How large, 100-AU scale, rotationally supported disks form around protostars remains unsettled, both observationally and theoretically. In this contribution, we discuss the theoretical difficulties with disk formation in the presence of a dynamically significant magnetic field and their possible resolutions. These difficulties are caused by the concentration of magnetic field lines close to the forming star by protostellar collapse, and the strong magnetic braking associated with the concentrated field. Possible resolutions include magnetic field-rotation axis misalignment, non-ideal MHD effects, and turbulence. The field-rotation misalignment has been shown to promote disk formation, especially when the field is relatively weak and the misalignment angle is relatively large. Non-ideal MHD effects can enable the formation of small disks at early times. How such disks grow at later times remains to be fully quantified. Turbulence has been found to enable disk formation in a number of simulations, but the exact reason for its beneficial effect is debated.

We report our systematic survey observations of protostellar sources with the SubMillimeter Array (SMA) and Atacama Large Millimeter/submillimeter Array (ALMA). The purpose of our survey is to investigate formation mechanism of protoplanetary disks, precursors of planetary systems, out of ~1000 AU-scale protostellar envelopes surrounding the protostars. We found that in the early protostars (B335, NGC1333 IRAS 4B), the envelopes do not show significant rotating motions but infalling motions toward the central protostars. In more evolved protostars (L1527 IRS, L1448-mm, L1551 IRS 5), the envelopes are infalling and rotating with the conserved specific angular momenta (that is, vrot ∝ r−1). In most evolved sources (L1551 NE, TMC-1A, L1489 IRS) large-scale (≳100 AU) disks in Keplerian rotation or protoplanetary disks are evident. These results demonstrate a systematic evolutionary trend of envelope gas motions toward the disk formation.

Recent progress is reviewed in describing the physical processes of star cluster formation, from the viewpoint of theoretical models and numerical simulations. In many studies, supersonic turbulent flows structure the gas into a network of clumps, filaments, and cores. Self-gravity drives star formation, moderated by turbulence, magnetic fields, and stellar feedback. Recent models and simulations describe the core mass function, the protostar mass function, and the star-formation rate. Several simulations indicate similar protostar birthrates, a mass advantage for firstborn protostars, and accretion rates that are superthermal and nearly constant. Recently observed core-filament systems with sonic line widths and parsec lengths present challenges for turbulent models.

The Antennae galaxies are a spectacular example of a burst of star formation triggered by the encounter of two galaxies, being an ideal source to understand how the dynamics of galaxy mergers drives star formation. We present archive ALMA CO(3−2) and VLT near-IR H2 spectro-imaging observations, and new ALMA 13CO(2−1) and dust continuum observations, at ~50 pc resolution. Combining tracers of density and velocity structure of the gas and its energetics, we demonstrate that star formation involves a complex interplay of merger-driven gas dynamics and turbulence, and the dissipation of the gas kinetic energy. We focus on a compact, bright H2 source, associated with cold molecular gas and dust continuum emission, located where the velocity gradient in the interaction region is observed to be the largest. The characteristics of this source suggest that we are witnessing the formation, initiated by turbulent dissipation, of a cloud massive enough (~4×106M⊙) to form a super star cluster within 1 Myr.

The availability of high spatial resolution molecular gas observations from ALMA, and similar resolution observations in the radio continuum using the VLA, is providing the opportunity to make comparisons with specific features seen in optical observations more directly than in the past. Using our ALMA observations of the Antennae galaxies as a springboard, we have compared the locations of small-scale CO (3−2) features with a variety of multi-wavelength observations, in particular optical and near-infrared imaging using both broad (UBVI) and narrow-band data (Hα and Paβ) taken with the HST, and radio (3.6 cm) continuum observations taken with the VLA. This comparison leads to the development of an evolutionary classification system which provides a framework for studying the sequence of star cluster formation and evolution, from diffuse Giant Molecular Clouds (GMCs), to proto, embedded, emerging, young, and intermediate/old star clusters. Using this evolutionary framework, we estimate the maximum age range of clusters formed in a single GMC is approximately 10 Myr. This suggests that the molecular gas is removed over this timescale, resulting in the cessation of star formation and the destruction of the GMC within a radius of about 200 pc.

