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

An Assessment of the Impact of Resource Room Placement on Elementary Student Self-Esteem

An assessment, in the form of an interview, was conducted to measure the effects of resource room placement and full-time classroom integration on special education student self-esteem. Sixty students in the Wenatchee School District participated in the project during the 1990-1991 school year. The results of the project indicated that the placement of special education students in a full-time integration program does not insure a greater enhancement of their total self-concept; although it may be of benefit to certain areas in their self-esteem. The project included conclusions and recommendations

Stellar feedback sets the universal acceleration scale in galaxies

It has been established for decades that rotation curves deviate from the Newtonian gravity expectation given baryons alone below a characteristic acceleration scale g†∼10⁻⁸ cm s⁻²⁠, a scale promoted to a new fundamental constant in MOND. In recent years, theoretical and observational studies have shown that the star formation efficiency (SFE) of dense gas scales with surface density, SFE ∼ Σ/Σ_(crit) with Σ_(crit)∼⟨p˙/m∗⟩/(πG)∼1000 M_⊙ pc⁻² (where ⟨p˙/m∗⟩ is the momentum flux output by stellar feedback per unit stellar mass in a young stellar population). We argue that the SFE, more generally, should scale with the local gravitational acceleration, i.e. that SFE ∼g_(tot)/g_(crit) ≡ (GM_(tot)/R²)/⟨p˙/m∗⟩⁠, where M_(tot) is the total gravitating mass and g_(crit) = ⟨p˙/m∗⟩ = πGΣ_(crit) ≈ 10⁻⁸ cm s⁻² ≈ g†. Hence, the observed g† may correspond to the characteristic acceleration scale above which stellar feedback cannot prevent efficient star formation, and baryons will eventually come to dominate. We further show how this may give rise to the observed acceleration scaling g_(obs) ∼ (g_(baryon)g†)^(1/2) (where g_(baryon) is the acceleration due to baryons alone) and flat rotation curves. The derived characteristic acceleration g† can be expressed in terms of fundamental constants (gravitational constant, proton mass, and Thomson cross-section): g†∼0.1Gmp_/σ_T⁠

From the Top Down and Back Up Again: Star Cluster Structure from Hierarchical Star Formation

Young massive star clusters spanning $\sim 10^4 - 10^8 M_\odot$ in mass have been observed to have similar surface brightness profiles. Recent hydrodynamical simulations of star cluster formation have also produced star clusters with this structure. We argue analytically that this type of mass distribution arises naturally in the relaxation from a hierarchically-clustered distribution of stars into a monolithic star cluster through hierarchical merging. We show that arbitrary initial profiles will tend to converge to a universal profile under hierarchical merging, owing to phase-space mixing obeying certain conservation constraints. We perform $N$-body simulations of a pairwise merger of model star clusters and find that mergers readily produce the shallow surface brightness profiles observed in young massive clusters. Finally, we simulate the relaxation of a hierarchically-clustered mass distribution constructed from an idealized fragmentation model. Assuming only power-law spatial and kinematic scaling relations, these numerical experiments are able to reproduce the surface density profiles of observed young massive star clusters. Thus we provide physical motivation for the structure of young massive clusters within the paradigm of hierarchical star formation. This has important implications for the structure of nascent globular clusters.Comment: 16 pages, 10 figure

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

When Feedback Fails: The Scaling and Saturation of Star Formation Efficiency

We present a suite of 3D multi-physics MHD simulations following star formation in isolated turbulent molecular gas disks ranging from 5 to 500 parsecs in radius. These simulations are designed to survey the range of surface densities between those typical of Milky Way GMCs (\sim 10^2 M_\odot\,pc^{-2}}) and extreme ULIRG environments (\sim 10^2 M_\odot\,pc^{-2}}) so as to map out the scaling of the cloud-scale star formation efficiency (SFE) between these two regimes. The simulations include prescriptions for supernova, stellar wind, and radiative feedback, which we find to be essential in determining both the instantaneous per-freefall ($\epsilon_{ff}$) and integrated ($\epsilon_{int}$) star formation efficiencies. In all simulations, the gas disks form stars until a critical stellar surface density has been reached and the remaining gas is blown out by stellar feedback. We find that surface density is a good predictor of $\epsilon_{int}$, as suggested by analytic force balance arguments from previous works. SFE eventually saturates to $\sim 1$ at high surface density. We also find a proportional relationship between $\epsilon_{ff}$ and $\epsilon_{int}$, implying that star formation is feedback-moderated even over very short time-scales in isolated clouds. These results have implications for star formation in galactic disks, the nature and fate of nuclear starbursts, and the formation of bound star clusters. The scaling of $\epsilon_{ff}$ with surface density is not consistent with the notion that $\epsilon_{ff}$ is always $\sim 1\%$ on the scale of GMCs, but our predictions recover the $\sim 1\%$ value for GMC parameters similar to those found in sprial galaxies, including our own.Comment: 21 pages, 7 figures. Accepted to MNRA

Can magnetized turbulence set the mass scale of stars?

Understanding the evolution of self-gravitating, isothermal, magnetized gas is crucial for star formation, as these physical processes have been postulated to set the initial mass function (IMF). We present a suite of isothermal magnetohydrodynamic (MHD) simulations using the GIZMO code that follow the formation of individual stars in giant molecular clouds (GMCs), spanning a range of Mach numbers found in observed GMCs (⁠M∼10−50⁠). As in past works, the mean and median stellar masses are sensitive to numerical resolution, because they are sensitive to low-mass stars that contribute a vanishing fraction of the overall stellar mass. The mass-weighted median stellar mass M₅₀ becomes insensitive to resolution once turbulent fragmentation is well resolved. Without imposing Larson-like scaling laws, our simulations find M₅₀∝∼M₀M⁻³α_(turb)SFE^(1/3) for GMC mass M₀, sonic Mach number M⁠, virial parameter α_(turb), and star formation efficiency SFE = M⋆/M₀. This fit agrees well with previous IMF results from the RAMSES, ORION2, and SPHNG codes. Although M₅₀ has no significant dependence on the magnetic field strength at the cloud scale, MHD is necessary to prevent a fragmentation cascade that results in non-convergent stellar masses. For initial conditions and SFE similar to star-forming GMCs in our Galaxy, we predict M₅₀ to be >20M⊙⁠, an order of magnitude larger than observed (⁠∼2M⊙⁠), together with an excess of brown dwarfs. Moreover, M₅₀ is sensitive to initial cloud properties and evolves strongly in time within a given cloud, predicting much larger IMF variations than are observationally allowed. We conclude that physics beyond MHD turbulence and gravity are necessary ingredients for the IMF

Dean Acheson and the Place of Korea in American Foreign and Security Policy, 1945-1950

The Korean War was a vital part of the career of Dean Acheson and has justly attracted a considerable number of studies. His involvement in policy to the peninsula before 1950, however, has seen little detailed analysis. This article explores Achesons view of Korea and his influence on policy to the country during his time as Under Secretary of State between August 1945 and June 1947, and as Secretary of State from January 1949. It concludes that Acheson was committed to Korean independence and the development of its political institutions and to its economic rehabilitation. The country was an important component of his Asian policy. But the territory itself, even during the War, was never a strategic priority. Before June 1950 Acheson advocated aid, but this was limited by Congressional restrictions on funding. The massive US military commitment in response to the attack was designed more to deter aggression and to resist communist expansion than to protect a strategically important territory. For most of the conflict the Americans and Acheson favored a limited war. Achesons outlook was realistic in terms of the geopolitical situation and domestic constraints