Density Of Molecular Clouds Research Articles

STAR FORMATION IN TWO LUMINOUS SPIRAL GALAXIES

We have examined star formation in two very luminous (M_V=-22 to -23) Sc-type spiral galaxies, NGC 801 and UGC 2885, using ultra-deep Halpha images. We combine these with UBV and 2MASS JHK images and HI maps to explore the star formation characteristics of disk galaxies at high luminosity. Halpha traces star formation in these galaxies to 4-6 disk scale lengths, but the lack of detection of Halpha further out is likely due to loss of Lyman continuum photons. Considering gravitational instabilities alone, we find that the gas and stars in the outer regions are marginally stable in an average sense, but considering dissipative gas and radial and azimuthal forcing, the outer regions are marginally unstable to form spiral arms. Star formation is taking place in spiral arms, which are regions of locally higher gas densities. Furthermore, we have traced smooth exponential stellar disks over 3-orders of magnitude and 4-6 disk scale lengths, in spite of a highly variable gravitational instability parameter. Thus, gravitational instability thresholds do not seem relevant to the stellar disk. One possibility for creating an exponential disk is that the molecular cloud densities and star formation rates have exponential profiles and this forces the stellar disk to build up such a profile. Another possibility is that the stellar disk is continuously adjusted to an exponential shape regardless of the star formation profile, for example through global dynamical process that scatter stars. However, such scattering processes are only known to operate in spiral systems, in which case they cannot explain the same dilemma of smooth exponential disks observed in dwarf irregular galaxies.

High-dynamic-range extinction mapping of infrared dark clouds

Measuring the mass distribution of infrared dark clouds (IRDCs) over the wide dynamic range of their column densities is a fundamental obstacle in determining the initial conditions of high-mass star formation and star cluster formation. We present a new technique to derive high-dynamic-range, arcsecond-scale resolution column density data for IRDCs and demonstrate the potential of such data in measuring the density variance - sonic Mach number relation in molecular clouds. We combine near-infrared data from the UKIDSS/Galactic Plane Survey with mid-infrared data from the Spitzer/GLIMPSE survey to derive dust extinction maps for a sample of ten IRDCs. We then examine the linewidths of the IRDCs using 13CO line emission data from the FCRAO/Galactic Ring Survey and derive a column density - sonic Mach number relation for them. For comparison, we also examine the relation in a sample of nearby molecular clouds. The presented column density mapping technique provides a very capable, temperature independent tool for mapping IRDCs over the column density range equivalent to A_V=1-100 mag at a resolution of 2". Using the data provided by the technique, we present the first direct measurement of the relationship between the column density dispersion, \sigma_{N/<N>}, and sonic Mach number, M_s, in molecular clouds. We detect correlation between the variables with about 3-sigma confidence. We derive the relation \sigma_{N/<N>} = (0.047 \pm 0.016) Ms, which is suggestive of the correlation coefficient between the volume density and sonic Mach number, \sigma_{\rho/<\rho>} = (0.20^{+0.37}_{-0.22}) Ms, in which the quoted uncertainties indicate the 3-sigma range. When coupled with the results of recent numerical works, the existence of the correlation supports the picture of weak correlation between the magnetic field strength and density in molecular clouds (i.e., B ~ \rho^{0.5}).

FORMALDEHYDE SILHOUETTES AGAINST THE COSMIC MICROWAVE BACKGROUND: A MASS-LIMITED, DISTANCE-INDEPENDENT, EXTINCTION-FREE TRACER OF STAR FORMATION ACROSS THE EPOCH OF GALAXY EVOLUTION

