A "Kane's Dynamics" Model for the Active Rack Isolation System

In the late 1980s, microgravity researchers began to voice their concern that umbilical-transmitted energy could significantly degrade the acceleration environment of microgravity space science experiments onboard manned spacecraft. Since umbilicals are necessary for many experiments, control designers began to seek ways to compensate for these "indirect" disturbances. Hampton, et al., used the Kane s method to develop a model of the active rack isolation system (ARIS) that includes (1) actuator control forces, (2) direct disturbance forces, and (3) indirect, actuator-transmitted disturbances. Their model does not, however, include the indirect, umbilical-transmitted disturbances. Since the umbilical stiffnesses are not negligible, these indirect disturbances must be included in the model. Until the umbilicals have been appropriately included, the model will be incomplete. This Technical Memorandum presents a nonlinear model of ARIS with umbilicals included. Model verification was achieved by utilizing two commercial-off-the-shelf software tools. Various forces and moments were applied to the model to yield simulated responses of the system. Plots of the simulation results show how various critical points on an ARIS-outfitted international standard payload rack behave under the application of direct disturbances, indirect disturbances, and control forces. Simulations also show system response to a variety of initial conditions

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

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

Multifractal Scaling, Geometrical Diversity, and Hierarchical Structure in the Cool Interstellar Medium

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 and justified in an appendix, 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: strong point-like concentrations, line- like filaments or fronts, and 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. (Abstract truncated)Comment: 27 pages, (LaTeX), 13 figures, 1 table, submitted to Astrophysical Journa

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

Structure Function Scaling in the Taurus and Perseus Molecular Cloud Complexes

We compute the structure function scaling of the integrated intensity images of two J=1-0 13CO maps of Taurus and Perseus. The scaling exponents of the structure functions follow the velocity scaling of supersonic turbulence, suggesting that turbulence plays an important role in the fragmentation of cold interstellar clouds. The data also allows to verify the validity of the two basic assumptions of the hierarchical symmetry model, originally proposed for the derivation of the velocity structure function scaling. This shows that the same hierarchical symmetry holds for the projected density field of cold interstellar clouds.Comment: submitted to Ap

The spatial distribution of star and cluster formation in M51

Aims. We study the connection between spatially resolved star formation and young star clusters across the disc of M51. Methods. We combine star cluster data based on B, V, and I-band Hubble Space Telescope ACS imaging, together with new WFPC2 U-band photometry to derive ages, masses, and extinctions of 1580 resolved star clusters using SSP models. This data is combined with data on the spatially resolved star formation rates and gas surface densities, as well as Halpha and 20cm radio-continuum (RC) emission, which allows us to study the spatial correlations between star formation and star clusters. Two-point autocorrelation functions are used to study the clustering of star clusters as a function of spatial scale and age. Results. We find that the clustering of star clusters among themselves decreases both with spatial scale and age, consistent with hierarchical star formation. The slope of the autocorrelation functions are consistent with projected fractal dimensions in the range of 1.2-1.6, which is similar to other galaxies, therefore suggesting that the fractal dimension of hierarchical star formation is universal. Both star and cluster formation peak at a galactocentric radius of 2.5 and 5 kpc, which we tentatively attribute to the presence of the 4:1 resonance and the co-rotation radius. The positions of the youngest (<10 Myr) star clusters show the strongest correlation with the spiral arms, Halpha, and the RC emission, and these correlations decrease with age. The azimuthal distribution of clusters in terms of kinematic age away from the spiral arms indicates that the majority of the clusters formed 5-20 Myr before their parental gas cloud reached the centre of the spiral arm.Comment: 14 pages, 21 figures, accepted for publication in A&