Size-linewidth Relation Research Articles

On the Turbulent Velocity Dispersion in Molecular Clouds

We model the width-size σ-Lα by averaging a power-law spectrum of turbulent motions over a region of size L. This model reproduces the index α = 0-1 of most line width-size relations observed in molecular clouds, provided that L lies within the range of component wavelengths, the turbulent energy spectrum has power-law index p = 1-2, and the spectral components have random relative phases. The relation between p and α is independent of the dimensionality of the turbulence. As p increases beyond ~3, α approaches unity, departing from the value (p - 1)/2 expected in a simpler model, because the velocity profile approaches that of its longest wavelength spectral component. Fixed relative phases, expected for excitation by coherent sources, also yield a power-law line width-size relation but require a much steeper energy spectrum to match observations. If the turbulent spectrum has sharp cutoffs, the slope α changes sharply as L goes beyond the range of component wavelengths, approaching α = 1 for L λmax, independent of p. These changes in slope are due to simple properties of sinusoids and offer observational signatures of the extreme turbulent wavelengths in a cloud.

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.

A 13 CO Survey of Molecular Clouds in Gemini and Auriga

A large-scale survey for molecular clouds in 13CO(J = 1-0) was performed toward the Gemini and Auriga regions (170° < l ≤ 196° and -10° ≤ b < 10°) with velocity coverages of -30 < VLSR < +30 km s-1 and -20 < VLSR < +40 km s-1 for 170° < l ≤ 188° and 188° < l ≤ 196°, respectively, by using the two 4 m millimeter-wave telescopes at Nagoya University. An area of 520 deg2 was covered at an 8' grid spacing with a 27 beam, and 29,250 positions were observed. Significant 13CO emission (≥1.2 K km s-1 = 3 σ) is detected at 1032 positions, and 139 distinct 13CO clouds are identified. Physical properties such as molecular column density, size, and mass are derived for each cloud. Comparison with known H II regions and other associated visible objects indicates that 98 of the 139 clouds are located at ~2 kpc, while the rest lie at 1 kpc. The candidates for protostars are selected from IRAS point sources and 141 sources are identified as protostellar candidates associated with the 13CO clouds. A statistical study of the 13CO clouds and of the candidates for protostars shows the following results: 1. The mass spectra of the 13CO clouds are well represented by a power law, Ncloud(≥Mcloud) = 1.4 × 104(Mcloud/M☉)-0.83 - 1.4 for the clouds at ~2 kpc and Ncloud(≥Mcloud) = 3.5 × 102(Mcloud/M☉)-0.64 - 2.4 for the rest. 2. The line width, ΔVcomp, and the size, R, of the 13CO clouds show a power-law relation with an index 0.24 ± 0.06, where the dispersion in the fitting is fairly large. 3. A virial analysis made for the 13CO clouds indicates that the relation between the virial mass, Mvir, and the mass measured in 13CO, Mcloud, is aproximated well by (Mvir/M☉) = 2.0 × 101(Mcloud/M☉)0.72, which suggests that smaller clouds tend to be more weakly bound gravitationally than larger clouds or are dispersing if the external pressure is negligible. This is probably the cuase of a small index value of the line width-size relation. 4. The luminosity function of the IRAS point sources associated with 13CO clouds are well represented by a power law with Nstar(≥Lstar) = 4.0 × 102L-1.9×10 for those at ~2 kpc and Nstar(≥Lstar) = 2.3 × 10L-3.2 for the rest. 5. The luminosity of the most luminous IRAS point source in a given molecular cloud increases systematically with the mass of the associated cloud. 6. The 13CO clouds associated with IRAS point sources, which are regarded as ongoing star-forming clouds, tend to be more massive and larger in size and to have higher column densities than those without any sign of star formation. These relations are found to be consistent with those derived in Cygnus by Dobashi, Bernard, & Fukui and in Cepheus-Cassiopeia by Yonekura et al. In order to study the star formation activities, we studied the ratio of virial mass and the mass measured in 13CO, Mvir/Mcloud, and its relation with star formation. It is clearly seen that the star-forming 13CO clouds have low Mvir/Mcloud, and all the clouds with high Mvir/Mcloud exhibit no sign of star formation. This suggests that star formation rarely occurs in clouds with overall kinetic energy higher than the gravitational energy.