We examine the absorption of cosmic microwave background (CMB) photons by formaldehyde (H2CO) over cosmic time. The K-doublet rotational transitions of H2CO become "refrigerated" - their excitation temperatures are driven below the CMB temperature - via collisional pumping by molecular hydrogen (H2). "Anti-inverted" H2CO line ratios thus provide an accurate measurement of the H2 density in molecular clouds. Using a radiative transfer model, we demonstrate that H2CO centimeter wavelength line excitation and detectability are nearly independent of redshift or gas kinetic temperature. Since the H2CO K-doublet lines absorb CMB light, and since the CMB lies behind every galaxy and provides an exceptionally uniform extended illumination source, H2CO is a distance-independent, extinction-free molecular gas mass-limited tracer of dense gas in galaxies. A Formaldehyde Deep Field could map the history of cosmic star formation in a uniquely unbiased fashion and may be possible with large bandwidth wide-field radio interferometers whereby the silhouettes of star-forming galaxies would be detected across the epoch of galaxy evolution. We also examine the possibility that H2CO lines may provide a standardizable galaxy ruler for cosmology similar to the Sunyaev-Zel'dovich effect in galaxy clusters but applicable to much higher redshifts and larger samples. Finally, we explore how anti-inverted meterwave H2CO lines in galaxies during the peak of cosmic star formation may contaminate HI 21 cm tomography of the Epoch of Reionization.

THE X-FACTOR IN GALAXIES. I. DEPENDENCE ON ENVIRONMENT AND SCALE

Characterizing the conversion factor between CO emission and column density of molecular hydrogen, X_CO, is crucial in studying the gaseous content of galaxies, its evolution, and relation to star formation. In most cases the conversion factor is assumed to be close to that of giant molecular clouds (GMCs) in the Milky Way, except possibly for mergers and star-bursting galaxies. However, there are physical grounds to expect that it should also depend on the gas metallicity, surface density, and strength of the interstellar radiation field. The XCO factor may also depend on the scale on which CO emission is averaged due to effects of limited resolution. We study the dependence of X_CO on gas properties and averaging scale using a model that is based on a combination of results of sub-pc scale magneto-hydrodynamic simulations and on the gas distribution from self-consistent cosmological simulations of galaxy formation. Our model predicts a value of X_CO that is consistent with the Galactic value for interstellar medium conditions typical for the Milky Way. For such conditions the predicted X_CO varies by only a factor of two for gas surfaced densities in the range \sim 50 - 500 M_sun / pc^2. However, the model also predicts that more generally on the scale of GMCs, X_CO is a strong function of metallicity, and depends on the column density and the interstellar UV flux. We show explicitly that neglecting these dependencies in observational estimates can strongly bias the inferred distribution of H2 column densities of molecular clouds to have a narrower and offset range compared to the true distribution. We find that when averaged on \sim kpc scales the X-factor depends only weakly on radiation field and column density, but is still a strong function of metallicity. The predicted metallicity dependence can be approximated as X_CO \sim Z^{-{\gamma}} with {\gamma} ~ 0.5 - 0.8.

LARGE-SCALE KINEMATICS, ASTROCHEMISTRY, AND MAGNETIC FIELD STUDIES OF MASSIVE STAR-FORMING REGIONS THROUGH HC3N, HNC, AND C2H MAPPINGS

We have mapped 27 massive star-forming regions associated with water masers using three dense gas tracers: HC3N 10-9, HNC 1-0 and C2H 1-0. The FWHM sizes of HNC clumps and C2H clumps are about 1.5 and 1.6 times higher than those of HC3N, respectively, which can be explained by the fact that HC3N traces more dense gas than HNC and C2H. We found evidence for increase in optical depth of C2H with `radius' from center to outer regions in some targets, supporting the chemical model of C2H. The C2H optical depth is found to decline as molecular clouds evolve to later stage, suggesting that C2H might be used as "chemical clock" for molecular clouds. Large-scale kinematic structure of clouds was investigated with three molecular lines. All these sources show significant velocity gradients. The magnitudes of gradient are found to increase towards the inner region, indicating differential rotation of clouds. Both the ratio of rotational to gravitational energy and specific angular momentum seem to decrease toward the inner region, implying obvious angular momentum transfer, which might be caused by magnetic braking. The average magnetic field strength and number density of molecular clouds is derived using the uniformly magnetic sphere model. The derived magnetic field strengths range from 3 to 88 \mu G, with a median value of 13 \mu G. The mass-to-flux ratio of molecular cloud is calculated to be much higher than critical value with derived parameters, which agrees well with numerical simulations.

