Reviving the stalled shock by jittering jets in core collapse supernovae: jets from the standing accretion shock instability

I present a scenario by which an accretion flow with alternating angular momentum on to a newly born neutron star in a core collapse supernova(CCSN) efficiently amplifies magnetic fields and by that launches jets. The accretion flow of a collapsing core on to the newly born neutron star suffers spiral standing accretion shock instability(SASI). This instability leads to a stochastically variable angular momentum of the accreted gas, which in turn forms an accretion flow with alternating directions of the angular momentum, and hence alternating shear, at any given time. I study the shear in this alternating-shear sub-Keplerian inflow in published simulations, and present a new comparison with Keplerian accretion disks. From that comparison I argue that it might be as efficient as Keplerian accretion disks in amplifying magnetic fields by a dynamo. I suggest that although the average specific angular momentum of the accretion flow is small,namely, sub-Keplerian, this alternating-shear accretion flow can launch jets with varying directions, namely,jittering jets. Neutrino heating is an important ingredient in further energizing the jets. The jittering jets locally revive the stalled accretion shock in the momentarily polar directions, and by that they explode the star. I repeat again my call for a paradigm shift from a neutrino-driven explosion of CCSNe to a jet-driven explosion mechanism that is aided by neutrino heating.     

Formation of stars and planets: the role of magnetic fields

Star formation is thought to be triggered by gravitational collapse of the dense cores of molecular clouds. Angular momentum conservation during the collapse results in the progressive increase of the centrifugal force, which eventually halts the inflow of material and leads to the development of a central mass surrounded by a disc. In the presence of an angular momentum transport mechanism, mass accretion onto the central object proceeds through this disc, and it is believed that this is how stars typically gain most of their mass. However, the mechanisms responsible for this transport of angular momentum are not well understood. Although the gravitational field of a companion star or even gravitational instabilities (particularly in massive discs) may play a role, the most general mechanisms are turbulence viscosity driven by the magnetorotational instability (MRI), and outflows accelerated centrifugally from the surfaces of the disc. Both processes are powered by the action of magnetic fields and are, in turn, likely to strongly affect the structure, dynamics, evolutionary path and planet-forming capabilities of their host discs. The weak ionisation of protostellar discs, however, may prevent the magnetic field from effectively coupling to the gas and shear and driving these processes. Here I examine the viability and properties of these magnetically-driven processes in protostellar discs. The results indicate that, despite the weak ionisation, the magnetic field is able to couple to the gas and shear for fluid conditions thought to be satisfied over a wide range of radii in these discs.     

Magnetic Fields in Star-Forming Regions: Theoretical Aspects

We review the basic theoretical elements leading to our current understanding of the role of magnetic fields in the process of star formation. In particular, we concentrate on: (i) the relevance of the mass-to-flux ratio for the stability of molecular clouds; (ii) the consequences of magnetic flux leakage for the evolution of cloud cores; (iii) the phase of anisotropic dynamical collapse following the formation of strongly peaked density distributions; (iv) the mechanism of magnetic braking as a possible solution to the angular momentum problem in star formation.     

Evolution of collapse nonuniformity for rotating magnetic interstellar clouds

We investigate the formation and evolution of isothermal collapse nonuniformity for rotating magnetic interstellar clouds. The initial and boundary conditions correspond to the statement of the problem of homogeneous cloud contraction from a pressure equilibrium with the external medium. The initial uniform magnetic field is collinear with the angular velocity. Fast and slow magnetosonic rarefaction waves are shown to be formed and propagate from the boundary of the cloud toward its center in the early collapse stages. The front of the fast rarefaction wave divides the gas mass into two parts. The density, angular velocity, and magnetic field remain uniform in the inner region and have nonuniform profiles in the outer region. The rarefaction wave front surface can take both prolate and oblate shapes along the rotation axis, depending on the relationship between the initial angular velocity and magnetic field. We derive a criterion that separates the two regimes of rarefaction wave dynamics with the dominant role of electromagnetic and centrifugal forces. Based on analytical estimations and numerical calculations, we discuss possible scenarios for the evolution of collapse nonuniformity for rotating magnetic interstellar clouds.     

