Willy Benz

Simulations of brittle solids using smooth particle hydrodynamics

Abstract We describe a version of the smooth particle hydrodynamics (SPH) method suitable for modeling solids. The model includes strength and implements a von Mises yielding relation for stresses beyond the Hugoniot elastic limit. At lower stresses associated with brittle failure we use a rate-dependent strength based on the nucleation and growth of explicit Weibull flaws. We illustrate the capabilities of our fracture model by examining the propagation of cracks in a simple tensile rod, and by comparing simulations with laboratory experiments for high speed impacts and cratering.

Population Syntheses for Neutron Star Systems with Intrinsic Kicks

We use a Monte Carlo binary synthesis code to model the formation and evolution of neutron star systems including high-mass X-ray binaries, low-mass X-ray binaries, double neutron star systems, and radio pulsars. Our focus is on the signature imprinted on such systems due to natal kicks to neutron stars over and above that imparted by orbital motions. The code incorporates the effect of the galactic potential (including rotation) on the velocities of these systems. A comparison between our models and the observations leads us to infer mean natal kicks 400-500 km s-1. Moreover, to be consistent with all the data, we require a bimodal kick distribution with one peak in the distribution near 0 km s-1 and the other above 600 km s-1.

Dynamics of circumstellar disks

We present a series of two-dimensional hydrodynamic simulations of massive disks around protostars. We simulate the same physical problem using both a Piecewise Parabolic Method (PPM) code and a Smoothed Particle Hydrodynamic (SPH) code and analyze their differences. The disks studied here range in mass from 0.05M* to 1.0M* and in initial minimum Toomre Q value from 1.1 to 3.0. We adopt simple power laws for the initial density and temperature in the disk with an isothermal (γ = 1) equation of state. The disks are locally isothermal. We allow the central star to move freely in response to growing perturbations. The simulations using each code are compared to discover differences due to error in the methods used. For this problem, the strengths of the codes overlap only in a limited fashion, but similarities exist in their predictions, including spiral arm pattern speeds and morphological features. Our results represent limiting cases (i.e., systems evolved isothermally) rather than true physical systems. Disks become active from the inner regions outward. From the earliest times, their evolution is a strongly dynamic process rather than a smooth progression toward eventual nonlinear behavior. Processes that occur in both the extreme inner and outer radial regions affect the growth of instabilities over the entire disk. Effects important for the global morphology of the system can originate at quite small distances from the star. We calculate approximate growth rates for the spiral patterns; the one-armed (m = 1) spiral arm is not the fastest growing pattern of most disks. Nonetheless, it plays a significant role because of factors that can excite it more quickly than other patterns. A marked change in the character of spiral structure occurs with varying disk mass. Low-mass disks form filamentary spiral structures with many arms while high-mass disks form grand design spiral structures with few arms. In our SPH simulations, disks with initial minimum Q = 1.5 or lower break up into protobinary or protoplanetary clumps. However, these simulations cannot follow the physics important for the flow and must be terminated before the system has completely evolved. At their termination, PPM simulations with similar initial conditions show uneven mass distributions within spiral arms, suggesting that clumping behavior might result if they were carried further. Simulations of tori, for which SPH and PPM are directly comparable, do show clumping in both codes. Concerns that the pointlike nature of SPH exaggerates clumping, that our representation of the gravitational potential in PPM is too coarse, and that our physics assumptions are too simple suggest caution in interpretation of the clumping in both the disk and torus simulations.

Three-dimensional simulations of protostellar jets

We present the first results of fully three-dimensional (3D) simulations of supersonic, radiatively cooling jets using the smoothed particle hydrodynamics technique (SPH). Our results qualitatively agree with the two-dimensional (2D) simulations of Blondin, Fryxell, & Konigl (1990), although the removal of the axisymmetry has resulted in relevant structural differences, especially at the jet head where a cold shell is formed from the condensation of shock-heated material. In particular, we found that the shell is not only dynamically unstable but also may undergo oscillations in density, which are attributed to global thermal instabilities. These effects may have important consequences on the dynamics and emission pattern of the observed HH objects associated to young stellar jets

A stellar audit: the computation of encounter rates for 47 Tucanae and ω Centauri

Using King-Mitchie Models, we compute encounter rates between the various stellar species in the globular clusters ω Cen, and 47 Tuc. We also compute event rates for encounters between single stars and a population of primordial binaries. Using these rates, and what we have learnt from hydrodynamical simulations of encounters performed earlier, we compute the production rates of objects such as low-mass X-ray binaries (LMXBs), smothered neutron stars and blue stragglers (massive main-sequence stars). If 10 per cent of the stars are contained in primordial binaries, the production rate of interesting objects from encounters involving these binaries is as large as that from encounters between single stars. For example, encounters involving binaries produce a significant number of blue stragglers in both globular cluster models. The number of smothered neutron stars may exceed the number of LMXBs by a factor of 5–20, which may help explain why millisecond pulsars are observed to outnumber LMXBs in globular clusters.