FORMALDEHYDE DENSITOMETRY OF GALACTIC STAR-FORMING REGIONS USING THE H{sub 2}CO 3{sub 12}-3{sub 13} AND 4{sub 13}-4{sub 14} TRANSITIONS

We present Green Bank Telescope observations of the 3{sub 12}-3{sub 13} (29 GHz) and 4{sub 13}-4{sub 14} (48 GHz) transitions of the H{sub 2}CO molecule toward a sample of 23 well-studied star-forming regions. Analysis of the relative intensities of these transitions can be used to reliably measure the densities of molecular cores. Adopting kinetic temperatures from the literature, we have employed a large velocity gradient (LVG) model to derive the average hydrogen number density (n(H{sub 2})) within a 16'' beam toward each source. Densities in the range of 10{sup 5.5}-10{sup 6.5} cm{sup -3} and ortho-formaldehyde column densities per unit line width between 10{sup 13.5} and 10{sup 14.5} cm{sup -2} (km s{sup -1}){sup -1} are found for most objects, in general agreement with existing measurements. A detailed analysis of the advantages and limitations to this densitometry technique is also presented. We find that H{sub 2}CO 3{sub 12}-3{sub 13}/4{sub 13}-4{sub 14} densitometry proves to be best suited to objects with T{sub K} {approx}> 100 K, above which the H{sub 2}CO LVG models become relatively independent of kinetic temperature. This study represents the first detection of these H{sub 2}CO K-doublet transitions in all but one object in our sample. The ease with whichmore » these transitions were detected, coupled with their unique sensitivity to spatial density, makes them excellent monitors of density in molecular clouds for future experiments. We also report the detection of the 9{sub 2}-8{sub 1} A {sup -} (29 GHz) transition of CH{sub 3}OH toward six sources.« less

FORMALDEHYDE DENSITOMETRY OF GALACTIC STAR-FORMING REGIONS USING THE H2CO 312–313AND 413–414TRANSITIONS

We present Green Bank Telescope (GBT) observations of the 3(12)-3(13) (29 GHz) and 4(13)-4(14) (48 GHz) transitions of the H2CO molecule toward a sample of 23 well-studied star-forming regions. Analysis of the relative intensities of these transitions can be used to reliably measure the densities of molecular cores. Adopting kinetic temperatures from the literature, we have employed a Large Velocity Gradient (LVG) model to derive the average hydrogen number density [n(H2)] within a 16 arcsecond beam toward each source. Densities in the range of 10^{5.5}--10^{6.5} cm^{-3} and ortho-formaldehyde column densities per unit line width between 10^{13.5} and 10^{14.5} cm^{-2} (km s^{-1})^{-1} are found for most objects, in general agreement with existing measurements. A detailed analysis of the advantages and limitations to this densitometry technique is also presented. We find that H2CO 3(12)-3(13)/4(13)-4(14) densitometry proves to be best suited to objects with T_K >~ 100 K, above which the H2CO LVG models become relatively independent of kinetic temperature. This study represents the first detection of these H2CO K-doublet transitions in all but one object in our sample. The ease with which these transitions were detected, coupled with their unique sensitivity to spatial density, make them excellent monitors of density in molecular clouds for future experiments. We also report the detection of the 9_2--8_1 A^- (29 GHz) transition of CH3OH toward 6 sources.

