We have modeled the emission from dust in pre-protostellar cores, including a self-consistent calculation of the temperature distribution for each input density distribution. Model density distributions include Bonnor-Ebert spheres and power laws. The Bonnor-Ebert spheres fit the data well for all three cores we have modeled. The dust temperatures decline to very low values (T d ∼ 7 K) in the centers of these cores, strongly affecting the dust emission. Compared to earlier models that assume constant dust temperatures, our models indicate higher central densities and smaller regions of relatively constant density. Indeed, for L1544, a power-law density distribution, similar to that of a singular, isothermal sphere, cannot be ruled out. For the three sources modeled herein, there seems to be a sequence of increasing central condensation, from L1512 to L1689B to L1544. The two denser cores, L1689B and L1544, have spectroscopic evidence for contraction, suggesting an evolutionary sequence for preprotostellar cores.

Observations have revealed prodigious amounts of star formation in starburst galaxies as traced by dust and molecular emission, even at large redshifts. Recent work shows that for both nearby spiral galaxies and distant starbursts, the global star formation rate, as indicated by the infrared luminosity, has a tight and almost linear correlation with the amount of dense gas as traced by the luminosity of HCN. Our surveys of Galactic dense cores in HCN 1−0 emission show that this correlation continues to a much smaller scale, with nearly the same ratio of infrared luminosity to HCN luminosity found over 7-8 orders of magnitude in L IR , with a lower cutoff around 10 4.5 L ⊙ of infrared luminosity. The linear correlation suggests that we may understand distant star formation in terms of the known properties of local star-forming regions. Both the correlation and the luminosity cutoff can be explained if the basic unit of star formation in galaxies is a dense core, similar to those studied in our Galaxy.

We have mapped over 50 massive, dense clumps with four dense gas tracers: HCN J = 1 − 0 and 3 − 2; and CS J = 2 − 1 and 7 − 6 transitions. Spectral lines of optically thin H 13 CN 3-2 and C 34 S 5-4 were also obtained towards the map centers. These maps usually demonstrate single well-peaked distributions at our resolution, even with higher J transitions. The size, virial mass, surface density, and mean volume density within a well-defined angular size (FWHM) were calculated from the contour maps for each transition. We found that transitions with higher effective density usually trace the more compact, inner part of the clumps but have larger linewidths, leading to an inverse linewidth-size relation using different tracers. The mean surface densities are 0.29, 0.33, 0.78, 1.09 g cm −2 within FWHM contours of CS 2-1, HCN 1-0, HCN 3-2 and CS 7-6, respectively. We find no correlation of L IR with surface density and a possible inverse correlation with mean volume density, contrary to some theoretical expectations. Molecular line luminosities L ′ mol were derived for each transition. We see no evidence in the data for the relation between L ′ mol and mean density posited by modelers. The correlation between L ′ mol and the virial mass is roughly linear for each dense gas tracer. No obvious correlation was found between the line luminosity ratio and infrared luminosity, bolometric temperature, or the L IR /M V ir ratio. A nearly -2linear correlation was found between the infrared luminosity and the line luminosity of all dense gas tracers for these massive, dense clumps, with a lower cutoff in luminosity at L IR = 10 4.5 L ⊙ . The L IR -L ′ HCN 1−0 correlation agrees well with the one found in galaxies. These correlations indicate a constant star formation rate per unit mass from the scale of dense clumps to that of distant galaxies when the mass is measured for dense gas. These results support the suggestion that starburst galaxies may be understood as having a large fraction of gas in dense clumps.

Fifty-one dense cores associated with water masers were mapped at 350 lm. These cores are very luminous, 10 3 < L bol =L < 10 6 , indicative of the formation of massive stars. Dust continuum contour maps, radial intensity profiles, and photometry are presented for these sources. The submillimeter dust emission peak is, on average, nearly coincident with the water maser position. The spectral energy distributions and normalized radial profiles of dust continuum emission were modeled for 31 sources using a one-dimensional dust radiative transfer code, assuming a power-law density distribution in the envelope, n ¼ n f ðr=r f Þ Àp . The bestfit density power-law exponent, p, ranged from 0.75 to 2.5 with hpi ¼ 1:8 AE 0:4, similar to the mean value found recently by Beuther and coworkers in a large sample of massive star-forming regions. The mean value of p is also comparable to that found in regions forming only low-mass stars, but hn f i is over 2 orders of magnitude greater for the massive cores. The mean p is incompatible with a logatropic sphere (p ¼ 1), but other star formation models cannot be ruled out. Different mass estimates are compared and mean masses of gas and dust are reported within a half-power radius determined from the dust emission, hlog Mð< r dec Þi ¼ 2:0 AE 0:6, and within a radius where the total density exceeds 10 4 cm À3 , hlog Mð< r n Þi ¼ 2:5 AE 0:6. Evolutionary indicators commonly used for low-mass star formation, such as T bol and L bol /L smm , may have some utility for regions forming massive stars. Additionally, for comparison with extragalactic star formation studies, the luminosity-to-dust mass ratio is calculated for these sources, hL bol =M D i ¼ 1:4 Â 10 4 L /M , with a method most parallel to that used in studies of distant galaxies. This ratio is similar to that seen in high-redshift starburst galaxies.

We have obtained 850 and 450 km continuum maps of 21 low-mass cores with SEDs ranging from pre-protostellar to Class I (18 K), using SCUBA at the JCMT. In this paper we present K \ T bol \ 370 the maps, radial intensity proÐles, and photometry. Pre-protostellar cores do not have power-law intensity proÐles, whereas the intensity proÐles of Class 0 and Class I sources can be Ðtted with power laws over a large range of radii. A substantial number of sources have companion sources within a few arcminutes (two out of Ðve pre-protostellar cores, nine out of 16 Class 0/I sources). The mean separation between sources is 10,800 AU. The median separation is 18,000 AU including sources without companions as a lower limit. The mean value of the spectral index between 450 and 850 km is 2.8^0.4, with pre-protostellar cores having slightly lower spectral indices (2.5^0.4). The mean mass of the sample, based on the dust emission in a 120A aperture, is 1.1^0.9For the sources Ðtted by power-law M _ . intensity distributions the mean value of m is 1.52^0.45 for Class 0 and I sources, at 850 km and 1.44^0.25 at 450 km. Based on a simple analysis, assuming the emission is in the Rayleigh-Jeans limit and that these values of m translate into power-law density distribu-T d (r) P r~0.4, tions (n P r~p) with p D 2.1. However, we show that this result may be changed by more careful consideration of e †ects such as beam size and shape, Ðnite outer radii, more realistic and failure of the T d (r), Rayleigh-Jeans approximation.