Star Formation in a Turbulent Framework: From Giant Molecular Clouds to Protostars

Turbulence is thought to be a primary driving force behind the early stages of star formation. In this framework large, self gravitating, turbulent clouds fragment into smaller clouds which in turn fragment into even smaller ones. At the end of this cascade we find the clouds which collapse into protostars. Following this process is extremely challenging numerically due to the large dynamical range so in this paper we propose a semi analytic framework which is able to follow star formation from the largest, giant molecular cloud (GMC) scale, to the final protostellar size scale. Due to the simplicity of the framework it is ideal for theoretical experimentation to explore the principal processes behind different aspects of star formation, at the cost of strong assumptions. The basic version of the model discussed in this paper only contains turbulence, gravity and crude assumptions about feedback, nevertheless it can reproduce the observed core mass function (CMF) and provide the protostellar system mass function (PSMF), which shows a striking resemblance to the observed IMF. Furthermore we find that to produce a universal IMF protostellar feedback must be taken into account otherwise the PSMF peak shows a strong dependence on the background temperature.Comment: 13 pages, 13 figure

Protostellar Feedback in Turbulent Fragmentation: Consequences for Stellar Clustering and Multiplicity

Stars are strongly clustered on both large (~pc) and small (~binary) scales, but there are few analytic or even semi-analytic theories for the correlation function and multiplicity of stars. In this paper we present such a theory, based on our recently-developed semi-analytic framework called MISFIT, which models gravito-turbulent fragmentation, including the suppression of fragmentation by protostellar radiation feedback. We compare the results including feedback to a control model in which it is omitted. We show that both classes of models robustly reproduce the stellar correlation function at >0.01 pc scales, which is well approximated by a power-law that follows generally from scale-free physics (turbulence plus gravity) on large scales. On smaller scales protostellar disk fragmentation becomes dominant over common core fragmentation, leading to a steepening of the correlation function. Multiplicity is more sensitive to feedback: we found that a model with the protostellar heating reproduces the observed multiplicity fractions and mass ratio distributions for both Solar and sub-Solar mass stars (in particular the brown dwarf desert), while a model without feedback fails to do so. The model with feedback also produces an at-formation period distribution consistent with the one inferred from observations. However, it is unable to produce short-range binaries below the length scale of protostellar disks. We suggest that such close binaries are produced primarily by disk fragmentation and further decrease their separation through orbital decay.Comment: 17 pages, 15 figures, submitted to MNRA

Universal Scaling Relations in Scale-Free Structure Formation

A large number of astronomical phenomena exhibit remarkably similar scaling relations. The most well-known of these is the mass distribution $\mathrm{d} N/\mathrm{d} M\propto M^{-2}$ which (to first order) describes stars, protostellar cores, clumps, giant molecular clouds, star clusters and even dark matter halos. In this paper we propose that this ubiquity is not a coincidence and that it is the generic result of scale-free structure formation where the different scales are uncorrelated. We show that all such systems produce a mass function proportional to $M^{-2}$ and a column density distribution with a power law tail of $\mathrm{d} A/\mathrm{d} \ln\Sigma\propto\Sigma^{-1}$. In the case where structure formation is controlled by gravity the two-point correlation becomes $\xi_{2D}\propto R^{-1}$. Furthermore, structures formed by such processes (e.g. young star clusters, DM halos) tend to a $\rho\propto R^{-3}$ density profile. We compare these predictions with observations, analytical fragmentation cascade models, semi-analytical models of gravito-turbulent fragmentation and detailed "full physics" hydrodynamical simulations. We find that these power-laws are good first order descriptions in all cases.Comment: 12 pages, 6 figures, 2 tables, submitted to MNRA