From the molecular-cloud- to the embedded-cluster-mass function with a density threshold for star formation

The mass function of molecular clouds and clumps is shallower than the mass function of young star clusters, gas-embedded and gas-free alike, as their respective mass function indices are $\beta_0 \simeq 1.7$ and $\beta_\star \simeq 2$. We demonstrate that such a difference can arise from different mass-radius relations for the embedded-clusters and the molecular clouds (clumps) hosting them. In particular, the formation of star clusters with a constant mean {\it volume} density in the central regions of molecular clouds of constant mean {\it surface} density steepens the mass function from clouds to embedded-clusters. This model is observationally supported since the mean surface density of molecular clouds is approximately constant, while there is a growing body of evidence, in both Galactic and extragalactic environments, that efficient star-formation requires a hydrogen molecule number density threshold of $n_{th} \simeq 10^{4-5}\,cm^{-3}$. In the framework of the same model, the radius distribution steepens from clouds (clumps) to embedded-clusters, which contributes to explaining observed cluster radius distributions. [Abridged]

THE “TRUE” COLUMN DENSITY DISTRIBUTION IN STAR-FORMING MOLECULAR CLOUDS

We use the COMPLETE Survey's observations of the Perseus star-forming region to assess and intercompare three methods for measuring column density in molecular clouds: extinction mapping (NIR); thermal emission mapping (FIR); and mapping the intensity of CO isotopologues. The structures shown by all three tracers are morphologically similar, but important differences exist. Dust-based measures give similar, log-normal, distributions for the full Perseus region, once careful calibration corrections are made. We also compare dust- and gas-based column density distributions for physically-meaningful sub-regions of Perseus, and we find significant variations in the distributions for those regions. Even though we have used 12CO data to estimate excitation temperatures, and we have corrected for opacity, the 13CO maps seem unable to give column distributions that consistently resemble those from dust measures. We have edited out the effects of the shell around the B-star HD 278942. In that shell's interior and in the parts where it overlaps the molecular cloud, there appears to be a dearth of 13CO, likely due either to 13CO not yet having had time to form in this young structure, and/or destruction of 13CO in the molecular cloud. We conclude that the use of either dust or gas measures of column density without extreme attention to calibration and artifacts is more perilous than even experts might normally admit. And, the use of 13CO to trace total column density in detail, even after proper calibration, is unavoidably limited in utility due to threshold, depletion, and opacity effects. If one's main aim is to map column density, then dust extinction seems the best probe. Linear fits amongst column density tracers are given, quantifying the inherent uncertainties in using one tracer (when compared with others). [abridged]

Can We Trust the Dust? Evidence of Dust Segregation in Molecular Clouds

Maps of estimated dust column density in molecular clouds are usually assumed to reliably trace the total gas column density structure. In this work we present results showing a clear discrepancy between the dust and the gas distribution in the Taurus molecular cloud complex. We compute the power spectrum of a 2MASS extinction map of the Taurus region and find it is much shallower than the power spectrum of a 13CO map of the same region previously analyzed. This discrepancy may be explained as the effect of grain growth on the grain extinction efficiency. However, this would require a wide range of maximum grain sizes, which is ruled out based on constraints from the extinction curve and the available grain models. We show that major effects due to CO formation and depletion are also ruled out. Our result may therefore suggest the existence of intrinsic spatial fluctuations of the dust to gas ratio, with amplitude increasing toward smaller scales. Preliminary results of numerical simulations of trajectories of inertial particles in turbulent flows illustrate how the process of clustering of dust grains by the cloud turbulence may lead to observable effects. However, these results cannot be directly applied to large scale supersonic and magnetized turbulence at present.

Understanding starbursts through giant molecular clouds in high density environments

AbstractStarburst galaxies are characterized by uncommonly high star formation efficiencies, but it remains unclear what physical conditions in the molecular gas produce this high efficiency. Invariably, high star formation efficiency is associated with high column densities of molecular material (e.g. the Kennicutt-Schmidt law), but what are the conditions in the molecular clouds in starburst galaxies? Direct observations of starburst are difficult or impossible with current instruments, so I present the properties of GMCs in the Local Group as a starting case and then extend the analysis of GMC properties to nearby systems with surface densities of gas intermediate between the Local Group and starbursts. Rather than being constant, molecular cloud properties follow a continuum with significant variation across the Local Group and the intermediate surface density systems. Concomitant with these variations in the macroscopic properties are significant changes in the internal pressure and densities of molecular clouds, which implies significant variability in the initial conditions of the star formation process.

