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In this chapter, we will cover how stars form from the stellar nurseries that are giant molecular clouds. We will first review the physical processes that compete to regulate star formation. We then review star formation in turbulent, magnetized molecular clouds and the associated statistics giving rise to the star formation rate and the initial mass function of stars. We then present the protostellar stages in detail from an observational perspective. We will primarily discuss low-mass ($<1.5\msun$) stars. Finally, we examine how multiplicity complicates the single-star formation picture. This chapter will focus on star formation at redshift~0, Comment: This is a pre-print of a chapter for the Encyclopedia of Astrophysics (edited by I. Mandel, section editor F.R.N. Schneider) to be published by Elsevier as a Reference Module. 18 pages, 8 Figures

Transiting planets in multiple-star systems, especially high-order multiples, make up a small fraction of the known planet population but provide unique opportunities to study the environments in which planets would have formed. Planet-hosting binaries have been shown to have an abundance of systems in which the stellar orbit aligns with the orbit of the transiting planet, which could give insights into the planet formation process in such systems. We investigate here if this trend of alignment extends to planet-hosting triple-star systems. We present long-term astrometric monitoring of a novel sample of triple-star systems that host Kepler transiting planets. We measured orbit arcs in 21 systems, including 12 newly identified triples, from a homogeneous analysis of our Keck adaptive optics data and, for some systems, Gaia astrometry. We examine the orbital alignment within the nine most compact systems ($\lesssim500$ au), testing if either (or both) of the stellar orbits align with the edge-on orbits of their transiting planets. Our statistical sample of triple systems shows a tendency toward alignment, especially when assessing the alignment probability using stellar orbital inclinations computed from full orbital fits, but is formally consistent with isotropic orbits. Two-population tests where half of the stellar orbits are described by a planet-hosting-binary-like moderately aligned distribution give the best match when the other half (non-planet-hosting) has a Kozai-like misaligned distribution. Overall, our results suggest that our sample of triple-star planet-hosting systems are not fully coplanar systems and have at most one plane of alignment., Comment: Accepted to MNRAS

(Edited) Many fast rotator stars (rotation periods of < 2 days) are found in unresolved binaries with separations of tens of au. This correlation leads to the question of whether the formation of binary stars inherently produces fast rotators. We aim to understand whether the formation of companions plays a role in spinning up stars. We use magneto-hydrodynamical simulations to study the formation of multiple star systems from turbulent and non-turbulent protostellar cores. We track the angular momentum accreted by individual star and inner disc systems by using a sink particle technique. We run a resolution study to extrapolate protostellar properties. We find in all simulations that the primary star can experience spin-up events that are correlated with the formation of companions. The primary star can spin up by up to 84% of its pre-fragmentation angular momentum and by up to 18% of its pre-fragmentation mass-specific angular momentum. The mechanism for the spin-up is gravitational disc instabilities in the circumstellar disc around the primary star, leading to the accretion of material with high specific angular momentum. The simulations that experience the strongest disc instabilities fragment to form companions. Simulations with weaker spin-up events experience disc instabilities triggered by a companion flyby, and the disc instability in these cases does not produce further fragments. We conclude that the primary star in multiple star systems may end up with a higher spin than single stars. This is because gravitational instabilities in the circumstellar disc around the primary star can trigger a spin-up event. In the strongest spin-up events, the instability is likely to cause disc fragmentation and the formation of companions. This companion formation coupled with shorter disc lifetimes, because the companion truncates the circumstellar disc, can help produce fast rotators., Comment: 14 pages, 11 Figures. Accepted to A&A

