Size distribution of dust grains: A problem of self-similarity

Distribution functions describing the results of natural processes frequently show the shape of power laws, e.g., mass functions of stars and molecular clouds, velocity spectrum of turbulence, size distributions of asteroids, micrometeorites and also interstellar dust grains. It is an open question whether this behavior is a result simply coming about by the chosen mathematical representation of the observational data or reflects a deep-seated principle of nature. The authors suppose the latter being the case. Using a dust model consisting of silicate and graphite grains Mathis et al. (1977) showed that the interstellar extinction curve can be represented by taking a grain radii distribution of power law type n(a) varies as a(exp -p) with 3.3 less than or equal to p less than or equal to 3.6 (example 1) as a basis. A different approach to understanding power laws like that in example 1 becomes possible by the theory of self-similar processes (scale invariance). The beta model of turbulence (Frisch et al., 1978) leads in an elementary way to the concept of the self-similarity dimension D, a special case of Mandelbrot's (1977) fractal dimension. In the frame of this beta model, it is supposed that on each stage of a cascade the system decays to N clumps and that only the portion beta N remains active further on. An important feature of this model is that the active eddies become less and less space-filling. In the following, the authors assume that grain-grain collisions are such a scale-invarient process and that the remaining grains are the inactive (frozen) clumps of the cascade. In this way, a size distribution n(a) da varies as a(exp -(D+1))da (example 2) results. It seems to be highly probable that the power law character of the size distribution of interstellar dust grains is the result of a self-similarity process. We can, however, not exclude that the process leading to the interstellar grain size distribution is not fragmentation at all. It could be, e.g., diffusion-limited growth discussed by Sander (1986), who applied the theory of fractal geometry to the classification of non-equilibrium growth processes. He received D=2.4 for diffusion-limited aggregation in 3d-space

Mechanical stiffness and anisotropy measured by MRE during brain development in the minipig

The relationship between brain development and mechanical properties of brain tissue is important, but remains incompletely understood, in part due to the challenges in measuring these properties longitudinally over time. In addition, white matter, which is composed of aligned, myelinated, axonal fibers, may be mechanically anisotropic. Here we use data from magnetic resonance elastography (MRE) and diffusion tensor imaging (DTI) to estimate anisotropic mechanical properties in six female Yucatan minipigs at ages from 3 to 6 months. Fiber direction was estimated from the principal axis of the diffusion tensor in each voxel. Harmonic shear waves in the brain were excited by three different configurations of a jaw actuator and measured using a motion-sensitive MR imaging sequence. Anisotropic mechanical properties are estimated from displacement field and fiber direction data with a finite element- based, transversely-isotropic nonlinear inversion (TI-NLI) algorithm. TI-NLI finds spatially resolved TI material properties that minimize the error between measured and simulated displacement fields. Maps of anisotropic mechanical properties in the minipig brain were generated for each animal at all four ages. These maps show that white matter is more dissipative and anisotropic than gray matter, and reveal significant effects of brain development on brain stiffness and structural anisotropy. Changes in brain mechanical properties may be a fundamental biophysical signature of brain development

Probing the envelopes of massive young stellar objects with diffraction limited mid-infrared imaging

Massive stars form whilst they are still embedded in dense envelopes. As a result, the roles of rotation, mass loss and accretion in massive star formation are not well understood. This study evaluates the source of the Q-band, lambda=19.5 microns, emission of massive young stellar objects (MYSOs). This allows us to determine the relative importance of rotation and outflow activity in shaping the circumstellar environments of MYSOs on 1000 AU scales. We obtained diffraction limited mid-infrared images of a sample of 20 MYSOs using the VLT/VISIR and Subaru/COMICS instruments. For these 8 m class telescopes and the sample selected, the diffraction limit, ~0.6", corresponds to approximately 1000 AU. We compare the images and the spectral energy distributions (SEDs) observed to a 2D, axis-symmetric dust radiative transfer model that reproduces VLTI/MIDI observations of the MYSO W33A. We vary the inclination, mass infall rate, and outflow opening angle to simultaneously recreate the behaviour of the sample of MYSOs in the spatial and spectral domains. The mid-IR emission of 70 percent of the MYSOs is spatially resolved. In the majority of cases, the spatial extent of their emission and their SEDs can be reproduced by the W33A model featuring an in-falling, rotating dusty envelope with outflow cavities. There is independent evidence that most of the sources which are not fit by the model are associated with ultracompact HII regions and are thus more evolved. We find that, in general, the diverse 20 micron morphology of MYSOs can be attributed to warm dust in the walls of outflow cavities seen at different inclinations. This implies that the warm dust in the outflow cavity walls dominates the Q-band emission of MYSOs. In turn, this emphasises that outflows are an ubiquitous feature of massive star formation.Comment: Accepted for publication in A&A. The images in this version have been compressed. A high resolution version is available on reques

