This section, or something similar to it, presents the reader with how you derived the physical properties of your collection of objects such as mass, temperature, luminosity, velocity or chemical composition. Only include those quantities that are important to the conclusions you will later be making.
You should provide the necessary formulae, the values of the quantities you are assuming such as distance, and citations of these formula and assumptions. For example, if your research involved determining the total mass of a cloud from its infrared emission, you have to tell the reader what formula you will use, and if you don't derive this formula yourself, who has previously used it in the published literature. If you don't feel like coming up with your own estimate for the distance of the cloud, cite someone else's value.
In Table 1, the far-IR properties of the cometary 100 micron clouds are presented based on measurements taken from the IRAS, HCON-3 database. The positions for the cloud cores represent the brightest 100 micron point in the region defined as the cloud's nucleus. The IRAS flux densities given in Janskys have been corrected for background emission. The estimated photometric errors at 12, 25, 60 and 100 microns are approximately 8 percent.
In Table 2, additional far-IR properties for the clouds are shown including their derived dust temperatures, optical depths at 100 microns, and their optical extinctions. The angular sizes of the cloud nuclei and tails, as well as the peak and average 100 micron surface brightnesses, were obtained directly from their HCON-3 images. The sizes correspond to the 100 micron full width at half maximum (FWHM) surface brightness uncorrected for beam smearing.
To obtain an estimate of the dust temperatures for each source, the 60 and 100 micron maps were divided and the resulting ratios at each map location were compared with tabulated values from dust grain models by Dwek(1986) for emissivities proportional to nu^1.5. The resulting dust temperature maps were then used to obtain the peak dust temperatures, Td, of the cloud nuclei and the average temperatures of the cloud tails. The uncertainty in Td was typically found to be about 5 K.
The values for the optical depth appearing in Table 3 were obtained by converting the derived dust temperatures in col. 4 to blackbody color temperature TB and then using the observed surface brightness to find Tau via Formula 1. The derived dust temperatures, Td, were converted into TB according to Formula 2 assuming that the clouds are optically thin and that the dust grain emissivity is proportional to nu^1.5. Table 2 also gives the inferred optical extinctions for each cloud component based on the relationship by deVries(1986) of I(100 micron)/AV = 9 MJy/str/mag.
Given the distance estimates in Table 2, additional physical parameters for each cloud appear in Table 3. The cloud dimensions are based on the angular sizes appearing in Table 2. The far-IR fluxes were obtained from the total 60 and 100lm flux densities in Table 1 together with Formula 3 as recommended by Lonsdale et al(1985). The use of this relation has been found to give an acceptable estimate of the total far-IR flux from 42.5 to 122.5 microns, for dust temperatures between 20 - 80 K, and dust grains with indices between 0 - 2. The total bolometric luminosity in Table 3 is the isotropic emission from the cloud based on its total flux and a correction factor of 1.5 to allow for emission outside of the 42.5 - 122.5 micron bandpass.
Mass estimates for the clouds will vary depending on the method used to relate the known far-IR properties to an equivalent mass of HI. If AV / N(HI) = 5.3 x 10^22 cm^2 mag ( Bohlin et al, 1978; Savage and Mathis, 1979) then n(HI) = 629 AV/L cc is the average density of a cloud whose thickness along the line-of-sight is L parsecs. For a cloud with a projected area of B square parsecs, then M/M(sun) = 13.6 AV B. Using the empirical relationship found by deVries for 'cirrus' clouds, together with I = S / Omega where S is the total cloud flux density at 100lm in Jys, and Omega is the clouds solid angle in steradians. From this one obtains M / M(sun) = 1.5 S(Jy) d(kpc)^2 where d is the distance to the cloud in kiloparsecs.
A comparison by Boulanger, Baud and van Albada(1985) of the 100 micron surface brightness to the HI column density for 'cirrus' clouds led to the empirical relation I(Jy/str) = 1.4 x 10^-14 N(HI). For a similar cloud geometry as in the previous example, one obtains M / M(sun) = 0.51 S(Jy) d(kpc)^2.
The relation, M /M(sun) = 1.0 S(Jy) d(kpc)^2, will be adopted for use in estimating cloud masses. The cloud masses determined in this way appear in Table 3. Also shown in Table 3 are two, distance- independent, quantities: the cloud mass to luminosity ratio (M/L), and surface brightness S( L(sun)/pc^2) . The latter assumes an elliptical projected surface area for the cloud.
A comparison of Tables 1-3 and the preceding discussions of the individual clouds leads to several conclusions about these clouds:
1) They have nearly constant M/L = 1.5 +/- 0.5
2) With the exception of G206+24, G208-28 and G110-13, members of Categories II and III have relatively low masses in the range 3 - 40 M(sun) while Category I clouds, wherein star formation is evidently occuring, are somewhat more massive with masses between 50 to 990 M(sum) 900.
3) The surface brightnesses of the Category II and III clouds are generally 0.1 - 2.0 L(sun)/pc^2, typical of clouds illuminated by the interstellar radiation field. Category I clouds have 5.0 - 60 L(sun) / pc^2 consistent with the presence of embedded sources.
4) The fraction of the cloud mass that has been converted into stars is potentially very high. In the case of G315+21, M* = 10 M(sun), the total mass of the cloud, according to TLD, is 30 M(sun) and so the fraction is about 40 percent.
5) The clouds with the most active star forming sites are found at the lowest galactic latitudes.
In general, Category I clouds bare a striking similarity to those studied by Reipurth(1983) in terms of their physical sizes and masses. The larger angular sizes of the clouds in this survey may be a result of their proximity to the observer since their inferred linear dimensions and masses are otherwise similar to those of the Gum Nebula population. The remaining clouds in Categories II and III have a more pronounced filamentary appearance, and do not show up well in optical photographs. It is possible that Category I clouds represent a qualitatively different mode of interaction with the ISM than do Categories II or III clouds. It is noteworthy that 4 of the objects, G96-15, G208-28, G255-66 and G228-27, are connected via their tails to much larger cloud-like features which appear diffuse at 100 micron. The nature of this association is uncertain.
RETURN to the Paper topic index.