# Research2

### The Evolution of Binaries in a Gaseous Medium: Three-Dimensional Simulations of Binary Bondi-Hoyle-Lyttleton Accretion

Time series movie of the binary system with semi-major axis $a = 0.41 R_a$, where $R_a= 2GM / v_\infty^{2}$ is the gravitational focusing impact parameter of the binary of total mass $M$. The frames show density slices through the orbital plane. A wind of initial density $\rho_\infty$ flows from left to right at speed $v_\infty$. The large scale structure of the primary shock inherits the shape of canonical BHL flow. Inside the primary shock, however, the orbital motion is supersonic and the binary excites spiral shock waves which propagate down stream.
Abstract: While only close binary stars will eventually interact with one another, even the widest binary systems interact with their gaseous surroundings. The rates of accretion and the gaseous drag forces arising in these interactions are the key to understanding how these systems evolve. We examine accretion flows around a binary system moving supersonically through a background gas. We perform three-dimensional hydrodynamic simulations of Bondi-Hoyle-Lyttleton accretion using the adaptive mesh refinement code FLASH. We simulate a range of values of semi-major axis of the orbit relative to the gravitational focusing impact parameter of the pair. On large scales, gas is gravitationally focused by the center-of-mass of the binary, leading to dynamical friction drag and to the accretion of mass and momentum. On smaller scales, the orbital motion imprints itself on the gas. Notably, the magnitude and direction of the forces acting on the binary inherit this orbital dependence. The long-term evolution of the binary is determined by the timescales for accretion, slow down of the center-of-mass, and decay of the orbit. We use our simulations to measure these timescales and to establish a hierarchy between them. In general, our simulations indicate that binaries moving through gaseous media will slow down before the orbit decays.

Orbit-averaged total accretion rate, $\langle \dot{M}_b \rangle$, in units of $\dot{M}_{\rm HL}$ versus initial semi-major axis, $a_0$, in units of $R_a$. The black points show the mean over an integer number of orbits between $t = 30 R_a / v_\infty$ and $t = 50 R_a / v_\infty$ while the error bars show the time variation of $\dot{M}_b$ over the same time period (to $1 \sigma$). The solid blue line is just $\dot{M}_{\rm HL} = 4 \pi G^2 M^2 \rho_\infty v_\infty^{-3}$, while the solid gray line is $\dot{M}_{\rm BH} =4 \pi G^2 M^2 \rho_\infty (v_\infty^2 + c_s^2)^{-3/2}$. The mass dependence of $\dot{M}_{\rm HL}$ and $\dot{M}_{\rm BH}$ is proportional to the total mass squared, $M^2 = ( m_1 + m_2 )^2$. The two dashed lines show the same formulas, but with $M^2$ replaced with $m_1^2 + m_2^2$. At smaller separations, the accretion rate approaches that of a single particle with $\dot{M}_b \sim \dot{M}_{\rm BH} \propto M^2$, while at larger separations, the accretion rate approaches that of two separate particles with $\dot{M}_b \propto (m_1^2 + m_2^2)$.

### Common Envelope Evolution

CE simulation of a secondary moving through the envelope of a giant. The density gradient breaks the symmetry of the gas. Dense material (bottom of the figure) is swept up into regions of less density. Streamlines entering in the upper part of the figure face a barrier and cannot be focused into a downstream wake. The fluid never fully circularizes into a disk around the accretor, but the flow (and the accompanying drag forces) are highly variable at very small radii. Things smooth out at larger radii.

Common envelope (CE) is an essential phase in the formation of many types of close binary systems. A CE phase occurs when one star in the binary becomes embedded in the expanding envelope of its giant companion. The relative motion between the embedded star and the envelope gas results in drag forces, which deposit orbital kinetic energy into the envelope material. As drag forces strip energy and angular momentum from the orbit, the embedded star spirals deeper within the envelope of the giant. Whether or not the envelope can be completely unbound and the binary survives the encounter depends on the amount of energy the drag forces deposit into the envelope and over what timescale this energy transfer occurs. Our results suggest that the inclusion of realistic density gradients in the calculation of drag forces could result in a shorter CE interaction and a more rapid inspiral than analytical estimates suggest.

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### How does a moving mass accrete matter from its environment?

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We investigate the accretion (or capture) of matter onto a point mass moving supersonically through a uniform gas in two ways. First, we use a particle simulation to demonstrate the Hoyle-Lyttleton Accretion (HLA) concept of an accretor radius.  We confirm HLA by showing that all gas particles in the simulation are accreted when they have an impact parameter less than one accretion radius. The HLA model neglects fluid pressure, so we use a hydrodynamic simulation to see how the accretion rate in a fluid compares to the HLA accretion rate. We find that the two are proportional, however, the rate is reduced because the gravitational pressure exerted on the gas by the accretor is overwhelmed by the fluid pressure of the gas at short distances from the accretor.