12COJ= 1–0 Observations of Individual Giant Molecular Clouds in M81

We present 12CO J=1-0 observations from the Caltech Millimeter Array of a field in the nearby spiral galaxy M81. We detect emission from three features that are the size of large giant molecular clouds (GMCs) in the Milky Way Galaxy and M31, but are larger than any known in M33 or the SMC. The M81 clouds have diameters approximately 100 pc and molecular masses 3 * 10^5 solar masses. These are the first GMCs to be detected in such an early type galaxy (Sab) or in a normal galaxy outside the Local Group. The clouds we have detected do not obey the size-linewidth relation obeyed by GMCs in our Galaxy and in M33, and some of them may be GMC complexes that contain several small GMCs. One of these does show signs of sub-structure, and is shaped like a ring section with three separate peaks. At the center of this ring section lies a giant HII region, which may be associated with the molecular clouds.

Cloud/Intercloud Structure from Nonlinear Magnetic Waves

One-dimensional numerical simulations of interacting plane-polarized Alfven waves including magnetic diffusion and thermal energy dissipation form structures between the sources of excitation that are analogous to clumpy cool diffuse clouds surrounded by a warm low-density intercloud medium. The cloud oscillates slightly after formation but has an average state that is in both thermal and total pressure equilibrium with the intercloud medium. The cloud substructure has a realistic size-line width relation, Δv ∝ R0.5, that is the result of a systematically decreasing correlation among random motions for increasingly large scales. The substructure also has a peak-density versus size relation ρ ∝ R-0.18 because of self-similar hierarchical structure. The gas continuously changes its temperature in response to density fluctuations in the turbulent medium, i.e., each region picks the temperature of the nearest equilibrium phase for the current density. The gas motions are generally less than the Alfven speed and comparable to the sound speed. This implies that supersonic turbulence in real clouds is probably the result of supersonic relative motions between very tiny clumps inside which the actual motions are nearly sonic. The magnetic field plays the important role of allowing energy from the perturbation to spread over a large distance with minimal dissipation.

Application of Principal Component Analysis to Large‐Scale Spectral Line Imaging Studies of the Interstellar Medium

The multivariate statistical technique of principal component analysis (PCA) is described and demonstrated to be a valuable tool to consolidate the large amount of information obtained with spectroscopic imaging observations of the interstellar medium. Simple interstellar cloud models with varying degrees of complexity and Gaussian noise are constructed and analyzed to demonstrate the ability of PCA to statistically extract physical features and phenomena from the data and to gauge the effects of random noise upon the analysis. Principal components are calculated for high spatial dynamic range 12CO and 13CO data cubes of the Sh 155 (Cep OB3) cloud complex. These identify the three major emission components within the cloud and the spatial differences between 12CO and 13CO emissions. Higher order eigenimages identify small velocity fluctuations and therefore provide spatial information to the turbulent velocity field within the cloud. A size line width relationship δv ~ Rα is derived from spatial and kinematic characterizations of the principal components of 12CO emission from the Sh 155, Sh 235, Sh 140, and Gem OB1 cloud complexes. The power-law indices for these clouds range from 0.42 to 0.55 and are similar to those derived from an ensemble of clouds within the Galaxy found by Larson (1981) and Solomon et al. (1987). The size-line width relationship within a given cloud provides an important diagnostic to the variation of kinetic energy with size scale within turbulent flows of the interstellar medium.

Can Nonlinear Hydromagnetic Waves Support a Self-gravitating Cloud?

