr] tex2html_wrap_inline10971 [W/m2 sr tex2html_wrap_inline10901m] S10 units tex2html_wrap_inline10981[Jy/sr]
0.36 (U) 2.31 10-5 5.27 1810 1.37 10-8 590 6.70 10-90.488 290
0.44 (B) 1.55 10-5 4.31 4260 2.17 10-8 1400 1.19 10-80.550 770
0.502 tex2html_wrap_inline11177 12 nm 1.19 10-53.7839601.55 10-8 1300 1.28 10-80.825 1070
0.530 tex2html_wrap_inline11177 3.5 nm 1.07 10-53.5837901.33 10-81240 1.24 10-80.935 1160
0.55 (V) 9.91 10-6 3.4536401.18 10-81200 1.18 10-8 1.0 1200
0.64 (tex2html_wrap_inline11201) 7.32 10-6 2.9630807.40 10-91010 1.05 10-81.42 1440
0.70 (tex2html_wrap_inline11209) 6.12 10-6 2.712840 5.70 10-9930 9.21 10-91.61 1510
0.79 (tex2html_wrap_inline11217) 4.80 10-6 2.342550 4.02 10-9840 7.80 10-91.94 1620
0.90 (tex2html_wrap_inline11225) 3.70 10-6 2.112250 2.73 10-9740 5.76 10-92.11 1560
1.25 (J) 1.92 10-6 1.521570-10515 2.93 10-92.97 1530
1.65 (H) 1.10 10-6 1.151020-10335 1.41 10-93.84 1290
2.2 (K) 6.19 10-7 0.862 636 -10 210 -104.06 850
 Table 2: Conversion factors for visual brightness units

aReferences: for U, B, V, tex2html_wrap_inline11201, tex2html_wrap_inline11217 Bessell (1979); for tex2html_wrap_inline11209, tex2html_wrap_inline11225 Allen (1985); for J, H, K Bessell & Brett (1988); for 502 nm and 530 nm Hayes (1985). The references give tex2html_wrap_inline11123 or tex2html_wrap_inline11281 for a star of magnitude zero, with uncertainties of about tex2html_wrap_inline11283. 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/tex2html_wrap_inline11293'', while 22 magtex2html_wrap_inline11293'' = 205 S10.
cThe definition of this unit depends on the solar UBVRIJHK values, which are uncertain by several % beyond 1.0 tex2html_wrap_inline10901m and below 400 nm. References: for U, B, V, tex2html_wrap_inline11209, tex2html_wrap_inline11225 Allen (1985); for tex2html_wrap_inline11201, tex2html_wrap_inline11217 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 tex2html_wrap_inline11123 [Jy] for star 1 S10 unit corresponds to
(tex2html_wrap_inline10901m) tex2html_wrap_inline10971 [W/m2 sr tex2html_wrap_inline10901m] tex2html_wrap_inline10971 [cgsa] of 0 mag Ref. tex2html_wrap_inline10971 [W/m2 sr tex2html_wrap_inline10901m] tex2html_wrap_inline10971 [cgsa] tex2html_wrap_inline10981 [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
Table 3: Conversion factors for infrared brightness units

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 tex2html_wrap_inline11123 or tex2html_wrap_inline11281 for a star of magnitude zero, with uncertainties of about tex2html_wrap_inline11283. These values are transformed to S10 units by: 1 zeroth magnitude star/sr = 3.046 S10 units.

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