4.5. Luminosity Function

An appropriate quantity for comparing the RBGS galaxies with other classes of extragalactic objects selected at other wavelengths is the infrared luminosity, L_ir(8 - 1000µm), computed using all four IRAS bands (Soifer et al. 1987; Sanders & Mirabel 1996). Soifer et al. (1987) first used the "infrared bolometric luminosity" to compare IRAS BGS galaxies with the total bolometric luminosity for several optically selected galaxy samples (Seyferts, starbursts, QSOs, etc). Here we reconstruct the infrared bolometric luminosity function using the new IRAS measurements listed in Table 1 for the RBGS galaxies. All of the RBGS objects have measured redshifts, and all have measured flux densities in all four IRAS bands (except for a very small percentage of objects with upper limits at 12 µm). The space density of the galaxies, , is the number of objects per cubic megaparsec per unit absolute magnitude interval. The units of are Mpc^-3 M_ir^-1, where M_ir signifies infrared absolute magnitude bins computed using logarithmic intervals in which each luminosity bin boundary is a factor of 10^0.4 larger than the previous one ¹² .

Figure 9 plots the distribution of heliocentric radial velocities (c * z) for the complete RBGS using the redshifts tabulated in Table 1 taken from the references given in Table 7. The sharp peak in the 1000-2000 km s^-1 redshift bin is largely due to the Virgo cluster. Otherwise, the redshift distribution for the RBGS shows a relatively smooth high redshift tail out to a cut-off near cz ~ 26,000 km s^-1.

Figure 9. Distribution of heliocentric radial velocities (c * z) for the RBGS.

Distances for the RBGS galaxies have been computed using the new cosmic attractor flow model outlined in Appendix A of Mould et al. (2000), assuming H_o = 75 km s^-1 Mpc^-1 and adopting a flat cosmology, _M = 0.3 and = 0.7. Figure 10 plots the distribution of distances (Mpc) as tabulated in Table 1. Again, the effect of the Virgo cluster can be seen as affecting the strength of the peak in the 10-20 Mpc bin (assuming our adopted distance to Virgo of 15.3 Mpc).

Figure 10. Distribution of estimated distances (Mpc) for sources in the RBGS.

The resulting distribution of infrared luminosities is shown in Figure 11. The prescription and references used for computing L_ir are given in the column notes to Table 1. Except for a modest excess of objects at L_ir ~ 10¹⁰ L (largely due to Virgo) the distribution shows a relatively broad peak over the luminosity range log(L_ir / L) ~ 9.8 - 11.4 (half-power). The median observed luminosity, log(L_ir / L) ~ 10.65, is somewhat larger than the total bolometric luminosity of the Milky Way, and the maximum observed luminosity in the sample, log(L_ir / L) = 12.51 (Mrk 231), is nearly 100 times larger than the median.

Figure 11. Distribution of the base ten logarithm of the total infrared luminosity in Solar units.

The luminosities plotted in Figure 11 were used to compute the infrared bolometric luminosity function for the RBGS (Figure 12), using the 1 / V_max method (Schmidt 1968). The computed values are listed in Table 6. The "double power-law" shape of the luminosity function for IRAS bright galaxies is similar to that derived earlier for the BGS₁ (e.g. Soifer et al. 1987), except for improved statistics at both low and high infrared luminosities, plus the decreased influence of the Virgo cluster in the all-sky sample as compared to its effect in the smaller BGS₁ survey. The best fit power-laws, (L) L, give = - 0.6(± 0.1) and = - 2.2 (± 0.1) below and above L_ir ~ 10^10.5 L respectively.

Figure 12. The infrared luminosity function for the RBGS, computed using the 1 / Vmax method. The space densities and uncertainties plotted are those listed in Table 6; the points represent the center of each luminosity bin, and each bin has a uniform width of 0.5 in units of log(Lir / L). The solid lines are linear least-square fits to the data points below and abov the "characteristic" infrared luminosity Lir* ~ 1010.5 L, respectively. The corresponding power laws, (L) L have = -0.6 (± 0.1) and = -2.2 (± 0.1).

Table 6. Infrared Luminosity Function

Lir	N	V / Vmax	(Mpc-3 Mir-1)
7.75	3	0.16 ± 0.03	11.2 ± 6.5 × 10-2
8.25	3	0.28 ± 0.05	14.0 ± 8.1 × 10-3
8.75	9	0.39 ± 0.04	13.2 ± 4.3 × 10-3
9.25	24	0.37 ± 0.02	6.7 ± 1.3 × 10-3
9.75	69	0.56 ± 0.02	32.9 ± 4.0 × 10-4
10.25	168	0.44 ± 0.01	17.0 ± 1.3 × 10-4
10.75	157	0.45 ± 0.01	26.5 ± 2.1 × 10-5
11.25	122	0.53 ± 0.02	38.6 ± 3.5 × 10-6
11.75	56	0.50 ± 0.02	30.1 ± 4.0 × 10-7
12.25	18	0.44 ± 0.03	14.5 ± 3.4 × 10-8

¹² This effectively converts intervals of infrared luminosity (L_ir / L) to equivalent intervals of absolute magnitude (M_ir); an alternate way to express the units of is Mpc^-3 [0.4 * log₁₀(L_ir / L)]^-1 . Back