Using self-consistent magnetohydrodynamic (MHD) simulations, we explore the hypothesis that nonlinear MHD waves dominate the internal dynamics of galactic molecular clouds. Our models employ an isothermal equation of state and allow for self-gravity. We adopt "slab symmetry," which permits motions V⊥ and fields B⊥ perpendicular to the mean field, but permits gradients only parallel to the mean field. This is the simplest possible geometry that relies on waves to inhibit gravitational collapse along the mean field. In our simulations, the Alfvén speed V<SUB>A</SUB> exceeds the sound speed C<SUB>s</SUB> by a factor 3-30, which is realistic for molecular clouds. We simulate the free decay of a spectrum of Alfvén waves, both with and without self-gravity. We also perform simulations with and without self-gravity that include small-scale stochastic forcing, meant to model the mechanical energy input from stellar outflows. <P />Our major results are as follows: (1) We confirm that the pressure associated with fluctuating transverse fields can inhibit the mean field collapse of clouds that are unstable by Jeans's criterion. Cloud support requires the energy in Alfvén-like disturbances to remain comparable to the cloud's gravitational binding energy. (2) We characterize the turbulent energy spectrum and density structure in magnetically dominated clouds. The perturbed magnetic and transverse kinetic energies are nearly in equipartition and far exceed the longitudinal kinetic energy. The turbulent spectrum evolves to a power-law , , approximately V<SUP>2</SUP><SUB>⊥,k</SUB> ≍ B2&amp;<SUB>#8869;,K</SUB>/4πρ ∝ k<SUP>-s</SUP> with s ∼2, i.e., approximately consistent with a "line width-size relation σ<SUB>v</SUB>(R) ∝ R<SUP>½</SUP>. The simulations show large density contrasts, with high-density regions confined in part by the pressure of the fluctuating magnetic field. (3) We evaluate the input power required to offset dissipation through shocks, as a function of c<SUB>s</SUB>/v<SUB>A</SUB>, the velocity dispersion σ, and the characteristic scale λ of the forcing. In equilibrium, the volume dissipation rate is ≍5.5(c<SUB>s</SUB>/v<SUB>A</SUB>)<SUP>½</SUP>(λ/L)<SUP>-½</SUP> × ρσ<SUP>3</SUP><SUB>v</SUB>/L, for a cloud of linear size L and density ρ. (4) Somewhat speculatively, we apply our results to a "typical" molecular cloud. The mechanical power input required for equilibrium (tens of L<SUB>sun</SUB>), and the implied star formation efficiency (∼1%), are in rough agreement with observations. Because this study is limited to slab symmetry and excludes ion-neutral friction, the dissipation rate we calculate probably provides a lower limit on the true value.

An Extension of Hierarchical Star Formation to Galactic Scales

view Abstract Citations (140) References (50) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS An Extension of Hierarchical Star Formation to Galactic Scales Elmegreen, Bruce G. ; Efremov, Yuri N. Abstract Star formation scaling laws and hierarchical patterns on galactic scales are investigated. The molecular cloud size-line width relation suggests that the duration of star formation in a region of size L should increase as L^1/2^. This conjecture is supported by observations of star- forming regions in our Galaxy and by the distribution of Cepheid variables in the LMC. Extending this relation to galactic scales, we suggest that coherent star formation exists over regions much larger than a single star complex ( > 1 kpc), taking the form of sheared spiral arms whenever the dimension is larger than the galactic thickness. The properties of star-forming spirals in nearby flocculent galaxies are measured; they typically extend for at least one-third of the galaxy diameter and consist of ~5 star complexes separated by ~1 kpc. Star- forming spirals appear to be as self-gravitating as all other scales in the star-formation hierarchy. We propose that stars form in hierarchically clustered systems ranging from less than 0.1 pc to multi- kpc scales, following the hierarchical distribution of the gas. This structure is generated on all scales by self-gravity and turbulence, with distortion from shear being relatively more important on large scales. Turbulent compression and energy loss (rather than collapse) determine the basic evolution time for a region. The hierarchical pattern disappears when the gas temporarily becomes structured by regular forces, as in spiral density waves and swept-up shells. Then clouds and young stars can appear like beads on a string because mild gravitational instabilities at the collapse threshold have a characteristic length of ~3 times the arm or filament width. Publication: The Astrophysical Journal Pub Date: August 1996 DOI: 10.1086/177554 Bibcode: 1996ApJ...466..802E Keywords: GALAXIES: SPIRAL; ISM: CLOUDS; STARS: FORMATION full text sources ADS | data products SIMBAD (12) NED (9)

