## 2. Dust mass evaluation from FIR observationsThe dust mass can be derived both from optical and from FIR observations. The value of the mass depends on the physical-chemical properties of the solid particles (i.e. grain radius, grain density and emissivity). The usual approach consists of assuming some values for the grain properties (Hildebrand 1983), while a color temperature is derived from the FIR emission. Different authors, however, present slightly different formulae for the evaluation of the dust mass (Thronson & Telesco 1986, Greenhouse et al. 1988, Young et al. 1989, Roberts et al. 1991 and Thuan & Sauvage 1992). The differences between these relations are only due to different assumptions on the grain parameters and to different derivations of the color temperature. It should be noticed that, within a flux uncertainty of 10 (which is typical of the high quality IRAS data), all the dust mass values obtained by using the different formulae are in agreement. A single temperature model is a rough approximation in describing a
galactic environment. The dust is in fact heated by the radiation
field, which in turn depends on the sources of luminosity and on their
spatial distribution in the galaxy. The total FIR emission is thus
likely due to the contribution of dust at different temperatures.
Moreover, the IRAS FIR measurements are not adequate to detect the
emission coming from cold dust (10-20 K) which peaks at wavelengths
between 200 and 300 I adopt the dust temperature distribution given by Kwan & Xie (1992): and are the lower and
upper limits of the temperature Due to the observed spectral range, I adopt =7 K and =60 K, taking into account only temperature distributions peaking at a value intermediate between and and excluding those pairs of and which produce unrealistic distributions (as, for instance, monotonically increasing or decreasing functions). The main problem in the present approach is to select the proper values for the parameters and , the choice being constrained by the ratio of the flux densities at two different wavelengths. I first identify a range of and pairs which produce the observed flux ratio. Since the same flux ratio can be obtained by functions having quite different shapes, a further constraint is needed. Unfortunately, for none of the galaxies in the sample submillimeter observations are available. Nevertheless, their color temperature may be derived from the flux density ratio (Henning et al. 1990). Taking into account the uncertainty in the computed color temperature, I select those distributions that produce the observed flux density ratio and whose peak temperature is comparable to the color temperature. The selected family of functions obviously satisfies two conditions which are not independent (being both related to the flux ratio). This fact could in principle affect the reliability of the results. It turns out, however, that pairs of and which satisfy the same constraints give the same dust mass within the flux uncertainty. In order to check the method a simple numerical simulation has been
performed. I considered an artificial galaxy which is not resolved by
IRAS both at 60 and 100 where Concerning the dust emissivity, the power-law approximation is used in the computations, with and (Hildebrand 1983). By assuming a value for and the temperature
distribution , and accounting for the spectral
responses of the IRAS detectors at 60 and 100 A galaxy with = turns out to contain about =1.6 dust grains. The galaxy distance is assumed to be 10 Mpc. By assuming a with and the flux ratio turns out to be about 0.5. I use the flux ratio as a constraint to select the pairs - producing a whose peak temperature is comparable to the galaxy color temperature of 36 K. Among these pairs also the pair and is found (i.e. exactly the values adopted for the input ). For the selected pairs of parameters I compute the dust mass which ranges between . Therefore, the derived values are in agreement with the dust mass of the galaxy within the flux uncertainties, thus confirming the reliability of the method. Futhermore, by using the single temperature model and taking into account the different formulae available (see Sect. 2) a dust mass of is derived. This result shows that the single temperature model underestimates the dust content. The same test was performed for different "artificial galaxies" with different temperature distributions obtaining always consistent results. © European Southern Observatory (ESO) 1998 Online publication: September 17, 1998 |