In a binary system, the shedding of gas from one star can have intriguing interactions with its companion.

The evolution of a star within a binary system can result in interesting modifications. Throughout its life, a star will go through intermediate phases—known as the giant phases—where it expands dramatically. If the star is one of a close pair, the expanding star will literally swallow its companion. In a November 2010 paper, Orsola De Marco, Jean-Claude Passy, and Mordecai-Mark Mac Low, all of the AMNH, sought to quantitatively describe this process, called a common envelope interaction.

In most binary star systems, mass is transferred between the two stellar components. Usually, the transfer of mass eventually stabilizes, with the companion absorbing the new material at a constant rate as it settles into a “dynamically speaking” steady orbit around the primary. However, in some systems, the process fails to stabilize. The primary star loses so much mass that the companion star is unable to accrete the new material. Instead, a cloud of mass known as a common envelope surrounds both stars. The evolution of the system is driven by the orbital energy of the inwardly-spiraling companion. If the orbital energy is high enough, the envelope ends up ejected into space. However, if it is too low, the companion will eventually merge with the core. The AMNH astrophysicists seek to quantify the former.

The process itself is quick, lasting anywhere from one to ten years. This means that virtually no one has been able to observe it. Astronomers know it has occurred only based on observing the results. An evolved star, such as a white dwarf, and its companion may have an orbital separation smaller than the radius star in the original system would generate. Only witnessing the end-stage makes understanding and simulating the process a challenge.

De Marco, Passy, and Mac Low, along with Maxwell Moe of Harvard University, Falk Herwig from the University of Victoria in Canada and Bill Paxton from UC Santa Barbara, sought to improve the main equation describing the common envelope interaction. The efficiency parameter, α, describes how efficiently the orbital energy released by the companion can be used to unbind the common envelope. Via a detailed study of the energetics and the use of stellar evolution models, De Marco, Passy, Mac Low et al. calculated the value of this efficiency parameter from a carefully selected and statistically analyzed sample of observed systems thought to be outcomes of a common envelope interaction. They eventually derived a possible inverse dependence of the efficiency with the companion to primary mass ratio. “We’re trying to make this formula more accurate,” Passy explains, “so it better describes the outcome of common envelopes and thus can be used by people specialized in population synthesis.”

As stated earlier, the speed of a common envelope interaction prevents us from observing it. However, it isn’t the only challenge. No one knows at exactly what phase during the evolution of the primary that the system actually enters the common envelope stage. This makes it difficult to deduce the initial parameters of the system. Numerical simulations can help gain information about the physics of common envelopes. The challenge is finding an optimal compromise between the relevant physics described in the simulation and the computational time - the more physics included in the code, the more time required. “Obviously, we can’t take three years to get the simulation done,” Passy chuckles.

As α is refined, and the physical equation clarified, astronomers can gain a better understanding of those events they have been thus far unable to observe. Such investigation could help answer some of the long-standing questions about common envelope interactions, such as the origin of supernovae Type Ia progenitors and the possible formation of young planets in those environments.

On the α formalism for the common envelope interaction