Estimating the Column Density in Molecular Clouds with Far-Infrared and Submillimeter Emission Maps

We have used a numerical simulation of a turbulent cloud to synthesize maps of the thermal emission from dust at a variety of far-IR and submillimeter wavelengths. The average column density and external radiation field in the simulation is well matched to clouds such as Perseus and Ophiuchus. We use pairs of single-wavelength emission maps to derive the dust color temperature and column density, and we compare the derived column densities with the true column density. We demonstrate that longer wavelength emission maps yield less biased estimates of column density than maps made toward the peak of the dust emission spectrum. We compare the scatter in the derived column density with the observed scatter in Perseus and Ophiuchus. We find that while in Perseus all of the observed scatter in the emission-derived versus the extinction-derived column density can be attributed to the flawed assumption of isothermal dust along each line of sight, in Ophiuchus there is additional scatter above what can be explained by the isothermal assumption. Our results imply that variations in dust emission properties within a molecular cloud are not necessarily a major source of uncertainty in column density measurements.

The Average Magnetic Field Strength in Molecular Clouds: New Evidence of Super-Alfvnic Turbulence

The magnetic field strength in molecular clouds is a fundamental quantity for theories of star formation. It is estimated by Zeeman splitting measurements in a few dense molecular cores, but its volume-averaged value within large molecular clouds (over several parsecs) is still uncertain. In this work, we provide a new method to constrain the average magnetic field strength in molecular clouds. We compare the power spectrum of gas density of molecular clouds with that of two 3503 numerical simulations of supersonic MHD turbulence. The numerical simulation with approximate equipartition of kinetic and magnetic energies (model A) yields the column density power spectrum P(k) ∝ k-2.25±0.01, the super-Alfvénic simulation (model B) P(k) ∝ k-2.71±0.01. The column density power spectrum of the Perseus, Taurus, and Rosetta molecular cloud complexes is found to be well approximated by a power law, P0(k) ∝ k-a, with a = 2.74 ± 0.07, 2.74 ± 0.08, and 2.76 ± 0.08, respectively. We conclude that the observations are consistent with the presence of super-Alfvénic turbulence in molecular clouds (model B), while model A is inconsistent (more than 99% confidence) with the observations.

The Nature of the Compact Supernova Remnants in Starburst Galaxies

Radio observations of starburst regions in galaxies have revealed groups of compact nonthermal sources that may be radiative supernova remnants expanding in the interclump medium of molecular clouds. Because of the high pressure in starburst regions, the interclump medium may have a density ~ 10^3 H atoms cm^{-3} in a starburst nucleus like M82 and ~ 10^4 H atoms cm^{-3} in an ultraluminous galaxy like Arp 220. In M82, our model can account for the sizes, the slow evolution, the high radio luminosities, and the low X-ray luminosities of the sources. We predict expansion velocities ~ 500 km/s, which is slower than the one case measured by VLBI techniques. Although we predict the remnants to be radiative, the expected radiation is difficult to detect because it is at infrared wavelengths and the starburst is itself very luminous; one detection possibility is broad [OI] 63 micron line emission at the positions of the radio remnants. The more luminous and compact remnants in Arp 220 can be accounted for by the higher molecular cloud density. In our model, the observed remnants lose most of the supernova energy to radiation. Other explosions in a lower density medium may directly heat a hot, low density interstellar component, leading to the superwinds that are associated with starburst regions.