On the formation of protostellar disks

An analysis is presented of the hydrodynamic aspects of the growth of protostellar disks from the accretion (or collapse) of a rotating gas cloud. The size, mass, and radiative properties of protostellar disks are determined by the distribution of mass and angular momentum in the clouds from which they are formed, as well as from the dissipative processes within the disks themselves. The angular momentum of the infalling cloud is redistributed by the action of turbulent viscosity on a shear layer near the surface of the disk (downstream of the accretion shock) and on the radial shear across cylindrical surfaces parallel to the rotation axis. The fraction of gas that is fed into a central core (protostar) during accretion depends on the ratio of the rate of viscous diffusion of angular momentum to the accretion rate; rapid viscous diffusion (or a low accretion rate) promotes a large core-to-disk mass ratio. The continuum radiation spectrum of a highly viscous disk is similar to that of a steady-state accretion disk without mass addition. It is possible to construct models of the primitive solar nebula as an accretion disk, formed by the collapse of a slowly rotating protostellar cloud, and containing the minimum mass required to account for the planets. Other models with more massive disks are also possible.     

Protostellar angular momentum transport by spiral density waves

The gravitational collapse of molecular clouds or cloud cores is expected to lead to the formation of stars that begin their lives in a state of rapid rotation. It is known that, in at least some specific cases, rapidly rotating, slf-gravitating bodies are subject to instabilities that cause them to assume ellipsoidal shapes. In this paper we investigate the consequences of such instabilities on the angular momentum evolution of a star in the process of formation from a collapsing cloud, and surrounded by a protostellar disk, with a view toward applications to the formation of the Solar System. We use a specific model of star formation to demonstrate the possibility that such a star would become unstable, that the resulting distortion of the star would generate spiral density waves in the circumstellar disk, and that the torque associated with these waves would regulate the angular momentum of the star as it feeds angular momentum to the disk. We conclude that the angular momentum so transported to the disk would not spread the disk to, say, Solar System dimensions, by the action of the spiral density waves alone. However, a viscous disk could effectively extract stellar angular momentum and attain Solar System size. Our results also indicate that viscous disks could feed mass and angular momentum to a growing protostar in such a manner that distortions of the star would occur before gravitational torques could balance the influx of angular momentum. In other situations (in which the viscosity was small), a gap could be cleared between the disk and star.     

The collapse of primordial stars: importance of radiation

We simulate the collapse of a primordial protostellar cloud by means of a 1D hydrodynamics code accounting for chemical evolution, radiative transfer and radiation pressure. We find that the role of radiation pressure is negligible throughout the whole simulations, i.e. Until shortly after the formation of a central hydrostatic core. We also estimate the luminosity and the spectrum of such collapsing clouds. The luminosity is initially due to a number of H₂ lines and is of the order of 10^33-34 erg s^-1. It then grows to values ≳10³⁶ erg s^-1 by the time the core forms, and results from both HH lines and continuum radiation. This revised version was published online in September 2006 with corrections to the Cover Date.     

Radiation–hydrodynamical collapse of pre-galactic clouds in the ultraviolet background

To explain the effects of the ultraviolet (UV) background radiation on the collapse of pre-galactic clouds, we implement a radiation–hydrodynamical calculation, combining one-dimensional spherical hydrodynamics with an accurate treatment of the radiative transfer of ionizing photons. Both absorption and scattering of UV photons are explicitly taken into account. It turns out that a gas cloud contracting within the dark matter potential does not settle into hydrostatic equilibrium, but undergoes run-away collapse even under the presence of the external UV field. The cloud centre is shown to become self-shielded against ionizing photons by radiative transfer effects before shrinking to the rotation barrier. Based on our simulation results, we further discuss the possibility of H₂ cooling and subsequent star formation in a run-away collapsing core. The present results are closely relevant to the survival of subgalactic Population III objects as well as to metal injection into intergalactic space.     

Matter infall in collapsing molecular cloud cores with an axial magnetic field

The magnetic fields affect collapse of molecular cloud cores. Here, we consider a collapsing core with an axial magnetic field and investigate its effect on infall of matter and formation of accretion disk. For this purpose, the equations of motion of ions and neutral infalling particles are numerically solved to obtain the streamlines of trajectories. The results show that in a non-steady state of ionization and ion–neutral coupling, which is not unexpected in the case of infall, the radius of accretion disk will be larger as a consequence of axial magnetic field.     

Binary formation with different metallicities: dependence on initial conditions

The fragmentation process in collapsing clouds with various metallicities is studied using three-dimensional nested-grid hydrodynamics. Initial clouds are specified by three parameters: cloud metallicity, initial rotation energy and initial cloud shape. For different combinations of these parameters, we calculate 480 models in total and study cloud evolution, fragmentation conditions, orbital separation and binary frequency. For the cloud to fragment during collapse, the initial angular momentum must be higher than a threshold value, which decreases with decreasing metallicity. Although the exact fragmentation conditions depend also on the initial cloud shape, this dependence is only modest. Our results indicate a higher binary frequency in lower metallicity gas. In particular, with the same median rotation parameter as in the solar neighbourhood, a majority of stars are born as members of binary/multiple systems for  <10⁻⁴ Z_⊙  . With initial mass  <0.1 M_⊙  , if fragments are ejected in embryo from the host clouds by multibody interaction, they evolve to substellar-mass objects. This provides a formation channel for low-mass stars in zero- or low-metallicity environments.     

