3.1. Basic Parameters and Statitics

3.1.1. Infrared Luminosity

A few key parameters have gained much currency in the study of the integrated emission from galaxies in the infrared. Foremost among these is infrared luminosity L(IR), used quite often as an indicator of the total level of activity in the ISM. Various authors have used different spectral definitions for L(IR), most commonly favoring either the far-infrared (FIR) or the total infrared L(TIR). The IRAS data naturally lead to the ``FIR'' definition (Helou et al. 1988) of a synthetic band combining in a simple way the 60 and 100 µm flux measurements. L_FIR in units of W m^-2 is defined by L_FIR = 1.26 10^-14[2.58 f(60 µm) + f(100 µm)], where f(60 µm) and f(100 µm) are in Jy. Helou et al. (1988) demonstrated that this combination approximates to within 1% the flux in a synthetic band with uniform transmission between 42.5 and 122.5 µm for blackbody and modified blackbody (with emissivity ⁿ) curves with temperatures between 20 and 80 K, and for emissivity index n between 0 and 2. They argued this property should therefore also apply to realistic spectral energy distributions of galaxies because those must be made up of a superposition of modified blackbodies in this temperature range. It is essentially a coincidental result of the properties of the IRAS filter shapes that the simple linear combination allows us to estimate the luminosity in a well defined spectral window. The real interest of FIR however is that this window encompasses a large fraction, and therefore a representative measure, of the total infrared luminosity. Fortunately, as discussed in Section 4 below, the ratio L(TIR) / L(FIR) is on the order of 2, and varies relatively slowly with the properties of galaxies.

While L(IR) is a good indicator of the total luminosity from the ISM of a galaxy, some authors have claimed it to be proportional to the star formation rate. This interpretation has been controversial, and is most probably erroneous, as discussed in Section 3.4 below. L(IR) is an extensive quantity, best approximated as an integral over the galaxy of the intensity of the interstellar radiation field times the effective local optical depth of the dust to this radiation. Its interpretation as a measure of star formations is valid only when the optical depth is high everywhere, and the radiation field is derived primarily from young stars.

The normal galaxies under discussion have L(IR) in the range 10⁷-10¹¹ L. Over this interval, the distribution of infrared luminosities is well described by a power-law function with an index in the range -2 to -2.5 (Kim & Sanders 1998). In ultra-luminous galaxies (Houck et al. 1985, Harwit & Houck 1987; Sanders & Mirabel 1996), L(IR) exceeds 10¹² L, emanating from an ISM heated by prodigious star formation or possibly by an active galactic nucleus. At the other extreme of L(IR), IRAS showed that a minimum luminosity in the mid-infrared can be expected from the photospheres of stars in galaxies (Soifer et al. 1986), but was not sufficiently sensitive to establish whether galaxies emit a minimum luminosity in the far infrared in addition to the photospheric emission, and apart from the ISM emission found even in Elliptical galaxies (Jura 1986; Knapp et al. 1989). Even ISO data may not be adequate to address this question.