Hydromagnetic waves and the linewidth-size relation in interstellar molecular clouds

Hydromagnetic waves and the linewidth-size relation in interstellar molecular clouds

A C(18)O survey of dense cores in the Taurus molecular cloud: Signatures of evolution and protostellar collapse

We have mapped 11 dense cores in the Taurus molecular cloud in the C(18)O J = 2 goes to 1 line at a linear resolution of 0.02 pc. The core masses derived from C(18)O range from 0.06 to 5 solar mass. Five of them have embedded infrared sources, and six do not. Dense cores without infrared sources show multiple emission peaks. In contrast, dense cores with infrared sources have a single peak and smaller sizes. The cores with infrared sources have line widths that are 2-3 times the value expected from correlations found in previous surveys. This enhancement may be accounted for by models of gravitational collapse. The data are consistent with the idea that dense cores evolve first toward smaller sizes and smaller line width along the line width-size relation, and then toward larger line width and constant or smaller sizes as an infrared source becomes observable. A good collapse candidate, L1527, is identified based on the shapes of C(18)O and H2CO lines.

Observational studies of dense core motions

Molecular lines have revealed various supporting motions in dense cores. Line widths and emission region sizes of NH3 and CS in the same kind of cores or of the same line in cores with or without sources are different and cannot be explained with the line width-size relationship. Outflows in dense cores show rich characteristics and could be responsible for the emission difference between the two kinds of cores for NH3 and C18O; CS emission is consistent with the chemical effects in shocked regions. Rotation exists in both kinds of cores and may be related to the observed polarities and collimations of the outflows.

Dense cores in dark clouds. VII - Line width-size relations

Observations of 14 dense cores in lines of CS, C 18 O and NH, are combined to examine the relations between the Doppler width of a line and the spatial extent of the map of line intensity. The line width increases with map size R as R p . The deduced width of the velocity distribution of the molecule of mean mass has p = 0.20 ± 0.04, and the deduced width of the nonthermal velocity distribution has p = 0.7 ± 0.1. The values of p for eight cores with embedded stars and for six cores without embedded stars are statistically indistinguishable, but p is better determined for cores without stars

Giant molecular clouds and the CO-to-H2 conversion factor in IC 10

Three molecular clouds have been mapped in the nearby metal-poor dwarf irregular galaxy IC 10 using the Owens Valley Millimeter-Wave Interferometer. The clouds have velocity widths, diameters, temperatures, and masses that are very similar to those of Galactic giant molecular clouds. However, the virial masses are substantially larger than the molecular masses. Two of these clouds obey the size-line width relation established for molecular clouds in the Galaxy and, thus, are probably gravitationally bound. Assuming these two clouds are self-gravitating and adopting a distance of 1 Mpc, the CO-to-H2 conversion factor of IC 10 is 6 x 10 to the 20th/sq cm per (K km/s), twice as large as the Galactic value. Thus, for a given mass of molecular gas, IC 10 is underluminous in CO by only a factor of 2 relative to the Galaxy. This observational result disagrees with recent theoretical predictions that the CO-to-H2 conversion factor should be a strong function of metallicity. 21 refs.

Analysis of (C-12)O and (C-13)O emission in a 3 square degree region of the Galactic plane between L = 23 deg and 25 deg

A 3-sq deg section of the inner Galactic plane centered at l = 24 deg, b = 0 deg in both (C-13)O and CS. The observations were supplemented by preexisting CO data from the Massachusetts-Stony Brook Galactic plane survey. It was possible to identify 47 molecular clouds in the region surveyed. Distances to the clouds were assigned using a size-line width relation which was derived for a set of calibrator clouds at known distances. By combining the CO and (C-13)O data, it was possible to calculate LTE masses for the clouds and to compare them with masses estimated from the virial theorem. Masses estimated from the two methods are tightly correlated, suggesting that the clouds observed in this study are close to virial equilibrium. The masses derived using the two methods are in reasonable agreement. Little CS emission was detected in this section or the Galactic plane; averaged over the region of the survey, the CO/CS integrated intensity ratio is found to be 660 + or - 160, considerably larger than the ratio in the Galactic center. 26 refs.

