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Mikhail Klassen

Radiative Transfer

Massive stars—those exceeding about eight times the mass of our Sun—are among the most influential objects in the universe. Their intense radiation shapes the interstellar medium, their winds sculpt molecular clouds, and their deaths as supernovae seed the cosmos with heavy elements. Yet how these stars form at all remains a puzzle: theory predicts that radiation pressure from a growing protostar should halt the infall of gas, preventing the star from ever becoming massive. Clearly, nature has found a way around this barrier.

For my PhD work at McMaster University under Prof. Ralph Pudritz, I tackled this problem head-on using large-scale radiation-hydrodynamic simulations run on supercomputers. The work spanned the development of new computational methods, their application to the formation of individual massive stars, and the simulation of entire star-forming molecular cloud clumps.

Edge-on view of a 100-solar-mass protostellar core collapsing under gravity (4000 AU across). A protostellar disk forms at the center, visible as limbs extending to either side. Radiation feedback from the forming star heats the surrounding gas, driving expanding bubbles through radiation pressure. Turbulent structures emerge throughout the volume.

The Hybrid Radiative Transfer Scheme

Modeling radiation in star-forming environments is challenging because conditions vary dramatically. Close to a young star, the gas is relatively transparent and starlight streams outward in well-defined beams. Deep inside the surrounding dust cocoon, however, the medium is so opaque that radiation is absorbed and re-emitted many times, diffusing outward like heat through a wall.

No single radiation transport method handles both regimes well. Raytracing excels at capturing the direct irradiation from a star but struggles in optically thick regions. Flux-limited diffusion handles the dense, opaque interior accurately but cannot reproduce the sharp shadows and beaming of direct starlight. I developed a hybrid scheme that combined both: a raytracer to follow direct stellar irradiation up to the point of first absorption, and a flux-limited diffusion solver to evolve the subsequent thermal re-emission through dense gas and dust.

This hybrid method was implemented in the FLASH adaptive mesh refinement (AMR) code, making it the first such scheme on a Cartesian adaptive grid. We validated it against a suite of standard benchmark tests, confirming that it captured the correct physics across a wide range of optical depths.

Massive Star Formation

With the hybrid radiation scheme in hand, I simulated the gravitational collapse of massive protostellar cores—dense clumps of gas and dust with initial masses of 30, 100, and 200 times that of the Sun. In each case, a massive protostar formed at the center, surrounded by a rotationally supported (Keplerian) accretion disk.

As the protostars grew, their disks became gravitationally unstable, developing prominent spiral arms. Despite this instability, the disks did not fragment into companion objects but instead channeled material inward, boosting accretion rates by factors of two to ten.

In the more massive simulations, the protostar’s luminosity exceeded the Eddington limit—the threshold at which radiation pressure overcomes gravity. This drove expanding bipolar outflow cavities above and below the disk. Remarkably, these radiation-pressure bubbles remained stable against Rayleigh–Taylor instabilities and did not disrupt the disk. Instead, gas was funneled through the circumstellar disk, slipping past the radiation barrier and continuing to feed the growing star. This demonstrated a viable pathway for building stars well above the theoretical mass limit set by radiation pressure alone.

Filamentary Molecular Clouds

Stars rarely form in isolation. They are born in clusters, within turbulent, magnetized molecular clouds threaded by filamentary structures. To study this larger-scale environment, I simulated the evolution of massive cloud clumps—500 and 1200 solar masses—including turbulence, magnetic fields, self-gravity, and radiative feedback.

In these simulations, turbulence and gravity conspired to form dense filaments, with clusters of protostars appearing at filament intersections. We studied how the geometry of the magnetic field related to the orientation of the filaments and found that for a coherent magnetic field structure to emerge, gravitational energy had to dominate over kinetic energy. In other words, only when gravity firmly controlled the dynamics did the field lines trace the large-scale filament geometry.

We also studied the impact of photoionization feedback from the most massive star in the cluster. As the star grew luminous enough to ionize hydrogen, it inflated an expanding HII region—a bubble of hot, ionized gas—that disrupted the surrounding filament and began to disperse the natal cloud, ultimately limiting the star formation efficiency of the clump.

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