The dominant mechanism forming multiple stellar systems in the high-mass regime (M$_\ast \gtrsim $ 8 $M_{\odot}$) remained unknown because direct imaging of multiple protostellar systems at early phases of high-mass star formation is very challenging. High-mass stars are expected to form in clustered environments containing binaries and higher-order multiplicity systems. So far only a few high-mass protobinary systems, and no definitive higher-order multiples, have been detected. Here we report the discovery of one quintuple, one quadruple, one triple and four binary protostellar systems simultaneously forming in a single high-mass protocluster, G333.23--0.06, using Atacama Large Millimeter/submillimeter Array high-resolution observations. We present a new example of a group of gravitationally bound binary and higher-order multiples during their early formation phases in a protocluster. This provides the clearest direct measurement of the initial configuration of primordial high-order multiple systems, with implications for the in situ multiplicity and its origin. We find that the binary and higher-order multiple systems, and their parent cores, show no obvious sign of disk-like kinematic structure. We conclude that the observed fragmentation into binary and higher-order multiple systems can be explained by core fragmentation, indicating its crucial role in establishing the multiplicity during high-mass star cluster formation., Comment: Published in Nature Astronomy at https://www.nature.com/articles/s41550-023-02181-9. 27 pages, 12 figures, 1 table

Star formation is a multi-scale problem, and only global simulations that account for the connection from the molecular cloud scale gas flow to the accreting protostar can reflect the observed complexity of protostellar systems. Star-forming regions are characterised by supersonic turbulence and as a result, it is not possible to simultaneously design models that account for the larger environment and in detail reproduce observed stellar systems. Instead, the stellar inventories can be matched statistically, and best matches found that approximate specific observations. Observationally, a combination of single-dish telescopes and interferometers are now able to resolve the nearest protostellar objects on all scales from the protostellar core to the inner 10 AU. We present a new non-parametric methodology which uses high-resolution simulations and post-processing methods to match simulations and observations using deep learning. Our goal is to perform a down-selection from large data sets of synthetic images to a ranked list of best-matching candidates with respect to the observation. This is particularly useful for binary and multiple stellar systems that form in turbulent environments. The objective is to accelerate the rate at which we can do such comparisons, remove biases from hand-picking matches, and contribute to identifying the underlying physical processes that drive the creation and evolution of observed protostellar systems., Comment: 13 pages, 8 figures, submitted to MNRAS

Protostellar binaries harbour complex environment morphologies. Observations represent a snapshot in time, and projection and optical depth effects impair our ability to interpret them. Careful comparison with high-resolution models that include the larger star-forming region can help isolate the driving physical processes and give observations context in the time domain. We carry out zoom-in simulations with AU-scale resolution, and for the first time ever we follow the evolution until a circumbinary disk is formed. We investigate the gas dynamics around the young stars and extract disk sizes. Using radiative transfer, we obtain evolutionary tracers of the binary systems. We find that the centrifugal radius in prestellar cores is a poor estimator of the resulting disk size due to angular momentum transport at all scales. For binaries, the disk sizes are regulated periodically by the binary orbit, having larger radii close to the apastron. The bolometric temperature differs systematically between edge-on and face-on views and shows a high frequency time dependence correlated with the binary orbit and a low frequency time dependence with larger episodic accretion events. These oscillations can bring the system appearance to change rapidly from class 0 to class I and for short time periods even bring it to class II. The highly complex structure in early stages, as well as the binary orbit itself, affects the classical interpretation of protostellar classes and direct translation to evolutionary stages has to be done with caution and include other evolutionary indicators such as the extent of envelope material., Comment: 15 pages, 13 figures, submitted to MNRAS

Magnetic fields are known to play a crucial role in the star formation process, particularly in the formation of jets and outflows from protostellar discs. The magnetic field structure in star forming regions is not always uniform and ordered, often containing regions of magnetic turbulence. We present grid-based, magneto-hydrodynamical simulations of the collapse of a 1$\,\mathrm{M}_{\odot}$ cloud core, to investigate the influence of complex magnetic field structures on outflow formation, morphology and efficiency. We compare three cases: a uniform field, a partially turbulent field and a fully turbulent field, with the same magnetic energy in all three cases. We find that collimated jets are produced in the uniform-field case, driven by a magneto-centrifugal mechanism. Outflows also form in the partially turbulent case, although weaker and less collimated, with an asymmetric morphology. The outflows launched from the partially turbulent case carry the same amount of mass as the uniform-field case but at lower speeds, having only have 71$\%$ of the momentum of the uniform-field case. In the case of a fully turbulent field, we find no significant outflows at all. Moreover, the turbulent magnetic field initially reduces the accretion rate and later induces fragmentation of the disc, forming multiple protostars. We conclude that a uniform poloidal component of the magnetic field is necessary for the driving of jets., Comment: 12 pages, 6 figures, accepted for publication in MNRAS