The size-line width relation and the mass of molecular hydrogen

view Abstract Citations (33) References (18) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Size--Line Width Relation and the Mass of Molecular Hydrogen Issa, M. ; MacLaren, I. ; Wolfendale, A. W. Abstract Some difficulties associated with the problem of cloud definition are considered, with particular regard to the crowded distribution of clouds and the difficulty of choosing an appropriate boundary in such circumstances. A number of tests carried out on the original data suggest that the delta(v) - S relation found by Solomon et al. (1987) is not a genuine reflection of the dynamical state of Giant Molecular Clouds. The Solomon et al. parameters, are insensitive to the actual cloud properties and are unable to distinguish true clouds from the consequences of sampling any crowded region of emission down to a low threshold temperature. The overall effect of such problems is to overestimate both the masses of Giant Molecular Clouds and the number of very large clouds. Publication: The Astrophysical Journal Pub Date: March 1990 DOI: 10.1086/168520 Bibcode: 1990ApJ...352..132I Keywords: Hydrogen Clouds; Molecular Clouds; Nebulae; Spectral Line Width; Carbon Monoxide; Emission Spectra; Interstellar Matter; Sky Surveys (Astronomy); Astrophysics; INTERSTELLAR: MOLECULES; NEBULAE: GENERAL; NEBULAE: INTERNAL MOTIONS full text sources ADS |

Are molecular clouds in virial equilibrium?

A correlation between CO luminosities and virial theorem masses of Galactic molecular clouds has been claimed to prove conclusively that molecular clouds are in gravitational virial equilibrium. This correlation is an artifact of the size-line width relation exhibited by molecular clouds, which does not require clouds to be virialized. Virial theorem masses do not provide an estimate of N(H2)/I(co). Comparison of the virial theorem-derived values of N(H2)/I(co) with the gamma-ray value shows that the masses of lower luminosity clouds are considerably overestimated by virial theorem analyses; these clouds are probably strongly influenced by nongravitational forces. 24 refs.

Carbon monoxide as a tracer of molecular cloud mass and the question of cloud gravitational stability

The nonlinear mass-CO luminosity law exhibited by virialized molecular clouds in the Galaxy obeying a certain size-line width relationship implies a scale-dependent ratio of CO luminosity to cloud virial mass. Using CO luminosity as a linear tracer of cloud mass is therefore likely to systematically underestimate molecular cloud mass, the discrepancy being greatest for smaller clouds. Many clouds reported to be gravitationally unbound are shown to be at least weakly self-gravitating and, considering observational uncertainties, may in fact be in approximate virial equilibrium. Magnetic fields not exceeding energy equipartition strength should not change the model predictions. 18 references.

Turbulent velocity structure in interstellar clouds

view Abstract Citations (91) References (20) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Turbulent velocity structure in interstellar clouds Scalo, J. M. Abstract The feasibility of directly measuring a spatially correlated turbulent velocity spectrum in interstellar clouds is investigated. It is argued on a number of grounds that relations between line width and scale size are unsuitable for this purpose. A more direct method is suggested for the determination of the turbulent velocity structure using well-sampled observations of mean velocities, to estimate the accuracy with which mean velocities must be measured for this purpose, and to point out the difficulties in the interpretation of this approach and of the line width-size relation. A preliminary C18O velocity autocorrelation function for the dense core of the ρ Oph cloud is presented as an example. Publication: The Astrophysical Journal Pub Date: February 1984 DOI: 10.1086/161726 Bibcode: 1984ApJ...277..556S Keywords: Interstellar Matter; Molecular Clouds; Optical Thickness; Spectral Line Width; Turbulent Flow; Velocity Distribution; Autocorrelation; Radial Velocity; Astrophysics full text sources ADS |