Background• Algol systems are close binaries consisting of two main sequence stars: the mass

gainer (primary), a B-A type star, and the donor (secondary), a cooler, more evolved subgiant G-K star.

• Mass transfer between the two stars occursvia an accretion stream at L1 due to Roche lobe overflow.

• Short-period Algols (P < 5 days) are extremely volatile systems, and display both (direct-impact) streamlike and transient disklike accretion modes.

• 3D Doppler tomography reveals a finer amount of detail within Algol binaries and has detected the presence of a tilted accretion disk in U CrB (ref. 1).

What causes this tilt?

• The fact that magnetically active regions on the donor star have similar z-velocities as that of L1 suggests the presence of a magnetically deflected accretion stream.

• We wish to determine the role that hydrodynamic effects alone play in this process after the stream has been magnetically deflected.

Analysis

• To obtain a measure of the disk’s tilt, we integrate the angular momentum across the grid zones corresponding to the disk. The angle at which the total angular momentum vector lies with respect to the vertical is the ‘tilt’ of the disk.

• Slight warping along the outer edges of the disk results in less than 1o of tilt. Overall, there is no significant tilt out of the orbital plane.

Why isn’t deflecting the stream enough?

• The ultimate behavior of the stream is relatively insensitive to the stream parameters at L1.

• Stream-disk interactions also transport angular momentum out of the system.

Accretion in RS VulpeculaeRS Vul (P=4.48 days, q=M2/M1=0.27) has been observed in a streamlike state, but not a disklikestate. Its stellar components are very similar to U CrB (P=3.45 days, q=0.29), so we expect a disklike mode to be possible. Analytic calculations give the stream parameters at L1 (ref. 3). Simulating the system with a stream that lies in the orbital plane results in disk accretion.

Schematic

Top / Side view (densities shown normalized to rho_L1=1).

Unmodified Stream

Tilted Stream

•Magnetic effects at L1 could deflect the stream out of the orbital plane as wellas boost the velocity beyond the local sound speed. Assume we have conditions very likely to produce tilt: qz=45o, vstream = 3cs.

Hydrodynamic Simulations of Algol Systems with Tilted

Accretion DisksEric Raymer, J. Blondin

Department of Physics, North Carolina State University

References(1) Aganov, et. al (2009), “Three-Dimensional Doppler Images of the Disklike and Streamlike States of U Coronae Borealis,” ApJ 690: 1730(2) Kageyama, A., and T. Sato (2004), “Yin-Yang grid: An overset grid in spherical geometry”, Geochem. Geophys. Geosyst., 5, Q09005(3) Lubow, S., and Shu, F. “Gas Dynamics of Semidetached Binaries,” ApJ 198: 383

ConclusionDeflecting the stream out of the orbital plane did not produce the expected tilt, even when boosting the speed of the stream to several times the local sound speed. While some warping occurs at the edges of the disk, the structure, evolution, and behavior of the system remain essentially the same.

Stream deflection due to magnetic activity at L1 is not solely responsible for tilted accretion disks in Algol binaries.

Other Explanations / Further Research

• Modeling the stellar atmosphere in more detail could introduce additional tilt, particularly in the case of a precessing primary star that could drag gas out of the orbital plane.

• Additional magnetic activity or plasma effects could interfere with the stream’s path to the primary. The primary is not likely to be magnetically active, but due to the close nature of the system, the secondary’s magnetic field could continue to influence the stream beyond L1.

Methods• Simulate the system using the 3D hydrodynamics code VH-1, which solves the Euler equations for fluid flow characterized by an adiabatic index, g.

• Set g ~ 1 to approximate an isothermal gas. We justify this approximation by noting that the photon field produced by the primary star will hold the gas at a relatively constant temperature.

• Implement a yin-yang grid to avoid coordinate singularities and grid convergence (ref. 2). Use a co-rotating reference frame centered on the primary star.

•Set the stream parameters at the grid zones corresponding to L1 and allow the system to naturally evolve. The secondary can be removed hydrodynamically provided we include it in the gravitational potential. This allows for maximal control over the stream parameters at L1.

Figure from (2).

AcknowledgementsThis research was supported by an allocation of advanced computing resources provided by the National Science Foundation. The computations were performed on Kraken at the National Institute for Computational Sciences.

A schematic diagram of RS Vul with ballistic trajectory of the accretion stream. The center of mass (located near the surface of the primary) is marked.

Secondary

Primary

L1

Top View Side View

Density Profile (Sliced along the binary axis )The structure of the disk remains largelyunchanged when we deflect the stream, although some widening of the disk occurs.

The ballistic trajectory of the tilted stream shows that it lacks the velocity to reach the primary before being pulled back towards the orbital plane.

Top View Side View