The planar two-body problem for spheroids and disks

We outline a new method suggested by Conway (CMDA 125:161–194, 2016) for solving the two-body problem for solid bodies of spheroidal or ellipsoidal shape. The method is based on integrating the gravitational potential of one body over the surface of the other body. When the gravitational potential can be analytically expressed (as for spheroids or ellipsoids), the gravitational force and mutual gravitational potential can be formulated as a surface integral instead of a volume integral and solved numerically. If the two bodies are infinitely thin disks, the surface integral has an analytical solution. The method is exact as the force and mutual potential appear in closed-form expressions, and does not involve series expansions with subsequent truncation errors. In order to test the method, we solve the equations of motion in an inertial frame and run simulations with two spheroids and two infinitely thin disks, restricted to torque-free planar motion. The resulting trajectories display precession patterns typical for non-Keplerian potentials. We follow the conservation of energy and orbital angular momentum and also investigate how the spheroid model approaches the two cases where the surface integral can be solved analytically, i.e., for point masses and infinitely thin disks.

Powerful Jets from Radiatively Efficient Disks, a Decades-Old Unresolved Problem in High Energy Astrophysics

The discovery of 3C 273 in 1963, and the emergence of the Kerr solution shortly thereafter, precipitated the current era in astrophysics focused on using black holes to explain active galactic nuclei (AGN). But while partial success was achieved in separately explaining the bright nuclei of some AGN via thin disks, as well as powerful jets with thick disks, the combination of both powerful jets in an AGN with a bright nucleus, such as in 3C 273, remained elusive. Although numerical simulations have taken center stage in the last 25 years, they have struggled to produce the conditions that explain them. This is because radiatively efficient disks have proved a challenge to simulate. Radio quasars have thus been the least understood objects in high energy astrophysics. But recent simulations have begun to change this. We explore this milestone in light of scale-invariance and show that transitory jets, possibly related to the jets seen in these recent simulations, as some have proposed, cannot explain radio quasars. We then provide a road map for a resolution.

Mitigation of End-Flux-Peaking in Fresh CANDU Fuel Bundles Using Neutron Absorbers

End-flux-peaking (EFP) is a phenomenon where a region of elevated neutron flux occurs between two adjoining fuel bundles, leading to an increase in fission rate and therefore greater heat generation. It is known that the addition of neutron absorbers into fuel bundles can mitigate EFP, yet the implementation in Canada deuterium uranium (CANDU) type reactors using natural uranium fuel has not been pursued. The computer code Monte Carlo N-Particle code (MCNP) 6.1 was used to develop a three-dimensional CANDU bundle–bundle contact model and simulate the addition of neutron absorbers positioned strategically within various locations of the fuel bundle. The burnable absorbers of interest include Gd2O3 and Eu2O3. The locations investigated include within the end pellets of a fuel stack, within the CANDU lubricant (CANLUB) layer, within thin disks located at the ends of the fuel stack, and alloyed in the endplate. Concentrations of the absorbers were varied to gain better insight into their effect on the thermal neutron axial flux profile of the fuel bundle. The results of the study indicated that adding a combination of ∼4 mg/∼12 mg of Eu2O3 into the pellet adjacent to the end pellet and the end pellet, respectively, at each end of all six of the fuel elements in the inner fuel ring, as well as, ∼2 mg/∼6 mg of Eu2O3 into the same respective pellets, at each end of the 18 fuel elements in the outer fuel ring, provides the most effective mitigation of the EFP phenomena in fresh CANDU fuel bundles.

Jeans analysis in energy–momentum-squared gravity

In this paper, we study the Jeans analysis in the context of energy–momentum-squared gravity (EMSG). More specifically we find the new Jeans mass for non-rotating infinite mediums as the smallest mass scale for local perturbations that can be stable against its own gravity. Furthermore, for rotating mediums, specifically for rotating thin disks in the context of EMSG, we find a new Toomre-like criterion for the local gravitational stability. Finally, the results are applied to a hyper-massive neutron star, as an astrophysical system. Using a simplified toy model we have shown that, for a positive (negative) value of the EMSG parameter $$\alpha $$α, the system is stable (unstable) in a wide range of $$\alpha $$α. On the other hand, no observational evidence has been reported on the existence of local fragmentation in HMNS. Naturally, this means that EMSG with positive $$\alpha $$α is more acceptable from the physical point of view.