The Fractal Dimension of Projected Clouds

The interstellar medium seems to have an underlying fractal structure which can be characterized through its fractal dimension. However, interstellar clouds are observed as projected two-dimensional images, and the projection of a tri-dimensional fractal distorts its measured properties. Here we use simulated fractal clouds to study the relationship between the tri-dimensional fractal dimension (D_f) of modeled clouds and the dimension resulting from their projected images. We analyze different fractal dimension estimators: the correlation and mass dimensions of the clouds, and the perimeter-based dimension of their boundaries (D_per). We find the functional forms relating D_f with the projected fractal dimensions, as well as the dependence on the image resolution, which allow to estimatethe "real" D_f value of a cloud from its projection. The application of these results to Orion A indicates in a self-consistent way that 2.5 < D_f < 2.7 for this molecular cloud, a value higher than the result D_per+1 = 2.3 some times assumed in literature for interstellar clouds.Comment: 27 pages, 13 figures, 1 table. Accepted for publication in ApJ. Minor change

Pre-Existing Superbubbles as the Sites of Gamma-Ray Bursts

According to recent models, gamma-ray bursts apparently explode in a wide variety of ambient densities ranging from ~ 10^{-3} to 30 cm^{-3}. The lowest density environments seem, at first sight, to be incompatible with bursts in or near molecular clouds or with dense stellar winds and hence with the association of gamma-ray bursts with massive stars. We argue that low ambient density regions naturally exist in areas of active star formation as the interiors of superbubbles. The evolution of the interior bubble density as a function of time for different assumptions about the evaporative or hydrodynamical mass loading of the bubble interior is discussed. We present a number of reasons why there should exist a large range of inferred afterglow ambient densities whether gamma-ray bursts arise in massive stars or some version of compact star coalescence. We predict that many gamma-ray bursts will be identified with X-ray bright regions of galaxies, corresponding to superbubbles, rather than with blue localized regions of star formation. Massive star progenitors are expected to have their own circumstellar winds. The lack of evidence for individual stellar winds associated with the progenitor stars for the cases with afterglows in especially low density environments may imply low wind densities and hence low mass loss rates combined with high velocities. If gamma-ray bursts are associated with massive stars, this combination might be expected for compact progenitors with atmospheres dominated by carbon, oxygen or heavier elements, that is, progenitors resembling Type Ic supernovae.Comment: 14 pages, no figures, submitted to The Astrophysical Journa

Modeling a high mass turn down in the stellar initial mass function

Statistical sampling from the stellar initial mass function (IMF) for all star-forming regions in the Galaxy would lead to the prediction of ~1000 Msun stars unless there is a rapid turn-down in the IMF beyond several hundred solar masses. Such a turndown is not necessary for dense clusters because the number of stars sampled is always too small. Here we explore several mechanisms for an upper mass cutoff, including an exponential decline of the star formation probability after a turbulent crossing time. The results are in good agreement with the observed IMF over the entire stellar mass range, and they give a gradual turn down compared to the Salpeter function above ~100 Msun for normal thermal Jeans mass, M_J. The upper mass turn down should scale with M_J in different environments. A problem with the models is that they cannot give both the observed power-law IMF out to the high-mass sampling limit in dense clusters, as well as the observed lack of supermassive stars in whole galaxy disks. Either there is a sharper upper-mass cutoff in the IMF, perhaps from self-limitation, or the IMF is different for dense clusters than for the majority of star formation that occurs at lower density. Dense clusters seem to have an overabundance of massive stars relative to the average IMF in a galaxy.Comment: 19 pages, 2 figures, Astrophysical Journal, Vol 539, August 10, 200

A Fractal Analysis of the HI Emission from the Large Magellanic Cloud

A composite map of HI in the LMC using the ATCA interferometer and the Parkes multibeam telescope was analyzed in several ways in an attempt to characterize the structure of the neutral gas and to find an origin for it. Fourier transform power spectra in 1D, 2D, and in the azimuthal direction were found to be approximate power laws over 2 decades in length. Delta-variance methods also showed the same power-law structure. Detailed models of these data were made using line-of-sight integrals over fractals that are analogous to those generated by simulations of turbulence with and without phase transitions. The results suggested a way to measure directly for the first time the line-of-sight thickness of the cool component of the HI disk of a nearly face-on galaxy. The signature of this thickness was found to be present in all of the measured power spectra. The character of the HI structure in the LMC was also viewed by comparing positive and negative images of the integrated emission. The geometric structure of the high-emission regions was found to be filamentary, whereas the geometric structure of the low-emission (intercloud) regions was found to be patchy and round. This result suggests that compressive events formed the high-emission regions, and expansion events, whether from explosions or turbulence, formed the low-emission regions. The character of the structure was also investigated as a function of scale using unsharp masks. All of these results suggest that most of the ISM in the LMC is fractal, presumably the result of pervasive turbulence, self-gravity, and self-similar stirring.Comment: 30 pages, 21 figures, scheduled for ApJ Vol 548n1, Feb 10, 200

