David Chappell - Academia.edu (original) (raw)

Papers by David Chappell

Bulletin of the American Astronomical Society, Nov 29, 1994

The global star formation rate in disk galaxies has traditionally been viewed as a slowly and mon... more The global star formation rate in disk galaxies has traditionally been viewed as a slowly and monotonically varying function of time, or even constant. Often, the energy injection of high-mass stars (ionization, winds, supernovae) is argued to produce a self-regulating mechanism which clamps the star formation rate at a value that can only change on a secular timescale. Studies using one-zone models to simulate the time evolution of the large-scale interstellar medium have indicated that, besides self-regulation solutions, oscillating and runaway states are also possible when either time delays or nonlinear interactions between the stars and the ISM components are included. All these models lack spatial degrees of freedom. An important question is whether the self-regulation or oscillations found in these one-zone models persist on a global scale when spatial couplings are introduced. We present a pair of two-dimensional model simulations of the large-scale ISM. In each model, newly formed stars pump energy back into the turbulence, but star formation occurs only when the turbulent energy density of the local gas decays below a critical value, assuming a particular cooling function. Also, a self-propagating star-formation mechanism is mediated through the turbulent field. The first model is a network of coupled ordinary differential equations (i.e. coupled one-zone models). The second is a probablistic cellular automaton. In each case the local and global temporal dynamics and the emergent spatial star-formation patterns are examined.

$Research paper thumbnail of Multifractal Column Density Scaling in Local Star-Forming Cloud Complexes$

Column density maps derived from 60 and 100 micron IRAS images of several regions of low mass sta... more Column density maps derived from 60 and 100 micron IRAS images of several regions of low mass star formation are presented. These maps contain as many as 3 times 10(5) resolution elements and display very complex and diverse patterns. The multifractal scaling of this structure is studied through the f(alpha ) spectrum of singularities, a tool commonly used in non-linear dynamics for characterizing complex images and time series. All subregions with adequate data were found to exhibit well-defined multifractal scaling. The shape of the f(alpha ) spectum was found to vary radically from region to region implying that the column density structures do not form a single `universality' class, in contrast to indications for incompressible turbulence. These results are intriguing in light of the apparently universal perimeter-area scaling exponents found for many of the same regions.

Bulletin of the American Astronomical Society, Dec 1, 1997

We investigate the form of the one-point probability distribution function (pdf) for the density ... more We investigate the form of the one-point probability distribution function (pdf) for the density field of the interstellar medium using numerical simulations that successively reduce the number of physical processes included. Two-dimensional simulations of self-gravitating supersonic MHD turbulence, of supersonic self-gravitating hydrodynamic turbulence, and of decaying Burgers turbulence, produce in all cases filamentary density structures and evidence for a power-law density pdf with logarithmic slope around -1.7. This suggests that the functional form of the pdf and the general filamentary morphology are the signature of the nonlinear advection operator. These results do not support previous claims that the pdf is lognormal. A series of 1D simulations of forced supersonic polytropic turbulence is used to resolve the discrepancy. They suggest that the pdf is lognormal only for effective polytropic indices gamma =1 (or nearly lognormal for gamma not =1 if the Mach number is sufficiently small), while power laws develop for densities larger than the mean if gamma <1.

Two simulations are developed to investigate the effects of star formation feedback on the spatio... more Two simulations are developed to investigate the effects of star formation feedback on the spatio-temporal organization of stars and gas in galaxies. In each model, the interstellar gas is viewed as a dissipative, reactive medium driven by stellar winds and supernovae. The dissipation is provided by gas interactions such as cloud or shell collisions and shocks. Star formation and subsequent stellar energy injection constitute the 'reactions.' The models are constructed to be computationally efficient and structurally simple, retaining only the essential physics of the problem such as conservation laws, symmetries, and spatial couplings. This approach is taken so that we may explore multiple models over a range of physical conditions and parameter values. The first model is a system of coupled nonequilibrium one-zone models in which star formation is driven by the action of gravitational disk instabilities. The gas velocity dispersion is controlled by stellar heating and collisional dissipation. Each one-zone model exhibits oscillations or bursts when a heating time delay exceeds a critical value. We find that the oscillations can persist globally and synchronously for a range of parameters. In addition, we find regimes in which star formation is scattered and uncorrelated and in which traveling waves of star formation develop. In the second model, stellar energy injection drives expanding shells of swept-up gas which evolve through the action of fluid advection to form a 'turbulent' network of shell fragments. Interactions between shells can lead to star formation which then generates new shells. This model may also be viewed generically as a 'reaction-advection' system, or as a driven Burgers turbulence with mass conservation. We find that coherent regions of star formation form, disperse, and wander throughout the simulation as the result of the collective action of many 'propagation' events. Bursts of star formation only occur when the average star formation rate is low. The distribution of velocities exhibits exponential tails over a broad range of parameter values, while the cloud mass spectra tend to be power laws with an index that depends weakly on the star formation activity. Comparison with observational and previous theoretical work is given.