The Herschel/HOBYS key program allows to statistically study the formation of 10−20 M⊙ stars. The IRAM/W43-HERO large program is itself dedicated to the much more extreme W43 molecular complex, which forms stars up to 50 M⊙. Both reveal high-density cloud filaments of several pc3, which are forming clusters of OB-type stars. Given their activity, these so-called mini-starburst cloud ridges could be seen as “miniature and instant models” of starburst galaxies. Both surveys also strongly suggest that high-mass prestellar cores do not exist, in agreement with the dynamical formation of cloud ridges. The HOBYS and W43 surveys are necessary steps towards Galaxy-wide studies of high-mass star formation.

I review theoretical models of star formation and how they apply across the stellar mass spectrum. Several distinct theories are under active study for massive star formation, especially Turbulent Core Accretion, Competitive Accretion and Protostellar Mergers, leading to distinct observational predictions. These include the types of initial conditions, the structure of infall envelopes, disks and outflows, and the relation of massive star formation to star cluster formation. Even for Core Accretion models, there are several major uncertainties related to the timescale of collapse, the relative importance of different processes for preventing fragmentation in massive cores, and the nature of disks and outflows. I end by discussing some recent observational results that are helping to improve our understanding of these processes.

The Central Molecular Zone (CMZ; inner ~100 pc) hosts some of the most dense and massive molecular clouds of the Milky Way. These clouds might serve as local templates for dense clouds seen in nearby starburst galaxies or in the early universe. The clouds have a striking feature: they form stars at a very slow pace, considering their mass and high average density. Here we use interferometer data from ALMA and the SMA to show that this slow star formation is a consequence of the cloud density structure: CMZ clouds have a very flat density structure. They might, for example, exceed the average density of the Orion A molecular cloud by an order of magnitude on spatial scales ~5 pc, but CMZ “cores” of ~0.1 pc radius have masses and densities lower than what is found in the Orion KL region. This absence of highest–density gas probably explains the suppression of star formation. The clouds are relatively turbulent, and ALMA observations of H2CO and SiO indicate that the turbulence is induced by high–velocity shocks. We speculate that these shocks might prevent the formation of high–mass cores. It has been argued that the state of CMZ clouds depends on their position along the orbit around Sgr A*. Our incomplete data indicate no evolution in the density structure, and only a modest evolution in star formation activity per unit mass.

On scales of ≳ several hundred parsec, there are relatively well defined observed relations between the star formation rate surface density of a galaxy and its gas content. I present a short summary of the so-called ‘star formation laws’ and discuss the most established models to explain their origin. Nevertheless, none of the models can explain the offset of these relations, which requires a low star formation efficiency within the total and/or molecular gas. Stellar feedback is proposed to limit the star formation efficiency locally. I discuss the available feedback mechanisms and show recent simulation results on the evolution of the multi-phase interstellar medium under the influence of gravity, cooling, feedback-driven outflows and heating.

A next main step in understanding star formation is to link the sharp but narrow view of Galactic molecular cloud studies to the wider context accessed by less detail by extragalactic work. In this proceeding, we discuss how new technology and large programs at millimeter wavelengths are improving our ability to access physical conditions in the interstellar medium (ISM) of other galaxies. We highlight results from the multi-line survey of Usero et al. (2015), which measured density sensitive lines across nearby galaxy disks, and two new mapping studies of M51: the high resolution Plateau de Bure Arcsecond Whirlpool Survey (PAWS) and the EMPIRE multi-line mapping survey. These results argue for a context-dependent role for gas density in star formation; that is, gas at a particular density does not appear to form stars in a universal way. They also demonstrate the influence of cloud-scale conditions, especially surface density and the velocity dispersion, in setting the small-scale density distribution and highlight gravitational boundedness as a main driver of the ability of gas to form stars. Beyond these specific results, we argue that ability to gauge detailed physical conditions in the star-forming gas of other galaxies promises major advances that will help unify the fields of Galactic and extragalactic star formation in the next few years.

We explore the relationship between the total gas surface density and star formation rate surface density, a.k.a., the “Kennicutt-Schmidt relation,” in a Galactic context. Specifically, we probe the origins of thresholds in the behaviour of the K-S relation at 10 M⊙ pc−2 and 100-200 M⊙ pc−2 using images from the Herschel Hi-GAL and Gould Belt surveys. In both cases, pervasive filamentary structures are seen, possibly due to turbulent motions. The Hi-GAL image supports the view that at ~10 M⊙ pc−2 gas becomes molecular, leading to the formation of clouds that harbour star formation. The GBS images suggest the 100-200 M⊙ pc−2 threshold originates from the nature of filaments being stable until a critical column density of ~160 M⊙ pc−2 is reached. Therefore, the transition between non-star-forming and star-forming gas in clouds (and galaxies) may be set universally by the dynamical properties of filaments.

