A fundamental issue in star formation is understanding the precise mechanisms leading to the formation of prestellar cores, and their subsequent gravitationally unstable evolution. To address this question, we carefully construct a suite of turbulent, self-gravitating numerical simulations, and analyze the development and collapse of individual prestellar cores. We show that the numerical requirements for resolving the sonic scale and internal structure of anticipated cores are essentially the same in self-gravitating clouds, calling for the number of cells per dimension to increase quadratically with the cloud's Mach number. In our simulations, we follow evolution of individual cores by tracking the region around each gravitational potential minimum over time. Evolution in nascent cores is towards increasing density and decreasing turbulence, and there is a wide range of critical density for initiating collapse. At given spatial scale the turbulence level also varies widely, and tends to be correlated with density. By directly measuring the radial forces acting within cores, we identify a distinct transition to a state of gravitational runaway. We use our new theory for turbulent equilibrium spheres to predict the onset of each core's collapse. Instability is expected when the critical radius becomes smaller than the tidal radius; we find good agreement with the simulations. Interestingly, the imbalance between gravity and opposing forces is only $\sim 20\%$ during core collapse, meaning that this is a quasi-equilibrium rather than a free-fall process. For most of their evolution, cores exhibit both subsonic contraction and transonic turbulence inherited from core-building flows; supersonic radial velocities accelerated by gravity only appear near the end of the collapse.
A fraction of the dense cores that form within a turbulent molecular cloud will eventually collapse, leading to star formation. Identifying the physical criteria for cores to become unstable, and analyzing critical core properties, thus constitutes a necessary step toward the complete theory of star formation. To this end, here we quantify the characteristics of an ensemble of ``critical cores'' that are on the verge of collapse. This critical epoch was identified in a companion paper, which followed the dynamical evolution of prestellar cores in numerical simulations of turbulent, self-gravitating clouds. We find that radial profiles of density and turbulent velocity dispersion constructed for individual critical cores are consistent with our new model for turbulent equilibrium spheres (TESs). While there exists a global linewidth--size relation for a cloud with given size and Mach number, the turbulent scaling relations constructed around each core exhibit significant variations, locally regulating the critical density for a core to become unstable. As a result, there is no single density threshold for collapse, but instead cores collapse at a wide range of densities determined by the local sonic scale, modulated by the local gravitational potential environment, with a distribution expected for TESs with a limited range of turbulent velocity dispersion. The critical cores found in our simulations are mostly transonic; we do not find either purely thermal or highly turbulent cores. We find that the core mass function (CMF) of critical cores peaks around the characteristic mass scale associated with the average properties of a turbulent cloud. We highlight the importance of constructing the CMF at the critical time instead of sink particle mass functions, and derive the resolution requirements to unambiguously identify the peak of the CMF.
Primordial black holes (PBH) can arise in a wide range of scenarios, from inflation to first-order phase transitions. Light PBHs, such as those produced during preheating or at the GUT scale, could induce an early matter-dominated phase given a moderate initial abundance. During the early matter-domination, the growth of initial PBH density perturbations can trigger collapse on horizon scales, producing much heavier PBHs. While the remaining original PBHs evaporate and reheat the Universe, these massive reformed PBHs survive for an extended period of time, producing potentially observable signatures at the present. We study this PBH reformation scenario and show that those reformed PBHs can emit significant quantities of gamma rays detectable by the next generation of experiments. The rapid reheating after matter domination generates a coincident stochastic gravitational wave background, which could be within range of the upcoming CMB-S4 experiment. The PBH reformation scenario provides an intriguing possibility of decoupling the current PBH population and the initial formation mechanism from early Universe physics, while providing opportunities for observation through multi-messenger astronomy.
The image of a Kerr-Newman (KN) black hole (BH) surrounded by a thin accretion disk is derived. By employing elliptic integrals and ray-tracing methods, we analyze photon trajectories around the KN BH. At low observation inclination angles, the secondary image of particles is embedded within the primary image. However, as the inclination increases, the primary and secondary images separate, forming a hat-like structure. The spin and charge of the BH, along with the observer's inclination angle, affect the image's asymmetry and the distortion of the inner shadow. To investigate the redshift distribution on the accretion disk, we extended the inner boundary of the accretion disk to the event horizon. The results show that the redshift distribution is significantly influenced by the observation inclination angle. Furthermore, we conducted a detailed analysis of the KN BH image using fisheye camera ray-tracing techniques and found that the optical appearance and intensity distribution of the BH vary at different observation frequencies (specifically at 230GHz and 86GHz). We also examined differences in intensity distribution for prograde and retrograde accretion disk scenarios. Comparing observational at the two frequencies, we found that both the total intensity and peak intensity at 86GHz are higher than those at 230GHz.
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