Handy units conversions, including some that are very bizarre: -------------------------------------------------------------------------------- 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] [Y photon/cm^2/s/A/deg^2] = 2.4240705E+01 [X Rayleigh] [Y photon/cm^2/s/A/arcsec^2] = 1.8704247E-06 [X Rayleigh] [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: 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 -------------------------------------------------------------------------------- Blanton & Roweis 2007 Table 1 AB to Vega band l_eff mAB-mVeg M_sun(AB) M_sun(Vega) -------------------------------------------------------------------------------- U 3571 0.79 6.35 5.55 B 4344 -0.09 5.36 5.45 V 5456 0.02 4.80 4.78 R 6442 0.21 4.61 4.41 I 7994 0.45 4.52 4.07 u 3546 0.91 6.38 5.47 g 4670 -0.08 5.12 5.20 r 6156 0.16 4.64 4.49 i 7472 0.37 4.53 4.16 z 8917 0.54 4.51 3.97 J 12355 0.91 4.56 3.65 H 16458 1.39 4.71 3.32 K_{s} 21603 1.85 5.14 3.29 ^{0.1}u 3224 1.25 6.78 5.53 ^{0.1}g 4245 -0.01 5.43 5.44 ^{0.1}r 5597 0.04 4.76 4.71 ^{0.1}i 6792 0.27 4.57 4.30 ^{0.1}z 8107 0.46 4.52 4.05 -------------------------------------------------------------------------------- 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 -------------------------------------------------------------------------------- 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] Line List Luis Ho *Wavelengths are "air" values for lambda > 2000 Ang. Species Lambda ------- ------ Lyg 792.537 N I 972.5 H I 972.5 C III 977.026 Lyb 1025.72 O VI 1031.95 O VI 1037.63 Si IV 1122.5 Fe III 1125.7 P V 1128.0 C III 1175.7 Lya 1215.67 O V] 1218 N V 1238.82 N V 1242.80 Si II 1260.4 O I 1303.5 C II 1334.5 C II 1335.7 O I 1355.6 O I 1358.5 Si IV 1393.76 Si IV 1402.77 O IV] 1393.23 O IV] 1399.78 O IV] 1401.16 O IV] 1404.81 O IV] 1407.38 N IV] 1488 C IV 1548.20 C IV 1550.77 Fe I 1610 He II 1640 O III] 1661,1663,1667 N III] 1750 Si II 1808,1817 Si III] 1892 C III] 1909 N II 2141? Fe II (2200-2800) C II] 2326 [Ne IV] 2438.6 [Ne IV] 2441.3 [O II] 2470.3 [O II] 2470.4 He II,[MgVII] 2512? He II 2734 Mg II 2795.528 Mg II 2802.705 Mg I 2852.1262 Fe I 2868 O III 3047? O III 3123,3133 He II 3204 Na I 3302.37 Na I 3302.98 O III 3312 [Ne III] 3342.9 [Ne V] 3345.9 [Ne V] 3425.8 O III 3444 [O II] 3726.16 [O II] 3728.91 O III 3760 [Fe VII] 3760.3 H 10 3797.90 H 9 3835.38 [Ne III] 3868.74 Hzeta 3889.05 He I 3888.65 Ca II K 3933.663 Ca II H 3968.468 [Ne III] 3967.51 Hepsil 3970.07 [S II] 4068.60 [S II] 4076.35 Hdelta 4101.73 [Fe II] 4250,4281 G band 4304 Hgamma 4340.46 [O III] 4363.21 He I 4471.5 N V 4619 N III 4640 C III 4650 C IV 4658 [Fe III] 4658.1 He II 4685.7 [Ar IV] 4711.33 [Ar IV] 4740.20 Hbeta 4861.32 [O III] 4958.91 [O III] 5005.84 [Fe VII] 5158.3 [Fe VIII] 5159.0? Mg Ib 5167.32 Mg Ib 5172.68 Mg Ib 5183.60 [Fe VI] 5176.4? [Fe VI] 5177.0 [Ar III] 5191.82 [N I] 5198.5 [N I] 5200.7 Fe I E2 5270 [Fe VII] 5277.8 [Fe XIV] 5303.0 [Ca V] 5309.2 [Fe VI] 5335.2 Fe II (4500-5400) [O I] 5577.35 [Fe VII] 5720.9 [N II] 5754.8 C IV 5801.51 C IV 5812.14 He I 5875.7 Na D2 5889.950 Na D1 5895.924 [Ca V] 6085.9 [Fe VII] 6086.9 O2 6258,6280 [O I] 6300.23 [S III] 6312.1 [O I] 6363.88 [Fe X] 6374.5 Ca+Fe 6495 [N II] 6548.1 Halpha 6562.80 [N II] 6583.6 He I 6678.15 TiO 6700 Ca I 6718 [S II] 6716.42 [S II] 6730.78 B Band 6868 [Ar V] 7005.67 He I 7065.3 [Ar III] 7135.80 [Fe II] 7155 [Ca II] 7291.46 [Ca II] 7323.88 [O II] 7318.6 [O II] 7319.4 [O II] 7329.9 [O II] 7330.7 K I 7664.872 K I 7698.977 [Ar III] 7751.06 [Fe XI] 7891.9 O I 8446 Ca II 8498.0 Ca II 8542.1 Ca II 8662.2 P9 9229.02 Pepsil 9545.98 Pdelta 10049.4 Pgamma 10938.1 Pbeta 12818.1 Palpha 18751.0 [S III] 9069.4 [S III] 9532.1 He I 10830 Bracket-gam 21655.0