The origin of mid-infrared emission in massive young stellar objects: multi-baseline VLTI observations of W33A

The circumstellar structure on 100 AU scales of the massive young stellar object W33A is probed using the VLTI and the MIDI instrument. N-band visibilities on 4 baselines are presented which are inconsistent with a spherically symmetric geometry. The visibility spectra and SED are simultaneously compared to 2D axi-symmetric dust radiative transfer models with a geometry including a rotationally flattened envelope and outflow cavities. We assume an O7.5 ZAMS star as the central source, consistent with the observed bolometric luminosity. The observations are also compared to models with and without (dusty and gaseous) accretion disks. A satisfactory model is constructed which reproduces the visibility spectra for each (u,v) point. It fits the silicate absorption, the mid-IR slope, the far-infrared peak, and the (sub)mm of the SED. It produces a 350 micron morphology consistent with observations. The 10 micron emission on 100 AU scales is dominated by the irradiated walls of the cavity sculpted by the outflow. The visibilities rule out the presence of dust disks with total (gas and dust) masses more than 0.01 Msun. However, optically thick accretion disks, interior to the dust sublimation radius, are allowed to accrete at rates equalling the envelope's mass infall rate (up to 10^(-3) Msun/yr) without substantially affecting the visibilities due to the extinction by the extremely massive envelope of W33A.Comment: Accepted for publication in A&

The Physical Conditions for Massive Star Formation: Dust Continuum Maps and Modeling

Fifty-one dense cores associated with water masers were mapped at 350 micron. These cores are very luminous, 10^3 < Lbol/Lsun < 10^6, indicative of the formation of massive stars. Dust continuum contour maps and photometry are presented for these sources. The spectral energy distributions and normalized radial profiles of dust continuum emission were modeled for 31 sources using a one-dimensional dust radiative transfer code, assuming a power law density distribution in the envelope, n = n_f (r/r_f)^{-p}. The best fit density power law exponent, p, ranged from 0.75 to 2.5 with = 1.8 +/- 0.4. The mean value of p is comparable to that found in regions forming only low mass stars. The mean p is incompatible with a logatropic sphere (p = 1), but other star formation models cannot be ruled out. Different mass estimates are compared and mean masses of gas and dust are reported within a half-power radius determined from the dust emission and within a radius where the total density exceeds 10^4 cm^3. Evolutionary indicators commonly used for low mass star formation may have some utility for regions forming massive stars. For comparison with extragalactic star formation studies, the luminosity to dust mass ratio is calculated for these sources with a method most parallel to that used in studies of distant galaxies and is found to be similar to that seen in high redshift starburst galaxies.Comment: 45 pages, 20 figures, accepted to ApJ Supplemen

Resolved 24.5 micron emission from massive young stellar objects

Massive young stellar objects (MYSO) are surrounded by massive dusty envelopes. Our aim is to establish their density structure on scales of ~1000 AU, i.e. a factor 10 increase in angular resolution compared to similar studies performed in the (sub)mm. We have obtained diffraction-limited (0.6") 24.5 micron images of 14 well-known massive star formation regions with Subaru/COMICS. The images reveal the presence of discrete MYSO sources which are resolved on arcsecond scales. For many sources, radiative transfer models are capable of satisfactorily reproducing the observations. They are described by density powerlaw distributions (n(r) ~ r^(-p)) with p = 1.0 +/-0.25. Such distributions are shallower than those found on larger scales probed with single-dish (sub)mm studies. Other sources have density laws that are shallower/steeper than p = 1.0 and there is evidence that these MYSOs are viewed near edge-on or near face-on, respectively. The images also reveal a diffuse component tracing somewhat larger scale structures, particularly visible in the regions S140, AFGL 2136, IRAS 20126+4104, Mon R2, and Cep A. We thus find a flattening of the MYSO envelope density law going from ~10 000 AU down to scales of ~1000 AU. We propose that this may be evidence of rotational support of the envelope (abridged).Comment: 21 pages, accepted for A&