Rotation Profiles of Solar-like Stars with Magnetic Fields

We investigate the rotation profile of solar-like stars with magnetic fields. A diffu-sion coefficient of magnetic angular momentum transport is deduced. Rotating stellar models with different mass incorporating the coefficient are computed to give the rotation profiles. The total angular momentum of a solar model with only hydrodynamic instabilities is about 13 times larger than that of the Sun at the age of the Sun, and this model can not reproduce quasi-solid rotation in the radiative region. However, the solar model with magnetic fields not only can reproduce an almost uniform rotation in the radiative region, but also a total angular momentum that is consistent with the helioseismic result at the 3 σ level at the age of the Sun. The rotation of solar-like stars with magnetic fields is almost uniform in the radiative region, but for models of 1.2-1.5 M⊙, there is an obvious transition region between the convective core and the radiative region, where angular velocity has a sharp radial gradient, which is different from the rotation profile of the Sun and of massive stars with magnetic fields. The change of angular velocity in the transition region increases with increasing age and mass.     

Collapse and fragmentation of rotating magnetized clouds – II. Binary formation and fragmentation of first cores

Subsequent to Paper I, the evolution and fragmentation of a rotating magnetized cloud are studied with use of three-dimensional magnetohydrodynamic nested grid simulations. After the isothermal runaway collapse, an adiabatic gas forms a protostellar first core at the centre of the cloud. When the isothermal gas is stable for fragmentation in a contracting disc, the adiabatic core often breaks into several fragments. Conditions for fragmentation and binary formation are studied. All the cores which show fragmentation are geometrically thin, as the diameter-to-thickness ratio is larger than 3. Two patterns of fragmentation are found. (1) When a thin disc is supported by centrifugal force, the disc fragments into a ring configuration (ring fragmentation). This is realized in a rapidly rotating adiabatic core as  Ω > 0.2τ⁻¹_ff  , where Ω and  τ_ff  represent the angular rotation speed and the free-fall time of the core, respectively. (2) On the other hand, the disc is deformed to an elongated bar in the isothermal stage for a strongly magnetized or rapidly rotating cloud. The bar breaks into 2–4 fragments (bar fragmentation). Even if a disc is thin, the disc dominated by the magnetic force or thermal pressure is stable and forms a single compact body. In either ring or bar fragmentation mode, the fragments contract and a pair of outflows is ejected from the vicinities of the compact cores. The orbital angular momentum is larger than the spin angular momentum in the ring fragmentation. On the other hand, fragments often quickly merge in the bar fragmentation, since the orbital angular momentum is smaller than the spin angular momentum in this case. Comparison with observations is also shown.     

Evolution of filamentary molecular clouds in the presence of magnetic fields

The purpose of this paper is to explore the effect of magnetic fields on the dynamics of magnetized filamentary molecular clouds.We suppose there is a filament with cylindrical symmetry and two components of axial and toroidal magnetic fields.In comparison to previous works,the novelty in the present work involves a similarity solution that does not define a function of the magnetic fields or density.We consider the effect of the magnetic field on the collapse of the filament in both axial and toroidal directions and show that the magnetic field has a braking effect,which means that the increasing intensity of the magnetic field reduces the velocity of collapse.This is consistent with other studies.We find that the magnetic field in the central region tends to be aligned with the filament axis.Also,the magnitude and the direction of the magnetic field depend on the magnitude and direction of the initial magnetic field in the outer region.Moreover,we show that more energy dissipation from the filament causes a rise in the infall velocity.     

Jets launched at magnetar birth cannot be ignored

I question models for powering super energetic supernovae (SESNe) with a magnetar central engine that do not include jets that are expected to be launched by the magnetar progenitor. I show that under reasonable assumptions the outflow that is expected during the formation of a magnetar can carry an amount of energy that does not fall much below, and even surpasses, the energy that is stored in the newly born spinning neutron star (NS). The rapidly spinning NS and the strong magnetic fields attributed to magnetars require that the accreted mass onto the newly born NS possesses high specific angular momentum and strong magnetic fields. These ingredients are expected, as in many other astrophysical objects, to form collimated outflows/jets. I argue that the bipolar outflow in the pre-magnetar phase transfers a substantial amount of energy to the supernova (SN) ejecta, and it cannot be ignored in models that attribute SESNe to magnetars. I conclude that jets launched by accretion disks and accretion belts are more likely to power SESNe than magnetars are. This conclusion is compatible with the notion that jets might power all core collapse SNe (CCSNe).     

