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

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

Evaluation of semiconductor devices for Electric and Hybrid Vehicle (EHV) ac-drive applications, volume 1

The results of evaluation of power semiconductor devices for electric hybrid vehicle ac drive applications are summarized. Three types of power devices are evaluated in the effort: high power bipolar or Darlington transistors, power MOSFETs, and asymmetric silicon control rectifiers (ASCR). The Bipolar transistors, including discrete device and Darlington devices, range from 100 A to 400 A and from 400 V to 900 V. These devices are currently used as key switching elements inverters for ac motor drive applications. Power MOSFETs, on the other hand, are much smaller in current rating. For the 400 V device, the current rating is limited to 25 A. For the main drive of an electric vehicle, device paralleling is normally needed to achieve practical power level. For other electric vehicle (EV) related applications such as battery charger circuit, however, MOSFET is advantageous to other devices because of drive circuit simplicity and high frequency capability. Asymmetrical SCR is basically a SCR device and needs commutation circuit for turn off. However, the device poses several advantages, i.e., low conduction drop and low cost

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

Numerical Problems in Coupling Photon Momentum (Radiation Pressure) to Gas

Radiation pressure (RP; or photon momentum absorbed by gas) is important in a tremendous range of astrophysical systems. But we show the usual method for assigning absorbed photon momentum to gas in numerical radiation-hydrodynamics simulations (integrating over cell volumes or evaluating at cell centers) can severely under-estimate the RP force in the immediate vicinity around un-resolved (point/discrete) sources (and subsequently under-estimate its effects on bulk gas properties), unless photon mean-free-paths are highly-resolved in the fluid grid. The existence of this error is independent of the numerical radiation transfer (RT) method (even in exact ray-tracing/Monte-Carlo methods), because it depends on how the RT solution is interpolated back onto fluid elements. Brute-force convergence (resolving mean-free paths) is impossible in many cases (especially where UV/ionizing photons are involved). Instead, we show a 'face-integrated' method -- integrating and applying the momentum fluxes at interfaces between fluid elements -- better approximates the correct solution at all resolution levels. The 'fix' is simple and we provide example implementations for ray-tracing, Monte-Carlo, and moments RT methods in both grid and mesh-free fluid schemes. We consider an example of star formation in a molecular cloud with UV/ionizing RP. At state-of-the-art resolution, cell-integrated methods under-estimate the net effects of RP by an order of magnitude, leading (incorrectly) to the conclusion that RP is unimportant, while face-integrated methods predict strong self-regulation of star formation and cloud destruction via RP.Comment: 9 pages, 4 figures. Updated to match accepted MNRAS versio

Galaxy disks do not need to survive in the L-CDM paradigm: the galaxy merger rate out to z~1.5 from morpho-kinematic data

About two-thirds of present-day, large galaxies are spirals such as the Milky Way or Andromeda, but the way their thin rotating disks formed remains uncertain. Observations have revealed that half of their progenitors, six billion years ago, had peculiar morphologies and/or kinematics, which exclude them from the Hubble sequence. Major mergers, i.e., fusions between galaxies of similar mass, are found to be the likeliest driver for such strong peculiarities. However, thin disks are fragile and easily destroyed by such violent collisions, which creates a critical tension between the observed fraction of thin disks and their survival within the L-CDM paradigm. Here we show that the observed high occurrence of mergers amongst their progenitors is only apparent and is resolved when using morpho-kinematic observations which are sensitive to all the phases of the merging process. This provides an original way of narrowing down observational estimates of the galaxy merger rate and leads to a perfect match with predictions by state-of-the-art L-CDM semi-empirical models with no particular fine-tuning needed. These results imply that half of local thin disks do not survive but are actually rebuilt after a gas-rich major merger occurring in the past nine billion years, i.e., two-thirds of the lifetime of the Universe. This emphasizes the need to study how thin disks can form in halos with a more active merger history than previously considered, and to investigate what is the origin of the gas reservoir from which local disks would reform.Comment: 19 pages, 7 figures, 2 tables. Accepted in ApJ. V2 to match proof corrections and added reference

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