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

  • 4*G*M/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