I briefly review recent observations of regions forming low mass stars. The discussion is cast in the form of seven questions that have been partially answered, or at least illuminated, by new data. These are the following: where do stars form in molecular clouds; what determines the IMF; how long do the steps of the process take; how efficient is star formation; do any theories explain the data; how are the star and disk built over time; and what chemical changes accompany star and planet formation. I close with a summary and list of open questions.

Magnetic diffusion plays a vital role in star formation. We trace its influence from interstellar cloud scales down to star-disk scales. On both scales, we find that magnetic diffusion can be significantly enhanced by the buildup of strong gradients in magnetic field structure. Large scale nonlinear flows can create compressed cloud layers within which ambipolar diffusion occurs rapidly. However, in the flux-freezing limit that may be applicable to photoionized molecular cloud envelopes, supersonic motions can persist for long times if driven by an externally generated magnetic field that corresponds to a subcritical mass-to-flux ratio. In the case of protostellar accretion, rapid magnetic diffusion (through Ohmic dissipation with additional support from ambipolar diffusion) near the protostar causes dramatic magnetic flux loss. By doing so, it also allows the formation of a centrifugal disk, thereby avoiding the magnetic braking catastrophe.

Major progress has been made over the last few years in understanding hydrodynamical processes on cosmological scales, in particular how galaxies get their baryons. There is increasing recognition that a large part of the baryons accrete smoothly onto galaxies, and that internal evolution processes play a major role in shaping galaxies – mergers are not necessarily the dominant process. However, predictions from the various assembly mechanisms are still in large disagreement with the observed properties of galaxies in the nearby Universe. Small-scale processes have a major impact on the global evolution of galaxies over a Hubble time and the usual sub-grid models account for them in a far too uncertain way. Understanding when, where and at which rate galaxies formed their stars becomes crucial to understand the formation of galaxy populations. I discuss recent improvements and current limitations in “resolved” modeling of star formation, aiming at explicitly capturing star-forming instabilities, in cosmological and galaxy-sized simulations. Such models need to develop three-dimensional turbulence in the ISM, which requires parsec-scale resolution at redshift zero.

Stars form predominantly in clusters inside dense clumps of molecular clouds that are both turbulent and magnetized. The typical size and mass of the cluster-forming clumps are ~1 pc and ~102 – 103 M⊙, respectively. Here, we discuss some recent progress on numerical simulations of clustered star formation in such parsec-scale dense clumps with emphasis on the role of magnetic fields. The simulations have shown that magnetic fields tend to slow down global gravitational collapse and thus star formation, especially in the presence of protostellar outflow feedback. Even a relatively weak magnetic field can retard star formation significantly, because the field is amplified by supersonic turbulence to an equipartition strength. However, in such a case, the distorted field component dominates the uniform one. In contrast, if the field is moderately-strong, the uniform component remains dominant. Such a difference in the magnetic structure is observed in simulated polarization maps of dust thermal emission. Recent polarization measurements show that the field lines in nearby cluster-forming clumps are spatially well-ordered, indicative of a rather strong field. In such strongly-magnetized clumps, star formation should proceed relatively slowly; it continues for at least several global free-fall times of the parent dense clump (tff ~ a few × 105 yr).

We review computational approaches to understanding the origin of the Initial Mass Function (IMF) during the formation of star clusters. We examine the role of turbulence, gravity and accretion, equations of state, and magnetic fields in producing the distribution of core masses - the Core Mass Function (CMF). Observations show that the CMF is similar in form to the IMF. We focus on feedback processes such as stellar dynamics, radiation, and outflows can reduce the accreted mass to give rise to the IMF. Numerical work suggests that filamentary accretion may play a key role in the origin of the IMF.

Radiative Transfer (RT) is considered to be one of the four Grand Challenges in Computational Astrophysics aside of Astrophysical Fluid Dynamics, N-Body Problems in Astrophysics, and Relativistic Astrophysics. The high dimensionality (7D instead of 4D for MHD) and the underlying integro-differential transport equation have forced coders to implement approximative RT methods in order to fit spectra and images or to treat RT in their HD and MHD codes.

The central role of RT in star formation (SF) is based on several facts: a) The dense dusty gas in SF regions alters the radiation substantially making SF one of the most complex applications of RT. b) Radiation transports energy within the object and is therefore an essential part of any dynamical SF model. c) RT calculations tell us which of the processes/structures are visible at what wavelength by which telescope/instrument. Hence, RT is the central tool to analyze simulation results or to explore the scientific capabilities of planned instruments. d) With inverse RT, we can obtain the 1D-3D density and temperature structure from observations, completely decoupled from any (M)HD modeling (and the approximations made within).

In this review, we summarize the main difficulties and the currently used computational techniques to calculate the RT in SF regions. Recent applications of 3D continuum RT in molecular clouds and disks around young massive stars are discussed to illustrate the capabilities and limits of current RT modeling.

The determination of prestellar core structure is often based on observations of (sub)millimeter dust continuum. However, recently the Spitzer Space Telescope provided us with IR images of many objects not only in emission but also in absorption. We developed a technique to reconstruct the density and temperature distributions of protostellar objects based on radiation transfer (RT) simulations both in mm and IR wavelengths. Best-fit model parameters are obtained with the genetic algorithm. We apply the method to two cores of Infrared Dark Clouds and show that their observations are better reproduced by a model with an embedded heating source despite the lack of 70 μm emission in one of these cores. Thus, the starless nature of massive cores can only be established with the careful case-by-case RT modeling.