A FOLLOW-UP STUDY OF FIFTY-TWO RICHMOND PUBLIC SCHOOL PUPILS GIVEN PSYCHIATRIC STAFFING DURING THE 1966-1967 SCHOOL YEAR

This research study is a descriptive study of the effectiveness of the psychiatric staffing as determined by a follow-up study of fifty-two Richmond Public School Pupils given such staffing during the l966-67 school year. The review of pertinent literature reveals what others have contributed to the knowledge of the nature and function of the school helping team. The teamwork approach, which involves the efforts of several professions and disciplines working closely together, is seen as the best present method to meet the complex, overlapping needs which have been found to affect students\u27 learning. As a means of establishing guidelines and limits for this study, five areas of concern were defined. The questions to be answered by this study were: 1. What are the socio-economic backgrounds represented by the sample? 2. Were the recommendations made by the school psychiatrist implemented? 3. Is the overall psychiatric staffing effective according to the improvement in pupils presenting problems and the extent to which the recommendations were carried out? 4. To what extent do the available records contain sufficient information for a follow-up study? 5. What are the attitudes of the key persons responsible for the psychiatric staffing toward the effective operation of these staffings? The Pupil Personnel Services gave its approval to conduct this study. The sample numbered fifty-two. The agency requested and it was agreed that no pupil, school, or agency be contacted and that information be obtained only from the files and employees of Pupil Personnel Services. An interview schedule was constructed to elicit information to determine the extent to which the recommendations made during the psychiatric staffing were initiated and carried out. This schedule was applied to the pupil records. Open ended questions were used in interview schedules to gather pertinent information from three key persons responsible for the effective operation of the psychiatric staffing. The fifty-two pupil cases revealed the pupils to be largely from low income families, mostly males with acting-out behavior problems, and with no significant concentration from any one school. A larger percentage of the recommendations that were initiated involved the use of school resources rather than community resources. In nearly half of the pupil cases the recommendations were completely carried out, with a remaining few being carried out to a lesser extent. The findings suggested that, if the recommendations were carried out, the pupil would show behavior improvement. To a large extent the statements made by the key persons generally reflected that methods of record keeping be improved within the Department of Visiting Teachers; that there be an increase in the number and quality of the visiting teachers, especially for elementary and Junior high school placements; that parents of the pupils given psychiatric staffings become involved in the staffings and be included in the treatment process themselves; and that the visiting teacher exercise more responsibility for follow-up on the pupils given psychiatric staffing

An acute bout of cycling does not induce compensatory responses in pre-menopausal women not using hormonal contraceptives

There is a clear need to improve understanding of the effects of physical activity and exercise on appetite control. Therefore, the acute and short-term effects (three days) of a single bout of cycling on energy intake and energy expenditure were examined in women not using hormonal contraceptives. Sixteen active (n = 8) and inactive (n = 8) healthy pre-menopausal women completed a randomised crossover design study with two conditions (exercise and control). The exercise day involved cycling for 1 h (50% of maximum oxygen uptake) and resting for 2 h, whilst the control day comprised 3 h of rest. On each experimental day participants arrived at the laboratory fasted, consumed a standardised breakfast and an ad libitum pasta lunch. Food diaries and combined heart rate-accelerometer monitors were used to assess free-living food intake and energy expenditure, respectively, over the subsequent three days. There were no main effects or condition (exercise vs control) by group (active vs inactive) interaction for absolute energy intake (P > 0.05) at the ad libitum laboratory lunch meal, but there was a condition effect for relative energy intake (P = 0.004, ηp2 = 0.46) that was lower in the exercise condition (1417 ± 926 kJ vs. 2120 ± 923 kJ). Furthermore, post-breakfast satiety was higher in the active than in the inactive group (P = 0.005, ηp2 = 0.44). There were no main effects or interactions (P > 0.05) for mean daily energy intake, but both active and inactive groups consumed less energy from protein (14 ± 3% vs. 16 ± 4%, P = 0.016, ηp2 = 0.37) and more from carbohydrate (53 ± 5% vs. 49 ± 7%, P = 0.031, ηp2 = 0.31) following the exercise condition. This study suggests that an acute bout of cycling does not induce compensatory responses in active and inactive women not using hormonal contraceptives, while the stronger satiety response to the standardised breakfast meal in active individuals adds to the growing literature that physical activity helps improve the sensitivity of short-term appetite control

Isothermal Fragmentation: Is there a low-mass cut-off?

The evolution of self-gravitating clouds of isothermal gas forms the basis of many star formation theories. Therefore it is important to know under what conditions such a cloud will undergo homologous collapse into a single, massive object, or will fragment into a spectrum of smaller ones. And if it fragments, do initial conditions (e.g. Jeans mass, sonic mass) influence the mass function of the fragments, as predicted by many theories of star formation? In this paper we show that the relevant parameter separating homologous collapse from fragmentation is not the Mach number of the initial turbulence (as suspected by many), but the infall Mach number $\mathcal{M}_{\rm infall}\sim\sqrt{G M/(R c_s^2)}$, equivalent to the number of Jeans masses in the initial cloud $N_J$. We also show that fragmenting clouds produce a power-law mass function with slopes close to the expected -2 (i.e. equal mass in all logarithmic mass intervals). However, the low-mass cut-off of this mass function is entirely numerical; the initial properties of the cloud have no effect on it. In other words, if $\mathcal{M}_{\rm infall}\gg 1$, fragmentation proceeds without limit to masses much smaller than the initial Jeans mass.Comment: 10 pages, 9 figure

The necessity of feedback physics in setting the peak of the initial mass function