Axisymmetric gravitational collapse of rotating interstellar gas clouds

Numerical calculations have been made of the gravitational axisymmetric collapse of isothermal gas clouds endowed with angular momentum. The evolutionary study is based on the so-called Fluid-in-Cell method coupled to an efficient algebraic algorithm which allows the Poisson equation to be integrated by means of block tri-diagonal matrices. The results, at ages slight larger than the initial free-fall time, indicate that flattened disk-shaped structures are formed in the central region of the clouds-in good agreement with the previous analytical results predicted by the authors.     

The cosmological dependence of galactic specific angular momenta

Hydrodynamical simulations of galaxy formation in spatially flat cold dark matter (CDM) cosmologies with and without a cosmological constant (Λ) are described. A simple star formation algorithm is employed and radiative cooling is allowed only after redshift z =1 so that enough hot gas is available to form large, rapidly rotating stellar discs if angular momentum is approximately conserved during collapse. The specific angular momenta of the final galaxies are found to be sensitive to the assumed background cosmology. This dependence arises from the different angular momenta contained in the haloes at the epoch when the gas begins to collapse and the inhomogeneity of the subsequent halo evolution. In the Λ-dominated cosmology, the ratio of stellar specific angular momentum to that of the dark matter halo (measured at the virial radius) has a median value of ∼0.24 at z =0. The corresponding quantity for the Λ=0 cosmology is over three times lower. It is concluded that the observed frequency and angular momenta of disc galaxies pose significant problems for spatially flat CDM models with Λ=0 but may be consistent with a Λ-dominated CDM universe.     

Star formation in a multi-phase ISM

We present a 3d code for the dynamical evolution of a multi-phase interstellar medium (ISM) coupled to stars via star formation (SF) and feedback processes. The multi-phase ISM consists of clouds (sticky particles) and diffuse gas (SPH): exchange of matter, energy and momentum is achieved by drag (due to ram pressure) and condensation or evaporation processes. The cycle of matter is completed by SF and feedback by SNe and PNe. A SF scheme based on a variable SF efficiency as proposed by Elmegreen and Efremov (1997) is presented. For a Milky Way type galaxy we get a SF rate of ∼1 M_⊙ yr^-1 with an average SF efficiency of ∼5%. This revised version was published online in August 2006 with corrections to the Cover Date.     

Collapse of weakly ionized rotating turbulent Cloud Cores

In view of the Turbulent Cooling Flows scenario we carry out several 3D axisymmetric calculations to follow the evolution of magnetically subcritical weakly ionized and rotating turbulent cloud cores. Turbulent Cooling Flows appear to pronounce the effects of ambipolar diffusion considerably, inducing thereby a runaway collapse of the core already on a diluted free-fall time scale. Ambipolar diffusion significantly weakens the efficiency of magnetic braking. This implies that most of the rotational energy is trapped into the dynamically collapsing core and that initiation of outflows is prevented at least in the early isothermal phases. The trapped rotational energy is found to enhance the formation of rings that may afterwards fragment. It is shown that the central region of a strongly ionized magnetically subcritical core is principally overdense, with central density up to one order of magnitude larger than the surroundings. These results confirm that large scale magnetic fields threading a cloud core relax the supersonic random motions on an Alfvén wave crossing time. Moreover, ambipolar diffusion enhances dissipation of supersonic turbulence even more.     

Three-dimensional calculations of the formation of the presolar nebula from a slowly rotating cloud

The presolar nebula may have formed from the collapse of a very slowly rotating interstellar cloud. The first three-dimensional, hydrodynamical calculations of the collapse of such clouds are presented. The models include radiative transfer in the Eddington approximation, as well as detailed equations of state appropriate for the nonisothermal regime of protostellar evolution. Very slowly rotating clouds, i.e., those with initial ratios of rotational energy to gravitational energy of 10^?3 or less, avoid fragmentation and instead collapse to form single central objects, containing quasistatic cores with densities of about 10^?10 g cm^?3. These cores are, however, surrounded by significantly nonaxisymmetric regions, such that the presolar nebula would have been bar-like over the scale of the present solar system. This nonaxisymmetry, coupled with differential rotation, results in gravitational torques that produce rapid outward transfer of angular momentum. The center of the presolar nebula should then be able to contract and collapse to pre-main-sequence densities without suffering fission or fragmentation.