Massive stars influence the surrounding universe far out of proportion to their numbers through ionizing radiation, supernova explosions, and heavy element production. Their formation requires the collapse of massive interstellar gas clouds with very high accretion rates. We discuss results from the first three-dimensional simulations of the gravitational collapse of a massive, rotating molecular cloud core that include heating by both non-ionizing and ionizing radiation. Local gravitational instabilities in the accretion flow lead to the build-up of a small cluster of stars. These lower-mass companions subsequently compete with the high-mass star for the same common gas reservoir and limit its overall mass growth. This process is called fragmentation-induced starvation, and explains why massive stars are usually found as members of high-order stellar systems. These simulations also show that the H ii regions forming around massive stars are initially trapped by the infalling gas, but soon begin to fluctuate rapidly. Over time, the same ultracompact H ii region can expand anisotropically, contract again, and take on any of the observed morphological classes. The total lifetime of H ii regions is given by the global accretion timescale, rather than their short internal sound-crossing time. This solves the so-called lifetime problem of ultracompact H ii region. We conclude that the the most significant differences between the formation of low-mass and high-mass stars are all explained as the result of rapid accretion within a dense, gravitationally unstable flow.

Recent numerical studies have focused their interest on the impact outflows have on the cloud's turbulence. The contradictory results obtained by these studies indicate that it is essential for observers to provide the required data to constrain the models. Here we discuss the impact of outflows on the environment surrounding clusters of young stellar objects, from an observer's point of view. We have conducted several studies of outflows in different active star-forming regions. In all cases it is clear that outflows have the power to sustain the observed turbulence in the gas surrounding protostellar clusters. We investigate whether there is a correlation between outflow strength and star formation efficiency, as predicted by numerical simulations, for six different regions in the Perseus molecular cloud complex. We argue that results of other recent studies that use CO line maps to study the turbulence driving length should not be used to discard outflows as major drivers of turbulence in clusters.

Firstly, we give a historical overview of attempts to incorporate magnetic fields into the Smoothed Particle Hydrodynamics method by solving the equations of Magnetohydrodynamics (MHD), leading an honest assessment of the current state-of-the-art in terms of the limitations to performing realistic calculations of the star formation process. Secondly, we discuss the results of a recent comparison we have performed on simulations of driven, supersonic turbulence with SPH and Eulerian techniques. Finally we present some new results on the relationship between the density variance and the Mach number in supersonic turbulent flows, finding σ2ln ρ = ln(1 + b22 with b = 0.33 up to Mach 20, consistent with other numerical results at lower Mach number (Lemaster & Stone 2008) but inconsistent with observational constraints on σρ and in Taurus and IC5146.

We report results from numerical simulations of star formation in the early universe that focus on the role of subsonic turbulence, and investigate whether it can induce fragmentation of the gas. We find that dense primordial gas is highly susceptible to fragmentation, even for rms turbulent velocity dispersions as low as 20% of the initial sound speed. The resulting fragments cover over two orders of magnitude in mass, ranging from ~0.1 M⊙ to ~40 M⊙. However, our results suggest that the details of the fragmentation depend on the local properties of the turbulent velocity field and hence we expect considerable variations in the resulting stellar mass spectrum in different halos.

Forming stars emit a significant amount of radiation into their natal environment. While the importance of radiation feedback from high-mass stars is widely accepted, radiation has generally been ignored in simulations of low-mass star formation. I use ORION, an adaptive mesh refinement (AMR) three-dimensional gravito-radiation-hydrodynamics code, to model low-mass star formation in a turbulent molecular cloud. I demonstrate that including radiation feedback has a profound effect on fragmentation and protostellar multiplicity. Although heating is mainly confined within the core envelope, it is sufficient to suppress disk fragmentation that would otherwise result in low-mass companions or brown dwarfs. As a consequence, turbulent fragmentation, not disk fragmentation, is likely the origin of low-mass binaries.

We present simulations of supersonic collisions between molecular clouds of mass 500 M⊙ and radius 2.24 pc. The simulations are performed with the SEREN SPH code. The code treats the energy equation and the associated transport of heating and cooling radiation. The formation of protostars is captured by introducing sink particles. Low velocity collisions form a shock-compressed layer which fragments to form stars. For high-velocity collisions, υrel ⪆ 5 km s−1, the non-linear thin shell instability strongly disrupts the shock-compressed layer, and may inhibit the formation of stars.

According to a Top500.org compilation, large computer systems have been doubling in sustained speed every 1.14 years for the last 17 years. If this rapid growth continues, we will have computers by 2020 that can execute an Exaflop (1018) per second. Storage is also improving in cost and density at an exponential rate. Several innovations that will accompany this growth are reviewed here, including shrinkage of basic circuit components on Silicon, three-dimensional integration, and Phase Change Memory. Further growth will require new technologies, most notably those surrounding the basic building block of computers, the Field Effect Transistor. Implications of these changes for the types of problems that can be solved are briefly discussed.