Partial Stellar Explosions - Ejected Mass and Minimal Energy

Many massive stars appear to undergo enhanced mass loss during late stages of their evolution. In some cases, the ejected mass likely originates from non-terminal explosive outbursts, rather than continuous winds. Here we study the dependence of the ejecta mass, mej, on the energy budget E of an explosion deep within the star, using both analytical arguments and numerical hydrodynamics simulations. Focusing on polytropic stellar models, we find that for explosion energies smaller than the stellar binding energy, the ejected mass scales as $m_{\rm ej} \propto E^{\varepsilon _{m}}$, where ϵm = 2.4 − 3.0 depending on the polytropic index. The loss of energy due to shock breakout emission near the stellar edge leads to the existence of a minimal mass-shedding explosion energy, corresponding to a minimal ejecta mass. For a wide range of progenitors, from Wolf-Rayet stars to red supergiants, we find a similar limiting energy of $E_{\rm min} \approx 10^{46}-10^{47} \rm \, erg$, almost independent of the stellar radius. The corresponding minimal ejecta mass varies considerably across different progenitors, ranging from $\sim \! 10^{-8} \, \rm M_\odot$ in compact stars, up to $\sim \! 10^{-2} \, \rm M_\odot$ in red supergiants. We discuss implications of our results for pre-supernova outbursts driven by wave heating, and complications caused by the non-constant opacity and adiabatic index of realistic stars.

Accretion bursts in low-metallicity protostellar disks

Aims. The early evolution of protostellar disks with metallicities in the Z = 1.0 − 0.01 Z⊙ range was studied with a particular emphasis on the strength of gravitational instability and the nature of protostellar accretion in low-metallicity systems. Methods. Numerical hydrodynamics simulations in the thin-disk limit were employed that feature separate gas and dust temperatures, and disk mass-loading from the infalling parent cloud cores. Models with cloud cores of similar initial mass and rotation pattern but distinct metallicity were considered to distinguish the effect of metallicity from that of the initial conditions. Results. The early stages of disk evolution in low-metallicity models are characterized by vigorous gravitational instability and fragmentation. Disk instability is sustained by continual mass-loading from the collapsing core. The time period that is covered by this unstable stage is much shorter in the Z = 0.01 Z⊙ models than in their higher metallicity counterparts thanks to the higher rates of mass infall caused by higher gas temperatures (which decouple from lower dust temperatures) in the inner parts of collapsing cores. Protostellar accretion rates are highly variable in the low-metallicity models reflecting the highly dynamic nature of the corresponding protostellar disks. The low-metallicity systems feature short but energetic episodes of mass accretion caused by infall of inward-migrating gaseous clumps that form via gravitational fragmentation of protostellar disks. These bursts seem to be more numerous and last longer in the Z = 0.1 Z⊙ models than in the Z = 0.01 Z⊙ case. Conclusions. Variable protostellar accretion with episodic bursts is not a particular feature of solar metallicity disks. It is also inherent to gravitationally unstable disks with metallicities up to 100 times lower than solar.

Thermal evolution of protoplanetary disks: from β-cooling to decoupled gas and dust temperatures

Aims. We explore the long-term evolution of young protoplanetary disks with different approaches to computing the thermal structure determined by various cooling and heating processes in the disk and its surroundings. Methods. Numerical hydrodynamics simulations in the thin-disk limit were complemented with three thermal evolution schemes: a simplified β-cooling approach with and without irradiation, where the rate of disk cooling is proportional to the local dynamical time; a fiducial model with equal dust and gas temperatures calculated taking viscous heating, irradiation, and radiative cooling into account; and a more sophisticated approach allowing decoupled dust and gas temperatures. Results. We found that the gas temperature may significantly exceed that of dust in the outer regions of young disks thanks to additional compressional heating caused by the infalling envelope material in the early stages of disk evolution and slow collisional exchange of energy between gas and dust in low-density disk regions. However, the outer envelope shows an inverse trend, with the gas temperatures dropping below that of dust. The global disk evolution is only weakly sensitive to temperature decoupling. Nevertheless, separate dust and gas temperatures may affect the chemical composition, dust evolution, and disk mass estimates. Constant-β models without stellar and background irradiation fail to reproduce the disk evolution with more sophisticated thermal schemes because of the intrinsically variable nature of the β-parameter. Constant-β models with irradiation more closely match the dynamical and thermal evolution, but the agreement is still incomplete. Conclusions. Models allowing separate dust and gas temperatures are needed when emphasis is placed on the chemical or dust evolution in protoplanetary disks, particularly in subsolar metallicity environments.

The origin of tail-like structures around protoplanetary disks

Aims. We study the origin of tail-like structures recently detected around the disk of SU Aurigae and several FU Orionis-type stars. Methods. Dynamic protostellar disks featuring ejections of gaseous clumps and quiescent protoplanetary disks experiencing a close encounter with an intruder star were modeled using the numerical hydrodynamics code FEOSAD. Both the gas and dust dynamics were taken into account, including dust growth and mutual friction between the gas and dust components. Only plane-of-the-disk encounters were considered. Results. Ejected clumps produce a unique type of tail that is characterized by a bow-shock shape. Such tails originate from the supersonic motion of ejected clumps through the dense envelope that often surrounds young gravitationally unstable protostellar disks. The ejected clumps either sit at the head of the tail-like structure or disperse if their mass is insufficient to withstand the head wind of the envelope. On the other hand, close encounters with quiescent protoplanetary disks produce three types of the tail-like structure; we define these as pre-collisional, post-collisional, and spiral tails. These tails can in principle be distinguished from one another by particular features of the gas and dust flow in and around them. We find that the brown-dwarf-mass intruders do not capture circumintruder disks during the encounter, while the subsolar-mass intruders can acquire appreciable circumintruder disks with elevated dust-to-gas ratios, which can ease their observational detection. However, this is true only for prograde collisions; the retrograde intruders fail to collect appreciable amounts of gas or dust from the disk of the target. The mass of gas in the tail varies in the range 0.85–11.8 MJup, while the total mass of dust lies in the 1.75–30.1 M⊕ range, with the spiral tails featuring the highest masses. The predicted mass of dust in the model tail-like structures is therefore higher than what was inferred for similar structures in SU Aur, FU Ori, and Z CMa, making their observational detection feasible. Conclusions. Tail-like structures around protostellar and protoplanetary disks can be used to infer interesting phenomena such as clump ejection or close encounters. In particular, the bow-shock morphology of the tails could point to clump ejections as a possible formation mechanism. Further numerical and observational studies are needed to better understand the detectability and properties of the tails.

