Isothermal Fragmentation: Is there a low-mass cut-off?

The evolution of self-gravitating clouds of isothermal gas forms the basis of many star formation theories. Therefore it is important to know under what conditions such a cloud will undergo homologous collapse into a single, massive object, or will fragment into a spectrum of smaller ones. And if it fragments, do initial conditions (e.g. Jeans mass, sonic mass) influence the mass function of the fragments, as predicted by many theories of star formation? In this paper we show that the relevant parameter separating homologous collapse from fragmentation is not the Mach number of the initial turbulence (as suspected by many), but the infall Mach number $\mathcal{M}_{\rm infall}\sim\sqrt{G M/(R c_s^2)}$, equivalent to the number of Jeans masses in the initial cloud $N_J$. We also show that fragmenting clouds produce a power-law mass function with slopes close to the expected -2 (i.e. equal mass in all logarithmic mass intervals). However, the low-mass cut-off of this mass function is entirely numerical; the initial properties of the cloud have no effect on it. In other words, if $\mathcal{M}_{\rm infall}\gg 1$, fragmentation proceeds without limit to masses much smaller than the initial Jeans mass.Comment: 10 pages, 9 figure

Numerical Problems in Coupling Photon Momentum (Radiation Pressure) to Gas

Radiation pressure (RP; or photon momentum absorbed by gas) is important in a tremendous range of astrophysical systems. But we show the usual method for assigning absorbed photon momentum to gas in numerical radiation-hydrodynamics simulations (integrating over cell volumes or evaluating at cell centers) can severely under-estimate the RP force in the immediate vicinity around un-resolved (point/discrete) sources (and subsequently under-estimate its effects on bulk gas properties), unless photon mean-free-paths are highly-resolved in the fluid grid. The existence of this error is independent of the numerical radiation transfer (RT) method (even in exact ray-tracing/Monte-Carlo methods), because it depends on how the RT solution is interpolated back onto fluid elements. Brute-force convergence (resolving mean-free paths) is impossible in many cases (especially where UV/ionizing photons are involved). Instead, we show a 'face-integrated' method -- integrating and applying the momentum fluxes at interfaces between fluid elements -- better approximates the correct solution at all resolution levels. The 'fix' is simple and we provide example implementations for ray-tracing, Monte-Carlo, and moments RT methods in both grid and mesh-free fluid schemes. We consider an example of star formation in a molecular cloud with UV/ionizing RP. At state-of-the-art resolution, cell-integrated methods under-estimate the net effects of RP by an order of magnitude, leading (incorrectly) to the conclusion that RP is unimportant, while face-integrated methods predict strong self-regulation of star formation and cloud destruction via RP.Comment: 9 pages, 4 figures. Updated to match accepted MNRAS versio

Using policy gradient reinforcement learning on autonomous robot controllers

Robot programmers can often quickly program a robot to approximately execute a task under specific environment conditions. However, achieving robust performance under more general conditions is significantly more difficult. We propose a framework that starts with an existing control system and uses reinforcement feedback from the environment to autonomously improve the controller’s performance. We use the Policy Gradient Reinforcement Learning (PGRL) framework, which estimates a gradient (in controller space) of improved reward, allowing the controller parameters to be incrementally updated to autonomously achieve locally optimal performance. Our approach is experimentally verified on a Cye robot executing a room entry and observation task, showing significant reduction in task execution time and robustness with respect to un-modelled changes in the environment