Alyssa A. Goodman

Dense cores in dark clouds. VIII: Velocity gradients

An analysis of motions consistent with uniform rotation in dense cores is presented. Twenty-nine of the 43 cores studied have a statistically significant gradient. Some gradients are spatially continuous and are consistent with uniform rotation, but other apparent gradients are caused by clump-clump motion, or sharp localized gradients, within a map. The motions in L1495, B217, L1251, L43, B361, and L1551 are discussed in detail. In L1551, the residuals of the fit to the NH3 velocity field indicate an outflow from IRS5 in the same direction as the CO outflow. Gradient orientation appears to be preserved over a range of density, as evidenced by comparing results of NH3 to fits of (C-18)O and CS maps. The specific angular momentum is found to scale roughly as F exp 3/2, where R represents the diameter of the FWHM intensity contour in a map.

BVRI Light Curves for 22 Type 1a Supernovae

We present 1210 Johnson/Cousins B, V, R, and I photometric observations of 22 recent Type Ia supernovae (SNe Ia): SNe 1993ac, 1993ae, 1994M, 1994S, 1994T, 1994Q, 1994ae, 1995D, 1995E, 1995al, 1995ac, 1995ak, 1995bd, 1996C, 1996X, 1996Z, 1996ab, 1996ai, 1996bk, 1996bl, 1996bo, and 1996bv. Most of the photometry was obtained at the Fred Lawrence Whipple Observatory of the Harvard-Smithsonian Center for Astrophysics in a cooperative observing plan aimed at improving the database for SNe Ia. The redshifts of the sample range from cz = 1200 to 37,000 km s-1 with a mean of cz = 7000 km s-1.

COHERENCE IN DENSE CORES. II. THE TRANSITION TO COHERENCE

After studying how line width depends on spatial scale in low-mass star-forming regions, we propose that dense cores (Myers & Benson 1983) represent an inner scale of a self-similar process that characterizes larger scale molecular clouds. In the process of coming to this conclusion, we define four distinct types of line width-size relation (ΔvRai), which have power-law slopes a1, a2, a3, and a4, as follows: Type 1—multitracer, multicloud intercomparison; Type 2—single-tracer, multicloud intercomparison; Type 3—multitracer study of a single cloud; and Type 4—single-tracer study of a single cloud. Type 1 studies (of which Larson 1981 is the seminal example) are compendia of Type 3 studies which illustrate the range of variation in the line width-size relation from one region to another. Using new measurements of the OH and C18O emission emanating from the environs of several of the dense cores studied in NH3 by Barranco & Goodman (1998; Paper I), we show that line width increases with size outside the cores with a4 ~ 0.2. On scales larger than those traced by C18O or OH,12CO and 13CO observations indicate that a4 increases to ~0.5 (Heyer & Schloerb 1997). By contrast, within the half-power contour of the NH3 emission from the cores, line width is virtually constant, with a4 ~ 0. We interpret the correlation between increasing density and decreasing Type 4 power-law slope as a transition to coherence. Our data indicate that the radius Rcoh at which the gas becomes coherent (i.e., a4 → 0) is of order 0.1 pc in regions forming primarily low-mass stars. The value of the nonthermal line width at which coherence is established is always less than but still of order of the thermal line width of H2. Thus coherent cores are similar to, but not exactly the same as, isothermal balls of gas. Two other results bolster our proposal that a transition to coherence takes place at ~0.1 pc. First, the OH, C18O, and NH3 maps show that the dependence of column density on size is much steeper (N R-0.9) inside Rcoh than outside of it (N R-0.2), which implies that the volume filling factor of coherent cores is much larger than in their surroundings. Second, Larson (1995) has recently found a break in the power law characterizing the clustering of stars in Taurus at 0.04 pc, just inside of Rcoh. Larson and we interpret this break in slope as the point at which stellar clustering properties change from being determined by the (fractal) gas distribution (on scales greater than 0.04 pc) to being determined by fragmentation processes within coherent cores (on scales less than 0.04 pc). We speculate that the transition to coherence takes place when a dissipation threshold for the MHD turbulence that characterizes the larger scale medium is crossed at the critical inner scale Rcoh. We suggest that the most likely explanation for this threshold is the marked decline in the coupling of the magnetic field to gas motions due to a decreased ion/neutral ratio in dense, high filling factor gas.