Most stars form in binaries and the evolution of their discs remains poorly understood. To shed light on this subject, we carry out 3D ideal MHD simulations with the AMR code FLASH of binary star formation for separations of $10-20\,\mathrm{AU}$. We run a simulation with no initial turbulence (NT), and two with turbulent Mach numbers of $\mathcal{M} = \sigma_v/c_s = 0.1$ and $0.2$ (T1 and T2) for $5000\,\mathrm{yr}$ after protostar formation. By the end of the simulations the circumbinary discs in NT and T1, if any, have radii of $\lesssim20\,\mathrm{AU}$ with masses $\lesssim0.02\,\mathrm{M}_\odot$, while T2 hosts a circumbinary disc with radius $\sim70-80\,\mathrm{AU}$ and mass $\sim0.12\,\mathrm{M}_\odot$. These circumbinary discs formed from the disruption of circumstellar discs and harden the binary orbit. Our simulated binaries launch large single outflows. We find that NT drives the most massive outflows, and also removes large quantities of linear and angular momentum. T2 produces the least efficient outflows concerning mass, momentum and angular momentum ($\sim$61 per cent, $\sim$71 per cent, $\sim$68 per cent of the respective quantities in NT). We conclude that while turbulence helps to build circumbinary discs which organise magnetic fields for efficient outflow launching, too much turbulence may also disrupt the ordered magnetic field structure required for magneto-centrifugal launching of jets and outflows. We also see evidence for episodic accretion during the binary star evolution. We conclude that the role of turbulence in building large circumbinary discs may explain some observed very old ($>10\,\mathrm{Myr}$) circumbinary discs. The longer lifetime of circumbinary discs may increase the likelihood of planet formation., Comment: Accepted to MNRAS. 17 pages, 11 figures. arXiv admin note: text overlap with arXiv:1705.08152

We present observations of disc-bearing stars in Upper Scorpius (US) and Upper Centaurus-Lupus (UCL) with moderate resolution spectroscopy in order to determine the influence of multiplicity on disc persistence after ~5-20 Myr. Discs were identified using infra-red (IR) excess from the Wide-field Infra-red Survey Explorer (WISE) survey. Our survey consists of 55 US members and 28 UCL members, using spatial and kinematic information to assign a probability of membership. Spectra are gathered from the ANU 2.3m telescope using the Wide Field Spectrograph (WiFeS) to detect radial velocity variations that indicate the presence of a companion. We identify 2 double-lined spectroscopic binaries, both of which have strong IR excess. We find the binary fraction of disc-bearing stars in US and UCL for periods up to 20 years to be $0.06^{0.07}_{0.02}$ and $0.13^{0.06}_{0.03}$ respectively. Based on the multiplicity of field stars, we obtain an expected binary fraction of $0.12^{0.02}_{0.01}$. The determined binary fractions for disc-bearing stars does not vary significantly from the field, suggesting that the overall lifetime of discs may not differ between single and binary star systems., Comment: 16 pages, 8 figures, 6 tables, Accepted to MNRAS

We carry out magnetohydrodynamical simulations with FLASH of the formation of a single, a tight binary ($a\sim$2.5 AU) and a wide binary star ($a\sim$45 AU). We study the outflows and jets from these systems to understand the contributions the circumstellar and circumbinary discs have on the efficiency and morphology of the outflow. In the single star and tight binary case we obtain a single pair of jets launched from the system, while in the wide binary case two pairs of jets are observed. This implies that in the tight binary case the contribution of the circumbinary disc on the outflow is greater than that in the wide binary case. We also find that the single star case is the most efficient at transporting mass, linear and angular momentum from the system, while the wide binary case is less efficient ($\sim$50$\%, \sim$33$\%, \sim$42$\%$ of the respective quantities in the single star case). The tight binary's efficiency falls between the other two cases ($\sim$71$\%, \sim$66$\%, \sim$87$\%$ of the respective quantities in the single star case). By studying the magnetic field structure we deduce that the outflows in the single star and tight binary star case are magnetocentrifugally driven, whereas in the wide binary star case the outflows are driven by a magnetic pressure gradient., Comment: Accepted for publication in MNRAS. 17 pages, 15 figures