Comparison of the ISM properties of a wide range of metal poor galaxies with normal metal-rich galaxies reveals striking differences. We find that the combination of the low dust abundance and the active star formation results in a very porous ISM filled with hard photons, heating the dust in dwarf galaxies to overall higher temperatures than their metal-rich counterparts. This results in photodissociation of molecular clouds to greater depths, leaving relatively large PDR envelopes and difficult-to-detect CO cores. From detailed modeling of the low-metallicity ISM, we find significant fractions of CO-dark H2 - a reservoir of molecular gas not traced by CO, but present in the [CII] and [CI]-emitting envelopes. Self-consistent analyses of the neutral and ionized gas diagnostics along with the dust SED is the necessary way forward in uncovering the multiphase structure of galaxies.

In understanding galaxy evolution, one central question is how star formation is regulated in galaxies. Changes in star formation rates are likely tied to changes in the interstellar medium, particularly the molecular gas which is the fuel for star formation. I will discuss our recent results which use data from the Herschel Space Observatory, the Atacama Large Millimeter/submillimeter Array, and other telescopes to determine the typical density, temperature, and surface density of the molecular gas in various nearby galaxies. Comparing the properties of molecular gas in starburst and other active galaxies with more quiescent spiral disks provides some clues as to how changes in the physical state of the gas, such as mean density, can lead to enhanced star formation rates.

Galaxy nuclei are a unique laboratory to study gas flows. Their high-resolution imaging in galactic nuclei are instrumental in the study of the fueling and feedback of star formation and nuclear activity in nearby galaxies. Several fueling mechanisms can now be confronted in detail with observations done with state-of-the-art interferometers. Furthermore, the study of gas flows in galactic nuclei can probe the feedback of activity on the interstellar medium of galaxies. Feedback action from star formation and AGN activity is invoked to prevent galaxies from becoming overly massive, but also to explain scaling laws like black hole (BH)-bulge mass correlations and the bimodal color distribution of galaxies. This close relationship between galaxies and their central supermassive BH can be described as co-evolution. There is mounting observational evidence for the existence of gas outflows in different populations of starbursts and active galaxies, a manifestation of the feedback of activity. We summarize the main results recently obtained from the observation of galactic inflows and outflows in a variety of active galaxies with current millimeter interferometers such as ALMA or the IRAM array.

In the central regions of active galaxies, dense molecular medium are exposed to various types of radiation and energy injections, such as UV, X-ray, cosmic ray, and shock dissipation. With the rapid progress of chemical models and implementation of new-generation mm/submm interferometry, we are now able to use molecules as powerful diagnostics of the physical and chemical processes in galaxies. Here we give a brief overview on the recent ALMA results to demonstrate how molecules can reveal underlying physical and chemical processes in galaxies. First, new detections of Galactic molecular absorption systems with elevated HCO/H13CO+ column density ratios are reported, indicating that these molecular media are irradiated by intense UV fields. Second, we discuss the spatial distributions of various types of shock tracers including HNCO, CH3OH and SiO in NGC 253 and NGC 1068. Lastly, we provide an overview of proposed diagnostic methods of nuclear energy sources using ALMA, with an emphasis on the synergy with sensitive mid-infrared spectroscopy, which will be implemented by JWST and SPICA to disentangle the complex nature of heavily obscured galaxies across the cosmic time.

AGN feedback from supermassive black holes (SMBHs) at the center of early type galaxies is commonly invoked as the explanation for the quenching of star formation in these systems. The situation is complicated by the significant amount of mass injected in the galaxy by the evolving stellar population over cosmological times. In absence of feedback, this mass would lead to unobserved galactic cooling flows, and to SMBHs two orders of magnitude more massive than observed. By using high-resolution 2D hydrodynamical simulations with radiative transport and star formation in state-of-the-art galaxy models, we show how the intermittent AGN feedback is highly structured on spatial and temporal scales, and how its effects are not only negative (shutting down the recurrent cooling episodes of the ISM), but also positive, inducing star formation in the inner regions of the host galaxy.

