Gravitational Collapse and Disk Formation in Magnetized Cores

We discuss the effects of the magnetic field observed in molecular clouds on the process of star formation, concentrating on the phase of gravitational collapse of low-mass dense cores, cradles of sunlike stars. We summarize recent analytic work and numerical simulations showing that a substantial level of magnetic field diffusion at high densities has to occur in order to form rotationally supported disks. Furthermore, newly formed accretion disks are threaded by the magnetic field dragged from the parent core during the gravitational collapse. These disks are expected to rotate with a sub-Keplerian speed because they are partially supported by magnetic tension against the gravity of the central star. We discuss how sub-Keplerian rotation makes it difficult to eject disk winds and accelerates the process of planet migration. Moreover, magnetic fields modify the Toomre criterion for gravitational instability via two opposing effects: magnetic tension and pressure increase the disk local stability, but sub-Keplerian rotation makes the disk more unstable. In general, magnetized disks are more stable than their nonmagnetic counterparts; thus, they can be more massive and less prone to the formation of giant planets by gravitational instability.

Cosmic-ray ionisation in collapsing clouds

Cosmic rays (CR) play an important role in dense molecular cores, affecting their thermal and dynamical evolution and initiating the chemistry. Several studies have shown that the formation of protostellar discs in collapsing clouds is severely hampered by the braking torque exerted by the entrained magnetic field on the infalling gas, as long as the field remains frozen to the gas. We examine the possibility that the concentration and twisting of the field lines in the inner region of collapse can produce a significant reduction of the ionisation fraction. To check whether the CR ionisation rate (CRir) can fall below the critical value required to maintain good coupling, we first study the propagation of CRs in a model of a static magnetised cloud varying the relative strength of the toroidal/poloidal components and the mass-to-flux ratio. We then follow the path of CRs using realistic magnetic field configurations generated by numerical simulations of a rotating collapsing core. We find that an increment of the toroidal component of the magnetic field, or, in general, a more twisted configuration of the field lines, results in a decrease in the CR flux. This is mainly due to the magnetic mirroring effect that is stronger where larger variations in the field direction are present. In particular, we find a decrease of the CRir below 10^-18 s-1 in the central 300-400 AU, where density is higher than about 10^9 cm-3. This very low value of the CRir is attained in the cases of intermediate and low magnetisation (mass-to-flux ratio lambda=5 and 17, respectively) and for toroidal fields larger than about 40% of the total field. Magnetic field effects can significantly reduce the ionisation fraction in collapsing clouds. We provide a handy fitting formula to compute approximately the attenuation of the CRir in a molecular cloud as a function of the density and the magnetic configuration.

Cosmic-ray propagation in molecular clouds

Cosmic-rays constitute the main ionising and heating agent in dense, starless, molecular cloud cores. We reexamine the physical quantities necessary to determine the cosmic-ray ionisation rate (especially the cosmic ray spectrum at E < 1 GeV and the ionisation cross sections), and calculate the ionisation rate as a function of the column density of molecular hydrogen. Available data support the existence of a low-energy component (below about 100 MeV) of cosmic-ray electrons or protons responsible for the ionisation of diffuse and dense clouds. We also compute the attenuation of the cosmic-ray flux rate in a cloud core taking into account magnetic focusing and magnetic mirroring, following the propagation of cosmic rays along flux tubes enclosing different amount of mass and mass-to-flux ratios. We find that mirroring always dominates over focusing, implying a reduction of the cosmic-ray ionisation rate by a factor of 3-4 depending on the position inside the core and the magnetisation of the core.

Effects of magnetic fields on the cosmic-ray ionization of molecular cloud cores

Low-energy cosmic rays are the dominant source of ionization for molecular cloud cores. The ionization fraction, in turn, controls the coupling of the magnetic field to the gas and hence the dynamical evolution of the cores. The purpose of this work is to compute the attenuation of the cosmic-ray flux rate in a cloud core taking into account magnetic focusing, magnetic mirroring, and all relevant energy loss processes. We adopt a standard cloud model characterized by a mass-to-flux ratio supercritical by a factor of about 2 to describe the density and magnetic field distribution of a low-mass starless core, and we follow the propagation of cosmic rays through the core along flux tubes enclosing different amount of mass. We then extend our analysis to cores with different mass-to-flux ratios. We find that mirroring always dominates over focusing, implying a reduction of the cosmic-ray ionization rate by a factor of about 2-3 over most of a solar-mass core with respect to the value in the intercloud medium outside the core. For flux tubes enclosing larger masses the reduction factor is smaller, since the field becomes increasingly uniform at larger radii and lower densities. We also find that the cosmic-ray ionization rate is further reduced in clouds with stronger magnetic field, e.g. by a factor of about 4 for a marginally critical cloud. The magnetic field threading molecular cloud cores affects the penetration of low-energy cosmic rays and reduces the ionization rate by a factor 3-4 depending on the position inside the core and the magnetization of the core.

Stability of Magnetized Disks and Implications for Planet Formation

This paper considers gravitational perturbations in geometrically thin disks with rotation curves dominated by a central object, but with substantial contributions from magnetic pressure and tension. The treatment is general, but the application is to the circumstellar disks that arise during the gravitational collapse phase of star formation. We find the dispersion relation for spiral density waves in these generalized disks and derive the stability criterion for axisymmetric $(m=0)$ disturbances (the analog of the Toomre parameter $Q_T$) for any radial distribution of the mass-to-flux ratio $lambda$. The magnetic effects work in two opposing directions: on one hand, magnetic tension and pressure stabilize the disk against gravitational collapse and fragmentation; on the other hand, they also lower the rotation rate making the disk more unstable. For disks around young stars the first effect generally dominates, so that magnetic fields allow disks to be stable for higher surface densities and larger total masses. These results indicate that magnetic fields act to suppress the formation of giant planets through gravitational instability. Finally, even if gravitational instability can form a secondary body, it must lose an enormous amount of magnetic flux in order to become a planet; this latter requirement represents an additional constraint for planet formation via gravitational instability and places a lower limit on the electrical resistivity.