c = 2.99792e10 cm/s
G = 6.6738e-8 cm^3/g/s^2
h = 6.62607e-27 erg s = 4.135668e-15 eV s
e = 4.8032e-10 statcoulombs
m_e = 9.1094e-28 g
m_u = 1.66e-24 g
k = 1.38065e-16 erg K^−1 = 8.617e−5 eV K^−1 (Boltzmann constant)
sigma = 5.6704e-5 erg/s/cm^2/K^4 (Stefan–Boltzmann constant)
sigma_t = 0.665246E-24 cm^2 (Thomson cross-section)
Fine-structure constant = 1/137.035999
1 pc = 3.0857215E+18 cm = 3.26168 ly
1 AU = 1.4959787E+13 cm = 1/206264.81 pc
Msun = 1.9892E+33 g
Rsun = 6.95987E+10 cm
Lsun = 3.839E+33 erg/s
1 sr = 3282.8 deg^2 (steradian)
1 keV = 1.16028E+7 K = 12.4 \AA
1 eV = 1.60184E-12 erg
1 Jy = 1e-23 erg/cm^2/s/Hz
1 Rayleigh = (1e6 / 4pi) photons/s/cm^2/sr
= 5.661e-18 erg/s/cm^2/arcsec^2 (Ha)
= 7.643e-18 (Hbeta) = 3.056e-17 (Lya)
lambda_max T = 2900 micro deg
critical density = 1.00e-29 g/cm^3 (H0/73)^2
delta lambda (nm) = -1.23986e3 E(eV)^-2 delta E(eV)
= -2.99793e8 v(Hz)^-2 delta v(Hz)
E(z) r_500 = 1197 h^-1 kpc [E(z) M_500 / 1e15 h^-1 M_sun]^1/3
M_2500 / 1e13 M_sun = 1.238 (r_2500 / 200 kpc)^3 E(z)^2
Important lines:
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(delta) 4101.73 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
O VI 1031.95, 1037.63
C IV 1548.20, 1550.77
Ca II K 3933.663
Ca II H 3968.468
G band 4304
Mg Ib 5167.32, 5172.68, 5183.60
He I 5875.7
Na D2/D1 5889.950, 5895.924
[O I] 6300.23, 6363.88
[N II] 6548.1, 6583.6
[S II] 6716.42, 6730.78
12C16O 1-0: 115.2712 GHz; 2-1: 230.5380; 3-2: 345.7960; 4-3: 461.0408
(T_min ~ v (J+1); 1-0: 5.5; 2-1: 16.6K; 4-3: 55K; 6-5: 117K)
13C16O 1-0: 110.2014 GHz; 2-1: 220.3987; 3-2: 330.5880; 4-3: 440.7652
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
--------------------------------------------------------------------------------
Oke+Gunn 83 AB calibration:
[Y ABnu] = -2.5 * log([X ergs/cm^2/s/Hz]) - 48.594
[Y ABnu] = -2.5 * log([X photon/cm^2/s/A]) + 16.852 - 2.5 * log(lambda A)
--------------------------------------------------------------------------------
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
Line List
------- ------
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
BH sphere of influence
R = 0.269 kpc (M_BH / 1e10 M_sun) (sigma_* / 400 km/s)^-2
Bondi accretion
R = 0.031 kpc (M_BH / 1e9 M_sun) (kT / 1 keV)^-1
M_dot = 0.0042 M_sun / yr (K / 2 keV cm^2)^-3/2 (M_BH / 1e9 M_sun)^2