The Probability Distribution Function of Column Density in Molecular Clouds

We discuss the probability distribution function (PDF) of column density resulting from density fields with lognormal PDFs, applicable to isothermal gas (e.g., probably molecular clouds). For magnetic and nonmagnetic numerical simulations of compressible, isothermal turbulence forced at intermediate scales ( of the box size), we find that the autocorrelation function (ACF) of the density field decays over relatively short distances compared to the simulation size. We suggest that a "decorrelation length" can be defined as the distance over which the density ACF has decayed to, for example, 10% of its zero-lag value, so that the density "events" along a line of sight can be assumed to be independent over distances larger than this, and the central limit theorem should be applicable. However, using random realizations of lognormal fields, we show that the convergence to a Gaussian is extremely slow in the high-density tail. As a consequence, the column density PDF is not expected to exhibit a unique functional shape, but to transit instead from a lognormal to a Gaussian form as the ratio η of the column length to the decorrelation length (i.e., the number of independent events in the cloud) increases. Simultaneously, the variance of the PDF decreases. For intermediate values of η, the column density PDF assumes a nearly exponential decay. For cases with a density contrast of 104, as found in intermediate-resolution simulations, and expected from giant molecular clouds (GMCs) to dense molecular cores, the required value of η for convergence to a Gaussian is at least a few hundred, or, for 106, several thousand. We then discuss the density power spectrum and the expected value of η in actual molecular clouds, concluding that they are uncertain since they may depend on several physical parameters. Observationally, our results suggest that η may be inferred from the shape and width of the column density PDF in optically thin line or extinction studies. Our results should also hold for gas with finite-extent power-law underlying density PDFs, which should be characteristic of the diffuse, nonisothermal neutral medium (with temperatures ranging from a few hundred to a few thousand degrees). Finally, we note that for η ≳ 100, the dynamic range in column density is small (less than a factor of 10), but this is only an averaging effect, with no implication on the dynamic range of the underlying density distribution.

Dust Growth Timescale and Mass Function of Molecular Clouds in the Galaxy

We examine the characteristic growth time of dust grains in the Galaxy, where the grain growth in molecular clouds is the dominant factor for dust-mass increase. Since the timescale of grain growth depends on the gas density of molecular clouds, we reconsider the typical molecular-cloud density by using the “density function” of clouds [denoted as N(n) dn]. Here, the density function expresses the probability that a cloud has a volume-averaged gas density between n and n+dn, and it can be calculated by combining the observed mass function and the scaling law of molecular clouds. Through the formulation that combines N(n) with the characteristic dust growth timescale, we find that the typical dust growth timescale is in the range of 107–108 yr. This range is equivalent to the timescale of the dust growth in molecular clouds whose molecular number density is 3 × 102−3 × 103 cm−3. Thus, the dense molecular clouds (n &amp;gt; 104 cm−3) contribute little to dust growth. The timescale supports the value constrained in our previous model and provides an upper limit for the lifetimes of molecular clouds.

A Comparison of13CO Local Thermodynamic Equilibrium and True Column Densities in Molecular Cloud Models

In this work we use models of molecular clouds and non-LTE radiative transfer calculations to compare the column densities of molecular clouds with their LTE 13CO column densities. The cloud models consist of three-dimensional grids of density and velocity fields obtained as solutions of the compressible magnetohydrodynamic equations in a 1283 periodic grid in both the supersonic and super-Alfvenic regimes. Because of the random nature of the velocity field and the presence of shocks, the densities span a continuous range of values covering about 6 orders of magnitude (from ~0.1 to ~105 cm-3). As a result, the LTE column densities can be calculated over 3 orders of magnitude. We find that LTE column densities of molecular clouds typically underestimate the mean 13CO true column densities by factors ranging from 1.3 to 7. These results imply that the standard LTE methods for the derivation of column densities from CO data systematically underestimate the true values independent of other major sources of uncertainty such as the relative abundance of CO.