It is often assumed that galaxies cannot generate large-scale coherent star- forming activity wit... more It is often assumed that galaxies cannot generate large-scale coherent star- forming activity without some organizing agent, such as spiral density waves, bars, large-scale instabilities, or external perturbations due to encounters with other galaxies. We present simulations of a simple model of star formation in which local spatial couplings lead to large-scale coherent, and even synchronized, patterns of star formation without any explicit propagation or any separate organizing agent. At a given location, star formation is assumed to occur when the gas velocity dispersion falls below a critical value dependent on the density. Young stars inject energy into the gas in their neighborhood, increasing the velocity dispersion and inhibiting the instability. A dissipation function continually "cools" the gas. The stability of this local inhibitory feedback model is examined both analytically and numerically. A large number of two-dimensional simulations are used to examine the effect of spatial couplings due to energy injection into neighboring regions. We find that several distinct types of behavior can be demarcated in a phase diagram whose parameter axes are the density (assumed constant in most models) and spatial coupling strength. These "phases" include, with decreasing density, a spatially homogeneous steady state, oscillatory "islands," traveling waves of star formation or global synchronization, and scattered "patches" of star formation activity. The coherence effects are explained in terms of the ability of the energy injected near a star formation site to introduce phase correlations in the subsequent cooling curves of neighboring regions.

We develop a set of parametric algebraic equations describing the shape, velocity field, and surf... more We develop a set of parametric algebraic equations describing the shape, velocity field, and surface density of the interface layer formed between two colliding thin shells. The solutions are exact in the limit that fluid advection and momentum conservation of the shells dominate both internal pressure effects and driving forces. Thus, they are most appropriate to interactions between shells when the zero-pressure snowplow assumption is valid. We briefly examine the gravitational instability of the interaction layer and compare the resulting growth rate with the growth rate in the individual shells. We also examine global statistics of pair-wise interactions in a system of expanding shells using Monte-Carlo simulations. The simulations may be relevant to either interacting superbubbles driven by cluster winds or to the interaction of smaller-scale shells driven by protostellar winds. Results include the mass spectra of interaction structures, velocity histograms, and dependence of t...

Two ideas appear frequently in theories of star formation and galaxy evolution: (1) star formatio... more Two ideas appear frequently in theories of star formation and galaxy evolution: (1) star formation is nonlocally excitatory, stimulating star formation in neighboring regions by propagation of a dense fragmenting shell or the compression of preexisting clouds; and (2) star formation is nonlocally inhibitory, making H2 regions and explosions which can create low-density and/or high temperature regions and increase the macroscopic velocity dispersion of the cloudy gas. Since it is not possible, given the present state of hydrodynamic modeling, to estimate whether one of these effects greatly dominates the other, it is of interest to investigate the predicted spatial pattern of star formation and its temporal behavior in simple models which incorporate both effects in a controlled manner. The present work presents preliminary results of such a study which is based on lattice galaxy models with various types of nonlocal inhibitory and excitatory couplings of the local SFR to the gas den...

The Astrophysical Journal, 1999

Several recent observational studies have shown that the clustering of young stars in local star-... more Several recent observational studies have shown that the clustering of young stars in local star-forming regions, and of Cepheids in the LMC, can be described by a power law two-point correlation function. We show by numerical simulations that the observed range in power law slopes can be accounted for by a model in which stellar winds drive expanding shells that are subjected to nonlinear fluid advection and interactions with other shells, and in which star formation occurs when a threshold shell column density is exceeded. The models predict how the power law slope should depend on the maximum age of the stellar sample and the average star formation rate, although a number of effects preclude a comparison with currently-available data. We also show how stellar migration flattens the power law slope below a scale that depends on the velocity dispersion and age of the sample, an effect which may explain the secondary breaks in the observed correlation functions of some regions at large separations. Problems with using the correlation function as a descriptor of clustering structure for statistically inhomogeneous data sets are discussed.