In the last decade, significant progress has been made to understand the evolution with redshift of star formation processes in galaxies. Its is now clear that the majority of galaxies at z<3 form a nearly linear correlation between their stellar mass and star formation rates and appear to create most of their stars in timescales of ~1 Gyr. At the highest luminosities, a significant fraction of galaxies deviate from this main-sequence, showing short duty cycles and thus producing most of their stars in a single burst of star formation within ~100 Myr, being likely driven by major merger activity. Despite the large luminosities of starbursts, main-sequence galaxies appear to dominate the star formation density of the Universe at its peak.

While progress has been impressive, a number of questions are still unanswered. In this paper, I briefly review our current observational understanding of this main-sequence vs starburst galaxy paradigm, and address how future observations will help us to have better insights into the fundamental properties of the interstellar medium of these galaxies. Finally, I show recent attempts to conduct molecular deep field observations and the motivation to perform molecular deep field spectroscopy with the Atacama Large Millimeter/submillimeter Array.

We investigate the influence of interactions on the star formation by studying a sample of almost 1500 of the nearest galaxies, all within a distance of ~45 Mpc. We define the massive star formation rate (SFR), as measured from far-IR emission, and the specific star formation rate (SSFR), which is the former quantity normalized by the stellar mass of the galaxy, and explore their distribution with morphological type and with stellar mass. We then calculate the relative enhancement of these quantities for each galaxy by normalizing them by the median SFR and SSFR values of individual control populations of similar non-interacting galaxies. We find that both SFR and SSFR are enhanced in interacting galaxies, and more so as the degree of interaction is higher. The increase is, however, moderate, reaching a maximum of a factor of 1.9 for the highest degree of interaction (mergers). The SFR and SSFR are enhanced statistically in the population, but in most individual interacting galaxies they are not enhanced at all. We discuss how those galaxies with the largest SFR and/or SSFR enhancement can be defined as starbursts. We argue that this study, based on a representative sample of nearby galaxies, should be used to place constraints on studies based on samples of galaxies at larger distances.

The cosmic star formation rate density first increases with time towards a pronounced peak 10 Gyrs ago (or z=1-2) and then slows down, dropping by more than a factor 10 since z=1. The processes at the origin of the star formation quenching are not yet well identified: either the gas is expelled by supernovae and AGN feedback, or prevented to inflow. Morphological transformation or environment effects are also invoked. Recent IRAM/NOEMA and ALMA results are reviewed about the molecular content of galaxies and its dynamics, as a function of redshift. Along the main sequence of massive star forming galaxies, the gas fraction was higher in the past (up to 80%), and galaxy disks were more unstable and more turbulent. The star formation efficiency increases with redshift, or equivalently the depletion time decreases, whatever the position of galaxies, either on the main sequence or above. Attempts have been made to determine the cosmic evolution of the H2 density, but deeper ALMA observations are needed to effectively compare with models.

Star formation processes in strongly self-gravitating cloud cores should be similar at all redshifts, forming single or multiple stars with a range of masses determined by local magneto-hydrodynamics and gravity. The formation processes for these cores, however, as well as their structures, temperatures, Mach numbers, etc., and the boundedness and mass distribution functions of the resulting stars, should depend on environment, as should the characteristic mass, density, and column density at which cloud self-gravity dominates other forces. Because the environments for high and low redshift star formation differ significantly, we expect the resulting gas to stellar conversion details to differ also. At high redshift, the universe is denser and more gas-rich, so the active parts of galaxies are denser and more gas rich too, leading to slightly shorter gas consumption timescales, higher cloud pressures, and denser, more massive, bound stellar clusters at the high mass end. With shorter consumption times corresponding to higher relative cosmic accretion rates, and with the resulting higher star formation rates and their higher feedback powers, the ISM has greater turbulent speeds relative to the rotation speeds, thicker gas disks, and larger cloud and star complex sizes at the characteristic Jeans length. The result is a more chaotic appearance at high redshift, bridging the morphology gap between today's quiescent spirals and today's major-mergers, with neither spiral nor major-merger processes actually in play at that time. The result is also a thick disk at early times, and after in-plane accretion from relatively large clump torques, a classical bulge. Today's disks are thinner, and torque-driven accretion is slower outside of inner barred regions. This paper reviews the basic processes involved with star formation in order to illustrate its evolution over time and environment.