This paper presents the first major data release and survey description for the ANU WiFeS SuperNovA Program (AWSNAP). AWSNAP is an ongoing supernova spectroscopy campaign utilising the Wide Field Spectrograph (WiFeS) on the Australian National University (ANU) 2.3m telescope. The first and primary data release of this program (AWSNAP-DR1) releases 357 spectra of 175 unique objects collected over 82 equivalent full nights of observing from July 2012 to August 2015. These spectra have been made publicly available via the WISeREP supernova spectroscopy repository. We analyse the AWSNAP sample of Type Ia supernova spectra, including measurements of narrow sodium absorption features afforded by the high spectral resolution of the WiFeS instrument. In some cases we were able to use the integral-field nature of the WiFeS instrument to measure the rotation velocity of the SN host galaxy near the SN location in order to obtain precision sodium absorption velocities. We also present an extensive time series of SN 2012dn, including a near-nebular spectrum which both confirms its "super-Chandrasekhar" status and enables measurement of the sub-solar host metallicity at the SN site., Comment: Submitted to Publications of the Astronomical Society of Australia (PASA). Spectra publicly released via WISeREP at http://wiserep.weizmann.ac.il/

The common envelope interaction is thought to be the gateway to all evolved compact binaries and mergers. Hydrodynamic simulations of the common envelope interaction between giant stars and their companions are restricted to the dynamical, fast, in-spiral phase. They find that the giant envelope is lifted during this phase, but remains mostly bound to the system. At the same time, the orbital separation is greatly reduced, but in most simulations it levels off? at values larger than measured from observations. We conjectured that during the post-in-spiral phase the bound envelope gas will return to the system. Using hydrodynamic simulations, we generate initial conditions for our simulation that result in a fall-back disk with total mass and angular momentum in line with quantities from the simulations of Passy et al. We find that the simulated fall-back event reduces the orbital separation efficiently, but fails to unbind the gas before the separation levels off once again. We also find that more massive fall-back disks reduce the orbital separation more efficiently, but the efficiency of unbinding remains invariably very low. From these results we deduce that unless a further energy source contributes to unbinding the envelope (such as was recently tested by Nandez et al.), all common envelope interactions would result in mergers. On the other hand, additional energy sources are unlikely to help, on their own, to reduce the orbital separation. We conclude by discussing our dynamical fall-back event in the context of a thermally-regulated post-common envelope phase., Comment: 12 pages, 12 pages, Accepted to MNRAS

We present observations of three FU Orionis objects (hereafter, FUors) with nonredundant aperture-mask interferometry (NRM) at 1.59 um and 2.12 um that probe for binary companions on the scale of the protoplanetary disk that feeds their accretion outbursts. We do not identify any companions to V1515 Cyg or HBC 722, but we do resolve a close binary companion to V1057 Cyg that is at the diffraction limit (rho = 58.3 +/- 1.4 mas or 30 +/- 5 AU) and currently much fainter than the outbursting star (delta(K') = 3.34 +/- 0.10 mag). Given the flux excess of the outbursting star, we estimate that the mass of the companion (M ~ 0.25 Msun) is similar to or slightly below that of the FUor itself, and therefore it resembles a typical T Tauri binary system. Our observations only achieve contrast limits of delta(K') ~ 4 mag, and hence we are only sensitive to companions that were near or above the pre-outburst luminosity of the FUors. It remains plausible that FUor outbursts could be tied to the presence of a close binary companion. However, we argue from the system geometry and mass reservoir considerations that these outbursts are not directly tied to the orbital period (i.e., occurring at periastron passage), but instead must only occur infrequently., Comment: 6 pages, 2 figures