$Research paper thumbnail of Multifractal Scaling, Geometrical Diversity, and Hierarchical Structure in the Cool Interstellar Medium$

The Astrophysical Journal, 2001

Multifractal scaling (MFS) refers to structures that can be described as a collection of interwov... more Multifractal scaling (MFS) refers to structures that can be described as a collection of interwoven fractal subsets which exhibit power-law spatial scaling behavior with a range of scaling exponents (concentration, or singularity, strengths) and dimensions. The existence of MFS implies an underlying multiplicative (or hierarchical, or cascade) process. Panoramic column density images of several nearby star-forming cloud complexes, constructed from IRAS data, are shown to exhibit such multifractal scaling, which we interpret as indirect but quantitative evidence for nested hierarchical structure. The relation between the dimensions of the subsets and their concentration strengths (the "multifractal spectrum") appears to satisfactorily order the observed regions in terms of the mixture of geometries present, from strong point-like concentrations, to line-like filaments or fronts, to space-filling diffuse structures. This multifractal spectrum is a global property of the regions studied, and does not rely on any operational definition of "clouds." The range of forms of the multifractal spectrum among the regions studied implies that the column density structures do not form a universality class, in contrast to indications for velocity and passive scalar fields in incompressible turbulence, providing another indication that the physics of highly compressible interstellar gas dynamics differs fundamentally from incompressible turbulence. There is no correlation between the geometrical properties of the regions studied and their level of internal star formation activity, a result that is also apparent from visual inspection. We discuss the viability of the multifractal spectrum as a measure of the structural "complexity" of the regions studied, and emphasize the problematic dependence of all structural descriptors on the subjective pre-selection of the region to be described. A comparison of IRAS 100 µm column density (not intensity) images with 13 CO, visual extinction, and C 18 O data suggests that structural details are captured by IRAS up to at least 30 magnitudes of visual extinction, except in the vicinity of embedded stars, and that lower-column density connective structure not seen by other methods is revealed.

Monthly Notices of the Royal Astronomical Society, 2001

The effects of wind-driven star formation feedback on the spatio-temporal organization of stars a... more The effects of wind-driven star formation feedback on the spatio-temporal organization of stars and gas in galaxies is studied using two-dimensional intermediaterepresentational quasi-hydrodynamical simulations. The model retains only a reduced subset of the physics, including mass and momentum conservation, fully nonlinear fluid advection, inelastic macroscopic interactions, threshold star formation, and momentum forcing by winds from young star clusters on the surrounding gas. Expanding shells of swept-up gas evolve through the action of fluid advection to form a "turbulent" network of interacting shell fragments whose overall appearance is a web of filaments (in two dimensions). A new star cluster is formed whenever the column density through a filament exceeds a critical threshold based on the gravitational instability criterion for an expanding shell, which then generates a new expanding shell after some time delay. A filament-finding algorithm is developed to locate the potential sites of new star formation.

Astrophysical Journal, 1998

We investigate the form of the one-point probability density function (pdf) for the density field... more We investigate the form of the one-point probability density function (pdf) for the density field of the interstellar medium using numerical simulations that successively reduce the number of physical processes included. Two-dimensional simulations of self-gravitating supersonic MHD turbulence, of supersonic self-gravitating hydrodynamic turbulence, and of decaying Burgers turbulence produce in all cases filamentary density structures and evidence for a power-law density pdf at large densities with logarithmic slope between -1.7 and -2.3. This suggests that a power-law shape of the pdf and the general filamentary morphology are the signature of the nonlinear advection operator. These results do not support previous claims that the pdf is lognormal. A series of one-dimensional simulations of forced supersonic polytropic turbulence is used to resolve the discrepancy. They suggest that the pdf is lognormal only for effective polytropic indices γ = 1 (or nearly lognormal for γ ≠ 1 if the Mach number is sufficiently small), while power laws develop for densities larger than the mean if γ < 1. We evaluate the polytropic index for conditions relevant to the cool interstellar medium using published cooling functions and different heating sources, finding that a lognormal pdf should probably occur at densities around 103 and is possible at larger densities, depending strongly on the role of gas-grain heating and cooling. Several applications are examined. First, we question a recent derivation of the initial mass function from the density pdf by Padoan, Nordlund, & Jones because (1) the pdf does not contain spatial information and (2) their derivation produces the most massive stars in the voids of the density distribution. Second, we illustrate how a distribution of ambient densities can alter the predicted form of the size distribution of expanding shells. Finally, a brief comparison is made with the density pdfs found in cosmological simulations.