Giant impacts on a primitive Uranus

Abstract Using smooth particle hydrodynamics, we have carried out a series of simulations of collisions between a model of a primative Uranus and impactors with masses ranging from 1.0 to 3.0 M⊕. These impactors were assumed to be differentiated and composed of iron, rock, and ices in solar proportions. The model Uranus had a mass equal to present day Uranus minus the mass of the impactor and was also assumed to be differentiated and composed of iron, rock, and ices in solar proportions with an additional 2 M⊕ mixed into the ices. We also assumed that the planet was not rotating prior to the collisions. All simulations reported here have been carried out assuming a relative velocity at infinity between the planets of 5 km/sec. For each impactor, a series of collisions were simulated varying the total angular momentum in the system (effectively varying the impact parameter since the velocity at infinity was kept constant). There was a range of angular momenta for each of the cases, except for the 1.0 M⊕ case, in which Uranus was set into rotation with a period less than the present one of 17.24 hr. Most of the runs left ices in orbit, derived from the Uranus atmosphere or the impactor (or both), and a subset of these runs also left some rock or iron from the impactor in orbit. From these simulations we conclude that there is a fairly large range of giant impacts that could have produced the present period and inclination of the spin axis to the plane of the ecliptic, and there is a subset of these that could have deposited suitable material in orbit from which the regular satellites of Uranus could have been assembled.

Neutron star accretion and the neutrino fireball

Abstract We suggest a mechanism for driving supernova explosions through neutrino energy deposition beyond the formation and the cooling of the neutron star. The mechanism depends upon convection next to the neutron star and terminates when the entropy of buoyant bubbles increases sufficiently due to neutrino heating to shut off the down flow of low entropy matter. This convection is initially caused by the heat deposited from neutrinos emitted by the cooling neutron star in a region gravitationally dominated by the neutron star. This convection by providing an efficient heat transport mechanism avoids the overheating and excessive neutrino energy losses in the regions close to the neutron stars and has been recently modeled by Herant, Benz and Colgate. In this model the explosion shock, initially driven by the bounce followed by neutron star derived neutrino heating is further driven by the up flow of the bouyant, high entropy bubbles. The down flow between the bubbles of low entropy matter originating from behind the bounce and later the explosion shock will build up a modest entropy atmosphere in pressure equilibrium with the surface of the cooling neutron star. For modest entropies, Srad ≈ 10 or Stotal ≈ 18 and condensed neutron stars, R/M ≈ 10 km per solar mass, the total mass of such an atmosphere is small, 1.7 × 10−3 M⊙, but the temperature at the base of such an atmosphere is extremely high, T ≈ 10 MeV. The paradoxical result of neutrino emission is to further condense the atmosphere and increase the temperature until the compression heating is exceeded by the neutrino emission. The absolute limit of compression heating is free fall collapse, which may be approached but not exceeded. Such an accretion event approaching this limit may reach a temperature high enough to create a neutrino “fireball”, a region hot enough, ≈ 11 MeV, so as to be partially opaque to its own (neutrino) radiation. The further heating of the already high entropy bubbles by the neutrino deposition resulting from less extreme, but a continuing high temperature atmosphere, will augment the explosion shock. This convection-driven accretion should continue until the low entropy matter fllowing downwards onto the neutron star is mixed to a high enough entropy by entrainment with the rising high entropy bubbles to prevent further accretion. This process, by providing for a feedback mechanism, may result in a robust supernova explosion in the sense that prior processes resulting in a failed or weak explosion will be augmented with further accretion energy until an explosion of the appropriate energy occurs.

Supernova explosions and hydrodynamical instabilities: from core bounce to 90 days

Abstract Since the advent of SN 1987A, considerable progress has been made in our understanding of supernova explosions. It is now realized that they are intrinsically multidimensional in nature due to the various hydrodynamical instabilities which take place at almost all stages of the explosion. These instabilities not only modify the observables from the supernova, but are also thought to be at the heart of the supernova mechanism itself, in a way which provides robust and self-regulated explosions. In this paper, we review these instabilities placing them into their appropriate context and identifying their role in the genesis of core-collapse supernovae.