The impact of planet wakes on the location and shape of the water ice line in a protoplanetary disk

Context. Planets in accretion disks can excite spiral shocks and if these planets are massive enough, they can even open gaps in their vicinity. Both of these effects can influence the overall thermal structure of the disk. Aims. We model planets of different masses and semimajor axes in disks of various viscosities and accretion rates to examine their impact on disk thermodynamics and to highlight the mutable, non-axisymmetric nature of ice lines in systems with massive planets. Methods. We conducted a parameter study using numerical hydrodynamics simulations where we treated viscous heating, thermal cooling, and stellar irradiation as additional source terms in the energy equation, with some runs including radiative diffusion. Our parameter space consists of a grid containing different combinations of planet and disk parameters. Results. Both gap opening and shock heating can displace the ice line, with the effects amplified for massive planets in optically thick disks. The gap region can split an initially hot (T > 170 K) disk into a hot inner disk and a hot ring just outside of the planet’s location, while shock heating can reshape the originally axisymmetric ice line into water-poor islands along spirals. We also find that radiative diffusion does not alter the picture significantly in this context. Conclusions. Shock heating and gap opening by a planet can effectively heat up optically thick disks and, in general, they can move or reshape the water ice line. This can affect the gap structure and migration torques. It can also produce azimuthal features that follow the trajectory of spiral arms, creating hot zones which lead to “islands” of vapor and ice around spirals that could affect the accretion or growth of icy aggregates.

Implicit Large-Eddy Simulation of Transition and Turbulence Decay

Accurate predictions with quantifiable uncertainties are essential to many practical turbulent flow applications exhibiting extreme geometrical complexity and broad ranges of length and time scales. Under-resolved computer simulations are typically unavoidable in such applications, and implicit large-eddy simulation (ILES) often becomes the effective strategy. We focus on ILES initialized with well-characterized 2563 homogeneous isotropic turbulence datasets generated with direct numerical simulation (DNS). ILES is based on the LANL xRAGE code, and solutions are examined as function of resolution for 643, 1283, 2563, and 5123 grids. The ILES performance of new directionally-unsplit high-order numerical hydrodynamics algorithms in xRAGE is examined. Compared to the initial 2563 DNS, we find longer inertial subranges and higher turbulence Re for directional-split 2563 & 5123 xRAGE — attributed to having linked DNS (Navier-Stokes based) solutions to nominally inviscid (higher Re) Euler based ILES solutions. Alternatively — for fixed resolution, we find that significantly higher simulated turbulence Re can be achieved with unsplit (vs. split) discretizations.

The Pattern of Water Flow in A Tidal Pond, Macro Water System on the Tidal Farms with Numerical Hydrodynamics Model Approach: A Case Study Of Tidal Farm In South Kalimantan

The water flow pattern and velocity caused by tidal water and the effect of wind in the tidal pond can be examined by developing a 2-D Hydrodynamic numerical model. The numerical model is based on the continuity equation and the 2-D momentum equation, these two equations are solved by finite different methods which are explicit Mac. Cormack. The validity of the model was tested with a numerical model experiment that is a 2-D water flow model simulation in a flow field in the form of a rectangular and rectangular pond water flow pattern. The application of this model will be carried out on tidal ponds, and is expected to provide satisfactory results.

Gravitational fragmentation and formation of giant protoplanets on orbits of tens of au

Aims. Migration of dense gaseous clumps that form in young protostellar disks via gravitational fragmentation is investigated to determine the likelihood of giant planet formation. Methods. High-resolution numerical hydrodynamics simulations in the thin-disk limit are employed to compute the formation and long-term evolution of a gravitationally unstable protostellar disk around a solar-mass star. Results. We show that gaseous clumps that form in the outer regions of the disk (>100 au) through disk fragmentation are often perturbed by other clumps or disk structures, such as spiral arms, and migrate toward the central star on timescales from a few thousand to few tens of thousands of years. The migration timescale is slowest when stellar motion in response to the disk gravity is considered. When approaching the star, the clumps first gain mass (up to several tens of MJup), but then quickly lose most of their diffuse envelopes through tidal torques. Part of the clump envelope can be accreted onto the central star causing an FU-Orionis-type accretion and luminosity outburst. The tidal mass loss helps the clumps to significantly slow down or even halt their inward migration at a distance of a few tens of au from the protostar. The resulting clumps are heavily truncated both in mass and size compared to their wider orbit counterparts, keeping only a dense and hot nucleus. During the inward migration, the temperature in the clump interiors may exceed the molecular hydrogen dissociation limit (2000 K) and the central region of the clump can collapse into a gas giant protoplanet. Moreover, migrating clumps may experience close encounters with other clumps, resulting in the ejection of the least massive (planetary-mass) clumps from the disk. We argue that FU-Orionis-type luminosity outbursts may be the end product of disk fragmentation and clump inward migration, preceding the formation of giant protoplanets on tens of au orbits in systems such as HR 8799.