# Energy Budget and Core-Envelope Motion in Common Envelope Evolution

## TL;DR

This study uses 3D hydrodynamic simulations to analyze energy transfer and core-envelope dynamics during common envelope evolution, revealing key phases of envelope unbinding and proposing explanations for planetary nebula offsets.

## Contribution

It provides new insights into energy transfer mechanisms and core-envelope motion during common envelope evolution through detailed simulation analysis.

## Key findings

- Envelope unbinding occurs mainly during the rapid plunge-in phase.
- Energy transfer from cores to envelope balances binding energy during plunge-in.
- Core-envelope relative motion may explain planetary nebula central star offsets.

## Abstract

We analyze a 3D hydrodynamic simulation of common envelope evolution to understand how energy is transferred between various forms and whether theory and simulation are mutually consistent given the setup. Virtually all of the envelope unbinding in the simulation occurs before the end of the rapid plunge-in phase, here defined to coincide with the first periastron passage. In contrast, the total envelope energy is nearly constant during this time because positive energy transferred to the gas from the core particles is counterbalanced by the negative binding energy from the closer proximity of the inner layers to the plunged-in secondary. During the subsequent slow spiral-in phase, energy continues to transfer to the envelope from the red giant core and secondary core particles. We also propose that relative motion between the centre of mass of the envelope and the centre of mass of the particles could account for the offsets of planetary nebula central stars from the nebula's geometric centre.