A Test of the Standard Hypothesis for the Origin of the HI Holes in Holmberg II

The nearby irregular galaxy Holmberg II has been extensively mapped in HI using the Very Large Array (VLA), revealing intricate structure in its interstellar gas component (Puche et al. 1992). An analysis of these structures shows the neutral gas to contain a number of expanding HI holes. The formation of the HI holes has been attributed to multiple supernova events occurring within wind-blown shells around young, massive star clusters, with as many as 10-200 supernovae required to produce many of the holes. From the sizes and expansion velocities of the holes, Puche et al. assigned ages of ~10^7 to 10^8 years. If the supernova scenario for the formation of the HI holes is correct, it implies the existence of star clusters with a substantial population of late-B, A and F main sequence stars at the centers of the holes. Many of these clusters should be detectable in deep ground-based CCD images of the galaxy. In order to test the supernova hypothesis for the formation of the HI holes, we have obtained and analyzed deep broad-band BVR and narrow-band H-alpha images of Ho II. We compare the optical and HI data and search for evidence of the expected star clusters in and around the HI holes. We also use the HI data to constrain models of the expected remnant stellar population. We show that in several of the holes the observed upper limits for the remnant cluster brightness are strongly inconsistent with the SNe hypothesis described in Puche et al. Moreover, many of the HI holes are located in regions of very low optical surface brightness which show no indication of recent star formation. Here we present our findings and explore possible alternative explanations for the existence of the HI holes in Ho II, including the suggestion that some of the holes were produced by Gamma-ray burst events.Comment: 30 pages, including 6 tables and 3 images. To appear in Astron. Journal (June 1999

Can Reflection from Grains Diagnose the Albedo?

By radiation transfer models with a realistic power spectra of the projected density distributions, we show that the optical properties of grains are poorly constrained by observations of reflection nebulae. The ISM is known to be hierarchically clumped from a variety of observations (molecules, H I, far-infrared). Our models assume the albedo and phase parameter of the dust, the radial optical depth of the sphere averaged over all directions, and random distributions of the dust within the sphere. The outputs are the stellar extinction, optical depth, and flux of scattered light as seen from various viewing angles. Observations provide the extinction and scattered flux from a particular direction. Hierarchical geometry has a large effect on the flux of scattered light emerging from a nebula for a particular extinction of the exciting star. There is a very large spread in both scattered fluxes and extinctions for any distribution of dust. Consequently, an observed stellar extinction and scattered flux can be fitted by a wide range of albedos. With hierarchical geometry it is not completely safe to determine even relative optical constants from multiwavelength observations of the same reflection nebula. The geometry effectively changes with wavelength as the opacity of the clumps varies. Limits on the implications of observing the same object in various wavelengths are discussed briefly. Henry (2002) uses a recipe to determine the scattered flux from a star with a given extinction. It is claimed to be independent of the geometry. It provides considerably more scattering than our models, probably leading to an underestimate of the grain albedos from the UV Diffuse Galactic Light.Comment: 27 pages, including 7 figures. Accepted by Ap

Fractal dimension of interstellar clouds: opacity and noise effects

There exists observational evidence that the interstellar medium has a fractal structure in a wide range of spatial scales. The measurement of the fractal dimension (Df) of interstellar clouds is a simple way to characterize this fractal structure, but several factors, both intrinsic to the clouds and to the observations, may contribute to affect the values obtained. In this work we study the effects that opacity and noise have on the determination of Df. We focus on two different fractal dimension estimators: the perimeter-area based dimension (Dper) and the mass-size dimension (Dm). We first use simulated fractal clouds to show that opacity does not affect the estimation of Dper. However, Dm tends to increase as opacity increases and this estimator fails when applied to optically thick regions. In addition, very noisy maps can seriously affect the estimation of both Dper and Dm, decreasing the final estimation of Df. We apply these methods to emission maps of Ophiuchus, Perseus and Orion molecular clouds in different molecular lines and we obtain that the fractal dimension is always in the range 2.6 < Df < 2.8 for these regions. These results support the idea of a relatively high (> 2.3) average fractal dimension for the interstellar medium, as traced by different chemical species.Comment: 17 pages including 6 figures and 1 table. Accepted for publication in Ap

On the use of fractional Brownian motion simulations to determine the 3D statistical properties of interstellar gas

Based on fractional Brownian motion (fBm) simulations of 3D gas density and velocity fields, we present a study of the statistical properties of spectro-imagery observations (channel maps, integrated emission, and line centroid velocity) in the case of an optically thin medium at various temperatures. The power spectral index gamma_W of the integrated emission is identified with that of the 3D density field (gamma_n) provided the medium's depth is at least of the order of the largest transverse scale in the image, and the power spectrum of the centroid velocity map is found to have the same index gamma_C as that of the velocity field (gamma_v). Further tests with non-fBm density and velocity fields show that this last result holds, and is not modified either by the effects of density-velocity correlations. A comparison is made with the theoretical predictions of Lazarian & Pogosyan (2000).Comment: 28 pages, 14 figures, accepted for publication in ApJ. For preprint with higher-resolution figures, see http://www.cita.utoronto.ca/~mamd/miville_fbm2003.pd

The initial stellar mass function from random sampling in hierarchical clouds II: statistical fluctuations and a mass dependence for starbirth positions and times

Observed variations in the slope of the initial stellar mass function are shown to be consistent with a model in which the protostellar gas is randomly sampled from hierarchical clouds at a rate proportional to the square root of the local density. RMS variations in the IMF slope around the Salpeter value are +/- 0.4 when only 100 stars are observed, and +/- 0.1 when 1000 stars are observed. The hierarchical-sampling model also reproduces the tendency for massive stars to form closer to the center of a cloud, at a time somewhat later than the formation time of the lower mass stars. The assumed density dependence for the star formation rate is shown to be appropriate for turbulence compression, magnetic diffusion, gravitational collapse, and clump or wavepacket coalescence. The low mass flattening in the IMF comes from the inability of gas to form stars below the thermal Jeans mass at typical temperatures and pressures. Consideration of heating and cooling processes indicate why the thermal Jeans mass should be nearly constant in normal environments, and why it might increase in some starburst regions. The steep IMF in the extreme field is not explained by the model, but other origins are suggested.Comment: 21 pages, 8 figures, scheduled for ApJ vol. 515, April 10, 199