Dense cores in dark clouds. VI, Shapes

A comparison is presently conducted between 48 line-intensity maps of 16 dense cores in dark clouds, based on observations in the 13-mm line of NH3 and the 3-mm lines of CS and C(O-18). Core elongation in this sample does not differ significantly between cores with and without embedded stars; elongation appears to be a condition prior to star formation, rather than the consequence of formation. The characteristic elongation of dense cores implies that models of equilibrium between self-gravity and isotropic random motions are incomplete. The observed elongation of dense cores in projection is modeled as arising from a group of either prolate or oblate spheroids. 50 refs.

CO Isotopologues in the Perseus Molecular Cloud Complex: the X-factor and Regional Variations

We use data gathered by the COMPLETE survey of star-forming regions to find new calibrations of the X-factor and 13CO abundance within the Perseus molecular cloud. We divide Perseus into six subregions, using groupings in a dust temperature vs. LSR velocity plot. The standard X-factor, -->X ? N(H2)/W(12CO) , is derived both for the whole Perseus complex and for each of the six subregions with values consistent with previous estimates. However, the X-factor is heavily affected by the saturation of the emission above -->AV ~ 4 mag, and variations are also found between regions. Linear fits to relate -->W(12CO) and -->AV using only points below 4 mag of extinction yield a better estimate of the -->AV than the X-factor. Linear relations of -->W(13CO) , N(13CO) , and -->W(C18O) with -->AV are derived. The extinction thresholds above which 13CO(1-0) and C18O(1-0) are detected are about 1 mag larger than previous estimates, so that a more efficient shielding is needed for the formation of CO than previously thought. The 12CO and 13CO lines saturate above 4 and 5 mag, respectively, whereas C18O(1-0) never saturates in the whole -->AV range probed by our study (up to 10 mag). Approximately 60% of the positions with 12CO(1-0) emission have subthermally excited lines, and almost all positions have excitation temperatures below the dust temperature. PDR models, using the Meudon code, can explain the 12CO(1-0) and 13CO(1-0) emission with densities ranging between 103 and 104 cm?3. In general, local variations in the volume density and nonthermal motions (linked to different star formation activity) can explain the observations. Higher densities are needed to reproduce CO data toward active star-forming sites, such as NGC 1333, where the larger internal motions driven by the young protostars allow more photons from the embedded high-density cores to escape the cloud. In the most quiescent region, B5, the 12CO and 13CO emission appears to arise from an almost uniform thin layer of molecular material at densities around 104 cm?3, and in this region the integrated intensities of the two CO isotopologues are the lowest in the whole complex.

Structural Analysis of Molecular Clouds: Dendrograms

We demonstrate the utility of dendrograms at representing the essential features of the hierarchical structure of the isosurfaces for molecular line data cubes. The dendrogram of a data cube is an abstraction of the changing topology of the isosurfaces as a function of contour level. The ability to track hierarchical structure over a range of scales makes this analysis philosophically different from local segmentation algorithms like CLUMPFIND. Points in the dendrogram structure correspond to specific volumes in data cubes defined by their bounding isosurfaces. We further refine the technique by measuring the properties associated with each isosurface in the analysis allowing for a multiscale calculation of molecular gas properties. Using COMPLETE13CO -->(J = 1? 0) data from the L1448 region in Perseus and mock observations of a simulated data cube, we identify regions that have a significant contribution by self-gravity to their energetics on a range of scales. We find evidence for self-gravitation on all spatial scales in L1448, although not in all regions. In the simulated observations, nearly all of the emission is found in objects that would be self-gravitating if gravity were included in the simulation. We reconstruct the size-line-width relationship within the data cube using the dendrogram-derived properties and find it follows the standard relation: -->?v R0.58. Finally, we show that constructing the dendrogram of CO -->(J = 1? 0) emission from the Orion-Monoceros region allows for the identification of giant molecular clouds in a blended molecular line data set using only a physically motivated definition (self-gravitating clouds with masses > -->5 ? 104 M?).

