Conversions Ulrich Hopp

Fundamental astronomical conversions:

[Y pc] = 3.2407332E-19 * [X cm]
[Y cm] = 3.0857215E+18 * [X parsec]
[Y cm] = 9.4605E+17 * [X ly]
[Y ephemeris s] = 3.1556926E+07 * [X yr]
[Y cm] = 1.496E+13 * [X A.U.]
[Y A.U.] = 2.0626480625E+05 * [X pc]
[Y solar day] = 1.0027379093 * [X sidereal day]
[Y gm] = 1.9892E+33 * [X Msun]
[Y cm] = 6.95987E+10 * [X Rsun]
[Y erg/s] = 3.826E+33 * [X Lsun]
[Y A] = 2.99792458E+18 / [X frequency (Hz)]
[Y sr] = 2.3504431E-11 * [X arcsec^2]
[Y sr] = 3.0461724E-04 * [X deg^2]
[Y sr] = 3.28280635E+03 * [X deg^2]
[Y erg] = 1.98644746E-08 * [X1 photon] / [X2 A]
[Y K] := 1.160485E+04 * [X keV]
[Y erg] = 1.60184E-12 * [X eV]
[Y Hz] := 2.41838E+14 * [X eV]
hc/k = 143843215 K^-1 A^-1
hc/k = 14384.3215 K^-1 micron^-1
Flux conversions:

[Y erg/cm^2/s] = 1000 * [X W/m^2]
[Y erg/cm^2/s/Hz] = 1000 * [X W/m^2/Hz]
[Y erg/cm^2/s/A] = 2.99792458E+21 * [X1 W/m^2/Hz] / [X2 A]^2
[Y W/m^2/um] = 2.99792458E+14 * [X1 W/m^2/Hz] / [X2 um]^2
[Y photon/cm^2/s/A] WRONG? = 1.50918896E+29 * [X1 W/m^2/Hz] / [X2 A]
[Y photon/cm^2/s/um] = 1.50918896E+22 * [X1 erg/cm^2/Hz] / [X2 um]
[Y photon/cm^2/s/um] = 5.03411250E+14 * [X1 W/m^2/um] * [X2 um]
[Y photon/cm^2/s/A] = 5.03411250E+07 * [X1 erg/cm^2/s/A] * [X2 A]
[Y Jy] = 1.0E+26 * [X W/m^2/Hz]
[Y Jy] = 1.0E+23 * [X erg/cm^2/s/Hz]
[Y Jy] = 3.33564095E+04 * [X1 erg/cm^2/s/A] * [X2 A]^2
[Y erg/cm^2/s/A] = 2.99792458E-05 * [X1 Jy] / [X2 A]^2
[Y photon/cm^2/s/A] = 1.50918896E+03 * [X1 Jy] / [X2 A]
[Y S10] = log([6.86E-06 * X erg/s/sr]) @ 5500 A
[Y S10] ?= log([3.77E-02 * X erg/s/Hz/sr] / [5500 A ])
[Y S10] = [X 10th mag A0 V stars / deg^2]
[Y S10] = 10^(-0.4([X B surface brightness] - 27.78))
Surface brightness conversions:

[Y photon/cm^2/s/A/sr] = 7.9577539E+04 [X Rayleigh/A]
[Y photon/cm^2/s/A/deg^2] = 2.4240705E+01 [X Rayleigh/A]
[Y photon/cm^2/s/A/arcsec^2] = 1.8704247E-06 [X Rayleigh/A]
[Y photon/cm^2/s/A/arcsec^2] = 3.54726271E+18 * [X1 W/m^2/Hz/sr] / [X2 A]
[Y photon/cm^2/s/A/arcsec^2] = 5.03411250E+04 * [X1 erg/cm^2/s/Hz/sr] / [X2 A]
[Y U surface brightness] = -2.5 * log[X1 erg/cm^2/s/Hz/sr] - 22.78
[Y B surface brightness] = -2.5 * log[X1 erg/cm^2/s/Hz/sr] - 21.85
[Y V surface brightness] = -2.5 * log[X1 erg/cm^2/s/Hz/sr] - 22.02
[Y R surface brightness] = -2.5 * log[X1 erg/cm^2/s/Hz/sr] - 22.21
[Y I surface brightness] = -2.5 * log[X1 erg/cm^2/s/Hz/sr] - 22.41
Typical surface brightnesses:

Obs. Band mag ph/cm^2/s/A/arcsec^2 W/m^2/Hz/arcsec^2 ergs/s/cm^2/A/arcsec^2

CTIO U 22.4 8.3e-07 1.99e-32 4.61e-18
CTIO B 22.9
KPNO B 23.0 9.2e-07 2.68e-32 4.16e-18
HST B 24.0 NEP 3.7e-07
CTIO V 22.0 5.75e-32 5.70e-18
KPNO V 21.9 1.7e-06
HST V 23.3 NEP 4.8e-07 1.73e-18
HST V 22.1 antisolar 1.4e-06
CTIO R 21.2 2.4e-06 1.02e-31 7.46e-18
HST Rc 22.8 NEP 5.6e-07
CTIO I 19.9 5.3e-06 2.81e-31 1.35e-17
UKIRT I 18.6
HST Ic 22.4 NEP 5.5e-07
UKIRT Z 17.6
VLT Z 18.8 +/- 0.5
VISTA Z 18.5 9.0e-06
LCO J 15.9 8.3e-05 7.04e-30 1.35e-16
UKIRT J 15.6
VLT J' 16.2 (1.16 - 1.32 micron)
LCO H 14.0 2.3e-04 2.64e-29 2.90e-16
UKIRT H 13.6
LCO K 11.8 8.6e-04 1.24e-28 7.68e-16
UKIRT K 13.4
Oke+Gunn 83 AB calibration:

[Y ABnu] = -2.5 * log([X ergs/cm^2/s/Hz]) - 48.594
[Y ABnu] = -2.5 * log([X ergs/cm^2/s/A]) - 2.402 - 5.0 * log(lambda A)
[Y ABnu] = -2.5 * log([X W/m^2/Hz]) - 56.094
[Y ABnu] = -2.5 * log([X photon/cm^2/s/A]) + 16.852 - 2.5 * log(lambda A)
[Y ABnu] = -2.5 * log([X photon/cm^2/s/um]) + 16.852 - 2.5 * log(lambda um)
[Y ABnu] = U + 0.762
[Y ABnu] = B - 0.168
[Y ABnu] = V + 0.003
[Y ABnu] = Rc + 0.185
[Y ABnu] = Ic + 0.390 (Note, CFRS claims Ic + 0.48)
[Y ABnu] = K + 1.875 (Note, CFRS used K', giving K + 1.78)
Johnson 1966 ARA&A 4, 193 calibration:

Flam(U = 0) = 4.35E-09 erg/cm^2/s/A (lambda = 3600)
Flam(B = 0) = 7.20E-09 erg/cm^2/s/A (lambda = 4400)
Flam(V = 0) = 3.92E-09 erg/cm^2/s/A (lambda = 5500)
Flam(R = 0) = 1.76E-09 erg/cm^2/s/A (lambda = 7000)
Flam(I = 0) = 8.30E-10 erg/cm^2/s/A (lambda = 9000)
Flam(J = 0) = 3.40E-10 erg/cm^2/s/A (lambda = 12500)
Flam(K = 0) = 3.90E-11 erg/cm^2/s/A (lambda = 22000)
Flam(L = 0) = 8.10E-12 erg/cm^2/s/A (lambda = 34000)
Flam(M = 0) = 2.20E-12 erg/cm^2/s/A (lambda = 50000)
Flam(N = 0) = 1.23E-12 erg/cm^2/s/A (lambda = 102000)
Bessell 1979 calibration:

Fnu(U = 0) = 1.81E-23 W/m^2/Hz ==> 759 photons/cm^2/s/A (lambda = 3600)
Fnu(B = 0) = 4.26E-23 W/m^2/Hz ==> 1461 photons/cm^2/s/A (lambda = 4400)
Fnu(V = 0) = 3.64E-23 W/m^2/Hz ==> 999 photons/cm^2/s/A (lambda = 5500)
Fnu(Rc = 0) = 3.08E-23 W/m^2/Hz ==> 726 photons/cm^2/s/A (lambda = 6400)
Fnu(Ic = 0) = 2.55E-23 W/m^2/Hz ==> 487 photons/cm^2/s/A (lambda = 7900)
Fnu(K = 0) = 6.49E-24 W/m^2/Hz ==> 45 photons/cm^2/s/A
Bessell & Brett (1988) calibration:

Fnu(J = 0) = 1.61E-23 W/m^2/Hz ==> 190 photons/cm^2/s/A
Fnu(H = 0) = 1.05E-23 W/m^2/Hz ==> 92 photons/cm^2/s/A
Fabregat & Reig (1996) Stromgren calibration

Fnu(u = 0) = 4.68E-23 W/m^2/Hz (lambda = 3450)
Fnu(v = 0) = 4.89E-23 W/m^2/Hz (lambda = 4110)
Fnu(b = 0) = 4.25E-23 W/m^2/Hz (lambda = 4670)
Fnu(y = 0) = 3.70E-23 W/m^2/Hz (lambda = 5480)
Fukugita (1996) calibration for SDSS photometry:

N/A
Claimed by VISTA:

Fnu(Z = 0) = ?.??E-?? W/m^2/Hz ==> 226 photons/cm^2/s/A
IRAS: (Fnu refered to as "flux-density")

Fnu(12 = 0) = 2.83E-25 W/m^2/Hz
Fnu(25 = 0) = 6.73E-26 W/m^2/Hz
Fnu(60 = 0) = 1.19E-26 W/m^2/Hz
Fnu(100 = 0) = 4.30E-27 W/m^2/Hz
[Y W/m^2] = 1.35E-13 * F12 for object with Fnu = nu^-1
[Y W/m^2] = 5.16E-14 * F25 for object with Fnu = nu^-1
[Y W/m^2] = 2.58E-14 * F60 for object with Fnu = nu^-1
[Y W/m^2] = 1.00E-14 * F100 for object with Fnu = nu^-1
Consolidation by Windhorst , et al, 1991, ApJ, 380, 262.