Tidally Compressed Gas in Centers of Early‐Type and Ultraluminous Galaxies

In this paper we propose that the compressive tidal held in the centers of flat-core early-type galaxies and ultraluminous galaxies compresses molecular clouds producing dense gas observed in the centers of these galaxies. The effect of galactic tidal fields is usually considered disruptive in the literature. However, for some galaxies, the mass profile flattens toward the center and the resulting galactic tidal field is not disruptive, but instead it is compressive within the flat-core region. We have used the virial theorem to determine the minimum density of a molecular cloud to be stable and gravitationally bound within the tidally compressive region of a galaxy. We have applied the mechanism to determine the mean molecular cloud densities in the centers of a sample of flat-core, early-type galaxies and ultraluminous galaxies. For early-type galaxies with a core-type luminosity profile, the tidal held of the galaxy is compressive within half the core radius. We have calculated the mean gas densities for molecular gas in a sample of early-type galaxies which have already been detected in CO emission, and we obtain mean densities of [n] similar to 10(3)-10(6) cm(-3) within the central 100 pc radius. We also use our model to calculate the molecular cloud densities in the inner few hundred parsecs of a sample of ultraluminous galaxies. From the observed rotation curves of these galaxies we show that they have a compressive core within their nuclear region. Our model predicts minimum molecular gas densities in the range 10(2)-10(4) cm(-3) in the nuclear gas disks; the smaller values are applicable typically for galaxies with larger core radii. The resulting density values agree well with the observed range. Also, for large core radii, even fairly low-density gas (similar to 10(2) cm(-3)) can remain bound and stable close to the galactic center.

Gravitational instability and star formation in disc galaxies

We present a general star formation law in which the star formation rate depends upon the efficiency α and the time-scale τ of star formation, and the gas component σg of the surface mass density. The current nominal Schmidt exponent nS for our model is 2<nS<3. Based on a gravitational instability parameter QA and another dimensionless parameter fP=(P/Gcσ2)1/2, where P = pressure and σc = column density of molecular clouds, we suggest a general equation for the star formation rate which depends upon the relative contributions of the two parameters for various physical circumstances. We find that QA turns out to be a better parameter for the star formation scenario than does the Toomre Q-parameter. The star formation rate in the solar neighbourhood is found to be in good agreement with values inferred from previous studies. In the closed box approximation model, we obtain a relationship between the metallicity of the gas and the efficiency of star formation. Our model calculations of metallicity in the solar neighbourhood agree with earlier estimates. We conclude that the metallicity dispersion for stars of the same age may result from a change in the efficiency with which different stars in the sample were processed. For no significant change of metallicity with age, we suggest that all stars in the sample were born with similar efficiencies.

Collapse and Fragmentation of Cylindrical Magnetized Clouds: Simulation with Nested Grid Scheme

The fragmentation process in a cylindrical magnetized cloud has been studied using the nested grid method. The nested grid scheme uses 15 levels of grids with increasing spatial resolution, which enabled us to trace the evolution from molecular cloud densities ∼ 100 cm−3 to that of protostellar disks, ∼ 1010 cm−3 or higher. Fluctuations with small amplitude grow due to a gravitational instability. A disk is formed whose symmetric plane is perpendicular to magnetic field lines which run in the direction parallel to the major axis of the cloud. Matter accretes onto the disk, mainly flowing along the magnetic fields. This increases the column density. The radial inflow velocity is slower than the flow perpendicular to the disk, which is driven by an increase of the gravity. The contraction continues indefinitely for an isothermal equation of state and while the magnetic fields are perfectly coupled to matter. Both conditions are realized in the density range of ρ ≲ 1010 cm−3. The structure of the contracting disk reaches that of a singular solution as the density and column density obey ρ(r) ∝ r−2 and σ(r) ∝ r−1, respectively. The magnetic field strength in the mid-plane is proportional to ρ(r)1/2 and the field at the center (Bc) evolves proportionally to the square root of the gas density (∝ ρc1/2). It is shown that isothermal clouds experience a “run-away„ collapse. The evolution, including a hardening of the equation of state due to radiation trapping, is also discussed.