The Turbulent Shock Origin of Proto-Stellar Cores

The fragmentation of molecular clouds (MC) into proto-stellar cores is a central aspect of the process of star formation. Because of the turbulent nature of supersonic motions in MCs, it has been suggested that dense structures such as filaments and clumps are formed by shocks in a turbulent flow. In this work we present strong evidence in favor of the turbulent origin of the fragmentation of MCs. The most generic result of turbulent fragmentation is that dense postshock gas traces a gas component with a smaller velocity dispersion than lower density gas, since shocks correspond to regions of converging flows, where the kinetic energy of the turbulent motion is dissipated. Using synthetic maps of spectra of molecular transitions, computed from the results of numerical simulations of supersonic turbulence, we show that the dependence of velocity dispersion on gas density generates an observable relation between the rms velocity centroid and the integrated intensity (column density), σ(V0)-I, which is indeed found in the observational data. The comparison between the theoretical model (maps of synthetic 13CO spectra) with 13CO maps from the Perseus, Rosette, and Taurus MC complexes shows excellent agreement in the σ(V0)-I relation. The σ(V0)-I relation of different observational maps with the same total rms velocity are remarkably similar, which is a strong indication of their origin from a very general property of the fluid equations, such as the turbulent fragmentation process.

Evidence for magnetic and virial equilibrium in molecular clouds

Recent measurements of the magnetic-field strength, velocity dispersion, and size of 14 molecular clouds agree, within uncertainty of a factor of about 2, with the predictions of a simple model in which the magnetic, kinetic, and gravitational energies are all equal. The clouds range from extended dark clouds to massive dense cores associated with OH masers and compact H II regions. Their field strengths range over a factor of about 1000, from about 10 microG to about 10 mG. This result suggests that the magnetic contribution to the internal motions and energy of many molecular clouds is crucial for cloud dynamics, cloud evolution, and star formation. 47 references.

THE EFFECT OF NOISE ON THE DUST TEMPERATURE-SPECTRAL INDEX CORRELATION

We investigate how uncertainties in flux measurements affect the results from modified blackbody spectral energy distribution (SED) fits. We show that an inverse correlation between the dust temperature T and spectral index β naturally arises from least-squares fits due to the uncertainties, even for sources with a single T and β. Fitting SEDs to noisy fluxes solely in the Rayleigh-Jeans regime produces unreliable T and β estimates. Thus, for long wavelength observations (λ 200 μm), or for warm sources (T 60 K), it becomes difficult to distinguish sources with different temperatures. We assess the role of noise in recent observational results that indicate an inverse and continuously varying T-β relation. Though an inverse and continuous T-β correlation may be a physical property of dust in the interstellar medium, we find that the observed inverse correlation may be primarily due to noise.

Measuring Galactic Extinction: A Test

We test the recently published all-sky reddening map of Schlegel, Finkbeiner, & Davis (hereafter SFD) using the extinction study of a region in the Taurus dark cloud complex by Arce & Goodman (hereafter AG). In their study, AG use four different techniques to measure the amount and structure of the extinction toward Taurus, and all four techniques agree very well. Thus, we believe that the AG results are a truthful representation of the extinction in the region and can be used to test the reliability of the SFD reddening map. The results of our test show that the SFD all-sky reddening map, which is based on data from COBE/DIRBE and IRAS/ISSA, overestimates the reddening by a factor of 1.3-1.5 in regions of smooth extinction with AV > 0.5 mag. In some regions of steep extinction gradients, the SFD map underestimates the reddening value, probably because of its low spatial resolution. We expect that the astronomical community will be using the SFD reddening map extensively. We offer this Letter as a cautionary note about using the SFD map in regions of high extinction (AV > 0.5 mag), since it might not be giving accurate reddening values there.