[Y Jy] = 10^-0.4([X AB_mag] - C)
filter C Reference Star
-------------------------------------
U -7.84
B -9.14
g -8.88 m = 0, F6 white dwarf
V -8.906 m = 0, A0V
r -9.10 m = 0, F6 white dwarf
R -8.73 m = 0, A0V
i -9.20 m = 0, F6 white dwarf
I -8.44 m = 0, A0V
z -9.21 m = 0, F6 white dwarf
J -8.01 m = 0, A0V
H -7.58 m = 0, A0V
K -7.06 m = 0, A0V
Conversion of Magnitudes to Janskys and F-Lambda:

One Jansky represents an incident energy flux density of 10**-26 Watt /m^2/Hz.
The table below gives Jansky equivalents S(nu,0) for a source with magnitude
0.00 in the standard photometric bands.

Conversion Table

Fnu(U = 0) = 1.81E-23 W/m^2/Hz ==> 759 photons/cm^2/s/A (lambda = 3600)
Fnu(B = 0) = 4.26E-23 W/m^2/Hz ==> 1461 photons/cm^2/s/A (lambda = 4400)
Fnu(V = 0) = 3.64E-23 W/m^2/Hz ==> 999 photons/cm^2/s/A (lambda = 5500)
Fnu(Rc = 0) = 3.08E-23 W/m^2/Hz ==> 726 photons/cm^2/s/A (lambda = 6400)
Fnu(Ic = 0) = 2.55E-23 W/m^2/Hz ==> 487 photons/cm^2/s/A (lambda = 7900)
Fnu(K = 0) = 6.49E-24 W/m^2/Hz ==> 45 photons/cm^2/s/A

Band S F-lambda
Microns (Jy) W/m2/um
--------------------------
U (0.360) 1810 4.19e-08 (Bessell gives 1810 Jy)
B (0.440) 4260 6.60e-08 (Bessell gives 4260 Jy)
V (0.5556) 3540 3.44e-08 (Bessell gives 3640 Jy)
R (0.640) 3080 2.25e-08 (Bessell gives 3080 Jy)
I (0.790) 2550 1.22e-08 (Bessell gives 2550 Jy)
Z (0.88) 7.7e-09 (estimated by interpolation)
J (1.25) 1600 3.07e-09 (Bessell & Brett give 1610 Jy)
H (1.65) 1020 1.12e-09 (Bessell & Brett give 1050 Jy)
K (2.20) 657 4.07e-10 (Bessell & Brett gives 649 Jy)
L (3.45) 290 7.30e-11
L'(3.80) 252 5.24e-11
M (4.80) 163 2.12e-11
(7.8) 65.3 3.22e-12
(8.7) 53.0 2.10e-12
(9.8) 42.3 1.32e-12
N (10.1) 39.8 1.17e-12
(10.3) 38.5 1.09e-12
(11.6) 30.5 6.81e-13
(12.5) 26.4 5.07e-13
Q (20.0) 10.4 7.80e-14

Wavelengths:

Lyman(alpha) 1215.67 A
Lyman(beta) 1025.72 A
Lyman(limit) 911.5 A
Balmer(alpha) 6562.80 A
Balmer(beta) 4861.32 A
Balmer(gamma) 4340.46 A
Balmer(limit) 3646.0 A
Paschen(alpha) 1.87510 um
Paschen(beta) 1.28181 um
Paschen(limit) 0.82036 um
Brackett(gamma) 2.1665 um
Astronomical and Physical Constants

4GM/c^2 = 1.9e-13 pc / Msun = 5.9 km / Msun
parsec = 3.09 x 1018 cm = 3.26 light years (lyr)
Newton's const. = 6.67 x 10-8 dyne cm2 g-2
Hubble parameter = 100h km s-1 Mpc-1 , 1/2 h 1
Hubble time = h-1 9.78 Gyr
Hubble radius = cH-1 = 3.00h-1 Gpc
critical density = 3H2 / 8 G = 1.88 x 10-29 h2 g cm-3
= 10.5h2 keV cm-3 = 2.78 x 1011 h2 M Mpc-3
= 2 x 10-30 g/cm-3 for h=0.63 OM = 0.3
= 1.3 H-atoms equiv/m-3 for h=0.63 OM = 0.3
H density = 0.05 H-atoms/m-3 for h=0.63 OM = 0.3
speed of light = 3.00 x 1010 cm s-1 = 306 Mpc Gyr-1
solar mass M = 1.99 x 1033 g
solar luminosity = 3.85 x 1033 erg s-1
Planck's const. = 1.05 x 10-27 erg s = 6.58 x 10-16 eV s
Planck mass = ( c/G)1/2 = 2.18 x 10-5 g = 1.22 x 1019 GeV

According to Reynolds:
EM (cm^-6 pc) = 2.75 * (T K/10000 K)^0.9 * [I(H-alpha) R]
email: hopp @ usm.uni-muenchen.de