A popular theory of star formation is gravito-turbulent fragmentation, in which self-gravitating structures are created by turbulence-driven density fluctuations. Simple theories of isothermal fragmentation successfully reproduce the core mass function (CMF) which has a very similar shape to the initialmass function (IMF) of stars. However, numerical simulations of isothermal turbulent fragmentation thus far have not succeeded in identifying a fragment mass scale that is independent of the simulation resolution. Moreover, the fluid equations for magnetized, selfgravitating, isothermal turbulence are scale-free, and do not predict any characteristic mass. In this paper we show that, although an isothermal self-gravitating flow does produce a CMF with a mass scale imposed by the initial conditions, this scale changes as the parent cloud evolves. In addition, the cores that form undergo further fragmentation and after sufficient time forget about their initial conditions, yielding a scale-free pure power-law distribution dN/dM ∝ M−2 for the stellar IMF. We show that this problem can be alleviated by introducing additional physics that provides a termination scale for the cascade. Our candidate for such physics is a simple model for stellar radiation feedback. Radiative heating, powered by accretion on to forming stars, arrests the fragmentation cascade and imposes a characteristic mass scale that is nearly independent of the time-evolution or initial conditions in the star-forming cloud, and that agrees well with the peak of the observed IMF. In contrast, models that introduce a stiff equation of state for denser clouds but that do not explicitly include the effects of feedback do not yield an invariant IMF

Mechanical Properties of Kentucky Oil Shales as Related to Mine Design Application

To develop oil shales as an alternate energy resource, it will be necessary to develop appropriate mining techniques. In this regard, the mechanical properties of the ore must be determined. Section I of this paper presents data from a laboratory study to determine these properties. Uniaxial compression tests, longitudinal frequency tests, indirect tensile tests, and triaxial tests were performed. Section II uses data from section I to design an example underground mine. Strength properties are considered in the design of roof spans and pillars. It is concluded that underground mining of Kentucky oil shale is feasible with a possible extraction rate of 70 percent or more through an aggressive rock mechanics program and good mining practices

Protostellar feedback in turbulent fragmentation: consequences for stellar clustering and multiplicity

Stars are strongly clustered on both large (∼pc) and small (∼binary) scales, but there are few analytic or even semi-analytic theories for the correlation function and multiplicity of stars. In this paper, we present such a theory, based on our recently developed semi-analytic framework called MISFIT (Minimalistic Star Formation Including Turbulence), which models gravitoturbulent fragmentation, including the suppression of fragmentation by protostellar radiation feedback. We compare the results including feedback to a control model in which it is omitted. We show that both classes of models robustly reproduce the stellar correlation function at >0.01 pc scales, which is well approximated by a power law that follows generally from scale-free physics (turbulence plus gravity) on large scales. On smaller scales, protostellar disc fragmentation becomes dominant over common core fragmentation, leading to a steepening of the correlation function. Multiplicity is more sensitive to feedback: we found that a model with the protostellar heating reproduces the observed multiplicity fractions and mass ratio distributions for both Solar and sub-Solar mass stars (in particular, the brown dwarf desert), while a model without feedback fails to do so. The model with feedback also produces an at-formation period distribution consistent with the one inferred from observations. However, it is unable to produce short-range binaries below the length-scale of protostellar discs. We suggest that such close binaries are produced primarily by disc fragmentation and further decrease their separation through orbital decay

Operation of a superconducting nanowire quantum interference device with mesoscopic leads

A theory describing the operation of a superconducting nanowire quantum interference device (NQUID) is presented. The device consists of a pair of thin-film superconducting leads connected by a pair of topologically parallel ultra-narrow superconducting wires. It exhibits intrinsic electrical resistance, due to thermally-activated dissipative fluctuations of the superconducting order parameter. Attention is given to the dependence of this resistance on the strength of an externally applied magnetic field aligned perpendicular to the leads, for lead dimensions such that there is essentially complete and uniform penetration of the leads by the magnetic field. This regime, in which at least one of the lead dimensions lies between the superconducting coherence and penetration lengths, is referred to as the mesoscopic regime. The magnetic field causes a pronounced oscillation of the device resistance, with a period not dominated by the Aharonov-Bohm effect through the area enclosed by the wires and the film edges but, rather, in terms of the geometry of the leads, in contrast to the well-known Little-Parks resistance of thin-walled superconducting cylinders. A theory, encompassing this phenomenology, is developed through extensions, to the setting of parallel superconducting wires, of the Ivanchenko-Zil'berman-Ambegaokar-Halperin theory for the case of short wires and the Langer-Ambegaokar-McCumber-Halperin theory for the case of longer wires. It is demonstrated that the NQUID acts as a probe of spatial variations in the superconducting order parameter.Comment: 20 pages, 18 figure