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Register a new userPhotoionisation Feedback in a Self-Gravitating, Magnetised, Turbulent Cloud
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We present a new set of analytic models for the expansion of HII regions powered by UV photoionisation from massive stars and compare them to a new suite of radiative magnetohydrodynamic simulations of turbulent, self-gravitating molecular clouds. To perform these simulations we use the Eulerian adaptive mesh magnetohydrodynamics code RAMSES-RT, including radiative transfer of UV photons. Our analytic models successfully predict the global behaviour of the HII region provided the density and velocity structure of the cloud is known. We give estimates for the HII region behaviour based on a power law fit to the density field assuming that the system is virialised. We give a radius at which the ionisation front should stop expanding (stall). If this radius is smaller than the distance to the edge of the cloud, the HII region will be trapped by the cloud. This effect is more severe in collapsing clouds than in virialised clouds, since the density in the former increases dramatically over time, with much larger photon emission rates needed for the HII region to escape a collapsing cloud. We also measure the response of Jeans unstable gas to the HII regions to predict the impact of UV radiation on star formation in the cloud. We find that the mass in unstable gas can be explained by a model in which the clouds are evaporated by UV photons, suggesting that the net feedback on star formation should be negative
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Externally driven interstellar turbulence plays an important role in shaping the density structure in molecular clouds. Here we study the dynamical role of internally driven turbulence in a self-gravitating molecular cloud core. Depending on the initial conditions and evolutionary stages, we find that a self-gravitating core in the presence of gravity-driven turbulence can undergo constant, decelerated, and accelerated infall, and thus has various radial velocity profiles. In the gravity-dominated central region, a higher level of turbulence results in a lower infall velocity, a higher density, and a lower mass accretion rate. As an important implication of this study, efficient reconnection diffusion of magnetic fields against the gravitational drag naturally occurs due to the gravity-driven turbulence, without invoking externally driven turbulence.
Molecular cloud structure is regulated by stellar feedback in various forms. Two of the most important feedback processes are UV photoionisation and supernovae from massive stars. However, the precise response of the cloud to these processes, and the interaction between them, remains an open question. In particular, we wish to know under which conditions the cloud can be dispersed by feedback, which in turn can give us hints as to how feedback regulates the star formation inside the cloud. We perform a suite of radiative magnetohydrodynamic simulations of a 10^5 solar mass cloud with embedded sources of ionising radiation and supernovae, including multiple supernovae and a hypernova model. A UV source corresponding to 10% of the mass of the cloud is required to disperse the cloud, suggesting that the star formation efficiency should be on the order of 10%. A single supernova is unable to significantly affect the evolution of the cloud. However, energetic hypernovae and multiple supernovae are able to add significant quantities of momentum to the cloud, approximately 10^{43} g cm/s of momentum per 10^{51} ergs of supernova energy. This is on the lower range of estimates in other works, since dense gas clumps that remain embedded inside the HII region cause rapid cooling in the supernova blast. We argue that supernovae alone are unable to regulate star formation in molecular clouds, and that strong pre-supernova feedback is required to allow supernova blastwaves to propagate efficiently into the interstellar medium
We present a model of star formation in self-gravitating turbulent gas. We treat the turbulent velocity $v_T$ as a dynamical variable, and assume that it is adiabatically heated by the collapse. The theory predicts the run of density, infall velocity, and turbulent velocity, and the rate of star formation in compact massive gas clouds. The turbulent pressure is dynamically important at all radii, a result of the adiabatic heating. The system evolves toward a coherent spatial structure with a fixed run of density, $rho(r,t)torho(r)$; mass flows through this structure onto the central star or star cluster. We define the sphere of influence of the accreted matter by $m_*=M_g(r_*)$, where $m_*$ is the stellar plus disk mass in the nascent star cluster and $M_g(r)$ is the gas mass inside radius $r$. The density is given by a broken power law with a slope $-1.5$ inside $r_*$ and $sim -1.6$ to $-1.8$ outside $r_*$. Both $v_T$ and the infall velocity $|u_r|$ decrease with decreasing $r$ for $r>r_*$; $v_T(r)sim r^p$, the size-linewidth relation, with $papprox0.2-0.3$, explaining the observation that Larsons Law is altered in massive star forming regions. The infall velocity is generally smaller than the turbulent velocity at $r>r_*$. For $r<r_*$, the infall and turbulent velocities are again similar, and both increase with decreasing $r$ as $r^{-1/2}$, with a magnitude about half of the free-fall velocity. The accreted (stellar) mass grows super-linearly with time, $dot M_*=phi M_{rm cl}(t/tau_{ff})^2$, with $phi$ a dimensionless number somewhat less than unity, $M_{rm cl}$ the clump mass and $tau_{ff}$ the free-fall time of the clump. We suggest that small values of p can be used as a tracer of convergent collapsing flows.
We investigate stationary, self-gravitating, magnetised disks (or tori) around black holes. The models are obtained by numerically solving the coupled system of the Einstein equations and the equations of ideal general-relativistic magnetohydrodynamics. The mathematical formulation and numerical aspects of our approach are similar to those reported in previous works modeling stationary self-gravitating perfect-fluid tori, but the inclusion of magnetic fields represents a new ingredient. Following previous studies of purely hydrodynamical configurations, we construct our models assuming Keplerian rotation in the disks and both spinning and spinless black holes. We focus on the case of a toroidal distribution of the magnetic field and build a large set of models corresponding to a wide range of values of the magnetisation parameter, starting with weakly magnetised disks and ending at configurations in which the magnetic pressure dominates over the thermal one. In all our models, the magnetic field affects the equilibrium structure of the torus mainly due to the magnetic pressure. In particular, an increasing contribution of the magnetic field shifts the location of the maximum of the rest-mass density towards inner regions of the disk. The total mass of the system and the angular momentum are affected by the magnetic field in a complex way, that depends on the black hole spin and the location of the inner radius of the disk. The non-linear dynamical stability of the solutions presented in this paper will be reported elsewhere.
The long timescale evolution of a self-gravitating system is generically driven by two-body encounters. In many cases, the motion of the particles is primarily governed by the mean field potential. When this potential is integrable, particles move on nearly fixed orbits, which can be described in terms of angle-action variables. The mean field potential drives fast orbital motions (angles) whose associated orbits (actions) are adiabatically conserved on short dynamical timescales. The long-term stochastic evolution of the actions is driven by the potential fluctuations around the mean field and in particular by resonant two-body encounters, for which the angular frequencies of two particles are in resonance. We show that the stochastic gravitational fluctuations acting on the particles can generically be described by a correlated Gaussian noise. Using this approach, the so-called $eta$-formalism, we derive a diffusion equation for the actions in the test particle limit. We show that in the appropriate limits, this diffusion equation is equivalent to the inhomogeneous Balescu-Lenard and Landau equations. This approach provides a new view of the resonant diffusion processes associated with long-term orbital distortions. Finally, by investigating the example of the Hamiltonian Mean Field Model, we show how the present method generically allows for alternative calculations of the long-term diffusion coefficients in inhomogeneous systems.
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