Effective Wavelength, Zeropoint and extinction
for Selected Photometric Systems
Band Eff. Wave. mag zpt zero flux (Jy) zero flux Absorption
U 3600 -20.94 1884 4.19e-9 1.57
B 4400 -20.45 4646 6.60e-9 1.34
V 5500 -21.12 3953 3.55e-9 1.00
R 6600 -21.61 2875 2.25e-9 0.75
r 6500 -21.69 2.10e-9 0.75
I 8000 -22.27 2241 1.22e-9 0.48
J 12500 -23.80 1602 3.01e-10 0.28
H 16000 -24.80 1010 1.19e-10 0.19
K 21800 -26.00 630 4.00e-11 0.112
L 34500 -27.87 278 7.08e-12 0.058
M 47500 153 0.023
N 106000 36.3 0.047
Columns give: 1) Photometric band: Uppercase letters refer to the standard Johnson-Morgan/Cousins system based on A0V stars. Lowercase letter to Schneider, Gunn & Hossel system.

2) Effective wavelength in Angstrom

3) Magnitude zeropoint. This is the magnitude of a source having a flux of 1 erg/s/cm^2/Angstrom. The magnitude of a source with flux F is: m = -2.5Log(F) + zeropoint

4) Flux from a star having m = 0 (Jy)

5) Flux from a star having m = 0 ( erg/s/cm^2/Angstrom)

6) Interstellar extinction relative to the extinction in the V band.
Sources:
Magnitude zero point from Bessel 1990, PASP 102, 1181
Extinction from Cardelli Clayton & Mathis 1989, ApJ 345, 245 or Rieke and Lebosky 1985, ApJ



Physical Properties of Main-Sequence Stars

Stars spend most of their life "burning" hydrogen into helium, and during this phase they have stable luminosity, temperature, and size. The mass is the only parameter that determine all the measurable properties of stars. For this reason, in the luminosity versus temperature plane (the H-R diagram) the stars follow a well defined narrow line called the main sequence. Stars in the main sequence are called dwarf, even if they can be very large. The following table gives the value of some useful parameters for main sequence stars.

Columms give:
1) spectral class, temperature increases going from class M to class O. The spectral type of the sun is G2.
2) Logarithm of the mass in solar mass units. The mass of the sun is 2*1033 grams.
3) Logarithm of the luminosity in solar units. The luminosity of the sun is 4*1033 erg/s.
4) Bolometric magnitude.
5) Visual magnitude.
6) Logarithm of the radius in solar units. The radius of the sun is 6.96*108 m.
7) 8) 9) 10) etc, Give the magnitude difference (the color) for varius bands


Class Lg(M/Msun) Lg(L/Lsun) Mbol MV Lg(R/Rsun) (U-B) (B-V) (V-R) (V-I) (V-K) (J-K)
M6 -1.0 -2.9 +12.1 +15.5 -0.9 ... ... ... ... 7.30 1.03
M5 -0.8 -2.5 +10.9 +13.9 -0.56 1.22 1.61 ... 2.8 6.12 0.94
M4 -0.6 -2.0 +9.7 +12.2 -0.5 ... ... ... ... 5.26 0.88
M2 -0.4 -1.5 +8.4 +10.2 -0.3 ... ... ... ... 4.11 0.87
M0 -0.3 -1.6 +7.5 +8.8 -0.22 1.25 1.40 ... ... 3.65 0.86
K5 -0.2 -0.8 +6.6 +7.5 -0.14 1.09 1.16 0.8 1.5 2.85 0.72
K0 -0.1 -0.4 +5.6 +5.9 -0.07 0.47 0.85 0.74 1.4 1.96 0.53
G5 -0.04 -0.1 +4.9 +5.2 -0.04 0.20 0.69 ... ... 1.59 0.40
G2 +0.0 +0.0 +4.7 +4.8 +0.00 0.13 0.65 0.41 0.75 1.46 0.37
G0 +0.02 +0.2 +4.2 +4.4 +0.04 0.05 0.58 0.52 0.93 1.41 0.36
F5 +0.11 +0.6 +3.3 +3.4 +0.11 0.01 0.42 ... ...1.10 0.27
F0 +0.20 +0.8 +2.6 +2.7 +0.18 0.06 0.29 0.30 0.47 0.70 0.16
A5 +0.30 +1.2 +1.8 +1.9 +0.23 0.11 0.15 ... ... 0.38 0.08
A2 +0.4 +1.6 +0.7 +1.1 +0.32 ... ... ... ... 0.14 0.02
A0 +0.46 +1.8 +0.3 +0.6 +0.38 -0.06 0.00 0.00 0.00 0.0 0.0
B8 +0.56 +2.3 -1.1 -0.2 +0.49 -0.34 -0.10 ... ... -0.35 -0.09
B5 +0.77 +3.0 -2.9 -1.1 +0.58 -0.56 -0.16 ... ...
B3 +0.88 +3.7 -4.6 -2.2 +0.72 -0.71 -0.20 ... ...
B0 +1.24 +4.4 -6.3 3.4 +0.86 -1.08 -0.30 ... ...
O8 +1.36 +4.9 -7.6 -4.6 +0.93 -1.13 -0.31 ... ...
O5 +1.77 +5.4 -8.9 -5.6 +1.08 -1.15 -0.32 ... ...
O4 +1.8 +6.0 -10.2 -6.3 +1.3 ... ... ... ...
Source: ``Galactic Astronomy'' by Mihalas & Binney; Ed. Freeman & Company.
IR colors from Bessell and Brett 1988, PASP, 100, 1134


Galaxies Luminosity Function

The galaxy luminosity function F(L), gives the number of galaxies per Mpc3 ( 1Mpc = 3.08*1024 cm) with luminosity between L and L+dL. It is expressed combining an exponential and a power law, obtaining the so called Schechter function (after Schechter 1976).

F(L)dL = n* (L/L*)a exp(-L/L*) dL/L*

The value of the three parameters that enter into the luminosity function depends on the class of galaxies considered and the wavelength (photometric band) where the luminosity function in evaluated. Some values valid for an Hubble constant of H0=100 km/s/Mpc are given in the following table. For different values of H0, n* becames (H/100)3 times larger, and L* becames (H/100)2 smaller.

Band n* a L* Reference
B 0.016 -1.25 1.2*1010 Efstathious et al. 1988, MNRAS 232, 431
V 0.012 -1.25 1.0*1010 Kirshner et al. 1983, AJ 88, 1285
R 0.019 -0.70 7.6*10 9 Lin et al. 1996, ApJ 464, 60
NB. Luminosities are expressed in solar luminosities, which is 4.64*1025 W in the V band.


Abell classes for galaxy clusters

Cluster of galaxies have a wildly variable number of members, ranging from just a few galaxies to several thousands. For each given cluster, the total number of members is, however, not known because most galaxies are too faint to be detectable at the telescope, and the fraction of undetected galaxies becomes larger as more distant cluster are considered. To cope with this observational limit, Abell has introduced a measure of the cluster richness which is as independent as possible on the cluster distance. The richness is defined as the number of galaxies in the range m3 to m3+2, where m3 is the magnitude of the third brightest member of the cluster. Accordingly with this definition, cluster are divided in 6 classes of richness, given in the following table.

Class Population Class Population
0 30 - 49 3 130 - 199
1 50 - 79 4 200 - 299
2 80 - 129 5 >300

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Absolute magnitudes of the sun


Band Absolute Magnitude
U 5.60
B 5.51
V 4.84
R 4.48
I 4.13
J 3.70
H 3.37
K 3.33
From Worthey et al. 1994.