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The engulfment of substellar bodies (SBs), such as brown dwarfs and planets, by giant stars is a possible explanation for rapidly rotating giants, lithium-rich giants, and the presence of SBs in close orbits around subdwarfs and white dwarfs. We perform three-dimensional hydrodynamical simulations of the flow in the vicinity of an engulfed SB. We model the SB as a rigid body with a reflective surface because it cannot accrete. This reflective boundary changes the flow morphology to resemble that of engulfed compact objects with outflows. We measure the drag coefficients for the ram-pressure and gravitational drag forces acting on the SB, and use them to integrate its trajectory inside the star. We find that engulfment can increase the luminosity of a 1M_⊙star by up to a few orders of magnitude. The time for the star to return to its original luminosity is up to a few thousand years when the star has evolved to ≈10R_⊙and up to a few decades at the tip of the red giant branch (RGB). No SBs can eject the envelope of a 1M_⊙star before it evolves to ≈10R_⊙if the orbit of the SB is the only energy source contributing to the ejection. In contrast, SBs as small as ≈10M_Jupcan eject the envelope at the tip of the RGB. The numerical framework we introduce here can be used to study planetary engulfment in a simplified setting that captures the physics of the flow at the scale of the SB.

 

The engulfment of substellar bodies (SBs) such as brown dwarfs and planets has been invoked as a possible explanation for the presence of SBs orbiting subdwarfs and white dwarfs, rapidly rotating giants, and lithium-rich giants. We perform three-dimensional hydrodynamical simulations of the flow in the vicinity of an SB engulfed in a stellar envelope. We model the SB as a rigid body with a reflective boundary because it cannot accrete. This reflective boundary changes the flow morphology to resemble that of engulfed compact objects with outflows. We measure the drag coefficients for the ram pressure and gravitational drag forces acting on the SB, and use them to integrate its trajectory during engulfment. We find that SB engulfment can increase the stellar luminosity of a 1M⊙ star by up to a few orders of magnitude for timescales of up to a few thousand years when the star is ≈10R⊙ and up to a few decades at the tip of the red giant branch. We find that no SBs can eject the envelope of a 1M⊙ star before it evolves to ≈10R⊙ . In contrast, SBs as small as ≈10MJup can eject the envelope at the tip of the red giant branch, shrinking their orbits by several orders of magnitude in the process. The numerical framework we introduce here can be used to study the dynamics of planetary engulfment in a simplified setting that captures the physics of the flow at the scale of the SB. 

We present a new polynomial-free prolongation scheme for Adaptive Mesh Re- finement (AMR) simulations of compressible and incompressible computational fluid dynamics. The new method is constructed using a multi-dimensional kernel-based Gaussian Process (GP) prolongation model. The formulation for this scheme was inspired by the two previous studies on the GP methods in- troduced by A. Reyes et al., Journal of Scientific Computing, 76 (2017), and Journal of Computational Physics, 381 (2019). In this paper, we extend the previous GP interpolations and reconstructions to a new GP-based AMR pro- longation method that delivers a third-order accurate prolongation of data from coarse to fine grids on AMR grid hierarchies. In compressible flow simulations, special care is necessary to handle shocks and discontinuities in a stable man- ner. To meet this, we utilize the shock handling strategy using the GP-based smoothness indicators developed in the previous GP work by A. Reyes et al. We compare our GP-AMR results with the test results using the second-order linear AMR method to demonstrate the efficacy of the GP-AMR method in a series of test suite problems using the AMReX library, in which the GP-AMR method has been implemented. 

The engulfment of substellar bodies (SBs) such as brown dwarfs and planets has been invoked as a possible explanation for the presence of SBs orbiting subdwarfs and white dwarfs, rapidly rotating giants, and lithium-rich giants. We perform three-dimensional hydrodynamical simulations of the flow in the vicinity of an SB engulfed in a stellar envelope. We model the SB as a rigid body with a reflective boundary because it cannot accrete. This reflective boundary changes the flow morphology to resemble that of engulfed compact objects with outflows. We measure the drag coefficients for the ram pressure and gravitational drag forces acting on the SB, and use them to integrate its trajectory during engulfment. We find that SB engulfment can increase the stellar luminosity of a 1M⊙ star by up to a few orders of magnitude for timescales of up to a few thousand years when the star is ≈10R⊙ and up to a few decades at the tip of the red giant branch. We find that no SBs can eject the envelope of a 1M⊙ star before it evolves to ≈10R⊙ . In contrast, SBs as small as ≈10MJup can eject the envelope at the tip of the red giant branch, shrinking their orbits by several orders of magnitude in the process. The numerical framework we introduce here can be used to study the dynamics of planetary engulfment in a simplified setting that captures the physics of the flow at the scale of the SB. 

The automatic evaluation and extraction of financial documents is a key process in business efficiency. Most of the extraction relies on the Optical Character Recognition (OCR), whose outcome is dependent on the quality of the document image. The image data fed to the automated systems can be of unreliable quality, inherently low-resolution or downsampled and compressed by a transmitting program. In this paper, we illustrate a novel Gaussian Process (GP) upsampling model for the purposes of improving OCR process and extraction through upsampling low resolution documents.