from prestellar cores to protostars - The University of Arizona Press

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´ 64 P. ANDRE ET AL. where B( Tdust) is the Planck function at frequency for a dust temperature Tdust, is the dust optical depth through a mass column density (see below), and is the source solid angle. In this simple modeling, the dust opacity per unit (gas dust) mass column density, , is assumed to scale as , with 1. 5–2, as usually appropriate in the submillimeter range (e.g., Hildebrand 1983). For L1544, a good fit to the SED is obtained with T dust 13 K, 2, 0. 12 at 100 m, and 2. 3 10 7 sr. Similar results are obtained in other starless cores. This confirms the lack of any warm dust in such cores and consequently the lack of any embedded protostellar object. The (sub)millimeter data show a morphology similar to the ISO images at much higher reso- lution, indicating that the same dust is being observed at all wavelengths. Consequently the temperature derived from the SED is representative of all the emitting dust and can be used to convert submillimeter fluxes into estimates of dust masses and, hence, to gas masses. C. Mass and Density Structure Dust emission is generally optically thin at (sub)millimeter wavelengths and hence is a direct tracer of the mass content of molecular cloud cores. For an isothermal dust source, the total (gas dust) mass M( r R) con- tained within a radius R from the center is related tothe submillimeter flux density S( ) integrated over a circle of projected angular radius R/ d by 2 2 R M( r R) R [ S ( ) d ]/[ B ( T )], where R is the average mass column density. The dust opacity is somewhat uncertain, but the uncertainties are much reduced when appropriate dust models are used (see Henning et al. 1995 for a review). n 5 For prestellar cores of intermediate densities ( 3 H 10 cm ), 2 is believed to be close to 1 2 13 . 0. 005 cm g at 1.3 mm (e.g., Hildebrand 1983; Preibisch et al. 1993). In denser cloud cores and protostellar envelopes, grain coagulation and the formation of ice mantles make a 2 factor of 2 larger, i.e., 1 13 . 0. 01 cm g assuming a gas-to-dust mass ratioof 100 (e.g., Ossenkopf and Henning 1994). A still higher value, 2 1 13 . 0. 02 cm g , is recommended in protoplanetary disks (Beckwith et al. 1990; Pollack et al. 1994). Following this method, FWHM masses ranging from 0. 5 M to 35 M are derived for the nine isolated cores mapped by Ward- Thompson et al. (1999). Although observed prestellar cores are generally not circularly or elliptically symmetric (see, e.g., Fig. 1), one can still usefully constrain their radial density profiles by averaging the (sub)millimeter emission in circular or elliptical annuli. Figure 3a shows the azimuthally averaged radial intensity profile of the prestellar core L1689B at 1.3 mm, compared to the profile of a spherical dust
(a) (b) Figure 3. (a) (left) Radial intensity pr ofile of L1689B at 1.3 mm, illustrating that prestellar c ores have flat inner density pr ofiles (fr om Andre ´ et al. 1996). F or c omparis on, the d otted curve sh ows a spherical is othermal m odel with ( r ) 12 2 2 r f or r 4000 AU and ( r) r f or r 4000 AU. The dash-d otted curve sh ows a m odel with ( r) r , such as a singular is othermal sphere (SIS). (b) (right) Typical density pr ofiles expected f or a magnetically supp orted c ore underg oing ambip olar diffusi on at vari ous times increasing fr om t0 t o t6 (fr om Ci olek and M ousch ovias 1994). The 3 3 n ormalizati on values are n n,c 0 2 . 6 10 cm and R 0 4 . 29 pc. Open circles mark the instantane ous radius of the unif orm-density central regi on; starred circles mark the radius of the magnetically supercritical regi on (present only fr o t t ). 2 .
Page 1 and 2: FROM PRESTELLAR CORES TO PROTOSTARS
Page 5: FROM PRESTELLAR CORES TO PROTOSTARS
Page 13 and 14: Property (i) distinguishes Class 0
Page 15 and 16: TABLE I (CONT’D) Dist. Lb ol Menv
Page 17 and 18: (a) (b) Figure 6. (a) Lbl o - Tbl o

from prestellar cores to protostars - The University of Arizona Press

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